Undergraduate Econometrics, R.C. HILL,W.E. GRIFFITHS, ANDG.G. JUDGE, JohnWiley, New York,1997, A$57.95, ISBN 0-471-13993-9, pp. xiv � 366.

Instructor's Resource Guide to Accompany Undergraduate Econometrics, W.E. GRIFFITHS, R.C. HILL,AND L.C. MARSH, John Wiley, New York, 1997, ISBN 0-471-19189-2, pp. 510 � ¯oppy disk.

Peter Phillips observed at the recent 1997 Australasian Meeting of the Econometric Society in Melbournethat `the way we teach econometrics has changed dramatically in the last ten years'. He was referring, inparticular, to the increased emphasis on applications and use of personal computers in undergraduateeconometrics courses. This is re¯ected in the text under review in several ways: ®rst, each chapter starts byidentifying a particular economic problem and data consistent with the problem; second, each chapterpresents empirical results and discusses their implications; third, many data sets are listed in the book or areavailable from the Wiley Web site; fourth, there is an emphasis on p-values rather than critical values; and®fth, a whole chapter (17) is devoted to economic data sources (including a list of useful and interestingInternet addresses, and a detailed discussion of Bill Go�e's Resources for Economists on the Internet(see also Go�e, 1994)), choosing a research project and writing a research report.Not only has the way we teach econometrics changed, but life for the undergraduate econometrics teacher

who wishes to minimize the amount of time devoted to teaching the course has become much easier. TheInstructor's Resource Guide provides not only fully worked solutions to all the exercises in the text but addi-tional problems that can be used for homework and exams, full SHAZAMand SAS instruction ®les and com-puting handouts, and copies of the PowerPoint slides and overheads for teaching. The ¯oppy disk containsthe PowerPoint slide and instruction ®les for SHAZAM and SAS, and all the data sets (all these ®les can alsobe down loaded from Wiley's Web site http://www.wiley.com). The only thing missing is a set of videos ofstandard lectures for the course and software to mark the homework and exams! In contrast to the text thathas a heavyemphasis on economic problems and applications, this emphasis is noticeably absent in thePower-Point slides. As is indicated by the discussion of the Instructor's Resource Guide, the text has been written withthe estimation options available in SAS and SHAZAM in mind. The rudimentary nature of graphics optionsin SHAZAM perhaps is the explanation for why the use of graphs is not highlighted at all in the text, despitethe ease with which graphs can be produced with some of the latest econometric software (although studentsneed to bemade aware of their potential shortcomings inmultiple regression analysis: seeMcAleer, 1997a, b).The text contains many excellent features including: lots of data sets; summaries of the main points at the

end of each chapter; many (mainly applied) problems at the end of every chapter: economic motivation foreach econometric problem considered; a nice integration of economic theory and econometric practice; andSkippy (re¯ecting the Australian in¯uence of one of the authors). For those non-Australians, Skippy is thename of an Australian kangaroo and is used by the authors to refer to more di�cult or advanced materialthat the student can skip without any signi®cant loss of understanding. I had a few minor quibbles with thelack of interpretation in the text of some of the Skippy-marked material. For example, the derivations ofboth the normal equations for the OLS estimator (p. 55 and p. 138), and the elasticity interpretationof parameters of the log-log model (p. 59) are included in Skippy material. However, there is no discussion ofthe elasticity interpretation or what the normal equations imply for the relationships between theexplanatory variables and the estimated residuals in the text.Hill et al. have written this book as a text for a one-semester introductory econometrics course which

assumes some introductory exposure to economics and statistics. Calculus is used in such a way (typically

CCC 0883±7252/97/060745±05$17.50 Received 31 July 1997# 1997 John Wiley & Sons, Ltd.

JOURNAL OF APPLIED ECONOMETRICS, VOL. 12, 745±749 (1997)

in Skippy material) that students who are not familiar with it will lose very little. Matrix algebra is totallyabsent. As the authors emphasize in their introduction, this `is not an econometrics cookbook, nor is it ina theorem-proof format. It emphasizes motivation, understanding and implementation' (p.v). The wholebook closely follows this emphasis. As might be expected in an introductory undergraduate econometricstext, there are very few surprises in the material covered. Chapter 2 covers basic statistical conceptslike the concepts of a random variable, expected value, variance and the four commonly used distribu-tions in econometrics (normal, chi-square, t and F). In this chapter, there is a discussion on how to read thestandard normal tables but not the other three distributions. This is partially corrected in later chapters.Four chapters (3±6) are devoted to the simple linear regression model (one explanatory variable). In

chapters 3±5, the assumptions of the simple linear regression are repeated for emphasis but do not includean assumption about the stochastic nature of the explanatory variable. Chapter 3 covers the relationshipbetween an economic and an econometric model, the reason for the error, the standard assumptions in thelinear regression model in terms of what they mean for both the error and the dependent variable, and theleast squares principle. Chapter 4 discusses the sampling properties of the least squares estimator includinglinearity, unbiasedness (although the explanatory variable is not explicitly assumed to be ®xed or non-stochastic), the impact of underspeci®cation, the Gauss±Markov theorem, estimation of variances of theleast squares estimators, and prediction. For the Gauss±Markov theorem, the required assumptions(excluding the required condition on the explanatory variable) are clearly stated, and in a Skippy section, thetheorem is formally proved. There is no discussion of Kruskal's theorem that provides the necessary andsu�cient conditions for OLS to be BLUE (see McAleer, 1992). It is claimed that the forecast error of theleast squares predictor is normally distributed if the errors are normally distributed (true) or if the samplesize is large (false) (pp. 82±3). Interval estimation and hypothesis testing based on the t-test are the principalfoci of Chapter 5. I liked the emphasis in this chapter (and the following chapters) of the ®ve components ofhypothesis tests: a null hypothesis, an alternative hypothesis, a test statistic, a rejection region and aconclusion, and these components are explicitly set out in each empirical illustration. Finally, theinterpretation of an acceptance of the null hypothesis as really being `we do not reject the null hypothesis'(p. 97) is correctly noted.Chapter 6 is devoted to the coe�cient of determination that is argued correctly to `not measure the quality

of the regression model' (p. 114), the reporting of regression results and the choice of functional form. Byintroducing six `useful functional forms' (p. 121), linear, log-log, log-linear, linear-log, log-inverse andreciprocal, the authors draw attention to this important issue both in the meaning of the parameters andelasticities associated with these models, and the sort of relationship they are likely to capture. How do wechoose between these functional forms? The authors suggest a major objective of choosing a functional formis to create a model whose errors satisfy the assumptions of the standard linear regression model. One of theproblems of raising this functional form choice issue before a discussion of the general linear regressionmodel is that it is di�cult to talk about testing the correctness of the functional form using say the RESETtest. In fact, the RESET test is not mentioned anywhere in the textbook!The general linear regression model is the subject of Chapters 7±9. Chapter 7 repeats the material covered

in Chapters 3 and 4 switching between discussions of a model with many regressors and a model with aconstant and two regressors where analytic expressions are available for the OLS estimators. Unlike theearlier chapters, Chapter 7 explicitly assumes that the explanatory variables are not random. After a reviewof the material in Chapters 5 and 6 (excluding the choice of functional form) for the general linear model,Chapter 8 goes on to look at the F-test, the use of non-sample information and multicollinearity. The smartstudent will realize that there is an important di�erence in the discussion of one-sided tests in Chapters 5and 8. In Chapter 5, the null and alternative hypotheses are speci®ed, for example, as b� 0 and b5 0,respectively, whereas in Chapter 8, they are speci®ed as b5 0 and b4 0 (pp. 151±2). Readers are not advisedabout how to read F tables but this is because the authors believe that `with the advent of sophisticatedstatistical software, the problem of ®nding the critical value has been eliminated' (p. 160). This approach thatsuggests students do not need to know how to ®nd critical values for themselves will create problems whenstudents graduate and work in places lacking access to the latest sophisticated software.

An excellent example of a log-log demand function is used to illustrate how to incorporate non-sampleinformation derived from economic theory in the form of the dependence of quantity demanded onrelative prices rather than absolute prices. The consequences of using incorrect non-sample informationare brie¯y addressed but the testing of the correctness of this information is not explicitly covered. Moresurprisingly, the consequences of underspeci®cation and overspeci®cation in the general linear model

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are not discussed at all. On the Williams (1992) multicollinearity criterion that the shorter the discussiondevoted to multicollinearity, the better, the authors do extremely well with a discussion under three pages!Interaction terms and the use of dummy variables as explanatory variables and the dependent variable are

discussed in Chapter 9. One of the empirical examples in Chapter 9 focuses on explaining pizza expenditureusing income, age and an income±age interaction term. Not surprisingly, in a sample of 40 people there arefour people with zero expenditure (and, of course, none with negative expenditure) so that this is probably agood introductory example to the Tobit estimator. The potential importance of the lower limit on thedependent variable is not noted. The discussion of logit and probit models is also problematic because onlybrief reference is made to non-linear models (discussed in Chapter 14) and maximum likelihood estimation(not discussed elsewhere). Although in a Skippy section, I wondered whether it would not have been betterjust to ¯ag the potential problems with probit and logit models and then leave them for more advancedcourses and texts.According to the authors, Chapters 1±8 should form the core of any course. Chapters 9±17 are devoted to

speci®c topics. Quite predictably there are chapters on heteroscedasticity (10), serial correlation (11), andsimultaneous equations models (13) and, perhaps less predictably, chapters on pooling time series and cross-sectional data (12), non-linear least squares (14), distributed lag models (15), and time-series modelsincluding unit roots and cointegration (16).Chapters 10 and 11 follow the approach of discussing the consequences of heteroscedasticity and serial

correlation for the e�ciency of OLS and inference; the White adjustment for heteroscedasticity but not theNewey±West adjustment for serial correlation and heteroscedasticity; the generalized least squares trans-formations in both cases; and testing in both cases. One major problem I had with both chapters was they donot introduce the potential alternative interpretations of a rejection of the null hypotheses of no serialcorrelation and homoscedasticity. For example, the possibility that misspeci®cation of the regressioncomponent of the model may lead to `spurious' serial correlation is not mentioned. As a result, the authorsleave the impression that a rejection of the null hypothesis of uncorrelated errors and homoscedasticityshould lead to automatic use of the presumed GLS transformation (the authors are not alone hereÐ see, forexample, McAleer's (1997a) discussion of Leamer's (1997) use of the Cochrane±Orcutt transformation). Asis common in other textbooks, the initial discussion of estimation and testing for serial correlation is limitedto non-stochastic explanatory variables. The Durbin h-test is discussed later in Chapter 15. Contrary to theemphasis elsewhere on computer usage, the discussion of estimators for the regression model with AR(1)errors is con®ned to the very traditional Cochrane±Orcutt and Prais±Winsten methods. In fairness, thechapter on non-linear least squares discusses estimation of this model but the discussion is not ¯agged inChapter 11. In fact, the book could generally do with a lot more ¯agging of problems to be treated in laterchapters so that students are aware that there are all sorts of potential problems lurking around. Teachers(and researchers) beware that the age of `critical bounds' for the Durbin±Watson test is over. There is in factonly passing reference to them. The authors assume that whatever econometric software is being used willcompute the exact p-value for the Durbin±Watson test for any problem being considered. This assumption isnot always warranted.

Chapter 12 is a little unusual for an introductory econometrics text as it introduces system estimation inthe form of SURE, and one-way ®xed and random e�ect models for panel-data. For the SURE model, alittle more motivation for why systems estimation is necessary would have helped, for example an explan-ation indicating that correlation across the errors or cross-equation restrictions can be exploited to obtainmore e�cient estimates. It is suggested that the errors of the investment equations in the classic Grunfeld±Griliches data set might be correlated because factors that in¯uence investment in di�erent ®rms likeliquidity and the general state of the economy have been omitted (p. 266). This is a case for misspeci®cationof the investment equations, not for correlation of the errors! The GLS transformation for the SURE modelis not discussed in detail because `the transformation is too complicated' and `it is automatically carried outby your computer software' (p. 267). This is true for a lot of things considered but does not give anymotivation for why GLS is being applied. The GLS transformation could easily be illustrated for thetwo-equation case and would indicate that the transformation eliminates a particular form of serialcorrelation and heteroscedasticity, reinforcing the material in Chapters 10 and 11.

Chapter 13 presents a traditional discussion of the simultaneous equation model, the distinction betweenexogenous/endogenous variables, and reduced-form/structural forms, the bias of OLS, the identi®cationproblem, and two-stage least squares. The demand and supply of tru�es make for a quite interestingempirical illustration of these results. Measurement error and the use of proxy variables (using realized

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values for an expected variable, for example) are not used as motivations for why there might be a correl-ation between the regressors and disturbance. The discussion of Koyck lags in Chapter 15 which leads tolagged dependent variables and moving average errors gives a di�erent motivation for correlation betweenexplanatory variables and disturbances, but this is not ¯agged in Chapter 13.Estimation of the CES production function and a regression model with AR(1) errors are used to motivate

the need for non-linear least squares in Chapter 14 but the properties of the non-linear least squares estimatorare not discussed. It is suggested that the standard t-test following a t-distribution will be an `approximateresult' (p. 303) with no explanation for why this is the case. Testing common factor restrictions is used as anillustration of testing non-linear restrictions and here the F-test for the common factor restrictions is said toonly have `a large sample justi®cation' (p. 305) but the reasons for this are not explained.

Modelling dynamics is the subject of Chapter 15, covering both ®nite and in®nite distributed lags, thelatter including the Koyck transformation, adaptive expectations hypothesis, and partial adjustmenthypothesis. I was surprised to ®nd a four-page discussion of Almon polynomial lags. The Koyck trans-formation, adaptive expectations hypothesis, and partial adjustment hypothesis provide justi®cations for thepresence of lagged dependent variables among the explanatory variables and for moving average errors.Unfortunately, the impacts of lagged dependent variables on the properties of the OLS estimator are notdiscussed and the introduction of MA errors is a little early since MA errors are not discussed until Chapter16. For those raised only on a menu of vector autoregressions, the reasons for including a lagged dependentvariable in the explanatory variables might seem `obvious' but there is still a case for the sort of discussion inthis chapter. I would have preferred an approach that says there are many cases where lagged dependentvariables appear as explanatory variables, followed by a motivating discussion and then an elaboration ofhow statistical properties of the OLS estimator are a�ected.The discussion of stationary time series models in Chapter 16 is limited to AR(1) and MA(1) models. As

we all know, material on unit roots and cointegration is a potential mine®eld for students (and lecturers). Dowe need to talk about vector autoregressive models and vector error correction models at this early stage?My answer is a de®nite no but the authors see this di�erently. I found the discussion of unit roots veryincomplete and potentially confusing: tests of a unit root are discussed in the context of an unnecessarilycomplicated ARMA(1,1) model; it is claimed that the Dickey±Fuller test `is implemented by specialcomputer programs' (p. 336), which would need to be the case for the ARMA(1,1) model but not in thestandard case of an AR model; there is no warning about the need for special tables of critical values; andthe critical value in the illustrative example is plucked from thin air. Unfortunately, apart from the spuriousregression case, the reader is not given any idea of why there is such a big fuss about I(1) variables and whytheir presence is potentially problematic in a time-series regression model.

The authors claim that Chapters 9±17 `can be taught in any order' `with minor discomfort' (p.v) but insome cases I do not think this is the case. For example, before discussing unit roots it is sensible to covermaterial on lagged dependent variables and serial correlation. The material on dynamics would make moresense if students knew something about lagged dependent variables and serial correlation. As the authorsimplicitly suggest, it is in the choice of the ordering of the material in Chapters 10±16 that lecturers canincrease their contribution to the value added of their undergraduate econometrics course.Getting students interested in econometrics and maintaining that interest is one of the di�cult tasks we

teachers face. Another di�cult task is convincing students that `economics research is fun' (p. 356) andpotentially very useful. By using many di�erent empirical examples and continuously linking the economicproblem at hand with the econometrics techniques, the authors have found an excellent solution to these twotasks. Not all our problems have been solved by this excellent applied text and all the additional teachingresources. There is still a chance to provide additional value added by highlighting di�erent issues, providingdi�erent motivations for the same problem, and providing forward ¯agging of issues that arise later. I amgiving serious consideration to using this text in my next applied econometrics course. Since the text is aimedat the undergraduate student market, the publishers need to give serious consideration to producing the textin paperback.

REFERENCES

Go�e, W. L. (1994), `Computer network resources for economists', Journal of Economic Perspectives, 8(3),97±119.

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Leamer, E. E. (1997), `Revisiting Tobin's 1950 study of food expenditure', to appear in Journal of AppliedEconometrics, 12.

McAleer, M. (1992), `E�cient estimation: the Rao±Zyskind condition, Kruskal's theorem and ordinaryleast squares', Economic Record, 68, 65±72.

McAleer, M. (1997a), `Discussion of ``Revisiting Tobin's 1950 study of food expenditure'' by Edward E.Leamer', to appear in Journal of Applied Econometrics, 12.

McAleer, M. (1997b), `Pictures at an exhibition: the experiment in Applied Econometrics Conference,Tilburg, The Netherlands, 1996', to appear in Journal of Economic Surveys, 11(4).

Williams, R. A. (1992), `Book review: Econometrics by J. Stewart', Economic Record, 68, 80±81.

COLIN McKENZIEOsaka School of International Public Policy

Osaka UniversityJapan

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