Structural Econometric Models: Volume 31
Table of contents(18 chapters)
List of Contributors
We derive marginal conditions of optimality (i.e., Euler equations) for a general class of Dynamic Discrete Choice (DDC) structural models. These conditions can be used to estimate structural parameters in these models without having to solve for approximate value functions. This result extends to discrete choice models the GMM-Euler equation approach proposed by Hansen and Singleton (1982) for the estimation of dynamic continuous decision models. We first show that DDC models can be represented as models of continuous choice where the decision variable is a vector of choice probabilities. We then prove that the marginal conditions of optimality and the envelope conditions required to construct Euler equations are also satisfied in DDC models. The GMM estimation of these Euler equations avoids the curse of dimensionality associated to the computation of value functions and the explicit integration over the space of state variables. We present an empirical application and compare estimates using the GMM-Euler equations method with those from maximum likelihood and two-step methods.
Many dynamic problems in economics are characterized by large state spaces which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of high-dimensional dynamic models based on sieves and establish results for the (a) consistency, (b) rates of convergence, and (c) bounds on the error of approximation. We embed this method for approximating the solution to the dynamic problem within an estimation routine and prove that it provides consistent estimates of the modelik’s parameters. We provide Monte Carlo evidence that our method can successfully be used to approximate models that would otherwise be infeasible to compute, suggesting that these techniques may substantially broaden the class of models that can be solved and estimated.
In this article, we consider the nonparametric identification of Markov dynamic games models in which each firm has its own unobserved state variable, which is persistent over time. This class of models includes most models in the Ericson and Pakes (1995) and Pakes and McGuire (1994) framework. We provide conditions under which the joint Markov equilibrium process of the firms’ observed and unobserved variables can be nonparametrically identified from data. For stationary continuous action games, we show that only three observations of the observed component are required to identify the equilibrium Markov process of the dynamic game. When agents’ choice variables are discrete, but the unobserved state variables are continuous, four observations are required.
We propose a methodology for estimating preference parameters in matching models. Our estimator applies to repeated observations of matchings among a fixed group of individuals. Our estimator is based on the stability conditions in matching models; we consider both transferable (TU) and nontransferable utility (NTU) models. In both cases, the stability conditions yield moment inequalities which can be taken to the data. The preference parameters are partially identified. We consider simple illustrative examples, and also an empirical application to aggregate marriage markets.
We provide a geometric formulation of the problem of identification of the matching surplus function and we show how the estimation problem can be solved by the introduction of a generalized entropy function over the set of matchings.
I show that the equilibrium distribution of matches associated with the empirical transferable utility one-to-one matching (TUM) model introduced by Choo and Siow (2006a, 2006b) corresponds to the fixed point of system of nonlinear equations; with and respectively equal to the number of discrete types of women and men. I use this representation to derive new comparative static results, showing how the match distribution varies with match surplus and the marginal distributions of agent types.
A Test for Monotone Comparative Statics
In this article we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable implications of the MCS prediction: that the extreme (high and low) conditiona l quantiles of the dependent variable increase monotonically with the explanatory variable. The main contribution of the article is to derive a likelihood-ratio test, which to the best of our knowledge is the first econometric test of MCS proposed in the literature. The test is an asymptotic “chi-bar squared” test for order restrictions on intermediate conditional quantiles. The key features of our approach are: (1) we do not need to estimate the underlying nonparametric model relating the dependent and explanatory variables to the latent disturbances; (2) we make few assumptions on the cardinality, location, or probabilities over equilibria. In particular, one can implement our test without assuming an equilibrium selection rule.
We propose a set-estimation approach to supermodular games using the restrictons of rationalizable strategies, which is a weaker solution concept than Nash equilibrium. The set of rationalizable strategies of a supermodular game forms a complete lattice, and are bounded above and below by two extremal Nash equilibria. We use a well-known alogrithm to compute the two extremal equilibria, and then construct moment inequalities for set estimation of the supermodular game. Finally, we conduct Monte Carlo experiments to illustrate how the estimated confidence sets vary in response to changes in the data generating process.
This article estimates the loan spread equation taking into account the endogenous matching between banks and firms in the loan market. To overcome the endogeneity problem, I supplement the loan spread equation with a two-sided matching model and estimate them jointly. Bayesian inference is feasible using a Gibbs sampling algorithm that performs Markov chain Monte Carlo (MCMC) simulations. I find that medium-sized banks and firms tend to be the most attractive partners, and that liquidity is also a consideration in choosing partners. Furthermore, banks with higher monitoring ability charge higher spreads, and firms that are more leveraged or less liquid are charged higher spreads.
We develop and estimate an empirical collective model with endogenous marriage formation, participation, and family labor supply. Intra-household transfers arise endogenously as the transfers that clear the marriage market. The intra-household allocation can be recovered from observations on marriage decisions. Introducing the marriage market in the collective model allows us to independently estimate transfers from labor supplies and from marriage decisions. We estimate a semiparametric version of our model using 1980, 1990, and 2000 US Census data. Estimates of the model using marriage data are much more consistent with the theoretical predictions than estimates derived from labor supply.
Throughout the 1990s, the supply of new condominiums in Tokyo significantly increased while prices persistently fell. This article investigates whether the market power of condominium developers is a factor in explaining the outcome in this market and whether there is a relationship between production cost trend and the degree of market power that the developers were able to exercise. In order to respond to these questions, we construct and structurally estimate a dynamic durable goods oligopoly model of the condominium market – one incorporating time-variant costs and a secondary market – using a nested GMM procedure. We find that the data provide no evidence that firms in the primary market have substantial market power in this industry. Moreover, the counterfactual experiment provides evidence that inflationary and deflationary expectations on production cost trends have asymmetric effects to the market power of condominium producers. The increase in their markup when cost inflation is anticipated is significantly higher than the decrease in the markup when the same magnitude of cost deflation is anticipated.
A dynamic oligopoly model of the cigarette industry is developed to study the responses of firms to various antismoking policies and to estimate the implications for the policy efficacy. The structural parameters are estimated using a combination of micro and macro level data and firms’ optimal price and advertising strategies are solved as a Markov Perfect Nash Equilibrium. The simulation results show that tobacco tax increase reduces both the overall smoking rate and the youth smoking rate, while advertising restrictions may increase the youth smoking rate. Firm’s responses strengthen the impact of antismoking policies in the short run.
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- Advances in Econometrics
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- Emerald Publishing Limited
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