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from hundreds of MIT courses visit mitop courseware at align:start position:0% align:start position:0% ocw.mit.edu align:start position:0% align:start position:0% okay so today we're going to continue align:start position:0% okay so today we're going to continue align:start position:0% okay so today we're going to continue the topic of uh consumption smoothing I align:start position:0% the topic of uh consumption smoothing I align:start position:0% the topic of uh consumption smoothing I mean this sort of sequence began with align:start position:0% mean this sort of sequence began with align:start position:0% mean this sort of sequence began with the optimal allocation of risk bearing align:start position:0% the optimal allocation of risk bearing align:start position:0% the optimal allocation of risk bearing and what you would see in the align:start position:0% and what you would see in the align:start position:0% and what you would see in the data uh we saw the Benchmark was doing align:start position:0% data uh we saw the Benchmark was doing align:start position:0% data uh we saw the Benchmark was doing well in many but not all cases and there align:start position:0% well in many but not all cases and there align:start position:0% well in many but not all cases and there were some examples align:start position:0% were some examples align:start position:0% were some examples where coefficients on income were higher align:start position:0% where coefficients on income were higher align:start position:0% where coefficients on income were higher and and uh for certain occupations and align:start position:0% and and uh for certain occupations and align:start position:0% and and uh for certain occupations and certain certain types of income align:start position:0% certain certain types of income align:start position:0% certain certain types of income um uh then we took that same Benchmark align:start position:0% um uh then we took that same Benchmark align:start position:0% um uh then we took that same Benchmark still uh clinging to it and uh looked at align:start position:0% still uh clinging to it and uh looked at align:start position:0% still uh clinging to it and uh looked at a whole different kind of data align:start position:0% a whole different kind of data align:start position:0% a whole different kind of data production data and we're going to come align:start position:0% production data and we're going to come align:start position:0% production data and we're going to come back to it next time when we talk about align:start position:0% back to it next time when we talk about align:start position:0% back to it next time when we talk about Labor Supply but while we're on the align:start position:0% Labor Supply but while we're on the align:start position:0% Labor Supply but while we're on the subject of consumption and consumption align:start position:0% subject of consumption and consumption align:start position:0% subject of consumption and consumption smoothing I thought it would be good to align:start position:0% smoothing I thought it would be good to align:start position:0% smoothing I thought it would be good to go some through some alternative models align:start position:0% go some through some alternative models align:start position:0% go some through some alternative models that are widely used and uh and align:start position:0% that are widely used and uh and align:start position:0% that are widely used and uh and different data sets and give you a sense align:start position:0% different data sets and give you a sense align:start position:0% different data sets and give you a sense of uh of what people do in the align:start position:0% of uh of what people do in the align:start position:0% of uh of what people do in the literature um align:start position:0% literature um align:start position:0% literature um so a lot of this has to do with the align:start position:0% so a lot of this has to do with the align:start position:0% so a lot of this has to do with the permanent income model which is kind of align:start position:0% permanent income model which is kind of align:start position:0% permanent income model which is kind of the uh basic sort of thing that people align:start position:0% the uh basic sort of thing that people align:start position:0% the uh basic sort of thing that people rely on and fall back on constantly or align:start position:0% rely on and fall back on constantly or align:start position:0% rely on and fall back on constantly or say consumption smoothing over the life align:start position:0% say consumption smoothing over the life align:start position:0% say consumption smoothing over the life cycle align:start position:0% cycle align:start position:0% cycle um these markets are not complete they align:start position:0% um these markets are not complete they align:start position:0% um these markets are not complete they shut down a lot of the risk align:start position:0% shut down a lot of the risk align:start position:0% shut down a lot of the risk contingencies allowing households to align:start position:0% contingencies allowing households to align:start position:0% contingencies allowing households to trade only in risk-free bonds or maybe align:start position:0% trade only in risk-free bonds or maybe align:start position:0% trade only in risk-free bonds or maybe uh you know have some other savings align:start position:0% uh you know have some other savings align:start position:0% uh you know have some other savings account which cannot go below zero or align:start position:0% account which cannot go below zero or align:start position:0% account which cannot go below zero or limited align:start position:0% limited align:start position:0% limited credit uh the papers we're going to align:start position:0% credit uh the papers we're going to align:start position:0% credit uh the papers we're going to cover first one there's one by Kaplan align:start position:0% cover first one there's one by Kaplan align:start position:0% cover first one there's one by Kaplan and align:start position:0% and align:start position:0% and violante which is going to look at the align:start position:0% violante which is going to look at the align:start position:0% violante which is going to look at the degree of com con assumption through align:start position:0% degree of com con assumption through align:start position:0% degree of com con assumption through smoothing from this Sim which is align:start position:0% smoothing from this Sim which is align:start position:0% smoothing from this Sim which is standard incomplete Market model they're align:start position:0% standard incomplete Market model they're align:start position:0% standard incomplete Market model they're also going to simulate it so align:start position:0% also going to simulate it so align:start position:0% also going to simulate it so that using a two two purposes there uh align:start position:0% that using a two two purposes there uh align:start position:0% that using a two two purposes there uh and we're going to look align:start position:0% and we're going to look align:start position:0% and we're going to look at uh smoothing through the lens of that align:start position:0% at uh smoothing through the lens of that align:start position:0% at uh smoothing through the lens of that model and in the data against permanent align:start position:0% model and in the data against permanent align:start position:0% model and in the data against permanent shocks and transitory shocks this is a align:start position:0% shocks and transitory shocks this is a align:start position:0% shocks and transitory shocks this is a language we have not been using so far align:start position:0% language we have not been using so far align:start position:0% language we have not been using so far uh but it is standard language align:start position:0% uh but it is standard language align:start position:0% uh but it is standard language in this other literature align:start position:0% in this other literature align:start position:0% in this other literature um and look at how smoothing varies align:start position:0% um and look at how smoothing varies align:start position:0% um and look at how smoothing varies against these various shocks varies over align:start position:0% against these various shocks varies over align:start position:0% against these various shocks varies over the life cycle the that the elante paper align:start position:0% the life cycle the that the elante paper align:start position:0% the life cycle the that the elante paper and others draw on this blundel pistar align:start position:0% and others draw on this blundel pistar align:start position:0% and others draw on this blundel pistar and Preston uh method which is looking align:start position:0% and Preston uh method which is looking align:start position:0% and Preston uh method which is looking at consumption and income uh data align:start position:0% at consumption and income uh data align:start position:0% at consumption and income uh data um and in fact there is not typically a align:start position:0% um and in fact there is not typically a align:start position:0% um and in fact there is not typically a very long time series in the US to use align:start position:0% very long time series in the US to use align:start position:0% very long time series in the US to use the best is a PSID which used to only align:start position:0% the best is a PSID which used to only align:start position:0% the best is a PSID which used to only have food so part of this paper is about align:start position:0% have food so part of this paper is about align:start position:0% have food so part of this paper is about how to splice together two different align:start position:0% how to splice together two different align:start position:0% how to splice together two different databases to create a longer panel um align:start position:0% databases to create a longer panel um align:start position:0% databases to create a longer panel um and measure the degree of smoothing in align:start position:0% and measure the degree of smoothing in align:start position:0% and measure the degree of smoothing in the data then we'll move to Deon and align:start position:0% the data then we'll move to Deon and align:start position:0% the data then we'll move to Deon and Paxton which is the same overall topic align:start position:0% Paxton which is the same overall topic align:start position:0% Paxton which is the same overall topic but actually uh quite interesting align:start position:0% but actually uh quite interesting align:start position:0% but actually uh quite interesting because they're going to be looking more align:start position:0% because they're going to be looking more align:start position:0% because they're going to be looking more at align:start position:0% at align:start position:0% at the uh variance of consumption in align:start position:0% the uh variance of consumption in align:start position:0% the uh variance of consumption in cross-sections uh which is an align:start position:0% cross-sections uh which is an align:start position:0% cross-sections uh which is an implication of the models but you don't align:start position:0% implication of the models but you don't align:start position:0% implication of the models but you don't need these panel you just need a bunch align:start position:0% need these panel you just need a bunch align:start position:0% need these panel you just need a bunch of align:start position:0% of align:start position:0% of cross-sections for various years so align:start position:0% cross-sections for various years so align:start position:0% cross-sections for various years so effectively if it's representative you align:start position:0% effectively if it's representative you align:start position:0% effectively if it's representative you can track people by align:start position:0% can track people by align:start position:0% can track people by age um and again they do that through align:start position:0% age um and again they do that through align:start position:0% age um and again they do that through permanent income model a buffer stock align:start position:0% permanent income model a buffer stock align:start position:0% permanent income model a buffer stock model model with borrowing align:start position:0% model model with borrowing align:start position:0% model model with borrowing constraints as well as in the background align:start position:0% constraints as well as in the background align:start position:0% constraints as well as in the background the full insurance model and related to align:start position:0% the full insurance model and related to align:start position:0% the full insurance model and related to things in the align:start position:0% things in the align:start position:0% things in the data then there's this Campbell and Deon align:start position:0% data then there's this Campbell and Deon align:start position:0% data then there's this Campbell and Deon paper uh which is about excess align:start position:0% paper uh which is about excess align:start position:0% paper uh which is about excess smoothness and I kind of smile every align:start position:0% smoothness and I kind of smile every align:start position:0% smoothness and I kind of smile every time I see this align:start position:0% time I see this align:start position:0% time I see this title uh because from the standpoint of align:start position:0% title uh because from the standpoint of align:start position:0% title uh because from the standpoint of the permanent income model you should align:start position:0% the permanent income model you should align:start position:0% the permanent income model you should respond to you know shocks to permanent align:start position:0% respond to you know shocks to permanent align:start position:0% respond to you know shocks to permanent income and uh align:start position:0% income and uh align:start position:0% income and uh and uh and they see in the data that align:start position:0% and uh and they see in the data that align:start position:0% and uh and they see in the data that consumption is smoother than that so align:start position:0% consumption is smoother than that so align:start position:0% consumption is smoother than that so they call it excess smoothness now you align:start position:0% they call it excess smoothness now you align:start position:0% they call it excess smoothness now you know my Smiles come from the fact that align:start position:0% know my Smiles come from the fact that align:start position:0% know my Smiles come from the fact that they haven't considered the full you align:start position:0% they haven't considered the full you align:start position:0% they haven't considered the full you know wrist sharing Benchmark which may align:start position:0% know wrist sharing Benchmark which may align:start position:0% know wrist sharing Benchmark which may not fit perfectly well either but may be align:start position:0% not fit perfectly well either but may be align:start position:0% not fit perfectly well either but may be part of the explanation in the align:start position:0% part of the explanation in the align:start position:0% part of the explanation in the background align:start position:0% background align:start position:0% background um and then finally we have this Krueger align:start position:0% um and then finally we have this Krueger align:start position:0% um and then finally we have this Krueger and Parry paper align:start position:0% and Parry paper align:start position:0% and Parry paper which looks at the US and Italian align:start position:0% which looks at the US and Italian align:start position:0% which looks at the US and Italian data and I hope we get time to say a few align:start position:0% data and I hope we get time to say a few align:start position:0% data and I hope we get time to say a few words about this today align:start position:0% words about this today align:start position:0% words about this today because uh so I'll do this in the align:start position:0% because uh so I'll do this in the align:start position:0% because uh so I'll do this in the recitation oh you're doing it in the align:start position:0% recitation oh you're doing it in the align:start position:0% recitation oh you're doing it in the recitation okay uh align:start position:0% align:start position:0% so yeah I originally had this as part of align:start position:0% so yeah I originally had this as part of align:start position:0% so yeah I originally had this as part of the primary lecture and then we thought align:start position:0% the primary lecture and then we thought align:start position:0% the primary lecture and then we thought there wasn't enough time in class which align:start position:0% there wasn't enough time in class which align:start position:0% there wasn't enough time in class which may yet turn out to be true and then align:start position:0% may yet turn out to be true and then align:start position:0% may yet turn out to be true and then uh I looked at it again and I really align:start position:0% uh I looked at it again and I really align:start position:0% uh I looked at it again and I really like it so I'm glad one way or the other align:start position:0% like it so I'm glad one way or the other align:start position:0% like it so I'm glad one way or the other you're going to you're going to see it align:start position:0% you're going to you're going to see it align:start position:0% you're going to you're going to see it something that's align:start position:0% something that's align:start position:0% something that's fine maybe we'll get a lot of align:start position:0% fine maybe we'll get a lot of align:start position:0% fine maybe we'll get a lot of questions okay align:start position:0% align:start position:0% um align:start position:0% align:start position:0% so so what's the problem well in the US align:start position:0% so so what's the problem well in the US align:start position:0% so so what's the problem well in the US as I was saying we need longitudinal align:start position:0% as I was saying we need longitudinal align:start position:0% as I was saying we need longitudinal data on consumption and income and and align:start position:0% data on consumption and income and and align:start position:0% data on consumption and income and and uh on consumption we need a align:start position:0% uh on consumption we need a align:start position:0% uh on consumption we need a comprehensive align:start position:0% comprehensive align:start position:0% comprehensive measure uh you know no one's been align:start position:0% measure uh you know no one's been align:start position:0% measure uh you know no one's been Gathering these kinds of data so how do align:start position:0% Gathering these kinds of data so how do align:start position:0% Gathering these kinds of data so how do people cope with it they could use the align:start position:0% people cope with it they could use the align:start position:0% people cope with it they could use the PS ID and just look at align:start position:0% PS ID and just look at align:start position:0% PS ID and just look at Food align:start position:0% Food align:start position:0% Food uh or they could look exclusively at the align:start position:0% uh or they could look exclusively at the align:start position:0% uh or they could look exclusively at the consumer expenditure survey which has a align:start position:0% consumer expenditure survey which has a align:start position:0% consumer expenditure survey which has a whole bunch of line items but people are align:start position:0% whole bunch of line items but people are align:start position:0% whole bunch of line items but people are not in that sample for more than 3 or align:start position:0% not in that sample for more than 3 or align:start position:0% not in that sample for more than 3 or four quarters ERS uh and uh or you could align:start position:0% four quarters ERS uh and uh or you could align:start position:0% four quarters ERS uh and uh or you could sort of basically create these sythetic align:start position:0% sort of basically create these sythetic align:start position:0% sort of basically create these sythetic cohorts uh by sort of extrapolating and align:start position:0% cohorts uh by sort of extrapolating and align:start position:0% cohorts uh by sort of extrapolating and merging uh which is increasingly common align:start position:0% merging uh which is increasingly common align:start position:0% merging uh which is increasingly common way to deal with a align:start position:0% align:start position:0% problem another way to sort of think align:start position:0% problem another way to sort of think align:start position:0% problem another way to sort of think about this up front is uh align:start position:0% about this up front is uh align:start position:0% about this up front is uh the these models are making a align:start position:0% the these models are making a align:start position:0% the these models are making a distinction between permanent and align:start position:0% distinction between permanent and align:start position:0% distinction between permanent and transitory shocks but we only see income align:start position:0% transitory shocks but we only see income align:start position:0% transitory shocks but we only see income we don't see each of these different align:start position:0% we don't see each of these different align:start position:0% we don't see each of these different kinds of shocks align:start position:0% kinds of shocks align:start position:0% kinds of shocks individually so what to do about that align:start position:0% individually so what to do about that align:start position:0% individually so what to do about that well you could ignore it and just look align:start position:0% well you could ignore it and just look align:start position:0% well you could ignore it and just look at the response to total income change align:start position:0% at the response to total income change align:start position:0% at the response to total income change which is kind of what we've been doing align:start position:0% which is kind of what we've been doing align:start position:0% which is kind of what we've been doing actually in the development uh data align:start position:0% actually in the development uh data align:start position:0% actually in the development uh data sets uh you could use align:start position:0% sets uh you could use align:start position:0% sets uh you could use proxies for permanent versus transitory align:start position:0% proxies for permanent versus transitory align:start position:0% proxies for permanent versus transitory shocks for example disability might align:start position:0% shocks for example disability might align:start position:0% shocks for example disability might rightly be thought of as a rather align:start position:0% rightly be thought of as a rather align:start position:0% rightly be thought of as a rather permanent shock uh short-term align:start position:0% permanent shock uh short-term align:start position:0% permanent shock uh short-term unemployment might be thought of as a align:start position:0% unemployment might be thought of as a align:start position:0% unemployment might be thought of as a transitory shock so that's another way align:start position:0% transitory shock so that's another way align:start position:0% transitory shock so that's another way to try to to deal with a align:start position:0% to try to to deal with a align:start position:0% to try to to deal with a problem uh and then there's sort of a align:start position:0% problem uh and then there's sort of a align:start position:0% problem uh and then there's sort of a Public Finance Tax align:start position:0% Public Finance Tax align:start position:0% Public Finance Tax literature different people assume align:start position:0% literature different people assume align:start position:0% literature different people assume different things about different kind of align:start position:0% different things about different kind of align:start position:0% different things about different kind of taxes some taxes assume to be permanent align:start position:0% taxes some taxes assume to be permanent align:start position:0% taxes some taxes assume to be permanent others assume to be transitory and then align:start position:0% others assume to be transitory and then align:start position:0% others assume to be transitory and then you kind of see how households react to align:start position:0% align:start position:0% that so the uh Benchmark model people align:start position:0% that so the uh Benchmark model people align:start position:0% that so the uh Benchmark model people use for saying quote how much insurance align:start position:0% use for saying quote how much insurance align:start position:0% use for saying quote how much insurance is there in actually in the data is this align:start position:0% is there in actually in the data is this align:start position:0% is there in actually in the data is this blondel uh pistar Preston paper I doubt align:start position:0% blondel uh pistar Preston paper I doubt align:start position:0% blondel uh pistar Preston paper I doubt if we'll get to that today it is in the align:start position:0% if we'll get to that today it is in the align:start position:0% if we'll get to that today it is in the appendix so I have it in the align:start position:0% appendix so I have it in the align:start position:0% appendix so I have it in the slides uh time permitting uh but it's align:start position:0% slides uh time permitting uh but it's align:start position:0% slides uh time permitting uh but it's basically a covariance decomposition of align:start position:0% basically a covariance decomposition of align:start position:0% basically a covariance decomposition of the income and consumption align:start position:0% the income and consumption align:start position:0% the income and consumption process um so that's the quote view of align:start position:0% process um so that's the quote view of align:start position:0% process um so that's the quote view of the data then for the models you start align:start position:0% the data then for the models you start align:start position:0% the data then for the models you start with the standard incomplete markets align:start position:0% with the standard incomplete markets align:start position:0% with the standard incomplete markets model assuming no access to contingent align:start position:0% model assuming no access to contingent align:start position:0% model assuming no access to contingent claims but allowing some kind of align:start position:0% claims but allowing some kind of align:start position:0% claims but allowing some kind of insurance uh through buying and selling align:start position:0% insurance uh through buying and selling align:start position:0% insurance uh through buying and selling bonds now let me pause for a second just align:start position:0% bonds now let me pause for a second just align:start position:0% bonds now let me pause for a second just in case it's not align:start position:0% in case it's not align:start position:0% in case it's not clear and this literature uses confusing align:start position:0% clear and this literature uses confusing align:start position:0% clear and this literature uses confusing language actually if you thought about a align:start position:0% language actually if you thought about a align:start position:0% language actually if you thought about a household in isolation or a business you align:start position:0% household in isolation or a business you align:start position:0% household in isolation or a business you know they have ups and downs of income align:start position:0% know they have ups and downs of income align:start position:0% know they have ups and downs of income and it's clear that by you know saving align:start position:0% and it's clear that by you know saving align:start position:0% and it's clear that by you know saving you kind of smooth off the Peaks so that align:start position:0% you kind of smooth off the Peaks so that align:start position:0% you kind of smooth off the Peaks so that higher income does not make its way into align:start position:0% higher income does not make its way into align:start position:0% higher income does not make its way into consumption and uh likewise in The align:start position:0% consumption and uh likewise in The align:start position:0% consumption and uh likewise in The Valleys when income is really low you align:start position:0% Valleys when income is really low you align:start position:0% Valleys when income is really low you can carry forward that savings to that align:start position:0% can carry forward that savings to that align:start position:0% can carry forward that savings to that spot or bar align:start position:0% spot or bar align:start position:0% spot or bar which makes the valley less deep so align:start position:0% which makes the valley less deep so align:start position:0% which makes the valley less deep so consumption is smooth to a large degree align:start position:0% consumption is smooth to a large degree align:start position:0% consumption is smooth to a large degree but not align:start position:0% but not align:start position:0% but not completely against these align:start position:0% completely against these align:start position:0% completely against these fluctuations now what's the difference align:start position:0% fluctuations now what's the difference align:start position:0% fluctuations now what's the difference between that and the full risk sharing align:start position:0% between that and the full risk sharing align:start position:0% between that and the full risk sharing model well the idea there is that you align:start position:0% model well the idea there is that you align:start position:0% model well the idea there is that you don't have not everyone's facing align:start position:0% don't have not everyone's facing align:start position:0% don't have not everyone's facing idiosyncratic and transitory shocks at align:start position:0% idiosyncratic and transitory shocks at align:start position:0% idiosyncratic and transitory shocks at the same time so as in the Rocky align:start position:0% the same time so as in the Rocky align:start position:0% the same time so as in the Rocky Mountains diagram you know Peaks and align:start position:0% Mountains diagram you know Peaks and align:start position:0% Mountains diagram you know Peaks and valleys come at different stages and align:start position:0% valleys come at different stages and align:start position:0% valleys come at different stages and even after align:start position:0% even after align:start position:0% even after you act as if a household would do align:start position:0% you act as if a household would do align:start position:0% you act as if a household would do everything that it could on its own align:start position:0% everything that it could on its own align:start position:0% everything that it could on its own you're still left left with this align:start position:0% you're still left left with this align:start position:0% you're still left left with this asynchronous timing so what the RIS align:start position:0% asynchronous timing so what the RIS align:start position:0% asynchronous timing so what the RIS sharing model is basically doing is align:start position:0% sharing model is basically doing is align:start position:0% sharing model is basically doing is transferring consumption around in the align:start position:0% transferring consumption around in the align:start position:0% transferring consumption around in the crosssection to get even flatter align:start position:0% crosssection to get even flatter align:start position:0% crosssection to get even flatter consumption and the only thing that align:start position:0% consumption and the only thing that align:start position:0% consumption and the only thing that would be left then if you believe the align:start position:0% would be left then if you believe the align:start position:0% would be left then if you believe the forris sharing model are those shocks align:start position:0% forris sharing model are those shocks align:start position:0% forris sharing model are those shocks that basically somehow get left in align:start position:0% that basically somehow get left in align:start position:0% that basically somehow get left in aggregate consumption after all that align:start position:0% aggregate consumption after all that align:start position:0% aggregate consumption after all that smoothing the only part of the Peaks and align:start position:0% smoothing the only part of the Peaks and align:start position:0% smoothing the only part of the Peaks and valleys that's common across all the align:start position:0% valleys that's common across all the align:start position:0% valleys that's common across all the households would be left and everything align:start position:0% households would be left and everything align:start position:0% households would be left and everything else would be flattened out so this align:start position:0% else would be flattened out so this align:start position:0% else would be flattened out so this literature you know it's true that you align:start position:0% literature you know it's true that you align:start position:0% literature you know it's true that you can do an enormous amount of smoothing align:start position:0% can do an enormous amount of smoothing align:start position:0% can do an enormous amount of smoothing by borrowing and align:start position:0% by borrowing and align:start position:0% by borrowing and lending but it is not true that you can align:start position:0% lending but it is not true that you can align:start position:0% lending but it is not true that you can do everything that would be possible align:start position:0% do everything that would be possible align:start position:0% do everything that would be possible with with greater amounts of insurance align:start position:0% with with greater amounts of insurance align:start position:0% with with greater amounts of insurance anyway so they start with the standard align:start position:0% anyway so they start with the standard align:start position:0% anyway so they start with the standard note that we standard it's standard for align:start position:0% note that we standard it's standard for align:start position:0% note that we standard it's standard for the certain branches of the macro align:start position:0% the certain branches of the macro align:start position:0% the certain branches of the macro literature in complete Marcus literature align:start position:0% literature in complete Marcus literature align:start position:0% literature in complete Marcus literature uh now you may or may not put on a life align:start position:0% uh now you may or may not put on a life align:start position:0% uh now you may or may not put on a life cycle to be realistic you'd say the align:start position:0% cycle to be realistic you'd say the align:start position:0% cycle to be realistic you'd say the household faces a stochastic probability align:start position:0% household faces a stochastic probability align:start position:0% household faces a stochastic probability of dying and align:start position:0% of dying and align:start position:0% of dying and uh align:start position:0% uh align:start position:0% uh um that makes them more and more align:start position:0% um that makes them more and more align:start position:0% um that makes them more and more vulnerable as they get older and older align:start position:0% vulnerable as they get older and older align:start position:0% vulnerable as they get older and older in some sense because they can't smooth align:start position:0% in some sense because they can't smooth align:start position:0% in some sense because they can't smooth it out into or they have to frontload align:start position:0% it out into or they have to frontload align:start position:0% it out into or they have to frontload stuff into savings to be able to cope align:start position:0% stuff into savings to be able to cope align:start position:0% stuff into savings to be able to cope with fluctuations as they get older so align:start position:0% with fluctuations as they get older so align:start position:0% with fluctuations as they get older so it does matter whether the Horizon is align:start position:0% it does matter whether the Horizon is align:start position:0% it does matter whether the Horizon is infinite or align:start position:0% infinite or align:start position:0% infinite or finite uh there are permanent and align:start position:0% finite uh there are permanent and align:start position:0% finite uh there are permanent and transitory shocks to earnings while they align:start position:0% transitory shocks to earnings while they align:start position:0% transitory shocks to earnings while they earn but if it's a life cycle model and align:start position:0% earn but if it's a life cycle model and align:start position:0% earn but if it's a life cycle model and as in the US where there is literally align:start position:0% as in the US where there is literally align:start position:0% as in the US where there is literally retirement then you know earnings go to align:start position:0% retirement then you know earnings go to align:start position:0% retirement then you know earnings go to zero now you may have some income stream align:start position:0% zero now you may have some income stream align:start position:0% zero now you may have some income stream from Social Security and these guys will align:start position:0% from Social Security and these guys will align:start position:0% from Social Security and these guys will load that align:start position:0% load that align:start position:0% load that in uh and you may have some assets align:start position:0% in uh and you may have some assets align:start position:0% in uh and you may have some assets you've put in a a pension fund which has align:start position:0% you've put in a a pension fund which has align:start position:0% you've put in a a pension fund which has kind of an insurance component to it in align:start position:0% kind of an insurance component to it in align:start position:0% kind of an insurance component to it in the sense that you're getting a income align:start position:0% the sense that you're getting a income align:start position:0% the sense that you're getting a income stream from the align:start position:0% stream from the align:start position:0% stream from the pension uh but averaging align:start position:0% pension uh but averaging align:start position:0% pension uh but averaging over the mortality risk in the align:start position:0% over the mortality risk in the align:start position:0% over the mortality risk in the population so there's a bit of insurance align:start position:0% population so there's a bit of insurance align:start position:0% population so there's a bit of insurance and standard Pension align:start position:0% align:start position:0% funds uh another version has uh align:start position:0% funds uh another version has uh align:start position:0% funds uh another version has uh borrowing limits there's something align:start position:0% borrowing limits there's something align:start position:0% borrowing limits there's something called the natural borrowing limit or align:start position:0% called the natural borrowing limit or align:start position:0% called the natural borrowing limit or the the zero zero is obvious you can't align:start position:0% the the zero zero is obvious you can't align:start position:0% the the zero zero is obvious you can't borrow anything at all or you'll put align:start position:0% borrow anything at all or you'll put align:start position:0% borrow anything at all or you'll put just a bound can borrow 10% of your align:start position:0% just a bound can borrow 10% of your align:start position:0% just a bound can borrow 10% of your assets or your income the the natural align:start position:0% assets or your income the the natural align:start position:0% assets or your income the the natural borrowing limit is something like align:start position:0% borrowing limit is something like align:start position:0% borrowing limit is something like this you always have to repay your debt align:start position:0% this you always have to repay your debt align:start position:0% this you always have to repay your debt so you can't borrow more than what you align:start position:0% so you can't borrow more than what you align:start position:0% so you can't borrow more than what you could repay in the worst possible income align:start position:0% could repay in the worst possible income align:start position:0% could repay in the worst possible income realization in the align:start position:0% realization in the align:start position:0% realization in the future and then it matters a lot what align:start position:0% future and then it matters a lot what align:start position:0% future and then it matters a lot what you're assuming about the income process align:start position:0% you're assuming about the income process align:start position:0% you're assuming about the income process right if there's a small chance of of align:start position:0% right if there's a small chance of of align:start position:0% right if there's a small chance of of zero income and your debt is due in align:start position:0% zero income and your debt is due in align:start position:0% zero income and your debt is due in that situation then effectively you align:start position:0% that situation then effectively you align:start position:0% that situation then effectively you can't borrow at all so it's a rather align:start position:0% can't borrow at all so it's a rather align:start position:0% can't borrow at all so it's a rather stringent align:start position:0% align:start position:0% Criterion and then they'll take C you'll align:start position:0% Criterion and then they'll take C you'll align:start position:0% Criterion and then they'll take C you'll see Klan and viilante then take the align:start position:0% see Klan and viilante then take the align:start position:0% see Klan and viilante then take the model and uh and they simulate hence the align:start position:0% model and uh and they simulate hence the align:start position:0% model and uh and they simulate hence the Sim artificial data from the model align:start position:0% Sim artificial data from the model align:start position:0% Sim artificial data from the model itself align:start position:0% itself align:start position:0% itself now align:start position:0% now align:start position:0% now um there's two reasons for doing that align:start position:0% um there's two reasons for doing that align:start position:0% um there's two reasons for doing that first of all this blundel pesari PR align:start position:0% first of all this blundel pesari PR align:start position:0% first of all this blundel pesari PR Preston align:start position:0% Preston align:start position:0% Preston paper uh is doing something with the align:start position:0% paper uh is doing something with the align:start position:0% paper uh is doing something with the data it's not a direct look at the data align:start position:0% data it's not a direct look at the data align:start position:0% data it's not a direct look at the data but the summary statistics come from align:start position:0% but the summary statistics come from align:start position:0% but the summary statistics come from this BPP algorithm so they want us if align:start position:0% this BPP algorithm so they want us if align:start position:0% this BPP algorithm so they want us if you want a common ground which is what's align:start position:0% you want a common ground which is what's align:start position:0% you want a common ground which is what's in the data through BPP then let's look align:start position:0% in the data through BPP then let's look align:start position:0% in the data through BPP then let's look at the data generated by the model align:start position:0% at the data generated by the model align:start position:0% at the data generated by the model through BPP and compare apples to align:start position:0% through BPP and compare apples to align:start position:0% through BPP and compare apples to apples align:start position:0% apples align:start position:0% apples uh on the other hand when you have a align:start position:0% uh on the other hand when you have a align:start position:0% uh on the other hand when you have a model and you simulated it that that is align:start position:0% model and you simulated it that that is align:start position:0% model and you simulated it that that is the reality you know align:start position:0% the reality you know align:start position:0% the reality you know exactly what the economy is like so you align:start position:0% exactly what the economy is like so you align:start position:0% exactly what the economy is like so you know they also use this pickup align:start position:0% know they also use this pickup align:start position:0% know they also use this pickup distortions where BPP is kind of giving align:start position:0% distortions where BPP is kind of giving align:start position:0% distortions where BPP is kind of giving you a summary statistic of the degree of align:start position:0% you a summary statistic of the degree of align:start position:0% you a summary statistic of the degree of insurance which is not actually what's align:start position:0% insurance which is not actually what's align:start position:0% insurance which is not actually what's going on in the underlying model so they align:start position:0% going on in the underlying model so they align:start position:0% going on in the underlying model so they use this to look at the biases or what align:start position:0% use this to look at the biases or what align:start position:0% use this to look at the biases or what can generate the bias the intuition align:start position:0% can generate the bias the intuition align:start position:0% can generate the bias the intuition there is pretty align:start position:0% there is pretty align:start position:0% there is pretty straightforward you know zero borrowing align:start position:0% straightforward you know zero borrowing align:start position:0% straightforward you know zero borrowing uh or limits to borrowing are like a align:start position:0% uh or limits to borrowing are like a align:start position:0% uh or limits to borrowing are like a corner and you're either constrained or align:start position:0% corner and you're either constrained or align:start position:0% corner and you're either constrained or you're not constrained so that's that's align:start position:0% you're not constrained so that's that's align:start position:0% you're not constrained so that's that's a align:start position:0% a align:start position:0% a nonlinearity whereas BPP algorithm is align:start position:0% nonlinearity whereas BPP algorithm is align:start position:0% nonlinearity whereas BPP algorithm is basically linear so so the distortions align:start position:0% basically linear so so the distortions align:start position:0% basically linear so so the distortions get introduced by you align:start position:0% get introduced by you align:start position:0% get introduced by you know the more likely you are to be hit align:start position:0% know the more likely you are to be hit align:start position:0% know the more likely you are to be hit Corners the more the higher the align:start position:0% Corners the more the higher the align:start position:0% Corners the more the higher the Distortion align:start position:0% Distortion align:start position:0% Distortion is align:start position:0% align:start position:0% okay align:start position:0% okay align:start position:0% okay so the uh standard incomplete markets align:start position:0% so the uh standard incomplete markets align:start position:0% so the uh standard incomplete markets model generates an insurance coefficient align:start position:0% model generates an insurance coefficient align:start position:0% model generates an insurance coefficient for transitory shocks of align:start position:0% for transitory shocks of align:start position:0% for transitory shocks of 94% align:start position:0% 94% align:start position:0% 94% uh in the natural borrowing constraint align:start position:0% uh in the natural borrowing constraint align:start position:0% uh in the natural borrowing constraint economy or 82% in the zero borrowing align:start position:0% economy or 82% in the zero borrowing align:start position:0% economy or 82% in the zero borrowing constraint economy now that's a align:start position:0% constraint economy now that's a align:start position:0% constraint economy now that's a coefficient for insurance so that's a align:start position:0% coefficient for insurance so that's a align:start position:0% coefficient for insurance so that's a good thing you know be careful you don't align:start position:0% good thing you know be careful you don't align:start position:0% good thing you know be careful you don't get flipped around because we've been align:start position:0% get flipped around because we've been align:start position:0% get flipped around because we've been looking align:start position:0% looking align:start position:0% looking at the degree to which consumption align:start position:0% at the degree to which consumption align:start position:0% at the degree to which consumption fluctuates with income you so you start align:start position:0% fluctuates with income you so you start align:start position:0% fluctuates with income you so you start to think High numbers are bad but this align:start position:0% to think High numbers are bad but this align:start position:0% to think High numbers are bad but this is one minus that okay so for them high align:start position:0% is one minus that okay so for them high align:start position:0% is one minus that okay so for them high numbers means insurance which means a align:start position:0% numbers means insurance which means a align:start position:0% numbers means insurance which means a good thing those are numbers you know align:start position:0% good thing those are numbers you know align:start position:0% good thing those are numbers you know 9482 compared to the BPP run on the align:start position:0% 9482 compared to the BPP run on the align:start position:0% 9482 compared to the BPP run on the actual data which is 95 so that's align:start position:0% actual data which is 95 so that's align:start position:0% actual data which is 95 so that's excellent align:start position:0% excellent align:start position:0% excellent fit uh but when they look at the align:start position:0% fit uh but when they look at the align:start position:0% fit uh but when they look at the insurance Co coefficient for permanent align:start position:0% insurance Co coefficient for permanent align:start position:0% insurance Co coefficient for permanent shocks it's 22 or 7% depending in the align:start position:0% shocks it's 22 or 7% depending in the align:start position:0% shocks it's 22 or 7% depending in the model what you assume about credit but align:start position:0% model what you assume about credit but align:start position:0% model what you assume about credit but in the actual data it's uh 36% and here align:start position:0% in the actual data it's uh 36% and here align:start position:0% in the actual data it's uh 36% and here already you're seeing you know this align:start position:0% already you're seeing you know this align:start position:0% already you're seeing you know this recurrent theme that there's better align:start position:0% recurrent theme that there's better align:start position:0% recurrent theme that there's better smoothing against even the permanent align:start position:0% smoothing against even the permanent align:start position:0% smoothing against even the permanent shocks in the data than than these align:start position:0% shocks in the data than than these align:start position:0% shocks in the data than than these models align:start position:0% models align:start position:0% models allow and then if you looked at the life align:start position:0% allow and then if you looked at the life align:start position:0% allow and then if you looked at the life cycle uh through the lens of the model align:start position:0% cycle uh through the lens of the model align:start position:0% cycle uh through the lens of the model you would see better insurance as people align:start position:0% you would see better insurance as people align:start position:0% you would see better insurance as people get align:start position:0% get align:start position:0% get older but in the data it's not there align:start position:0% older but in the data it's not there align:start position:0% older but in the data it's not there there's no age profile in the data so uh align:start position:0% there's no age profile in the data so uh align:start position:0% there's no age profile in the data so uh the so the model another way to say this align:start position:0% the so the model another way to say this align:start position:0% the so the model another way to say this is generating too much consumption align:start position:0% is generating too much consumption align:start position:0% is generating too much consumption smoothing for the for the older workers align:start position:0% smoothing for the for the older workers align:start position:0% smoothing for the for the older workers relative to the data or too little align:start position:0% relative to the data or too little align:start position:0% relative to the data or too little smoothing for workers in the early stage align:start position:0% smoothing for workers in the early stage align:start position:0% smoothing for workers in the early stage of their life cycle relative to the data align:start position:0% of their life cycle relative to the data align:start position:0% of their life cycle relative to the data now if you're skeptical you've got to be align:start position:0% now if you're skeptical you've got to be align:start position:0% now if you're skeptical you've got to be skeptical about BPP because it's align:start position:0% skeptical about BPP because it's align:start position:0% skeptical about BPP because it's supposed to be quote a fact that they're align:start position:0% supposed to be quote a fact that they're align:start position:0% supposed to be quote a fact that they're finding we'll look at some of that data align:start position:0% finding we'll look at some of that data align:start position:0% finding we'll look at some of that data though align:start position:0% though align:start position:0% though through the lens of the cross-sectional align:start position:0% through the lens of the cross-sectional align:start position:0% through the lens of the cross-sectional distributions when we get to Deton and align:start position:0% distributions when we get to Deton and align:start position:0% distributions when we get to Deton and taxon and then you'll kind of see align:start position:0% taxon and then you'll kind of see align:start position:0% taxon and then you'll kind of see something else and I haven't thought align:start position:0% something else and I haven't thought align:start position:0% something else and I haven't thought about how to reconcile that align:start position:0% about how to reconcile that align:start position:0% about how to reconcile that yet um this is what I said about the align:start position:0% yet um this is what I said about the align:start position:0% yet um this is what I said about the reliability when they simulate and use align:start position:0% reliability when they simulate and use align:start position:0% reliability when they simulate and use the data from the model it's fine for align:start position:0% the data from the model it's fine for align:start position:0% the data from the model it's fine for the transitory shocks align:start position:0% the transitory shocks align:start position:0% the transitory shocks largely um but it tends to underestimate align:start position:0% largely um but it tends to underestimate align:start position:0% largely um but it tends to underestimate the true coefficient for the permanent align:start position:0% the true coefficient for the permanent align:start position:0% the true coefficient for the permanent shocks uh well that's actually making align:start position:0% shocks uh well that's actually making align:start position:0% shocks uh well that's actually making the situation worse because then the BPP align:start position:0% the situation worse because then the BPP align:start position:0% the situation worse because then the BPP measure which shows good insurance for align:start position:0% measure which shows good insurance for align:start position:0% measure which shows good insurance for the permanent shocks is a lower bound align:start position:0% the permanent shocks is a lower bound align:start position:0% the permanent shocks is a lower bound estimate of the actual Insurance in the align:start position:0% estimate of the actual Insurance in the align:start position:0% estimate of the actual Insurance in the data so there's an even greater align:start position:0% data so there's an even greater align:start position:0% data so there's an even greater Divergence yes um can I just make sure I align:start position:0% Divergence yes um can I just make sure I align:start position:0% Divergence yes um can I just make sure I understood so in the data we see changes align:start position:0% understood so in the data we see changes align:start position:0% understood so in the data we see changes in align:start position:0% in align:start position:0% in how I smooth over the life cycle but in align:start position:0% how I smooth over the life cycle but in align:start position:0% how I smooth over the life cycle but in the model we don't see any changes or align:start position:0% the model we don't see any changes or align:start position:0% the model we don't see any changes or have I got it wrong way around no it's align:start position:0% have I got it wrong way around no it's align:start position:0% have I got it wrong way around no it's it's almost the other way around okay align:start position:0% it's almost the other way around okay align:start position:0% it's almost the other way around okay right yeah right so the model we see align:start position:0% right yeah right so the model we see align:start position:0% right yeah right so the model we see this profile but real life we don't see align:start position:0% this profile but real life we don't see align:start position:0% this profile but real life we don't see any so that that seems kind of align:start position:0% any so that that seems kind of align:start position:0% any so that that seems kind of counterintuitive I guess to us wouldn't align:start position:0% counterintuitive I guess to us wouldn't align:start position:0% counterintuitive I guess to us wouldn't we expect oh maybe I'm maybe I'm align:start position:0% we expect oh maybe I'm maybe I'm align:start position:0% we expect oh maybe I'm maybe I'm thinking of a different align:start position:0% thinking of a different align:start position:0% thinking of a different model well yeah the problem is align:start position:0% align:start position:0% taking the model is gener align:start position:0% taking the model is gener align:start position:0% taking the model is gener generating differences by age because of align:start position:0% generating differences by age because of align:start position:0% generating differences by age because of the life cycle but the data does not align:start position:0% the life cycle but the data does not align:start position:0% the life cycle but the data does not show that so that's why you get this align:start position:0% show that so that's why you get this align:start position:0% show that so that's why you get this sort of oddl looking align:start position:0% sort of oddl looking align:start position:0% sort of oddl looking statement align:start position:0% statement align:start position:0% statement uh that looks like it's more criticism align:start position:0% uh that looks like it's more criticism align:start position:0% uh that looks like it's more criticism of the model but it's of the model align:start position:0% of the model but it's of the model align:start position:0% of the model but it's of the model relative to the flat data yeah so you align:start position:0% relative to the flat data yeah so you align:start position:0% relative to the flat data yeah so you know I mean someone once said if if the align:start position:0% know I mean someone once said if if the align:start position:0% know I mean someone once said if if the data don't fit the model it must be align:start position:0% data don't fit the model it must be align:start position:0% data don't fit the model it must be something wrong with the align:start position:0% something wrong with the align:start position:0% something wrong with the data align:start position:0% data align:start position:0% data so you know we're feeling that pressure align:start position:0% align:start position:0% here I didn't say that align:start position:0% align:start position:0% uh align:start position:0% uh align:start position:0% uh okay now how can you get more smoothing align:start position:0% okay now how can you get more smoothing align:start position:0% okay now how can you get more smoothing uh to generate you know less sensitivity align:start position:0% align:start position:0% uh of consumption to these permanent align:start position:0% uh of consumption to these permanent align:start position:0% uh of consumption to these permanent shocks align:start position:0% shocks align:start position:0% shocks um align:start position:0% um align:start position:0% um because again align:start position:0% because again align:start position:0% because again there's say to get turned around so align:start position:0% there's say to get turned around so align:start position:0% there's say to get turned around so easily there's more smoothing in the align:start position:0% easily there's more smoothing in the align:start position:0% easily there's more smoothing in the data than in the model so you want the align:start position:0% data than in the model so you want the align:start position:0% data than in the model so you want the model to allow more smoothing to catch align:start position:0% model to allow more smoothing to catch align:start position:0% model to allow more smoothing to catch up to the data and uh one thing you align:start position:0% up to the data and uh one thing you align:start position:0% up to the data and uh one thing you could do is give households a little align:start position:0% could do is give households a little align:start position:0% could do is give households a little more information about the future and align:start position:0% more information about the future and align:start position:0% more information about the future and then the idea you know it's a smoothing align:start position:0% then the idea you know it's a smoothing align:start position:0% then the idea you know it's a smoothing model so you know if they know things align:start position:0% model so you know if they know things align:start position:0% model so you know if they know things are going to get better or worse they align:start position:0% are going to get better or worse they align:start position:0% are going to get better or worse they can take actions now uh and adjust align:start position:0% can take actions now uh and adjust align:start position:0% can take actions now uh and adjust consumption so the overall profile that align:start position:0% consumption so the overall profile that align:start position:0% consumption so the overall profile that would result would be smoother if they align:start position:0% would result would be smoother if they align:start position:0% would result would be smoother if they could anticipate future income rather align:start position:0% could anticipate future income rather align:start position:0% could anticipate future income rather than having to align:start position:0% than having to align:start position:0% than having to react to you know sudden align:start position:0% react to you know sudden align:start position:0% react to you know sudden information uh and a close cousin of align:start position:0% information uh and a close cousin of align:start position:0% information uh and a close cousin of that is align:start position:0% that is align:start position:0% that is to uh is to move away from some random align:start position:0% to uh is to move away from some random align:start position:0% to uh is to move away from some random walk to put in some you know serially align:start position:0% walk to put in some you know serially align:start position:0% walk to put in some you know serially correlated uh income process uh and that align:start position:0% correlated uh income process uh and that align:start position:0% correlated uh income process uh and that actually does a better job in align:start position:0% actually does a better job in align:start position:0% actually does a better job in getting getting the model to match the align:start position:0% getting getting the model to match the align:start position:0% getting getting the model to match the data align:start position:0% data align:start position:0% data um as I said you know so far in this align:start position:0% um as I said you know so far in this align:start position:0% um as I said you know so far in this class we haven't talked too too much align:start position:0% class we haven't talked too too much align:start position:0% class we haven't talked too too much about these income processes but it's align:start position:0% about these income processes but it's align:start position:0% about these income processes but it's really front and center here uh what you align:start position:0% really front and center here uh what you align:start position:0% really front and center here uh what you assume about a income process is it IID align:start position:0% assume about a income process is it IID align:start position:0% assume about a income process is it IID is it auto regressive you know for that align:start position:0% is it auto regressive you know for that align:start position:0% is it auto regressive you know for that matter with high frequency data what align:start position:0% matter with high frequency data what align:start position:0% matter with high frequency data what about the seasonality and align:start position:0% about the seasonality and align:start position:0% about the seasonality and everything align:start position:0% everything align:start position:0% everything [Music] align:start position:0% [Music] align:start position:0% [Music] um it makes you aware of the both the align:start position:0% um it makes you aware of the both the align:start position:0% um it makes you aware of the both the great strength and vulnerability of the align:start position:0% great strength and vulnerability of the align:start position:0% great strength and vulnerability of the risk sharing model which says it doesn't align:start position:0% risk sharing model which says it doesn't align:start position:0% risk sharing model which says it doesn't matter what time it is or what state it align:start position:0% matter what time it is or what state it align:start position:0% matter what time it is or what state it is just add up total consumption and align:start position:0% is just add up total consumption and align:start position:0% is just add up total consumption and smooth it out there's a fixed static align:start position:0% smooth it out there's a fixed static align:start position:0% smooth it out there's a fixed static rule for allocating risk you know there align:start position:0% rule for allocating risk you know there align:start position:0% rule for allocating risk you know there could be predictable periodic seasonal align:start position:0% could be predictable periodic seasonal align:start position:0% could be predictable periodic seasonal fluctuations or Trends in income it align:start position:0% fluctuations or Trends in income it align:start position:0% fluctuations or Trends in income it doesn't matter for the risk sharing align:start position:0% doesn't matter for the risk sharing align:start position:0% doesn't matter for the risk sharing model but here with incomplete models it align:start position:0% model but here with incomplete models it align:start position:0% model but here with incomplete models it matters much more align:start position:0% matters much more align:start position:0% matters much more because you said that Two Is Better Than align:start position:0% because you said that Two Is Better Than align:start position:0% because you said that Two Is Better Than One like if it's AR is going be better align:start position:0% One like if it's AR is going be better align:start position:0% One like if it's AR is going be better than predicting the future but like AR align:start position:0% than predicting the future but like AR align:start position:0% than predicting the future but like AR is this to a degree is also ability to align:start position:0% is this to a degree is also ability to align:start position:0% is this to a degree is also ability to predict the future right yeah it's very align:start position:0% predict the future right yeah it's very align:start position:0% predict the future right yeah it's very related so there's something else from align:start position:0% related so there's something else from align:start position:0% related so there's something else from the AR that's making it better is it align:start position:0% the AR that's making it better is it align:start position:0% the AR that's making it better is it because there are I guess there are align:start position:0% because there are I guess there are align:start position:0% because there are I guess there are other ways to predict the future like in align:start position:0% other ways to predict the future like in align:start position:0% other ways to predict the future like in even if the process itself is not Auto align:start position:0% even if the process itself is not Auto align:start position:0% even if the process itself is not Auto regressive you could get signals about align:start position:0% regressive you could get signals about align:start position:0% regressive you could get signals about what it's going to be in the future align:start position:0% what it's going to be in the future align:start position:0% what it's going to be in the future that's not as good as that's what the align:start position:0% that's not as good as that's what the align:start position:0% that's not as good as that's what the claim is yeah that's what they align:start position:0% claim is yeah that's what they align:start position:0% claim is yeah that's what they find um okay so here's the model finally align:start position:0% find um okay so here's the model finally align:start position:0% find um okay so here's the model finally there's no aggregate uncertainty align:start position:0% there's no aggregate uncertainty align:start position:0% there's no aggregate uncertainty um agents work until align:start position:0% um agents work until align:start position:0% um agents work until retirement but they don't die then align:start position:0% retirement but they don't die then align:start position:0% retirement but they don't die then there's a probability C of align:start position:0% there's a probability C of align:start position:0% there's a probability C of surviving uh align:start position:0% surviving uh align:start position:0% surviving uh this align:start position:0% this align:start position:0% this is I guess you know retirement is a align:start position:0% is I guess you know retirement is a align:start position:0% is I guess you know retirement is a really bad thing because uh if you don't align:start position:0% really bad thing because uh if you don't align:start position:0% really bad thing because uh if you don't retire you're going to live with align:start position:0% retire you're going to live with align:start position:0% retire you're going to live with probability one so anyway this is a a align:start position:0% probability one so anyway this is a a align:start position:0% probability one so anyway this is a a simplification uh so they only they only align:start position:0% simplification uh so they only they only align:start position:0% simplification uh so they only they only start using these Actuarial align:start position:0% start using these Actuarial align:start position:0% start using these Actuarial tables uh after age 60 or 65 whatever align:start position:0% tables uh after age 60 or 65 whatever align:start position:0% tables uh after age 60 or 65 whatever they put in for retirement age uh so align:start position:0% they put in for retirement age uh so align:start position:0% they put in for retirement age uh so it's maximizing discounted expected align:start position:0% it's maximizing discounted expected align:start position:0% it's maximizing discounted expected utility common utility align:start position:0% utility common utility align:start position:0% utility common utility function we've been doing a lot of that align:start position:0% function we've been doing a lot of that align:start position:0% function we've been doing a lot of that too beta is the standard discount rate align:start position:0% too beta is the standard discount rate align:start position:0% too beta is the standard discount rate exceed is this you know you only get the align:start position:0% exceed is this you know you only get the align:start position:0% exceed is this you know you only get the utility if you're alive basically so align:start position:0% utility if you're alive basically so align:start position:0% utility if you're alive basically so that's a standard adjustment to the align:start position:0% that's a standard adjustment to the align:start position:0% that's a standard adjustment to the discount rate the income process is align:start position:0% discount rate the income process is align:start position:0% discount rate the income process is uh a bit complicated first of all align:start position:0% uh a bit complicated first of all align:start position:0% uh a bit complicated first of all there's a possible non-stochastic align:start position:0% there's a possible non-stochastic align:start position:0% there's a possible non-stochastic Trend uh sort of the deterministic part align:start position:0% Trend uh sort of the deterministic part align:start position:0% Trend uh sort of the deterministic part which could move income along with t and align:start position:0% which could move income along with t and align:start position:0% which could move income along with t and then you have income quote standard align:start position:0% then you have income quote standard align:start position:0% then you have income quote standard here's the decomposition income is equal align:start position:0% here's the decomposition income is equal align:start position:0% here's the decomposition income is equal to Z which is this permanent thing in align:start position:0% to Z which is this permanent thing in align:start position:0% to Z which is this permanent thing in this case entirely a random walk and align:start position:0% this case entirely a random walk and align:start position:0% this case entirely a random walk and Epsilon which is align:start position:0% Epsilon which is align:start position:0% Epsilon which is the IID transitory shock okay so these align:start position:0% the IID transitory shock okay so these align:start position:0% the IID transitory shock okay so these papers use different notation and this align:start position:0% papers use different notation and this align:start position:0% papers use different notation and this paper Z is permanent and Epsilon is align:start position:0% paper Z is permanent and Epsilon is align:start position:0% paper Z is permanent and Epsilon is transitory and Ada is another shock and align:start position:0% transitory and Ada is another shock and align:start position:0% transitory and Ada is another shock and that's the shock to permanent income align:start position:0% that's the shock to permanent income align:start position:0% that's the shock to permanent income basically you align:start position:0% basically you align:start position:0% basically you know so in expectation you expect your align:start position:0% know so in expectation you expect your align:start position:0% know so in expectation you expect your income to be what it was you expect the align:start position:0% income to be what it was you expect the align:start position:0% income to be what it was you expect the permanent part of your income to be align:start position:0% permanent part of your income to be align:start position:0% permanent part of your income to be exactly what it was last period but this align:start position:0% exactly what it was last period but this align:start position:0% exactly what it was last period but this thing will move move that align:start position:0% thing will move move that align:start position:0% thing will move move that around and then these have variances align:start position:0% around and then these have variances align:start position:0% around and then these have variances Sigma Ada Sigma align:start position:0% Sigma Ada Sigma align:start position:0% Sigma Ada Sigma Epsilon uh the budget constraint again align:start position:0% Epsilon uh the budget constraint again align:start position:0% Epsilon uh the budget constraint again is like this Bond Bond uh which you may align:start position:0% is like this Bond Bond uh which you may align:start position:0% is like this Bond Bond uh which you may or may not be able to short so you know align:start position:0% or may not be able to short so you know align:start position:0% or may not be able to short so you know you've got your assets from last align:start position:0% you've got your assets from last align:start position:0% you've got your assets from last period That's earning align:start position:0% period That's earning align:start position:0% period That's earning interest plus your income so this is align:start position:0% interest plus your income so this is align:start position:0% interest plus your income so this is like your disposable income which you align:start position:0% like your disposable income which you align:start position:0% like your disposable income which you can spend on align:start position:0% can spend on align:start position:0% can spend on consumption and assets going forward you align:start position:0% consumption and assets going forward you align:start position:0% consumption and assets going forward you know watch the subscripts of the jve you align:start position:0% know watch the subscripts of the jve you align:start position:0% know watch the subscripts of the jve you crazy it does me you know this is dated align:start position:0% crazy it does me you know this is dated align:start position:0% crazy it does me you know this is dated uh t plus one but it's decided on a t align:start position:0% uh t plus one but it's decided on a t align:start position:0% uh t plus one but it's decided on a t and consumption is also decided on a t align:start position:0% and consumption is also decided on a t align:start position:0% and consumption is also decided on a t so in some of these formulas you're align:start position:0% so in some of these formulas you're align:start position:0% so in some of these formulas you're going to see a mysterious interest rate align:start position:0% going to see a mysterious interest rate align:start position:0% going to see a mysterious interest rate adjustment and it has to do with you align:start position:0% adjustment and it has to do with you align:start position:0% adjustment and it has to do with you know this sort of Convention of the align:start position:0% know this sort of Convention of the align:start position:0% know this sort of Convention of the timing uh this looks the same except as align:start position:0% timing uh this looks the same except as align:start position:0% timing uh this looks the same except as I said it's like a pension fund in your align:start position:0% I said it's like a pension fund in your align:start position:0% I said it's like a pension fund in your assets so effectively you know this gets align:start position:0% assets so effectively you know this gets align:start position:0% assets so effectively you know this gets adjusted um you're it's not like align:start position:0% adjusted um you're it's not like align:start position:0% adjusted um you're it's not like everyone has their own individual align:start position:0% everyone has their own individual align:start position:0% everyone has their own individual retirement account which you draw down align:start position:0% retirement account which you draw down align:start position:0% retirement account which you draw down there's a pool of money there some align:start position:0% there's a pool of money there some align:start position:0% there's a pool of money there some people continue to live and some don't align:start position:0% people continue to live and some don't align:start position:0% people continue to live and some don't and so you know those in other words if align:start position:0% and so you know those in other words if align:start position:0% and so you know those in other words if you're quote lucky and you keep living align:start position:0% you're quote lucky and you keep living align:start position:0% you're quote lucky and you keep living you could actually draw more from the align:start position:0% you could actually draw more from the align:start position:0% you could actually draw more from the fund than your than what you put in align:start position:0% fund than your than what you put in align:start position:0% fund than your than what you put in there and and this is a very convenient align:start position:0% there and and this is a very convenient align:start position:0% there and and this is a very convenient way to kind of align:start position:0% way to kind of align:start position:0% way to kind of adjust align:start position:0% adjust align:start position:0% adjust um okay oh and if you're hired you get align:start position:0% um okay oh and if you're hired you get align:start position:0% um okay oh and if you're hired you get you know your Social Security align:start position:0% you know your Social Security align:start position:0% you know your Social Security benefits uh they're going to put some align:start position:0% benefits uh they're going to put some align:start position:0% benefits uh they're going to put some numbers in here from the life cycle align:start position:0% numbers in here from the life cycle align:start position:0% numbers in here from the life cycle literature and other sources uh using align:start position:0% literature and other sources uh using align:start position:0% literature and other sources uh using various you know us data sets and I'm align:start position:0% various you know us data sets and I'm align:start position:0% various you know us data sets and I'm not going to dwell on the numbers but align:start position:0% not going to dwell on the numbers but align:start position:0% not going to dwell on the numbers but this is a classic align:start position:0% this is a classic align:start position:0% this is a classic picture of the life align:start position:0% picture of the life align:start position:0% picture of the life cycle align:start position:0% cycle align:start position:0% cycle so here are the align:start position:0% so here are the align:start position:0% so here are the earnings going up you guys are down here align:start position:0% earnings going up you guys are down here align:start position:0% earnings going up you guys are down here somewhere align:start position:0% somewhere align:start position:0% somewhere uh on average you you can expect to do align:start position:0% uh on average you you can expect to do align:start position:0% uh on average you you can expect to do better align:start position:0% better align:start position:0% better eventually uh and then you you get to be align:start position:0% eventually uh and then you you get to be align:start position:0% eventually uh and then you you get to be 60 and it doesn't go to zero that's if align:start position:0% 60 and it doesn't go to zero that's if align:start position:0% 60 and it doesn't go to zero that's if you were a US citizen that's where you align:start position:0% you were a US citizen that's where you align:start position:0% you were a US citizen that's where you start drawing well actually it's you align:start position:0% start drawing well actually it's you align:start position:0% start drawing well actually it's you just be an immigrant you start drawing align:start position:0% just be an immigrant you start drawing align:start position:0% just be an immigrant you start drawing uh Social Security benefits now with align:start position:0% uh Social Security benefits now with align:start position:0% uh Social Security benefits now with this profile you try to keep consumption align:start position:0% this profile you try to keep consumption align:start position:0% this profile you try to keep consumption steady align:start position:0% steady align:start position:0% steady you know now it's not completely flat it align:start position:0% you know now it's not completely flat it align:start position:0% you know now it's not completely flat it just looks flat relative to everything align:start position:0% just looks flat relative to everything align:start position:0% just looks flat relative to everything else on this diagram it's it's actually align:start position:0% else on this diagram it's it's actually align:start position:0% else on this diagram it's it's actually increasing somewhat um but but you know align:start position:0% increasing somewhat um but but you know align:start position:0% increasing somewhat um but but you know the goal of the life cycle smoothing is align:start position:0% the goal of the life cycle smoothing is align:start position:0% the goal of the life cycle smoothing is to is to try to have more or less steady align:start position:0% to is to try to have more or less steady align:start position:0% to is to try to have more or less steady consumption align:start position:0% consumption align:start position:0% consumption um now again this is there's two lines align:start position:0% um now again this is there's two lines align:start position:0% um now again this is there's two lines here there's a natural borrowing align:start position:0% here there's a natural borrowing align:start position:0% here there's a natural borrowing constraint and a zero borrowing align:start position:0% constraint and a zero borrowing align:start position:0% constraint and a zero borrowing constraint doesn't make too much align:start position:0% constraint doesn't make too much align:start position:0% constraint doesn't make too much different for consumption align:start position:0% align:start position:0% um I guess here the zero borrowing align:start position:0% um I guess here the zero borrowing align:start position:0% um I guess here the zero borrowing constraint looks more constraining so align:start position:0% constraint looks more constraining so align:start position:0% constraint looks more constraining so when you're young you know expecting on align:start position:0% when you're young you know expecting on align:start position:0% when you're young you know expecting on average higher future income you might align:start position:0% average higher future income you might align:start position:0% average higher future income you might want to borrow against that uh and repay align:start position:0% want to borrow against that uh and repay align:start position:0% want to borrow against that uh and repay the debt later but you hit one or the align:start position:0% the debt later but you hit one or the align:start position:0% the debt later but you hit one or the other of these constraints so you can't align:start position:0% other of these constraints so you can't align:start position:0% other of these constraints so you can't do that too much of course align:start position:0% do that too much of course align:start position:0% do that too much of course the the gorilla in the room is uh is align:start position:0% the the gorilla in the room is uh is align:start position:0% the the gorilla in the room is uh is this wealth profile and that's where all align:start position:0% this wealth profile and that's where all align:start position:0% this wealth profile and that's where all the action is basically you know in fact align:start position:0% the action is basically you know in fact align:start position:0% the action is basically you know in fact um you you're basically over the life align:start position:0% um you you're basically over the life align:start position:0% um you you're basically over the life cycle accumulating and then de align:start position:0% cycle accumulating and then de align:start position:0% cycle accumulating and then de accumulating wealth you know that's what align:start position:0% accumulating wealth you know that's what align:start position:0% accumulating wealth you know that's what that's what's keeping consumption steady align:start position:0% that's what's keeping consumption steady align:start position:0% that's what's keeping consumption steady you remember when income goes to align:start position:0% you remember when income goes to align:start position:0% you remember when income goes to virtually zero apart from Social align:start position:0% virtually zero apart from Social align:start position:0% virtually zero apart from Social Security you've got to live off the align:start position:0% Security you've got to live off the align:start position:0% Security you've got to live off the interest in your uh either you know you align:start position:0% interest in your uh either you know you align:start position:0% interest in your uh either you know you have Social Security Plus the adjusted align:start position:0% have Social Security Plus the adjusted align:start position:0% have Social Security Plus the adjusted Actuarial interest off the pension fund align:start position:0% Actuarial interest off the pension fund align:start position:0% Actuarial interest off the pension fund and that's typically a lot smaller flow align:start position:0% and that's typically a lot smaller flow align:start position:0% and that's typically a lot smaller flow than was your previous income so you align:start position:0% than was your previous income so you align:start position:0% than was your previous income so you need a a ton of assets to be able to you align:start position:0% need a a ton of assets to be able to you align:start position:0% need a a ton of assets to be able to you know survive into old age this has run align:start position:0% know survive into old age this has run align:start position:0% know survive into old age this has run out looks like to 90 something align:start position:0% out looks like to 90 something align:start position:0% out looks like to 90 something align:start position:0% align:start position:0% um now oh so that you know that could align:start position:0% um now oh so that you know that could align:start position:0% um now oh so that you know that could have been shown first but that's kind of align:start position:0% have been shown first but that's kind of align:start position:0% have been shown first but that's kind of a summary of the life cycle model and align:start position:0% a summary of the life cycle model and align:start position:0% a summary of the life cycle model and and what Kaplan and viante are are doing align:start position:0% and what Kaplan and viante are are doing align:start position:0% and what Kaplan and viante are are doing and they're generating these smoothing align:start position:0% and they're generating these smoothing align:start position:0% and they're generating these smoothing statistics uh align:start position:0% statistics uh align:start position:0% statistics uh from date by date with shocks you know align:start position:0% from date by date with shocks you know align:start position:0% from date by date with shocks you know but this is the overall pattern you align:start position:0% but this is the overall pattern you align:start position:0% but this is the overall pattern you would see now let's go to Deon and align:start position:0% would see now let's go to Deon and align:start position:0% would see now let's go to Deon and Paxon for a very different look at it align:start position:0% Paxon for a very different look at it align:start position:0% Paxon for a very different look at it through the lens of these align:start position:0% through the lens of these align:start position:0% through the lens of these cross-sections align:start position:0% cross-sections align:start position:0% cross-sections um starting point again is that with a align:start position:0% um starting point again is that with a align:start position:0% um starting point again is that with a permanent income hypothesis align:start position:0% permanent income hypothesis align:start position:0% permanent income hypothesis consumption of each person should align:start position:0% consumption of each person should align:start position:0% consumption of each person should basically follow a random align:start position:0% basically follow a random align:start position:0% basically follow a random walk uh yeah again the idea is you align:start position:0% walk uh yeah again the idea is you align:start position:0% walk uh yeah again the idea is you should you could you should Bas align:start position:0% should you could you should Bas align:start position:0% should you could you should Bas basically be eating at the level of your align:start position:0% basically be eating at the level of your align:start position:0% basically be eating at the level of your permanent income and uh and when your align:start position:0% permanent income and uh and when your align:start position:0% permanent income and uh and when your permanent income is shocked then your align:start position:0% permanent income is shocked then your align:start position:0% permanent income is shocked then your consumption is align:start position:0% consumption is align:start position:0% consumption is shocked align:start position:0% align:start position:0% um but the implication that consumption align:start position:0% um but the implication that consumption align:start position:0% um but the implication that consumption follow was a random walk you know means align:start position:0% follow was a random walk you know means align:start position:0% follow was a random walk you know means basically you'll see the equations for align:start position:0% basically you'll see the equations for align:start position:0% basically you'll see the equations for it uh date by datee by date you you know align:start position:0% it uh date by datee by date you you know align:start position:0% it uh date by datee by date you you know you get hit with positive or negative align:start position:0% you get hit with positive or negative align:start position:0% you get hit with positive or negative shocks and their IID so basically you align:start position:0% shocks and their IID so basically you align:start position:0% shocks and their IID so basically you know some people have their ups and align:start position:0% know some people have their ups and align:start position:0% know some people have their ups and other people have their downs so you align:start position:0% other people have their downs so you align:start position:0% other people have their downs so you start getting this Fanning out and then align:start position:0% start getting this Fanning out and then align:start position:0% start getting this Fanning out and then you go then you take the cohort that is align:start position:0% you go then you take the cohort that is align:start position:0% you go then you take the cohort that is still all alike go one more period they align:start position:0% still all alike go one more period they align:start position:0% still all alike go one more period they have ups and downs those guys fan out a align:start position:0% have ups and downs those guys fan out a align:start position:0% have ups and downs those guys fan out a a bit so you know the the align:start position:0% a bit so you know the the align:start position:0% a bit so you know the the cross-sectional distribution just keeps align:start position:0% cross-sectional distribution just keeps align:start position:0% cross-sectional distribution just keeps getting fatter and fatter with bigger align:start position:0% getting fatter and fatter with bigger align:start position:0% getting fatter and fatter with bigger and bigger align:start position:0% and bigger align:start position:0% and bigger Tails um align:start position:0% Tails um align:start position:0% Tails um so all of the slides basically are going align:start position:0% so all of the slides basically are going align:start position:0% so all of the slides basically are going to be align:start position:0% to be align:start position:0% to be about this increasing consumption align:start position:0% about this increasing consumption align:start position:0% about this increasing consumption inequality in the cross-section say align:start position:0% inequality in the cross-section say align:start position:0% inequality in the cross-section say measured by the standard deviation of align:start position:0% measured by the standard deviation of align:start position:0% measured by the standard deviation of the log of align:start position:0% the log of align:start position:0% the log of consumption age group by age align:start position:0% consumption age group by age align:start position:0% consumption age group by age group uh align:start position:0% group uh align:start position:0% group uh but again if you thought about full risk align:start position:0% but again if you thought about full risk align:start position:0% but again if you thought about full risk sharing align:start position:0% sharing align:start position:0% sharing um you get this dramatic align:start position:0% um you get this dramatic align:start position:0% um you get this dramatic contrast you know at least for the cases align:start position:0% contrast you know at least for the cases align:start position:0% contrast you know at least for the cases where people have uniform risk aversion align:start position:0% where people have uniform risk aversion align:start position:0% where people have uniform risk aversion and so on then we know that what pins align:start position:0% and so on then we know that what pins align:start position:0% and so on then we know that what pins down the level of your consumption on align:start position:0% down the level of your consumption on align:start position:0% down the level of your consumption on average is going to be your paral weight align:start position:0% average is going to be your paral weight align:start position:0% average is going to be your paral weight and you kind of have those fixed at T align:start position:0% and you kind of have those fixed at T align:start position:0% and you kind of have those fixed at T equals z that's going to fix the align:start position:0% equals z that's going to fix the align:start position:0% equals z that's going to fix the intercepts and you know your consumption align:start position:0% intercepts and you know your consumption align:start position:0% intercepts and you know your consumption might fluctuate with aggregate shocks align:start position:0% might fluctuate with aggregate shocks align:start position:0% might fluctuate with aggregate shocks around that but it's not going to move align:start position:0% around that but it's not going to move align:start position:0% around that but it's not going to move with age or anything else so basically align:start position:0% with age or anything else so basically align:start position:0% with age or anything else so basically the cross-sectional dispersion of align:start position:0% the cross-sectional dispersion of align:start position:0% the cross-sectional dispersion of consumption does not increase in the align:start position:0% consumption does not increase in the align:start position:0% consumption does not increase in the full risk sharing model but you'll see align:start position:0% full risk sharing model but you'll see align:start position:0% full risk sharing model but you'll see that in the align:start position:0% that in the align:start position:0% that in the data uh depending on the country it does align:start position:0% align:start position:0% happen uh now you have to be a little align:start position:0% happen uh now you have to be a little align:start position:0% happen uh now you have to be a little mindful align:start position:0% mindful align:start position:0% mindful of going back back and forth between align:start position:0% of going back back and forth between align:start position:0% of going back back and forth between this align:start position:0% this align:start position:0% this cross-sectional age dependent inequality align:start position:0% cross-sectional age dependent inequality align:start position:0% cross-sectional age dependent inequality and inequality for the economy as a align:start position:0% and inequality for the economy as a align:start position:0% and inequality for the economy as a whole align:start position:0% whole align:start position:0% whole uh because demographics can shift you align:start position:0% uh because demographics can shift you align:start position:0% uh because demographics can shift you know even if you give me someone's age align:start position:0% know even if you give me someone's age align:start position:0% know even if you give me someone's age and I'll tell you sort of what the align:start position:0% and I'll tell you sort of what the align:start position:0% and I'll tell you sort of what the cross-sectional dispersion is in the align:start position:0% cross-sectional dispersion is in the align:start position:0% cross-sectional dispersion is in the population when you have D demographics align:start position:0% population when you have D demographics align:start position:0% population when you have D demographics going on you may have an increasing align:start position:0% going on you may have an increasing align:start position:0% going on you may have an increasing number of young people or old people align:start position:0% number of young people or old people align:start position:0% number of young people or old people depending on the economy so you're align:start position:0% depending on the economy so you're align:start position:0% depending on the economy so you're basically taking an age weighted average align:start position:0% basically taking an age weighted average align:start position:0% basically taking an age weighted average as the demographic shift and that will align:start position:0% as the demographic shift and that will align:start position:0% as the demographic shift and that will shift in equality so an issue in this align:start position:0% shift in equality so an issue in this align:start position:0% shift in equality so an issue in this literature is how much of aggregate align:start position:0% literature is how much of aggregate align:start position:0% literature is how much of aggregate inequality can be explained by these align:start position:0% inequality can be explained by these align:start position:0% inequality can be explained by these kinds align:start position:0% kinds align:start position:0% kinds of life cycle smoothing considerations align:start position:0% of life cycle smoothing considerations align:start position:0% of life cycle smoothing considerations and how much align:start position:0% and how much align:start position:0% and how much by uh you know baby booms versus uh align:start position:0% by uh you know baby booms versus uh align:start position:0% by uh you know baby booms versus uh fertility drops and all of align:start position:0% align:start position:0% that align:start position:0% align:start position:0% so this is kind of nice because they align:start position:0% so this is kind of nice because they align:start position:0% so this is kind of nice because they have the US Britain and Taiwan uh where align:start position:0% have the US Britain and Taiwan uh where align:start position:0% have the US Britain and Taiwan uh where which are three countries that have align:start position:0% which are three countries that have align:start position:0% which are three countries that have quite ample amount of align:start position:0% quite ample amount of align:start position:0% quite ample amount of cross-sectional consumption for that align:start position:0% cross-sectional consumption for that align:start position:0% cross-sectional consumption for that matter also income align:start position:0% matter also income align:start position:0% matter also income data uh they're going to use align:start position:0% data uh they're going to use align:start position:0% data uh they're going to use 47 annual surveys spread out over the align:start position:0% 47 annual surveys spread out over the align:start position:0% 47 annual surveys spread out over the three align:start position:0% three align:start position:0% three countries and look at the implications align:start position:0% countries and look at the implications align:start position:0% countries and look at the implications of these models for align:start position:0% of these models for align:start position:0% of these models for the kind of cross-sectional inequality align:start position:0% the kind of cross-sectional inequality align:start position:0% the kind of cross-sectional inequality and see what it takes to to explain it align:start position:0% and see what it takes to to explain it align:start position:0% and see what it takes to to explain it so how does this work exactly align:start position:0% so how does this work exactly align:start position:0% so how does this work exactly um so we want to follow cohort cohorts align:start position:0% um so we want to follow cohort cohorts align:start position:0% um so we want to follow cohort cohorts over time we cannot follow an individual align:start position:0% over time we cannot follow an individual align:start position:0% over time we cannot follow an individual person over time because it's not panel align:start position:0% person over time because it's not panel align:start position:0% person over time because it's not panel data but you make the assumption that uh align:start position:0% data but you make the assumption that uh align:start position:0% data but you make the assumption that uh that for example if you see a bunch of align:start position:0% that for example if you see a bunch of align:start position:0% that for example if you see a bunch of 31y olds in 1976 in align:start position:0% 31y olds in 1976 in align:start position:0% 31y olds in 1976 in Taiwan align:start position:0% Taiwan align:start position:0% Taiwan uh uh you're you're getting a good align:start position:0% uh uh you're you're getting a good align:start position:0% uh uh you're you're getting a good summary statistic of the cross-sectional align:start position:0% summary statistic of the cross-sectional align:start position:0% summary statistic of the cross-sectional dispersion of their consumption in 1976 align:start position:0% dispersion of their consumption in 1976 align:start position:0% dispersion of their consumption in 1976 and then you go to 1977 and they are now align:start position:0% and then you go to 1977 and they are now align:start position:0% and then you go to 1977 and they are now 32 actually they isn't quite correct align:start position:0% 32 actually they isn't quite correct align:start position:0% 32 actually they isn't quite correct because it's a different set of people align:start position:0% because it's a different set of people align:start position:0% because it's a different set of people but again you hope you have enough of align:start position:0% but again you hope you have enough of align:start position:0% but again you hope you have enough of them and that there the basic align:start position:0% them and that there the basic align:start position:0% them and that there the basic assumptions are align:start position:0% assumptions are align:start position:0% assumptions are correct uh that you can take these kinds align:start position:0% correct uh that you can take these kinds align:start position:0% correct uh that you can take these kinds of align:start position:0% of align:start position:0% of statistics as representative of what align:start position:0% statistics as representative of what align:start position:0% statistics as representative of what would you would have seen if you could align:start position:0% would you would have seen if you could align:start position:0% would you would have seen if you could have been able to continue to track the align:start position:0% have been able to continue to track the align:start position:0% have been able to continue to track the same align:start position:0% same align:start position:0% same people align:start position:0% people align:start position:0% people um some people actually think this is align:start position:0% um some people actually think this is align:start position:0% um some people actually think this is better than panel data in the sense that align:start position:0% better than panel data in the sense that align:start position:0% better than panel data in the sense that you don't have to worry about people align:start position:0% you don't have to worry about people align:start position:0% you don't have to worry about people dropping out and the data becomes align:start position:0% dropping out and the data becomes align:start position:0% dropping out and the data becomes unrepresentative and there is some truth align:start position:0% unrepresentative and there is some truth align:start position:0% unrepresentative and there is some truth to that align:start position:0% to that align:start position:0% to that um there are issues about whether the align:start position:0% um there are issues about whether the align:start position:0% um there are issues about whether the data are coming from households or align:start position:0% data are coming from households or align:start position:0% data are coming from households or individuals you have to make some align:start position:0% individuals you have to make some align:start position:0% individuals you have to make some adjustments for household align:start position:0% adjustments for household align:start position:0% adjustments for household composition and the surveys being used align:start position:0% composition and the surveys being used align:start position:0% composition and the surveys being used here are the personal income align:start position:0% here are the personal income align:start position:0% here are the personal income distribution survey in Taiwan the align:start position:0% distribution survey in Taiwan the align:start position:0% distribution survey in Taiwan the consumer expenditure survey in the US align:start position:0% consumer expenditure survey in the US align:start position:0% consumer expenditure survey in the US that's the same one we've referred to align:start position:0% that's the same one we've referred to align:start position:0% that's the same one we've referred to before and this family expenditure align:start position:0% before and this family expenditure align:start position:0% before and this family expenditure survey in Great Britain align:start position:0% survey in Great Britain align:start position:0% survey in Great Britain so takes a bit of staring to get used to align:start position:0% so takes a bit of staring to get used to align:start position:0% so takes a bit of staring to get used to this but so we start out with people who align:start position:0% this but so we start out with people who align:start position:0% this but so we start out with people who are age 15 and 19 align:start position:0% are age 15 and 19 align:start position:0% are age 15 and 19 align:start position:0% align:start position:0% um and they kind of start here in align:start position:0% um and they kind of start here in align:start position:0% um and they kind of start here in calendar time in know 1982 or something align:start position:0% calendar time in know 1982 or something align:start position:0% calendar time in know 1982 or something like that now again we don't track the align:start position:0% like that now again we don't track the align:start position:0% like that now again we don't track the same people but we can look what align:start position:0% same people but we can look what align:start position:0% same people but we can look what happens this paper is not the most align:start position:0% happens this paper is not the most align:start position:0% happens this paper is not the most recent thing in the world it's just a align:start position:0% recent thing in the world it's just a align:start position:0% recent thing in the world it's just a really nice one so they basically align:start position:0% really nice one so they basically align:start position:0% really nice one so they basically stopped using data after 1990 so we go align:start position:0% stopped using data after 1990 so we go align:start position:0% stopped using data after 1990 so we go back to you know uh the 1976 survey all align:start position:0% back to you know uh the 1976 survey all align:start position:0% back to you know uh the 1976 survey all the way up to the 1990 survey with align:start position:0% the way up to the 1990 survey with align:start position:0% the way up to the 1990 survey with repeated cross-sections and looking what align:start position:0% repeated cross-sections and looking what align:start position:0% repeated cross-sections and looking what happens to inequality in this align:start position:0% happens to inequality in this align:start position:0% happens to inequality in this cohort as they age now you know these align:start position:0% cohort as they age now you know these align:start position:0% cohort as they age now you know these guys were 15 these these guys were 20 in align:start position:0% guys were 15 these these guys were 20 in align:start position:0% guys were 15 these these guys were 20 in 1976 so they start older and they're align:start position:0% 1976 so they start older and they're align:start position:0% 1976 so they start older and they're going to end a bit older and and then align:start position:0% going to end a bit older and and then align:start position:0% going to end a bit older and and then you keep going align:start position:0% you keep going align:start position:0% you keep going here uh you know to the Aged 55 people align:start position:0% here uh you know to the Aged 55 people align:start position:0% here uh you know to the Aged 55 people in 1976 and so on now you know these are align:start position:0% in 1976 and so on now you know these are align:start position:0% in 1976 and so on now you know these are pretty flat then these profiles start to align:start position:0% pretty flat then these profiles start to align:start position:0% pretty flat then these profiles start to pick up you kind of in your align:start position:0% pick up you kind of in your align:start position:0% pick up you kind of in your mind sort of can imagine and I'll show align:start position:0% mind sort of can imagine and I'll show align:start position:0% mind sort of can imagine and I'll show you what happens when we splice all all align:start position:0% you what happens when we splice all all align:start position:0% you what happens when we splice all all this align:start position:0% this align:start position:0% this together align:start position:0% together align:start position:0% together um um so it seems like a lot of the align:start position:0% um um so it seems like a lot of the align:start position:0% um um so it seems like a lot of the action is is brought about by the boards align:start position:0% action is is brought about by the boards align:start position:0% action is is brought about by the boards like the middleaged align:start position:0% like the middleaged align:start position:0% like the middleaged Cs Those Who start middleaged in 7 align:start position:0% Cs Those Who start middleaged in 7 align:start position:0% Cs Those Who start middleaged in 7 like from 40 to align:start position:0% like from 40 to align:start position:0% like from 40 to 55 well let me just the rest is kind of align:start position:0% 55 well let me just the rest is kind of align:start position:0% 55 well let me just the rest is kind of flat well let me just jump okay cuz I align:start position:0% flat well let me just jump okay cuz I align:start position:0% flat well let me just jump okay cuz I those are the three countries here's align:start position:0% those are the three countries here's align:start position:0% those are the three countries here's what's going to when you use all the align:start position:0% what's going to when you use all the align:start position:0% what's going to when you use all the surveys over all the years and just align:start position:0% surveys over all the years and just align:start position:0% surveys over all the years and just focus on the age yeah so this you see align:start position:0% focus on the age yeah so this you see align:start position:0% focus on the age yeah so this you see this you're right you see this is pretty align:start position:0% this you're right you see this is pretty align:start position:0% this you're right you see this is pretty flat and then it picks up around age align:start position:0% flat and then it picks up around age align:start position:0% flat and then it picks up around age whatever 45 or 50 or something align:start position:0% align:start position:0% now and these are the results from the align:start position:0% now and these are the results from the align:start position:0% now and these are the results from the other align:start position:0% other align:start position:0% other countries so is there align:start position:0% countries so is there align:start position:0% countries so is there any explanation for why that's the case align:start position:0% any explanation for why that's the case align:start position:0% any explanation for why that's the case yeah we're going to get into that you'll align:start position:0% yeah we're going to get into that you'll align:start position:0% yeah we're going to get into that you'll be sorry you align:start position:0% align:start position:0% asked uh and only Tai huh and only taian align:start position:0% asked uh and only Tai huh and only taian align:start position:0% asked uh and only Tai huh and only taian the other well okay align:start position:0% the other well okay align:start position:0% the other well okay so this is kind of flat and then it kind align:start position:0% so this is kind of flat and then it kind align:start position:0% so this is kind of flat and then it kind of comes up and then it you know it align:start position:0% of comes up and then it you know it align:start position:0% of comes up and then it you know it flattens out again so Taiwan is align:start position:0% flattens out again so Taiwan is align:start position:0% flattens out again so Taiwan is flattening out align:start position:0% flattening out align:start position:0% flattening out although unfortunately you know the align:start position:0% although unfortunately you know the align:start position:0% although unfortunately you know the cohorts are getting thin the older they align:start position:0% cohorts are getting thin the older they align:start position:0% cohorts are getting thin the older they are so you get some sort of shaky data align:start position:0% are so you get some sort of shaky data align:start position:0% are so you get some sort of shaky data because you can't average quite so well align:start position:0% because you can't average quite so well align:start position:0% because you can't average quite so well this one flattens out Great Britain kind align:start position:0% this one flattens out Great Britain kind align:start position:0% this one flattens out Great Britain kind of flattens out the US I don't know align:start position:0% of flattens out the US I don't know align:start position:0% of flattens out the US I don't know wasn't very steeply climbing to begin align:start position:0% wasn't very steeply climbing to begin align:start position:0% wasn't very steeply climbing to begin with it's not so align:start position:0% with it's not so align:start position:0% with it's not so obvious this kind of looks align:start position:0% obvious this kind of looks align:start position:0% obvious this kind of looks concave this looks concave but almost align:start position:0% concave this looks concave but almost align:start position:0% concave this looks concave but almost linear this actually has almost an align:start position:0% linear this actually has almost an align:start position:0% linear this actually has almost an inflection point and then comes in so align:start position:0% inflection point and then comes in so align:start position:0% inflection point and then comes in so the question is concave align:start position:0% the question is concave align:start position:0% the question is concave convex Etc and align:start position:0% convex Etc and align:start position:0% convex Etc and that's where you know we'll do a little align:start position:0% align:start position:0% modeling by the way you've saw a little align:start position:0% modeling by the way you've saw a little align:start position:0% modeling by the way you've saw a little bit about align:start position:0% bit about align:start position:0% bit about demographics when we did China one of align:start position:0% demographics when we did China one of align:start position:0% demographics when we did China one of those explanations of the savings rates align:start position:0% those explanations of the savings rates align:start position:0% those explanations of the savings rates Etc wasn't so much about state-owned align:start position:0% Etc wasn't so much about state-owned align:start position:0% Etc wasn't so much about state-owned Enterprise as it was the different align:start position:0% Enterprise as it was the different align:start position:0% Enterprise as it was the different demographics and you know young Savers align:start position:0% demographics and you know young Savers align:start position:0% demographics and you know young Savers in China and you know sort align:start position:0% in China and you know sort align:start position:0% in China and you know sort of debt loaded or less saving inclined align:start position:0% of debt loaded or less saving inclined align:start position:0% of debt loaded or less saving inclined households in the US and so different align:start position:0% households in the US and so different align:start position:0% households in the US and so different demographics just to remind you it's not align:start position:0% demographics just to remind you it's not align:start position:0% demographics just to remind you it's not the first time we've align:start position:0% the first time we've align:start position:0% the first time we've uh that we've thought about demographics align:start position:0% uh that we've thought about demographics align:start position:0% uh that we've thought about demographics so align:start position:0% so align:start position:0% so it's possible to put that there's a align:start position:0% it's possible to put that there's a align:start position:0% it's possible to put that there's a there's trivial demographics and some of align:start position:0% there's trivial demographics and some of align:start position:0% there's trivial demographics and some of the macro models in the sense that they align:start position:0% the macro models in the sense that they align:start position:0% the macro models in the sense that they start with a life cycle model or two align:start position:0% start with a life cycle model or two align:start position:0% start with a life cycle model or two period overlapping Generations model but align:start position:0% period overlapping Generations model but align:start position:0% period overlapping Generations model but we haven't actually focused align:start position:0% we haven't actually focused align:start position:0% we haven't actually focused on in much of this in the uh sort of align:start position:0% on in much of this in the uh sort of align:start position:0% on in much of this in the uh sort of micro part of the align:start position:0% micro part of the align:start position:0% micro part of the class align:start position:0% class align:start position:0% class okay so this is what I said in words align:start position:0% okay so this is what I said in words align:start position:0% okay so this is what I said in words they claim Britain is slightly convex I align:start position:0% they claim Britain is slightly convex I align:start position:0% they claim Britain is slightly convex I didn't see that just now align:start position:0% didn't see that just now align:start position:0% didn't see that just now but align:start position:0% but align:start position:0% but um align:start position:0% align:start position:0% and again you know don't misread those align:start position:0% and again you know don't misread those align:start position:0% and again you know don't misread those things to be measures of the total align:start position:0% things to be measures of the total align:start position:0% things to be measures of the total increases or decreases in inequality align:start position:0% increases or decreases in inequality align:start position:0% increases or decreases in inequality because the demographic structure you align:start position:0% because the demographic structure you align:start position:0% because the demographic structure you know is moving is moving around by age align:start position:0% know is moving is moving around by age align:start position:0% know is moving is moving around by age over those 20 or so align:start position:0% over those 20 or so align:start position:0% over those 20 or so years align:start position:0% years align:start position:0% years um all right let's start with the basics align:start position:0% um all right let's start with the basics align:start position:0% um all right let's start with the basics here's basically Hall's permanent align:start position:0% here's basically Hall's permanent align:start position:0% here's basically Hall's permanent income uh align:start position:0% income uh align:start position:0% income uh implication for consumption consumption align:start position:0% implication for consumption consumption align:start position:0% implication for consumption consumption should essentially be a random align:start position:0% should essentially be a random align:start position:0% should essentially be a random walk uh and it's only moving around align:start position:0% walk uh and it's only moving around align:start position:0% walk uh and it's only moving around because of the Innovations or the shock align:start position:0% because of the Innovations or the shock align:start position:0% because of the Innovations or the shock to permanent align:start position:0% to permanent align:start position:0% to permanent income uh I think that was JP align:start position:0% income uh I think that was JP align:start position:0% income uh I think that was JP 1970 the dates here I think it was in align:start position:0% 1970 the dates here I think it was in align:start position:0% 1970 the dates here I think it was in the align:start position:0% the align:start position:0% the jpe uh there are assumptions this isn't align:start position:0% jpe uh there are assumptions this isn't align:start position:0% jpe uh there are assumptions this isn't always true you know he assumed align:start position:0% always true you know he assumed align:start position:0% always true you know he assumed quadratic utility you know additive align:start position:0% quadratic utility you know additive align:start position:0% quadratic utility you know additive preferences discount rates equal to align:start position:0% preferences discount rates equal to align:start position:0% preferences discount rates equal to interest align:start position:0% interest align:start position:0% interest rates align:start position:0% rates align:start position:0% rates um and I think you know no life align:start position:0% um and I think you know no life align:start position:0% um and I think you know no life cycle uh this is supposed to be an align:start position:0% cycle uh this is supposed to be an align:start position:0% cycle uh this is supposed to be an innovation so for every person at least align:start position:0% innovation so for every person at least align:start position:0% innovation so for every person at least you align:start position:0% you align:start position:0% you know there's no co uh covariance between align:start position:0% know there's no co uh covariance between align:start position:0% know there's no co uh covariance between lagged consumption and this Innovation align:start position:0% lagged consumption and this Innovation align:start position:0% lagged consumption and this Innovation because it wasn't supposed to be align:start position:0% because it wasn't supposed to be align:start position:0% because it wasn't supposed to be predictable that's the same conversation align:start position:0% predictable that's the same conversation align:start position:0% predictable that's the same conversation is how much if anything you see about align:start position:0% is how much if anything you see about align:start position:0% is how much if anything you see about the future here zero is seen okay so I align:start position:0% the future here zero is seen okay so I align:start position:0% the future here zero is seen okay so I described this in words that align:start position:0% described this in words that align:start position:0% described this in words that basically you know if it were stable align:start position:0% basically you know if it were stable align:start position:0% basically you know if it were stable like this on average then align:start position:0% like this on average then align:start position:0% like this on average then consumption dispersion shouldn't be align:start position:0% consumption dispersion shouldn't be align:start position:0% consumption dispersion shouldn't be changing but you're just layering on align:start position:0% changing but you're just layering on align:start position:0% changing but you're just layering on repeatedly shock After Shock After Shock align:start position:0% repeatedly shock After Shock After Shock align:start position:0% repeatedly shock After Shock After Shock so with that zero covariance assumption align:start position:0% so with that zero covariance assumption align:start position:0% so with that zero covariance assumption the variances are increasing by the align:start position:0% the variances are increasing by the align:start position:0% the variances are increasing by the variance of that UT align:start position:0% variance of that UT align:start position:0% variance of that UT shock align:start position:0% align:start position:0% um and basically if you started plotting align:start position:0% um and basically if you started plotting align:start position:0% um and basically if you started plotting these distributions you align:start position:0% these distributions you align:start position:0% these distributions you know the one at T is going to have align:start position:0% know the one at T is going to have align:start position:0% know the one at T is going to have fatter Tails than the one at T minus one align:start position:0% fatter Tails than the one at T minus one align:start position:0% fatter Tails than the one at T minus one so T minus one quote first order align:start position:0% so T minus one quote first order align:start position:0% so T minus one quote first order stochastically align:start position:0% stochastically align:start position:0% stochastically dominates align:start position:0% align:start position:0% you have to be a little bit careful align:start position:0% you have to be a little bit careful align:start position:0% you have to be a little bit careful throughout all of this align:start position:0% throughout all of this align:start position:0% throughout all of this stuff you think about things from the align:start position:0% stuff you think about things from the align:start position:0% stuff you think about things from the point of view of a person tracking a align:start position:0% point of view of a person tracking a align:start position:0% point of view of a person tracking a person over time but that statement align:start position:0% person over time but that statement align:start position:0% person over time but that statement about CT and UT is actually a statement align:start position:0% about CT and UT is actually a statement align:start position:0% about CT and UT is actually a statement about the cross-section as well as the align:start position:0% about the cross-section as well as the align:start position:0% about the cross-section as well as the intertemporal align:start position:0% intertemporal align:start position:0% intertemporal dimension align:start position:0% align:start position:0% um okay align:start position:0% align:start position:0% this doesn't this model typically didn't align:start position:0% this doesn't this model typically didn't align:start position:0% this doesn't this model typically didn't have taste sh shifters or heterogeneous align:start position:0% have taste sh shifters or heterogeneous align:start position:0% have taste sh shifters or heterogeneous preferences uh you can put those things align:start position:0% preferences uh you can put those things align:start position:0% preferences uh you can put those things in depending on how you put them in it align:start position:0% in depending on how you put them in it align:start position:0% in depending on how you put them in it does make a align:start position:0% does make a align:start position:0% does make a difference arguably if we hadn't done align:start position:0% difference arguably if we hadn't done align:start position:0% difference arguably if we hadn't done the demographics right with a claim Deon align:start position:0% the demographics right with a claim Deon align:start position:0% the demographics right with a claim Deon in Paxon claim for Taiwan you know then align:start position:0% in Paxon claim for Taiwan you know then align:start position:0% in Paxon claim for Taiwan you know then you kind of need preference shocks to uh align:start position:0% you kind of need preference shocks to uh align:start position:0% you kind of need preference shocks to uh to help with the observed dispersion align:start position:0% align:start position:0% now here's the basic sort of budget align:start position:0% now here's the basic sort of budget align:start position:0% now here's the basic sort of budget equation align:start position:0% equation align:start position:0% equation again align:start position:0% align:start position:0% um and I'm afraid each one of these align:start position:0% um and I'm afraid each one of these align:start position:0% um and I'm afraid each one of these papers kind of has different convention align:start position:0% papers kind of has different convention align:start position:0% papers kind of has different convention about the timing so it's really kind of align:start position:0% about the timing so it's really kind of align:start position:0% about the timing so it's really kind of hard to keep tracking it track it but align:start position:0% hard to keep tracking it track it but align:start position:0% hard to keep tracking it track it but but basically you know you have align:start position:0% align:start position:0% um sources and uses of money the sources align:start position:0% um sources and uses of money the sources align:start position:0% um sources and uses of money the sources of previous assets plus interest uh the align:start position:0% of previous assets plus interest uh the align:start position:0% of previous assets plus interest uh the uses are a source also is income and the align:start position:0% uses are a source also is income and the align:start position:0% uses are a source also is income and the use is consumption and then what you align:start position:0% use is consumption and then what you align:start position:0% use is consumption and then what you don't spend accumulates on to the uh to align:start position:0% don't spend accumulates on to the uh to align:start position:0% don't spend accumulates on to the uh to the next period if you do do the life align:start position:0% the next period if you do do the life align:start position:0% the next period if you do do the life cycle uh with a terminal align:start position:0% cycle uh with a terminal align:start position:0% cycle uh with a terminal date for sure say age 99 or whatever you align:start position:0% date for sure say age 99 or whatever you align:start position:0% date for sure say age 99 or whatever you want align:start position:0% want align:start position:0% want um then you can actually get a formula align:start position:0% um then you can actually get a formula align:start position:0% um then you can actually get a formula closed form for consumption under these align:start position:0% closed form for consumption under these align:start position:0% closed form for consumption under these other maintained align:start position:0% other maintained align:start position:0% other maintained assumptions and uh you know align:start position:0% assumptions and uh you know align:start position:0% assumptions and uh you know basically it's kind of saying align:start position:0% basically it's kind of saying align:start position:0% basically it's kind of saying consumption ought to equal something align:start position:0% consumption ought to equal something align:start position:0% consumption ought to equal something about the return stream through the align:start position:0% about the return stream through the align:start position:0% about the return stream through the interest rate on assets and something align:start position:0% interest rate on assets and something align:start position:0% interest rate on assets and something about the forward-looking part which is align:start position:0% about the forward-looking part which is align:start position:0% about the forward-looking part which is you know expected future income shocks align:start position:0% you know expected future income shocks align:start position:0% you know expected future income shocks so so this kind of helps align:start position:0% so so this kind of helps align:start position:0% so so this kind of helps you see you know how future things are align:start position:0% you see you know how future things are align:start position:0% you see you know how future things are already if this is going to be very high align:start position:0% already if this is going to be very high align:start position:0% already if this is going to be very high for example then this is already going align:start position:0% for example then this is already going align:start position:0% for example then this is already going up uh so it's kind of smooth against or align:start position:0% up uh so it's kind of smooth against or align:start position:0% up uh so it's kind of smooth against or low vice versa now It's Tricky with a align:start position:0% low vice versa now It's Tricky with a align:start position:0% low vice versa now It's Tricky with a finite Horizon and a cap T because align:start position:0% finite Horizon and a cap T because align:start position:0% finite Horizon and a cap T because there's a coefficient premultiplying align:start position:0% there's a coefficient premultiplying align:start position:0% there's a coefficient premultiplying this but but it's for that reason align:start position:0% this but but it's for that reason align:start position:0% this but but it's for that reason basically obviously the the close closer align:start position:0% basically obviously the the close closer align:start position:0% basically obviously the the close closer you are to to the end to cap T the less align:start position:0% you are to to the end to cap T the less align:start position:0% you are to to the end to cap T the less smoothing you can accomplish and that's align:start position:0% smoothing you can accomplish and that's align:start position:0% smoothing you can accomplish and that's inherited into this align:start position:0% inherited into this align:start position:0% inherited into this formula so yep the shocks here are ID align:start position:0% formula so yep the shocks here are ID align:start position:0% formula so yep the shocks here are ID over time align:start position:0% align:start position:0% yes oh align:start position:0% yes oh align:start position:0% yes oh well the the shock to permanent income align:start position:0% well the the shock to permanent income align:start position:0% well the the shock to permanent income is align:start position:0% align:start position:0% IID but permanent income has is an auto align:start position:0% IID but permanent income has is an auto align:start position:0% IID but permanent income has is an auto regressive process so align:start position:0% align:start position:0% um the standard incomplete markets model align:start position:0% um the standard incomplete markets model align:start position:0% um the standard incomplete markets model had an infinite Horizon and had a align:start position:0% had an infinite Horizon and had a align:start position:0% had an infinite Horizon and had a discount rate equal to one or basically align:start position:0% discount rate equal to one or basically align:start position:0% discount rate equal to one or basically you know beta * 1 + r equal 1 align:start position:0% you know beta * 1 + r equal 1 align:start position:0% you know beta * 1 + r equal 1 uh in the finite Horizon case beta that align:start position:0% uh in the finite Horizon case beta that align:start position:0% uh in the finite Horizon case beta that thing premultiplying consumption turns align:start position:0% thing premultiplying consumption turns align:start position:0% thing premultiplying consumption turns out if you stare at it is concave we're align:start position:0% out if you stare at it is concave we're align:start position:0% out if you stare at it is concave we're already beginning to anticipate these align:start position:0% already beginning to anticipate these align:start position:0% already beginning to anticipate these formulas uh and decreasing in T and if align:start position:0% formulas uh and decreasing in T and if align:start position:0% formulas uh and decreasing in T and if you go back to those two equations align:start position:0% you go back to those two equations align:start position:0% you go back to those two equations you'll get kind of a simplified version align:start position:0% you'll get kind of a simplified version align:start position:0% you'll get kind of a simplified version that beta T times the change in align:start position:0% that beta T times the change in align:start position:0% that beta T times the change in consumption is equal to this quote align:start position:0% consumption is equal to this quote align:start position:0% consumption is equal to this quote consumption align:start position:0% align:start position:0% Innovation and here's a formula for the align:start position:0% Innovation and here's a formula for the align:start position:0% Innovation and here's a formula for the consumption Innovation which is align:start position:0% consumption Innovation which is align:start position:0% consumption Innovation which is again align:start position:0% again align:start position:0% again uh you know the difference in align:start position:0% uh you know the difference in align:start position:0% uh you know the difference in expectations so you're forecasting the align:start position:0% expectations so you're forecasting the align:start position:0% expectations so you're forecasting the future all the time but you're also align:start position:0% future all the time but you're also align:start position:0% future all the time but you're also getting these align:start position:0% getting these align:start position:0% getting these shocks align:start position:0% shocks align:start position:0% shocks so as of T and T minus one you were align:start position:0% so as of T and T minus one you were align:start position:0% so as of T and T minus one you were forecasting YT at at t plus k Sorry y of align:start position:0% forecasting YT at at t plus k Sorry y of align:start position:0% forecasting YT at at t plus k Sorry y of t+ K not either to either to T or T align:start position:0% t+ K not either to either to T or T align:start position:0% t+ K not either to either to T or T minus one it could be 10 years out and align:start position:0% minus one it could be 10 years out and align:start position:0% minus one it could be 10 years out and you're constantly adjusting your align:start position:0% you're constantly adjusting your align:start position:0% you're constantly adjusting your expectations based on the current align:start position:0% expectations based on the current align:start position:0% expectations based on the current information you have from the income align:start position:0% information you have from the income align:start position:0% information you have from the income process and you're summing up over all align:start position:0% process and you're summing up over all align:start position:0% process and you're summing up over all those future income shocks and align:start position:0% those future income shocks and align:start position:0% those future income shocks and discounting backwards align:start position:0% discounting backwards align:start position:0% discounting backwards uh to get these quote align:start position:0% uh to get these quote align:start position:0% uh to get these quote Innovations so well so you know then align:start position:0% Innovations so well so you know then align:start position:0% Innovations so well so you know then imagine starting this out at some date T align:start position:0% imagine starting this out at some date T align:start position:0% imagine starting this out at some date T equals align:start position:0% equals align:start position:0% equals zero uh and then t equal 1 and t equal 2 align:start position:0% zero uh and then t equal 1 and t equal 2 align:start position:0% zero uh and then t equal 1 and t equal 2 and so on and you could just write out align:start position:0% and so on and you could just write out align:start position:0% and so on and you could just write out literally consumption in each one of align:start position:0% literally consumption in each one of align:start position:0% literally consumption in each one of those align:start position:0% those align:start position:0% those dates align:start position:0% dates align:start position:0% dates um of course when you go from one date align:start position:0% um of course when you go from one date align:start position:0% um of course when you go from one date to another you can hit with this shock align:start position:0% to another you can hit with this shock align:start position:0% to another you can hit with this shock and you're pre-multiplying by the beta align:start position:0% and you're pre-multiplying by the beta align:start position:0% and you're pre-multiplying by the beta so you end up with this you know an align:start position:0% so you end up with this you know an align:start position:0% so you end up with this you know an explicit formula align:start position:0% explicit formula align:start position:0% explicit formula for consumption equal to its initial align:start position:0% for consumption equal to its initial align:start position:0% for consumption equal to its initial given level plus the beta moves on the align:start position:0% given level plus the beta moves on the align:start position:0% given level plus the beta moves on the right hand side this sort of beta align:start position:0% right hand side this sort of beta align:start position:0% right hand side this sort of beta discounted but it's not beta in the align:start position:0% discounted but it's not beta in the align:start position:0% discounted but it's not beta in the preference function this is that that align:start position:0% preference function this is that that align:start position:0% preference function this is that that data thing that had to do with little T align:start position:0% data thing that had to do with little T align:start position:0% data thing that had to do with little T Big T and all of that that took care of align:start position:0% Big T and all of that that took care of align:start position:0% Big T and all of that that took care of the life cycle align:start position:0% the life cycle align:start position:0% the life cycle considerations align:start position:0% considerations align:start position:0% considerations um so finally we see again you know the align:start position:0% um so finally we see again you know the align:start position:0% um so finally we see again you know the familiar theme that the variance at align:start position:0% familiar theme that the variance at align:start position:0% familiar theme that the variance at T is related to the initial align:start position:0% T is related to the initial align:start position:0% T is related to the initial cross-sectional variance at zero you align:start position:0% cross-sectional variance at zero you align:start position:0% cross-sectional variance at zero you know plus the sum of of variance terms align:start position:0% know plus the sum of of variance terms align:start position:0% know plus the sum of of variance terms um you know so the issue well so at align:start position:0% um you know so the issue well so at align:start position:0% um you know so the issue well so at roughly speaking it looks like yeah it align:start position:0% roughly speaking it looks like yeah it align:start position:0% roughly speaking it looks like yeah it ought to increase unless you know you align:start position:0% ought to increase unless you know you align:start position:0% ought to increase unless you know you retire and you have no more things to align:start position:0% retire and you have no more things to align:start position:0% retire and you have no more things to forecast and this piece goes align:start position:0% forecast and this piece goes align:start position:0% forecast and this piece goes away but before that happens you're align:start position:0% away but before that happens you're align:start position:0% away but before that happens you're looking at Future and making align:start position:0% looking at Future and making align:start position:0% looking at Future and making expectations of future income so you align:start position:0% expectations of future income so you align:start position:0% expectations of future income so you just keep adding on now so that's why align:start position:0% just keep adding on now so that's why align:start position:0% just keep adding on now so that's why inequality is increasing in the data align:start position:0% inequality is increasing in the data align:start position:0% inequality is increasing in the data through the lens of these models and align:start position:0% through the lens of these models and align:start position:0% through the lens of these models and then the issue align:start position:0% then the issue align:start position:0% then the issue is you know is it linear or concave or align:start position:0% is you know is it linear or concave or align:start position:0% is you know is it linear or concave or convex that has to do with this beta and align:start position:0% convex that has to do with this beta and align:start position:0% convex that has to do with this beta and also has to do you know with align:start position:0% also has to do you know with align:start position:0% also has to do you know with what we can infer about Sigma about the align:start position:0% what we can infer about Sigma about the align:start position:0% what we can infer about Sigma about the consumption align:start position:0% consumption align:start position:0% consumption Innovations align:start position:0% align:start position:0% um align:start position:0% um align:start position:0% um so so in response to your align:start position:0% so so in response to your align:start position:0% so so in response to your question you know if we assume that this align:start position:0% question you know if we assume that this align:start position:0% question you know if we assume that this Innovation is entirely White align:start position:0% Innovation is entirely White align:start position:0% Innovation is entirely White Noise you know normalized by the align:start position:0% Noise you know normalized by the align:start position:0% Noise you know normalized by the interest rate then Sigma Square Ada at T align:start position:0% interest rate then Sigma Square Ada at T align:start position:0% interest rate then Sigma Square Ada at T is a constant that doesn't depend on T align:start position:0% is a constant that doesn't depend on T align:start position:0% is a constant that doesn't depend on T and this is the resulting align:start position:0% and this is the resulting align:start position:0% and this is the resulting expression with the sign Square Ada align:start position:0% expression with the sign Square Ada align:start position:0% expression with the sign Square Ada pulled out front and then it's you know align:start position:0% pulled out front and then it's you know align:start position:0% pulled out front and then it's you know entirely the align:start position:0% entirely the align:start position:0% entirely the convexity is entirely to do due to this align:start position:0% convexity is entirely to do due to this align:start position:0% convexity is entirely to do due to this beta thing which if you start taking align:start position:0% beta thing which if you start taking align:start position:0% beta thing which if you start taking some derivatives and so on it's a bit align:start position:0% some derivatives and so on it's a bit align:start position:0% some derivatives and so on it's a bit messy you can convince yourself that it align:start position:0% messy you can convince yourself that it align:start position:0% messy you can convince yourself that it that that thing is align:start position:0% that that thing is align:start position:0% that that thing is convex here's an orthogonal align:start position:0% convex here's an orthogonal align:start position:0% convex here's an orthogonal example I guess Yan I jumped the gun a align:start position:0% example I guess Yan I jumped the gun a align:start position:0% example I guess Yan I jumped the gun a bit because this actually allows align:start position:0% bit because this actually allows align:start position:0% bit because this actually allows something a bit different which align:start position:0% something a bit different which align:start position:0% something a bit different which is uh this Auto regressive thing well align:start position:0% is uh this Auto regressive thing well align:start position:0% is uh this Auto regressive thing well this is IID and then this is auto align:start position:0% this is IID and then this is auto align:start position:0% this is IID and then this is auto regressive so this income process align:start position:0% regressive so this income process align:start position:0% regressive so this income process is uh align:start position:0% is uh align:start position:0% is uh persistent align:start position:0% align:start position:0% um align:start position:0% um align:start position:0% um it's a bit odd because you know this was align:start position:0% it's a bit odd because you know this was align:start position:0% it's a bit odd because you know this was the Innovation that had to align:start position:0% the Innovation that had to align:start position:0% the Innovation that had to do with the Innovation to the right hand align:start position:0% do with the Innovation to the right hand align:start position:0% do with the Innovation to the right hand side would had to do with all those align:start position:0% side would had to do with all those align:start position:0% side would had to do with all those expectation differences so it's like align:start position:0% expectation differences so it's like align:start position:0% expectation differences so it's like let's just assume it looks something align:start position:0% let's just assume it looks something align:start position:0% let's just assume it looks something like this this is more explicit about align:start position:0% like this this is more explicit about align:start position:0% like this this is more explicit about the income process and you can derive align:start position:0% the income process and you can derive align:start position:0% the income process and you can derive the formula for the change in align:start position:0% the formula for the change in align:start position:0% the formula for the change in consumption uh where this beta R thing align:start position:0% consumption uh where this beta R thing align:start position:0% consumption uh where this beta R thing is now this mess align:start position:0% is now this mess align:start position:0% is now this mess um and it turns out this will be align:start position:0% um and it turns out this will be align:start position:0% um and it turns out this will be concave align:start position:0% align:start position:0% uh if you can sign this align:start position:0% uh if you can sign this align:start position:0% uh if you can sign this expression and it may also be decreasing align:start position:0% expression and it may also be decreasing align:start position:0% expression and it may also be decreasing in align:start position:0% in align:start position:0% in age if this is align:start position:0% age if this is align:start position:0% age if this is true uh and so actually except for some align:start position:0% true uh and so actually except for some align:start position:0% true uh and so actually except for some values of theta both things you know align:start position:0% align:start position:0% so you know so two of those three align:start position:0% so you know so two of those three align:start position:0% so you know so two of those three countries the profile align:start position:0% countries the profile align:start position:0% countries the profile was say not concave it could have been align:start position:0% was say not concave it could have been align:start position:0% was say not concave it could have been linear which is a weak case of concavity align:start position:0% linear which is a weak case of concavity align:start position:0% linear which is a weak case of concavity or even convex and so basically then you align:start position:0% or even convex and so basically then you align:start position:0% or even convex and so basically then you could rule this out because these are align:start position:0% could rule this out because these are align:start position:0% could rule this out because these are you know this kind of persistence would align:start position:0% you know this kind of persistence would align:start position:0% you know this kind of persistence would give you concavity but you don't see align:start position:0% give you concavity but you don't see align:start position:0% give you concavity but you don't see that align:start position:0% that align:start position:0% that um but it but then we have the sort of align:start position:0% um but it but then we have the sort of align:start position:0% um but it but then we have the sort of paradox that that something like you align:start position:0% paradox that that something like you align:start position:0% paradox that that something like you know these align:start position:0% know these align:start position:0% know these uh White Noise product processes must be align:start position:0% uh White Noise product processes must be align:start position:0% uh White Noise product processes must be closer to the truth if we're going to align:start position:0% closer to the truth if we're going to align:start position:0% closer to the truth if we're going to get convex profiles but that's an align:start position:0% get convex profiles but that's an align:start position:0% get convex profiles but that's an assumption align:start position:0% assumption align:start position:0% assumption about the income align:start position:0% about the income align:start position:0% about the income process and in align:start position:0% process and in align:start position:0% process and in particular you know you know one way to align:start position:0% particular you know you know one way to align:start position:0% particular you know you know one way to get it is to say that there's a large align:start position:0% get it is to say that there's a large align:start position:0% get it is to say that there's a large stationary component to income so you're align:start position:0% stationary component to income so you're align:start position:0% stationary component to income so you're not getting those Innovations in your align:start position:0% not getting those Innovations in your align:start position:0% not getting those Innovations in your forecast and uh and we don't see that in align:start position:0% forecast and uh and we don't see that in align:start position:0% forecast and uh and we don't see that in the align:start position:0% the align:start position:0% the data income profiles are not stationary align:start position:0% data income profiles are not stationary align:start position:0% data income profiles are not stationary there's heavy life align:start position:0% there's heavy life align:start position:0% there's heavy life cycle uh align:start position:0% cycle uh align:start position:0% cycle uh components align:start position:0% align:start position:0% so um so nothing's perfect I guess um align:start position:0% so um so nothing's perfect I guess um align:start position:0% so um so nothing's perfect I guess um you know every model is a align:start position:0% you know every model is a align:start position:0% you know every model is a benchmark almost every model is going to align:start position:0% benchmark almost every model is going to align:start position:0% benchmark almost every model is going to deliver something that might fit well align:start position:0% deliver something that might fit well align:start position:0% deliver something that might fit well otherwise we probably not reading it in align:start position:0% otherwise we probably not reading it in align:start position:0% otherwise we probably not reading it in a align:start position:0% a align:start position:0% a journal uh or it all may actually also align:start position:0% journal uh or it all may actually also align:start position:0% journal uh or it all may actually also generate things that are not consistent align:start position:0% generate things that are not consistent align:start position:0% generate things that are not consistent with the data and if you're a good align:start position:0% with the data and if you're a good align:start position:0% with the data and if you're a good scholar you're reporting that align:start position:0% scholar you're reporting that align:start position:0% scholar you're reporting that too align:start position:0% too align:start position:0% too um now what about the permanent align:start position:0% um now what about the permanent align:start position:0% um now what about the permanent income and the dispersion of income by align:start position:0% income and the dispersion of income by align:start position:0% income and the dispersion of income by age align:start position:0% align:start position:0% um so again disposable align:start position:0% um so again disposable align:start position:0% um so again disposable income takes on this align:start position:0% income takes on this align:start position:0% income takes on this form align:start position:0% form align:start position:0% form uh align:start position:0% uh align:start position:0% uh you know which is sort of asset return align:start position:0% you know which is sort of asset return align:start position:0% you know which is sort of asset return stream plus income and then you use it align:start position:0% stream plus income and then you use it align:start position:0% stream plus income and then you use it for consumption and savings adjusting align:start position:0% for consumption and savings adjusting align:start position:0% for consumption and savings adjusting for where you are in the life cycle or align:start position:0% for where you are in the life cycle or align:start position:0% for where you are in the life cycle or you could take the difference savings is align:start position:0% you could take the difference savings is align:start position:0% you could take the difference savings is a difference between income and this align:start position:0% a difference between income and this align:start position:0% a difference between income and this beta adjusted align:start position:0% beta adjusted align:start position:0% beta adjusted consumption and in some of these align:start position:0% consumption and in some of these align:start position:0% consumption and in some of these models you can get a close form align:start position:0% models you can get a close form align:start position:0% models you can get a close form expression for savings namely the align:start position:0% expression for savings namely the align:start position:0% expression for savings namely the so-called Campbell's rainy day which is align:start position:0% so-called Campbell's rainy day which is align:start position:0% so-called Campbell's rainy day which is really kind of cool align:start position:0% really kind of cool align:start position:0% really kind of cool uh which is you save enough at te to be align:start position:0% uh which is you save enough at te to be align:start position:0% uh which is you save enough at te to be able to cover the discounted align:start position:0% able to cover the discounted align:start position:0% able to cover the discounted shortfalls in uh sort of these earnings align:start position:0% align:start position:0% Innovations so you want to smooth those align:start position:0% Innovations so you want to smooth those align:start position:0% Innovations so you want to smooth those out and you save just enough to do that align:start position:0% out and you save just enough to do that align:start position:0% out and you save just enough to do that in align:start position:0% align:start position:0% expectation anyway align:start position:0% expectation anyway align:start position:0% expectation anyway so rewriting disposable align:start position:0% so rewriting disposable align:start position:0% so rewriting disposable income you know equal to the savings align:start position:0% income you know equal to the savings align:start position:0% income you know equal to the savings component we already had that you know align:start position:0% component we already had that you know align:start position:0% component we already had that you know uh you know less the savings uh plus the align:start position:0% uh you know less the savings uh plus the align:start position:0% uh you know less the savings uh plus the savings component sorry I get confused align:start position:0% savings component sorry I get confused align:start position:0% savings component sorry I get confused because savings was negative used to be align:start position:0% because savings was negative used to be align:start position:0% because savings was negative used to be here and now it's out align:start position:0% here and now it's out align:start position:0% here and now it's out here savings is not negative but these align:start position:0% here savings is not negative but these align:start position:0% here savings is not negative but these Innovations are negative because you align:start position:0% Innovations are negative because you align:start position:0% Innovations are negative because you save to cover shortfalls and then you align:start position:0% save to cover shortfalls and then you align:start position:0% save to cover shortfalls and then you get implications here align:start position:0% get implications here align:start position:0% get implications here for you align:start position:0% for you align:start position:0% for you know if one thing is a random walk and align:start position:0% know if one thing is a random walk and align:start position:0% know if one thing is a random walk and the other thing is a random walk then align:start position:0% the other thing is a random walk then align:start position:0% the other thing is a random walk then the sum of two things that are random align:start position:0% the sum of two things that are random align:start position:0% the sum of two things that are random walks is also a random align:start position:0% walks is also a random align:start position:0% walks is also a random walk uh align:start position:0% align:start position:0% so so basically savings ought to be align:start position:0% so so basically savings ought to be align:start position:0% so so basically savings ought to be stationary in that sense and it ought to align:start position:0% stationary in that sense and it ought to align:start position:0% stationary in that sense and it ought to be dispersing at the rate that align:start position:0% be dispersing at the rate that align:start position:0% be dispersing at the rate that consumption is align:start position:0% consumption is align:start position:0% consumption is dispersing and they don't see that in align:start position:0% dispersing and they don't see that in align:start position:0% dispersing and they don't see that in the data either align:start position:0% the data either align:start position:0% the data either um and well in particular earnings is align:start position:0% um and well in particular earnings is align:start position:0% um and well in particular earnings is dispersing align:start position:0% dispersing align:start position:0% dispersing so which is a point that was made on the align:start position:0% so which is a point that was made on the align:start position:0% so which is a point that was made on the on the other slide on the other slide as align:start position:0% on the other slide on the other slide as align:start position:0% on the other slide on the other slide as well align:start position:0% align:start position:0% um and then align:start position:0% um and then align:start position:0% um and then finally I guess this is like the fourth align:start position:0% finally I guess this is like the fourth align:start position:0% finally I guess this is like the fourth version of something that starts to look align:start position:0% version of something that starts to look align:start position:0% version of something that starts to look like the same align:start position:0% like the same align:start position:0% like the same thing uh most of the most of those align:start position:0% thing uh most of the most of those align:start position:0% thing uh most of the most of those analytically analytic Expressions we're align:start position:0% analytically analytic Expressions we're align:start position:0% analytically analytic Expressions we're assuming something like quadratic align:start position:0% assuming something like quadratic align:start position:0% assuming something like quadratic utility that's how you manage to get align:start position:0% utility that's how you manage to get align:start position:0% utility that's how you manage to get this really tight reduced form analytic align:start position:0% this really tight reduced form analytic align:start position:0% this really tight reduced form analytic expression if you don't do that if you align:start position:0% expression if you don't do that if you align:start position:0% expression if you don't do that if you have constant relative risk aversion for align:start position:0% have constant relative risk aversion for align:start position:0% have constant relative risk aversion for example or a more General utility align:start position:0% example or a more General utility align:start position:0% example or a more General utility function then the oiler equation align:start position:0% function then the oiler equation align:start position:0% function then the oiler equation basically is is going to equate the the align:start position:0% basically is is going to equate the the align:start position:0% basically is is going to equate the the marginal utility align:start position:0% marginal utility align:start position:0% marginal utility today to something like marginal utility align:start position:0% today to something like marginal utility align:start position:0% today to something like marginal utility tomorrow align:start position:0% align:start position:0% um you might say well where's the align:start position:0% um you might say well where's the align:start position:0% um you might say well where's the expectation operator well instead the align:start position:0% expectation operator well instead the align:start position:0% expectation operator well instead the shock is put over here on the right hand align:start position:0% shock is put over here on the right hand align:start position:0% shock is put over here on the right hand side so this is like an Oiler equation align:start position:0% side so this is like an Oiler equation align:start position:0% side so this is like an Oiler equation now if this were align:start position:0% now if this were align:start position:0% now if this were zero and the interest rate were equal to align:start position:0% zero and the interest rate were equal to align:start position:0% zero and the interest rate were equal to this you know Delta discount rate then align:start position:0% this you know Delta discount rate then align:start position:0% this you know Delta discount rate then basically the marginal utility of align:start position:0% basically the marginal utility of align:start position:0% basically the marginal utility of consumption if we could deduce it would align:start position:0% consumption if we could deduce it would align:start position:0% consumption if we could deduce it would be uh not going anywhere it would be the align:start position:0% be uh not going anywhere it would be the align:start position:0% be uh not going anywhere it would be the same over align:start position:0% same over align:start position:0% same over time align:start position:0% time align:start position:0% time but uh again with r equal to align:start position:0% but uh again with r equal to align:start position:0% but uh again with r equal to Delta we kick on this extra orthogonal align:start position:0% Delta we kick on this extra orthogonal align:start position:0% Delta we kick on this extra orthogonal shock which makes the marginal utility align:start position:0% shock which makes the marginal utility align:start position:0% shock which makes the marginal utility of consumption dispersing in the future align:start position:0% of consumption dispersing in the future align:start position:0% of consumption dispersing in the future relative today and you can even have you align:start position:0% relative today and you can even have you align:start position:0% relative today and you can even have you know R not equal to Delta as long as align:start position:0% know R not equal to Delta as long as align:start position:0% know R not equal to Delta as long as Delta is greater than than r align:start position:0% Delta is greater than than r align:start position:0% Delta is greater than than r the same logic align:start position:0% the same logic align:start position:0% the same logic applies because you're kind of like align:start position:0% applies because you're kind of like align:start position:0% applies because you're kind of like amplifying this align:start position:0% amplifying this align:start position:0% amplifying this thing carrying it through to tomorrow align:start position:0% thing carrying it through to tomorrow align:start position:0% thing carrying it through to tomorrow along with the U the U shock align:start position:0% align:start position:0% um so that's another way to get at the align:start position:0% um so that's another way to get at the align:start position:0% um so that's another way to get at the variance of consumption align:start position:0% variance of consumption align:start position:0% variance of consumption increasing align:start position:0% increasing align:start position:0% increasing [Music] align:start position:0% [Music] align:start position:0% [Music] um depending on what you assume about align:start position:0% um depending on what you assume about align:start position:0% um depending on what you assume about the utility function some functions align:start position:0% the utility function some functions align:start position:0% the utility function some functions though you know have align:start position:0% align:start position:0% uh a force that go the other way in align:start position:0% uh a force that go the other way in align:start position:0% uh a force that go the other way in particular you know if you're really align:start position:0% particular you know if you're really align:start position:0% particular you know if you're really really into it you get into third align:start position:0% really into it you get into third align:start position:0% really into it you get into third derivatives uh but when you're really align:start position:0% derivatives uh but when you're really align:start position:0% derivatives uh but when you're really sort of cautious you know that align:start position:0% sort of cautious you know that align:start position:0% sort of cautious you know that Lambda is uh is align:start position:0% Lambda is uh is align:start position:0% Lambda is uh is convex you know so you're you're taking align:start position:0% convex you know so you're you're taking align:start position:0% convex you know so you're you're taking a second derivative of already the align:start position:0% a second derivative of already the align:start position:0% a second derivative of already the margin of utility that's what I comment align:start position:0% margin of utility that's what I comment align:start position:0% margin of utility that's what I comment about third derivatives of utility align:start position:0% about third derivatives of utility align:start position:0% about third derivatives of utility functions but but and that if you start align:start position:0% functions but but and that if you start align:start position:0% functions but but and that if you start staring at this thing can actually push align:start position:0% staring at this thing can actually push align:start position:0% staring at this thing can actually push you back against this dispersion disper align:start position:0% you back against this dispersion disper align:start position:0% you back against this dispersion disper dispersion of align:start position:0% dispersion of align:start position:0% dispersion of consumption align:start position:0% align:start position:0% um align:start position:0% align:start position:0% so I you know I'm having a sense that align:start position:0% so I you know I'm having a sense that align:start position:0% so I you know I'm having a sense that just going on and on but the point is to align:start position:0% just going on and on but the point is to align:start position:0% just going on and on but the point is to take each of these different forces and align:start position:0% take each of these different forces and align:start position:0% take each of these different forces and then tell stories about what must be align:start position:0% then tell stories about what must be align:start position:0% then tell stories about what must be true in Taiwan versus Britain versus the align:start position:0% true in Taiwan versus Britain versus the align:start position:0% true in Taiwan versus Britain versus the US you know to try to rationalize what align:start position:0% US you know to try to rationalize what align:start position:0% US you know to try to rationalize what we're seeing in the align:start position:0% we're seeing in the align:start position:0% we're seeing in the data align:start position:0% data align:start position:0% data um and similarly align:start position:0% align:start position:0% here okay so let's just say three words align:start position:0% here okay so let's just say three words align:start position:0% here okay so let's just say three words about excess align:start position:0% about excess align:start position:0% about excess smoothness align:start position:0% smoothness align:start position:0% smoothness um to repeat the life cycle model align:start position:0% um to repeat the life cycle model align:start position:0% um to repeat the life cycle model implies that shocks to permanent income align:start position:0% implies that shocks to permanent income align:start position:0% implies that shocks to permanent income should be fully incorporated into align:start position:0% should be fully incorporated into align:start position:0% should be fully incorporated into consumption align:start position:0% consumption align:start position:0% consumption uh while Innovations to to uh the align:start position:0% uh while Innovations to to uh the align:start position:0% uh while Innovations to to uh the transitory part are are align:start position:0% transitory part are are align:start position:0% transitory part are are not align:start position:0% align:start position:0% um you know basically all the all the align:start position:0% um you know basically all the all the align:start position:0% um you know basically all the all the income all the transitory income align:start position:0% income all the transitory income align:start position:0% income all the transitory income fluctuation should should not be align:start position:0% fluctuation should should not be align:start position:0% fluctuation should should not be appearing in consumption which actually align:start position:0% appearing in consumption which actually align:start position:0% appearing in consumption which actually is something we've talked about with align:start position:0% is something we've talked about with align:start position:0% is something we've talked about with regards to the full risk sharing model align:start position:0% regards to the full risk sharing model align:start position:0% regards to the full risk sharing model except there we didn't make this align:start position:0% except there we didn't make this align:start position:0% except there we didn't make this distinction between transitory and align:start position:0% distinction between transitory and align:start position:0% distinction between transitory and permanent align:start position:0% align:start position:0% um but when they go and look at the data align:start position:0% um but when they go and look at the data align:start position:0% um but when they go and look at the data they say hey consumption is too smooth align:start position:0% they say hey consumption is too smooth align:start position:0% they say hey consumption is too smooth it doesn't react to Innovations in the align:start position:0% it doesn't react to Innovations in the align:start position:0% it doesn't react to Innovations in the permanent component of income and other align:start position:0% permanent component of income and other align:start position:0% permanent component of income and other people have uh have found something align:start position:0% people have uh have found something align:start position:0% people have uh have found something similar align:start position:0% similar align:start position:0% similar um and we're inching forward to models align:start position:0% um and we're inching forward to models align:start position:0% um and we're inching forward to models where we're going to we're going to need align:start position:0% where we're going to we're going to need align:start position:0% where we're going to we're going to need to modify the models we're going to have align:start position:0% to modify the models we're going to have align:start position:0% to modify the models we're going to have to introduce something else like private align:start position:0% to introduce something else like private align:start position:0% to introduce something else like private information align:start position:0% information align:start position:0% information uh and more on that in a align:start position:0% align:start position:0% second yep we always assume the market align:start position:0% second yep we always assume the market align:start position:0% second yep we always assume the market is incomplete so maybe just because the align:start position:0% is incomplete so maybe just because the align:start position:0% is incomplete so maybe just because the market is is relatively complete so uh align:start position:0% market is is relatively complete so uh align:start position:0% market is is relatively complete so uh the consumers can this so that's my gut align:start position:0% the consumers can this so that's my gut align:start position:0% the consumers can this so that's my gut reaction align:start position:0% reaction align:start position:0% reaction although well align:start position:0% although well align:start position:0% although well actually so this this pavoni paper you align:start position:0% actually so this this pavoni paper you align:start position:0% actually so this this pavoni paper you know puts in sort of some unobserved align:start position:0% know puts in sort of some unobserved align:start position:0% know puts in sort of some unobserved savings and and other things and it it align:start position:0% savings and and other things and it it align:start position:0% savings and and other things and it it actually comes close to the data so it align:start position:0% actually comes close to the data so it align:start position:0% actually comes close to the data so it isn't all the way toward full insurance align:start position:0% isn't all the way toward full insurance align:start position:0% isn't all the way toward full insurance but it is more full insurance than what align:start position:0% but it is more full insurance than what align:start position:0% but it is more full insurance than what these models align:start position:0% these models align:start position:0% these models imply so trying to reconcile the align:start position:0% imply so trying to reconcile the align:start position:0% imply so trying to reconcile the puzzle align:start position:0% puzzle align:start position:0% puzzle uh I'd like to think I'm you know quite align:start position:0% uh I'd like to think I'm you know quite align:start position:0% uh I'd like to think I'm you know quite agnostic uh you know in my rural tie align:start position:0% agnostic uh you know in my rural tie align:start position:0% agnostic uh you know in my rural tie data certainly when you include other align:start position:0% data certainly when you include other align:start position:0% data certainly when you include other variables and not just assumption we see align:start position:0% variables and not just assumption we see align:start position:0% variables and not just assumption we see rejections of full risk sharing I'm not align:start position:0% rejections of full risk sharing I'm not align:start position:0% rejections of full risk sharing I'm not you know determined to always find full align:start position:0% you know determined to always find full align:start position:0% you know determined to always find full risk sharing in the data but align:start position:0% risk sharing in the data but align:start position:0% risk sharing in the data but likewise I I would hope these guys align:start position:0% likewise I I would hope these guys align:start position:0% likewise I I would hope these guys aren't clinging to the permanent income align:start position:0% aren't clinging to the permanent income align:start position:0% aren't clinging to the permanent income model as the only game in town because align:start position:0% model as the only game in town because align:start position:0% model as the only game in town because it's clearly also you know suffering align:start position:0% it's clearly also you know suffering align:start position:0% it's clearly also you know suffering from its its own sort of anomalies align:start position:0% from its its own sort of anomalies align:start position:0% from its its own sort of anomalies relative to the data and you know and align:start position:0% relative to the data and you know and align:start position:0% relative to the data and you know and there's no reason to think that it has align:start position:0% there's no reason to think that it has align:start position:0% there's no reason to think that it has to be the same model for every village align:start position:0% to be the same model for every village align:start position:0% to be the same model for every village or every align:start position:0% or every align:start position:0% or every country and align:start position:0% country and align:start position:0% country and and and actually Deon and Paxton stuff align:start position:0% and and actually Deon and Paxton stuff align:start position:0% and and actually Deon and Paxton stuff looking at the cross-sections kind of align:start position:0% looking at the cross-sections kind of align:start position:0% looking at the cross-sections kind of saying that it's different it could be align:start position:0% saying that it's different it could be align:start position:0% saying that it's different it could be different in different countries if align:start position:0% different in different countries if align:start position:0% different in different countries if you're going to try to reconcile The align:start position:0% you're going to try to reconcile The align:start position:0% you're going to try to reconcile The observed align:start position:0% observed align:start position:0% observed movements align:start position:0% align:start position:0% um but anyway you guys need to know align:start position:0% um but anyway you guys need to know align:start position:0% um but anyway you guys need to know about this literature I mean you know align:start position:0% about this literature I mean you know align:start position:0% about this literature I mean you know you need you need to have a view of the align:start position:0% you need you need to have a view of the align:start position:0% you need you need to have a view of the different consumption smoothing align:start position:0% different consumption smoothing align:start position:0% different consumption smoothing literature I guess I should also say you align:start position:0% literature I guess I should also say you align:start position:0% literature I guess I should also say you know sort align:start position:0% align:start position:0% of you know it looks as though it's a align:start position:0% of you know it looks as though it's a align:start position:0% of you know it looks as though it's a macro is ussh literature but that's not align:start position:0% macro is ussh literature but that's not align:start position:0% macro is ussh literature but that's not true certainly for Paxton and Deon who align:start position:0% true certainly for Paxton and Deon who align:start position:0% true certainly for Paxton and Deon who are you know Avid development economists align:start position:0% are you know Avid development economists align:start position:0% are you know Avid development economists and looking at uh at data from align:start position:0% and looking at uh at data from align:start position:0% and looking at uh at data from developing countries and likewise the align:start position:0% developing countries and likewise the align:start position:0% developing countries and likewise the initial you know risk sharing stuff that align:start position:0% initial you know risk sharing stuff that align:start position:0% initial you know risk sharing stuff that wasn't peculiar to development that was align:start position:0% wasn't peculiar to development that was align:start position:0% wasn't peculiar to development that was being tested by Cochran and mace and so align:start position:0% being tested by Cochran and mace and so align:start position:0% being tested by Cochran and mace and so on in US data so you know there's really align:start position:0% on in US data so you know there's really align:start position:0% on in US data so you know there's really never been this idea that somehow macro align:start position:0% never been this idea that somehow macro align:start position:0% never been this idea that somehow macro is in one room using one subset of data align:start position:0% is in one room using one subset of data align:start position:0% is in one room using one subset of data and micro is in another room using align:start position:0% and micro is in another room using align:start position:0% and micro is in another room using another subset that would be rather align:start position:0% another subset that would be rather align:start position:0% another subset that would be rather silly so we really need to align:start position:0% silly so we really need to align:start position:0% silly so we really need to know how all these models align:start position:0% know how all these models align:start position:0% know how all these models work uh okay align:start position:0% align:start position:0% so so this is again Campbell's you know align:start position:0% so so this is again Campbell's you know align:start position:0% so so this is again Campbell's you know saving for a rainy align:start position:0% align:start position:0% day uh it's repeated because it's a align:start position:0% day uh it's repeated because it's a align:start position:0% day uh it's repeated because it's a different align:start position:0% different align:start position:0% different paper align:start position:0% paper align:start position:0% paper um they look at Campbell and Deon now align:start position:0% um they look at Campbell and Deon now align:start position:0% um they look at Campbell and Deon now are looking at align:start position:0% are looking at align:start position:0% are looking at uh us align:start position:0% uh us align:start position:0% uh us data and saying the labor income is align:start position:0% data and saying the labor income is align:start position:0% data and saying the labor income is described by this autor regressive align:start position:0% described by this autor regressive align:start position:0% described by this autor regressive process with a positive you know serial align:start position:0% process with a positive you know serial align:start position:0% process with a positive you know serial correlation align:start position:0% align:start position:0% uh and what that means is align:start position:0% uh and what that means is align:start position:0% uh and what that means is Innovations are quote unquote more than align:start position:0% Innovations are quote unquote more than align:start position:0% Innovations are quote unquote more than permanent not just random walk is but align:start position:0% permanent not just random walk is but align:start position:0% permanent not just random walk is but basically now now you get even into more align:start position:0% basically now now you get even into more align:start position:0% basically now now you get even into more trouble because if consumption should align:start position:0% trouble because if consumption should align:start position:0% trouble because if consumption should reflect the Innovations to permanent align:start position:0% reflect the Innovations to permanent align:start position:0% reflect the Innovations to permanent income and what you see in Innovations align:start position:0% income and what you see in Innovations align:start position:0% income and what you see in Innovations is is more than permanent that means align:start position:0% is is more than permanent that means align:start position:0% is is more than permanent that means consumption should respond even align:start position:0% consumption should respond even align:start position:0% consumption should respond even more and it's not in the data responding align:start position:0% more and it's not in the data responding align:start position:0% more and it's not in the data responding that much it's much less align:start position:0% that much it's much less align:start position:0% that much it's much less variable um so either they're getting align:start position:0% variable um so either they're getting align:start position:0% variable um so either they're getting this fact wrong or again maybe you know align:start position:0% this fact wrong or again maybe you know align:start position:0% this fact wrong or again maybe you know the households have more information align:start position:0% the households have more information align:start position:0% the households have more information somehow uh or they have stupid align:start position:0% somehow uh or they have stupid align:start position:0% somehow uh or they have stupid expectations or or whatever these guys align:start position:0% expectations or or whatever these guys align:start position:0% expectations or or whatever these guys were not able to resolve the puzzle I align:start position:0% were not able to resolve the puzzle I align:start position:0% were not able to resolve the puzzle I mean if you want to see the equations align:start position:0% mean if you want to see the equations align:start position:0% mean if you want to see the equations there they are I'm not sure at this align:start position:0% there they are I'm not sure at this align:start position:0% there they are I'm not sure at this point that it adds all that much more to align:start position:0% point that it adds all that much more to align:start position:0% point that it adds all that much more to the discussion um align:start position:0% align:start position:0% and this is what I was saying about align:start position:0% and this is what I was saying about align:start position:0% and this is what I was saying about atanasio and align:start position:0% align:start position:0% pavoni align:start position:0% pavoni align:start position:0% pavoni So the plan is align:start position:0% So the plan is align:start position:0% So the plan is uh there's a little more coming today align:start position:0% uh there's a little more coming today align:start position:0% uh there's a little more coming today don't worry but uh or you might say OD align:start position:0% don't worry but uh or you might say OD align:start position:0% don't worry but uh or you might say OD darn but uh but the plan in the in the align:start position:0% darn but uh but the plan in the in the align:start position:0% darn but uh but the plan in the in the ordering of the lectures is to do labor align:start position:0% ordering of the lectures is to do labor align:start position:0% ordering of the lectures is to do labor uh and wage you know wage variation and align:start position:0% uh and wage you know wage variation and align:start position:0% uh and wage you know wage variation and smoothing adding labor Supply to a align:start position:0% smoothing adding labor Supply to a align:start position:0% smoothing adding labor Supply to a consumption model and talk about align:start position:0% consumption model and talk about align:start position:0% consumption model and talk about elasticities and align:start position:0% elasticities and align:start position:0% elasticities and sensitivities that will be done with align:start position:0% sensitivities that will be done with align:start position:0% sensitivities that will be done with both the full risk sharing model as well align:start position:0% both the full risk sharing model as well align:start position:0% both the full risk sharing model as well as a version of these incomplete Market align:start position:0% as a version of these incomplete Market align:start position:0% as a version of these incomplete Market models so we'll see what survives you align:start position:0% models so we'll see what survives you align:start position:0% models so we'll see what survives you know depending on what you assume about align:start position:0% know depending on what you assume about align:start position:0% know depending on what you assume about the market structure and then we're align:start position:0% the market structure and then we're align:start position:0% the market structure and then we're going to go align:start position:0% going to go align:start position:0% going to go to have a whole lecture on you know align:start position:0% to have a whole lecture on you know align:start position:0% to have a whole lecture on you know models that are much more explicit about align:start position:0% models that are much more explicit about align:start position:0% models that are much more explicit about moral hazard you know unobserved align:start position:0% moral hazard you know unobserved align:start position:0% moral hazard you know unobserved income and so on uh and this provon align:start position:0% income and so on uh and this provon align:start position:0% income and so on uh and this provon paper is one of them in that literature align:start position:0% paper is one of them in that literature align:start position:0% paper is one of them in that literature we're not going to cover it in class align:start position:0% we're not going to cover it in class align:start position:0% we're not going to cover it in class but okay align:start position:0% align:start position:0% so so align:start position:0% align:start position:0% actually so the front part of the align:start position:0% actually so the front part of the align:start position:0% actually so the front part of the lecture was out was about this BPP was align:start position:0% lecture was out was about this BPP was align:start position:0% lecture was out was about this BPP was probably a bit mysterious what it was uh align:start position:0% probably a bit mysterious what it was uh align:start position:0% probably a bit mysterious what it was uh so we can review that for a align:start position:0% so we can review that for a align:start position:0% so we can review that for a second align:start position:0% second align:start position:0% second uh the idea is that you postulate align:start position:0% uh the idea is that you postulate align:start position:0% uh the idea is that you postulate that um that log of align:start position:0% align:start position:0% earnings takes on this align:start position:0% earnings takes on this align:start position:0% earnings takes on this process where X is a vector of shot a is align:start position:0% process where X is a vector of shot a is align:start position:0% process where X is a vector of shot a is some Vector of align:start position:0% some Vector of align:start position:0% some Vector of coefficients uh the shocks are align:start position:0% coefficients uh the shocks are align:start position:0% coefficients uh the shocks are IID the X's align:start position:0% IID the X's align:start position:0% IID the X's are and they have you know align:start position:0% are and they have you know align:start position:0% are and they have you know variances uh you know this align:start position:0% variances uh you know this align:start position:0% variances uh you know this allows whole bunches of stuff not only align:start position:0% allows whole bunches of stuff not only align:start position:0% allows whole bunches of stuff not only just random walks but align:start position:0% just random walks but align:start position:0% just random walks but uh autor regressive integrated moving align:start position:0% uh autor regressive integrated moving align:start position:0% uh autor regressive integrated moving average uh uh processes on on income align:start position:0% average uh uh processes on on income align:start position:0% average uh uh processes on on income this is what you align:start position:0% this is what you align:start position:0% this is what you see uh and then you know this General align:start position:0% see uh and then you know this General align:start position:0% see uh and then you know this General formulation allows a bunch of align:start position:0% formulation allows a bunch of align:start position:0% formulation allows a bunch of uh different specifications which align:start position:0% uh different specifications which align:start position:0% uh different specifications which they're going to try to align:start position:0% they're going to try to align:start position:0% they're going to try to estimate align:start position:0% estimate align:start position:0% estimate [Music] align:start position:0% align:start position:0% um and and and somehow what they want to align:start position:0% um and and and somehow what they want to align:start position:0% um and and and somehow what they want to back align:start position:0% back align:start position:0% back out is this insurance coefficient so align:start position:0% out is this insurance coefficient so align:start position:0% out is this insurance coefficient so here's you know again how it's easy to align:start position:0% here's you know again how it's easy to align:start position:0% here's you know again how it's easy to get turned around this is how sort of align:start position:0% get turned around this is how sort of align:start position:0% get turned around this is how sort of like quote unquote a regression align:start position:0% like quote unquote a regression align:start position:0% like quote unquote a regression coefficient of how consumption is moving align:start position:0% coefficient of how consumption is moving align:start position:0% coefficient of how consumption is moving with this particular align:start position:0% with this particular align:start position:0% with this particular shock inferred align:start position:0% shock inferred align:start position:0% shock inferred somehow but one minus that is then the align:start position:0% somehow but one minus that is then the align:start position:0% somehow but one minus that is then the degree of align:start position:0% degree of align:start position:0% degree of insurance because when consumption align:start position:0% insurance because when consumption align:start position:0% insurance because when consumption doesn't move with that shock this is align:start position:0% doesn't move with that shock this is align:start position:0% doesn't move with that shock this is zero and so insurance is like perfect align:start position:0% zero and so insurance is like perfect align:start position:0% zero and so insurance is like perfect measured at align:start position:0% measured at align:start position:0% measured at one align:start position:0% align:start position:0% and you could put te's on these things align:start position:0% and you could put te's on these things align:start position:0% and you could put te's on these things if you sort the align:start position:0% if you sort the align:start position:0% if you sort the data by align:start position:0% data by align:start position:0% data by age which came up align:start position:0% align:start position:0% earlier so we don't really see all align:start position:0% earlier so we don't really see all align:start position:0% earlier so we don't really see all those align:start position:0% those align:start position:0% those uh you know know permanent versus align:start position:0% uh you know know permanent versus align:start position:0% uh you know know permanent versus transitory align:start position:0% transitory align:start position:0% transitory shocks uh we kind of have to infer them align:start position:0% shocks uh we kind of have to infer them align:start position:0% shocks uh we kind of have to infer them [Music] align:start position:0% [Music] align:start position:0% [Music] somehow align:start position:0% somehow align:start position:0% somehow uh and this is a bit align:start position:0% uh and this is a bit align:start position:0% uh and this is a bit like align:start position:0% align:start position:0% um you know using align:start position:0% um you know using align:start position:0% um you know using some assumed function on the income align:start position:0% some assumed function on the income align:start position:0% some assumed function on the income process uh align:start position:0% process uh align:start position:0% process uh um and then filtering the data through align:start position:0% um and then filtering the data through align:start position:0% um and then filtering the data through that function and looking at the align:start position:0% that function and looking at the align:start position:0% that function and looking at the covariance with with income align:start position:0% align:start position:0% change but they don't just do three align:start position:0% change but they don't just do three align:start position:0% change but they don't just do three alone because this would align:start position:0% alone because this would align:start position:0% alone because this would be uh you know a statement about income align:start position:0% be uh you know a statement about income align:start position:0% be uh you know a statement about income alone they they jointly align:start position:0% alone they they jointly align:start position:0% alone they they jointly estimate this function G align:start position:0% estimate this function G align:start position:0% estimate this function G essentially jointly with consumption align:start position:0% align:start position:0% so for align:start position:0% so for align:start position:0% so for example uh if you assume align:start position:0% example uh if you assume align:start position:0% example uh if you assume income took on this classic form that align:start position:0% income took on this classic form that align:start position:0% income took on this classic form that that we were actually tracking through align:start position:0% that we were actually tracking through align:start position:0% that we were actually tracking through the lectures then income would be the align:start position:0% the lectures then income would be the align:start position:0% the lectures then income would be the sum of align:start position:0% sum of align:start position:0% sum of a a random walk with its own Innovation align:start position:0% a a random walk with its own Innovation align:start position:0% a a random walk with its own Innovation and variance and Epsilon which would be align:start position:0% and variance and Epsilon which would be align:start position:0% and variance and Epsilon which would be this IID transitory align:start position:0% this IID transitory align:start position:0% this IID transitory shock uh if you believe this to be the align:start position:0% shock uh if you believe this to be the align:start position:0% shock uh if you believe this to be the structure and there are many many other align:start position:0% structure and there are many many other align:start position:0% structure and there are many many other candidates Ates then you take a first align:start position:0% candidates Ates then you take a first align:start position:0% candidates Ates then you take a first difference and uh you know by align:start position:0% difference and uh you know by align:start position:0% difference and uh you know by construction then what would be left align:start position:0% construction then what would be left align:start position:0% construction then what would be left would be this innovation in align:start position:0% would be this innovation in align:start position:0% would be this innovation in the in the permanent align:start position:0% the in the permanent align:start position:0% the in the permanent part and a time difference in the align:start position:0% part and a time difference in the align:start position:0% part and a time difference in the transitory part which is still align:start position:0% transitory part which is still align:start position:0% transitory part which is still transitory align:start position:0% transitory align:start position:0% transitory [Music] align:start position:0% [Music] align:start position:0% [Music] um so then the consumption model tells align:start position:0% um so then the consumption model tells align:start position:0% um so then the consumption model tells you align:start position:0% align:start position:0% about align:start position:0% about align:start position:0% about puts align:start position:0% puts align:start position:0% puts restrictions align:start position:0% align:start position:0% um on how you know the change in align:start position:0% um on how you know the change in align:start position:0% um on how you know the change in consumption should align:start position:0% consumption should align:start position:0% consumption should be uh align:start position:0% align:start position:0% responding uh basically taking align:start position:0% responding uh basically taking align:start position:0% responding uh basically taking advantage of of the time delays you know align:start position:0% advantage of of the time delays you know align:start position:0% advantage of of the time delays you know if you go back like two three periods align:start position:0% if you go back like two three periods align:start position:0% if you go back like two three periods there's nothing that happened that far align:start position:0% there's nothing that happened that far align:start position:0% there's nothing that happened that far back that's influencing anything at all align:start position:0% back that's influencing anything at all align:start position:0% back that's influencing anything at all today so those past data kind of become align:start position:0% today so those past data kind of become align:start position:0% today so those past data kind of become like predetermined variables almost as align:start position:0% like predetermined variables almost as align:start position:0% like predetermined variables almost as if they were instruments and so that align:start position:0% if they were instruments and so that align:start position:0% if they were instruments and so that kind of mysterious notation about G on E align:start position:0% kind of mysterious notation about G on E align:start position:0% kind of mysterious notation about G on E on on y that you know this is a version align:start position:0% on on y that you know this is a version align:start position:0% on on y that you know this is a version of align:start position:0% of align:start position:0% of it u postulating a model and then going align:start position:0% it u postulating a model and then going align:start position:0% it u postulating a model and then going back far enough time so you would see align:start position:0% back far enough time so you would see align:start position:0% back far enough time so you would see basically zero align:start position:0% align:start position:0% covariance align:start position:0% align:start position:0% so here it is actually this G is just align:start position:0% so here it is actually this G is just align:start position:0% so here it is actually this G is just basically the uh the time difference in align:start position:0% basically the uh the time difference in align:start position:0% basically the uh the time difference in income uh at t + align:start position:0% income uh at t + align:start position:0% income uh at t + one uh and given the other assumptions align:start position:0% one uh and given the other assumptions align:start position:0% one uh and given the other assumptions they align:start position:0% they align:start position:0% they make uh you back align:start position:0% make uh you back align:start position:0% make uh you back out the key some of the key things that align:start position:0% out the key some of the key things that align:start position:0% out the key some of the key things that you want for example how on Earth are we align:start position:0% you want for example how on Earth are we align:start position:0% you want for example how on Earth are we going to know about the variance of the align:start position:0% going to know about the variance of the align:start position:0% going to know about the variance of the transitory shocks if we never see align:start position:0% transitory shocks if we never see align:start position:0% transitory shocks if we never see transitory align:start position:0% transitory align:start position:0% transitory shocks well align:start position:0% shocks well align:start position:0% shocks well basically that turns out to be the align:start position:0% basically that turns out to be the align:start position:0% basically that turns out to be the co-variance of two things we do see the align:start position:0% co-variance of two things we do see the align:start position:0% co-variance of two things we do see the time difference of consumption at income align:start position:0% time difference of consumption at income align:start position:0% time difference of consumption at income at T and the time difference of income align:start position:0% at T and the time difference of income align:start position:0% at T and the time difference of income at t+ align:start position:0% at t+ align:start position:0% at t+ one hopefully you're seeing the spirit align:start position:0% one hopefully you're seeing the spirit align:start position:0% one hopefully you're seeing the spirit of this if not following every line of align:start position:0% of this if not following every line of align:start position:0% of this if not following every line of the algebra align:start position:0% the algebra align:start position:0% the algebra so that's where we get that align:start position:0% so that's where we get that align:start position:0% so that's where we get that object and uh and how would you get the align:start position:0% object and uh and how would you get the align:start position:0% object and uh and how would you get the variance of the permanent income part align:start position:0% variance of the permanent income part align:start position:0% variance of the permanent income part The Innovation to permanent income well align:start position:0% The Innovation to permanent income well align:start position:0% The Innovation to permanent income well remember that thing is persisting over align:start position:0% remember that thing is persisting over align:start position:0% remember that thing is persisting over time so it's a bit more align:start position:0% time so it's a bit more align:start position:0% time so it's a bit more complicated um it turns out to be align:start position:0% complicated um it turns out to be align:start position:0% complicated um it turns out to be this uh daunting object which is the and align:start position:0% this uh daunting object which is the and align:start position:0% this uh daunting object which is the and everything here you see that's Point align:start position:0% everything here you see that's Point align:start position:0% everything here you see that's Point number one it's the co-variance of the align:start position:0% number one it's the co-variance of the align:start position:0% number one it's the co-variance of the time difference of income at T against align:start position:0% time difference of income at T against align:start position:0% time difference of income at T against the sum of the changes in income at T align:start position:0% the sum of the changes in income at T align:start position:0% the sum of the changes in income at T minus one t and t + one so there again align:start position:0% minus one t and t + one so there again align:start position:0% minus one t and t + one so there again you see this sort of time structure at align:start position:0% you see this sort of time structure at align:start position:0% you see this sort of time structure at work the spirit of it is you know go align:start position:0% work the spirit of it is you know go align:start position:0% work the spirit of it is you know go back far enough in time so everything is align:start position:0% back far enough in time so everything is align:start position:0% back far enough in time so everything is predetermined align:start position:0% predetermined align:start position:0% predetermined um and this is the co-variance of cons align:start position:0% um and this is the co-variance of cons align:start position:0% um and this is the co-variance of cons consumption with that permanent shock so align:start position:0% consumption with that permanent shock so align:start position:0% consumption with that permanent shock so this this is a key object remember that align:start position:0% this this is a key object remember that align:start position:0% this this is a key object remember that insurance formula is how much is align:start position:0% insurance formula is how much is align:start position:0% insurance formula is how much is consumption moving when you with the align:start position:0% consumption moving when you with the align:start position:0% consumption moving when you with the Innovation to permanent income it all align:start position:0% Innovation to permanent income it all align:start position:0% Innovation to permanent income it all seemed quite mysterious but here is a align:start position:0% seemed quite mysterious but here is a align:start position:0% seemed quite mysterious but here is a you know an explicit formula for how align:start position:0% you know an explicit formula for how align:start position:0% you know an explicit formula for how they get align:start position:0% they get align:start position:0% they get it so clearly it's a linear align:start position:0% it so clearly it's a linear align:start position:0% it so clearly it's a linear model you know using a lot of these align:start position:0% model you know using a lot of these align:start position:0% model you know using a lot of these variance covariance formulas given the align:start position:0% variance covariance formulas given the align:start position:0% variance covariance formulas given the the assume align:start position:0% the assume align:start position:0% the assume structure uh they don't have to their align:start position:0% structure uh they don't have to their align:start position:0% structure uh they don't have to their starting point could have been something align:start position:0% starting point could have been something align:start position:0% starting point could have been something else uh as I said you have these ARA align:start position:0% else uh as I said you have these ARA align:start position:0% else uh as I said you have these ARA processes but it is some structure when align:start position:0% processes but it is some structure when align:start position:0% processes but it is some structure when you align:start position:0% you align:start position:0% you specify the order of the moving average align:start position:0% specify the order of the moving average align:start position:0% specify the order of the moving average part and the Order of the auto align:start position:0% part and the Order of the auto align:start position:0% part and the Order of the auto regressive part you know you get align:start position:0% regressive part you know you get align:start position:0% regressive part you know you get restrictions on the align:start position:0% restrictions on the align:start position:0% restrictions on the data align:start position:0% data align:start position:0% data um align:start position:0% um align:start position:0% um so hopefully that helps resolve some of align:start position:0% so hopefully that helps resolve some of align:start position:0% so hopefully that helps resolve some of the mysteries about what this align:start position:0% the mysteries about what this align:start position:0% the mysteries about what this BPP algorithm and what they do to the align:start position:0% BPP algorithm and what they do to the align:start position:0% BPP algorithm and what they do to the data to measure these insurance against align:start position:0% data to measure these insurance against align:start position:0% data to measure these insurance against against idiosyncratic and permanent align:start position:0% against idiosyncratic and permanent align:start position:0% against idiosyncratic and permanent shocks okay so I'm going to leave for align:start position:0% shocks okay so I'm going to leave for align:start position:0% shocks okay so I'm going to leave for wit to do the align:start position:0% wit to do the align:start position:0% wit to do the uh version of align:start position:0% uh version of align:start position:0% uh version of smoothing B in the Italian data but I I align:start position:0% smoothing B in the Italian data but I I align:start position:0% smoothing B in the Italian data but I I will just say by way of motivation it's align:start position:0% will just say by way of motivation it's align:start position:0% will just say by way of motivation it's again looking at you know various models align:start position:0% again looking at you know various models align:start position:0% again looking at you know various models although they're not exactly nested and align:start position:0% although they're not exactly nested and align:start position:0% although they're not exactly nested and looking at the response es of of align:start position:0% looking at the response es of of align:start position:0% looking at the response es of of consumption to align:start position:0% consumption to align:start position:0% consumption to Innovations but also of wealth to in align:start position:0% Innovations but also of wealth to in align:start position:0% Innovations but also of wealth to in Innovations so we saw in my data you align:start position:0% Innovations so we saw in my data you align:start position:0% Innovations so we saw in my data you know sort of how wealth and various align:start position:0% know sort of how wealth and various align:start position:0% know sort of how wealth and various lectures is moving around in the align:start position:0% lectures is moving around in the align:start position:0% lectures is moving around in the cross-section and moving around over align:start position:0% cross-section and moving around over align:start position:0% cross-section and moving around over time we talked about responses to shocks align:start position:0% time we talked about responses to shocks align:start position:0% time we talked about responses to shocks and you know whether they're using align:start position:0% and you know whether they're using align:start position:0% and you know whether they're using savings accounts and so on so these guys align:start position:0% savings accounts and so on so these guys align:start position:0% savings accounts and so on so these guys in their own way are doing something align:start position:0% in their own way are doing something align:start position:0% in their own way are doing something similar and uh and the paper backs out align:start position:0% similar and uh and the paper backs out align:start position:0% similar and uh and the paper backs out the movements in consumption and wealth align:start position:0% the movements in consumption and wealth align:start position:0% the movements in consumption and wealth that are predicted from certain kinds of align:start position:0% that are predicted from certain kinds of align:start position:0% that are predicted from certain kinds of Innovations but not just between you align:start position:0% Innovations but not just between you align:start position:0% Innovations but not just between you know this year and next year but this align:start position:0% know this year and next year but this align:start position:0% know this year and next year but this year and two years from now all the way align:start position:0% year and two years from now all the way align:start position:0% year and two years from now all the way up to six years or even longer so you align:start position:0% up to six years or even longer so you align:start position:0% up to six years or even longer so you kind of get you know the sort of time align:start position:0% kind of get you know the sort of time align:start position:0% kind of get you know the sort of time profiles of align:start position:0% profiles of align:start position:0% profiles of responsiveness and uh you know very much align:start position:0% responsiveness and uh you know very much align:start position:0% responsiveness and uh you know very much in the spirit of what we're talking align:start position:0% in the spirit of what we're talking align:start position:0% in the spirit of what we're talking about today but yet again a bit align:start position:0% about today but yet again a bit align:start position:0% about today but yet again a bit different those respons patterns are align:start position:0% different those respons patterns are align:start position:0% different those respons patterns are very different depending on whether align:start position:0% very different depending on whether align:start position:0% very different depending on whether you're talking about the permanent align:start position:0% you're talking about the permanent align:start position:0% you're talking about the permanent income model or you know the life cycle align:start position:0% income model or you know the life cycle align:start position:0% income model or you know the life cycle buffer stock type align:start position:0% buffer stock type align:start position:0% buffer stock type model so okay that's all for align:start position:0% align:start position:0% today