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...

Under stationarity, the heterogeneous stoahastic processes are the non-ergodic ones. We show that if a distributed lag is of finite order, then its coefficients are unconditional means of the underlying random coefficients. This result is applied to linear transformations of the process. The...

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...

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...

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...

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...

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. The mean variance...

In this paper, we explore Bayesian inference in models with many instrumental variables that are potentially weakly correlated with the endogenous regressor. The prior distribution has a hierarchical (nested) structure. We apply the methods to the Angrist-Krueger (AK, 1991) analysis of returns...

The paper evaluates the usefulness of a nonparametric approach to Bayesian inference by presenting two applications. The approach is due to Ferguson (1973, 1974) and Rubin (1981). Our first application considers an educational choice problem. We focus on obtaining a predictive distribution for...