Technology Adoption under Relative Factor Price Uncertainty: The Putty-Clay Investment Model

A plant has more flexibility in choosing among different technologies before undertaking an investment than after installing a specific 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 investmentirreversible investment; putty-clay; technology adoption; uncertainty

Technology Adoption Under Relative Factor Price Uncertainty: The Putty-Clay Investment Model

A plant has more flexibility in choosing among different technologies before undertaking an investment than after installing a specific 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---leads to a larger negative effect of uncertainty in relative factor prices on investment. The empirical implications 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 play an important role in explaining the impact of exchange rate volatility on investment.Irreversible Investment, Putty-Clay, Technology Adoption, Uncertainty

Nested Pseudo-likelihood Estimation and Bootstrap-based Inference for Structural Discrete Markov Decision Models

This paper analyzes the higher-order properties of nested pseudo-likelihood (NPL) estimators and their practical implementation for parametric discrete Markov decision models in which the probability distribution is defined as a fixed point. We propose a new NPL estimator that can achieve quadratic convergence without fully solving the fixed point problem in every iteration. We then extend the NPL estimators to develop one-step NPL bootstrap procedures for discrete Markov decision models and provide some Monte Carlo evidence based on a machine replacement model of Rust (1987). The proposed one-step bootstrap test statistics and confidence intervals improve upon the first order asymptotics even with a relatively small number of iterations. Improvements are particularly noticeable when analyzing the dynamic impacts of counterfactual policies.Edgeworth expansion, k-step bootstrap, maximum pseudo-likelihood estimators, nested fixed point algorithm, Newton-Raphson method, policy iteration

Nonparametric Identification of Multivariate Mixtures

This article analyzes the identifiability of k-variate, M-component finite 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 and the component distributions from the distribution function of the observed data. We reveal an important link between the number of variables (k), the number of values each variable can take, and the number of identifiable components. A lower bound on the number of components (M) is nonparametrically identifiable if k >= 2, and the maximum identifiable number of components is determined by the number of different values each variable takes. When M is known, the mixing proportions and the component distributions are nonparametrically identified from matrices constructed from the distribution function of the data if (i) k >= 3, (ii) two of k variables take at least M different values, and (iii) these matrices satisfy some rank and eigenvalue conditions. For the unknown M case, we propose an algorithm that possibly identifies M and the component distributions from data. We discuss a condition for nonparametric identi fication and its observable implications. In case M cannot be identified, we use our identification condition to develop a procedure that consistently estimates a lower bound on the number of components by estimating the rank of a matrix constructed from the distribution function of observed variables.finite mixture, latent class analysis, latent class model, model selection, number of components, rank estimation

Sequential Estimation of Structural Models with a Fixed Point Constraint

This paper considers the estimation problem of structural models for which empirical restrictions are characterized by a fixed point constraint, such as structural dynamic discrete choice models or models of dynamic games. We analyze the conditions under which the nested pseudo-likelihood (NPL) algorithm converges to a consistent estimator and derive its convergence rate. We find that the NPL algorithm may not necessarily converge to a consistent estimator when the fixed 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.contraction, dynamic games, nested pseudo likelihood, recursive projection method

Nonparametric Identification and Estimation of Multivariate Mixtures

We study nonparametric identifiability of finite mixture models of k-variate data with M subpopulations, in which the components of the data vector are independent conditional on belonging to a subpopulation. We provide a sufficient condition for nonparametrically identifying M subpopulations when k>=3. Our focus is on the relationship between the number of values the components of the data vector can take on, and the number of identifiable subpopulations. Intuition would suggest that if the data vector can take many different values, then combining information from these different values helps identification. Hall and Zhou (2003) show, however, when k=2, two-component finite mixture models are not nonparametrically identifiable regardless of the number of the values the data vector can take. When k>=3, there emerges a link between the variation in the data vector, and the number of identifiable subpopulations: the number of identifiable subpopulations increases as the data vector takes on additional (different) values. This points to the possibility of identifying many components even when k=3, if the data vector has a continuously distributed element. Our identification method is constructive, and leads to an estimation strategy. It is not as efficient as the MLE, but can be used as the initial value of the optimization algorithm in computing the MLE. We also provide a sufficient condition for identifying the number of nonparametrically identifiable components, and develop a method for statistically testing and consistently estimating the number of nonparametrically identifiable components. We extend these procedures to develop a test for the number of components in binomial mixtures.finite mixture, binomial mixture, model selection, number of components, rank estimation