Granular Instrumental Variables

Ecological Inferencewith Instrumental Variables

This note observes that instrumental variables techniques are useful not only for estimating causal effects, but that they simultaneously solve the ecological inference problem. ∗Correspondence can be addressed to the author at MEDS Department, Kellogg School of Management, 2001 Sheridan Rd, Evanston, IL 60208, or by email: [email protected]. The ecological inference problem i...

Mediating Instrumental Variables

Averaged Instrumental Variables Estimators

We develop averaged instrumental variables estimators as a way to deal with many weak instruments. We propose a weighted average of the preliminary k-class estimators, where each estimator is obtained using different subsets of the available instrumental variables. The averaged estimators are shown to be consistent and to satisfy asymptotic normality. Furthermore, its approximate mean squared e...

Generalized Instrumental Variables

This paper concerns the assessment of direct causal effects from a combination of: (i) non­ experimental data, and (ii) qualitative do­ main knowledge. Domain knowledge is en­ coded in the form of a directed acyclic graph (DAG), in which all interactions are assumed linear, and some variables are presumed to be unobserved. We provide a generalization of the well-known method of Instrumental Var...

Estimation with Many Instrumental Variables∗

Using many valid instrumental variables has the potential to improve efficiency but makes the usual inference procedures inaccurate. We give corrected standard errors, an extension of Bekker (1994) to nonnormal disturbances, that adjust for many instruments. We find that this adujstment is useful in empirical work, simulations, and in the asymptotic theory. Use of the corrected standard errors ...