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.     

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.     

Comparing features of convenient estimators for binary choice models with endogenous regressors

Abstract We discuss the relative advantages and disadvantages of four types of convenient estimators of binary choice models when regressors may be endogenous or mismeasured or when errors are likely to be heteroscedastic. For example, such models arise when treatment is not randomly assigned and outcomes are binary. The estimators we compare are the two‐stage least squares linear probability model, maximum likelihood estimation, control function estimators, and special regressor methods. We specifically focus on models and associated estimators that are easy to implement. Also, for calculating choice probabilities and regressor marginal effects, we propose the average index function (AIF), which, unlike the average structural function (ASF), is always easy to estimate.     

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.     

Feasible bias-corrected OLS, within-groups, and first-differences estimators for typical micro and macro AR(1) panel data models

In this paper we suggest several alternative ways of constructing feasible bias-corrected (FBC) pooled least squares, within-groups, and first-differences estimators for AR(1) panel data models. In a Monte Carlo simulation study involving data with the qualities normally encountered by both microeconomists and macroeconomists we found that the estimators proposed seem to possess better finite sample properties than the GMM estimators usually employed in this setting: most FBC estimators are unbiased, even when the time series is highly persistent, display less variability, and are not affected by the relative magnitude of the variances for the individual effect and the idiosyncratic error.     

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.     

When are two-stage and three-stage least squares estimators identical?

Necessary and sufficient conditions are derived for the numerical equivalence of the two-stage and three-stage least squares estimators in a linear simultaneous equations model. The conditions are easy to verify in any practical application.     

Drug‐related violence and the decline in the number of Mexican cross‐border workers

This study examines how variations in homicide rates in Mexico are associated with the likelihood of participating in cross‐border work, that is, living in Mexico but working in the U.S. Based on Mexican census data from 2000, 2010, and 2015, and information on homicides, a series of ordinary least squares models are estimated to analyze the relationship between cross‐border commuting and homicide rates at the individual level. Fixed effects models are also estimated to study this relationship at the municipal level. The results show that from 2000 to 2010 the increase in homicide rates in northern border municipalities in Mexico reduced the likelihood of being a cross‐border worker, while from 2010 to 2015 the decrease in the homicide rate increased the probability that workers engage in cross‐border work. The decline in the number of cross‐border workers is likely in part a result of the escalation in drug‐related violence that may have led them to change their country of residence.     

Improved estimators in some linear errors-in-variables models in finite samples

The paper uses a Monte Carlo study to demonstrate the dominance under mean squared errors or quadratic loss of a new improved estimator for some linear errors-in-variables models in finite samples. The new estimator is non-linear and biased in a conventional sense and has a smaller risk than the least squares and the Stein estimators. Standard errors for this estimator can be conveniently obtained by bootstrapping methods.     

An empirical estimation for mean-reverting coal prices with long memory

In this paper we discuss the calibration issues of power models built on mean-reverting processes combined with long memory. The unknown parameters of fractional mean-reversion processes are estimated by a hybrid estimation method, which is built upon the marriage of the quadratic variation and the least squares. We perform a simulation study to test the efficiency of these estimators and to compare with the approach proposed by Høg (1999). Moreover, we apply our estimation procedure to some sample series of Chinese coal spot prices in real life situations. These results support the use of fractional mean-reversion processes in modeling Chinese coal prices.     

Misspecification in Dynamic Panel Data Models and Model‐Free Inferences

This paper discusses the issue of model misspecification and model‐free methods in dynamic panel data analysis. We primarily review existing results, but also provide several new results. When the dynamics are homogeneous, we show that several widely used estimators for panel first‐order autoregressive AR(1) models converge to first‐order autocorrelation, even under misspecification. Under heterogeneity, these estimators converge to the ratio of the means of the first‐order autocovariances and variances. We also discuss the estimation of autocovariances, the estimation of panel AR(∞) models, and the estimation of the distribution of the heterogeneous mean and autocovariances.     

Rent‐Sharing and Workers' Bargaining Power: An Empirical Cross‐Country/ Cross‐Industry Panel Analysis

In this paper, we study how rents are shared between capital and labour, using industry‐level panel data for 19 OECD countries from 1988 through to 2007. The first step is an explanation of the rent‐creation process. We provide evidence of a significant impact of regulation on value‐added prices at the industry level relative to the value‐added price for the overall economy (rent). In the second step, we dissect the value‐added sharing process. By running ordinary least‐squares and instrumental variables estimations, we obtain results that confirm the Blanchard–Giavazzi prediction: the impact of rents on the capital share depends on workers' bargaining power.     

A necessary and sufficient condition for the dominance of an improved family of estimators in linear regression models

This article presents a necessary and sufficient condition for the dominance, with respect to the risk under a general quadratic loss function, of the double k-class estimators (characterized by non-stochastic scalars) over the least squares estimator of coefficients in linear regression models.     

Forecasting Inflation Using Constant Gain Least Squares

This paper assesses the usefulness of constant gain least squares when forecasting inflation. An out‐of‐sample forecast exercise is conducted, in which univariate autoregressive models for inflation in Australia, Sweden, the United Kingdom and the United States are used. The results suggest that it is possible to improve the forecast accuracy by employing constant gain least squares instead of ordinary least squares. In particular, when using a gain of 0.05, constant gain least squares generally outperforms the corresponding autoregressive model estimated with ordinary least squares. In fact, at longer forecast horizons, the root mean square forecast error is reliably lowered for all four countries and for all lag lengths considered in the study.     

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.     

Institutions and Cultural Heterogeneity as Determinants of National Income: A Random‐coefficients Stochastic Frontier Model

Previous research on total factor productivity (TFP) shows that cross‐country differences in income cannot be fully explained by stocks of capital (K), labor (L) and human capital (E). In addition, the omission of major production inputs or the use of proxies to estimate unobservable inputs leads to biased estimation results. This study addresses the above issues by employing a novel econometric approach and provides empirical evidence that a fixed production input, and therefore a country's income, is positively correlated with the existence of British‐style institutions and negatively correlated with cultural heterogeneity and Spanish‐style institutions. Our methodology is twofold. First, using data for 62 countries from 1980 to 2004, we regressed a random‐coefficients stochastic production frontier that allows estimating a fixed unobservable production input without using proxies. Second, the estimated fixed production input is shown to be related to colonial institutions and cultural heterogeneity by means of ordinary least squares and feasible generalized least squares regressions.     

TESTING UNCOVERED INTEREST PARITY: A CONTINUOUS‐TIME APPROACH*

Nowadays researchers can choose the sampling frequency of exchange rates and interest rates. If the degree of overlap is large relative to the sample size, standard GMM asymptotic theory provides unreliable inferences in uncovered interest parity (UIP) regression tests. We specify a continuous‐time model for exchange rates and forward premia robust to temporal aggregation, unlike existing discrete‐time models. We test the UIP restrictions on the continuous‐time model parameters and propose a novel specification test that compares estimators at different frequencies. Our results based on correctly specified models provide little support for UIP at both short and long horizons.     

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.     

Marginal Tax Rates and Tax‐Favoured Pension Savings of the Self‐Employed: Evidence from Sweden*

In recent years, the study of how individuals respond to policies that aim at promoting pension savings has emerged as a vital area of economic research. This paper adds to this body of literature by estimating the tax price elasticity of contributions to tax‐favoured pension‐savings accounts on a population of self‐employed individuals. I exploit a unique total database over the Swedish population that covers the years 1999–2005. Using instrumental variables, I obtain a tax price elasticity estimate of ?0.51 and an income elasticity estimate of 0.13, whereas ordinary least‐squares (OLS) produces estimates that conflict with consumer theory.     

Generalized least squares and maximum likelihood estimation of the logistic function for technology diffusion

Given a simple stochastic model of technology adoption, we derive a function for technological diffusion that is logistic in the deterministic part and has an error term based on the binomial distribution. We derive two estimators—a generalized least squares (GLS) estimator and a maximum likelihood (ML) estimator—which should be more efficient than the ordinary least squares (OLS) estimators typically used to estimate technological diffusion functions. We compare the two new estimators with OLS using Monte-Carlo techniques and find that under perfect specification, GLS and ML are equally efficient and both are more efficient than OLS. There was no evidence of bias in any of the estimators. We used the estimators on some example data and found evidence suggesting that under conditions of misspecification, the estimated variance-covariance of the ML estimator is badly biased. We verified the existence of the bias with a second Monte-Carlo experiment performed with a known misspecification. In the second experiment, GLS was the most efficient estimator, followed by ML, and OLS was least efficient. We conclude that the GLS estimator of choice.