Introduction

How do we test econometric models? The question invites a series of lessons and precautions about statistical inference. Before we take up these lessons we need to answer a prior question. What kind of information is the econometric model at hand supposed to represent? I want to focus on two broad answers: (1) the econometric model summarizes information about a probability distribution, and in addition (2) the model makes claims about causal relations. The second project clearly brings with it new and difficult problems. Even if we had full information about the probability distribution over a set of variables, that would not tell us the causal relations among them. Nevertheless probabilities may be a useful tool for inferring causal structure even if they cannot do the job on their own.

It is widely acknowledged that probabilities are most useful as a tool for causal inference in the context of a controlled experiment. For many, information about what would happen in an ideal controlled experiment is enough: we can count that as just the information we are looking for under the heading ‘causation’. Suppose we take that point of view. That still leaves us a long way from conventional econometric models, which describe statistical relations in population data and not in data generated in the highly controlled environment of an experiment. Or does it?