Estimating average marginal effects in nonseparable structural systems

We provide nonparametric estimators of derivative ratio-based average marginal effects of an endogenous cause, X, on a response of interest, Y , for a system of recursive structural equations. The system need not exhibit linearity, separability, or monotonicity. Our estimators are local indirect least squares estimators analogous to those of Heckman and Vytlacil (1999, 2001) who treat a latent index model involving a binary X. We treat the traditional case of an observed exogenous instrument (OXI)and the case where one observes error-laden proxies for an unobserved exogenous instrument (PXI). For PXI, we develop and apply new results for estimating densities and expectations conditional on mismeasured variables. For both OXI and PXI, we use infnite order flat-top kernels to obtain uniformly convergent and asymptotically normal nonparametric estimators of instrument-conditioned effects, as well as root-n consistent and asymptotically normal estimators of average effects.

Identification of Local Treatment Effects Using a Proxy for an Instrument

The method of indirect least squares (ILS) using a proxy for a discrete instrument is shown to identify a weighted average of local treatment effects. The weights are nonnegative if and only if the proxy is intensity preserving for the instrument. A similar result holds for instrumental variables (IV) methods such as two stage least squares. Thus, one should carefully interpret estimates for causal effects obtained via ILS or IV using an error-laden proxy of an instrument, a proxy for an instrument with missing or imputed observations, or a binary proxy for a multivalued instrument. Favorably, the proxy need not satisfy all the assumptions required for the instrument. Specifically, an individual's proxy can depend on others' instrument and the proxy need not affect the treatment nor be exogenous. In special cases such as with binary instrument, ILS using any suitable proxy for an instrument identifies local average treatment effects.causality, compliance, indirect least squares, instrumental variables, local average treatment effect, measurement error, proxy, quadrant dependence, two stage least squares.

Essays on the definition, identification, and estimation of causal effects

This dissertation studies the definition, identification, and estimation of causal effects within the settable system framework of White and Chalak. Chapter 1 provides definitions of direct and indirect causality, as well as notions of causality via and exclusive of a set of variables, based on functional dependence to study the interrelations between independence or conditional independence and causal relations in recursive settable systems. We provide formal conditions ensuring the validity of Reichenbach's principle of common cause and introduce a new conditional counterpart, the conditional Reichenbach principle of common cause. We then provide necessary and sufficient causal conditions for probabilistic dependence and conditional dependence among certain random vectors in settable systems. We demonstrate how these results relate to and generalize results in the artificial intelligence literature. Chapter 2 studies the structural identification of average effects and average marginal effects with conditioning instruments within the settable system framework. In particular, we build on the results of Chapter 1 to provide causal and predictive conditions sufficient for conditional exogeneity to hold. We provide two procedures based on (Ã)-causality matrices and the direct causality matrix for inferring conditional causal isolation among vectors of settable variables. Similarly, we provide sufficient conditions for conditional stochastic isolation in terms of the sigma algebras generated by the conditioning variables. We distinguish between structural proxies and predictive proxies. Chapter 3 applies the results of chapters 1 and 2 within the structural equations framework to study the identification and estimation of causal effects. We begin by providing a causal interpretation for standard exogenous regressors and standard "valid" and "relevant" instrumental variables. We then build on this interpretation to characterize extended instrumental variables (EIV) methods, that is methods that make use of variables that need not be valid instruments in the standard sense, but that are nevertheless instrumental in the recovery of causal effects of interest. After examining special cases of single and double EIV methods, we provide necessary and sufficient conditions for the identification of causal effects by means of EIV and provide consistent and asymptotically normal estimators for the effects of interes