Working Paper: NBER ID: w17039
Authors: Lance Lochner; Enrico Moretti
Abstract: Many empirical microeconomic studies estimate econometric models that assume a single finite-valued discrete endogenous regressor (for example: different levels of schooling), exogenous regressors that are additively separable and enter the equation linearly; and coefficients (including per-unit treatment effects) that are homogeneous in the population. Empirical researchers interested in the causal effect of the endogenous regressor often use instrumental variables. When few valid instruments are available, researchers typically estimate restricted specifications that impose uniform per-unit treatment effects, even when these effects are likely to vary depending on the treatment level. In these cases, ordinary least squares (OLS) and instrumental variables (IV) estimators identify different weighted averages of all per-unit effects, so the traditional Hausman test (based on the restricted specification) is uninformative about endogeneity. Addressing this concern, we develop a new exogeneity test that compares the IV estimate from the restricted model with an appropriately weighted average of all per-unit effects estimated from the more general model using OLS. Notably, our test works even when the true model cannot be estimated using IV methods as long as a single valid instrument is available (e.g. a single binary instrument). We re-visit three recent empirical examples that examine the role of educational attainment on various outcomes to demonstrate the practical value of our test.
Keywords: Instrumental Variables; Causal Inference; Educational Attainment; Endogeneity
JEL Codes: C01; J0
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Educational attainment (I21) | Incarceration rates (K14) |
| Educational attainment (I21) | Health outcomes (I14) |
| OLS estimates (L00) | IV estimates (C26) |
| Educational attainment (I21) | Endogeneity issues for black men (J79) |
| Nonlinear relationship between educational attainment and incarceration (I21) | OLS and IV estimates yield different averages (C36) |