Distributions You Can Count On …But What’s the Point?

The Poisson regression model remains an important tool in the econometric analysis of count data. In a pioneering contribution to the econometric analysis of such models, Lung-Fei Lee presented a specification test for a Poisson model against a broad class of discrete distributions sometimes called the Katz family. Two members of this alternative class are the binomial and negative binomial distributions, which are commonly used with count data to allow for under- and over-dispersion, respectively. In this paper we explore the structure of other distributions within the class and their suitability as alternatives to the Poisson model. Potential difficulties with the Katz likelihood leads us to investigate a class of point optimal tests of the Poisson assumption against the alternative of over-dispersion in both the regression and intercept only cases. In a simulation study, we compare score tests of ‘Poisson-ness’ with various point optimal tests, based on the Katz family, and conclude that it is possible to choose a point optimal test which is better in the intercept only case, although the nuisance parameters arising in the regression case are problematic. One possible cause is poor choice of the point at which to optimize. Consequently, we explore the use of Hellinger distance to aid this choice. Ultimately we conclude that score tests remain the most practical approach to testing for over-dispersion in this context.</jats:p

A note on Amemiya's form of the weighted least squares estimator

Includes bibliographical references (p. 13)

Some Exact Results for Estimators of the Coefficients on the Exogenous Variables in a Single Equation

This paper is devoted to a detailed examination of the exact sampling properties of the instrumental variables (IV) estimator of the vector of coefficients on the exogenous variables in a single structural equation. The first two moments of a linear combination of the elements of this estimator and the joint distribution of these elements are considered. Estimable bounds for the first moment that can readily be incorporated into any IV estimation package are provided. The results obtained are in terms of the same special functions as those that characterize other results for this model, allowing a unified treatment of the model.

Instrumental Variables Estimation in Misspecified Single Equations

This paper examines the exact sampling behavior of a family of instrumental variables estimators of the coefficients in a single structural equation when the model has been misspecified by the incorrect inclusion or exclusion of variables. It is found that such specification errors can have implications for the structure of the exact results obtained. A brief numerical examination of the analytical results is also provided.

The Impact of Cannabis & Cigarette Use on Health

Chronic daily cannabis use has been shown to have long term harmful health effects,which in turn is expected to reduce labour market productivity. The evidence is less clear on thehealth impact of less frequent consumption, which is the more typical mode of use, and previousempirical studies fail to find robust evidence of an adverse impact of these modes of use on labourmarket productivity. This paper attempts to shed some light on this issue by directly estimating theimpact of cannabis consumption in the past week and past year on health status using information onprime age individuals living in Australia. We find that cannabis use does reduce self-assessed healthstatus, with the effect of weekly use being of a similar magnitude as smoking cigarettes daily. Moreover,we find evidence of a dose-response relationship in the health impact of cannabis use, with annual usehaving roughly half the impact of weekly use

Market Arbitrage of CashDividends and Franking Credits

Research Paper Number 947, ISSN 0819-2642, ISBN 0 7340 2603 XSince 1986 dividend imputation has influenced the ex-dividend daybehaviour of Australian share prices. Between 1 April 1986 and 30May 2004 the Government of the day introduced six major legislativeamendments intent on improving the efficiency of the dividend imputationsystem. This paper explores the impact of dividend imputation,in its various forms, on ex-dividend share price adjustments. We findthat only the most recent tax change, which provided full income rebatesfor unused franking credits, appears to have caused the marketto put a statistically significant value on franking credits

Some Further Exact Results for Structural Equation Estimators

In the context of the single structural equation model, we derive a number of exact results that extend and/or simplify results hitherto available. First, we obtain expressions for both the conditional and unconditional densities of the limited information maximum likelihood estimator for the coefficients of the endogenous variables. The unconditional result is considerably simpler than the corresponding result obtained earlier by Phillips (1985), and we indicate how this result can be used to obtain distribution results for the coefficients of the exogenous variables in exactly the manner used in Phillips (1984a) for the ordinary least squares and two-stage least squares estimators. Next, we obtain expressions for the mean square error of the ordinary least squares/two-stage least squares estimators for the coefficients of the exogenous variables. Finally, a number of generalizations of these results are indicated, and we explain briefly how these results can contribute to further attempts to understand the general problems of inference in this model

Prediction in linear index models with endogenous regressors

In this article, we examine prediction in the context of linear index models when one or more of the regressors are endogenous. To facilitate both within-sample and out-of-sample predictions, Stata offers the postestimation command predict (see [R] predict). We believe that the usefulness of the predictions provided by this command is limited, especially if one is interested in out-of-sample predictions. We demonstrate our point using a probit model with continuous endogenous regressors, although it clearly generalizes readily to other linear index models. We subsequently provide a program that offers one possible implementation of a new command, ivpredict, that can be used to address this shortcoming of predict, and we then illustrate its use with an empirical example