On ridge estimators for the negative binomial regression model

The negative binomial (NB) regression model is very popular in applied research when analyzing count data. The commonly used maximum likelihood (ML) estimator is very sensitive to highly intercorrelated explanatory variables. Therefore, a NB ridge regression estimator (NBRR) is proposed as a robust option of estimating the parameters of the NB model in the presence of multicollinearity. To investigate the performance of the NBRR and the traditional ML approach the mean squared error (MSE) is calculated using Monte Carlo simulations. The simulated result indicated that some of the proposed NBRR methods should always be preferred to the ML method.     

RIDGE ESTIMATORS FOR PROBIT REGRESSION: WITH AN APPLICATION TO LABOUR MARKET DATA

In this paper we propose ridge regression estimators for probit models since the commonly applied maximum likelihood (ML) method is sensitive to multicollinearity. An extensive Monte Carlo study is conducted where the performance of the ML method and the probit ridge regression (PRR) is investigated when the data are collinear. In the simulation study we evaluate a number of methods of estimating the ridge parameter k that have recently been developed for use in linear regression analysis. The results from the simulation study show that there is at least one group of the estimators of k that regularly has a lower mean squared error than the ML method for all different situations that have been evaluated. Finally, we show the benefit of the new method using the classical Dehejia and Wahba dataset which is based on a labour market experiment.     

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.     

Combination forecasts of tourism demand with machine learning models

The main objective of this study is to analyse whether the combination of regional predictions generated with machine learning (ML) models leads to improved forecast accuracy. With this aim, we construct one set of forecasts by estimating models on the aggregate series, another set by using the same models to forecast the individual series prior to aggregation, and then we compare the accuracy of both approaches. We use three ML techniques: support vector regression, Gaussian process regression and neural network models. We use an autoregressive moving average model as a benchmark. We find that ML methods improve their forecasting performance with respect to the benchmark as forecast horizons increase, suggesting the suitability of these techniques for mid- and long-term forecasting. In spite of the fact that the disaggregated approach yields more accurate predictions, the improvement over the benchmark occurs for shorter forecast horizons with the direct approach.     

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.     

Estimation of hedonic price functions via additive nonparametric regression

We model a hedonic price function for housing as an additive nonparametric regression. Estimation is done via a backfitting procedure in combination with a local polynomial estimator. It avoids the pitfalls of an unrestricted nonparametric estimator, such as slow convergence rates and the curse of dimensionality. Bandwidths are chosen using a novel plug in method that minimizes the asymptotic mean average squared error (AMASE) of the regression. We compare our results to alternative parametric models and find evidence of the superiority of our nonparametric model. From an empirical perspective our study is interesting in that the effects on housing prices of a series of environmental characteristics are modeled in the regression. We find these characteristics to be important in the determination of housing prices.First version received: October 2002/Final version received: October 2003We thank B. Baltagi and two anonymous referees for their comments. The authors retain responsibility for any remaining errors.     

Maximum-likelihood estimation of misspecified models

Misspecified models occur frequently in econometric practice. It is therefore important to study the sampling distribution of maximum-likelihood estimators of parameters of misspecified models. This note exhibits the asymptotic covariance matrix of the ML estimator of a misspecified model. It points out that the expression for this matrix given by White is incorrect except for the very special case, rarely occuring in econometrics, that each observation is independent and identically distributed. An illustration using the standard linear regression model is provided.     

Estimation of Censored Regression Model: A Simulation Study

We investigate the finite sample performance of several estimators proposed for the panel data Tobit regression model with individual effects, including Honoré estimator, Hansen’s best two-step GMM estimator, the continuously updating GMM estimator, and the empirical likelihood estimator (ELE). The latter three estimators are based on more conditional moment restrictions than the Honoré estimator, and consequently are more efficient in large samples. Although the latter three estimators are asymptotically equivalent, the last two have better finite sample performance. However, our simulation reveals that the continuously updating GMM estimator performs no better, and in most cases is worse than Honoré estimator in small samples. The reason for this finding is that the latter three estimators are based on more moment restrictions that require discarding observations. In our designs, about seventy percent of observations are discarded. The insufficiently few number of observations leads to an imprecise weighted matrix estimate, which in turn leads to unreliable estimates. This study calls for an alternative estimation method that does not rely on trimming for finite sample panel data censored regression model.     

Estimating gravity equations: to log or not to log?

In this study we compare the traditional OLS approach applied to the log-linear form of the gravity model with the Poisson Quasi Maximum Likelihood (PQML) estimation procedure applied to the non-linear multiplicative specification of the gravity model. We use the trade flows for all products, for all manufacturing products as well as for manufacturing products broken down by three-digit ISIC Rev.2 categories. We base our conclusions on the gravity model of Bergstrand (Rev Econ Stat 71(1):143--153, 1989) for disaggregate trade flows that allows us to investigate differences in factor-proportions and home-market effects at the industry level. In addition, we compare the effects of other explanatory variables such as exporter and importer total income, distance, preferential trade agreements, common border, historical ties, and common language on the volume of trade. Our main conclusion is that both estimation results as well as results of the regression mis-specification tests provide supporting evidence for the PQML estimation approach over the OLS estimation method. The paper has benefited from comments by an anonymous referee and by the participants at the following conferences: the 4th Nordic Econometrics Meeting, Tartu, Estonia, the 8th Annual Conference of the European Trade Study Group (ETSG), Vienna, Austria, the 21th Annual Congress of the European Economic Association (EEA), Vienna, Austria, the XIth Spring Meeting of Young Economists (SMYE), Sevilla, Spain, and the 5th Annual Conference of the European Economics and Finance Society (EEFS), Heraklion, Greece.     

Beta-convergence and sigma-convergence in corporate governance in Europe

This paper tests for beta-convergence and sigma-convergence in the corporate governance models, using a sample of corporate governance ratings for 198 European corporations listed on the FTSE Eurofirst 300 index. A piecewise linear regression is deployed to select a model and the Poisson pseudo-maximum likelihood estimator is also applied to estimate an exponential model. It concludes that there is statistical evidence of beta- and sigma-convergence within countries and the results suggest that institutional differences between countries are statistically relevant.     

Competing-destinations gravity model applied to trade in intermediate goods

The competing-destinations formulation of the gravity model ensues from the fact that unlike the classic version, this approach explicitly acknowledges the interdependence of the flows between a set of alternative countries. This article applies the competing-destinations gravity model to the analysis of trade in intermediate goods. The results of the model were then tested empirically with an international input–output data set and using the Poisson pseudo-maximum-likelihood estimator. The empirical results suggest that the analytical model can explain trade in intermediate goods. Indeed, as predicted, import of intermediate goods is increasing in the importing country’s demand for inputs, in the competitiveness of the exporting country, and decreasing in distance and competition posed by alternative countries.     

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。     

Constrained nonparametric regression analysis of load curves

In this paper, we analyze household load curves through the use of Constrained Smoothing Splines. These estimators are natural smoothing splines that allow to incorporate periodic shape constraints. Since the time pattern of electricity demand combines strong periodical regularities with abrupt changes along time, a nonparametric regression estimator that is able to incorporate regularity constrains appears to be very well suited to approach load curves. In the paper we also propose a method to compute the penalty parameters that appear in the constrained smoothing spline estimator, we show some statistical properties and finally we construct confidence intervals. First version received: February 1998/final version accepted: July 1999     

百分位数回归及应用研究

在进行定量分析时,最小二乘法已经成为一种可信赖的工具。但是运用最小二乘法的条件比较高,在实际问题中,完全满足条件的情况并不多见,那么在应用时就难以得到无偏的、有效的参数估计量。针对上述问题,以OILPLUS公司取暖用燃油消耗的分布为主要研究对象,在进行参数估计时,应用百分位数回归方法,既可以看到采用百分位数回归方法与采用最小二乘法得到的模型显著不同,又可以得到比最小二乘法更为丰富的信息。     

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.     

Estimation of a Tobit model with unknown censoring threshold

Conventional wisdom suggests that only the estimated intercept is affected by imposition of a zero censoring threshold on a Tobit model. This is true for Heckman-Lee estimation. For maximum likelihood (ML) estimation, however, it is only true if the censoring threshold is known and is subtracted from the dependent variable. Failure to properly transform the dependent variable prior to ML estimation of a zero threshold Tobit model will generally bias the coefficient estimates. A long neglected topic is ML estimation of a Tobit model with common, but unknown, censoring threshold. This paper shows that the ML estimator of the censoring threshold is the minimum order statistic from the observed subsample, and that existing software for estimation of a zero-threshold Tobit model is easily adapted to include estimation of the censoring threshold.     

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.     

Do former athletes make better managers? Evidence from a partially adaptive grouped-data regression model

The goal of this paper is to introduce a partially adaptive estimator for the grouped-data regression model based on an error structure described by a mixture of two normal distributions. The model we introduce is easily estimated by maximum likelihood using the EM algorithm adapted from the work of Bartolucci and Scaccia (Comput Stat Data Anal 48:821–834, 2005). The partially adaptive estimator is applied to data used by Long and Caudill (Rev Econ Stat 73:525–531, 1991) to examine the impact of intercollegiate athletics on income. We estimate a variation of the original regression model and find that there is a considerable financial advantage for those male athletes now working in business management. This finding is consistent with the idea that athletes acquire team-building and organizational skills that are helpful in business.     

Cycles in basic innovations

Basic innovations are believed to be one of the drivers of economic growth. In this paper we examine if cycle periods found for economic data correspond with cycles in basic innovations. For an annual time series of count data on innovations covering 1764-1976, we fit a harmonic Poisson regression model. We find the presence of multiple cycles with periods 5, 13, 24, 34 and 61, and these show a remarkable resemblance with commonly found economic cycles.     

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.