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.

Causal discourse in a game of incomplete information

Notions of cause and effect are fundamental to economic explanation. Although concepts such as price effects are intuitive, rigorous foundations justifying causal discourse in the wide range of economic settings remain lacking. We illustrate this deficiency using an N-bidder private-value auction, posing causal questions that cannot be addressed within existing frameworks. We extend the frameworks of Pearl (2000) and White and Chalak (2009) to introduce topological settable systems (TSS), a causal framework capable of delivering the missing answers. Particularly, TSS accommodate choices belonging to general function spaces. Our analysis suggests how TSS enable causal discourse in various areas of economics

Identification of average effects under magnitude and sign restrictions on confounding

This paper studies measuring various average effects of X on Y in general structural systems with unobserved confounders U, a potential instrument Z, and a proxy W for U. We do not require X or Z to be exogenous given the covariates or W to be a perfect one‐to‐one mapping of U. We study the identification of coefficients in linear structures as well as covariate‐conditioned average nonparametric discrete and marginal effects (e.g., average treatment effect on the treated), and local and marginal treatment effects. First, we characterize the bias, due to the omitted variables U, of (nonparametric) regression and instrumental variables estimands, thereby generalizing the classic linear regression omitted variable bias formula. We then study the identification of the average effects of X on Y when U may statistically depend on X and Z. These average effects are point identified if the average direct effect of U on Y is zero, in which case exogeneity holds, or if W is a perfect proxy, in which case the ratio (contrast) of the average direct effect of U on Y to the average effect of U on W is also identified. More generally, restricting how the average direct effect of U on Y compares in magnitude and/or sign to the average effect of U on W can partially identify the average effects of X on Y. These restrictions on confounding are weaker than requiring benchmark assumptions, such as exogeneity or a perfect proxy, and enable a sensitivity analysis. After discussing estimation and inference, we apply this framework to study earnings equations. </jats:p

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.