Heteroskedasticity-Robust Inference in Linear Regression Models with Many Covariates

We consider inference in linear regression models that is robust to heteroskedasticity and the presence of many control variables. When the number of control variables increases at the same rate as the sample size the usual heteroskedasticity-robust estimators of the covariance matrix are inconsistent. Hence, tests based on these estimators are size distorted even in large samples. An alternative covariance-matrix estimator for such a setting is presented that complements recent work by Cattaneo, Jansson and Newey (2018). We provide high-level conditions for our approach to deliver (asymptotically) size-correct inference as well as more primitive conditions for three special cases. Simulation results and an empirical illustration to inference on the union premium are also provided

Two-way models for gravity

© 2017 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Empirical models for dyadic interactions between n agents often feature agent-specific parameters. Fixed-effect estimators of such models generally have bias of order n-1, which is nonnegligible relative to their standard error. Therefore, confidence sets based on the asymptotic distribution have incorrect coverage. This paper looks at models with multiplicative unobservables and fixed effects. We derive moment conditions that are free of fixed effects and use them to set up estimators that are n-consistent, asymptotically normally distributed, and asymptotically unbiased. We provide Monte Carlo evidence for a range of models. We estimate a gravity equation as an empirical illustration

Testing Random Assignment to Peer Groups

Identification of peer effects is complicated by the fact that the individuals under study may self-select their peers. Random assignment to peer groups has proven useful to sidestep such a concern. In the absence of a formal randomization mechanism it needs to be argued that assignment is `as good as' random. This paper introduces a simple yet powerful test to do so. We provide theoretical results for this test and explain why it dominates existing alternatives. Asymptotic power calculations and an analysis of the assignment mechanism of players to playing partners in tournaments of the Professional Golfer's Association is used to illustrate these claims. Our approach can equally be used to test for the presence of peer effects. To illustrate this we test for the presence of peer effects in the classroom using kindergarten data collected within Project STAR. We find no evidence of peer effects once we control for classroom fixed effects and a set of student characteristics

Semiparametric Analysis of Network Formation

© 2018, American Statistical Association. We consider a statistical model for directed network formation that features both node-specific parameters that capture degree heterogeneity and common parameters that reflect homophily among nodes. The goal is to perform statistical inference on the homophily parameters while treating the node-specific parameters as fixed effects. Jointly estimating all parameters leads to incidental-parameter bias and incorrect inference. As an alternative, we develop an approach based on a sufficient statistic that separates inference on the homophily parameters from estimation of the fixed effects. The estimator is easy to compute and can be applied to both dense and sparse networks, and is shown to have desirable asymptotic properties under sequences of growing networks. We illustrate the improvements of this estimator over maximum likelihood and bias-corrected estimation in a series of numerical experiments. The technique is applied to explain the import and export patterns in a dense network of countries and to estimate a more sparse advice network among attorneys in a corporate law firm

A note on sufficiency in binary panel models

© 2017 Royal Economic Society. Consider estimating the slope coefficients of a fixed-effect binary-choice model from two-period panel data. Two approaches to semiparametric estimation at the regular parametric rate have been proposed: one is based on a sufficiency requirement, and the other is based on a conditional-median restriction. We show that, under standard assumptions, both conditions are equivalent

Instrumental-Variable Estimation of Gravity Equations

We present an instrumental-variable approach to estimate gravity equations. Our procedure accommodates the potential endogeneity of policy variables and is fully theory-consistent. It is based on the model in levels and accounts for multilateral resistance terms by means of importer and export fixed effects. The implementation is limited-information in nature, and so is silent on the form of the mechanism that drives the actual policy decisions. The procedure spawns specification tests for the validity of the instruments used as well as a test for exogeneity. We estimate gravity equations from five cross-sections of bilateral-trade data where the policy decision of interest is the engagement in a free trade agreement. We rely on the interaction of the countries in the pair with third-party trading partners to construct a credible instrumental variable based on the substantial transitivity in the formation of trade agreements that is observed in the data. This instrument is strongly correlated with the policy variable. Our point estimate of the average impact of a free trade agreement increases over the sampling period, starting at 61% and clocking o_ at a 117% increase in bilateral trade volume. Not correcting for endogeneity yields stable estimates of around 25%

Fixed-Effect Regressions on Network Data

This paper considers inference on fixed effects in a linear regression model estimated from network data. An important special case of our setup is the two-way regression model. This is a workhorse technique in the analysis of matched data sets, such as employer-employee or student-teacher panel data. We formalize how the structure of the network affects the accuracy with which the fixed effects can be estimated. This allows us to derive sufficient conditions on the network for consistent estimation and asymptotically-valid inference to be possible. Estimation of moments is also considered. We allow for general networks and our setup covers both the dense and sparse case. We provide numerical results for the estimation of teacher value-added models and regressions with occupational dummies

Estimating multivariate latent-structure models

© Institute of Mathematical Statistics, 2016. A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden Markov models. The key step to show identification is the joint diagonalization of a set of matrices in the same nonorthogonal basis. An estimator of the latent-structure model may then be based on a sample version of this joint-diagonalization problem. Algorithms are available for computation and we derive distribution theory. We further develop asymptotic theory for orthogonal-series estimators of component densities in mixture models and emission densities in hidden Markov models.Supported by European Research Council Grant ERC-2010-StG-0263107-ENMUH. Supported by Sciences Po’s SAB grant “Nonparametric estimation of finite mixtures.” Supported by European Research Council Grant ERC-2010-AdG-269693-WASP and by Economic and Social Research Council Grant RES-589-28-0001 through the Centre for Microdata Methods and Practice

Nonparametric estimation of non-exchangeable latent-variable models

We propose a two-step method to nonparametrically estimate multivariate models in which the observed outcomes are independent conditional on a discrete latent variable. Applications include microeconometric models with unobserved types of agents, regime-switching models, and models with misclassification error. In the first step, we estimate weights that transform moments of the marginal distribution of the data into moments of the conditional distribution of the data for given values of the latent variable. In the second step, these conditional moments are estimated as weighted sample averages. We illustrate the method by estimating a model of wages with unobserved heterogeneity on PSID data

Non-parametric estimation of finite mixtures from repeated measurements

SummaryThis paper provides methods to estimate finite mixtures from data with repeated measurements non-parametrically. We present a constructive identification argument and use it to develop simple two-step estimators of the component distributions and all their functionals. We discuss a computationally efficient method for estimation and derive asymptotic theory. Simulation experiments suggest that our theory provides confidence intervals with good coverage in small samples.</jats:p