Jeffrey M. Wooldridge

Michigan State University | MSU · Department of Economics

We reconsider the pros and cons of using a linear model to approximate partial effects on a response probability for a binary outcome. In particular, we study the ramp model in Horrace and Oaxaca (2006), but focus on average partial effects (APE) rather than the parameters of the underlying linear index. We use existing theoretical results to verif...

The recent thought-provoking paper by Hansen [2022, Econometrica] proved that the Gauss-Markov theorem continues to hold without the requirement that competing estimators are linear in the vector of outcomes. Despite the elegant proof, it was shown by the authors and other researchers that the main result in the earlier version of Hansen's paper do...

For the panel data case where cross-sectional units are nested within higher-level groups, and there are many such groups, we propose a test that allows one to determine whether controlling for fixed effects at the more aggregate level is sufficient. The alternative is that one should allow for fixed effects at the unit level. The regression-based...

For the panel data case where cross-sectional units are nested within higher-level groups, and there are many such groups, we propose a test that allows one to determine whether controlling for fixed effects at the more aggregate level is sufficient. The alternative is that one should allow for fixed effects at the unit level. The regression-based...

When observing spatial data, what standard errors should we report? With the finite population framework, we identify three channels of spatial correlation: sampling scheme, assignment design, and model specification. The Eicker-Huber-White standard error, the cluster-robust standard error, and the spatial heteroskedasticity and autocorrelation con...

I derive simple, flexible strategies for difference-indifferences settings where the nature of the response variable may warrant a nonlinear model. In addition to covering the case of common treatment timing, I allow for staggered interventions, with and without covariates. Under an index version of parallel trends, I show that average treatment ef...

We revisit the problem of estimating the local average treatment effect (LATE) and the local average treatment effect on the treated (LATT) when control variables are available, either to render the instrumental variable (IV) suitably exogenous or to improve precision. Unlike previous approaches, our doubly robust (DR) estimation procedures use qua...

For the panel data case where cross-sectional units are nested within higher-level groups, and there are many such groups, we propose a test that allows one to determine whether controlling for fixed effects at the more aggregate level is sufficient. The alternative is that one should allow for fixed effects at the unit level. The regression-based...

In this paper we study the finite sample and asymptotic properties of various weighting estimators of the local average treatment effect (LATE), several of which are based on Abadie (2003)'s kappa theorem. Our framework presumes a binary endogenous explanatory variable ("treatment") and a binary instrumental variable, which may only be valid after...

This paper suggests a doubly robust method of estimating potential outcome means for multivariate fractional outcomes when the treatment of interest is unconfounded and can take more than two values. The method involves using a multinomial logit conditional mean estimated using a propensity score weighted quasi-maximum-likelihood in the linear expo...

We study estimation of factor models in a fixed-T panel data setting and significantly relax the common correlated effects (CCE) assumptions pioneered by Pesaran (2006) and used in dozens of papers since. In the simplest case, we model the unobserved factors as functions of the cross-sectional averages of the explanatory variables and show that thi...

We examine the conditional logit estimator for binary panel data models with unobserved heterogeneity. A key assumption used to derive the conditional logit estimator is conditional serial independence (CI), which is problematic when the underlying innovations are serially correlated. A Monte Carlo experiment suggests that the conditional logit est...

I establish the equivalence between the two-way fixed effects (TWFE) estimator and an estimator obtained from a pooled ordinary least squares regression that includes unit-specific time averages and time-period specific cross-sectional averages, which I call the two-way Mundlak (TWM) regression. This equivalence furthers our understanding of the an...

The second Asia-Pacific edition of Introductory Econometrics is designed specifically for introductory second-year students. The second edition has the following new features: (i) expanded content in Part 3 on time series (ii) local data sets provide a practical approach to teaching this highly mathematical subject and demonstrate the application...

We provide a systematic approach in obtaining an estimator asymptotically more efficient than the popular fixed effects Poisson (FEP) estimator for panel data models with multiplicative heterogeneity in the conditional mean. In particular, we derive the optimal instrumental variables under appealing "working" second moment assumptions that allow un...

In the context of random sampling, we show that linear full (separate) regression adjustment (FRA) on the control and treatment groups is, asymptotically, no less efficient than both the simple difference-in-means estimator and the pooled regression adjustment estimator; with heterogeneous treatment effects, FRA is usually strictly more efficient....

We study efficiency improvements in estimating a vector of potential outcome means using linear regression adjustment when there are more than two treatment levels. We show that using separate regression adjustments for each assignment level is never worse, asymptotically, than using the subsample averages. We also show that separate regression adj...

We study efficiency improvements in estimating a vector of potential outcome means using linear regression adjustment when there are more than two treatment levels. We show that using separate regression adjustments for each assignment level is never worse, asymptotically, than using the subsample averages. We also show that separate regression adj...

For estimating the parameters of a linear conditional mean, I show that the quasi-maximum likelihood estimator (QMLE) obtained under the nominal assumption that the error term is independent of the explanatory variables with a logistic distribution is consistent provided the conditional distribution of the error term is symmetric. No other restrict...

We propose a simple procedure based on an existing “debiased” l1-regularized method for inference of the average partial effects (APEs) in approximately sparse probit and fractional probit models with panel data, where the number of time periods is fixed and small relative to the number of cross-sectional observations. Our method is computationally...

Nations, states, and districts must choose among an array of different approaches to measuring school effectiveness in implementing their accountability policies, and the choice can be difficult because different approaches yield different results. This study compares two approaches to computing school effectiveness: a “beating the odds” type appro...

We propose a generalized method of moments (GMM) estimator, where our specific moment conditions, where our specific moment conditions ensure that the GMM estimator is asymptotically at least as efficient as ordinary least squares (OLS) and whatever competing weighted least squares (WLS) we wish to consider. With a popular exponential model of hete...

This paper shows how the correlated random effects approach can be extended to linear panel data models when instrumental variables are needed and the panel is unbalanced. We obtain the algebraic equivalence between the fixed effects two stage least squares (FE2SLS) estimator and a pooled 2SLS (P2SLS) estimator on a transformed equation. This equiv...

We extend Vuong’s (1989) model-selection statistic to allow for complex survey samples. As a further extension, we use an M-estimation setting so that the tests apply to general estimation problems – such as linear and nonlinear least squares, Poisson regression and fractional response models, to name just a few – and not only to maximum likelihood...

In this paper, we study estimation of nonlinear models with cross sectional data using two-step generalized estimating equations (GEE) in the quasi-maximum likelihood estimation (QMLE) framework. In the interest of improving efficiency, we propose a grouping estimator to account for the potential spatial correlation in the underlying innovations. W...

Despite little attention or exposure in the evaluation literature, the two SAS® EVAAS®models for estimating teacher effectiveness are used by several states and districts, in some cases for high stakes policies regarding teacher tenure, retention, or incentive pay. The EVAAS approach involves using one of two distinct models, the Multivariate Respo...

A regression meta-analysis is a statistical summary of results from a set of empirical studies. While, a meta-analysis is typically used to drawn inferences regarding the collective insights from an empirical literature, a regression meta-analysis can also be used to predict outcomes as a substitute for the conduct of a new study. Within the nonmar...

In empirical work in economics it is common to report standard errors that account for clustering of units. Typically, the motivation given for the clustering adjustments is that unobserved components in outcomes for units within clusters are correlated. However, because correlation may occur across more than one dimension, this motivation makes it...

In empirical work it is common to estimate parameters of models and report associated standard errors that account for "clustering" of units, where clusters are defined by factors such as geography. Clustering adjustments are typically motivated by the concern that unobserved components of outcomes for units within clusters are correlated. However,...

We consider estimating binary response models on an unbalanced panel, where the outcome of the dependent variable may be missing due to nonrandom selection, or there is self-selection into a treatment. In the present paper, we first consider estimation of sample selection models and treatment effects using a fully parametric approach, where the err...

Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard errors? In practice, researchers typically assume that the sample is randomly drawn from a large population of i...

Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard errors? In practice, researchers typically assume that the sample is randomly drawn from a large population of i...

If treated as a single economy, the European Union is the largest in the world, with an estimated GDP of over 14 trillion euros. Despite its size, European economic policy has often lagged behind the rest of the world in its ability to generate growth and innovation. Much of the European economic research itself often trails behind that of the USA,...

When large-scale accidents cause catastrophic damage to natural or cultural resources, government and industry are faced with the challenge of assessing the extent of damages and the magnitude of restoration that is warranted. Although market transactions for privately owned assets provide information about how valuable they are to the people invol...

We use a particular quasi-generalized least squares (QGLS) approach to study a linear regression model with spatially correlated error terms. The QGLS estimator is consistent, asymptotically normal, computationally easier than GLS, and it appears to not lose much efficiency. A variance–covariance estimator for QGLS, which is robust to heteroskedast...

Econometrics is the combined study of economics and statistics and is an ‘applied’ unit. It is increasingly becoming a core element in finance degrees at upper levels. This first local adaptation of Wooldridge’s text offers a version of Introductory Econometrics with a structural redesign that will better suit the market along with Asia-Pacific ex...

In this paper we study doubly robust estimators of various average and quantile treatment effects under unconfoundedness; we also consider an application to a setting with an instrumental variable. We unify and extend much of the recent literature by providing a very general identification result which covers binary and multi-valued treatments; unn...

We propose a simple procedure based on existing “debiased” versions of the l_{1}-regularized method for inference of the average partial effects (APEs) in approximately sparse probit and fractional probit models with panel data where the number of time periods is fixed and small relative to the number of cross-sectional observations. Our method is...

We derive simple, multi-step estimation methods for a linear model with heterogeneous coefficients when there are both continuous and discrete endogenous explanatory variables. We consider both cross-sectional and panel data settings. When we extend our model to panel data, we use the Chamberlain-Mundlak device to allow heterogeneity to be correlat...

We compare three different approaches to obtaining partial effects in binary response models. Among the three approaches, we maintain that the average structural function (ASF) due to Blundell and Powell (2003, 2004) defines the marginal effect of primary interest, for it is based on the unconditional marginal distribution of the structural error....

This paper provides an overview of control function (CF) methods for solving the problem of endogenous explanatory variables (EEVs) in linear and nonlinear models. CF methods often can be justifi ed in situations where "plug- in" approaches are known to produce inconsistent estimators of parameters and partial effects. Usually, CF approaches requir...

Empirical Bayes’s (EB) estimation has become a popular procedure used to calculate teacher value added, often as a way to make imprecise estimates more reliable. In this article, we review the theory of EB estimation and use simulated and real student achievement data to study the ability of EB estimators to properly rank teachers. We compare the p...

School districts and state departments of education frequently must choose among a variety of methods to estimate teacher quality. This article investigates the consequences of some of these choices. We examine estimates derived from student growth percentile and commonly used value-added models. Using simulated data, we examine how well the estima...

We study the properties of two specification tests that have been applied to a variety of estimators in the context of value-added measures (VAMs) of teacher and school quality: the Hausman test for choosing between student-level random and fixed effects, and a test for feedback (sometimes called a “falsification test”). We discuss theoretical prop...

I propose a quasi-maximum likelihood framework for estimating nonlinear models with continuous or discrete endogenous explanatory variables. Joint and two-step estimation procedures are considered. The joint procedure is a quasi-limited information maximum likelihood procedure, as one or both of the log likelihoods may be misspecified. The two-step...

The federal government's Race to the Top competition has promoted the adoption of test-based performance measures as a component of teacher evaluations throughout many states, but the validity of these measures has been controversial among researchers and widely contested by teachers' unions. A key concern is the extent to which nonrandom sorting o...

The purpose of this paper is to help empirical economists think through when and how to weight the data used in estimation. We start by distinguishing two purposes of estimation: to estimate population descriptive statistics and to estimate causal effects. In the former type of research, weighting is called for when it is needed to make the analysi...

This paper analyzes spatial Probit models for cross sectional dependent data in a binary choice context. Observations are divided by pairwise groups and bivariate normal distributions are specified within each group. Partial maximum likelihood estimators are introduced and they are shown to be consistent and asymptotically normal under some regular...

We investigate whether commonly used value-added estimation strategies can produce accurate estimates of teacher effects. We estimate teacher effects in simulated student achievement data sets that mimic plausible types of student grouping and teacher assignment scenarios. No one method accurately captures true teacher effects in all scenarios, and...

I propose a general, simple approach to recovering an unconditional heterogeneity distribution when a conditional distribution has been estimated. The approach can be applied to cross section models and panel data models-both static and dynamic-with unobserved heterogeneity.

April 1990. -- August 1989. Latest revision: April 1990.--3rd prelim. page

We thank the editor M. Hashem Pesaran and three anonymous referees for their useful comments. 1 Summary We propose a new method for estimating dynamic panel data models with selection. The method uses backward substitution for the lagged dependent variable, which leads to an estimating equation that requires correcting for contemporaneous selection...

In this talk, I will discuss ways of using Stata to fit fractional response models when explanatory variables are not exogenous. Two questions are of primary concern: First, how does one account for endogenous explanatory variables, both continuous and discrete, when the response variable is fractional and may take values at the corners? Second, ho...

We consider estimation of panel data models with sample selection when the equation of interest contains endogenous explanatory variables as well as unobserved heterogeneity. Assuming that appropriate instruments are available, we propose several tests for selection bias and two estimation procedures that correct for selection in the presence of en...

In the common case where polynomial approximations are used for unknown functions, I show how proxy variable approaches to controlling for unobserved productivity, proposed by Olley and Pakes [Olley, S. and Pakes, A., 1996. The dynamics of productivity in the telecommunications equipment industry. Econometrica 64, 1263-1298.] and Levinsohn and Petr...

The paper focuses on satisfaction with income and proposes a utility model built on two value systems, the `Ego' system - described as one own income assessment relatively to one own past and future income - and the `Alter' system - described as one own income assessment relatively to a reference group. We show how the union of these two value syst...

The Asymptotic Power of RESET for Detecting Omitted Variables - Volume 12 Issue 1 - Jeffrey Wooldridge

Glossary Definition of the Subject Introduction Overview of Linear Panel Data Models Sequentially Exogenous Regressors and Dynamic Models Unbalanced Panel Data Sets Nonlinear Models Future Directions Bibliography

I propose some strategies for allowing unobserved,heterogeneity to be correlated with observed covariates and sample selection for unbalanced,panels. The methods,are extensions of the Chamberlain-Mundlak approach for balanced panels. Even for nonlinear models, in many cases the estimators can be implemented using standard software. The framework,su...

I show that for a linear model and estimating a coefficient on an endogenous explanatory variable, adding covariates that that satisfy instrumental variables assumptions increases the amount of inconsistency. A special case is an endogenous binary treatment and estimating a constant treatment effect when matching on covariates that satisfy instrume...

This article provides an overview of difference-in-differences estimation, starting with a review of the basic methodology, discussing in some detail recent advances in inference, and concluding with new methods for estimating treatment effects in various nonlinear and semiparametric models.

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 theoretical literature has built on, and combined features of, earlier work in both the statistics and...

This paper evaluates a pilot program run by a company called OPOWER, previously known as Positive Energy, to mail home energy reports to residential utility consumers. The reports compare a household’s energy use to that of its neighbors and provide energy conservation tips. Using data from randomized natural field experiment at 80,000 treatment an...

Based on the empirical firm growth literature and on heterogeneous (microeconomic) adjustment models, this paper empirically investigates the impact of European industry fluctuations and domestic business cycles on the growth performance of European firms. Since the implementation of the Single Market program the EU 27 member countries share a comm...

The analysis of events involving nonnegative integer counts has a long and distinguished history in mathematical statistics. Stigler (1986, chapter 5) contains an interesting discussion of early uses of the Poisson distribution for analyzing counts. Most of the early applications focused on unconditional univariate analysis, and the primary interes...

I propose a general framework for instrumental variables estimation of the average treatment effect in the correlated random coefficient model, focusing on the case where the treatment variable has some discreteness. The approach involves adding a particular function of the exogenous variables to a linear model containing interactions in observable...

We provide a set of conditions sufficient for consistency of a general class of fixed effects instrumental variables (FE-IV) estimators in the context of a correlated random coefficient panel data model, where one ignores the presence of individual-specific slopes. We discuss cases where the assumptions are met and violated. Monte Carlo simulations...