中文摘要
我们基于两阶段最小二乘（2SLS）的偏误，开发了一种工具变量强度检验，该检验(1)将Stock和Yogo以及Sanderson和Windmeijer的检验推广至对异方差和自相关稳健，并且(2)将Montiel Olea和Pflueger针对单一内生回归元模型的稳健检验扩展至多个内生回归元。我们的检验既可以基于绝对偏误准则，也可以基于相对于最差情况基准的2SLS偏误。我们还开发了扩展方法，用于检验弱工具变量是否会导致单个2SLS系数产生偏误。在模拟中，我们的检验能够控制检验水平且具有功效，并且我们提供了高效的代码包以支持其实际应用。在遵循近期领先估计的背景下，我们演示了我们的检验程序在估计状态依赖型财政乘数中的应用。
Abstract
Abstract We develop a test for instrument strength based on the bias of two-stage least squares (2SLS) that (1) generalizes Stock and Yogo’s and Sanderson and Windmeijer’s tests to be robust to heteroskedasticity and autocorrelation, and (2) extends Montiel Olea and Pflueger’s robust test for models with a single endogenous regressor to multiple endogenous regressors. Our test can be based either on an absolute bias criterion or on the 2SLS bias relative to a worst-case benchmark. We also develop extensions to test whether weak instruments cause bias in individual 2SLS coefficients. In simulations, our test controls size and is powerful, and we provide efficient code packages for its practical implementation. We demonstrate our testing procedures in the context of the estimation of state-dependent fiscal multipliers, following recent leading estimates.