Simple Estimators for the Parameters of Discrete Dynamic Games (with Entry/Exit Samples)

Pakes, Ariél; Ostrovsky, Michael; Berry, Steve

doi:10.3386/w10506

Cited by 43 publications

(12 citation statements)

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“…The objective may be a maximum likelihood function or pseudo-maximum likelihood function (see Mira 2002, 2007). Alternatively, it may be a (generalized) method-of-moments norm (see, e.g., Pakes et al 2007). The characterization of the equilibria p as the solutions to the FOC equations (29) helps, once again, enormously for any of these estimation methods: Traditional estimation methods, starting with Rust's (1987) (nested) fixed point algorithmic approach, have projected the associated optimization problems onto the parameter space , solving an optimization problem of the type min L p ∈ and p is an equilibrium under (45) This means that a search is conducted through the parameter space, and whenever a specific trial parameter vectorˆ ∈ is evaluated, all associated price equilibria p ˆ are computed.…”

Section: Structural Estimation Of the Game In Thementioning

confidence: 99%

Price Competition Under Mixed Multinomial Logit Demand Functions

2013

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I n this paper, we postulate a general class of price competition models with mixed multinomial logit demand functions under affine cost functions. In these models, the market is partitioned into a finite set of market segments. We characterize the equilibrium behavior of this class of models in the case where each product in the market is sold by a separate, independent firm. We identify a simple and very broadly satisfied condition under which a pure Nash equilibrium exists and the set of Nash equilibria coincides with the solutions of the system of first-order-condition equations, a property of essential importance to empirical studies. This condition specifies that in every market segment, each firm captures less than 50% of the potential customer population when pricing at a specific level that, under the condition, is an upper bound for a rational price choice for the firm irrespective of the competitors' prices. We show that under a somewhat stronger, but still broadly satisfied, version of the above condition, a unique equilibrium exists. We complete the picture by establishing the existence of a Nash equilibrium, indeed a unique Nash equilibrium, for markets with an arbitrary degree of concentration, under sufficiently tight price bounds. We discuss how our results extend to a continuum of customer types. A discussion of the multiproduct case is included. The paper concludes with a discussion of implications for structural estimation methods.

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Section: Structural Estimation Of the Game In Thementioning

confidence: 99%

Price Competition Under Mixed Multinomial Logit Demand Functions

2013

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“…Consistent with this research agenda, we study the long-run industry equilibrium properties, in our case the spatial distribution of ships and exporters. Moreover, our empirical methodology borrows from the literature on the estimation of dynamic setups (e.g., Rust (1987), Bajari, Benkard, and Levin (2007), Pakes, Ostrovsky, and Berry (2007); applications include Ryan (2012) and Collard-Wexler (2013)). Buchholz (2019) and Frechette, Lizzeri, and Salz (2019) also explored dynamic decisions in the context of taxi cabs' search and shift choices, respectively.…”

Section: Related Literaturementioning

confidence: 99%

Geography, Transportation, and Endogenous Trade Costs

Brancaccio

Kalouptsidi

Papageorgiou

2020

ECTA

120

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In this paper, we study the role of the transportation sector in world trade. We build a spatial model that centers on the interaction of the market for (oceanic) transportation services and the market for world trade in goods. The model delivers equilibrium trade flows, as well as equilibrium trade costs (shipping prices). Using detailed data on vessel movements and shipping prices, we document novel facts about shipping patterns; we then flexibly estimate our model. We use this setup to demonstrate that the transportation sector (i) attenuates differences in the comparative advantage across countries; (ii) generates network effects in trade costs; and (iii) dampens the impact of shocks on trade flows. These three mechanisms reveal a new role for geography in international trade that was previously concealed by the frequently‐used assumption of exogenous trade costs. Finally, we illustrate how our setup can be used for policy analysis by evaluating the impact of future and existing infrastructure projects (e.g., Northwest Passage, Panama Canal).

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“…Our bootstrap sample is generated using the multinomial logit choice and transition probabilities for each player in each market in the same manner as a parametric bootstrap; cf. Kasahara and Shimotsu (2008) and Pakes, Ostrovsky, and Berry (2007). We use 500 bootstrap samples and report the standard errors in italics.…”

Section: Empirical Illustrationmentioning

confidence: 99%

“…Beside from explicitly separating out past actions from other observed state variables, MN(i) to MN(iii) are standard in the dynamic discrete choice game literature; for example, see Aguirregabiria and Mira (2007), Bajari, Benkard, and Levin (2007), Pakes, Ostrovsky, and Berry (2007), and Pesendorfer and Schmidt-Dengler (2008). MN(iv) extends N(i).…”

Section: A1 Identification Of the Switching Costs In Dynamic Gamesmentioning

confidence: 99%

Joint analysis of the discount factor and payoff parameters in dynamic discrete choice models

Komarova¹,

Sanches²,

Silva³

et al. 2018

Quantitative Economics

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Most empirical and theoretical econometric studies of dynamic discrete choice models assume the discount factor to be known. We show the knowledge of the discount factor is not necessary to identify parts, or even all, of the payoff function. We show the discount factor can be generically identified jointly with the payoff parameters. On the other hand, it is known the payoff function cannot be nonparametrically identified without any a priori restrictions. Our identification of the discount factor is robust to any normalization choice on the payoff parameters. In IO applications, normalizations are usually made on switching costs, such as entry costs and scrap values. We also show that switching costs can be nonparametrically identified, in closed‐form, independently of the discount factor and other parts of the payoff function. Our identification strategies are constructive. They lead to easy to compute estimands that are global solutions. We illustrate with a Monte Carlo study and the dataset used in Ryan ().

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Simple Estimators for the Parameters of Discrete Dynamic Games (with Entry/Exit Samples)

Abstract: This paper considers the problem of estimating the distribution of payoffs in a discrete dynamic game, focusing on models where the goal is to learn about the distribution of firms' entry and exit

Cited by 43 publications

References 0 publications

Price Competition Under Mixed Multinomial Logit Demand Functions

Price Competition Under Mixed Multinomial Logit Demand Functions

Geography, Transportation, and Endogenous Trade Costs

Joint analysis of the discount factor and payoff parameters in dynamic discrete choice models

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