A New Asymptotic Theory for Heteroskedasticity Autocorrelation Robust Tests

Cornell University, Ithaca NY

Investigators

Abstract

One of the most widely used statistical tools in empirical social sciences is regression models. By its very nature, social science and economic data is non-experimental and this leads to a host of statistical issues that are not encountered with data generated from controlled experiments. In particular, in cross section models a common problem is non-constancy of error variances across observations (heteroskedasticity) while in time series regressions a common problem is serial correlation (correlation across errors). It is now a well known textbook result that in regression models with heteroskedasticity and/or serial correlation, ordinary least squares (OLS) estimation of regression parameters often yields good estimates (e.g. unbiased). The problem is that the usual formulas for standard errors are invalid. This means that hypothesis tests (e.g. tests of statistical significance) are also invalid. This fact has long been known in the econometrics literature and over the past 20 years there has been intensive research devoted to finding ways of computing standard errors that are valid in the presence of heteroskedasticity or serial correlation of unknown form. Such standard errors are very useful to applied practitioners because the form of heteroskedasticity or serial correlation is rarely known in practice. Standard errors valid for regressions with heteroskedasticity (White standard errors) are now widely implemented in statistical programs and are covered by undergraduate econometrics texts. The appeal of White standard errors is that they are easy to compute and work for very general forms of heteroskedasticity. In models with serial correlation, computing robust standard errors is more difficult in practice. The practical problem with these standard errors is that the practitioner is required to make choices of so-called tuning parameters. According to the standard asymptotic theory (approximation theory) these choices are, for the most part, arbitrary. This leaves room for one researcher to use one tuning parameter while another researcher uses a different one. These researchers could very likely draw different conclusions from the same regression model. Unfortunately, there is no established standard for the computation of serial correlation robust standard errors. (The statistical packages SAS and E-Views, for example, use different tuning parameters). This project develops a new asymptotic theory that explicitly captures, in a practical sense, the choice of tuning parameters. This new theory allows a systematic treatment of the tuning parameter choice and has the potential for developing a standard of practice for the computation of serial correlation robust standard errors. The research generated from this project will make inference in regression models more reliable and easier to implement for practitioners. This will lead to higher quality empirical studies in economics and other social sciences.