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**A**: Whereas confidence bands in the low-dimensional case are mostly built using kernel methods, the estimators for high-dimensional sparse additive models typically rely on sieve estimators based on dictionaries. To derive their results, Lu et al. (2020) combine both kernel and sieve methods to draw upon the advantages of each, resulting in a kernel-sieve hybrid estimator**B**: This is a two-step estimator with tuning parameters for kernel estimation and sieves estimation, such as the bandwidth and penalization levels, which must be chosen by cross-validation. Because of the local structure of the hybrid estimator, the framework of Lu et al. (2020) differs from ours in that they consider an additive local approximation model with sparsity (ATLAS), in which they need to impose a local sparsity structure.**C**: A procedure explicitly addressing the construction of uniformly valid confidence bands for the components in high-dimensional additive models has been developed by Lu et al. (2020). The authors emphasize that achieving uniformly valid inference in these models is challenging due to the difficulty of directly generalizing the ideas from the fixed-dimensional case
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Selection 2
**A**: For this paper we focus on \chCO2 emissions as the main output of an ensemble of coupled climate-economy-energy models. Each model-scenario produces a vector of \chCO2 emissions defined from the year 2010 to 2090 at 10-years time intervals**B**: This was one of the first paper to apply global sensitivity techniques to an ensemble of climate economy models, thus addressing both parametric and model uncertainty. We use the scenarios developed in [17] which involve five models (IMAGE, IMACLIM, MESSAGE-GLOBIOM, TIAM-UCL and WITCH-GLOBIOM) that provide output data until the end of the interval T𝑇Titalic_T. **C**: This discretization of the output space is in any case arbitrary, since \chCO2 emissions do exist in every time instant in the interval T=[2010,2090]𝑇20102090T=[2010,2090]italic_T = [ 2010 , 2090 ]. A thorough description of the dataset used as a testbed for the application of the methods described before can be found in [17]
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Selection 4
**A**: The theorem is best understood as a corollary of a welfare bound regardless of whether there is learning**B**: We now return to the general characterization of adequate learning, Theorem 1, to explain how it is derived**C**: Stating that result requires some notation. Abusing notation, let
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Selection 4
**A**: Figure 3 illustrates these for experimental papers published in “top-5” economics journals, plotting the share that conduct at least one MHT adjustment (defined here as either control of a compound error rate or indexing) in the left-hand panel, and the distribution of adjustment types (not mutually exclusive) in the right-hand panel**B**: A little over a decade ago not a single paper used any adjustment, while by 2020 we were drawing near to an even split between those that did and those that did not. The methods used also vary a great deal, with control of the FWER most common, followed by indexing, and then by control of the FDR. These figures suggest—consistent with our personal experiences as authors and as referees—that there is no clear consensus at the moment on whether and how authors should be asked to perform MHT adjustments.**C**: MHT norms are also a salient issue within applied economics, given recent publication trends
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Selection 1
**A**: The IA rule is exactly the so-called Boston mechanism. It is well-known that such mechanism is not strategy-proof. **B**: Sönmez (2003)**C**: defined in Example 1 below satisfies truncation-invariance but violates strategy-proofness.111111From the procedure of the immediate acceptance algorithm, one can easily obtain that the IA rule satisfies truncation-invariance
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Selection 3
**A**: More broadly, this paper contributes to the literature on fixed-T𝑇Titalic_T identification and estimation in nonlinear panel models with fixed effects (see Honoré 2002, Arellano 2003, and Arellano and Bonhomme 2011 for overviews)**B**: For example, the static panel ordered logit model with fixed effects was studied by Das and van Soest (1999), Johnson (2004b), Baetschmann, Staub, and Winkelmann (2015), and Muris (2017); results for static and dynamic binomial and multinomial choice models are in Chamberlain (1980), Honoré and Kyriazidou (2000), Magnac (2000), Shi, Shum, and Song (2018), Aguirregabiria, Gu, and Luo (2021),**C**: The literature contains results for several models adjacent to ours
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Selection 1
**A**: In words, after some pre-processing (Step 1 and 2), we propose estimating a nonlinear model in both directions, i.e**B**: Algorithm 1 shows detailed steps of the implementation of the test**C**: with Y𝑌Yitalic_Y and X𝑋Xitalic_X as dependent variables respectively (Step 3), calculating residuals for both models (Step 4) and testing for conditional independence using a kernel conditional independence test (KCI) introduced by \textcitezhang11conditional (Step 5). We discuss this test statistic, see eq. (7), and its development in Section 2.5; see the detailed discussion in Section 2.6.
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Selection 4
**A**: The dashed lines are those of the economy that does not experience the increase in land supply (Economy 2)**B**: One period is equivalent to 25 years; that is, four periods are equivalent to one century**C**: I normalize the initial values of per capita income, per capita intermediate inputs for agriculture, and population to be unity.
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Selection 3
**A**: We incorporate this phenomenon into our structural model, by placing strategies on an evolutionary spectrum from reactionary to predictive. When playing a purely reactive strategy under bounded rationality, simultaneous play may not converge to a stage-game equilibrium (Alós-Ferrer and Netzer, 2010; Hommes and Ochea, 2012).**B**: Finally, in the exogenous/fixed network case, Boosey (2017) uses data from a laboratory experiment to examine the mechanisms for cooperation in a repeated network public goods game**C**: Experimental results showed a significant portion of subjects playing strategies of conditional cooperation, in which subjects play strategies which react strongly to the behavior of their neighbors in previous rounds
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Selection 4
**A**: The rest of the paper is organized as follows. After a brief introduction of the basic notations and preliminaries of tensor analysis in Section 1.1, we introduce a tensor factor model with CP low-rank structure in Section 2**B**: Section 5 develops some alternative algorithms to tensor factor models, which extend existing popular CP methods to the auto-covariance tensors with cPCA as initialization, and provides some simulation studies to demonstrate the numerical performance of all the estimation procedures. Section 6 illustrates the model and its interpretations in real data applications. Section 7 provides a short concluding remark. All technical details and more simulation results are relegated to the supplementary materials.**C**: The estimation procedures of the factors and the loading vectors are presented in Section 3. Section 4 investigates the theoretical properties of the proposed methods
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Selection 4
**A**: In Section 4, we take the perspective of a privacy-conscious designer who wants to implement a choice rule through a maximally contextually private protocol**B**: First, maximally contextually private protocols involve a deliberate decision about the protection set, i.e. a set of agents whose privacy ought to be protected if possible. Second, given that protection set, maximally contextually private protocols delay asking questions to protected agents as much as possible.**C**: Our discussion yields two central insights
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Selection 4
**A**: This is a feature of the present paper in this context. The quasi-linear condition is itself a primitive condition for the economy, and thus avoids the above criticisms**B**: On the other hand, this paper provides conditions for the uniqueness of the equilibrium price in an economy where there are L𝐿Litalic_L commodities, n𝑛nitalic_n consumers, and μ𝜇\muitalic_μ producers. Unlike the various conditions discussed above, our conditions are requirements on the utility functions and production sets, not on the excess demand function or the offer curve**C**: Moreover, as mentioned at the end of section 2, the quasi-linear condition is independent of gross substitution. Therefore, as far as we can assess, the theorem in this paper is a good enough result in this context.
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Selection 2
**A**: In the latter case, the sum of the even-numbered terms must diverge to −∞-\infty- ∞ (as the sum of all terms is convergent), and therefore cannot diverge to ∞\infty∞**B**: Thus player B is chosen on this step with probability 00, finishing the proof. ∎**C**: Almost surely either a player was chosen on Step 1 or 2 or the sum of just the odd-numbered terms (given by B’s moves) of expression (2) diverges to ∞\infty∞, by Lemma 3.6
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Selection 1
**A**: Therefore, an additional assumption is needed for the continuity result we desire. Namely, the range of the function in the limit must also be sufficiently wide**B**: For a unique derivation of the utility function, however, the range of the demand function must be sufficiently wide, as discussed above. We have found an example of a sequence of demand functions that satisfy all the assumptions of Corollary 3 and have a sufficiently wide range, yet the range in the limit is very small (Example 2)**C**: In addition, when all functions satisfy the “C axiom” introduced by Hosoya (2017, 2020), then the desired continuity proposition can be obtained (Theorem 2). That is, when a sequence of demand functions converges to a demand function with respect to the topology discussed above, then the corresponding sequence of utility functions also converges to the corresponding utility function uniformly on any compact set consisting of strictly positive consumption vectors.
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Selection 3
**A**: Hence, the Lorenz dominance order we propose is an implementable inequality dominance criterion. Using recent advances on the asymptotic properties of multivariate quantiles, surveyed in Hallin (2022), our Lorenz dominance criterion can be the basis for inequality dominance testing that accounts for sampling uncertainty. This contrasts our proposal with the growing literature on multivariate inequality dominance criteria proposed for finite populations. See for instance Gravel and Moyes (2012), Banerjee (2016), Faure and Gravel (2021) and references within.**B**: It also shares the desirable properties of the Lorenz curve and dominance ordering. Like the Lorenz zonoid of Koshevoy and Mosler (1996, 1999), it characterizes the distribution of an allocation (see section 1.4.1 for a definition and discussion). Unlike the Lorenz zonoid, the vector Lorenz map we propose can be efficiently computed as an unconstrained convex optimization problem and connected to recent developments in computational optimal transport theory333An account of recent advances is given in Peyré and Cuturi (2018).**C**: The vector Lorenz map we propose, therefore, is the vector of shares of each resource held by individuals below a given rank. The associated Lorenz inequality dominance criterion deems a multivariate allocation more equal if this share of resources is larger for each rank. Hence, our proposal shares the interpretation of the traditional Lorenz curve and Lorenz dominance
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Selection 4
**A**: This assumption essentially states that agents with the same raw covariates and cost function for covariate modification, on average, have the same potential outcomes upon being accepted or rejected**B**: This is plausible in the context of college admissions if space of raw features and cost functions is rich**C**: In addition, we also require that the conditional mean outcome is continuous with respect to the raw covariates and cost function for covariate modification.
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Selection 4
**A**: These papers are designed as methods for inference for parameters defined via linear models or estimating equations rather than parameters like our equally-weighted or size-weighed cluster-level average treatment effects that are defined explicitly in terms of potential outcomes. Importantly, in almost all of these papers, the sampling framework treats cluster sizes as non-random, though we note that in some cases the results are rich enough to permit the distribution of the data to vary across clusters: further discussion is provided in Remark 2.2. Finally, none of these papers seem to explicitly consider the additional complications stemming from sampling only a subset of the units within each cluster.**B**: Miller (2015) and MacKinnon et al**C**: (2023)
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Selection 1
**A**: Under the assumptions of the newsvendor model, the cost-optimal inventory level can be derived by the ratio between costs for excess inventory and costs for excess demand. In their review, Qin et al., (2011) give suggestions for future research based on the newsvendor model, such as the integration of stochastic supply and demand in the same model as well as the introduction of (stochastic) lead times and multi-period models.**B**: While most inventory management models consider the case of backordering, especially in the practice of grocery retailing the assumption of lost sales is more realistic, leading to models that are in general more difficult to solve (see Bijvank and Vis,, 2011 for a review on inventory models with lost sales)**C**: In case of stochastic customer demand, two situations can arise at the end of a demand period: (1) demand exceeds the inventory level leading to either lost sales or backordering of orders and (2) excess inventory
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Selection 1
**A**: We examine how well these tests are able to detect p𝑝pitalic_p-hacking in practice**B**: To do this, we examine four situations where we might expect researchers to p𝑝pitalic_p-hack: searching over control variables in linear regressions, searching over available instruments in IV regressions, selecting amongst datasets, and selecting bandwidth in variance estimation**C**: In a stylized version of each of these, we show how p𝑝pitalic_p-hacking affects the distribution of p𝑝pitalic_p-values under the alternative, which tells us which types of tests might have power. These results motivate Monte Carlo experiments in more general settings.
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Selection 2
**A**: Sarkodie et al., (2020) find that increasing human capital positively affects environmental degradation in China, whereas Pata and Caglar, (2021) find an opposite result. Hassan et al., (2019) find insignificant effects of human capital on the ecological footprint in Pakistan.**B**: (Pata and Caglar, , 2021). Poudel et al., (2009) find that the illiteracy rate, defined as the percentage of the population aged 15 years who are not able to read, is negatively correlated with carbon emissions**C**: A human capital index as a proxy for the environmental quality demand. A society with a high human capital level is likely to be more aware of the negative consequences of environmental degradation and, thus, would demand environmental quality in the form of regulations, carbon taxes, environmentally friendly technologies, etc
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Selection 4
**A**: In our first exercise, we exclude California (the true treated state)**B**: Instead, we assume that one other state from the control group (the “pseudo-treated” state) has been treated with a cigarette sales tax in 1989**C**: We mask the post-1988 cigarette sales of the pseudo-treated state and apply each of the alternative causal inference methods. For each method, we assess the prediction error for the (actually untreated) outcome in the pseudo-treated state in the post-treatment period. This exercise will yield a valid assessment of the prediction errors for California in 1989 to the extent that, for each method we consider, the 1989 prediction error for California is drawn from the same distribution as the 1989 prediction error for the control states.
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Selection 1
**A**: The green-shaded region indicates the treatment block in the switchback experiment, while the blue-shaded region indicates the control block in the switchback experiment.**B**: Figure 4: A sample trajectory of aggregated profit from the ride-sharing simulator under a fixed environment**C**: The red solid curve represents the profit observed in a switchback experiment, while the green and blue curves represent the profit observed in counterfactual scenarios where the treatment assignment is fixed to always treated and always in control, respectively
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Selection 3
**A**: During recessions with low unemployment, there is a negative impact response for both government spending and GDP, which becomes insignificant after a few periods. In the high unemployment state, in contrast, we see a large, positive, and persistent effect on both variables.**B**: The impulse responses out of recessions resemble the state-dependent model of Figure 4, both in shape and magnitude, but we see a different pattern in the recession state**C**: Figure 5 displays the impulse response functions with four states
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Selection 2
**A**: The anchoring effect refers to “a systematic influence of initially presented numerical values on subsequent judgments of uncertain quantities,” where the judgement is biased toward the anchor (Teovanović (2019))**B**: Given the prevalence of the anchoring effect, one would expect to find an anchoring bias generated by one of the most controversial figures of the economy: the minimum wage.**C**: The anchoring effect has been replicated across a variety of contexts, as I discuss in Sect. 1.1, including with judgements involving money and anchors established by government policy
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Selection 4
**A**: For general extensive-form games, there is a further consideration about what trembles should be considered for future moves beyond the current path of play. Extensive-form trembling hand perfect equilibrium assumes that all players may tremble in future actions, while an alternative concept called quasi-perfect equilibrium (QPE) assumes that only the opposing players tremble for future actions (even if we have trembled previously ourselves) [28]**B**: We can extend Definition 1 to general n𝑛nitalic_n-player extensive-form imperfect-information games by adding analogous constraints for all observed actions (i.e., by requiring that the sum of the probabilities of strategy sequences taken consistent with our observations is nonzero). This is useful because we are no longer required to reason about trembles that are incompatible with the current path of play, which are irrelevant at this point**C**: The related concept of one-sided quasi-perfect equilibrium (OSQPE) assumes that only the opposing players can tremble at all and we cannot [9]. OSQPE is the most computationally efficient and is also the most similar to observable perfect equilibrium.
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Selection 2
**A**: As a result, the receiver learns their private information and makes fully informed decisions. No resources are wasted in the attempt to persuade the receiver. All players obtain the payoff they would get if there were no information asymmetries in the first place. **B**: Importantly, it is the only minimal communication protocol to have these desirable properties. A characterization of the efficient equilibrium is provided, showing the mechanism through which the receiver achieves efficiency: the report delivered by the first speaker sets the burden of proof borne by the second speaker, who has to prove its case “beyond a reasonable doubt.” The endogenously determined burden of proof ensures that both senders consistently report truthfully**C**: The second part of this paper focuses on the last type of minimal arrangement left to analyze: public advocacy, that is, the sequential and public consultation of senders with conflicting interests over decision-making. The main result shows that public advocacy is efficient and robust to collusion
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Selection 3
**A**: There are a total of J=kz⁢2kz−1𝐽subscript𝑘𝑧superscript2subscript𝑘𝑧1J=k_{z}2^{k_{z-1}}italic_J = italic_k start_POSTSUBSCRIPT italic_z end_POSTSUBSCRIPT 2 start_POSTSUPERSCRIPT italic_k start_POSTSUBSCRIPT italic_z - 1 end_POSTSUBSCRIPT end_POSTSUPERSCRIPT transformed instruments**B**: Let 𝒁~~𝒁\widetilde{\boldsymbol{Z}}over~ start_ARG bold_italic_Z end_ARG**C**: when constructing the different FASs
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Selection 2
**A**: We find that under homogeneous probabilities of success, the average expected market value of an approved drug is $1.62 billion**B**: We compare this estimate with discounted sales revenue to verify that it is sensible**C**: The Cortellis Competitive Intelligence database includes information on yearly drug-level total sales for a subset of drugs. The average ten-year and fifteen-year discounted revenues for those drugs are $1.40 and $1.99 billion per drug, respectively, suggesting that our approach is reasonable.
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Selection 1
**A**: Assuming that the priorities are common knowledge is a natural stylized version of real markets such as school choice mechanisms, where the priorities are determined by pre-committed policies which are typically publicly available information for each school**B**: But the number one reason we make this modeling assumption is that it is the most generic way to handle the fact that some knowledge of the priorities must be present before the mechanism is run: we do not consider the institutions to be agents actively participating in the protocol or reporting their priorities, so we treat these priorities as fixed.222222 We also remark that, to keep our model and paper theoretically cohesive, all of the lower bounds in Section 3 and 4 construct a fixed set of priorities where the lower bound holds, so these results also hold for the model where priorities are common knowledge. In contrast, our positive results for the options-effect complexity of 𝖣𝖠𝖣𝖠\mathsf{DA}sansserif_DA in Section 4.2 hold even when the priorities are not known in advance by the applicants.**C**: Moreover, assuming common knowledge of the priorities only makes our lower bounds stronger
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Selection 4
**A**: There is**B**: i𝑖iitalic_i votes at all q′⁢(i)>q⁢(i)superscript𝑞′𝑖𝑞𝑖q^{\prime}(i)>q(i)italic_q start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ( italic_i ) > italic_q ( italic_i ))**C**: As we document in the Appendix, individual behavior in the experiment is mostly monotonic
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Selection 1
**A**: Nonetheless, our modeling of the innovation sector renders the model scale-neutral. As such, its spatial outcomes are driven by the spatial nature of knowledge spillovers (and by its interplay with pecuniary externalities), rather than by implicit assumptions about scale returns in the innovation sector.555For a comprehensive discussion on how these implicit assumptions regarding returns to scale generate mistaken conclusions in geographical economics, we refer the reader to Bond-Smith, (2021).**B**: However, knowledge transfers imperfectly between regions, in accordance with the findings in the seminal work of Audretsch and Feldman, (1996)**C**: We follow the literature of Quantitative Spatial Economics (Redding and Rossi-Hansberg,, 2017; Behrens and Murata,, 2021; Kleinman et al.,, 2023) and purposefully abstract from modeling growth or the explicit use of dynamics in the innovation sector, thus ensuring analytical tractability
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Selection 4
**A**: To better understand the intuition behind Proposition 3 and Proposition 4, recall that the optimality of standard debt contracts in Innes (1990) is due to (i) the risk-neutrality and the limited-liability structure of the problem, and (ii) the monotone likelihood ratio property of the profit distributions. Indeed, for any incentive-compatible and individually-rational contract, risk neutrality allows one to construct a standard debt contract with the same expected payment**B**: This is because when MLRP fails, high profit may sometimes indicate low effort. In this regard, Proposition 4 follows since the optimal contingent debt contract is designed to maximally reward the entrepreneur only when high profit strongly suggests high effort. Moreover, Proposition 3 shows that contingent debt contracts are enough to replicate the expected payments of all other feasible contracts while preserving incentive compatibility. In essence, these propositions separate the effects of risk neutrality and limited liability on security design from the effects of the monotone likelihood ratio property.**C**: Meanwhile, MLRP—which implies that higher profit is always a stronger indication of high effort—ensures that this debt contract—which maximally rewards the entrepreneur in the events when the profit is high—incentivizes the entrepreneur to exert higher effort, thus leading to a higher expected project profit. Without the monotone likelihood ratio assumption, simply replicating an individually-rational contract with a standard debt contract may distort incentives and lead to less efficient effort and suboptimal outcomes
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Selection 4
**A**: The left y-axis margin states the saved relative CO2 emissions by the cumulative removal of firms (brown)**B**: The x-axis of the different panels depicts the firm rank (firms are sorted) according to different criteria: (A) CO2 emissions in descending order, (B) number of employees in ascending order, (C) EW-ESRI in ascending order, and (D) CO2/EW-ESRI in descending order**C**: The y-axis on the right margin shows the expected job (blue) and output (green) loss from the cumulative removal of firms, as measured by the EW-ESRI and the OW-ESRI, respectively.
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Selection 2
**A**: Next, the VRE generation-capacity subsidies are varied**B**: Similarly to the previous subsection, we consider the values of the remaining parameters to be fixed**C**: In particular, we assume the carbon tax to remain at 0 € / MWh, the TEB at €10M while considering the GEB values as defined in Table 2 but excluding the case where both GenCos have €1M GEB, due to the similarities in optimal decisions values with the case in which they have the same budget set to €10M.
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Selection 1
**A**: We also find out that the characterized family can be easily implemented in two steps and with few information. Finally, we establish that all strategy-proof rules are also group strategy-proof and show that Pareto efficiency implies a strong restriction on the range of the strategy-proof rules.**B**: It is relevant to point out that the characterized family generalizes existing results in the literature; in particular, the results in Moulin (1980) and Barberà and Jackson (1994) for only single-peaked and the result in Manjunath (2014) for only single-dipped preferences**C**: We characterize all strategy-proof rules on this new domain
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Selection 1
**A**: The remaining Gaussian shocks are only identified up to a rotation of the Gaussian shocks. Therefore, if there are more than two Gaussian shocks, the first-step estimator cannot provide evidence against restrictions on the impact of the Gaussian shocks**B**: In this case, the second term of the adaptive weights leads to an increase in the weights of the restrictions corresponding to Gaussian shocks. This ensures that only those restrictions where the data actually provide evidence against them receive low weights. **C**: The introduction of the second term, which adjusts the weights based on the Gaussianity of the shocks, is designed to ensure proper weights when multiple shocks are Gaussian. In such cases, the first-step estimator can only identify and consistently estimate the impact of non-Gaussian shocks
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Selection 1
**A**: The pricing policy maps those same variables into an advertised price**B**: In the remainder of this section, we focus on a specific instance of a managed campaign and then show that these pricing and steering policies are revenue optimal for the platform.**C**: In other words, the steering policy steers each consumer to a firm, depending on all firms’ participation decisions, their posted prices, and the consumer’s own value
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Selection 4
**A**: and again label this set of countries as m𝑚mitalic_m**B**: We can calculate how much P can potentially flow through a country i𝑖iitalic_i as **C**: We will now look at all the countries with PR mining101010Countries with less than 1% of global PR production have been excluded from this correction
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Selection 3
**A**: For the one-to-one and many-to-one markets with responsive preferences, Kara and Sönmez (1996, 1997) show that the stable rules are Nash implementable. Ehlers (2004) obtains positive implementation results in one-to-one markets when agents are allowed to have weak preferences**B**: All of the above articles demonstrate the implementability of stable rules using some implementation conditions; e.g. monotonicity Maskin (1999), essential monotonicity Yamato (1992) or the implementability condition of Moore and Repullo (1990). In contrast, we focus on studying a game and identifying the strategies that are Nash equilibria of the game and that allow us to implement**C**: In a many-to-one market with contracts, Haake and Klaus (2009) show that stable rules are Maskin monotonic and implementable
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Selection 1
**A**: This is a 50% drop in total credit limits over the 2010 average reported in Table 1. Finally, in Panel (vii) of Figure 3 we show the impact of a soft default onto intensive margin of mortgages, or the balance on open mortgages, the profile closely mimics that of total credit limit, in fact mortgages are included in that definition, with a fall overtime up to about 60,000USD, that is a lower balance by about 30% of the sample average in 2010**B**: In Panel (vi) of Figure 3 we study the impact of soft default on total credit limit on all accounts, we notice a small (positive), but significant difference in the amounts prior to default of about 10,000USD, however after default the difference becomes more and more negative up to about 80,000USD five to six years after default**C**: Therefore, defaulted consumers have a harder time originating a mortgage, and when they do their balances are about 30% lower, which would be consistent with all the previous findings, of lower income and lower House Value zip codes, it could also be that at origination these individuals would have to come up with a larger down-payment.
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Selection 3
**A**: (2021a) and Flanigan et al. (2021b) study the selection probabilities of optimal solutions for sortition, which is the problem of randomly selecting a panel of representatives from the population to decide on policy questions**B**: The constraints in their model are simply quota stating lower and upper bounds for various subsets of the population (e.g., female, older than 65). While Flanigan et al. (2021a) study the distribution rules that we discuss in Sections 5.1-5.3, and propose a column generation framework for them, Flanigan et al. (2021b) study how to implement these distribution rules as a uniform lottery over a set of m𝑚mitalic_m panels. **C**: We will first discuss two specific problem settings, which are both special cases of the general setting studied in this paper, in which the fair integer programming problem has been studied. First, Flanigan et al
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Selection 3
**A**: However, with the increase of n𝑛nitalic_n we observe the development of ”potential” DK with statistically significant deviations upward from the straight line. This trend terminates with the data points returning to the straight line and then abruptly plunging into nDK territory. **B**: The main result of this paper is that the largest values of RV are in fact nDK**C**: We find that daily returns are the closest to the BS behavior
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Selection 1
**A**: We consider the 10th, 25th, 40th, 50th, 60th, 75th and 90th percentiles of these distributions, all of which lie in the interval [0,3]03[0,3][ 0 , 3 ], and re-normalize the corresponding probabilities**B**: The resulting probability distributions are provided in Table 8 below.**C**: For the present paper, we generated three possible “true” value distributions: uniform on [0,3]03[0,3][ 0 , 3 ], “right-skewed”, and “left-skewed.” The latter two are, respectively, a discretized log-normal (with location parameter 0 and scale parameter 0.70.70.70.7) and its mirror image
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Selection 3
**A**: Importantly, their Theorem 1 also shows that the broader strongly symmetric equilibrium concept does not remedy the inefficiency in a pure good-news environment; thus, in this paper, it is more striking that payoff externalities can restore efficiency within the stronger Markov solution concept. That is, Hörner et al. (2022) show that the inefficiency arising in the good-news environment cannot be removed by broadening the solution concept and dropping the Markov assumption.**B**: A number of papers have extended the original Keller et al. (2005) model; however, this paper specifically focuses on payoff externalities of a different form relative to those in the literature. Theorem 1 of Hörner et al**C**: (2022) shows that when one of two conditions is met, the inefficiency arising in Keller et al. (2005) disappears when weakening the Markov solution concept to strongly symmetric equilibria; either there must be a Brownian drift component to the information process, or the belief jump from a breakthrough at the efficient threshold belief must be lower than the individual belief cutoff
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Selection 3
**A**: 2008; Herrmann and Thöni 2009; Fischbacher and Gächter 2010; Teyssier 2012; Martinsson et al. 2013; Katuščák and Miklánek 2023), while previous studies found no statistical differences in subjects’ responses between the strategy and the direct response method (see Brandts and Charness 2000; Brandts and Charness 2011, or Keser and Kliemt 2021 for a discussion). Figure 2 presents a screenshot from the experimental interface, of what a player in position 3 or 4 could see. In that case, the only information the subject has is that she is positioned in one of the two last positions of the sequence and is asked about her contribution choice, conditional on the potential total contribution of the two immediate players before her (either of players 1 and 2, if she is player 3, or players 2 and 3, if she is player 4) but she cannot distinguish her position. Therefore, the subject does not know whether there is another player following in the sequence. The available options for players at positions 1 and 2 were adapted accordingly. **B**: There are in total three treatments. Treatment 1 (T1subscript𝑇1T_{1}italic_T start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT) was designed to test Hypothesis 1. In that treatment, participants received a sample of past decisions of length equal to two (they would receive information on what the combined contribution of the immediate 2 predecessors was131313In line with the theoretical model, the subject could only observe whether the combined contribution of the two previous players was equal to 0, 10 or 20. That is, by observing a sample of length 2 with total contribution 10, the subject could infer that one of the previous two players defected, but had no way to tell which one.) and also, participants were not informed of their position in the sequence unless they were Player 1 or Player 2141414Subjects at positions 1 and 2 could infer their position, given their observed sample was of length 0 and 1 respectively.. To rigorously test the predictions of the model, we need information on what subjects’ choices are, in all potential samples they can observe (i.e. the combined contribution they observe)**C**: In particular, the model predicts that if a player receives a full contribution sample (i.e. the combined contribution of the two previous players is equal to 20), she will contribute herself, otherwise, if the contribution is 0 or 10, she will defect. We elicit behaviour using the Selten (1967) strategy response method and collect the participants’ choices for each possible scenario. This means participants were asked to make conditional decisions for each possible information set depending on their randomly assigned position in the sequence. While this can be seen as a potential limitation of our design, this elicitation method was necessary to allow us to elicit the full strategy profile of the participants, and therefore, to be able to test the theoretical predictions of the model.151515The strategy method has been extensively used in the framework of public goods games (see Bardsley 2000; Fischbacher et al. 2001; Kocher et al
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Selection 3
**A**: Each investor is matched with an expert who is either a human with fixed or aligned incentives or a robo-advisor, i.e., an appropriately programmed algorithm.222Germann and Merkle (2023), Gaudeul and Giannetti (2023) and Lambrecht et al. (2023) also report experiments where investors can delegate to an algorithm.**B**: (2022) study delegation in a more traditional setting using a subject pool of finance professionals and members of the general public, both drawn from the Swedish population**C**: Holzmeister et al
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Selection 4
**A**: Our other two applications relate to existing work on sensitivity analysis. Our proposed sensitivity analysis for sharp regression discontinuity (RD) applies when data on the running variable fails tests for manipulation (McCrary, 2008; Otsu et al., 2013; Bugni and Canay, 2021)**B**: There is other work in the RD context on partial identification bounds under manipulation (Rosenman et al., 2019; Ishihara and Sawada, 2020) but to our knowledge, our proposal is the first sensitivity analysis for manipulation. There are sensitivity analysis for exclusion failure with instrumental variables (Ramsahai, 2012; Van Kippersluis and Rietveld, 2018; Masten and Poirier, 2021; Freidling and Zhao, 2022), but to our knowledge our proposal is the first sensitivity analysis whose underlying assumptions are invariant to invertible transformations of variables. **C**: Our proposal nests both an exogeneity-type assumption and Gerard et al. (2020)’s bounds as special cases
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Selection 4
**A**: Our main result (Theorem 2) shows that relaxing strategy-proofness to NOM generates an abundance of simple rules. This embarrassment of riches follows from the fact that for each conceivable claims rule, there is a corresponding simple allocation rule. Note, however, that such expansion can be performed without any essential change in the maximality of the domain of preferences involved, which continues to be single-plateaued.**B**: Table 1 summarizes the different characterizations obtained**C**: This paper presents several families of efficient and own-peak-only allocation rules that satisfy the NOM requirement
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**A**: Let g𝑔gitalic_g be a continuous map of a closed interval I𝐼Iitalic_I into itself:**B**: First, we clarify what we mean by a Li-Yorke chaos, a turbulence, and a topological chaos**C**: (There are several definitions of a chaos in the literature.) The following definitions are taken from [Ruette, 2017, Def. 5.1] and [Block and Coppel, 1992, Chap. \@slowromancapii@]
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Selection 1
**A**: For example, as shown in the solid line of figure 1, the top 100 packages account for about 71 percent of all package downloads even though they correspond to about 3 percent of the SSC universe. **B**: Their usage, however, is not uniform**C**: As of April 2024, there were roughly 3,500 packages available in the SSC
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Selection 4
**A**: This result holds true in general for any possible non-cooperative game without making assumptions on cost functions or constraint sets. In order to use this result for numerical computations, one would need to compute the set of Pareto optimal points for multi-objective problems**B**: It is well known that a Nash equilibrium does not need to be Pareto optimal and a Pareto optimal point does not need to be a Nash equilibrium (when considering the corresponding naïve Pareto optimization problem, see e.g. [6] for details). However, in [6], it was shown that the set of Nash equilibria can be equivalently characterized by the set of Pareto optimal points of a specific vector optimization problem with a non-convex ordering cone, or equivalently, by the intersection of the Pareto optimal points of N𝑁Nitalic_N specific multi-objective problems**C**: So far, algorithms that provide the set of Pareto optimal points exist only for the special case of linear multi-objective optimization, see e.g. [1, 25, 24]. This restricts computational methods of finding the set of Nash equilibria via that characterization to linear games so far.
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Selection 4
**A**: The key problem here is one of trust and transparency. Can we give users the tools such that they can perform analysis that reflects real-world data-generating processes? Can we also make sure they understand the model well enough to work well in collaboration with it, that is to weight its evidence correctly and not underweight (mistrust) or overweight (naively trust) its findings just because it is an inscrutable black box?**B**: This need means we need to see these tools through more of a management theory lens, looking at how to get the best possible information to decision-makers for a given model**C**: When trying to build a theory of transparency then, the philosophical basis of the critical predictive literature which focuses on questions of power, ethics and information asymmetries between the user and the subjects of algorithms misses usability — the role of transparency in explaining causal effects to help inform decisions
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Selection 3
**A**: In each metric, the first column represents the bias in comparison to the true global treatment effect (GTE)**B**: The second column displays the standard deviation calculated from the results of the 100 A/B tests. Lastly, the third column showcases the standard error estimates obtained through two-sample t-tests in a single A/B test i.e.,**C**: We further provide information on the bias and standard errors of treatment effect estimators obtained using various methods in Table 1
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Selection 1
**A**: Probabilistic notions such as common p𝑝pitalic_p belief remain an important tool for analyzing these and other settings. As we have demonstrated, extending such concepts using similar ideas to those that we develop in this paper for common knowledge seems promising as well, and future work might look to explore such extensions in greater depth and detail. **B**: We do not view this as a shortcoming: Indeed, since unreliable deliveries are known not only to lose us the ability to harness common knowledge, but also to cause consequences of common knowledge to formally fail, any epistemic notion that nevertheless holds in such situations certainly should not be called common knowledge**C**: While our definition of common knowledge overcomes timing frictions, it does not aid with attaining common knowledge in settings with probabilistically successful deliveries (as in Rubinstein, 1989, and as in the case of the “defective” deliveries of Steiner and Stewart, 2011)
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Selection 4
**A**: The estimation step needs to account for two sources of errors, that is, the usaul estimation error in obtaining a consistent estimator that corresponds to the IVX instrumentation of the nearly integrated regressors, and the second source of error is the sampling error in generating the forecast for the VaR from the first stage of the process**B**: More specifically, this implies that using a Bahadur representation of the QR-IVX estimator we need to determine the precise stochastic order of the remainder term when the generated regressor is included in the conditional quantile specification of the model**C**: Although when the parameter vector from the first stage is obtained via the IVX filtration, it has the usual convergence rate that the IVX estimator has, an estimation error carries in the second-stage estimation procedure, which requires us to consider a suitable correction to the overall variance due to the presence of the generated regressor.
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Selection 2
**A**: Before we describe FETWFE, we discuss sparse fusion penalties in linear regression, which play a key role in our estimator. **B**: We propose the fused extended two-way fixed effects (FETWFE) estimator, a novel machine learning method for difference-in-differences estimation**C**: The first goal of this paper is to propose a novel estimator that imposes these restrictions in an automatic, data-driven way
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Selection 4
**A**: These results are not obvious owing to the incidental parameters problem.**B**: Further, the system maximum likelihood estimator achieves the efficiency bound**C**: The preceding corollaries imply that, under normality, we are able to establish the asymptotic efficiency bound in the presence of increasing number of nuisance parameters
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Selection 3
**A**: In Section 3 we fit HP and HPI with mGB and GB 2, as well as the fit tails directly using LF. For each test we conduct a U-test, for which a null hypothesis is formulated, and plot p-values which reflect on the goodness of fit, as well as whether DK or nDK behavior may be present. We conclude in Section 4 with discussion of our results. **B**: In Section 2 we present the analytical form of mGB and GB2 distributions and discuss the limiting behaviors of both**C**: This paper is organized as follows
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Selection 3
**A**: Finally, questions about temporal aggregation also arise in event study and other panel data models, suggesting further avenues for fruitful research. **B**: We could also explore choosing an optimal level of temporal aggregation for a single SCM objective**C**: There are many directions for future work that incorporate recent innovations in panel data methods, including first de-noising (e.g., Amjad, Shah and Shen, 2018) or seasonally adjusting the disaggregated outcome series
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Selection 3
**A**: In particular, note that the inequality in the first line of (2.11) becomes an equality precisely in the ‘least favorable’ case discussed therein**B**: This paper further develops the minimax rearrangement displayed in (2.9) and provides asymptotic characterizations of a much broader class of test statistics, as well as means of estimating those limiting distributions. For instance, Theorem 2.1 below allows (2.11) to be further decomposed using the structure of ΘΘ\Thetaroman_Θ as it relates to C𝐶Citalic_C.**C**: Proposition 2.1 complements and extends Theorem 3.1 of Fang and Seo, (2021) in a Banach space setting featuring arbitrary parameter spaces
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Selection 3
**A**: vector of observations for the target variable**B**: Additionally, there is a vector of**C**: Suppose we have a vector of pre-selected covariates denoted by 𝐳t=(z1⁢t,z2⁢t,⋯,zm⁢t)′subscript𝐳𝑡superscriptsubscript𝑧1𝑡subscript𝑧2𝑡⋯subscript𝑧𝑚𝑡′\mathbf{z}_{t}=\left(z_{1t},z_{2t},\cdots,z_{mt}\right)^{\prime}bold_z start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT = ( italic_z start_POSTSUBSCRIPT 1 italic_t end_POSTSUBSCRIPT , italic_z start_POSTSUBSCRIPT 2 italic_t end_POSTSUBSCRIPT , ⋯ , italic_z start_POSTSUBSCRIPT italic_m italic_t end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT
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Selection 1
**A**: However, even when there is a Condorcet winner in 𝐏𝐏\mathbf{P}bold_P and we are using a Condorcet voting method, a voter may still have an incentive to submit an insincere ranking in order to create a majority cycle, possibly resulting in a different winner**B**: On the other hand, such possibilities are evidently rare and difficult to learn to exploit. On the other hand, the comparative usefulness, for manipulating against each voting method, of the different types of limited information is largely the same under the spatial model as under the uniform utility model (this is true even for Minimax, Nanson, and Split Cycle, looking at which types of information produce less negative results). We conjuncture that these findings about types of limited information are robust across other standard probability models as well.**C**: Comparing Figure 1 for the uniform utility model and Figure 2 for the 2D spatial model model, the most striking differences are (1) that all voting methods become less profitably manipulable (roughly by one half) under the spatial model and (2) even the best MLP’s could not learn to profitably manipulate against Minimax, Nanson, and Split Cycle under the spatial model.111111A natural thought to explain (2) is that Minimax, Nanson, and Split Cycle are Condorcet consistent, and there is a high frequency of Condorcet winners under the 2D spatial model (yet this must be squared with the results for Stable Voting)
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Selection 3
**A**: Round 11 introduces either skill investments or an algorithmic decision aid as an external technological shock. Each round, experts can increase their maximum diagnostic precision to 90% by paying 10 Coins, which also automatically increases their prices by 10 Coins**B**: Over all 15 rounds, experts invest 64% of the time. Investments start at around 80%, but deteriorate significantly (see Table 2). Thus, while popular, investment shares lie substantially below the predicted (and optimal) 100%. **C**: Figure 5 shows investment shares for the two treatments and expert types in Phase 2. As predicted, there are no differences between expert types for skill investments
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Selection 3
**A**: For simplicity, furthermore, prices are assumed identical. **B**: And we defer the pricing decision to a further study, so that the service price is assumed to be set, and therefore a parameter**C**: We focus on the investment and procurement decisions to be taken by each SP in order to maximize its profits, that is, the network capacity (investment) and the sensor traffic (procurement)
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Selection 4
**A**: Many process do not satisfy them, either because the data exhibits long-range dependency or long-memory and this feature is modeled using slowly decaying dependence structure, e.g**B**: see [4] in the context of Markov processes; or the data is described by a so-called infinite memory chain (see [18]); or simply because the β𝛽\betaitalic_β-mixing coefficients decay at a slow polynomial rate (see [8]). More generally, there is the open question of how do the mixing properties affect the concentration rate of the maximal inequality 1. This paper aims to provide insights into these questions.**C**: These results leave open the question of what type of maximal inequality one can obtain in contexts where the mixing coefficients do not satisfy these conditions
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Selection 1
**A**: We also analyze the consequences of the resulting decision on the principal’s utility and on total welfare.**B**: We now consider the agent’s decision of whether to conceal or reveal the existence X𝑋Xitalic_X at time t=1𝑡1t=1italic_t = 1 in the agency game with information transfer outlined in Figure 1**C**: To analyze this decision, we compare the agent’s utility in the information-agnostic contract that results from keeping X𝑋Xitalic_X concealed and in the informed contract that depends on X𝑋Xitalic_X
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Selection 4
**A**: Li and Ding (2017) consider the case where q⁢(⋅)𝑞⋅q(\cdot)italic_q ( ⋅ ) is an identity function and ρ⁢(Z)𝜌𝑍\rho(Z)italic_ρ ( italic_Z ) is a vector of binary IVs, and derive the null asymptotic distribution of the statistic in (4.1)**B**: The general CLT provided in Theorem 2.1 allows us to derive the asymptotic distribution of the statistic T𝑇Titalic_T in (4.1) at once under general conditions, allowing for many strata without categorizing them into large and small ones or restricting their sizes**C**: The following proposition gives a formal justification for this argument.
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Selection 1
**A**: In the first, Lemma 3.2, we discover that a finite collection of ranked experiments identifies the agent’s undominated actions (up to relabeling and duplication) as well as the regions of beliefs on which each such action is optimal**B**: The three main results of this paper are two positive ones, with a negative one sandwiched in between**C**: The second result, Proposition 3.5, reveals an important indeterminacy about the agent’s utility function that cannot be resolved with only ordinal rankings of experiments. The third result, Theorem 3.7, states that an additional finite collection of utility differences between experiments (the difference in utils from observing one experiment versus another) identifies the agent’s utility function up to a decision-irrelevant payoff.
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Selection 4
**A**: Overall, our discussion in this section shows that edge decomposability is a weaker identifying restriction on supports than two recent identifying restrictions**B**: Further, edge decomposability is an easy to check and constructive criterion for identification.**C**: We note that while edge decomposability is a strictly weaker condition on supports than single-crossing, part of the novelty of SCRUM is that there is an endogenous mapping from ⊳contains-as-subgroup\rhd⊳ and p𝑝pitalic_p to the support of ν𝜈\nuitalic_ν
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Selection 1
**A**: For example, Inception Net’s architecture is designed to accommodate visual information that varies in scale and complexity, while VGG architecture is particularly well suited to detect differences in texture and detail (Szegedy et al., 2015; Kumar et al., 2022)**B**: This means that by including multiple encoders, we can capture more information from these images. In our setting, this leads to large increases in in-sample model fit and a 3% improvement in out-of-sample prediction accuracy. Given the growing interest in using images and other unstructured data in economics, we expect these methods will be beneficial to a broad set of applications.**C**: Different encoders, such as Inception Network, ResNet50, MobileNet, and the others used here, are designed with different architectures and are trained on different datasets (Szegedy et al., 2015; He et al., 2016; Howard et al., 2017)
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Selection 4
**A**: Reference (8) reported their results in terms of both health and economic outcomes. Reference (9) examined the nexus between job loss and mental health. They found that the effects of being unemployed are different for every individual. Some were more anxious and stressed than others (9).**B**: There were two more main coronaviruses (SARS-CoV in 2002 and MARS-CoV in 2012) before COVID-19, but they could not spread as much as the COVID-19 pandemic did. As a result, the economic and health consequences of COVID-19 were more damaging and ubiquitous than those of the other two outbreaks**C**: Reference (6) disentangled these economic and health effects, and they argued that health should be prioritized over material well-being. They provided an example to support their claim pointing out the fact that the expenditure on health does not say anything about the outcomes on health (21, 6)
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Selection 3
**A**: In practice, this amounts to estimating a linear regression where, in addition to standard unit and period-specific fixed effects, the researcher includes unit and period-specific controls that enter the regression with unrestricted period and unit-specific coefficients, respectively. Versions of such regressions are common in empirical practice, e.g., researchers often include unit-specific trends and interact time fixed effects with observed unit-specific variables in their regression specifications. The oracle estimator we consider has the same structure, using the correct interactions, that we, as analysts, do not know.**B**: In particular, we look at the oracle that knows the subspaces spanned by interactive fixed effects and uses them to construct the standard OLS estimator**C**: To analyze the properties of our method, we connect it to an infeasible “oracle” estimator, which has access to the part of the data that we, as analysts, do not observe
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Selection 4
**A**: Our analysis yields a number of new and practical results. First, our extensive communications records allow us to assess the importance of a comprehensive set of work-related shocks on worker retention simultaneously**B**: By far the most common, and the most strongly related to retention are equipment-related shocks (32%), and pay-related shocks (18%). Whereas shocks where interests are aligned, such as those related to equipment, tend to reduce turnover, pay-related shocks result in increased turnover precisely because interests are not aligned**C**: We also contribute by performing a sentiment analysis allowing us to view the shocks from two distinct theoretical lenses (Philip & Medina-Craven, 2022): embeddedness theory (Mitchell et al., 2001), and organizational commitment(Meyer & Allen, 1991). Shocks that highlight interest alignment have positive associated sentiments, demonstrating increased commitment.
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Selection 4
**A**: According to the estimated policy, teachers with less than or equal to 19 years of experience should be allocated to small-size classes in kindergarten.**B**: Figure 2 exhibits the DTR estimated by the proposed approach**C**: The policy for the first stage utilizes teacher experience to allocate students to either the small-size class or the regular-size class with a teacher aide
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Selection 1
**A**: In particular, strongly shill-proof optimal auctions must be iterative (with a possibly large number of rounds) and cannot be strategy-proof**B**: The rough intuition for the proof of this result is that: (i) for any auction format other than a Dutch auction, there exists a history in which some bidder i𝑖iitalic_i can indicate that her value is strictly larger than the reserve price without the auction ending immediately; (ii) optimality in tandem with the public setting then implies that this information effectively induces the auction to revise its reserve price upward; and thus (iii) there exist valuations for the bidders such that, if bidder i𝑖iitalic_i happens to be a shill bidder, shilling will increase the seller’s revenue.**C**: Our first result (Theorem 3.5) is a uniqueness result for strongly shill-proof auctions: the Dutch auction (with consistent tie-breaking and reserve price equal to the valuation distribution’s monopoly price) is strongly shill-proof and optimal (i.e., maximizes the seller’s expected revenue), and it is the only such auction in the public setting
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Selection 3
**A**: which is given by**B**: The exact values are 1/(3⁢2)≈0.2361320.2361/(3\sqrt{2})\approx 0.2361 / ( 3 square-root start_ARG 2 end_ARG ) ≈ 0.236, 1/2≈0.707120.7071/\sqrt{2}\approx 0.7071 / square-root start_ARG 2 end_ARG ≈ 0.707, and 2⁢2/3≈0.9432230.9432\sqrt{2}/3\approx 0.9432 square-root start_ARG 2 end_ARG / 3 ≈ 0.943**C**: for readability
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Selection 2
**A**: An illustration as to why the value of information may not be concave in its “quantity,” and in particular why the marginal value of information at quantity 00 may be zero goes something as follows**B**: Take a decision problem with finitely many undominated actions**C**: This means that the set of beliefs at which an action is optimal is a convex body: it is compact, convex, and possesses a non-empty interior. Accordingly, for a prior in the interior of one of these regions any information that does not move the prior much is worthless.
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Selection 4
**A**: Since a resolute and symmetric mm can be seen as a resolute and symmetric refinement of T⁢O𝑇𝑂TOitalic_T italic_O and since many properties of matching mechanisms can be described using the concept of refinement (e.g. stability, weak Pareto optimality, minimal optimality), the aforementioned existence problem can be seen as a special case of the following general existence problem.**B**: stability, weak Pareto optimality, minimal optimality), is certainly an interesting and not trivial problem**C**: Proving or disproving the existence of resolute and symmetric mms, possibly satisfying further properties (e.g
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Selection 3
**A**: In Example 2, Chetty and Hendren (2018a) and Chetty and Hendren (2018b) construct predictors of neighborhood-specific income effects**B**: A key input to answering these questions is the set of conditional means given by (7).**C**: Bergman, Chetty, DeLuca, Hendren, Katz, and Palmer (2019) use effect predictors to select the top census tracts for income mobility.333See Gu and Koenker (2023) for a broad account of ranking problems and selection of groups of units based on noisy estimates
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Selection 3
**A**: Furthermore, both the wheat and maize markets are susceptible to geopolitical risks faced by various combinations of economies with global influence in production, import, and export. The composite geopolitical risks of major wheat exporters and major maize producers better explain volatility in the international maize and soybean markets, respectively. For rice, increasing global geopolitical risks and acts significantly exacerbate the long-term rice market volatility, with the geopolitical risk in North America serving as an important macro-factor in explaining fluctuations in the international rice market. **B**: One possible reason is that the occurrence of adverse geopolitical events leads to the growth of global risk aversion, which in turn affects investment behavior and reduces long-run fluctuations in the international food market. Additionally, the geopolitical risk indices we use are quantified based on newspapers, so the amount of information, the level of noise, and the accuracy of political signals in news tend to influence investors’ decisions in the agricultural futures market, thereby affecting market volatility. At the regional level, composite geopolitical risks in North America, Europe, the Middle East and Africa, as well as Asia and Oceania considerably and negatively impact long-term maize market volatility, while composite geopolitical risks in North America, South America, and Europe exhibit significantly negative effects on the long-run fluctuations of the soybean market**C**: Specifically, a single geopolitical risk factor has limited explanatory power for long-term wheat market volatility, but performs well in explaining the long-term components of the maize and soybean markets. From a global perspective, both the global geopolitical threats index and our constructed global geopolitical risk index exert significant negative influences on long-run maize and soybean market volatility. This conclusion seems counterintuitive
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Selection 3
**A**: Raghavan (1970) provides a necessary condition in terms of the rank of the payoff matrix, but the condition is not sufficient. Milchtaich (2006) and Milchtaich and Ostrowski (2008) compute expected payoffs in completely mixed equilibria and provide a necessary and sufficient condition for a unique completely-mixed Nash-equilibrium in terms of the determinants of certain transformations of the payoff matrices. Weinstein (2020, Corollary 1) shows that a two-player game has a totally mixed Nash equilibrium if and only if neither player has a pair of mixed strategies such that one weakly dominates the other.**B**: Parthasarathy et al. (2020) extends these results to 3×3333\times 33 × 3 non-zero sum bimatrix games with skew symmetric payoff matrices**C**: There are several papers identifying necessary and/or sufficient conditions for completely mixed equilibria. Kaplansky (1945) and Kaplansky (1995) identify necessary and sufficient conditions for zero-sum games to have a completely mixed Nash equilibrium in terms of cofactors of the payoff matrix
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Selection 1
**A**: Some but not all of the analyses presented here were indeed pre-registered, and there are also further analyses from the pre-registration that are not presented in this paper**B**: We stuck with the pre-registration as much as we could, but the unfortunate need to depart from the pre-registered plan of analysis is explained in Appendix B.**C**: Remark: With the best intentions, we had fully pre-registered design and analysis of our experiments
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Selection 2
**A**: We can also reconstruct - for CRH notes - the exact minute at which the note reached its Helpful status and thus became visible by everyone on the platform. **B**: We download the Community Notes dataset, made publicly available by X for research purposes, which contains Community Notes that have been proposed, ratings on each Note from X users and Note Status History Data**C**: From those dataset, we can distinguish Notes Currently Rated Helpful (CRH) from Notes that Needs More Ratings (NMR) and Notes Currently Rated Not Helpful (CRNH)
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Selection 3
**A**: It is important to note that although the company’s optimal control problem for a fixed average production trajectory q𝑞qitalic_q is linear-quadratic, due to the nonlinear dependence of the net profit functional on q𝑞qitalic_q, the overall mean-field problem is not of linear-quadratic type**B**: [3], Delarue and Tchuendom [12], Tchuendom [19], among others, which focus on linear-quadratic mean-field games. **C**: In this regard, our results differ from those presented in Bensoussan et al
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Selection 2
**A**: Then D⁢(z2)≥D⁢(z1)𝐷subscript𝑧2𝐷subscript𝑧1D\left(z_{2}\right)\geq D\left(z_{1}\right)italic_D ( italic_z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ) ≥ italic_D ( italic_z start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ) for all agents**B**: A marginal treatment effect is then defined as the average**C**: assumes Imbens-Angrist monotonicity.444Consider two instrument values z1≥z2subscript𝑧1subscript𝑧2z_{1}\geq z_{2}italic_z start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ≥ italic_z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT
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Selection 2
**A**: According to a 2022 World Bank report, commodity market plays a pivotal role for this economy, for example, gold and cotton make up 30.8%percent30.830.8\%30.8 % and 11%percent1111\%11 % of the country’s export, respectively.333“Toward a Prosperous and Inclusive Future : The Second Systematic Country Diagnostic for Uzbekistan (English)”. Washington, D.C**B**: with refined petroleum (2.5%percent2.52.5\%2.5 % of the country’s imports) and wheat (2.2%percent2.22.2\%2.2 % of imports) making up the largest imports shares. It is natural to assume that the equity market of this open economy**C**: : World Bank Group. http://documents.worldbank.org/curated/en/933471650320792872/Toward-a-Prosperous-and-Inclusive-Future-The-Second-Systematic-Country-Diagnostic-for-Uzbekistan Imports structure is more homogeneous
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CAB
ABC
Selection 1
**A**: However, these findings are explained by the fact that while the Eastern bloc countries had very limited overall trade relations with the non-Soviet world, Western countries were generally more open and became increasingly so during the period when European institutions were being established**B**: This view is supported by a recent study by Head and Mayer (2021), where the authors use a gravity model to analyze the evolution of trade costs among EU members, and between EU members and the rest of the world.**C**: The simultaneous opening to trading partners outside Europe meant that the European integration process did not lead to significant trade diversion
ACB
BAC
ABC
BAC
Selection 1
**A**: Our goal is also concerned with using other architectures than linear-quadratic ones for the return function, namely, neural networks**B**: The approximation of Bellman’s value and policy functions with neural networks was originally proposed by Bertsekas and Tsitsiklis [1996] with lately developments described by Bertsekas [2011, 2020]**C**: Two broad approaches are available in neuro-dynamic programming (NDP): the direct estimation of the parameters using temporal differences or its indirect estimation using a least squares scheme on a projected Bellman equation.
BAC
CAB
ABC
BCA
Selection 3
**A**: This pattern hints at an early beneficial impact that seems to moderate with time. Conversely, the trajectory for women follows a different pattern, indicating initial adverse effects on employment and labor force participation rates. The pre-trends look fairly parallel, which, while not directly confirming the parallel trends assumption for the post-period, lends it greater plausibility. These visualizations indicate a temporary increase in labor force participation and employment rates for gay men following the enactment of ENDAs, contrasting with a negative impact on the same metrics for lesbian women. **B**: First, we present the event study regressions for male and female extensive labor supply outcomes in Figure 3. Panel (a) illustrates the effects on labor force participation rates, whereas Panel (b) shows the effects on employment levels. The plots reveal an initial jump in both employment and labor force participation rates among gay men, a trend that appears to wane over subsequent years**C**: We use Equation (1) with the inclusion of occupation-fixed effects and conduct event study regressions via Borusyak et al. (2021). This approach allows us to analyze how the impact estimates evolve
CBA
CAB
ACB
ABC
Selection 1
**A**: For the short-term profit, we do not include strategic long-term considerations but only a revenue p𝑝pitalic_p per unit, i.e. the additional value of selling the SKU instead of returning or depreciating it after the demand period, and supply costs of c𝑐citalic_c per unit. We assume these values to be fixed in the short run, and thus they do not affect the buying probability of each customer segment. Assuming that remaining units fully depreciate after the period, the ex-post profit z𝑧zitalic_z depends on whether the retailer is faced with excess inventory or excess demand in a certain period in the following way: **B**: To achieve a formulation for the (short-term) profit of the retailer, we rely on the well-established newsvendor model, a classical framework for modelling stochastic customer demand (see, e.g. Silver et al.,, 1998; Zipkin,, 2000). The newsvendor model operates under the assumption of independent demand periods, where a period typically represents a fixed time interval, such as a day or a week, during which the SKU remains available for sale**C**: Importantly, the model requires the retailer to make a single order decision for a specific quantity of the SKU before the actual customer demand becomes known. Once the order is placed, the retailer cannot make further adjustments to the quantity in this period
BAC
CBA
ABC
CAB
Selection 4
**A**: This implies according to Theorem 5 that one of the values applied by the social planner in this situation is that increases in lifetime among unproductive individuals following an intervention (axiom TIUP) will not increase the desirability of that intervention**B**: The social planner subscribes to two further values regarding invariance between different effect components where the first states that if an intervention leads to extra life years, it does not matter to the social planner which particular individual (among individuals with the same level of health and productivity) receives these extra life years (axiom TICHP). The second value specifies that if an intervention leads to improved productivity, it does not matter which particular individual (among individuals with the same level of health and lifespan) is able to perform better in the workplace (axiom PICHT). **C**: A social planner may view both health effects and productivity effects as important outcomes of interventions and may therefore choose an evaluation function like the PQALY (5), where health status and productivity of individuals enter the evaluation function multiplicatively
BAC
ACB
BAC
BCA
Selection 4
**A**: in general because by (10) g∗⁢(x)≠g⁢(x)superscript𝑔∗𝑥𝑔𝑥g^{\ast}\left(x\right)\neq g\left(x\right)italic_g start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ( italic_x ) ≠ italic_g ( italic_x )**B**: As before, this problem can be overcome if we know π𝜋\piitalic_π**C**: It is because
ABC
ACB
ACB
ACB
Selection 1
**A**: The claims in Theorem 1 are not new in the sense that they can easily be pieced together using existing results**B**: The equivalence between statements 2, 3, and 4 is found in Browning (1989) and the equivalence between statements 2, 5, and 6 is found in Brown and Calsamiglia (2007). To keep this article reasonably self-contained, we provide a proof of Theorem 1 in the Appendix.**C**: In particular, the equivalence between statements 1 and 2 is obvious
BAC
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ACB
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Selection 3
**A**: This is complemented with another characterization based on easily verifiable properties of an associated directed graph, called the tight digraph (more details below). **B**: We begin by providing axiomatic characterizations of these rules on the domain of many-to-one assignment markets, based on those for the optimal stable rules of the general (many-to-many) multiple-partners assignment market in (Domènech and Núñez, 2022)**C**: Applications such as some auction markets, usually consider only the maximum competitive prices (salaries) rule and the minimum competitive prices (salaries) rule
CAB
CBA
CAB
CAB
Selection 2
**A**: The obtained research results have important implications for the touristic affirmation of caves. The implementation of advanced forecasting modeling enables management structures to make various strategic moves such as sustainable management of resources and conservation efforts**B**: The use of such analytical techniques indicates effective modeling approaches that are crucial for the sustainability and protection of subterranean karst environments. Observed trends in tourism demand and the impact of factors such as seasonality and external events point to the fact that a continuous increase in tourist visitation to Stopića cave is to be expected**C**: Due to this prediction, it is necessary to establish adequate protection measures that can ensure long-term subterranean environmental sustainability. This primarily involves monitoring microclimate indicators such as temperature fluctuations, air humidity, and CO2 emissions. The analysis of monitoring results can greatly contribute to the understanding of the anthropogenic impact on Stopića cave, as well as the level of its vulnerability. Establishing monitoring programs and tracking visitor trends are crucial for tourism authorities so they can assess the effectiveness of carrying capacity measures and adapt management strategies in order to ensure the long-term sustainability of Stopića cave as a tourist destination.
BAC
ABC
CAB
BCA
Selection 2
**A**: For comparison, Figure 2 includes the cumulative frequency for Drupp’s 181 experts**B**: Geographically limiting the calibration sample makes the global distribution look much like Drupp’s sample. Population-weighting shifts the entire distribution to the left. The median person would prefer a carbon tax of $4/tC. **C**: The median scholar favours $24/tC, much higher than the median country
ACB
CAB
BAC
ABC
Selection 1
**A**: For sake of generality, for each of these model specifications, we verify our model performance under different Neural network architectures, such that for each given architecture we generated 100100100100 data sets**B**: These data sets are used to calculate the means and the standard error of our estimates.**C**: We consider various specifications for the structural equations of X𝑋Xitalic_X and Y𝑌Yitalic_Y, each one is chosen from the following functions: the Trans-log utility functions in (i); the Almost Ideal Demand System (AIDS) functions in (ii); the Constant Elasticity of Substitution (CES) production functions in (iii); the backward-bending supply curves in (iv); a Cobb-Douglas production function in (v) and the hyperbolic tangent model in (vi)
CBA
CBA
CBA
BCA
Selection 4
**A**: To highlight such fragility, we establish a stronger result**B**: In particular, Proposition 2 shows that every menu profile that induces an equilibrium where the platform’s revenue is close to the maximum possible surplus extraction also induces an equilibrium where the revenue is close to 0. **C**: Second, there is another extremely bad equilibrium where the platform gains no surplus, so the optimal menu profile in the standard framework is extremely fragile to strategic uncertainty
ABC
CAB
ACB
BCA
Selection 4
**A**: In these two cases, disclosing the red flag together with the additional evidence induces a higher price volatility than disclosing a red flag alone. However, if the speculator’s additional evidence is inconclusive about the value implication of the high inventory level, its disclosure only offsets the initial negative price impact, resulting in small price volatility. Thus, the speculator still takes a short position but issues a simple report pointing out the unusually high inventory level without disclosing the additional evidence. **B**: If he concludes that the high inventory is prepared for anticipated higher future sales, he takes a long position and issues an elaborate report explaining both the high level inventory and its positive value implications.777This result is supported by anecdotal evidence. For example, in Muddy Waters Research’s report on Bollore, the famous short-seller firstly points out a red flag on Bollore, a “horrifically complex corporate structure”. However, in the same report, the short-seller provided detailed evidence and reasons for why the opacity of Bollore is actually the reason to long the company**C**: Using our running example, Proposition 2 could be illustrated as follows. The speculator discovers that the target firm has an unusually high level of inventory, a red flag. If he further discovers that it results from an accounting fraud, he takes a short position and then issues an elaborate report with both the initial and additional information
CAB
ACB
ABC
CBA
Selection 4
**A**: Employees’ explanations from the survey for why this is unappealing include “Admin and bureaucracy which leaves little time for operative tasks.” and “Having to spend all your time on HR tasks, which is a necessity if team sizes are very large.” Second, 28%**B**: First, 55% of respondents name the administrative burden that team leadership entails, especially for large teams**C**: Employees’ survey responses point to the role of two position features of team leadership that are perceived as particularly unappealing
CBA
BCA
ACB
BCA
Selection 1
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