Gerd Ronning

Maximum likelihood estimation of dirichlet distributions

Global concavity of the likelihood function is proved by means of an inequality involving the trigamma function. The computation of maximum likelihood estimates is discussed.

Panel Analysis for Qualitative Variables

In this chapter we consider models which take the special structure of qualitative panel data into consideration. Models for qualitative dependent variables in cross-section analysis are discussed by Arminger in Chapter 3. Hsiao, in Chapter 7, presents panel models for metric dependent variables. Therefore, these two chapters are closely related to the present one.

Discrete Choice Analysis of Foreign Travel Demand

The paper reports estimation results from a micro-econometric model of travel demand. A nested multinomial logit model is used to determine the country in which vacation is spent. As an extension of the model, we also consider the simultaneous explanation of both qualitative choice of destination and quantitative demand as measured by per capita expenditure.

Estimation in conditional first order autoregression with discrete support

We consider estimation in the class of first order conditional linear autoregressive models with discrete support that are routinely used to model time series of counts. Various groups of estimators proposed in the literature are discussed: moment-based estimators; regression-based estimators; and likelihood-based estimators. Some of these have been used previously and others not. In particular, we address the performance of new types of generalized method of moments estimators and propose an exact maximum likelihood procedure valid for a Poisson marginal model using backcasting. The small sample properties of all estimators are comprehensively analyzed using simulation. Three situations are considered using data generated with: a fixed autoregressive parameter and equidispersed Poisson innovations; negative binomial innovations; and, additionally, a random autoregressive coefficient. The first set of experiments indicates that bias correction methods, not hitherto used in this context to our knowledge, are some-times needed and that likelihood-based estimators, as might be expected, perform well. The second two scenarios are representative of overdispersion. Methods designed specifically for the Poisson context now perform uniformly badly, but simple, bias-corrected, Yule-Walker and least squares estimators perform well in all cases.

Efficient Estimation of Ordered Probit Models

Abstract This article discusses a model in which both the dependent variable and the explanatory variables are ordinal and have an arbitrary number of categories. Assuming joint normality of the underlying continuous latent variables, we compare estimation based on the joint distribution to estimation based on the conditional distribution. Because the explanatory variables are not weakly exogenous in this model, the latter approach implies a loss in efficiency that can be substantial in many cases, as shown in detail for the special case of trichotomous data with symmetric thresholds. Therefore, latent variables underlying the observed ordinal variables should always be considered to be jointly endogenous; that is, the joint distribution should be considered.

Estimation of a First Order Autoregressive Process with Poisson Marginals for Count Data

Count data play an important role in modern microeconometric models. However, a proper dynamic specification in case of panel data has not yet been discussed: So far only variance components have been specified which show constant autocorrelation over time. In the present paper an autoregressive process for count data is considered as suggested independently by Al-Osh and Alzaid (Journal of Time Series Analysis 1987) and McKenzie (Advances in Applied Probability 1988). Simulation results demonstrate that it is necessary to take proper account of the ’initial conditions’ of the stochastic process when small sample sizes (about 5 or 10) are considered which is the typical number of waves in panel data collected for econometric reseach.

Share equations in econometrics: A story of repression, frustation and dead ends

Share equations play an important role in applied economic research, notably in marketing and demand analysis. Both market shares and budget shares have been used as dependent variables in econometric models which were partly motivated by microeconomic theory. However attempts of econometricians (and other statisticians) to treat share equations adequately led mostly to unsatisfactory approaches: Some researchers although admitting that shares satisfy a sum constraint simply repressed the fact that shares cannot be normally distributed. Some researchers looked in vain for a stochastic specification which at the same time is consistent and allows a flexible covariance structure. Last not least almost nobody has properly taken care of additional problems arising from dynamic share models. The paper discusses these three issues and proposes a possible way out of this dilemma which was first suggested by Aitchison (1982) and has been applied to econometric demand analysis by Considine and Mount (1984). Demandtheoretic implications as well as methods of estimation are discussed. An example using German import data illustrates some of the results.

ESTIMATION OF DISCRETE CHOICE MODELS WITH MINIMAL VARIATION OF ALTERNATIVE-SPECIFIC VARIABLES

The paper states conditions for minimal variation within the explanatory variables such that the maximum likelihood estimate of the coefficient vector in the discrete choice logit model is unique. Special emphasis is given to the case that (almost) all individuals observe the same set of alternative-specific explanatory variables. The aspect of ‘experimental design’ in discrete choice models is discussed.

On the curvature of the trigamma function

The trigamma function ψ1(x). satisfies the inequality ψ1(x)−αψ1(αx) 0 and 0 < α < 1. This can be viewed as a characterization of the curvature of this function.

Remote data access and the risk of disclosure from linear regression: an empirical study

In the endeavor of finding ways for easy data access for researchers not employed at a statistical agency remote data access seems to be an attractive alternative to the current standard of either altering the data substantially before release or allowing access only at designated data archives or research data centers. Data perturbation is often not accepted by the researchers since they do not trust the results from the altered data sets. But on-site access puts some heavy burdens on the researcher and the data providing agency both in terms of time and money. Remote data access or remote analysis servers that allow to submit queries without actually seeing the microdata have the potential of overcoming both these disadvantages. However, even if the microdata is not available to the researcher directly, disclosure of sensitive information for individual survey respondents is still possible. In this paper we illustrate how an intruder could use some commonly available background information to reveal sensitive information using simple linear regression. We demonstrate the real risks from this approach with an empirical evaluation based on a German establishment survey, the IAB Establishment Panel. Although these kind of attacks can easily be prevented once the agency is aware of the problem, this small simulation aims to emphasize that there might be many ways to obtain sensitive information using multivariate analysis and not all of them are obvious. Thus, agencies thinking about actually implementing some form of remote data access should consider carefully which queries could be allowed by the system.