Estimation from the First Order Conditions for Dynamic Controls VERY PRELIMINARY and INCOMPLETE

This note introduces an estimation technique based on the first order conditions from dynamic models of interacting agents. The examples of particular interest to us are all dynamic models of oligopolistic industries. The technique itself has at least two virtues; i)it is easy to implement, and ii) it is logically consistent with the underlying model (and hence can be used to analyze the model’s implications). The assumption which underlies our estimator is an assumption which is used extensively in applied work; we assume that agents perceptions of the distribution of the discounted value of future net cash flows are rational in the sense that they are, at least on average, consistent with the realizations of those net cash flows. Three applications motivated the development of our estimator. First, the first order conditions currently used in empirical models of markets are typically the equations from a static Nash equilibrium in either prices or quantities. These equations either implicitly or explicitly assume that the conditional distribution of the firm’s future states, conditional on whatever investment decisions are made in the interim, does not depend on the price (or quantity) decision being studied. There are many important examples in which current prices or quantities will have independent impacts on future states, as well as on current profits, and in these cases the logic behind the static price or quantity setting equation falls apart. Examples include models with: learning by doing; either durable, experience, addictive, or network goods; and collusion. Our technique can allow for any (or all) of these extensions, and nests the standard static models as testable special cases. ∗This is a rough first draft, prepared for the Cowles Foundation Conference on the “Econometrics of Strategy and Decision-Making” at Yale in May, 2000. This version is incomplete and also lacks proper references, acknowledgements and so forth. †Yale University and the NBER, and Harvard University and the NBER, respectively.