Linear Programming-Based Estimators in Simple Linear Regression

Oxford Bulletin of Economics and Statistics, 1994

Journal of Business & Economic Statistics, 2001

Applied economists have long struggled with the question of how to accommodate binary endogenous regressors in models with binary and nonnegative outcomes. I argue here that much of the dif culty with limited dependent variables comes from a focus on structural parameters, such as index coef cients, instead of causal effects. Once the object of estimation is taken to be the causal effect of treatment, several simple strategies are available. These include conventional two-stage least squares, multiplicative models for conditional means, linear approximation of nonlinear causal models, models for distribution effects, and quantile regression with an endogenous binary regressor. The estimation strategies discussed in the article are illustrated by using multiple births to estimate the effect of childbearing on employment status and hours of work.

2009

This paper considers the problem of estimating model parameters in the case of endogenous regressors when the problem involves a large number of weak and/or invalid instruments. A Latent generalized method of moments estimator in a data rich environment (LGMM) is presented in the broader context of the generalized method of moments estimators (GMM), and a nonlinear simultaneous latent-factors GMM estimation routine is described that provides estimates of both the latent instruments and the structural parameters. The potential weak instruments are allowed to be highly correlated with the innovation of the regression equation. Consistency of the single equation LGMM estimator is established. We show that this estimator is consistent even if the observed instruments are invalid. A Monte Carlo experiment, that compares the relative performance of this estimator with some other estimators, is reviewed. Simulations indicate that the method outperforms OLS and other estimators when the instruments are both valid and invalid and, the idiosyncratic errors may be weakly cross-correlated and heteroskedastic.

This study compares the estimators of linear model when the least square assumptions of independence of the error terms and the zero correlation between the regressor and the error terms are violated using a Monte Carlo experiment. OLS, OLSA, 2SLS and 2SLSA estimators were considered in 10,000 replications of the experiment on single equation model where the error terms are AR(1) autocorrelated and at the same time significantly correlated with the regressor(endogeneity). We consider autocorrelation levels (ρ) 0.4, 0.8 and 0.9, significant correlation levels (α) between the regressor and the error terms at 0.01, 0.02 and 0.05 each at the sample size (N) 20, 40 and 60. The estimators are adjudged using the RMSE criteria on the 108 scenarios. The result shows that 2SLS perform best when N≤40 at all ρ and α levels. OLSA is the best estimator when N is large (N = 60) and ρ ≤ 0.8, while 2SLSA performs best when N and ρ are large, at all α levels. All estimators perform worse as autocorre...

Applications of Mathematics, 1999

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The Japanese Economic Review, 1997

Two approaches have been developed for deriving the properties of ef®ciency 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 ef®ciency of two step estimators are outlined.

Journal of Econometrics, 1986

The purpose of this paper is to present and analyze an instrumental variables estimator for limited dependent variable models that does not require functional form assumptions for the distribution of disturbances. This estimator is a weighted instrumental variables estimator, where the weight is the ratio of a multivariate normal density to the actual density of the instrumental variables. A semi-non-parametric estimator of the weights is presented and some conJectures concerning the asymptotic distribution of the estimator are discussed.

Empirical Economics, 2015

This study examines the consequences of using an estimated aggregate measure as an explanatory variable in linear regression. We show that neglecting the seemingly small sampling error in the estimated regressor could severely contaminate the estimates. We propose a simple statistical framework to account for the error. In particular, we apply our analysis to two aggregate indicators of economic development, the Gini coefficient and sex ratio. Our findings suggest that the impact of the estimated regressor could be substantially underestimated, when the sampling error is not accounted for.

Journal of Econometrics, 2007

Global Journal of Pure and Applied Sciences, 2008

In linear regression model, regressors are assumed fixed in repeated sampling. This assumption is not always satisfied especially in business, economics and social sciences. Consequently in this paper, effort is made to compare the performances of some estimators of linear model with autocorrelated error terms when normally distributed regressors are fixed (non-stochastic) with when they are stochastic. The estimators are the ordinary least square (OLS) estimator and four feasible generalized least estimators which are Cochrane Orcutt (CORC), Hidreth-Lu (HILU), Maximum Likelihood (ML), Maximum Likelihood Grid (MLGD) estimator. These estimators are compared using the finite properties of estimators' criteria namely; sum of biases, sum of variances and sum of the mean squared error of the estimated parameter of the model at different levels of autocorrelation and sample size through Monte-Carlo studies.