Research Database

This paper provides an algorithm for computing Markov Perfect Nash Equilibria (Maskin and Tirole, 1988a and b) for dynamic models that allow for heterogeneity among firms and idiosyncratic (or firm specific) sources of uncertainty. It has two purposes. To illustrate the ability of such models to reproduce important aspects of reality, and to provide a tool which, given appropriate parameter estimates, can be used for both descriptive and policy analysis in a setting which allows firms to differ from one another in ways that are consistent with the information in firm level data sets.

We illustrate by computing the policy functions, and simulating the industry structures, generated by a class of dynamic differentiated product models in which the idiosyncratic uncertainty is due to both the random outcomes of each firm's research process, and to an autonomous aggregate demand process. The illustration focuses on comparing the effect of different regulatory and behavioral assumptions on market structure and on welfare for one particular set of parameter values. The results here are of some independent interest and can be read without delving into the technical detail of the computational algorithm.

The last part of the paper begins with an explicit consideration of the computational burden of the algorithm, and then introduces approximation techniques designed to make computation easier. The purpose of this section is to enable us to compute equilibria for industries in which a large number of firms are typically active. Its major result is analytic. We show that if the value function of a given firm is exchangeable in the state vectors of its competitors, then the number of polynomial coefficients one needs for a given order of a polynomial approximation to that function is both independent of the number of firms active in the market, and a relatively small number. This enables us to use the approximation technique to reduce the computational burden of the algorithm dramatically.

We study the aggregate implications of (S,s) inventory policies in a dynamic general equilibrium model. Firms in the model's retail sector face idiosyncratic demand risk, and (S,s) inventory policies are optimal because of fixed order costs. The model economy replicates salient features of the business cycle and reconciles evidence that orders are more volatile than sales, and that inventory investment is positively correlated with sales. There are two main results. First, we find that general equilibrium effects and the optimal order size are important for the economy's response to exogenous shocks. Second, we find that key features of our results are independent of the presence of idiosyncratic risk.

The paper examines the literature that attempts to resolve the equity premium and riskfree rate puzzles. It demonstrates that the puzzles will confront any model of asset prices that relies on three crucial assumptions: preferences have a particular parametric form, asset markets are complete, and asset trade is frictionless. A survey of the literature that relaxes these assumptions reveals that there are now several plausible explanations of the seemingly low riskfree rate, but the large size of the equity premium remains a puzzle.

For the first-order univariate autoregression without constant term, the joint p.d.f (corresponding to a flat prior) for the true coeffecient p and the least squares estimate p-hat is estimated by Monte Carlo and graphically displayed. The graphs show how the symmetric distribution of p|p-hat coexists with the assymetric distribution of p-hat|p. Treating tail areas of the p-hat|p distribution as if they summarized evidence in the data about the location of p amounts to ignoring the shrinkage in the variance of p-hat|p as p approaches one. Prior p.d.f.'s implicit in treating classical significance levels as if they were Bayesian conditional probabilities are calculated. They are shown to depend sensitively on p-hat and to put substantial probability on p's above one.

In welfare theory it is standard to pick the consumption stream that maximizes the welfare of the representative agent. We argue against this position, and show that a benevolent social planner will generally place a greater weight on future consumption than does the representative agent.