Alternative models for moment inequalities

Behavioral choice models generate inequalities which, when combined with additional assumptions, can be used as a basis for estimation. This paper considers two sets of such assumptions and uses them in two empirical examples. The second example examines the structure of payments resulting from the upstream interactions in a vertical market. We then mimic the empirical setting for this example in a numerical analysis which computes actual equilibria, examines how their characteristics vary with the market setting, and compares them to the empirical results. The final section uses the numerical results in a Monte Carlo analysis of the robustness of the two approaches to estimation to their underlying assumptions.

Common Sense and Simplicity in Empirical Industrial Organization

This paper is a revised version of a keynote address delivered at the inaugural International Industrial Organization Conference in Boston, April 2003. I argue that new econometric tools have facilitated the estimation of models with realistic theoretical underpinnings, and because of this, have made empirical I. O. much more useful. The tools solve computational problems thereby allowing us to make the relationship between the economic model and the estimating equations transparent. This, in turn, enables us to utilize the available data more eectively. It also facilitates robustness analysis and clarifies the assumptions needed to analyze the causes of past events and/or make predictions of the likely impacts of future policy or environmental changes. The paper provides examples illustrating the value of simulation for the estimation of demand systems and of semiparametrics for the estimation of entry models.

A Framework for Applied Dynamic Analysis in I.O.

This paper outlines a framework which computes and analyzes the equilibria from a class of dynamic games. The framework dates to Ericson and Pakes (1995), and allows for a finite number of heterogeneous firms, sequential investments with stochastic outcomes, and entry and exit. The equilibrium analyzed is a Markov Perfect equilibrium in the sense of Maskin and Tirole (1988). The simplest version of the framework is supported by a publically accessible computer program which computes equilibrium policies for user-specified primitives, and then analyzes the evolution of the industry from user-specified initial conditions. We begin by outlining the publically accessible framework. It allows for three types of competition in the spot market for current output (specified up to a set of parameter values set by the user), and has modules which allow the user to compare the industry structures generated by the Markov Perfect equilibrium to those that would be generated by a social planner and to those that would be generated by prefect collusion.' Next we review extensions that have been made to the simple framework. These were largely made by other authors who needed to enrich the framework so that it could be used to provide a realistic analysis of particular applied problems. The third section provides a simple way of evaluating the computational burden of the algorithm for a given set of primitives, and then shows that computational constraints are still binding in many applied situations. The last section reviews two computational algorithms designed to alleviate this computational constraint; one of which is based on functional form approximations and the other on learning techniques similar to those used in the artificial intelligence literature.

Empirical Implications of Alternative Models of Firm Dynamics

This paper considers two models for analyzing the dynamics of firm behavior that allow for heterogeneity among firms, idiosyncratic (or firm specific) sources of uncertainty, and discrete outcomes (exit and/or entry). Models with these characteristics are needed for the structural econometric analysis of several economic phenomena, including the behavior of capital markets when there are significant failure probabilities, and the analysis of productivity movements in industries with large amounts of entry and exit. In addition, these models provide a means of correcting for the self-section induced by liquidation decisions in empirical studies of firms responses to alternative policy and environmental changes. It is shown that the two models have different nonparametric implications - implications that depend only on basic behavioral assumptions and mild regularity conditions on the functional forms of interest (one distinction between them corresponds to the distinction between heterogeneity and an ergodic form of state-dependence; a form in which the effect of being in a state in a particular period erodes away as time from that period lapses). The nonparametric implications enable the construction of testing and selection correction procedures that are easy to implement (they do not require the computationally difficult, and functional-form specific, estimation algorithms that have been used to empirically analyze stochastic control models with discrete outcomes in the past). The paper concludes by checking for the implications of the two models on an eight-year panel of Wisconsin firms. We find one model to be consistent with the data for retail trade.

Measuring the Variance-Age Profile of Lifetime Income

This paper presents an operational meaning to the concept of the variance in lifetime income in terms of the discounted variance of T mutually uncorrelated, sequentially realized, random variables. It is then shown how the logical implications of the lifecycle consumption model can be used to estimate this series of variances, called the variance-age profile of lifetime income, and we refer to an earlier paper by Eden (1977) to show how this variance-age profile can be used to compare the riskiness of alternative labor income paths. Finally the estimation technique is applied to Israeli data in order to compare the riskiness of the earnings path of those who attended college with that of those who terminated their education at the high school level in that economy, and to consider data requirements and estimation problems in greater depth.

Estimating Distributed Lags in Short Panels with an Application to the Specification of Depreciation Patterns and Capital Stock Constructs

In this paper, we investigate the problem of estimating distributed lags in short panels. Estimates of the parameter of distributed lag relationships based on single time-series of observations have been usually rather imprecise. The promise of panel data is in the N repetitions of the time-series that it contains which should allow one to estimate the identified lag parameters with greater precision. On the other hand, panels tend to track their observations only over a relatively short time interval. Thus, some assumptions will have to be made on the contribution of the unobserved presample x's to the current values of y before any lag parameters can be identified from such data. In this paper we suggest two such assumptions; both of which are, at least in part, testable, and outline appropriate estimation techniques. The first places reasonable restrictions on the relationship between the presample and in sample x's while the second imposes conventional functional form constraints on the lag coefficients. The paper concludes with an example which investigates empirically how to construct a "capital stock" for profit or rate of return regressions.

The Rate of Obsolescence Of Knowledge, Research Gestation Lags, and the Private Rate of Return to Research Resources

This paper points out the conceptual distinction between the rates of decay in the physical productivity of traditional capital goods and that of the appropriate revenues accruing to knowledge-producing activities, and notes that it is the latter parameter which is required in any study which constructs a stock of privately marketable knowledge. The rate of obsolescence of knowledge is estimated from a simple patent renewal and the estimates are found to be comparable to evidence provided by firms on the lifespan of the output of their R&D activities. These estimates, together with mean R&D gestation lags, are then used to correct previous estimates of the private excess rate of return to investment in research. We find that after the correction, the private excess rate of return to investment in research, at least in the early 1960's, was close to zero, which may explain why firms reduced the fraction of their resources allocated to research over the subsequent decade.