The dynamic invariant multinomial probit model: Identification,pretesting and estimation

We present a new specification for the multinomial multiperiod probit model with autocorrelated errors. In sharp contrast with commonly used specifications, ours is invariant with respect to the choice of a baseline alternative for utility differencing. It also nests these standard models as special cases, allowing for data-based selection of the baseline alternatives for the latter. Likelihood evaluation is achieved under an Efficient Importance Sampling (EIS) version of the standard GHK algorithm. Several simulation experiments highlight identification, estimation and pretesting within the new class of multinomial multiperiod probit models.     

Partial maximum likelihood estimation of spatial probit models

This paper analyzes spatial Probit models for cross sectional dependent data in a binary choice context. Observations are divided by pairwise groups and bivariate normal distributions are specified within each group. Partial maximum likelihood estimators are introduced and they are shown to be consistent and asymptotically normal under some regularity conditions. Consistent covariance matrix estimators are also provided. Estimates of average partial effects can also be obtained once we characterize the conditional distribution of the latent error. Finally, a simulation study shows the advantages of our new estimation procedure in this setting. Our proposed partial maximum likelihood estimators are shown to be more efficient than the generalized method of moments counterparts.     

Trending time-varying coefficient time series models with serially correlated errors

This paper studies a time-varying coefficient time series model with a time trend function and serially correlated errors to characterize the nonlinearity, nonstationarity, and trending phenomenon. A local linear approach is developed to estimate the time trend and coefficient functions. The asymptotic properties of the proposed estimators, coupled with their comparisons with other methods, are established under the α$\alpha$-mixing conditions and without specifying the error distribution. Further, the asymptotic behaviors of the estimators at the boundaries are examined. The practical problem of implementation is also addressed. In particular, a simple nonparametric version of a bootstrap test is adapted for testing misspecification and stationarity, together with a data-driven method for selecting the bandwidth and a consistent estimate of the standard errors. Finally, results of two Monte Carlo experiments are presented to examine the finite sample performances of the proposed procedures and an empirical example is discussed.     

GMM estimation of spatial autoregressive models with unknown heteroskedasticity

In the presence of heteroskedastic disturbances, the MLE for the SAR models without taking into account the heteroskedasticity is generally inconsistent. The 2SLS estimates can have large variances and biases for cases where regressors do not have strong effects. In contrast, GMM estimators obtained from certain moment conditions can be robust. Asymptotically valid inferences can be drawn with consistently estimated covariance matrices. Efficiency can be improved by constructing the optimal weighted estimation.     

Fixed effects estimation of structural parameters and marginal effects in panel probit models

Fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper, I characterize the leading term of a large-T expansion of the bias of the MLE and estimators of average marginal effects in parametric fixed effects panel binary choice models. For probit index coefficients, the former term is proportional to the true value of the coefficients being estimated. This result allows me to derive a lower bound for the bias of the MLE. I then show that the resulting fixed effects estimates of ratios of coefficients and average marginal effects exhibit no bias in the absence of heterogeneity and negligible bias for a wide variety of distributions of regressors and individual effects in the presence of heterogeneity. I subsequently propose new bias-corrected estimators of index coefficients and marginal effects with improved finite sample properties for linear and nonlinear models with predetermined regressors.     

Efficient estimation in dynamic conditional quantile models

In this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data. We construct an M-estimator which achieves the semiparametric efficiency bound recently derived by Komunjer and Vuong (forthcoming). Our efficient M-estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density. The estimator is new and not yet seen in the literature. We illustrate its performance through a Monte Carlo experiment.     

Maximum likelihood estimation of partially observed diffusion models

This paper develops a maximum likelihood (ML) method to estimate partially observed diffusion models based on data sampled at discrete times. The method combines two techniques recently proposed in the literature in two separate steps. In the first step, the closed form approach of Aït-Sahalia (2008) is used to obtain a highly accurate approximation to the joint transition probability density of the latent and the observed states. In the second step, the efficient importance sampling technique of Richard and Zhang (2007) is used to integrate out the latent states, thereby yielding the likelihood function. Using both simulated and real data, we show that the proposed ML method works better than alternative methods. The new method does not require the underlying diffusion to have an affine structure and does not involve infill simulations. Therefore, the method has a wide range of applicability and its computational cost is moderate.     

Estimating a generalized correlation coefficient for a generalized bivariate probit model

In this paper we consider semiparametric estimation of a generalized correlation coefficient in a generalized bivariate probit model. The generalized correlation coefficient provides a simple summary statistic measuring the relationship between the two binary decision processes in a general framework. Our semiparametric estimation procedure consists of two steps, combining semiparametric estimators for univariate binary choice models with the method of maximum likelihood for the bivariate probit model with nonparametrically generated regressors. The estimator is shown to be consistent and asymptotically normal. The estimator performs well in our simulation study.     

Efficient estimation and inference in linear pseudo-panel data models

We consider pseudo-panel data models constructed from repeated cross sections in which the number of individuals per group is large relative to the number of groups and time periods. First, we show that, when time-invariant group fixed effects are neglected, the OLS estimator does not converge in probability to a constant but rather to a random variable. Second, we show that, while the fixed-effects (FE) estimator is consistent, the usual t statistic is not asymptotically normally distributed, and we propose a new robust t statistic whose asymptotic distribution is standard normal. Third, we propose efficient GMM estimators using the orthogonality conditions implied by grouping and we provide t tests that are valid even in the presence of time-invariant group effects. Our Monte Carlo results show that the proposed GMM estimator is more precise than the FE estimator and that our new t test has good size and is powerful.     

Method of moments estimation and identifiability of semiparametric nonlinear errors-in-variables models

This paper deals with a nonlinear errors-in-variables model where the distributions of the unobserved predictor variables and of the measurement errors are nonparametric. Using the instrumental variable approach, we propose method of moments estimators for the unknown parameters and simulation-based estimators to overcome the possible computational difficulty of minimizing an objective function which involves multiple integrals. Both estimators are consistent and asymptotically normally distributed under fairly general regularity conditions. Moreover, root-n consistent semiparametric estimators and a rank condition for model identifiability are derived using the combined methods of the nonparametric technique and Fourier deconvolution.     

Indirect estimation of large conditionally heteroskedastic factor models,with an application to the Dow 30 stocks

We derive indirect estimators of conditionally heteroskedastic factor models in which the volatilities of common and idiosyncratic factors depend on their past unobserved values by calibrating the score of a Kalman-filter approximation with inequality constraints on the auxiliary model parameters. We also propose alternative indirect estimators for large-scale models, and explain how to apply our procedures to many other dynamic latent variable models. We analyse the small sample behaviour of our indirect estimators and several likelihood-based procedures through an extensive Monte Carlo experiment with empirically realistic designs. Finally, we apply our procedures to weekly returns on the Dow 30 stocks.     

Identification and estimation of econometric models with group interactions,contextual factors and fixed effects

This paper considers identification and estimation of structural interaction effects in a social interaction model. The model allows unobservables in the group structure, which may be correlated with included regressors. We show that both the endogenous and exogenous interaction effects can be identified if there are sufficient variations in group sizes. We consider the estimation of the model by the conditional maximum likelihood and instrumental variables methods. For the case with large group sizes, the possible identification can be weak in the sense that the estimates converge in distribution at low rates.     

Fixed effects instrumental variables estimation in correlated random coefficient panel data models

We provide a set of conditions sufficient for consistency of a general class of fixed effects instrumental variables (FE-IV) estimators in the context of a correlated random coefficient panel data model, where one ignores the presence of individual-specific slopes. We discuss cases where the assumptions are met and violated. Monte Carlo simulations verify that the FE-IV estimator of the population averaged effect performs notably better than other standard estimators, provided a full set of period dummies is included. We also propose a simple test of selection bias in unbalanced panels when we suspect the slopes may vary by individual.     

GMM and 2SLS estimation of mixed regressive,spatial autoregressive models

The GMM method and the classical 2SLS method are considered for the estimation of mixed regressive, spatial autoregressive models. These methods have computational advantage over the conventional maximum likelihood method. The proposed GMM estimators are shown to be consistent and asymptotically normal. Within certain classes of GMM estimators, best ones are derived. The proposed GMM estimators improve upon the 2SLS estimators and are applicable even if all regressors are irrelevant. A best GMM estimator may have the same limiting distribution as the ML estimator (with normal disturbances).     

Panel data models with spatially correlated error components

In this paper we consider a panel data model with error components that are both spatially and time-wise correlated. The model blends specifications typically considered in the spatial literature with those considered in the error components literature. We introduce generalizations of the generalized moments estimators suggested in Kelejian and Prucha (1999. A generalized moments estimator for the autoregressive parameter in a spatial model. International Economic Review 40, 509–533) for estimating the spatial autoregressive parameter and the variance components of the disturbance process. We then use those estimators to define a feasible generalized least squares procedure for the regression parameters. We give formal large sample results for the proposed estimators. We emphasize that our estimators remain computationally feasible even in large samples.     

Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models

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.     

Semiparametric identification of binary decision games of incomplete information with correlated private signals

This paper studies the identification and estimation of a static binary decision game of incomplete information. We make no parametric assumptions on the joint distribution of private signals and allow them to be correlated. We show that the parameters of interest can be point-identified subject to a scale normalization under mild support requirements for the regressors (publicly observed state variables) and errors (private signals). Following Manski and Tamer (2002), we propose a maximum score type estimator for the structural parameters and establish the asymptotic properties of the estimator.     

The method of elimination and substitution in the GMM estimation of mixed regressive,spatial autoregressive models

This paper proposes a computationally simple GMM for the estimation of mixed regressive spatial autoregressive models. The proposed method explores the advantage of the method of elimination and substitution in linear algebra. The modified GMM approach reduces the joint (nonlinear) estimation of a complete vector of parameters into estimation of separate components. For the mixed regressive spatial autoregressive model, the nonlinear estimation is reduced to the estimation of the (single) spatial effect parameter. We identify situations under which the resulting estimator can be efficient relative to the joint GMM estimator where all the parameters are jointly estimated.     

Spatial correlation robust inference with errors in location or distance

This paper presents results from a Monte Carlo study concerning inference with spatially dependent data. We investigate the impact of location/distance measurement errors upon the accuracy of parametric and nonparametric estimators of asymptotic variances. Nonparametric estimators are quite robust to such errors, method of moments estimators perform surprisingly well, and MLE estimators are very poor. We also present and evaluate a specification test based on a parametric bootstrap that has good power properties for the types of measurement error we consider.