A Poisson ridge regression estimator

The standard statistical method for analyzing count data is the Poisson regression model, which is usually estimated using maximum likelihood (ML) method. The ML method is very sensitive to multicollinearity. Therefore, we present a new Poisson ridge regression estimator (PRR) as a remedy to the problem of instability of the traditional ML method. To investigate the performance of the PRR and the traditional ML approaches for estimating the parameters of the Poisson regression model, we calculate the mean squared error (MSE) using Monte Carlo simulations. The result from the simulation study shows that the PRR method outperforms the traditional ML estimator in all of the different situations evaluated in this paper.     

Moment Estimation of the Probit Model with an Endogenous Continuous Regressor

We propose a generalized method of moments (GMM) estimator with optimal instruments for a probit model that includes a continuous endogenous regressor. This GMM estimator incorporates the probit error and the heteroscedasticity of the error term in the first‐stage equation in order to construct the optimal instruments. The estimator estimates the structural equation and the first‐stage equation jointly and, based on this joint moment condition, is efficient within the class of GMM estimators. To estimate the heteroscedasticity of the error term of the first‐stage equation, we use the k‐nearest neighbour (k‐nn) non‐parametric estimation procedure. Our Monte Carlo simulation shows that in the presence of heteroscedasticity and endogeneity, our GMM estimator outperforms the two‐stage conditional maximum likelihood estimator. Our results suggest that in the presence of heteroscedasticity in the first‐stage equation, the proposed GMM estimator with optimal instruments is a useful option for researchers.     

A more general class of biased estimators of the co-efficients in linear regression

In a recent paper, Ullah and Ullah (1978) proposed a class of biased estimators, namely double k-class (k₁, k₂) for the coefficients in a linear regression model. Even though, this set of estimators contains James and Stein (1961) as a special case, in its present form, it does not contain the ridge type estimators. The aim of this note is to extend Ullah and Ullah set of estimators and then establish a relationship with the various operational ridge estimators. The conditions under which the extended set of estimators dominates the ordinary least squares estimator are analyzed.     

State dependence,serial correlation and heterogeneity in the union membership dynamics

In order to distinguish the true and spurious state dependence from the complicated dynamics of union membership, the simulation estimators incorporating the lagged dependent variables, unobserved individual heterogeneity and correlations among the errors are implemented in this article to study union membership dynamics. It is found that the true state dependence of union membership under multivariate t assumption is much higher than the standard dynamic panel probit estimators which are under multivariate normal assumptions. On the other hand, the spurious state dependence (the variance of the unobserved individual heterogeneity) is estimated to be higher when using the standard dynamic panel probit estimators than under multivariate t assumption. Moreover, blacks and married men are found to have higher union membership true state dependence than whites and unmarried men.     

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.     

Does the constraint matter? A note on the asymptotic properties of nonparametric instrumental variable estimation under monotonicity shape constraint

I show that constrained monotone instrumental variable estimators are asymptotically equivalent to their unconstrained counterparts whenever the true regression function is in the interior of the constrained set. In a simulation study, a sieve-based constrained estimator is shown to outperform the unconstrained one even in cases where both are asymptotically equivalent.     

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.     

Semi-parametric models for satisfaction with income

An overview is presented of some parametric and semi-parametric models, estimators, and specification tests that can be used to analyze ordered response variables. In particular, limited dependent variable models that generalize ordered probit are compared to regression models that generalize the linear model. These techniques are then applied to analyze how self-reported satisfaction with household income relates to household income, family composition, and other background variables. Data are drawn from the 1998 wave of the German Socio-Economic Panel. The results are used to estimate equivalence scales and the cost of children. We find that the standard ordered probit model is rejected, while some semi-parametric specifications survive specification tests against nonparametric alternatives. The estimated equivalence scales, however, are often similar for the parametric and semi-parametric specifications.JEL Classification: C14, C35, D12Correspondence to: Charles BellemareWe are grateful to an anonymous referee and to participants of a CeMMAP/ESG workshop at University College London and seminars at CentER (Tilburg University) and Humboldt University Berlin for useful comments.     

Probit Analysis and Economic Education

Spector and Mazzeo assert that ordinary least squares regression analysis has been misused by many economics education researchers. They explain that OLS is inappropriate for the analysis of discrete dependent variables, and they suggest the use of probit analysis instead. They then show how probit analysis can be employed in an economics education research project and compare the results of this approach with the results obtained by using OLS. (Those who want to know more about probit analysis might be interested in a new book, Carlos Daganzo's Multinomial Probit: The Theory and Its Application to Demand Forecasting, published in 1979 by Academic Press, Inc. Also see the bibliography provided by Spector and Mazzeo.)     

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.     

Nonparametric methods for estimating and testing for constant betas in asset pricing models

In this article, we study the performance of a smoothing spline method in estimating and testing for constant betas in two well-known asset pricing models, the usual market model and the three-factor model. The spline estimator is computed taking into account the conditional heteroscedasticity of the errors. Using the right model and estimation procedure for the variance term plays a crucial role in gaining efficiency in beta estimators. A simulation study shows the good performance of our method; in all the scenarios simulated, it outperforms the benchmark rolling estimator. The method enables users to obtain confidence intervals and to test for the significance and constancy of betas. Finally, the method is applied to US data, comprising 25 portfolios formed based on size and the ratio of book equity to market equity. The results show that the time-variability of the betas plays an important role, mainly when sensitivity to the HML factor is considered.     

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.     

Auctions in which losers set the price

We study auctions of a single asset among symmetric bidders with affiliated values. We show that the second-price auction minimizes revenue among all efficient auction mechanisms in which only the winner pays, and the price only depends on the losers' bids. In particular, we show that the kth price auction generates higher revenue than the second-price auction, for all k>2. If rationing is allowed, with shares of the asset rationed among the t highest bidders, then the (t+1)st price auction yields the lowest revenue among all auctions with rationing in which only the winners pay and the unit price only depends on the losers' bids. Finally, we compute bidding functions and revenue of the kth price auction, with and without rationing, for an illustrative example much used in the experimental literature to study first-price, second-price and English auctions.     

On the equivalence of indirect inference and bootstrap bias correction for linear IV estimators

This note shows that two ways of simulation based bias correction–indirect inference and bootstrap bias correction–are equivalent for two-stage-least-squares, as well as k$k$-class estimators for the standard linear model with endogenous regressors.     

Investor opinion divergence and post-repurchase announcement stock price drift

This study examines whether investor opinion divergence is a significant determinant of post-repurchase abnormal returns. We examine the effect using abnormal trading turnover (ATO) ratio as a proxy for investor opinion divergence. While the OLS regression results show that investor opinion divergence is not related to post-repurchase performance, the quantile regression results show that the effect of investor opinion divergence on post-repurchase performance is not homogeneous across various quantile levels of post-repurchase performance. We find a positive relation between ATO ratio and post-repurchase performance for firms with lower-to-middle performance groups. For firms with middle-to-higher post-repurchase performance, pre-repurchase stock undervaluation is a key determinant of the post-repurchase performance.     

Testing for normality in linear regression models using regression and scale equivariant estimators

In this paper we provide a general solution to the problem of controlling the probability of a type I error in normality tests for the disturbances in linear regressions when using robust-regression residuals. We show that many classes of well-known robust regression estimators belong to the class of regression and scale equivariant estimators. It is these equivariance properties that are used to reduce the nuisance parameter space under the null, from which we develop Monte Carlo and Maximized Monte Carlo tests for the null of disturbance normality. Finally, we illustrate in a simulation experiment the potential power gains from using robust-regression residuals in testing this null hypothesis.     

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     

Economies of scale in Norwegian electricity distribution: a quantile regression approach

In this article, we investigate scale economies in Norwegian electricity distribution companies using a quantile regression approach. To the best of our knowledge, this is the first attempt to apply this estimation technique when analysing scale economies. We estimate the cost elasticities of the two output components: network length and number of customers, to calculate returns to scale. Our results show large potential of scale economies, particularly for the smallest companies. We also find that returns to scale is increasing over time. These findings have important implications for policymakers when they are deciding the structure of the industry in the future.     

Beta trigonometric distributions

Beta distributions are popular models for economic data. In this paper, six new distributions are introduced which generalize the standard beta distribution. These distributions involve the trigonometric functions, sine and cosine. Expressions are derived for their analytical shapes, nth moments, method of moments estimators, maximum likelihood estimators and the associated Fisher information matrices. These calculations involve several special functions. A numerical study is performed to show the flexility of these distributions as compared to the standard beta distribution. An application to consumer expenditure data is illustrated to show that the proposed distributions are better models to economic data than one based on the standard beta distribution. Possible ways of extending the models are also discussed.     

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.