The greatest problem for empirical analysis is how best to allow the context to affect the inferences. Econometric theory presupposes contextual "restrictions" that can be taken as given or assigned a probability distribution. These contextual inputs are rarely available. I illustrate this point...

This chapter relates the literature on the econometric evaluation of social programs to the literature in statistics on "causal inference". In it, we develop a general evaluation framework that addresses well-posed economic questions and analyzes agent choice rules and subjective evaluations of...

This chapter develops three topics. (1) Identification of the distributions of treatment effects and the distributions of agent subjective evaluations of treatment effects. Methods for identifying ex ante and ex post distributions are presented and empirical examples are given. (2)...

This chapter uses the marginal treatment effect (MTE) to unify and organize the econometric literature on the evaluation of social programs. The marginal treatment effect is a choice-theoretic parameter that can be interpreted as a willingness to pay parameter for persons at a margin of...

We study structural models of stochastic discount factors and explore alternative methods of estimating such models using data on macroeconomic risk and asset returns. Particular attention is devoted to recursive utility models in which risk aversion can be modified without altering...

We discuss the use of calibration techniques in economic models. Calibration contrasts with estimation in relying on deterministic calculation of model parameter values consistent with data, rather than econometric estimation. The reasons why calibrators use these methods, as well as the main...

This chapter reviews the recent developments in Markov chain Monte Carlo simulation methods. These methods, which are concerned with the simulation of high dimensional probability distributions, have gained enormous prominence and revolutionized Bayesian statistics. The chapter provides...