Ulrich Doraszelski

A Framework for Applied Dynamic Analysis in IO

This paper reviews a framework for numerically analyzing dynamic interactions in imperfectly competitive industries. The framework dates back to Ericson and Pakes [1995. Review of Economic Studies 62, 53–82], but it is based on equilibrium notions that had been available for some time before, and it has been extended in many ways by different authors since. The framework requires as input a set of primitives which describe the institutional structure in the industry to be analyzed. The framework outputs profits and policies for every incumbent and potential entrant at each possible state of the industry. These policies can be used to simulate the distribution of sample paths for all firms from any initial industry structure. The sample paths generated by the model can be quite different depending on the primitives, and most of the extensions were designed to enable the framework to accommodate empirically relevant cases that required modification of the initial structure. The sample paths possess similar properties to those observed in (the recently available) panel data sets on industries. These sample paths can be used either for an analysis of the likely response to a policy or an environmental change, or as the models implication in an estimation algorithm. We begin with a review of an elementary version of the framework and a report on what is known about its analytic properties. Much of the rest of the paper deals with computational issues. We start with an introduction to iterative techniques for computing equilibrium that are analogous to the techniques used to compute the solution to single agent dynamic programming problems. This includes discussions of the determinants of the computational burden of these techniques, and the mechanism implicitly used to select an equilibrium when multiple equilibria are possible. We then outline a number of techniques that might be used to reduce the computational burden of the iterative algorithm. This section includes discussions of both the implications of differences in modeling assumptions used in the alternative techniques, and a discussion of the likely relevance of the different techniques for different institutional structures. A separate section reports on a technique for computing multiple equilibria from the same set of primitives. The paper concludes with a review of applications of the framework and a brief discussion of areas where further development of the framework would seem warranted.

Capacity Dynamics and Endogenous Asymmetries In Firm Size

Empirical evidence suggests that there are substantial and persistent differences in the sizes of firms in most industries. We propose a dynamic model of capacity accumulation that is consistent with the observed facts. The model highlights the mode of product market competition and the extent of investment reversibility as key determinants of the size distribution of firms in an industry. In particular, if firms compete in prices and the rate of depreciation is large, then the industry moves toward an outcome with one dominant firm and one small firm. Industry dynamics in this case resemble a preemption race. Contrary to the usual intuition, this preemption race becomes more brutal as investment becomes more reversible.

Innovations, improvements, and the optimal adoption of new technologies

Abstract This paper extends the literature on technology adoption by introducing a distinction between technological breakthroughs (‘innovations’) and the engineering refinements (‘improvements’) that follow such a breakthrough. Firms do not necessarily wait for a future technological breakthrough, but instead have an incentive to delay the adoption of a new technology until it is sufficiently advanced. We characterize a firms adoption decision as the solution to a continuous time, infinite horizon dynamic programming problem, which gives rise to an ordinary differential equation that is highly non-linear and does not have a closed-form solution. We thus employ projection techniques and show how these techniques can be applied to the analysis of optimal stopping problems.

R&D and Productivity: Estimating Production Functions when Productivity is Endogenous

We develop a simple estimator for production functions in the presence of endogenous productivity change that allows us to retrieve productivity and its relationship with R&D at the flrm level. Our dynamic investment model can be viewed as a generalization of the knowledge capital model (Griliches 1979) that has remained a cornerstone of the productivity literature for more than 25 years. We relax the assumptions on the R&D process and examine the impact of the investment in knowledge on the productivity of flrms. We illustrate our approach on an unbalanced panel of more than 1800 Spanish manufacturing flrms in nine industries during the 1990s. Our flndings indicate that the link between R&D and productivity is subject to a high degree of uncertainty, nonlinearity, and heterogeneity across flrms. Abstracting from uncertainty and nonlinearity, as is done in the knowledge capital model, or assuming an exogenous process for productivity, as is done in the recent literature on structural estimation of production functions, overlooks some of its most interesting features.

Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity

We provide a general model of dynamic competition in an oligopolistic industry with investment, entry, and exit. To ensure that there exists a computationally tractable Markov perfect equilibrium, we introduce firm heterogeneity in the form of randomly drawn, privately known scrap values and setup costs into the model. Our game of incomplete information always has an equilibrium in cutoff entry/exit strategies. In contrast, the existence of an equilibrium in the Ericson & Pakes (1995) model of industry dynamics requires admissibility of mixed entry/exit strategies, contrary to the assertion in their paper, that existing algorithms cannot cope with. In addition, we provide a condition on the models primitives that ensures that the equilibrium is in pure investment strategies. Building on this basic existence result, we first show that a symmetric equilibrium exists under appropriate assumptions on the models primitives. Second, we show that, as the distribution of the random scrap values/setup costs becomes degenerate, equilibria in cutoff entry/exit strategies converge to equilibria in mixed entry/exit strategies of the game of complete information. Finally, we provide the first example of multiple symmetric equilibria in this literature.

A User's Guide to Solving Dynamic Stochastic Games Using the Homotopy Method

This paper provides a step-by-step guide to solving dynamic stochastic games using the homotopy method. The homotopy method facilitates exploring the equilibrium correspondence in a systematic fashion; it is especially useful in games that have multiple equilibria. We discuss the theory of the homotopy method and its implementation and present two detailed examples of dynamic stochastic games that are solved using this method.

The net present value method versus the option value of waiting: A note on Farzin, Huisman and Kort (1998)

Abstract Using the tools of real-options theory, Farzin, Huisman and Kort (1998) investigate the optimal timing of technology adoption in a model in which there is ongoing technological progress and the firms investment decision is irreversible. When the firm can switch technologies n Farzin et al. (1998) obtain the surprising result that the criterion for adopting a new technology derived from real-options theory coincides with the net present value criterion for all but the last switch. This note points out a mistake in Farzin et al.s (1998) derivations that leads to the above result. We show that, compared to the net present value approach, the firm will defer the adoption of a new technology when it takes the option value of waiting into account.

A Dynamic Quality Ladder Model with Entry and Exit: Exploring the Equilibrium Correspondence Using the Homotopy Method

This paper explores the equilibrium correspondence of a dynamic quality ladder model with entry and exit using the homotopy method. This method is ideally suited for systematically investigating the economic phenomena that arise as one moves through the parameter space and is especially useful in games that have multiple equilibria. We briefly discuss the theory of the homotopy method and its application to dynamic stochastic games. We then present three main findings: First, the more costly and/or less beneficial it is to achieve or maintain a given quality level, the more a leader invests in striving to induce the follower to give up; the more quickly the follower does so; and the more asymmetric is the industry structure that arises. Second, the possibility of entry and exit gives rise to predatory and limit investment. Third, we illustrate and discuss the multiple equilibria that arise in the quality ladder model, highlighting the presence of entry and exit as a source of multiplicity.

Restricted feedback in long term relationships

This paper studies long term relationships, modeled as repeated games, with restricted feedback. Players condition current play on summary statistics of past play rather than the entire history, as may be the case in online markets. Our state strategy equilibrium framework allows for arbitrary restrictions on strategies. We derive a recursive characterization for the set of equilibrium payoffs similar to that of Abreu, Pearce, and Stacchetti (1986, 1990) [2,3] for perfect public equilibria and show that the set of equilibrium payoffs is the largest fixed point of a monotone operator. We use our characterization to derive necessary and sufficient conditions for efficient trade in a repeated product choice game where costumers condition their purchase decisions only on the last performance signal.

Measuring the bias of technological change

Technological change can increase the productivity of the various factors of production in equal terms, or it can be biased toward a specific factor. We directly assess the bias of technological change by measuring, at the level of the individual firm, how much of it is labor augmenting and how much is factor neutral. To do so, we develop a framework for estimating production functions when productivity is multidimensional. Using panel data from Spain, we find that technological change is biased, with both its labor-augmenting and its factor-neutral components causing output to grow by about 1.5 percent per year.