Working Paper: NBER ID: w17519
Authors: Michal Kolesár; Raj Chetty; John N. Friedman; Edward L. Glaeser; Guido W. Imbens
Abstract: We analyze linear models with a single endogenous regressor in the presence of many instrumental variables. We weaken a key assumption typically made in this literature by allowing all the instruments to have direct effects on the outcome. We consider restrictions on these direct effects that allow for point identification of the effect of interest. The setup leads to new insights concerning the properties of conventional estimators, novel identification strategies, and new estimators to exploit those strategies. A key assumption underlying the main identification strategy is that the product of the direct effects of the instruments on the outcome and the effects of the instruments on the endogenous regressor has expectation zero. We argue in the context of two specific examples with a group structure that this assumption has substantive content.
Keywords: No keywords provided
JEL Codes: C01; C2; C26; C36
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Instrumental variables (C36) | Outcome (Y60) |
| Instrumental variables (C36) | Endogenous regressor (C51) |
| Expectation of product of direct effects of instruments on Outcome and effects on Endogenous regressor = 0 (C36) | BTSLS and JIVE estimators consistent (C51) |
| Direct effects of instruments on Outcome (C26) | LIML estimator loses consistency (C51) |
| Direct effects of instruments uncorrelated with effects on Endogenous variable (C36) | Identification possible (Y50) |