The asymptotic efficiency of semiparametric estimators for censored linear regression models

This paper presents numerical comparisons of the asymptotic mean square estimation errors of semiparametric generalized least squares (SGLS), quantite, symmetrically censored least squares (SCLS), and tobit maximum likelihood estimators of the slope parameters of censored linear regression models with one explanatory variable. The results indicate that the SCLS estimator is less efficient than the other two semiparametric estimators. The SGLS estimator is more efficient than quantile estimators when the tails of the distribution of the random component of the model are not too thick and the probability of censoring is not too large. The most efficient semiparametric estimators usually have smaller mean square estimation errors than does the tobit estimator when the random component of the model is not normally distributed and the sample size is 500–1,000 or more.     

Estimation of Censored Regression Model: A Simulation Study

We investigate the finite sample performance of several estimators proposed for the panel data Tobit regression model with individual effects, including Honoré estimator, Hansen’s best two-step GMM estimator, the continuously updating GMM estimator, and the empirical likelihood estimator (ELE). The latter three estimators are based on more conditional moment restrictions than the Honoré estimator, and consequently are more efficient in large samples. Although the latter three estimators are asymptotically equivalent, the last two have better finite sample performance. However, our simulation reveals that the continuously updating GMM estimator performs no better, and in most cases is worse than Honoré estimator in small samples. The reason for this finding is that the latter three estimators are based on more moment restrictions that require discarding observations. In our designs, about seventy percent of observations are discarded. The insufficiently few number of observations leads to an imprecise weighted matrix estimate, which in turn leads to unreliable estimates. This study calls for an alternative estimation method that does not rely on trimming for finite sample panel data censored regression model.     

Endogeneity in Semiparametric Binary Response Models

This paper develops and implements semiparametric methods for estimating binary response (binary choice) models with continuous endogenous regressors. It extends existing results on semiparametric estimation in single-index binary response models to the case of endogenous regressors. It develops a control function approach to account for endogeneity in triangular and fully simultaneous binary response models. The proposed estimation method is applied to estimate the income effect in a labour market participation problem using a large micro data-set from the British Family Expenditure Survey. The semiparametric estimator is found to perform well, detecting a significant attenuation bias. The proposed estimator is contrasted to the corresponding probit and linear probability specifications.     

On the estimation and forecasting of international migration: how relevant is heterogeneity across countries?

This paper performs a comparative analysis of estimation as well as of out-of-sample forecasting results of more than 20 estimators common in the panel data literature using the data on migration to Germany from 18 source countries in the period 1967–2001. Our results suggest that the choice of an estimation procedure has a substantial impact on the parameter estimates of the migration function. Out-of-sample forecasting results indicate the following: (1) the standard fixed effects estimators clearly outperforms the pooled OLS estimator, (2) both the fixed effects estimators and the hierarchical Bayes estimator exhibit the superior forecast performance, (3) the fixed effects estimators outperform GMM and other instrumental variables estimators, (4) forecasting performance of heterogenous estimators is mediocre in our data set.     

MODELLING EXPECTATIONS: A REVIEW OF LIMITED INFORMATION ESTIMATION METHODS

The plethora of limited information estimation methods applied to expectations models are presented within a coherent framework based on standard econometric estimators. It is then possible to isolate those problems that arise solely because of the inclusion of expectations variables. The relationship between the economic solution of RE models and the appropriate choice of estimator is examined.     

Simulated Non-Parametric Estimation of Dynamic Models

This paper introduces a new class of parameter estimators for dynamic models, called simulated non-parametric estimators (SNEs). The SNE minimizes appropriate distances between non-parametric conditional (or joint) densities estimated from sample data and non-parametric conditional (or joint) densities estimated from data simulated out of the model of interest. Sample data and model-simulated data are smoothed with the same kernel, which considerably simplifies bandwidth selection for the purpose of implementing the estimator. Furthermore, the SNE displays the same asymptotic efficiency properties as the maximum-likelihood estimator as soon as the model is Markov in the observable variables. The methods introduced in this paper are fairly simple to implement, and possess finite sample properties that are well approximated by the asymptotic theory. We illustrate these features within typical estimation problems that arise in financial economics.     

General instrumental variables estimation under stochastic linear restrictions

This letter extends the Theil-Goldberger ‘mixed’ regression estimator, for models subject to stochastic linear restrictions, to the case of stochastic regressors. A general instrumental variables ‘mixed’ estimator is discussed. The asymptotic distribution of the estimator is obtained, and an asymptotic test of the compatibility of the sample and prior information is presented.     

An improved single equation estimation procedure for rational expectations models

This paper introduces a new readily programmable single-equation errors in variables estimation procedure for rational expectations models. For the illustrative example provided, this new estimator outperforms the currently available estimators.     

Estimation of Discrete Choice Dynamic Programming Models

This study reviews estimation methods for the infinite horizon discrete choice dynamic programming models and conducts Monte Carlo experiments. We consider: the maximum likelihood estimator (MLE), the two‐step conditional choice probabilities estimator, sequential estimators based on policy iterations mapping under finite dependence, and sequential estimators based on value iteration mappings. Our simulation result shows that the estimation performance of the sequential estimators based on policy iterations and value iteration mappings is largely comparable to the MLE, while they achieve substantial computation gains over the MLE by a factor of 100 for a model with a moderately large state space.     

Redundancy of Moment Conditions in Restricted GMM Estimation

Using a novel approach to calculating the rank of the difference of two asymptotic variance matrices, The author derives the necessary and sufficient conditions for an extra set of moment conditions to be redundant given a set of moment conditions in GMM estimation with general nonlinear restrictions. The necessary and sufficient conditions derived in this paper include as a special case the redundancy of moment conditions for GMM estimation without restrictions that was first derived by Breusch et al. (1999). Therefore this paper advances the research on redundancy of moment conditions from unrestricted GMM estimation to a larger class of GMM estimation. To show their usefulness, the main results of the current paper are applied to instrumental variables estimation of linear regression models and the efficient estimation of seemingly unrelated regressions models, subject to restrictions.     

Instrumental variables estimation with partially missing instruments

This paper shows that instrumental variables estimators currently in use, require strong but neglected auxiliary assumptions to be consistent in situations with partially missing instruments. We introduce an alternative instrumental variables estimator that does not require auxiliary assumptions.     

Estimation of Dynamic Panel Data Sample Selection Models

This paper considers the problem of identification and estimation in panel data sample selection models with a binary selection rule, when the latent equations contain strictly exogenous variables, lags of the dependent variables, and unobserved individual effects. We derive a set of conditional moment restrictions which are then exploited to construct two-step GMM-type estimators for the parameters of the main equation. In the first step, the unknown parameters of the selection equation are consistently estimated. In the second step, these estimates are used to construct kernel weights in a manner such that the weight that any two-period individual observation receives in the estimation varies inversely with the relative magnitude of the sample selection effect in the two periods. Under appropriate assumptions, these "kernel-weighted" GMM estimators are consistent and asymptotically normal. The finite sample properties of the proposed estimators are investigated in a small Monte-Carlo study.     

Some simulation studies of nonparametric estimators

This paper constructs a number of Monte Carlo studies to assess the quality of various nonparametric estimators that have been proposed recently for the estimation of nonlinear econometric models. We consider both kernel and Fourier series based methods of estimation, and also examine techniques that have been suggested to improve the bias properties of the kernel estimator. The two models examined are a production function and a model emphasising the effects of risk. The Fourier estimator does very well in estimating the first of these, but not the second, while the kernel estimator shows substantial bias for the first, which is only partially alleviated by the procedures advocated for bias correction, and good results for the second.     

Efficient Estimation of Additive Partially Linear Models

I consider the problem of estimating an additive partially linear model using general series estimation methods with polynomial and splines as two leading cases. I show that the finite-dimensional parameter is identified under weak conditions. I establish the root-n-normality result for the finite-dimensional parameter in the linear part of the model and show that it is asymptotically more efficient than a semiparametric estimator that ignores the additive structure. When the error is conditional homoskedastic, my finite-dimensional parameter estimator reaches the semiparametric efficiency bound. Efficient estimation when the error is conditional heteroskedastic is also discussed.     

Estimating average economic growth in time series data with persistency

This paper studies estimation of average economic growth in time series models with persistency. In particular, a joint estimation of the trend coefficient and the autoregressive parameter is considered. An analysis on the proposed estimator is provided. Our analysis is also extended to the case with general disturbance distributions. A nonlinear M estimator and a class of partially adaptive M estimators which adapt themselves with respect to a measure of the tailthickness are considered. The joint estimator and its partially adapted version are compared with several conventional estimators. Monte Carlo experiments indicate that the proposed estimators have good finite sample performance. We use the proposed estimation procedure to estimate the growth rates for real GNP and consumer price index in 40 countries.     

Semiparametric Bayesian estimation of mixed count regression models

This paper develops semiparametric Bayesian estimation approach for Poisson regression models with unobserved heterogeneity of unknown density. This approach is computationally efficient and allows automatic adaptation of the approximating density to data during estimation. Simulations show the estimator performs well.     

On Efficient Estimation and Correct Inference in Models with Generated Regressors: a General Approach

Two approaches have been developed for deriving the properties of efficiency and consistency of standard errors of two step estimators of linear models containing current or lagged unobserved expectations of a single variable. One method is based on the derivatives of the likelihood function and information matrix, while the other uses the true covariance matrix of the disturbance vector when unknown parameters or variables are replaced by corresponding estimates. In this paper, the second approach is extended to cases where the structural equation is nonlinear and the model contains expectations of more than one variable or expectations of future variables. The properties of a frequently used estimator to deal with missing observations problems, a model involving a variance as an explanatory variable, and a recently developed estimator for autoregressive moving average models can be easily derived using the results of the paper. Methods for improving the efficiency of two step estimators are outlined.
JEL Classification Number: C13     

Efficiency of two-step estimators for censored systems of equations: Shonkwiler and Yen reconsidered

This study analyses a parametric estimator for a system of equations with limited dependent variables that was recently proposed. Its performance is compared with those of alternative estimation procedures using Monte Carlo methods. The comparison shows that this new estimator is less efficient for a wide range of parameter regions than multivariate generalizations of the classical Heckman model. This result can be explained by its variance depending on the squared conditional mean of the dependent variables. Additionally, it turns out that within the class of generalized Heckman estimators, rather simple ones display the best performance.     

Estimation of Structural Nonlinear Errors‐in‐Varibles Models by Simulated Least‐Squares Method

This article proposes a simulation approach to obtain least‐squares or generalized least‐squares estimators of structural nonlinear errors‐in‐variables models. The proposed estimators are computationally attractive because they do not need numerical integration nor huge numbers of simulations per observable. In addition, the asymptotic covariance matrix of the estimator has a simple decomposition that may be used to guide selection of appropriate simulation sizes. The method is also useful for models with missing data or imperfect surrogate covariates, where application of conventional least‐squares and maximum‐likelihood methods is restricted by numerical multidimensional integrations.     

The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish

In markets where prices are determined by the intersection of supply and demand curves, standard identification results require the presence of instruments that shift one curve but not the other. These results are typically presented in the context of linear models with fixed coefficients and additive residuals. The first contribution of this paper is an investigation of the consequences of relaxing both the linearity and the additivity assumption for the interpretation of linear instrumental variables estimators. Without these assumptions, the standard linear instrumental variables estimator identifies a weighted average of the derivative of the behavioural relationship of interest. A second contribution is the formulation of critical identifying assumptions in terms of demand and supply at different prices and instruments, rather than in terms of functional-form specific residuals. Our approach to the simultaneous equations problem and the average-derivative interpretation of instrumental variables estimates is illustrated by estimating the demand for fresh whiting at the Fulton fish market. Strong and credible instruments for identification of this demand function are available in the form of weather conditions at sea.