ALBERT

Description: [This paper responds to “Frequentist and Subjectivist Perspectives on the Problems of Model Building in Economics,” by Dale J. Poirier, in this same issue.] Professor Dale Poirier has preached a rousing sermon for the Bayesian cause and in doing so has concisely exposed some of the cracks in the foundations of statistics. One of these cracks is the very interpretation of the concept of probability, a philosophical question that has never been fully resolved and has led to the schism that currently exists in statistics between the Bayesian and classical schools. The paper is valuable for econometricians because it challenges them to think more deeply about the meaning of the statistical procedures they employ. However a basic question was not addressed; namely, what is the purpose of statistical inference? I think the answer to this question has at least as much bearing upon whether someone adopts Bayesian or classical methodology as whether one interprets the meaning of probability in subjectivist or frequentist terms. I think that the purpose of statistical inference is to “learn.” This view treats statistical inference as a process of formulating a sequence of models that are abstract but in some sense increasingly accurate representations of certain aspects of reality that we seek to understand. In the rest of this piece, I will discuss the limitations of Bayesian estimation theory and the limitations of Classical Estimation theory.

Description: This essay reviews Kenneth I. Wolpin's (2013) monograph The Limits of Inference without Theory, which arose from lectures he presented at the Cowles Foundation in 2010 in honor of Tjalling Koopmans. While I readily agree with Wolpin's basic premise that empirical work that eschews the role of economic theory faces unnecessary self-imposed limits relative to empirical work that embraces and tries to test and improve economic theory, it is important to be aware that the use of economic theory is not a panacea. I point out that there are also serious limits to inference with theory: 1) there may be no truly “structural” (policy invariant) parameters, a key assumption underpinning the structural econometric approach that Wolpin and the Cowles Foundation have championed; 2) there is a curse of dimensionality that makes it very difficult for us to elucidate the detailed implications of economic theories, which is necessary to empirically implement and test these theories; 3) there is an identification problem that makes it impossible to decide between competing theories without imposing ad hoc auxiliary assumptions (such as parametric functional form assumptions); and 4) there is a problem of multiplicity and indeterminacy of equilibria that limits the predictive empirical content of many economic theories. I conclude that though these are very challenging problems, I agree with Wolpin and the Cowles Foundation that economists have far more to gain by trying to incorporate economic theory into empirical work and test and improve our theories than by rejecting theory and presuming that all interesting economic issues can be answered by well-designed controlled, randomized experiments and assuming that difficult questions of causality and evaluation of alternative hypothetical policies can be resolved by simply allowing the “data to speak for itself.” (JEL B41, C18)