In many countries holders of patents must pay an annual renewal fee in order to keep their patents in force. This paper uses data on the proportion of patents renewed, and the renewal fees faced by, post World War II cohorts of patents in France, the United Kingdom, and Germany, in conjunction with a model of patent holders' renewal decisions, to estimate the returns earned from holding patents in these countries. Since patents are often applied for at a nearly stage in the innovation process, the model allows agents to be uncertain about the sequence of returns that will be earned if the patent is kept inforce. Formally, then, the paper presents and solves a discrete choice optimal stochastic control model, derives the implications of the model on aggregate behaviour, and then estimates the parameters of the model from aggregate data. The estimates enable a detailed description of the evolution of the distribution of returns earned from holding patents over their life spans,and calculations of both; the annual returns earned from holding the patents still in force (or the patent stocks) in the alternative countries, and the distribution of the discounted value of returns earned from holding the patents in a cohort.

This paper introduces a stochastic algorithm for computing symmetric Markov perfect equilibria. The algorithm computes equilibrium policy and value functions, and generates a transition kernel for the (stochastic) evolution of the state of the system. It has two features that together imply that it need not be subject to the curse of dimensionality. First, the integral that determines continuation values is never calculated; rather it is approximated by a simple average of returns from past outcomes of the algorithm, an approximation whose computational burden is not tied to the dimension of the state space. Second, iterations of the algorithm update value and policy functions at a single (rather than at all possible) points in the state space. Random draws from a distribution set by the updated policies determine the location of the next iteration's updates. This selection only repeatedly hits the recurrent class of points, a subset whose cardinality is not directly tied to that of the state space. Numerical results for industrial organization problems show that our algorithm can increase speed and decrease memory requirements by several orders of magnitude.

A general central limit theorem is proved for estimators defined by minimization of the length of a vector-valued, random criterion function. No smoothness assumptions are imposed on the criterion function in order that the results might apply to a broad class of simulation estimators. Complete analyses of two simulation estimators, one introduced by A. Pakes (1986) and the other by D. McFadden (1989), illustrate the application of the general theorems. These examples illustrate how simulation can be used to circumvent two computational problems that arise frequently in applied econometrics: evaluating intractable aggregation formulae and evaluating discrete response probabilities. Copyright 1989 by The Econometric Society.

Technological change and deregulation have caused a major restructuring of the telecommunications equipment industry over the last two decades. We estimate the parameters of a production function for the equipment industry and then use those estimates to analyze the evolution of plant level productivity over this period. The restructuring involved significant entry and exit and large changes in the sizes of incumbents. Since firms' choices on whether to liquidate and on the quantities of inputs demanded should they continue depend on their productivity, we use an equilibrium model to suggest an estimation algorithm that takes into account the relationship between productivity on the one hand. and both input demand and survival on the other. A fully parametric version of the estimation algorithm would be both computationally burdensome and require a host of auxiliary assumptions. So we develop a semi parametric technique which is both consistent with a quite general version of the theoretical framework and easy to use. The algorithm produces markedly different estimates of both production function parameters and of productivity movements than traditional estimation procedures. We find an increase in the rate of industry productivity growth after deregulation. This in spite of the fact there was no increase in the average of the plants' rates of productivity growth, and there was actually a fall in our index of the efficiency of the allocation of variable factors conditional on the existing distribution of fixed factors. Deregulation was, however, followed by a reallocation of capital towards more productive establishments (by a down sizing, often shutdown. of unproductive plants and by disproportionate growth of productive establishments) which more than offset the other factors' negative impacts on aggregate productivity.

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