An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Units
TL;DR: The authors illustrates the danger of spurious regression from this kind of misspecification, using as an example a wage regression estimated on data for individual workers that includes in the specification aggregate regressors for characteristics of geographical states.
Abstract: Many economic researchers have attempted to measure the effect of aggregate market or public policy variables on micro units by merging aggregate data with micro observations by industry, occupation, or geographical location, then using multiple regression or similar statistical models to measure the effect of the aggregate variable on the micro units. The methods are usually based upon the assumption of independent disturbances, which is typically not appropriate for data from populations with grouped structure. Incorrectly using ordinary least squares can lead to standard errors that are seriously biased downward. This note illustrates the danger of spurious regression from this kind of misspecification, using as an example a wage regression estimated on data for individual workers that includes in the specification aggregate regressors for characteristics of geographical states. Copyright 1990 by MIT Press.
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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
TL;DR: In this article, the authors randomly generate placebo laws in state-level data on female wages from the Current Population Survey and use OLS to compute the DD estimate of its "effect" as well as the standard error of this estimate.
Abstract: Most papers that employ Differences-in-Differences estimation (DD) use many years of data and focus on serially correlated outcomes but ignore that the resulting standard errors are inconsistent. To illustrate the severity of this issue, we randomly generate placebo laws in state-level data on female wages from the Current Population Survey. For each law, we use OLS to compute the DD estimate of its “effect” as well as the standard error of this estimate. These conventional DD standard errors severely understate the standard deviation of the estimators: we find an “effect” significant at the 5 percent level for up to 45 percent of the placebo interventions. We use Monte Carlo simulations to investigate how well existing methods help solve this problem. Econometric corrections that place a specific parametric form on the time-series process do not perform well. Bootstrap (taking into account the autocorrelation of the data) works well when the number of states is large enough. Two corrections based on asymptotic approximation of the variance-covariance matrix work well for moderate numbers of states and one correction that collapses the time series information into a “pre”- and “post”-period and explicitly takes into account the effective sample size works well even for small numbers of states.
9,397 citations
TL;DR: In this article, the authors examine the different methods used in the literature and explain when the different approaches yield the same (and correct) standard errors and when they diverge, and give researchers guidance for their use.
Abstract: In both corporate finance and asset pricing empirical work, researchers are often confronted with panel data. In these data sets, the residuals may be correlated across firms and across time, and OLS standard errors can be biased. Historically, the two literatures have used different solutions to this problem. Corporate finance has relied on clustered standard errors, while asset pricing has used the Fama-MacBeth procedure to estimate standard errors. This paper examines the different methods used in the literature and explains when the different methods yield the same (and correct) standard errors and when they diverge. The intent is to provide intuition as to why the different approaches sometimes give different answers and give researchers guidance for their use.
7,647 citations
TL;DR: This work considers statistical inference for regression when data are grouped into clusters, with regression model errors independent across clusters but correlated within clusters, when the number of clusters is large and default standard errors can greatly overstate estimator precision.
Abstract: We consider statistical inference for regression when data are grouped into clus- ters, with regression model errors independent across clusters but correlated within clusters. Examples include data on individuals with clustering on village or region or other category such as industry, and state-year dierences-in-dierences studies with clustering on state. In such settings default standard errors can greatly overstate es- timator precision. Instead, if the number of clusters is large, statistical inference after OLS should be based on cluster-robust standard errors. We outline the basic method as well as many complications that can arise in practice. These include cluster-specic �xed eects, few clusters, multi-way clustering, and estimators other than OLS.
3,236 citations
TL;DR: In the last two decades, much research has been done on the econometric and statistical analysis of such causal effects as discussed by the authors, which has reached a level of maturity that makes it an important tool in many areas of empirical research in economics, including labor economics, public finance, development economics, industrial organization, and other areas in empirical microeconomics.
Abstract: Many empirical questions in economics and other social sciences depend on causal effects of programs or policies. In the last two decades, much research has been done on the econometric and statistical analysis of such causal effects. This recent theoreti- cal literature has built on, and combined features of, earlier work in both the statistics and econometrics literatures. It has by now reached a level of maturity that makes it an important tool in many areas of empirical research in economics, including labor economics, public finance, development economics, industrial organization, and other areas of empirical microeconomics. In this review, we discuss some of the recent developments. We focus primarily on practical issues for empirical research- ers, as well as provide a historical overview of the area and give references to more technical research.
3,175 citations
References
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01 Jan 1878
TL;DR: The Red River of the North basin of the Philippines was considered a part of the Louisiana Purchase by the United States Department of Commerce in the 1939 Census Atlas of the United Philippines as discussed by the authors.
Abstract: 1 Includes drainage basin of Red River of the North, not a part of any accession, but in the past sometimes considered a part of the Louisiana Purchase. i Includes Baker, Canton, Enderbury, Rowland, Jarvis, Johnston, and Midway Islands; and also certain other outlying islands (21 square miles). 3 Commonwealth of the Philippines, Commission of the Census; 1939 Census, Census Atlas of the Philippines. Source: Department of Commerce, Bureau of the Census.
10,650 citations
TL;DR: The Elements of Econometrics as mentioned in this paper is a textbook for upper-level undergraduate and master's degree courses and may usefully serve as a supplement for traditional Ph.D. courses in economics.
Abstract: This classic text has proven its worth in university classrooms and as a tool kit in research--selling over 40,000 copies in the United States and abroad in its first edition alone. Users have included undergraduate and graduate students of economics and business, and students and researchers in political science, sociology, and other fields where regression models and their extensions are relevant. The book has also served as a handy reference in the "real world" for people who need a clear and accurate explanation of techniques that are used in empirical research.Throughout the book the emphasis is on simplification whenever possible, assuming the readers know college algebra and basic calculus. Jan Kmenta explains all methods within the simplest framework, and generalizations are presented as logical extensions of simple cases. And while a relatively high degree of rigor is preserved, every conflict between rigor and clarity is resolved in favor of the latter. Apart from its clear exposition, the book's strength lies in emphasizing the basic ideas rather than just presenting formulas to learn and rules to apply.The book consists of two parts, which could be considered jointly or separately. Part one covers the basic elements of the theory of statistics and provides readers with a good understanding of the process of scientific generalization from incomplete information. Part two contains a thorough exposition of all basic econometric methods and includes some of the more recent developments in several areas.As a textbook, "Elements of Econometrics" is intended for upper-level undergraduate and master's degree courses and may usefully serve as a supplement for traditional Ph.D. courses in econometrics. Researchers in the social sciences will find it an invaluable reference tool.A solutions manual is also available for teachers who adopt the text for coursework.Jan Kmenta is Professor Emeritus of Economics and Statistics, University of Michigan.
3,838 citations
Book•
01 Jan 1971
TL;DR: The emphasis is on simplification whenever possible, assuming the readers know college algebra and basic calculus, and Jan Kmenta explains all methods within the simplest framework, and generalizations are presented as logical extensions of simple cases.
Abstract: This classic text has proven its worth in university classrooms and as a tool kit in research--selling over 40,000 copies in the United States and abroad in its first edition alone. Users have included undergraduate and graduate students of economics and business, and students and researchers in political science, sociology, and other fields where regression models and their extensions are relevant. The book has also served as a handy reference in the "real world" for people who need a clear and accurate explanation of techniques that are used in empirical research.Throughout the book the emphasis is on simplification whenever possible, assuming the readers know college algebra and basic calculus. Jan Kmenta explains all methods within the simplest framework, and generalizations are presented as logical extensions of simple cases. And while a relatively high degree of rigor is preserved, every conflict between rigor and clarity is resolved in favor of the latter. Apart from its clear exposition, the book's strength lies in emphasizing the basic ideas rather than just presenting formulas to learn and rules to apply.The book consists of two parts, which could be considered jointly or separately. Part one covers the basic elements of the theory of statistics and provides readers with a good understanding of the process of scientific generalization from incomplete information. Part two contains a thorough exposition of all basic econometric methods and includes some of the more recent developments in several areas.As a textbook, "Elements of Econometrics" is intended for upper-level undergraduate and master's degree courses and may usefully serve as a supplement for traditional Ph.D. courses in econometrics. Researchers in the social sciences will find it an invaluable reference tool.A solutions manual is also available for teachers who adopt the text for coursework.Jan Kmenta is Professor Emeritus of Economics and Statistics, University of Michigan.
3,096 citations
TL;DR: In this paper, the authors proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects, and developed a satisfactory asymptotic theory for estimators of variance components.
Abstract: Recent developments promise to increase greatly the popularity of maximum likelihood (ml) as a technique for estimating variance components. Patterson and Thompson (1971) proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects. Miller (1973) developed a satisfactory asymptotic theory for ml estimators of variance components. There are many iterative algorithms that can be considered for computing the ml or reml estimates. The computations on each iteration of these algorithms are those associated with computing estimates of fixed and random effects for given values of the variance components.
2,440 citations
TL;DR: The authors analyzes several empirical examples to investigate the applicability of random effects models and the consequences of inappropriately using ordinary least squares (OLS) estimation in the presence of random group effects.
1,789 citations