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.     

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.     

Estimation of Structural Nonlinear Errors‐in‐Varibles Models by Simulated Least‐Squares Method

This article proposes a simulation approach to obtain least‐squares or generalized least‐squares estimators of structural nonlinear errors‐in‐variables models. The proposed estimators are computationally attractive because they do not need numerical integration nor huge numbers of simulations per observable. In addition, the asymptotic covariance matrix of the estimator has a simple decomposition that may be used to guide selection of appropriate simulation sizes. The method is also useful for models with missing data or imperfect surrogate covariates, where application of conventional least‐squares and maximum‐likelihood methods is restricted by numerical multidimensional integrations.     

Immigrants,occupations and firm export performance

This paper investigates the export‐enhancing effect of immigrant workers and how this effect varies across occupations. We use a dataset made of French manufacturing firms from 1997 to 2009 and address the problem of endogenous employment choice using an instrumental variable‐two‐stage least squares (IV‐2SLS) strategy and a doubly robust estimator. Our results show that immigrants in both low‐ and high‐skilled occupations foster exports at both the intensive and the extensive margins. In addition, we show that this effect is spread across all export destinations.     

Estimation of Binary Response Models With Endogenous Regressors

This paper reviews six approaches to binary response (y₁) structural forms with an endogenous regressor y₂: (i) the two‐stage least squares estimator‐like substitution approach, (ii) the control function approach, (iii) the system reduced‐form approach, (iv) the artificial instrumental regressor approach, (v) the transformed‐response instrumental variable estimator approach and (vi) the classical maximum likelihood estimator approach. The applicability of the six methods differs greatly, depending on whether y₂ is a continuously distributed random variable or a discrete transformation of a latent . We conduct a real‐data‐based simulation study, and provide an empirical illustration. Our overall recommendation is using (i) and (ii), as the others have undesirable features such as analytic complexity in (iii), computational difficulty in (iv) and (vi), and poor finite‐sample performance in (v).     

Time-varying exchange rate exposure and exchange rate risk pricing in the Canadian Equity Market

This paper aims to extend the existing literature on foreign exchange rate risk pricing. Unlike the existing studies on Canada, we use six alternative bilateral and one multilateral exchange rate proxies. Furthermore, using both a two-factor and a three-factor capital asset pricing model (CAPM), we test for the presence of a long-run relationship among exchange rate risk pricing, herding behavior, term structure and the interest rate. The estimated results based on both the ordinary least squares (OLS) and generalized least squares (GLS) estimation techniques confirm that exchange rate risk in the Canadian equity market is priced and that the pricing of this risk is time-varying. This result holds for all seven exchange rate proxies. Our empirical analysis also suggests the presence of a long-run relationship among exchange rate risk pricing, herding behavior, term structure and the interest rate. This relationship is found to be insensitive to variations in the world market return.     

The Impact of Inequality and Redistribution on Growth

In this paper, we reassess the impact of inequality on growth. The majority of previous papers have employed (system) GMM estimation. However, recent simulation studies indicate that the problems of GMM when using non‐stationary data such as GDP have been grossly underestimated in applied research. Concerning predetermined regressors such as inequality, GMM is outperformed by a simple least‐squares dummy variable estimator. Additionally, new data have recently become available that not only double the sample size compared to most previous studies, but also address the substantial measurement issues that have plagued past research. Using these new data and an LSDV estimator, we provide an analysis that both accounts for the conditions where inequality is beneficial or detrimental to growth and distinguishes between market‐driven inequality and redistribution. We show that there are situations where market inequality affects growth positively while redistribution is simultaneously beneficial.     

Taking down the wall: Transition and inequality

In this article, we investigate the main determinants of income inequality in the transition countries of Central and Eastern Europe and the Commonwealth of Independent States during the period 1990–2018. To this end, we address a major methodological challenge that lies at the core of the cross‐country literature on income inequality: the potential endogeneity of income per capita, which is largely ignored by most empirical studies. We adopt a two‐pronged empirical strategy by (1) using trading partners’ weighted average real GDP as an instrumental variable and (2) estimating the model via the two‐stage least squares approach for static models and the generalized method of moments estimator for dynamic models. Our empirical findings are consistent with the Kuznets curve that illustrates a nonlinear relationship between income inequality and the level of economic development. We also find that the redistributive impact of fiscal policy is statistically insignificant and taxation and government spending appear to have the opposing effects on income inequality in transition economies over the sample period.     

A NEW APPROXIMATE GLS ESTIMATOR FOR THE REGRESSION MODEL WITH MA(1) DISTURBANCES

This paper introduces a new approximate GLS estimator for the regression model with MA(1) disturbances, which outperforms both the Balestra (1980) and the Park and Heikes (1983) approximations and which is almost as efficient as the exact GLS estimator.     

Estimating Demand Response with Panel Data

In this paper, we extend to panel data the iterated linear least squares estimator of Blundell and Robin (in J Appl Econometrics 14: 209–232 1999). It is shown to be consistent when total expenditure and regression residuals are correlated, either because of simultaneity or because of unobserved heterogeneity. We propose separate tests for these two effects. Monte Carlo experiments are then conducted and the estimator is applied to data drawn from a French Consumer Panel.     

A regression model of the heteroscedastic error variance

We introduce a regression model of the heteroscedastic error variance. A repetitive use of the least squares method is shown to provide the best linear unbiased estimator of the parameter vector of the model.     

The bias of the least squares estimator over interval constraints

We show that the interval constrained least squares estimator for a regression model is in general bias. The bias and some of its properties are given when the regression residuals are normally distributed.     

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.     

Intergenerational Earnings and Income Mobility in Spain

This paper contributes to the large number of studies on intergenerational earnings and income mobility by providing new evidence for Spain. Since there are no Spanish surveys covering long‐term information on both children and their fathers' income or earnings, we deal with this selection problem using the two‐sample two‐stage least squares estimator. We find that intergenerational mobility in Spain is similar to that in France, lower than in the Nordic countries and Britain, and higher than in Italy and the United States. Furthermore, we use the Chadwick and Solon approach to explore intergenerational mobility in the case of daughters and we find similar results by gender.     

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.     

Money,inflation and untested common factors

Bairam's (1990) model of world inflation is reconsidered. This model gives the surprising result that increases in the money supply act to decrease inflation rates. I find that this result is due to the imposition of an untested (and invalid) common factor restriction. This restriction is implicit in the generalized least squares (GLS) transformation for autocorrelated regression residuals. Bairam's autocorrelated residuals appear to be caused by mis-specified dynamics. In a more correctly specified model money supply increases have the expected positive influence on inflation rates. The prevalence of the GLS transformation, and the rarity of testing for implied common factor restrictions, suggests that there may be other, equally mis-specified, models existing in the literature.     

The jackknife and heteroskedasticity: Consistent variance estimation for regression models

The weighted jackknife leads to a consistent estimator for the covariance matrix of the least squares estimators of the parameters in a regression model. In this note we show that this estimator has a simple relationship to the White estimator which is widely used in econometrics.     

Interval bidding in a distribution elicitation format

Interval bidding allows people to report a range of values for a non-market good. Herein, we allow people to choose their distribution over this range endogenously. We consider a multiplicative error model explaining the willingness to pay (WTP) which is estimated using a feasible generalized least squares estimator. We apply our framework to a representative sample of the French population who were asked about the valuation of a bear conservation programme. We find that most participants prefer stating their WTP as a range rather than a point, but the shape of the distribution greatly varies across people. Our results support the use of the interval bidding with endogenous distribution approach in valuation studies.     

Engineering robust instruments for GMM estimation of panel data regression models with errors in variables: a note

Econometricians have long recognized the need to account in some way for measurement errors, specification errors and endogeneity to ensure that the ordinary least squares estimator is consistent. This article introduces a new generalized method of moments estimator that relies on robust instruments to estimate panel data regression models containing errors in variables. We show how this GMM approach can be generalized for the panel data framework using higher moments and cumulants as instruments. The new instruments, engineered for greater robustness, are proposed to tackle the pervasive problem of weak instruments.     

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.