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Journal ArticleDOI

Specification Tests in Econometrics

01 Nov 1978-Econometrica (Cambridge, Mass. : M.I.T. Dept. of Economics)-Vol. 46, Iss: 6, pp 1251-1272
TL;DR: In this article, the null hypothesis of no misspecification was used to show that an asymptotically efficient estimator must have zero covariance with its difference from a consistent but asymptonically inefficient estimator, and specification tests for a number of model specifications in econometrics.
Abstract: Using the result that under the null hypothesis of no misspecification an asymptotically efficient estimator must have zero asymptotic covariance with its difference from a consistent but asymptotically inefficient estimator, specification tests are devised for a number of model specifications in econometrics. Local power is calculated for small departures from the null hypothesis. An instrumental variable test as well as tests for a time series cross section model and the simultaneous equation model are presented. An empirical model provides evidence that unobserved individual factors are present which are not orthogonal to the included right-hand-side variable in a common econometric specification of an individual wage equation.

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Citations
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Book
01 Jan 2001
TL;DR: This is the essential companion to Jeffrey Wooldridge's widely-used graduate text Econometric Analysis of Cross Section and Panel Data (MIT Press, 2001).
Abstract: The second edition of this acclaimed graduate text provides a unified treatment of two methods used in contemporary econometric research, cross section and data panel methods. By focusing on assumptions that can be given behavioral content, the book maintains an appropriate level of rigor while emphasizing intuitive thinking. The analysis covers both linear and nonlinear models, including models with dynamics and/or individual heterogeneity. In addition to general estimation frameworks (particular methods of moments and maximum likelihood), specific linear and nonlinear methods are covered in detail, including probit and logit models and their multivariate, Tobit models, models for count data, censored and missing data schemes, causal (or treatment) effects, and duration analysis. Econometric Analysis of Cross Section and Panel Data was the first graduate econometrics text to focus on microeconomic data structures, allowing assumptions to be separated into population and sampling assumptions. This second edition has been substantially updated and revised. Improvements include a broader class of models for missing data problems; more detailed treatment of cluster problems, an important topic for empirical researchers; expanded discussion of "generalized instrumental variables" (GIV) estimation; new coverage (based on the author's own recent research) of inverse probability weighting; a more complete framework for estimating treatment effects with panel data, and a firmly established link between econometric approaches to nonlinear panel data and the "generalized estimating equation" literature popular in statistics and other fields. New attention is given to explaining when particular econometric methods can be applied; the goal is not only to tell readers what does work, but why certain "obvious" procedures do not. The numerous included exercises, both theoretical and computer-based, allow the reader to extend methods covered in the text and discover new insights.

28,298 citations


Cites background or methods from "Specification Tests in Econometrics..."

  • ...Hausman (1978) suggested comparing the OLS and 2SLS estimators of b1 1 ðd 0 1; a1Þ 0 as a formal test of endogeneity: if y2 is uncorrelated with u1, the OLS and 2SLS estimators should di¤er only by sampling error....

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  • ...See Lahiri and Schmidt (1978) and Hausman, Newey, and Taylor (1987). Chapter 9 228...

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  • ...A classic example of selection based on yi is Hausman and Wise’s (1977) study of the determinants of earnings....

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  • ...Breusch, Mizon, and Schmidt (1989) studied the Hausman-Taylor model under the additional assumption that Eðx 0 it2ciÞ is constant across t. This adds more orthogonality conditions that can be exploited in estimation. See IASW (1999) for a recent analysis....

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  • ...In the Hausman and Wise (1977) example, a2ðxÞ was a function of family size because the poverty income level depends on family size....

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Journal ArticleDOI
TL;DR: In this article, the generalized method of moments (GMM) estimator optimally exploits all the linear moment restrictions that follow from the assumption of no serial correlation in the errors, in an equation which contains individual effects, lagged dependent variables and no strictly exogenous variables.
Abstract: This paper presents specification tests that are applicable after estimating a dynamic model from panel data by the generalized method of moments (GMM), and studies the practical performance of these procedures using both generated and real data. Our GMM estimator optimally exploits all the linear moment restrictions that follow from the assumption of no serial correlation in the errors, in an equation which contains individual effects, lagged dependent variables and no strictly exogenous variables. We propose a test of serial correlation based on the GMM residuals and compare this with Sargan tests of over-identifying restrictions and Hausman specification tests.

26,580 citations

Journal ArticleDOI
TL;DR: In this article, a parameter covariance matrix estimator which is consistent even when the disturbances of a linear regression model are heteroskedastic is presented, which does not depend on a formal model of the structure of the heteroSkewedness.
Abstract: This paper presents a parameter covariance matrix estimator which is consistent even when the disturbances of a linear regression model are heteroskedastic. This estimator does not depend on a formal model of the structure of the heteroskedasticity. By comparing the elements of the new estimator to those of the usual covariance estimator, one obtains a direct test for heteroskedasticity, since in the absence of heteroskedasticity, the two estimators will be approximately equal, but will generally diverge otherwise. The test has an appealing least squares interpretation.

25,689 citations

Posted Content
TL;DR: In this article, the authors examined the linkages between systems of high performance work practices and firm performance and found that these practices have an economically and statistically significant impact on both intermediate outcomes (turnover and productivity) and short and long-term measures of corporate financial performance.
Abstract: This paper comprehensively examined the linkages between systems of High Performance Work Practices and firm performance. Results based on a national sample of nearly one thousand firms indicate that these practices have an economically and statistically significant impact on both intermediate outcomes (turnover and productivity) and short- and long-term measures of corporate financial performance. Support for the predictions that the impact of High Performance Work Practices is in part contingent on their interrelationships and links with competitive strategy was limited.

8,131 citations


Cites background or methods from "Specification Tests in Econometrics..."

  • ...Second, to assess the magnitude of any simultaneity between High Performance Work Practices and firm profits, I used Hausman's (1978) test to evaluate the ordinary-least-squares (OLS) regression assumption that the High Performance Work Practices scales are exogenous in the profitability models. In analyses whose results are not shown, I generated a predicted value for the employee skills and organizational structures and employee motivation scales using a reduced-form model. Then I included each scale and its predicted value in an OLS model for Tobin's q and GRATE. A significant coefficient on the predicted value for each scale would indicate it is endogenous in the model being estimated (Hausman, 1978). Although these results showed that the High Performance Work Practices scales were not in fact endogenous in the profitability models, the general controversy surrounding the use of this test (Addison & Portugal, 1989) led me to estimate two-stage least-squares models for each dependent variable as a formal correction for simultaneity. Not only were these results consistent with the OLS results, but they were in each case somewhat larger than the OLS results presented here. Survey response bias was also considered directly. The presence of response bias implies that unobserved determinants of the decision to respond to this study’s survey are related to both firm performance and High Performance Work Practices. Given the extensive control variables included in my models, such bias is unlikely. However, to formally test this possibility, I used Heckman's (1979) procedure, which generates an inverse Mills' ratio that I then included in the OLS and two-stage least-squares regression models for each dependent variable to control for selectivity bias....

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  • ...Second, to assess the magnitude of any simultaneity between High Performance Work Practices and firm profits, I used Hausman's (1978) test to evaluate the ordinary-least-squares (OLS) regression assumption that the High Performance Work Practices scales are exogenous in the profitability models....

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  • ...A significant coefficient on the predicted value for each scale would indicate it is endogenous in the model being estimated (Hausman, 1978)....

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Book
01 Jan 2003
TL;DR: In this paper, the authors describe the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation, and compare simulation-assisted estimation procedures, including maximum simulated likelihood, method of simulated moments, and methods of simulated scores.
Abstract: This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum simulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. No other book incorporates all these fields, which have arisen in the past 20 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.

7,768 citations


Cites background or methods from "Specification Tests in Econometrics..."

  • ...(1981), Chapman and Staelin (1982), and Hausman and Ruud (1987). A mixed logit model can be estimated on ranked data with the same explosion....

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  • ...Following the practice suggested by Hausman (1997), they used the prices in other cities by the same company as instuments for each city....

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  • ...Berndt, Hall, Hall, and Hausman (1974), hereafter referred to as BHHH (and commonly pronounced B-triple H), proposed using this relationship in the numerical search for the maximum of the log-likelihood function....

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  • ...Hausman and McFadden (1984) provide an appropriate statistic for this type of test....

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References
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Journal ArticleDOI

4,733 citations


"Specification Tests in Econometrics..." refers background in this paper

  • ... Однако возникает важная проблема спецификации, что было отмечено в (Maddala, 1971, p. 357) и затем подчеркивалось  в работе (Mundlak, 1976)....

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  • ...Mundlak Y. (1976)....

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  • ...357] and has been further emphasized by Mundlak [14]....

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  • ...27 Работа была позже опубликована как: Mundlak Y. (1978)....

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Book
01 Jan 1971

3,429 citations


Additional excerpts

  • ... В работах (Scheffé,  1959) и (Searle, 1971) можно найти превосходные обсуждения этой темы в рамках дисперси- 16 Такой метод оценивания модели со случайными эффектами остался незамеченным в литературе....

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Journal ArticleDOI
TL;DR: In this article, the asymptotic error variance matrix for the coefficients of one of the relationships is obtained in the case in which these relationships are estimated using instrumental variables, and the problem of choice that arises when there are more instrumental variables available than the minimum number required to enable the method to be used is discussed.
Abstract: which the relationships are not exact, so that a set of ideal economic variables is assumed to be generated by a set of dynamic stochastic relationships, as in Koopmans [12], and the actual economic time series are assumed to differ from the ideal economic variables because of random disturbances or measurement errors. The asymptotic error variance matrix for the coefficients of one of the relationships is obtained in the case in which these relationships are estimated using instrumental variables. With this variance matrix we are able to discuss the problem of choice that arises when there are more instrumental variables available than the minimum number required to enable the method to be used. A method of estimation is derived which involves a characteristic equation already considered by Hotelling in defining the canonical correlation [10]. This method was previously suggested by Durbin [7]. The same estimates would be obtained by the maximum-likelihood limited

2,976 citations


"Specification Tests in Econometrics..." refers methods in this paper

  • ... Проверка того, что  0a= в уравнении (2.20) при нулевой гипотезе, основана на статистике  2 2 ˆ ˆˆ ˆ( )xx Q x s = a a. Однако  10 Тест инструментальных переменных может быть также рассмотрен как формализация и улучшение предложений Sargan (1958), который рекомендовал проверять, лежат ли оценки метода наименьших квадратов вне  доверительных интервалов для IV оценок....

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  • ...9The instrumental variable test can also be considered a formalization and an improvement of a suggestion by Sargan [20] who recommended checking whether the least squares estimates lie outside the confidence regions of the IV estimates....

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  • ...Sargan J. D. (1958)....

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  • ... Проверка того, что  0a= в уравнении (2.20) при нулевой гипотезе, основана на статистике  2 2 ˆ ˆˆ ˆ( )xx Q x s = a a. Однако  10…...

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  • ... Таким образом, предложенная процедура дает более короткие доверительные интервалы, чем процедура Sargan....

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Journal ArticleDOI
01 Jul 1925
TL;DR: It has been pointed out to me that some of the statistical ideas employed in the following investigation have never received a strictly logical definition and analysis, and it is desirable to set out for criticism the manner in which the logical foundations of these ideas may be established.
Abstract: It has been pointed out to me that some of the statistical ideas employed in the following investigation have never received a strictly logical definition and analysis The idea of a frequency curve, for example, evidently implies an infinite hypothetical population distributed in a definite manner; but equally evidently the idea of an infinite hypothetical population requires a more precise logical specification than is contained in that phrase The same may be said of the intimately connected idea of random sampling These ideas have grown up in the minds of practical statisticians and lie at the basis especially of recent work; there can be no question of their pragmatic value It was no part of my original intention to deal with the logical bases of these ideas, but some comments which Dr Burnside has kindly made have convinced me that it may be desirable to set out for criticism the manner in which I believe the logical foundations of these ideas may be established

2,464 citations


Additional excerpts

  • ...  5 Утверждение этой леммы для случая конечной выборки и одного параметра содержится в статье (Fisher,  1925), ссылка на которую получена от W. Taylor....

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  • ...Fisher [8], a reference supplied by W....

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Book
01 Jan 1987
TL;DR: The authors have improved on their widely used first edition by adding material on how to do ANOVA using statistical packages for microcomputers, linking the use of ANOVA to regression analysis, and enchancing their discussion on using ANOVA for experimentally gathered data.
Abstract: The authors have improved on their widely used first edition by providing updated examples, adding material on how to do ANOVA using statistical packages for microcomputers, linking the use of ANOVA to regression analysis, and enchancing their discussion on using ANOVA for experimentally gathered data.

1,472 citations