Research
RESEARCH PAPERS
Title: Encompassing Tests for Nonparametric Regressions (Econometric Theory, forthcoming )
Authors: Elia Lapenta and Pascal Lavergne
Abstract: We set up a formal framework to characterize encompassing of nonparametric models through the L2 distance. We contrast it to previous literature on the comparison of nonparametric regression models. We then develop testing procedures for the encompassing hypothesis that are fully nonparametric. Our test statistics depend on kernel regression, raising the issue of bandwidth's choice. We investigate two alternative approaches to obtain a "small bias property" for our test statistics. We show the validity of a wild bootstrap method, and we illustrate the attractive features of our tests for small and moderate samples.
Title: A Bootstrap Specification Test for Semiparametric Models with Generated Regressors (submitted)
Author: Elia Lapenta
Abstract: This paper provides a specification test for semiparametric models with nonparametrically generated regressors. Such variables are not observed by the researcher but are nonparametrically identified and estimable. Applications of the test include models with endogenous regressors identified by control functions, semiparametric sample selection models, or binary games with incomplete information. The statistic is built from the residuals of the semiparametric model. A novel wild bootstrap procedure is shown to provide valid critical values. We consider nonparametric estimators with an automatic bias correction that makes the test implementable without undersmoothing. In simulations the test exhibits good small sample performances, and an application to women’s labor force participation decisions shows its implementation in a real data context.
Supplementary Material R files arXiv
Title: One-Step Nonparametric Instrumental Regression Using Smoothing Splines (submitted)
Authors: Jad Beyhum, Elia Lapenta, and Pascal Lavergne
Abstract: We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique regularization parameter. We derive uniform rates of the convergence for the estimator and its first derivative. We also address the issue of imposing monotonicity in estimation. Simulations confirm the good performances of our estimator compared to some popular two-step procedures. Our method yields economically sensible results when used to estimate Engel curves.
Title: Testing for Homogeneous Treatment Effects in Linear and Nonparametric Instrumental Variable Models (Econometric Reviews, forthcoming )
Authors: Jad Beyhum, Jean-Pierre Florens, Elia Lapenta, Ingrid Van Keilegom
Abstract: The hypothesis of homogeneous treatment effects is central to the instrumental variables literature. This assumption signifies that treatment effects are constant across all subjects. It allows to interpret instrumental variable estimates as average treatment effects over the whole population of the study. When this assumption does not hold, the bias of instrumental variable estimators can be larger than that of naive estimators ignoring endogeneity. This paper develops two tests for the assumption of homogeneous treatment effects when the treatment is endogenous and an instrumental variable is available. The tests leverage a covariable that is (jointly with the error terms) independent of a coordinate of the instrument. This covariate does not need to be exogenous. The first test assumes that the potential outcomes are linear in the regressors and is computationally simple. The second test is nonparametric and relies on Tikhonov regularization. The treatment can be either discrete or continuous. We show that the tests have asymptotically correct level and asymptotic power equal to one against a range of alternatives. Simulations demonstrate that the proposed tests attain excellent finite sample performances. The methodology is also applied to the evaluation of returns to schooling and the effect of price on demand in a fish market.
Title: Partly Linear Instrumental Variables Regression without Smoothing on the Instruments (R&R to TEST)
Authors: Jean-Pierre Florens and Elia Lapenta
Abstract: We consider a semiparametric partly linear model identified by instrumental variables. We propose an estimation method that does not smooth on the instruments and we extend the Landweber-Fridman regularization scheme to the estimation of this semiparametric model. We then show the asymptotic normality of the parametric estimator and obtain the convergence rates for the nonparametric estimator. Our estimator that does not smooth on the instruments coincides with a typical estimator that does smooth on the instruments but keeps the respective bandwidth fixed as the sample size increases. We propose a data driven method for the selection of the regularization parameter, and in a simulation study we show the attractive performance of our estimators.
Title: Testing Bayesian-Nash Behavior in Binary Games with Incomplete Information and Correlated Types
Authors: Elia Lapenta and Pascal Lavergne
Abstract: We provide a test to check if the distribution of the observed data can be rationalized by a unique Bayesian-Nash equilibrium of a binary game with incomplete information, where agents' types can be mutually correlated. The hypothesis tested is often imposed in game-theoretical models and is key to identify the fundamentals of the game. The game structure is nonparametrically specified. Since the null asymptotic distribution of the statistic depends on unknown features of the data, we obtain the critical value by a novel multinomial bootstrap and prove its validity. This scheme resamples the observations by imposing that a unique Bayesian-Nash equilibrium is played. A Monte Carlo experiment shows the good small-sample performance of the test.