This paper studies robust inference methods for nonlinear moment restriction models with weakly identified parameters in time series contexts+ Our methods are based on generalized empirical likelihood with kernel smoothing+ The proposed test statistics, which follow the standard x 2 limiting distributions, are robust to weak identification and dependent data+
Abstract. Abadie and Imbens (2008) showed that the naive bootstrap is not asymptotically valid for a matching estimator of the average treatment effect with a fixed number of matches. In this article, we propose asymptotically valid inference methods for matching estimators based on the weighted bootstrap. The key is to construct bootstrap counterparts by resampling based on certain linear forms of the estimators.Our weighted bootstrap is applicable for the matching estimators of both the average treatment effect and its counterpart for the treated population. Also, by incorporating a bias correction method in Abadie and Imbens (2011), our method can be asymptotically valid even for matching based on a vector of covariates. A simulation study indicates that the weighted bootstrap method is favorably comparable with the asymptotic normal approximation by Abadie and Imbens (2006). As an empirical illustration, we apply the proposed method to the National Supported Work data.
Continuity or discontinuity of probability density functions of data often plays a fundamental role in empirical economic analysis. For example, for identification and inference of causal effects in regression discontinuity designs it is typically assumed that the density function of a conditioning variable is continuous at a cutoff point that determines assignment of a treatment. Also, discontinuity in density functions can be a parameter of economic interest, such as in analysis of bunching behaviors of taxpayers. In order to facilitate researchers to conduct valid inference for these problems, this paper extends the binning and local likelihood approaches to estimate discontinuity of density functions and proposes empirical likelihood-based tests and confidence sets for the discontinuity.In contrast to the conventional Wald-type test and confidence set using the binning estimator, our empirical likelihood-based methods (i) circumvent asymptotic variance estimation to construct the test statistics and confidence sets; (ii) are invariant to nonlinear transformations of the parameters of interest; (iii) offer confidence sets whose shapes are automatically determined by data; and (iv) admit higher-order refinements, so-called Bartlett corrections. First-and second-order asymptotic theories are developed. Simulations demonstrate the superior finite sample behaviors of the proposed methods. In an empirical application, we assess the identifying assumption of no manipulation of class sizes in the regression discontinuity design studied by Angrist and Lavy (1999).
Abstract. This paper examines asymptotic properties of local M-estimators under three sets of high-level conditions. These conditions are sufficiently general to cover the minimum volume predictive region, conditional maximum score estimator for a panel data discrete choice model, and many other widely used estimators in statistics and econometrics. Specifically, they allow for discontinuous criterion functions of weakly dependent observations, which may be localized by kernel smoothing and contain nuisance parameters whose dimension may grow to infinity. Furthermore, the localization can occur around parameter values rather than around a fixed point and the observation may take limited values, which leads to set estimators. Our theory produces three different nonparametric cube root rates and enables valid inference for the local M-estimators, building on novel maximal inequalities for weakly dependent data. Our results include the standard cube root asymptotics as a special case. To illustrate the usefulness of our results, we verify our conditions for various examples such as the Hough transform estimator with diminishing bandwidth, maximum score-type set estimator, and many others.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.