No abstract

We introduce two Stata commands implementing automatic manipulation tests based on density discontinuity, constructed using the results for local polynomial density estimators in Cattaneo, Jansson, and Ma (2017a). These new tests exhibit better size properties (and more power under additional assumptions) than other conventional approaches currently available in the literature. The first command, rddensity, implements manipulation tests based on a novel local polynomial density estimation technique that avoids pre-binning of the data (improving size properties) and allows for restrictions on other features of the model (improving power properties). The second command, rdbwdensity, implements several bandwidth selectors specifically tailored for the manipulation tests discussed herein. A companion R package with the same syntax and capabilities as rddensity and rdbwdensity is also provided.

Abstract.We derive the family of tests for a unit root with maximal power against a point alternative when an arbitrary number of stationary covariates are modeled with the potentially integrated series. We show that very large power gains are available when such covariates are available. We then derive tests which are simple to construct (involving the running of vector autoregressions) and achieve at a point the power envelopes derived under very general conditions. These tests have excellent properties in small samples. We also show that these are obvious and internally consistent tests to run when identifying structural VAR's using long run restrictions.

This paper considers the problem of conducting inference on the regression coefficient in a bivariate regression model with a highly persistent regressor. Gaussian asymptotic power envelopes are obtained for a class of testing procedures that satisfy a conditionality restriction. In addition, the paper proposes testing procedures that attain these power envelopes whether or not the innovations of the regression model are normally distributed. Copyright The Econometric Society 2006.

The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model speci…cation in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are obtained using high-dimensional approximations, where the number of included covariates are allowed to grow as fast as the sample size. We …nd that all of the usual versions of Eicker-White heteroskedasticity consistent standard error estimators for linear models are inconsistent under this asymptotics. We then propose a new heteroskedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroskedasticity of unknown form and the inclusion of possibly many covariates. We apply our …ndings to three settings: parametric linear models with many covariates, linear panel models with many …xed e¤ects, and semiparametric semi-linear models with many technical regressors. Simulation evidence consistent with our theoretical results is also provided. The proposed methods are also illustrated with an empirical application.