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71
Estimating dynamic models of imperfect competition. Working Paper
, 2006
"... We describe a twostep algorithm for estimating dynamic games under the assumption that behavior is consistent with Markov perfect equilibrium. In the first step, the policy functions and the law of motion for the state variables are estimated. In the second step, the remaining structural parameters ..."
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Cited by 194 (15 self)
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We describe a twostep algorithm for estimating dynamic games under the assumption that behavior is consistent with Markov perfect equilibrium. In the first step, the policy functions and the law of motion for the state variables are estimated. In the second step, the remaining structural parameters are estimated using the optimality conditions for equilibrium. The second step estimator is a simple simulated minimum distance estimator. The algorithm applies to a broad class of models, including industry competition models with both discrete and continuous controls such as the Ericson and Pakes (1995) model. We test the algorithm on a class of dynamic discrete choice models with normally distributed errors and a class of dynamic oligopoly models similar to that of Pakes and McGuire (1994).
Demand Estimation with Heterogeneous Consumers and Unobserved Product Characteristics: A Hedonic Approach
, 2005
"... We reconsider the identification and estimation of GormanLancasterstyle hedonic models of demand for differentiated products in the spirit of Sherwin Rosen. We generalize Rosen’s first stage to account for product characteristics that are not observed and to allow the hedonic pricing function to ha ..."
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Cited by 69 (2 self)
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We reconsider the identification and estimation of GormanLancasterstyle hedonic models of demand for differentiated products in the spirit of Sherwin Rosen. We generalize Rosen’s first stage to account for product characteristics that are not observed and to allow the hedonic pricing function to have a general nonseparable form. We take an alternative semiparametric approach to Rosen’s second stage in which we assume that the parametric form of utility is known, but we place no restrictions on the aggregate distribution of utility parameters. If there are only a small number of products, we show how to construct bounds on individuals’ utility parameters, as well as other economic objects such as aggregate demand and consumer surplus. We apply our methods to estimating the demand for personal computers.
Markov perfect industry dynamics with many firms. Forthcoming, Econometrica
, 2008
"... The copyright to this Article is held by the Econometric Society. It may be downloaded, printed and reproduced only for educational or research purposes, including use in course packs. No downloading or copying may be done for any commercial purpose without the explicit permission of the Econometric ..."
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Cited by 44 (9 self)
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The copyright to this Article is held by the Econometric Society. It may be downloaded, printed and reproduced only for educational or research purposes, including use in course packs. No downloading or copying may be done for any commercial purpose without the explicit permission of the Econometric Society. For such commercial purposes contact the Office of the Econometric Society (contact information may be found at the website http://www.econometricsociety.org or in the back cover of Econometrica). This statement must the included on all copies of this Article that are made available electronically or in any other
Foundations of Markovperfect industry dynamics: Existence, purification, and multiplicity, Working paper
, 2003
"... In this paper we show that existence of a Markov perfect equilibrium (MPE) in the Ericson & Pakes (1995) model of dynamic competition in an oligopolistic industry with investment, entry, and exit requires admissibility of mixed entry/exit strategies, contrary to Ericson & Pakes’s (1995) ass ..."
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Cited by 30 (6 self)
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In this paper we show that existence of a Markov perfect equilibrium (MPE) in the Ericson & Pakes (1995) model of dynamic competition in an oligopolistic industry with investment, entry, and exit requires admissibility of mixed entry/exit strategies, contrary to Ericson & Pakes’s (1995) assertion. This is problematic because the existing algorithms cannot cope with mixed strategies. To establish a firm basis for computing dynamic industry equilibria, we introduce firm heterogeneity in the form of randomly drawn, privately known scrap values and setup costs into the model. We show that the resulting game of incomplete information always has a MPE in cutoff entry/exit strategies and is computationally no more demanding than the original game of complete information. Building on our basic existence result, we first show that a symmetric and anonymous MPE exists under appropriate assumptions on the model’s primitives. Second, we show that, as the distribution of the random scrap values/setup costs becomes degenerate, MPEs in cutoff entry/exit strategies converge to MPEs in mixed entry/exit strategies of the game of complete information. Next, we provide a condition on the model’s primitives that ensures the existence of a MPE in pure investment strategies. Finally, we provide the first example of multiple symmetric and anonymous MPEs in this literature. 1
A Framework for Applied Dynamic Analysis in IO
, 2006
"... This paper reviews a framework for numerically analyzing dynamic interactions in imperfectly competitive industries. The framework dates back to Ericson & Pakes (1995), but it is based on equilibrium notions that had been available for some time before, and it has been extended in many ways by ..."
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Cited by 25 (0 self)
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This paper reviews a framework for numerically analyzing dynamic interactions in imperfectly competitive industries. The framework dates back to Ericson & Pakes (1995), 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 that are fed into it, 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 made 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,
Avoiding the curse of dimensionality in dynamic stochastic games
, 2008
"... Discretetime stochastic games with a finite number of states have been widely applied to study the strategic interactions among forwardlooking players in dynamic environments. However, these games suffer from a “curse of dimensionality” since the cost of computing players’ expectations over all po ..."
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Cited by 24 (3 self)
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Discretetime stochastic games with a finite number of states have been widely applied to study the strategic interactions among forwardlooking players in dynamic environments. However, these games suffer from a “curse of dimensionality” since the cost of computing players’ expectations over all possible future states increases exponentially in the number of state variables. We explore the alternative of continuoustime stochastic games with a finite number of states and show that continuous time has substantial advantages. Most important, continuous time avoids the curse of dimensionality, thereby speeding up the computations by orders of magnitude in games with more than a few state variables. This much smaller computational burden greatly extends the range and richness of applications of stochastic games.
Learningbydoing, organizational forgetting, and industry dynamics
, 2008
"... Learningbydoing and organizational forgetting have been shown to be important in a variety of industrial settings. This paper provides a general model of dynamic competition that accounts for these economic fundamentals and shows how they shape industry structure and dynamics. Previously obtained ..."
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Cited by 21 (10 self)
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Learningbydoing and organizational forgetting have been shown to be important in a variety of industrial settings. This paper provides a general model of dynamic competition that accounts for these economic fundamentals and shows how they shape industry structure and dynamics. Previously obtained results regarding the dominance properties of firms ’ pricing behavior no longer hold in this more general setting. We show that forgetting does not simply negate learning. Rather, learning and forgetting are distinct economic forces. In particular, a model with learning and forgetting can give rise to aggressive pricing behavior, market dominance, and multiple equilibria, whereas a model with learning alone cannot.
Leasing and Secondary Markets: Theory and Evidence from Commercial Aircraft,” mimeo
, 2007
"... I construct a dynamic model of transactions in used capital to understand the role of leasing when trading is subject to frictions. Firms trade assets to adjust their productive capacity in response to shocks to profitability. Transaction costs hinder the efficiency of the allocation of capital, and ..."
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Cited by 15 (4 self)
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I construct a dynamic model of transactions in used capital to understand the role of leasing when trading is subject to frictions. Firms trade assets to adjust their productive capacity in response to shocks to profitability. Transaction costs hinder the efficiency of the allocation of capital, and lessors act as trading intermediaries who reduce trading frictions. The model predicts that leased assets trade more frequently and produce more output than owned assets, for two reasons. First, highvolatility firms are more likely to lease than lowvolatility firms, since they expect to adjust their capacity more frequently. Second, ownership’s larger transaction costs widen owners ’ inaction bands relative to lessees’. Using data on commercial aircraft, I find that leased aircraft have holding durations 38percent shorter and fly 6.5percent more hours than owned aircraft. Additional tests indicate that most of these differential patterns in trading and utilization arise because owners have wider inaction bands than lessees, and carriers ’ selfselection into leasing plays a minor role. 1
A structural empirical model of R&D, firm heterogeneity, and industry evolution. working paper, NYU University. A Proof of Theorem 5.1 Proof of Theorem 5.1. Under Assumptions 3.1 and 5.1, the sequence {(µ (m) , λ (m) )m ∈ N} possesses the AME property. P
 V ∈M (∞) (xµ ′ , µ, λ) = sup µ′ ∈ ˜ ˜V M (∞) (xµ ′ , µ, λ) = ˜ V (∞) (xµ, λ), ∀x ∈ X , where the
, 2008
"... This paper develops and estimates a dynamic industry equilibrium model of R&D, R&D spillovers, and productivity evolution of manufacturing plants in the Korean electric motor industry from 1991 to 1996. Plantlevel decisions for R&D, physical capital investment, entry, and exit are inte ..."
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Cited by 12 (0 self)
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This paper develops and estimates a dynamic industry equilibrium model of R&D, R&D spillovers, and productivity evolution of manufacturing plants in the Korean electric motor industry from 1991 to 1996. Plantlevel decisions for R&D, physical capital investment, entry, and exit are integrated in an equilibrium model with imperfectly competitive product market. Estimates of the structural parameters explains observed heterogeneity in plant R&D choice, size, and turnover, and quantifies how R&D and R&D spillovers drive the change of plant productivity and industry structure. Given the structural estimates, I study an important policy question: how does product market competition affect individual firm innovation and aggregate industry productivity? The empirical model is estimated in two steps. In the first step, a model of static market competition is used to estimate the demand elasticity, returns to scale in production, and the process of plant level productivity. The initial productivity distribution for new entrants is also recovered. In the second step, I use a Simulated Method of Moments estimator to estimate the cost of R&D, the magnitude of the R&D spillover, adjustment costs of physical
Equilibria of dynamic games with many players: Existence, approximation, and market structure Submitted
, 2010
"... In this paper we study stochastic games with many players; such games are relevant for a wide range of social, economic, and engineering applications. The standard solution concept for such games is Markov perfect equilibrium (MPE), but it is well known that MPE computation becomes intractable as th ..."
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Cited by 9 (3 self)
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In this paper we study stochastic games with many players; such games are relevant for a wide range of social, economic, and engineering applications. The standard solution concept for such games is Markov perfect equilibrium (MPE), but it is well known that MPE computation becomes intractable as the number of players increases. Further, MPE demands a perhaps implausible level of rationality on the part of players in large games. In this paper we instead consider stationary equilibrium (SE), where players optimize assuming the empirical distribution of others ’ states remains constant at its long run average.We make three main contributions. First, we provide exogenous conditions over model primitives to ensure stationary equilibria exist, in a general model with possibly unbounded state spaces. Second, we show that the same conditions that ensure existence of SE also ensure that SE is a good approximation to MPE in large finite games. Finally, we consider a series of applications, including dynamic oligopoly models, supply chain competition, and consumer learning. These examples highlight that our conditions amount to a dichotomy between “decreasing ” and “increasing ” returns to larger states; SE approximates MPE well in the former case in which the equilibrium market structure becomes fragmented in the limit. In the latter case, SE may not approximate MPE well. 1.