Structural Estimation, Method of Moments, BLP
I’ve been thinking about structural estimation, a style of econometrics in which the analyst builds a model of firms maximizing their profits and consumers maximizing utility and then estimates that very model. The model must allow for heterogenous firms and consumers, since the observed data won’t fit an identical-player model exactly, and it will involve some fixed parameters unobserved by the analyst and some observed variables that results from maximizing behavior given those parameters. The method is to pick some guesses for the parameters (let’s name one of them H), perhaps including Monte Carlo draws from an error distribution with a guess at the variance, then see what endogenous variable values result (let’s call one of them Y- hat, and then see how they compare with the actual observed values (Y). To see how they compare, you need to take a weighted average of the distances between the various endogenous variable predictions and actual values, and this is done with the Generalized Method of Moments by estimating a covariance matrix. There is a “distance” between predicted and actual values, and the analyst sees whether he can get that distance to shrink by picking different values for parameters such as H. He does that by an iterative search on a computer. Eventually, he stops, and uses his results to “bootstrap” some standard errors as a gauge of how accurate the estimates are.
This method is difficult, because the details are different for every model, and it takes a lot of computer time, since it is re- estimating for lots of different possible parameter values.
An older method is to start with a maximizing model, as in structural estimation, but to use a simpler, heuristic, model, often of identical agents. This model generates a prediction that when variable X rises that causes variable Y to rise too. Then, for the estimation, there is no pretence of trying to estimate the parameters of the model. Instead, a reduced form is used: the analyst sees if X and Y really do move together as predicted. He uses some relatively simple technique such as OLS or logit, and includes various control variables that aren’t in the theoretical model but which ought to be held constant to truly check whether X causes Y.
Structural estimation is clearly better in the abstract, but it seems to have a problem in practice: it narrows one’s view towards estimation of one model, to the neglect of alternatives. In the older method, the model was never trusted very far. The theoretical model was simple enough that it was supposed to illustrate only one particular causal link, so nobody took it literally– it was “other things equal”. The empirical regression, on the other hand, was supposed to test that link while adjusting for any other variables that might cause the analyst to mistakenly think that X caused Y. In structural estimation, on the other hand, people do not try to test a radically different explanation by throwing another variable Z into the equation and seeing if X still remains significant.
Here’s an example I saw recently. We could construct a structural model of movie sales in which consumers base their decision as to whether to go to a new movie in the first week on private information and on the fact that if they go second week instead, they can observe first-week sales and indirectly learn about other people’s private information. We might estimate such a model, and find that all the evidence confirms it. But that model omits a possibly important variable: whether the first week newspaper reviews are favorable. That is an alternative explanation, because good reviews are correlated with first-week sales (if it’s good, more people will have favorable private info ex ante and will go see it).
It might be hard to nest a review-based theory and a sales-based theory. But could the extra variable of review favorableness, irrelevant in the sales theory, be stuck into the sales theory estimation somewhere? In that theory, it should come out insignificant. If, instead, it was significant and first-week sales lost its significance, we’d have truly tested the sales theory. But I don’t think that’s done in structural estimation, even though it’s commonplace in reduced-form estimation.