The Computation of Opportunity Costs in Polytomous Choice Models with Selectivity

This article provides general formulas for the computation of opportunity costs (or forgone earnings) of unchosen alternatives in sample selection models with binary or polytomous choices. With observed choice probabilities and outcomes of chosen alternatives, the opportunity costs of unchosen alternatives can be evaluated. The derived formulas for the general model involve only single integrals. For the probability indexed sample selection models with conditional logit choice probabilities, which include the polytomous choice model of Lee [1983], the formulas have simple closed form expressions. These formulas are useful for empirical studies.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100845/1/ECON300.pd

Semiparametric Estimation of Simultaneous Equation Microeconometric Models with Index Restrictions

This article introduces semiparametric methods for the estimation of simultaneous-equation microeconometric models with index restrictions. The methods are motivated by a semiparametric minimum-distance procedure, which unifies the estimation of both regression-type and linear or nonlinear simultaneous-equation models without emphasis on the construction of instrumental variables. Single-equation and systematic estimation methods and optimal weighting procedures are considered. The estimators are √n-consistent and asymptotically normal. For the estimation of nonparametric regression and some sample selection models where the variances of disturbances are functions of the same indices, the optimal weighted estimator attains Chamberlain's efficient bound for models with conditional moment restrictions. The weighted estimator is shown to be optimal within a class of semiparametric instrumental variables estimators.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100839/1/ECON296.pd

Semiparametric Minimum-distance Estimation

Semiparametric minimum-distance estimation methods are introduced for the estimation of parametric or semiparametric econometric models. The semiparametric minimum-distance estimation methods share some familiar properties of the classical minimum-distance estimation method. However, they can be applied to the estimation of models with disagregated data. Asymptotic properties of the estimators are analyzed. Some goodness-of-fit test statistics are introduced. For the estimation of some econometric models, weighted minimum-distance estimators can be asymptotically efficient. The minimum-distance estimators are asympototically invariant with respect to some transformations.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100840/1/ECON297.pd

Simulated Maximum Likelihood Estimation of Discrete Models with Group Data

This article has compared the performance of two methods of simulated maximum likelihood for the estimation of discrete choice models with group data. One method of simulated likelihood uses simulators which are sstatistically independent across individuals in the sample. The alternative method allows simulators to be correlated across individuals. the comparisons are based on the criteria of statistical efficiency and computation time cost. As the simulated maximum likelihood method with dependent simulators can take into account the presence of sufficient statistics in group data, it can have advantages over the simulated likelihood method with independent simulators in term of computation cost saving and statistical efficiency. The computation time cost of the simulated likelihood method with dependent simulators can be inexpensive as the method of simulated moments of McFadden (1989). This is so especially for group data with either large sample sizes or small number of groups. Besides theoretical analysis, Monte Carlo results provide some evidence.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100841/1/ECON298.pd

Asymptotic Distribution of the Maximum Likelihood Estimator for a Stochastic Frontier Function Model with a Singular Information Matrix

This article has investigated the asymptotic distribution of the maximum likelihood estimator in a stochastic frontier function when the firms are all technically efficient. For such a situation, the true parameter vector is on the boundary of the parameter space, and the scores are linearly dependent. The maximum likelihood estimator is shown to be a mixture of certain truncated distributions. The maximum likelihood estimates for different parameters may have different rates of convergence. The model can be reparameterized into one with a regular likelihood function. The likelihood ratio test statistic has the usual mixture of chi-square distributions as in the regular case.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100837/1/ECON294.pd

Simulated Maximum Likelihood Estimation of Dynamic Discrete Choice Statistical Models--Some Monte Carlo Results

This article reports Monte Carlo results on the simulated maximum likelihood estimation of discrete panel statistical models. Among them are Markov, Generalized Poly, Renewal, and Havit Persistence Models with or without unobserved heterogeneity and serially correlated disturbances. We investigate statistical properties and computational performance of simulated maximum likelihood methods and a bias-correction procedure. With a moderate number of simulation draws for the construction of simulator and the bias adjusted procedure, most of these complex dynamic models can be adequately estimated for panels with length up to 30. The Polya model and the Renewal model can be accurately estimated for panels with 50 periods.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100844/1/ECON299.pd

Microeconometric Models of Rationing, Imperfect Markets, and Non-Negativity Constraints

This paper provides a theoretically consistent approach to estimating demand relationships in which kink points occur either in the interior or on the vertices of the budget set. There are important classes of problems in developing countries which demonstrate such kinked budget sets including binding non-negativity constraints. This paper also extends these methods to the estimation of production structures. As an application a translog cost function for three energy inputs is estimated from cross-sections of individual Indonesian firms.Political Economy,

Asymptotic Bias in Maximum Simulated Likelihood Estimation of Discrete Choice Models

In this article, we have investigated a bias in an asymptotic expansion of the maximum simulated likelihood estimator introduced by Lerman and Manski for the estimation of discrete choice models. This bias occurs due to the nonlinearity of the derivatives of the log likelihood function and the statistically independent simulation errors of the choice probabilities across observations. This bias can be the dominated bias in an asymptotic expansion of the maximum simulated likelihood estimator when the number of simulated random variables per observationdoes not increase as fast as or faster than the sample size. The properly normalized maximum simulated likelihood estimator has even an asymptotic bias in its limiting distribution if the number of simulated random variables increase only as fast as the square root of the sample size. A bias-adjustment is introduced which can reduce the bias. Some Monte Carlo experiments have demonstrated the usefulness of the bias-adjustment procedure.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100836/1/ECON293.pd

Simulated Maximum Likelihood Estimation of the Linear Expenditure System with Binding Non-Negativity Constraints

This paper discusses issues on the estimation of consumer demand equations subject to binding non-negative constraints. We propose computationally feasible specifications and a simulated maximum likelihood (SML) method for demand systems. Our study shows that the econometric implementation of the SML estimates can avoid high-dimensional integration problems. As contrary to the simulation method of moments and simulated pseudo-likelihood methods that require the simulation of demand quantities subject to nonnegativity constraints for consumers in the sample, the SML approach requires only simulation of the likelihood function. The SML approach avoids solving for simulated demand quantities because the likelihood function is conditional on observed demand quantities. We have applied SML approach for the linear expenditure system (LES) with non-negativity constraints. The results of a seven-goods demand system are presented. The results provide empirical evidence on the importance of taking into account possible cross equation correlations in disturbances.Simulated likelihood, Linear expenditure system, Non-negativity constraints, Multivariate censored variables, Nonlinear simultaneous equations