A New Asymptotic Theory for Heteroskedasticity Autocorrelation Robust Tests

异方差自相关稳健检验的新渐近理论

• 批准号: 0095211
• 负责人: Timothy Vogelsang
• 金额: $ 23万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-04-01 至 2004-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0095211&HistoricalAwards=false
• 关键词: New; Asymptotic; Theory; Heteroskedasticity; Autocorrelation

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.

经验社会科学中使用最广泛的统计工具之一是回归模型。就其本质而言，社会科学和经济数据是非实验性的，这导致了许多统计问题，这些问题不会与受控实验产生的数据遇到。特别是，在横截面模型中，一个常见的问题是跨观测值（异性恋）的误差方差的不构度，而在时间序列回归中，常见问题是序列相关性（跨误差相关）。现在，这是一个众所周知的教科书结果，在具有异方差性和/或串行相关性的回归模型中，回归参数的普通最小二乘（OLS）估计通常会产生良好的估计值（例如，无偏见）。问题在于，标准错误的通常公式无效。这意味着假设检验（例如统计显着性的检验）也无效。这一事实在计量经济学文献中一直是已知的，在过去的20年中，有大量的研究致力于寻找计算标准误差的方法，这些误差在存在异性恋或串行相关性的情况下有效的标准误差。这种标准误差对应用的从业人员非常有用，因为在实践中，异方差或串行相关性的形式很少知道。对于异性疾病的回归（白色标准错误）有效的标准错误现在已在统计程序中广泛实现，并被本科计量经济学文本所涵盖。白色标准错误的吸引力在于，它们易于计算并为异性恋的非常普遍的形式工作。在具有串行相关的模型中，计算鲁棒标准误差在实践中更加困难。这些标准错误的实际问题在于，从业人员必须选择所谓的调整参数。根据标准的渐近理论（近似理论），这些选择在大多数情况下是任意的。这为一个研究人员提供了一个调音参数的空间，而另一个研究人员则使用另一个研究人员。这些研究人员很可能会从同一回归模型中得出不同的结论。不幸的是，尚无确定计算串行相关性鲁棒标准误差的标准。 （例如，统计软件包SAS和电子视图使用不同的调谐参数）。该项目开发了一种新的渐近理论，该理论从实际意义上明确捕获了调谐参数的选择。 这种新理论允许对调谐参数选择进行系统处理，并具有为计算串行相关性鲁棒标准误差的实践标准的潜力。 该项目产生的研究将使回归模型更可靠，更易于实施从业者。 这将导致在经济学和其他社会科学方面进行更高质量的经验研究。