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 compares hedonic to matched model indexes. Matched model indexes are averages of the price changes of goods that remain on sampled stores’ shelves. Since goods that disappear tend to have falling market values, matched model indexes select from the right tail of price changes. The BLS can construct hedonic indexes that correct for this selection and are justified by standard arguments. In an empirical study of PC’s hedonics produce sharp price declines while matched model indexes are near zero. Also, though there are modifications to hedonics that seem desirable, they are not those in current use.

Empirical work on the causes and effects of inventive activity has had difficulty in finding measures that can indicate when and where changes in either inventive inputs or inventive output have occurred. The recent computerization of the U.S. Patent Office's data base may prove helpful in this context, but there is the problem that a priori we do not know the relationships between patent applications and economically meaningful measures of these inputs and outputs. To help solve this problem, this paper investigates the dynamic relationships among the number of successful patent applications of firms, a measure of the firm's investment in inventive activity (its R & D expenditures), and an indicator of its inventive output (the stock market value of the firm).

This paper considers the problem of estimating distributed lags in short panels. Though the N time series contained in a panel may allow for relatively precise estimates of identified lag coefficients, identification requires restrictions on the contribution of the unobserved pre-sample x's to the current values of y, and the shortness of panels focuses attention on this matter. We investigate two such restrictions. The first constrains the relationship between the presample and insample x's, while the second constrains the lag distribution itself. An example, which investigates empirically how to construct “capital stocks” for the analysis of rates of return, closes the paper.

Benjamin Eden, Ariél Pakes; On Measuring the Variance-Age Profile of Lifetime Earnings, The Review of Economic Studies, Volume 48, Issue 3, 1 July 1981, Pa

Abstract We develop a framework for the analysis of dynamic oligopolies with persistant sources of asymmetric information that enables applied analysis of situations of empirical importance that have been difficult to deal with. The framework generates policies that are “relatively” easy for agents to use while still being optimal in a meaningful sense, and is amenable to empirical research in that its equilibrium conditions can be tested and equilibrium policies are relatively easy to compute. We conclude with an example that endogenizes the maintenance decisions of electricity generators when the costs states of the generators are private information.

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.