Estimating and Testing Models with Many Treatment Levels and Limited Instruments
当工具变量有限且处理效应可能变化时，传统Hausman检验无法有效检验内生性；本文提出一种新的外生性检验，仅需一个有效工具变量即可使用，并通过三个实证例子展示其实用价值。
Empirical researchers interested in the causal effect of the endogenous regressor often use instrumental variables. When few valid instruments are available, they typically estimate restricted specifications that impose uniform per unit treatment effects, even when these effects are likely to vary. We show that in these cases, ordinary least squares and instrumental variables estimators identify different weighted averages of all per unit effects, so the traditional Hausman test is uninformative about endogeneity. We develop a new exogeneity test that works even when the true model cannot be estimated using IV methods as long as a single valid instrument is available. We revisit three recent empirical examples to demonstrate the practical value of our test. © 2015 The President and Fellows of Harvard College and the Massachusetts Institute of Technology