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.     

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.     

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.     

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.     

Tests for additive heteroskedasticity: Goldfeld and Quandt revisited

A number of new tests for heteroskedasticity have recently become available. Using Monte Carlo methods this paper explores the small sample properties of some of these tests in the context of additive heteroskedasticity. Lagrange multiplier and Wald tests (and variants thereof) are found to be inferior to the likelihood ratio and Goldfeld and QuandtF tests. This is a reconfirmation of the conclusions obtained byGoldfeld/Quandt [1972] in their study of additive heteroskedasticity. The paper also contains some new results onAmemiya's GLS estimator of the additive heteroskedastic structure.     

A modified logit model for time series with an application to the pricing behaviour of manufacturing firms in Australia

The modified logit model (Amemiya and Nold, 1975) is generalised to the case where the error term is autocorrelated. The asymptotic distribution (as n →∞ and T →∞) of a feasible GLS estimator of β is derived. Tests of linear restrictions on β and the significance of ρ are presented. The results of the applied work suggest that the factors which explain the pricing behaviour of manufacturing firms, as reported in the tendency survey conducted by the Australian Chamber of Commerce and Industry and the Westpac Banking Corporation, include historical inflation rates of up to 7 quarters and capacity utilisation. First version received: March 2001/Final version received: July 2002 RID="*" ID="*"  The first draft of this paper was written while the author was on study leave at the Department of Econometrics, University of Sydney, Australia.     

Comparison of SML and GMM estimators for the random coefficient logit model using aggregate data

A simulated maximum likelihood (SML) estimator for the random coefficient logit model using aggregate data is found to be more efficient than the widely used generalized method of moments estimator (GMM) of Berry et?al. (Econometrica 63:841?C890, 1995). In particular, the SML estimator is better than the GMM estimator in recovery of heterogeneity parameters which are often of central interest in marketing research. With the GMM estimator, the analyst must determine what moment conditions to use for parameter identification, especially the heterogeneity parameters. With the SML estimator, the moment conditions are automatically determined as the gradients of the log-likelihood function, and these are the most efficient ones if the model is correctly specified. Another limitation of the GMM estimator is that the product market shares must be strictly positive while the SML estimator can handle zero market share observations. Properties of the SML and GMM estimators are demonstrated in simulated data and in data from the US photographic film market.     

Bootstrapping regression estimators under first-order serial correlation

It is well known that with highly trended time series data and strongly autocorrelated disturbances, there will be a marked tendency for standard GLS techniques to over-reject true null hypothesis in finite samples. There is also a potential problem because most applications of GLS are in conjunction with a pretest such as a Durbin-Watson test. An application of bootstrapping to these problems is considered here using a small Monte Carlo experiment; the results provide no evidence that standard bootstrapping provides an improvement.     

GLS detrending-based unit root tests in nonlinear STAR and SETAR models

We extend GLS detrending procedure to testing for unit roots against STAR and SETAR alternatives. Monte Carlo simulations and applications to DM/Yen real exchange rates demonstrate that GLS detrending-based nonlinear unit root tests are more powerful than OLS detrending-based counterparts.     

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.     

ENGLE AND YOO THREE STEP ESTIMATION OF CONSUMERS' EXPENDITURE AND HOUSING EQUITY WITHDRAWAL

This paper reports a substantive application of Engle and Yoo's three-step estimator for cointegrated systems. Their estimator was proposed as a computationally convenient alternative to a number of FIML systems estimators. In part this estimator was developed to overcome some drawbacks of the OLS estimator of the first stage Engle-Granger cointegrating regression which, despite its widespread use, is not asymptotically efficient and does not provide (even) asympototically correct ' t ' statistics. Our application, which is of interest in its own right, is to an explanation of expenditure on nondurables and services in the UK. In formulating an empirical explanation for this variable we find it necessary to extend our framework to consider a system of dynamic error correction equations with feedbacks — or error correction mechanisms — from consumption and housing equity withdrawal.     

政府规模与公共服务水平关系研究——基于中国省际面板数据的分析

本文运用1997-2006年中国21个代表性省市相关数据,在Lynn MacDonald(2008)的模型基础上进一步拓展,引入其他一些决定模型的因素,运用固定效应GLS(Cross-Section Weiht)计量方法考察政府规模与公共服务水平之间的关系.实证分析表明,政府规模与公共服务水平呈正相关关系,这与当前政府机构改革中"精简机构"的改革思路有所偏离,从而引发我们对政府机构改革中"精简机构"实质的重新思考与定位.     

A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model

This paper is concerned with the estimation of the autoregressive parameter in a widely considered spatial autocorrelation model. The typical estimator for this parameter considered in the literature is the (quasi) maximum likelihood estimator corresponding to a normal density. However, as discussed in this paper, the (quasi) maximum likelihood estimator may not be computationally feasible in many cases involving moderate- or large-sized samples. In this paper we suggest a generalized moments estimator that is computationally simple irrespective of the sample size. We provide results concerning the large and small sample properties of this estimator.     

Intercountry evidence on the performance of the simple error correction mechanism model of consumption

This paper estimates a simple error correction mechanism (SECM) model of consumption a la Davidson, Hendry, Srba and Yeo (1978) for 13 OECD countries over the period 1951–1982. This is done for each country separately as well as for the pooled data. The basic results of this study are the following: (i) The SECM model appears as an adequate approximation to the data generating process on an individual country basis as well as in a pooled context. (ii) The pooled within estimator indicates a large and significant disequilibrium term while the between estimator indicates a small and insignificant disequilibrium term. This is consistent with the belief that the within estimator tend to yield short-run estimates while the between estimator tend to yield long-run estimates.The authors would like to thank Baldev Raj and an anonymous referee for helpful comments and suggestions. Mokhtari's research was supported by a grant from UHD/ORG.     

On Liu estimators for the logit regression model

This paper introduces a shrinkage estimator for the logit model which is a generalization of the estimator proposed by Liu (1993) for the linear regression. This new estimation method is suggested since the mean squared error (MSE) of the commonly used maximum likelihood (ML) method becomes inflated when the explanatory variables of the regression model are highly correlated. Using MSE, the optimal value of the shrinkage parameter is derived and some methods of estimating it are proposed. It is shown by means of Monte Carlo simulations that the estimated MSE and mean absolute error (MAE) are lower for the proposed Liu estimator than those of the ML in the presence of multicollinearity. Finally the benefit of the Lie estimator is shown in an empirical application where different economic factors are used to explain the probability that municipalities have net increase of inhabitants.     

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.     

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.     

参数异质性、经济趋同与中国区域经济发展

本文首次采用分量回归方法来研究中国城市间经济的趋同方式。已有文献研究大都采用条件均值回归的实证方法,无法从本质上揭示不同地区本身存在的异质性而导致的增长方式的差别,本文利用中国182个地级及以上城市的数据,先采用OLS方法,然后采用Koenker和Hallock(2001)发展的条件分量回归的方法,对城市之间的经济趋同方式进行了检验。结果表明,与OLS方法不同,我们发现参数异质性的证据,表明不同城市的经济增长方式存在差异。新古典经济增长模型认为存在条件收敛,但分量回归的结论不支持这个预测。我们发现条件收敛不是普遍现象,增长率分布处于低分位点的地区存在条件收敛特点,但对于增长率分布处于高分位点的地区而言,结论并不显著。这一结果对于制定区域经济协调发展的政策非常重要。     

A simple estimator for the correlated random coefficient model

This note presents an estimator for the linear correlated random coefficient model which is an extension of Garen's (1984) selectivity bias method. The choice between the proposed estimator and IV estimation reflects a trade-off between efficiency and first-stage reduced form robustness.     

Estimation and arbitrage opportunities for exchange rate baskets

This paper analyses short-term portfolio investment opportunities in a capital market where a currency is defined as a currency basket. In line with the mean-variance hedging approach, a self-financed optimal investment strategy is determined which minimizes the expected quadratic cost function. The successful implementation of the speculative strategy requires a precise estimate of the basket weights, which are possibly non-constant over time. To this end, an adaptive non-parametric procedure is suggested which provides satisfactory results both on simulated and real data. The optimal investment strategy is applied to the case of the Thai Baht basket whereby the weights are computed by means of the adaptive estimator. A recursive estimator, a rolling estimator and the Kalman filter, are implemented and serve as benchmark models. Results are compared with the literature. The different estimators are evaluated with profit-based criteria and the performance of the adaptive estimator turns out to be the best one.