A New Asymptotic Theory for Heteroskedasticity Autocorrelation Robust Tests

回归模型是实证社会科学中使用最广泛的统计工具之一。就其本质而言，社会科学和经济数据是非实验性的，这导致了大量的统计问题，而这些问题是由受控实验产生的数据所没有遇到的。特别是，在横截面模型中，一个常见的问题是不同观测值的误差方差不恒定（异方差），而在时间序列回归中，一个常见的问题是序列相关（误差之间的相关）。现在一个众所周知的教科书结果是，在异方差和/或序列相关的回归模型中，回归参数的普通最小二乘（OLS）估计通常会产生良好的估计（例如无偏）。问题是通常的标准误差公式是无效的。这意味着假设检验（例如统计显著性检验）也是无效的。这一事实在计量经济学文献中早已为人所知，在过去的20年里，人们进行了大量的研究，致力于寻找在异方差或未知形式的序列相关存在时有效的计算标准误差的方法。这种标准误差对应用从业者非常有用，因为异方差或序列相关的形式在实践中很少为人所知。异方差回归的有效标准误差（白标准误差）现在广泛应用于统计程序中，并涵盖在本科计量经济学教材中。怀特标准误差的吸引力在于它们易于计算，并且适用于非常一般的异方差形式。在序列相关模型中，鲁棒标准误差的计算在实际应用中较为困难。这些标准误差的实际问题是，从业者需要选择所谓的调优参数。根据标准的渐近理论（近似理论），这些选择在很大程度上是任意的。这为一个研究人员使用一个调优参数而另一个研究人员使用不同的参数留下了空间。这些研究人员很可能从相同的回归模型中得出不同的结论。遗憾的是，对于序列相关鲁棒标准误差的计算，目前还没有确定的标准。（例如，统计软件包SAS和E-Views使用不同的调优参数）。这个项目发展了一个新的渐近理论，它在实际意义上明确地捕获了调谐参数的选择。这一新理论允许对调谐参数的选择进行系统的处理，并有可能为序列相关鲁棒标准误差的计算制定一个实践标准。从这个项目中产生的研究将使回归模型中的推理更可靠，更容易为从业者实现。这将导致经济学和其他社会科学领域更高质量的实证研究。

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.