ORDINARY LEAST SQUARES ESTIMATION OF A DYNAMIC GAME MODEL

Estimation of dynamic games is known to be a numerically challenging task. A common form of the payoff functions employed in practice takes the linear‐in‐parameter specification. We show a least squares estimator taking a familiar OLS/GLS expression is available in such a case. Our proposed estimator has a closed form. It can be computed without any numerical optimization and always minimizes the least squares objective function. We specify the optimally weighted GLS estimator that is efficient in the class of estimators under consideration. Our estimator appears to perform well in a simple Monte Carlo experiment.     

Nonparametric Generalized Least Squares in Applied Regression Analysis

This paper compares a nonparametric generalized least squares (NPGLS) estimator to parametric feasible GLS (FGLS) and variants of heteroscedasticity robust standard error estimators (HRSE) in an applied setting. NPGLS consistently estimates the unknown scedastic function and produces more efficient parameter estimates than HRSE. We apply these various approaches for handling heteroscedasticity to data on professor rankings obtained from RateMyProfessors.com. We find that the statistical significance of key variables differs across seven versions of HRSE, leading to different conclusions, and a standard parametric approach to FGLS suffers from misspecification. NPGLS combines the virtues of both of these parametric approaches.     

The small sample properties of several limited information estimators in interdependent structures with scalar and vector autoregressive errors

This study is concerned with an examination of the finite sample behaviour of several limited information estimators in interdependent structures with error terms related over time and in certain specifications across equations. The Monte Carlo or simulation approach is adopted and applied to computationally manageable structures containing lagged dependent variables. The analysis of the Monte Carlo experiments is formulated in terms of estimating response functions, the dependent variables of which are the first two moments of target model estimators. In addition to the impact of simultaneity, autocorrelation and lagged dependent variables on the estimators, evidence is also accumulated on the small sample effects of misspecification in terms of the faulty inclusion and deletion of regressors. The results of the experiments revealed the substantial impact which autocorrelation can have on ordinary least squares (OLS) and two-stage least squares (2SLS) in terms of efficiency loss. Averaging over all the coefficients in the models, estimators which take account of both autocorrelation and simultaneity had a relative efficiency factor of about 1.5 to 1.9. Many of the parameters in the Monte Carlo model (including misspecification errors, multicollinearity) had qualitatively the same effect on bias and dispersion properties of the estimators.     

Small sample properties in a heterogenous Weibull model

Neglected heterogeneity implies bias for estimators in, e.g., the Weibull duration model. In a Monte Carlo experiment the proper maximum likelihood estimator is better than a new least squares estimator. The likelihood estimator neglecting heterogeneity is inferior.     

Interval regression models with endogenous explanatory variables

We consider the estimation of linear models where the dependent variable is observed by intervals and some continuous regressors may be endogenous. Our approach, an IV version of the technique devised by Stewart (Rev Econ Stud 50(3):737?C753, 1983), is fully parametric and two estimators are proposed: a two-step estimator and a limited-information maximum-likelihood estimator. The results can be summarized as follows: the two-step estimator has an intuitive appeal, and a Monte Carlo experiment suggests that its relative efficiency is rather satisfactory. The limited-information maximum-likelihood estimator, however, is probably simpler to implement and has the advantage of providing a framework in which several testing procedures are more straightforward to perform. The application of two-stage least squares to a proxy of the dependent variable built by taking midpoints, on the other hand, leads to inconsistent estimates; Monte Carlo evidence suggests that the bias arising from the ??midpoint?? technique is much worse than the effect of distributional misspecification. An example application is also included, which uses Australian data on migrants?? remittances; endogeneity effects are substantial and using conventional estimation methods leads to substantially misleading inference.     

Gasoline demand in the OECD: An application of pooling and testing procedures

This study utilizes a pooled inter-country data set, finding the long-run price-elasticity falls in the range ?0.55 to ?0.9, depending on the choice of pooled estimators. The estimators included the OLS, within-, and between-country estimators, plus five feasible GLS estimators. Even allowing for a ten-year distributed lag on price to reflect changes in auto-efficiency characteristics, the within-country estimator yields appreciably more inelastic estimates than did the O:S estimator, which was heavily influenced by the between- or inter-country variation. This difference raises intriguing questions for future research.     

Results on the bias and inconsistency of ordinary least squares for the linear probability model

This note formalizes bias and inconsistency results for ordinary least squares (OLS) on the linear probability model and provides sufficient conditions for unbiasedness and consistency to hold. The conditions suggest that a “trimming estimator” may reduce OLS bias.     

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.     

Moments of OLS estimators in an autoregressive moving average model with explanatory variables

In this paper we derive the moments of the ordinary least squares (OLS) estimators in an autoregressive moving average model by a straightforward technique compared to the one used in Carter and Ullah (1979). The model contains exogenous variables and the technique also provides simpler moment expressions and can be used to derive the moments in more general dynamic models.     

Purchasing Power Parity and aggregation bias for a developing country: The case of Mexico

This paper investigates long-run Purchasing Power Parity (PPP) between the US and Mexico. We use a panel of disaggregated price data between the US and Mexico with a long time series to look at two types of aggregation bias. The first is examined in Imbs et al. — which we refer to as estimator aggregation bias — and the second is put forth by Broda and Weinstein — hereafter, data aggregation bias. The findings indicate substantial estimator aggregation bias and data aggregation bias. Although estimates using aggregate data and imposing homogeneous coefficients provide little evidence of PPP, findings with disaggregated data and heterogeneous coefficient estimators offer strong support. The results also suggest the presence of small-sample bias as examined in Chen and Engel, but with little effect on the qualitative results. Tradable goods and non-tradable goods show little distinction in convergence rates. Estimated half-lives are lower under flexible than fixed exchange rates and indicate rapid convergence during the Mexican peso crisis.     

A Monte Carlo study of growth regressions

Using Monte Carlo simulations, this paper evaluates the bias properties of estimators commonly used to estimate growth regressions derived from the Solow model. We explicitly allow for measurement error, country-specific fixed effects and regressor endogeneity. An OLS estimator applied to a single cross-section of variables averaged over time (the between estimator) performs best in terms of the extent of bias on each of the estimated coefficients. Fixed-effects and the Arellano–Bond GMM estimator overstate the speed of convergence under a wide variety of assumptions, while the between estimator understates it. Finally, fixed effects and Arellano–Bond bias towards zero the slope estimates on the human and physical capital accumulation variables, while the between estimator and the Blundell–Bond system GMM estimator bias these coefficients upwards.      

A Monte Carlo comparison of the maximum likelihood and the corrected ols estimators for Tobit models

Green (1981,1983) proposed a simple way to correct the bias of OLS in Tobit models. In this paper, I present some Monte Carlo results comparing the performance of the Corrected OLS (COLS) with the Maximum Likelihood (ML) estimator.     

Asymptotic Properties Of The Estimator Of The Long-Run Coefficient In A Dynamic Model With Integrated Regressors And Serially Correlated Errors

In this paper we examine the asymptotic properties of the estimator of the long-run coefficient (LRC) in a dynamic regression model with integrated regressors and serially correlated errors. We show that the OLS estimators of the regression coefficients are inconsistent but the OLS-based estimator of the LRC is superconsistent. Furthermore, we propose an alternative consistent estimator of the LRC, compare the two estimators through a Monte Carlo experiment, and find that the proposed estimator is MSE-superior to the OLS-based estimator.     

A note on estimating disequilibrium models with aggregation

When an aggregate disequilibrium is the result of disequilibrium in several submarkets, the usual maximum likelihood estimation, which is based on the min of aggregate demand and supply, represents a misspecification. The present paper compares ML with several nonlinear least squares methods that are appropriate for this situation. Monte Carlo experiments suggest that ML is robust with respect to the misspecification and may be preferable to the nonlinear least suqares methods in some situations.     

Small Sample Properties Of Existing And New Estimators Of The Autocorrelation Coefficient And Regression Coefficients In The Context Of Ar(1) Errors

This study systematically and comprehensively investigates the small sample properties of the existing and some new estimators of the autocorrelation coefficient and of the regression coefficients in a linear regression model when errors follow an autoregressive process of order one. The new estimators of autocorrelation coefficient proposed here are based on the jackknife procedure. The jackknife procedure is applied in two alternative ways: first to the regression itself, and second to the residuals of the regression model. Next, the performance of the existing and new estimators of autocorrelation coefficient (thirty-three in total) is investigated in terms of bias and the root mean squared errors. Finally, we have systematically compared all of the estimators of the regression coefficients (again thirty-three) in terms of efficiency and their performance in hypothesis testing. We observe that the performance of the autocorrelation coefficient estimators is dependent upon the degree of autocorrelation and whether the autocorrelation is positive or negative. We do not observe a direct link between the bias and efficiency of an estimator. The performance of the estimators of the regression coefficients also depends upon the degree of autocorrelation. If the efficiency of regression estimator is of concern, then the iterative Prais-Winsten estimator should be used since it is most efficient for the widest range of independent variables and values of the autocorrelation coefficient. If testing of the hypothesis is of concern, then the estimators based on jackknife technique are certainly superior and are highly recommended. However, for negative values of the autocorrelation coefficient, the estimators based on Quenouille procedure and iterative Prais-Winsten estimator are comparable. But, for computational ease iterative Prais-Winsten estimator is recommended.

     

Does the labour supply of wives respond to husbands' wages? Canadian evidence from micro data and grouped data

Abstract. Using micro data and grouped data, we assess the extent to which Canadian wives adjusted their labour supply in response to changes in husbands' wages during the period 1980‐2000. Grouped data parameters based on weighted least squares and the unbiased‐error‐in‐variables estimator developed by Devereux (2004, 2007a,b) yield cross‐wage elasticities that are substantially higher (in absolute value) than those derived from OLS regressions run on micro data. Both grouping estimators indicate that the labour supply of Canadian wives responded strongly to changes in husbands' wages during the 1980s. For the 1990s, our estimates of wives' cross‐wage elasticity display greater dispersion.     

Monte Carlo studies on the effectiveness of the bootstrap bias reduction method on 2SLS estimates

If first moments exist, two stage least squares estimators are consistent although biased. In this paper several bias correction methods are compared including bootstrap two stage least squares, Nagar's k-class and jackknife estimators for both parametric and non-parametric cases. Monte Carlo experiments on several models investigate the non-large sample properties of these estimators. The results strongly favor the bootstrap procedure judged by the amount of bias reduction and comparative variances.     

On Calculation of the Extended Gini Coefficient

The conventional formula for estimating the extended Gini coefficient is a covariance formula provided by Lerman and Yitzhaki (1989). We suggest an alternative estimator, obtained by approximating the Lorenz curve by a series of linear segments. In a Monte Carlo experiment designed to assess the relative bias and efficiency of the two estimators, we find that, when using grouped data with 20 or fewer groups, our new estimator has less bias and lower mean squared error than the covariance estimator. When individual observations are used, or the number of groups is 30 or more, there is little or no difference in the performance of the two estimators.     

Hierarchically spatial autoregressive and moving average error model

This paper considers a hierarchically spatial autoregressive and moving average error (HSEARMA) model. This model captures the spatially autoregressive and moving average error correlation, the county-level random effects, and the district-level random effects nested within each county. We propose optimal generalized method of moments (GMM) estimators for the spatial error correlation coefficient and the error components' variances terms, as well as a feasible generalized least squares (FGLS) estimator for the regression parameter vector. Further, we prove consistency of the GMM estimator and establish the asymptotic distribution of the FGLS estimator. A finite-scale Monte Carlo simulation is conducted to demonstrate the good finite sample performances of our GMM-FGLS estimators.