We consider linear predictor definitions of noncausality or strict exogeneity and show that it is restrictive to assert that there exists a time-invariant latent variable c such that x is strictly exogenous conditional on c. A restriction of this sort is necessary to justify standard techniques...

In data with a group structure, incidental parameters are included to control for missing variables. Applications include longitudinal data and sibling data. In general, the joint maximum likelihood estimator of the structural parameters is not consistent as the number of groups increases, with...

I review recent work in the statistics literature on instrumental variables methods from an econometrics perspective. I discuss some of the older, economic, applications including supply and demand models and relate them to the recent applications in settings of randomized experiments with...

There is a large theoretical literature on methods for estimating causal effects under unconfoundedness, exogeneity, or selection--on--observables type assumptions using matching or propensity score methods. Much of this literature is highly technical and has not made inroads into empirical...

In this essay I discuss potential outcome and graphical approaches to causality, and their relevance for empirical work in economics. I review some of the work on directed acyclic graphs, including the recent "The Book of Why," ([Pearl and Mackenzie, 2018]). I also discuss the potential outcome...

We examine the implications of arbitrage in a market with many assets. The absence of arbitrage opportunities implies that the linear functionals that give the mean and cost of a portfolio are continuous; hence there exist unique portfolios that represent these functionals. These portfolios span...

In this paper we study methods for estimating causal effects in settings with panel data, where a subset of units are exposed to a treatment during a subset of periods, and the goal is estimating counterfactual (untreated) outcomes for the treated unit/period combinations. We develop a class of...

It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such methods can be misleading, and we recommend researchers do not use them, and instead use...

The statistical and econometrics literature on causality is more focused on "effects of causes" than on "causes of effects." That is, in the standard approach it is natural to study the effect of a treatment, but it is not in general possible to define the causes of any particular outcome. This...

Matching estimators (Rubin, 1973a, 1977; Rosenbaum, 2002) are widely used in statistical data analysis. However, the large sample distribution of matching estimators has been derived only for particular cases (Abadie and Imbens, 2006). This article establishes a martingale representation for...