This article analyzes the identifiability of the number of components in k-variate, M-component nite mixture models in which each component distribution has independent marginals, including models in latent class analysis. Without making parametric assumptions on the component distributions, we investigate how one can identify the number of components from the distribution function of the observed data. When k  2, a lower bound on the number of components (M) is nonparametrically identiable from the rank of a matrix constructed from the distribution function of the observed variables. Building on this identification condition, we develop a procedure to consistently estimate a lower bound on the number of components.

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This paper develops an open economy model with heterogeneous final goods producers who simultaneously choose whether to export their output and whether to use imported intermediates. Using the theoretical model, we develop and estimate a structural empirical model that incorporates heterogeneity in productivity, transport costs, and other costs using Chilean plant-level data for a set of manufacturing industries. The estimated model is consistent with many key features of the data regarding productivity, exporting, and importing. We perform a variety of counterfactual experiments to assess quantitatively the positive and normative effects of barriers to trade in import and export markets. These experiments suggest that there are substantial gains in aggregate productivity and welfare due to trade. Furthermore, because of import and export complementarities, policies which inhibit the importation of foreign intermediates can have a large adverse effect on the exportation of final goods.

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This paper considers the estimation problem of structural models for which empirical restrictions are characterized by a xed point constraint, such as structural dynamic discrete choice models or models of dynamic games. We analyze a local condition under which the nested pseudo likelihood (NPL) algorithm converges to a consistent estimator and derive its convergence rate. We nd that the NPL algorithm may not necessarily converge to a consistent estimator when the xed point mapping does not have a local contraction property. To address the issue of divergence, we propose alternative sequential estimation procedures that can converge to a consistent estimator even when the NPL algorithm does not.

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This article develops a structural dynamic programming model of investment and estimates the model using panel data on Chilean manufacturing plants for 19801983 at a substantially faster rate had there been no temporary increase in import prices associated with higher tariffs in the mid-1980s.

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In dynamic discrete choice analysis, controlling for unobserved heterogeneity is an important issue, and finite mixture models provide flexible ways to account for it. This paper studies nonparametric identifiability of type probabilities and type-specific component distributions in finite mixture models of dynamic discrete choices. We derive sufficient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in applied work under different assumptions on the Markov property, stationarity, and type-invariance in the transition process. Three elements emerge as the important determinants of identification: the time-dimension of panel data, the number of values the covariates can take, and the heterogeneity of the response of different types to changes in the covariates. For example, in a simple case where the transition function is type-invariant, a time-dimension of T = 3 is sufficient for identification, provided that the number of values the covariates can take is no smaller than the number of types and that the changes in the covariates induce sufficiently heterogeneous variations in the choice probabilities across types. Identification is achieved even when state dependence is present if a model is stationary first-order Markovian and the panel has a moderate time-dimension (T⩾ 6). Copyright 2009 The Econometric Society.

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This paper examines whether importing intermediate goods improves plant performance. While addressing the issue of simultaneous productivity shocks and decisions to import intermediates, we estimate the impact foreign intermediates have on plants' productivity using plant-level Chilean manufacturing panel data. Across different estimators, we find evidence that becoming an importer of foreign intermediates improves productivity.

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This paper analyzes the higher-order properties of the estimators based on the nested pseudo-likelihood (NPL) algorithm and the practical implementation of such estimators for parametric discrete Markov decision models. We derive the rate at which the NPL algorithm converges to the MLE and provide a theoretical explanation for the simulation results in Aguirregabiria and Mira [Aguirregabiria, V., Mira, P., 2002. Swapping the nested fixed point algorithm: A class of estimators for discrete Markov decision models. Econometrica 70, 1519-1543], in which iterating the NPL algorithm improves the accuracy of the estimator. We then propose a new NPL algorithm that can achieve quadratic convergence without fully solving the fixed point problem in every iteration and apply our estimation procedure to a finite mixture model. We also develop one-step NPL bootstrap procedures for discrete Markov decision models. The Monte Carlo simulation evidence based on a machine replacement model of Rust [Rust, J., 1987. Optimal replacement of GMC bus engines: An empirical model of Harold Zurcher. Econometrica 55, 999-1033] shows that the proposed one-step bootstrap test statistics and confidence intervals improve upon the first order asymptotics even with a relatively small number of iterations.

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This paper considers likelihood-based testing of the null hypothesis of m0 components against the alternative of m0 + 1 components in a nite mixture model. The number of components is an important parameter in the applications of nite mixture models. Still, testing the number of components has been a long-standing challenging problem because of its non-regularity. We develop a framework that facilitates the analysis of the likelihood function of finite mixture models and derive the asymptotic distribution of the likelihood ratio test statistic for testing the null hypothesis of m0 components against the alternative of m0 + 1 components. Furthermore, building on this framework, we propose a likelihood-based testing procedure of the number of components. The proposed test, extending the EM approach of Li et al. (2009), does not use a penalty term and is implementable even when the likelihood ratio test is dicult to implement because of non-regularity and computational complexity.

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This paper develops a new computationally attractive procedure for estimating dynamic discrete choice models that is applicable to a wide range of dynamic programming models. The proposed procedure can accommodate unobserved state variables that (i) are neither additively separable nor follow generalized extreme value distribution, (ii) are serially correlated, and (iii) aect the choice set. Our estimation algorithm sequentially updates the parameter estimate and the value function estimate. It builds upon the idea of the iterative estimation algorithm proposed by Aguirregabiria and Mira (2002, 2007) but conducts iteration using the value function mapping rather than the policy iteration mapping. Its implementation is straightforward in terms of computer programming; unlike the Hotz-Miller type estimators, there is no need to reformulate a xed point mapping in the value function space as that in the space of probability distributions. It is also applicable to estimate models with unobserved heterogeneity. We analyze the convergence property of our sequential algorithm and derive the conditions for its convergence. We develop an approximated procedure which reduces computational cost substantially without deteriorating the convergence rate. We further extend our sequential procedure for estimating dynamic programming models with an equilibrium constraint, which include dynamic game models and dynamic macroeconomic models.

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To what extent does a tax credit aect rms' R&D activity? What are the mechanisms? This paper examines the eect of R&D tax credits on rms' R&D expenditure by exploiting the variation across rms in the changes in the eligible tax credit rate between 2000 and 2003. Estimating the rst-dierence equation of the linear R&D model by panel GMM, we
find the estimated coecient of an interaction term between the eligible tax credit rate and the debt-to-asset ratio is positive and signicant, indicating that the eect of tax credit is signicantly larger for rms with relatively large outstanding debts. Conducting counterfactual experiments, we found that the aggregate R&D expenditure in 2003 would have been lower by 3.0-3.4 percent if there had been no tax credit reform in 2003, where 0.3-0.6 percent is attributable to the eect of nancial constraint, and that the aggregate R&D expenditure would have been larger by 3.1-3.9 percent if there had been no cap on the amount of tax credits, where 0.3-0.8 percent is attributable to relaxing the nancial constraint of rms with outstanding debts.

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A plant has more flexibility in choosing among different technologies before undertaking an investment than after installing a speci¯c machine. This paper argues that the irreversibility of factor intensity choice may play an important role in explaining the dynamics of investment in the presence of relative factor price uncertainty. A higher degree of irreversibility in the choice of factor intensity|characterized by the ex ante elasticity of substitution between different factors|leads to a larger negative effect of uncertainty in relative factor prices on investment. The empirical implications of the putty-clay investment model are examined using the plant-level Chilean manufacturing data for the period of time-varying exchange rate volatility. The econometric results show that the elasticity of substitution between imported materials and domestic materials is substantially higher at the time of a large investment and suggest that the irreversibility of factor intensity choice may potentially play an important role in explaining the impact of exchange rate volatility on investment.

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