Volume 5, Issue 1

We study the properties of the quantile regression estimator when data are sampled from independent and identically distributed clusters, and show that the estimator is consistent and asymptotically normal even when there is intra-cluster correlation. A consistent estimator of the covariance matrix of the asymptotic distribution is provided, and we propose a specification test capable of detecting the presence of intra-cluster correlation. A small simulation study illustrates the finite sample performance of the test and of the covariance matrix estimator.

We interpret an ecological inference model as a treatment effects model in which the outcomes of interest and the conditional covariates come from separate datasets. In this setting, the counterfactual distributions and policy parameters of interest are only partially identified under a selection on observables assumption. In this paper, we provide estimation and inference procedures for structural prediction and counterfactual analysis in such models. We also illustrate the procedures with an application to US presidential elections.

Count data regressions are an important tool for empirical analyses ranging from analyses of patent counts to measures of health and unemployment. Along with negative binomial, Poisson panel regressions are a preferred method of analysis because the Poisson conditional fixed effects maximum likelihood estimator (PCFE) and its sandwich variance estimator are consistent even if the data are not Poisson-distributed, or if the data are correlated over time. Analyses of counts may however also be affected by correlation in the cross-section. For example, patent counts or publications may increase across related research fields in response to common shocks. This paper shows that the PCFE and its sandwich variance estimator are consistent in the presence of such dependence in the cross-section – as long as spatial dependence is time-invariant. We develop a test for time-invariant spatial dependence and provide code in STATA and MATLAB to implement the test.

Whether interested in the differential impact of a particular factor in various institutional settings or in the heterogeneous effect of policy or random experiment, the empirical researcher confronts a problem if the factor of interest is correlated with an omitted variable. This paper presents the circumstances under which it is possible to arrive at a consistent estimate of the mentioned effect. We find that if the source of heterogeneity and omitted variable are jointly independent of policy or treatment, then the OLS estimate on the interaction term between the treatment and endogenous factor turns out to be consistent.

This paper studies the connections among the asymmetric Laplace probability density (ALPD), maximum likelihood, maximum entropy and quantile regression. We show that the maximum likelihood problem is equivalent to the solution of a maximum entropy problem where we impose moment constraints given by the joint consideration of the mean and median. The ALPD score functions lead to joint estimating equations that delivers estimates for the slope parameters together with a representative quantile. Asymptotic properties of the estimator are derived under the framework of the quasi maximum likelihood estimation. With a limited simulation experiment we evaluate the finite sample properties of our estimator. Finally, we illustrate the use of the estimator with an application to the US wage data to evaluate the effect of training on wages.

Parametric (polynomial) models are popular in research employing regression discontinuity designs and are required when data are discrete. However, researchers often choose a parametric model based on data inspection or pretesting. These approaches lead to standard errors and confidence intervals that are too small because they do not incorporate model uncertainty. I propose using Frequentist model averaging to incorporate model uncertainty into parametric models. My Monte Carlo experiments show that Frequentist model averaging leads to mean square error and coverage probability improvements over pretesting. An application to [Lee, D. S. 2008. “Randomized Experiments From Non-Random Selection in US House Elections.” Journal of Econometrics 142 (2): 675–697.] shows how this approach works in practice, and how conventionally selected models may not be ideal.

This paper describes and implements a simple partial solution to the most common problem in applied microeconometrics: estimating a linear causal effect with a potentially endogenous explanatory variable and no suitable instrumental variables. Empirical researchers faced with this situation can either assume away the endogeneity or accept that the effect of interest is not identified. This paper describes a middle ground in which the researcher assumes plausible but nontrivial restrictions on the correlation between the variable of interest and relevant unobserved variables relative to the correlation between the variable of interest and observed control variables. Given such relative correlation restrictions, the researcher can then estimate informative bounds on the effect and assess the sensitivity of conventional estimates to plausible deviations from exogeneity. Two empirical applications demonstrate the potential usefulness of this method for both experimental and observational data.

We present an algorithm to estimate the two-way fixed effect linear model. The algorithm relies on the Frisch-Waugh-Lovell theorem and applies to ordinary least squares (OLS), two-stage least squares (TSLS) and generalized method of moments (GMM) estimators. The coefficients of interest are computed using the residuals from the projection of all variables on the two sets of fixed effects. Our algorithm has three desirable features. First, it manages memory and computational resources efficiently which speeds up the computation of the estimates. Second, it allows the researcher to estimate multiple specifications using the same set of fixed effects at a very low computational cost. Third, the asymptotic variance of the parameters of interest can be consistently estimated using standard routines on the residualized data.

This paper investigates recent developments in the literature on nonparametric instrumental variables estimation and considers the practical importance of the features of these estimators in the context of typically applied econometric models. Our primary focus is on the estimation of econometric models with endogenous regressors, and their marginal effects, without a known functional form. We develop an estimator for the marginal effects and investigate its finite sample performance. We show that when instruments are weak, in the classic sense, the nonparametric estimates of the marginal effect outperforms the classic two-stage least squares estimator, even when the model is correctly specified. When the instruments are strong, we show that the nonparametric estimator for the partial effects is still effective compared to the two-stage least squares estimator even as the number of IVs increases. We also investigate bandwidth choice and find that a rule-of-thumb bandwidth performs relatively well. Whereas cross-validation leads to a better fit when the number of instruments is small, as the number of instruments increases the rule-of-thumb standard actually results in better model fit. In an empirical application we estimate the work-horse aggregate logit demand model, discuss the required nonparametric identification properties, and document the differences between nonparametric and parametric specifications on the estimation of demand elasticities.

Given the popularity of nonparametric methods in applied econometric research, it is beneficial if students have exposure to these methods. We provide a simple, heuristic overview that can be used to discuss smoothing and nonparametric density and regression estimation suitable for an undergraduate econometrics class. We make connections to existing methods known to students (e.g. weighted least-squares through the idea of local weighting) which allows easy access to these methods. Examples are given as well as a discussion of available methods across an array of statistical software to fit the needs of educators.