Estimation of sample selection bias models

Econometric models with sample selection biases are widely used in various fields of economics, such as labor economics. The Maximum Likelihood Estimator (MLE) is seldom used to estimate models because of computational difficulty, while Heckman's two-step estimator is widely used to estimate these models. However, Heckman's two-step estimator sometimes performs poorly. In this paper, methods of calculating the MLE are analysed, and finite sample properties of the MLE and Heckman's two-step estimator are compared using Monte Carlo experiments and empirical examples.     

Uniqueness of the least-distances estimator in regression models with multivariate response

In a regression model with univariate response, the quantities derived from the least-absolute-deviations method need not be unique. In this note, we show that, contrary to the univariate case, in a regression model with multivariate response, the least-distances method typically yields quantities that exhibit uniqueness properties that are similar to those obtained by the least-squares method.     

Sample Partitioning Estimation for Ergodic Diffusions

In this article, we present a new technique to obtain estimators for parameters of ergodic processes. When a diffusion is ergodic its transition density converges to the invariant density Durett (1996 Durett, R. (1996). Stochastic Calculus. A Practical Introduction. New York: CRC Press. [Google Scholar]). This convergence enabled us to introduce a sample partitioning technique that gives, in each subsample, observations that can be treated as independent and identically distributed. Within this framework, is possible the construction of estimators like maximum likelihood estimators or others.     

Linear model estimation errors with estimated design parameters

The problem of error estimation of parameters b in a linear model,Y = Xb+ e, is considered when the elements of the design matrix X are functions of an unknown ‘design’ parameter vector c. An estimated value c is substituted in X to obtain a derived design matrix [Xtilde]. Even though the usual linear model conditions are not satisfied with [Xtilde], there are situations in physical applications where the least squares solution to the parameters is used without concern for the magnitude of the resulting error. Such a solution can suffer from serious errors.

This paper examines bias and covariance errors of such estimators. Using a first-order Taylor series expansion, we derive approximations to the bias and covariance matrix of the estimated parameters. The bias approximation is a sum of two terms:One is due to the dependence between ? and Y; the other is due to the estimation errors of ? and is proportional to b, the parameter being estimated. The covariance matrix approximation, on the other hand, is composed of three omponents:One component is due to the dependence between ? and Y; the second is the covariance matrix ∑_b corresponding to the minimum variance unbiased b, as if the design parameters were known without error; and the third is an additional component due to the errors in the design parameters. It is shown that the third error component is directly proportional to bb'. Thus, estimation of large parameters with wrong design matrix [Xtilde] will have larger errors of estimation. The results are illustrated with a simple linear example.     

Basic structure of the asymptotic theory in dynamic nonlineaerco nometric models,part i: consistency and approximation concepts

This is the first of two papers that provide an expository discussion of the basic structure of the asymptotic theory of M-estimators in dynamic nonlinear models and a revlew of the literature. In this paper we discuss consistency,uniform laws of large numbers and develop a new framework for laws of large numbers for dependent and heterogeneous processes, encompassing the theory of stochastically stable as well as near epoch dependent processes. This framework results in simplified catalogues of sufficient conditions for consistency. The second paper, Potscher and Prucha (1990b), deals with asymptotic distribution theory.     

A Strongly Consistent Criterion to Decide Between I(1) and I(0) Processes Based on Different Convergence Rates

The usual procedure to determine whether a univariate time series is stationary or first-difference stationary is to perform some unit root test. In this article, an alternative methodology is presented that leads to a strongly consistent two-step criterion to estimate the number of unit roots. The criterion is based on estimating some autoregressive polynomials using regression procedures and exploiting the fact that the nonstationary roots converge at a faster rate than the stationary ones. The proposed procedure requires at most four regressions and is easy to implement. A simulation study demonstrates that it can perform significantly better in practice than the Dickey–Fuller and the generalized least squares (GLS)-detrended Dickey–Fuller tests.     

ON ASYMPTOTIC PROPERTIES OF A TWO DIMENSIONAL FREQUENCY ESTIMATOR

Estimating parameters of a two dimensional frequency model is an important problem in statistical signal processing. In this paper, we consider the two-dimensional frequency model in presence of an additive stationary noise. We consider two different estimators and obtain their asymptotic properties. The asymptotic properties can be used to construct confidence intervals of the unknown parameters and for testing purposes also. The small sample performances of these estimators are observed using numerical simulations.     

Estimating the error variance in nonparametric regression by a covariate-matched u-statistic

For nonparametric regression models with fixed and random design, two classes of estimators for the error variance have been introduced: second sample moments based on residuals from a nonparametric fit, and difference-based estimators. The former are asymptotically optimal but require estimating the regression function; the latter are simple but have larger asymptotic variance. For nonparametric regression models with random covariates, we introduce a class of estimators for the error variance that are related to difference-based estimators: covariate-matched U-statistics. We give conditions on the random weights involved that lead to asymptotically optimal estimators of the error variance. Our explicit construction of the weights uses a kernel estimator for the covariate density.     

论“省力原则”在沟通决策中的应用

根据经济原则，分析了沟通过程中的诸要素，以及各要素之间的关系，闸述了省力原则在沟通决策中的 应用，并重新构建了沟通过程。     

On the efficiency of two-stage and three-stage least squares estimators

This paper utilizes the results of Kruskal (1968), Zyskind (1967), and more recently Milliken and Albohali (1984) to derive a simple necessary and sufficient condition for 3SLS to be equivalent to 2SLS. This condition depends upon the inverse of the variance:covariance matrix of the disturbances, and the set of second stage regressors of each structural equation. More importantly, this condition should prove useful for econometric students and provides an easy method for checking sufficiency.