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.     

A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model

This paper is concerned with the estimation of the autoregressive parameter in a widely considered spatial autocorrelation model. The typical estimator for this parameter considered in the literature is the (quasi) maximum likelihood estimator corresponding to a normal density. However, as discussed in this paper, the (quasi) maximum likelihood estimator may not be computationally feasible in many cases involving moderate- or large-sized samples. In this paper we suggest a generalized moments estimator that is computationally simple irrespective of the sample size. We provide results concerning the large and small sample properties of this estimator.     

Fractional integration with drift: estimation in small samples

We examine the finite-sample behavior of estimators of the order of integration in a fractionally integrated time-series model. In particular, we compare exact time-domain likelihood estimation to frequency-domain approximate likelihood estimation. We show that over-differencing is of critical importance for time-domain maximum-likelihood estimation in finite samples. Overdifferencing moves the differencing parameter (in the over-differenced model) away from the boundary of the parameter space, while at the same time obviating the need to estimate the drift parameter. The two estimators that we compare are asymptotically equivalent. In small samples, however, the time-domain estimator has smaller mean squared error than the frequency-domain estimator. Although the frequency-domain estimator has larger bias than the time-domain estimator for some regions of the parameter bias, it can also have smaller bias. We use a simulation procedure which exploits the approximate linearity of the bias function to reduce the bias in the time-domain estimator.     

Semiparametric Estimation of the Intercept of a Sample Selection Model

This paper provides a consistent and asymptotically normal estimator for the intercept of a semiparametrically estimated sample selection model. The estimator uses a decreasingly small fraction of all observations as the sample size goes to infinity, as in Heckman (1990). In the semiparametrics literature, estimation of the intercept has typically been subsumed in the nonparametric sample selection bias correction term. The estimation of the intercept, however, is important from an economic perspective. For instance, it permits one to determine the "wage gap" between unionized and nonunionized workers, decompose the wage differential between different socio-economic groups (e.g. male–female and black–white), and evaluate the net benefits of a social programme.     

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.     

An MPEC estimator for misclassification models

In this paper, we propose a constrained maximum likelihood estimator for misclassification models, by formulating the estimation as an MPEC (Mathematical Programming with Equilibrium Constraints) problem. Our approach improves the numerical accuracy and avoids the singularity problem. Monte Carlo simulations confirm that the proposed estimator reduces bias and standard deviation of the estimator, especially when the sample is small/medium and/or the dimension of latent variable is large.     

Identification and estimation of endogenous selection models in the presence of misclassification errors

This paper shows the semi-parametric identification and estimation of sample selection models when the primary equation contains a discrete mismeasured endogenous covariate. Assuming that appropriate instruments for the presence of endogeneity are available, I apply a control function approach to remove the possible endogeneity. Based on the conditional mean independence between the model error and the selection error, the model can be regarded as a semi-parametric regression model with a discrete mismeasured covariate, thereby permitting a non-classical measurement error. Additional identification assumptions include monotonicity restrictions on the regression function and an empirical testable rank condition. I then use the identification result to construct a sieve maximum likelihood estimation estimator to estimate the model parameters consistently and recover the selection rule and joint probabilities of the accurately measured endogenous variable and the mismeasured observed variable. The proposed estimation method allows for a rather flexible functional form of the mismeasured endogenous covariate, requires only one valid instrument to control for both endogeneity and measurement errors for the variable of interest, and imposes no distribution assumptions on the selection rule.     

A COMPUTATIONALLY PRACTICAL SIMULATION ESTIMATION ALGORITHM FOR DYNAMIC PANEL DATA MODELS WITH UNOBSERVED ENDOGENOUS STATE VARIABLES*

This article develops a simulation estimation algorithm that is particularly useful for estimating dynamic panel data models with unobserved endogenous state variables. Repeated sampling experiments on dynamic probit models with serially correlated errors indicate the estimator has good small sample properties. We apply the estimator to a model of female labor supply and show that the rarely used Polya model fits the data substantially better than the popular Markov model. The Polya model also produces far less state dependence and many fewer race effects and much stronger effects of education, young children, and husband's income on female labor supply decisions.     

Estimating Housing Price: Kriging the Mean

The price of houses and its evolution in recent years is one of the issues that citizens and, of course, political and economic authorities are worried about. In most of the developed countries the mean price (per square meter) of houses in an area is estimated by a simple average of single prices from a sample of houses that does not take into account the spatial correlation among the prices. As an alternative to this classic procedure, in this paper we propose a linear estimator of the mean price of houses, using the kriging estimator, which has been specially designed for the case of spatially correlated data in a given domain. This estimator is the best unbiased linear one and provides a more realistic estimate of the mean price of houses in the urban area we are interested in. Obviously, the modelling of the variogram function is a central point in the global estimation process.     

Bootstrap confidence intervals for total value in small area statistics

In small area statistics, many problems deal with the estimation of unknown parameters. This paper will consider interval estimation. Three bootstrap confidence intervals of the total value for the small area are proposed. They are obtained by the percentile method, the t-bootstrap method, and the two-stage t-bootstrap method in the case of application of the count post-stratification estimator for total value. The proposed procedures are illustrated with simulation examples in which the investigated variable has the normal or Poisson distribution in population strata. We do not have to know the population or small area distribution for determining the bootstrap confidence intervals for small area parameters. This is the great advantage of bootstrap methods.     

SPECTRAL DENSITY ESTIMATION AND ROBUST HYPOTHESIS TESTING USING STEEP ORIGIN KERNELS WITHOUT TRUNCATION*

A new class of kernels for long‐run variance and spectral density estimation is developed by exponentiating traditional quadratic kernels. Depending on whether the exponent parameter is allowed to grow with the sample size, we establish different asymptotic approximations to the sampling distribution of the proposed estimators. When the exponent is passed to infinity with the sample size, the new estimator is consistent and shown to be asymptotically normal. When the exponent is fixed, the new estimator is inconsistent and has a nonstandard limiting distribution. It is shown via Monte Carlo experiments that, when the chosen exponent is small in practical applications, the nonstandard limit theory provides better approximations to the finite sample distributions of the spectral density estimator and the associated test statistic in regression settings.     

Dynamic Seemingly Unrelated Cointegrating Regressions

We propose the parametric Dynamic Seemingly Unrelated Regression (DSUR) estimator for simultaneous estimation of multiple cointegrating regressions. DSUR is efficient when the equilibrium errors are correlated across equations and is applicable for panel cointegration estimation in environments where the cross section is small relative to the available time series. We study the asymptotic and small sample properties of the DSUR estimator for both heterogeneous and homogeneous cointegrating vectors. We then apply the method to analyse two long-standing problems in international economics. Our first application revisits the estimation of long-run correlations between national investment and national saving. Our second application revisits the question of whether the forward exchange rate is an unbiased predictor of the future spot rate.     

CONSISTENT VARIANCE OF THE LAPLACE‐TYPE ESTIMATORS: APPLICATION TO DSGE MODELS

The Laplace‐type estimator has become popular in applied macroeconomics, in particular for estimation of dynamic stochastic general equilibrium (DSGE) models. It is often obtained as the mean and variance of a parameter's quasi‐posterior distribution, which is defined using a classical estimation objective. We demonstrate that the objective must be properly scaled; otherwise, arbitrarily small confidence intervals can be obtained if calculated directly from the quasi‐posterior distribution. We estimate a standard DSGE model and find that scaling up the objective may be useful in estimation with problematic parameter identification. It this case, however, it is important to adjust the quasi‐posterior variance to obtain valid confidence intervals.     

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.     

The non-monotonicity of the bias and mean squared error of the two stage least squares estimators of exogenous variable coefficients

Owen (1976) [Owen, A.D., 1976. A proof that both the bias and mean squared error of the two stage least squares estimator are monotonically non-increasing functions of sample size. Econometrica 44, 409–411.] has shown that in a two equation static simultaneous equation model both the bias and mean squared error of the two stage least squares estimator of the endogenous variable coefficient are monotonically non-increasing functions of the sample size. This paper shows that neither property carries over to the exogenous variable coefficient estimator.     

The combined estimator approach to model transferability and updating

The idea of transferability is to employ in model estimation, fitted model parameters computed from a different data set. Thecombined estimator approach to the transferability problem is expressed as a linear combination of the unbiased direct estimators on the two data sets. The major gain is in variance reduction. The combined estimator is shown to have superior accuracy, in a Mean Square Error sense, to a unbiased direct estimator whenever the transfer bias is relatively small. A test that indicates if the combined estimator is superior to the direct estimator is provided. Variances of the direct estimators are assumed to be known. Monte Carlo experiments are performed to assess the quality of the approximations. The results show that the approximations used are highly conservative. An empirical example of the combined estimator applied to a discrete choice problem is presented.     

Accounting for missing data in M-estimation: a general matching approach

This paper addresses M-estimation of conditional mean functions when observations are missing at random. The usual approach of correcting for missing data, when the missing data mechanism is ignorable, is inverse probability weighting (IPW). An alternative semiparametric M-estimator which involves local polynomial matching techniques is proposed and its asymptotic distribution is derived. Like IPW, the proposed estimation approach has a double robustness property for the estimation of unconditional means. Monte Carlo evidence suggests slightly better finite sample properties of the semiparametric M-estimator relatively to IPW. A version of the proposed estimator is applied to estimate the impact of noncognitive skills on wages in Germany for two different educational treatment regimes.     

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.     

Estimation of nonparametric inefficiency effects stochastic frontier models with an application to British manufacturing

The purpose of this paper is to propose a simple stochastic frontier model with a non-parametric specification for covariates affecting the mean of technical inefficiency. We derive a simple two-step semiparametric estimation procedure to estimate the frontier parameters as well as the mean of the technical inefficiency. The consistency of the estimator and its asymptotic normality are shown. The proposed method is illustrated using a large panel data set of British manufacturing firms.     

On Liu estimators for the logit regression model

This paper introduces a shrinkage estimator for the logit model which is a generalization of the estimator proposed by Liu (1993) for the linear regression. This new estimation method is suggested since the mean squared error (MSE) of the commonly used maximum likelihood (ML) method becomes inflated when the explanatory variables of the regression model are highly correlated. Using MSE, the optimal value of the shrinkage parameter is derived and some methods of estimating it are proposed. It is shown by means of Monte Carlo simulations that the estimated MSE and mean absolute error (MAE) are lower for the proposed Liu estimator than those of the ML in the presence of multicollinearity. Finally the benefit of the Lie estimator is shown in an empirical application where different economic factors are used to explain the probability that municipalities have net increase of inhabitants.