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BASIC
ECONOMETRICS
FOURTH EDITION
Damodar N.Gujarati
UnitedStatesMilitaryAcademy, WestPoint
BostonBurrRidge,ILDubuque, IAMadison, WINewYorkSanFrancisco St.Louis
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McGraw-Hill HigherEducatio... |
duction to econometrics without resorting to matrix algebra, calculus, orstatistics beyond the elementary level.
In this edition I have attempted to incorporate some of the developments
in the theory and practice of econometrics that have taken place since thepublication of the third edition in 1995. With the availabil... |
places old Chapter 16, on dummy dependent variable regression models,provides a fairly extensive discussion of regression models that involve adependent variable that is qualitative in nature. The main focus is on logit
Gujarati: Basic
Econometrics, Fourth EditionFront Matter Preface
© The McGraw−Hill
Companies, 2004... |
Free to instructors and salable to students is a Student Solutions Manual(ISBN 0072427922) that contains detailed solutions to the 475 questionsand problems in the text.
EViews
With this fourth edition we are pleased to provide Eviews Student Ver-sion 3.1 on a CD along with all of the data from the text. This software ... |
the application of mathematical statistics to economic data to lend empirical sup-port to the models constructed by mathematical economics and to obtainnumerical results.
1
. . . econometrics may be defined as the quantitative analysis of actual economicphenomena based on the concurrent development of theory and observa... |
for collecting data on gross national product (GNP), employment, unem-ployment, prices, etc. The data thus collected constitute the raw data foreconometric work. But the economic statistician does not go any further,not being concerned with using the collected data to test economic theories.Of course, one who does that... |
consumption function, Eq. (I.3.1), consumption (expenditure) is the depen-dent variable and income is the explanatory variable.
3. Specification of the Econometric Model of Consumption
The purely mathematical model of the consumption function given inEq. (I.3.1) is of limited interest to the econometrician, for it assum... |
obtain the estimates. Using this technique and the data given in Table I.1,we obtain the following estimates of β
1andβ2, namely, −184.08 and 0.7064.
Thus, the estimated consumption function is:
ˆY=−184.08+0.7064 Xi (I.3.3)
The hat on the Yindicates that it is an estimate.11The estimated consump-
tion function (i.e., r... |
the actual consumption expenditure by about 37.82 billion dollars. Wecould say the forecast error is about 37.82 billion dollars, which is about
0.76 percent of the actual GDP value for 1997. When we fully discuss thelinear regression model in subsequent chapters, we will try to find out ifsuch an error is “small” or “l... |
ample, Milton Friedman has developed a model of consumption, called thepermanent income hypothesis .
15Robert Hall has also developed a model of
consumption, called the life-cycle permanent income hypothesis .16Could one
or both of these models also fit the data in Table I.1?
In short, the question facing a researcher i... |
Although this book is written at an elementary level, the author assumesthat the reader is familiar with the basic concepts of statistical estimationand hypothesis testing. However, a broad but nontechnical overview of thebasic statistical concepts used in this book is provided in Appendix A for
Gujarati: Basic
Econom... |
In such models it is assumed implicitly that causal relationships, if any,between the dependent and explanatory variables flow in one direction only,namely, from the explanatory variables to the dependent variable.
In Chapter 1, we discuss the historical as well as the modern interpreta-
tion of the term regression and ... |
that the average height of sons of a group of tall fathers was less than theirfathers’ height and the average height of sons of a group of short fatherswas greater than their fathers’ height, thus “regressing” tall and short sonsalike toward the average height of all men. In the words of Galton, this was“regression to ... |
knowing the age, we may be able to predict from the regression line theaverage height corresponding to that age.
3.Turning to economic examples, an economist may be interested in
studying the dependence of personal consumption expenditure on after-tax or disposable real personal income. Such an analysis may be helpfuli... |
ability distributions. In functional or deterministic dependency, on theother hand, we also deal with variables, but these variables are not randomor stochastic.
The dependence of crop yield on temperature, rainfall, sunshine, and
fertilizer, for example, is statistical in nature in the sense that the explana-tory vari... |
Closely related to but conceptually very much different from regressionanalysis is correlation analysis, where the primary objective is to measure
thestrength ordegree oflinear association between two variables. The cor-
relation coefficient, which we shall study in detail in Chapter 3, measures
this strength of (linear... |
In other words, in two-variable regression there is only one explanatoryvariable, whereas in multiple regression there is more than one explana-tory variable.
The term random is a synonym for the term stochastic. As noted earlier,
a random or stochastic variable is a variable that can take on any set ofvalues, positive... |
conducted by the Census Bureau every 10 years (the latest being in year2000), the surveys of consumer expenditures conducted by the University ofMichigan, and, of course, the opinion polls by Gallup and umpteen other or-ganizations. A concrete example of cross-sectional data is given in Table 1.1This table gives data o... |
of that household since the last survey. By interviewing the same householdperiodically, the panel data provides very useful information on the dynam-ics of household behavior, as we shall see in Chapter 16.
Gujarati: Basic
Econometrics, Fourth EditionI. Single−Equation
Regression Models1. The Nature of
Regression A... |
of income spent on health care, one cannot do that analysis except at a veryhighly aggregate level. But such macroanalysis often fails to reveal thedynamics of the behavior of the microunits. Similarly, the Department ofCommerce, which conducts the census of business every 5 years, is notallowed to disclose information... |
ability of the appropriate data. This chapter discussed the nature, sources,and limitations of the data that are generally available for research, espe-cially in the social sciences.
4.In any research, the researcher should clearly state the sources of the
data used in the analysis, their definitions, their methods of c... |
tion as the U.S. inflation rate, would that suggest that U.S. inflation“causes” inflation in the other countries? Why or why not?
1.3. Table 1.3 gives the foreign exchange rates for seven industrialized countries
for years 1977–1998. Except for the United Kingdom, the exchange rate isdefined as the units of foreign currenc... |
1984:07 542.1300 542.3900 543.8600 543.8700 547.3200 551.19001985:01 555.6600 562.4800 565.7400 569.5500 575.0700 583.17001985:07 590.8200 598.0600 604.4700 607.9100 611.8300 619.36001986:01 620.4000 624.1400 632.8100 640.3500 652.0100 661.52001986:07 672.2000 680.7700 688.5100 695.2600 705.2400 724.28001987:01 729.340... |
10. Ford 40.1 166.211. Levi’s 40.8 27.012. Bud Lite 10.4 45.613. ATT/Bell 88.9 154.914. Calvin Klein 12.0 5.015. Wendy’s 29.2 49.716. Polaroid 38.0 26.917. Shasta 10.0 5.718. Meow Mix 12.3 7.619. Oscar Meyer 23.4 9.220. Crest 71.1 32.4
21. Kibbles ‘N Bits 4.4 6.1
Source: http://lib.stat.cmu.edu/DASL/Datafiles/tvadsdat.h... |
3As shown in App. A , in general the conditional and unconditional mean values are different.tion expenditure within each income bracket, on the average, weekly con-
sumption expenditure increases as income increases. To see this clearly, inTable 2.1 we have given the mean, or average, weekly consumption expen-diture c... |
tional) mean values. And the regression line (or curve) passes through these(conditional) mean values.
With this background, the reader may find it instructive to reread the
definition of regression given in Section 1.2.
2.2 THE CONCEPT OF POPULATION REGRESSION
FUNCTION (PRF)
From the preceding discussion and Figures. 2... |
vant for the development of the regression theory to be presented shortly.Therefore, from now on the term “linear” regression will always mean a regres-
sion that is linear in the parameters; the β’s (that is, the parameters are raised
to the first power only). It may or may not be linear in the explanatory vari-ables, ... |
explicitly that E(ui|Xi)=0. See Sec. 3.2.Now if we take the expected value of (2.4.1) on both sides, we obtain
E(Yi|Xi)=E[E(Y|Xi)]+E(ui|Xi)
=E(Y|Xi)+E(ui|Xi) (2.4.4)
where use is made of the fact that the expected value of a constant is that
constant itself.8Notice carefully that in (2.4.4) we have taken the condi-
tio... |
accurately, in practice the data may be plagued by errors of measurement.Consider, for example, Milton Friedman’s well-known theory of the con-sumption function.
11He regards permanent consumption (Yp)as a function
ofpermanent income (Xp).But since data on these variables are not directly
observable, in practice we use... |
resents the “true” population regression line? If we avoid the temptation oflooking at Figure 2.1, which purportedly represents the PR, there is no waywe can be absolutely sure that either of the regression lines shown in Fig-ure 2.4 represents the true population regression line (or curve). The re-gression lines in Fi... |
Reading, Mass., 1991. Incidentally, this is an excellent book that the reader may want to readto find out how econometricians go about doing research.The answer to this question will occupy much of our attention in Chap-
ter 3. We note here that we can develop procedures that tell us how toconstruct the SRF to mirror th... |
chastic error term). Are they linear regression models? If not, is it possible,by suitable algebraic manipulations, to convert them into linear models?
a.
Yi=1
β1+β2Xi
b.Yi=Xi
β1+β2Xi
c.Yi=1
1+exp(−β1−β2Xi)
2.10. You are given the scattergram in Figure 2.7 along with the regression line.
What general conclusion do you ... |
2 196.0000 388.0000 30 385.0000 662.00003 303.0000 391.0000 31 470.0000 663.00004 270.0000 415.0000 32 322.0000 677.00005 325.0000 456.0000 33 540.0000 680.00006 260.0000 460.0000 34 433.0000 690.00007 300.0000 472.0000 35 295.0000 695.00008 325.0000 478.0000 36 340.0000 695.00009 336.0000 494.0000 37 500.0000 695.0000... |
function (PRF) on the basis of the sample regression function (SRF) asaccurately as possible. In Appendix A we have discussed two generally used
methods of estimation: (1) ordinary least squares (OLS) and (2) maxi-
mum likelihood (ML). By and large, it is the method of OLS that is used
extensively in regression analysi... |
for the least-squares method lies in the fact that the estimators obtained byit have some very desirable statistical properties, as we shall see shortly.
It is obvious from (3.1.2) that
/summationdisplay
ˆu
2
i=f(ˆβ1,ˆβ2) (3.1.3)
that is, the sum of the squared residuals is some function of the estima-
torsˆβ1andˆβ2.Fo... |
Note 2:/summationtextxiyi=/summationtextxi(Yi−¯Y)=/summationtextxiYi−¯Y/summationtextxi=/summationtextxiYi−¯Y/summationtext(Xi−¯X)=/summationtextxiYi,since ¯Y
is a constant and since the sum of deviations of a variable from its mean value [e.g., /summationtext(Xi−¯X)]
is always zero. Likewise, /summationtextyi=/summati... |
can always be estimated by (3.1.7), that is, from the fact that thesample regression line passes through the sample means of YandX.
An advantage of the deviation form is that it often simplifies com-puting formulas.
In passing, note that in the deviation form, the SRF can be writ-
ten as
(3.1.14)
whereas in the original... |
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