ß-expectation tolerance region for the heteroscedastic multiple regression model with multivariate Student-t error

A ß-expectation tolerance region has been constructed for the multivariate regression model with heteroscedastic errors which follow a multivariate Student-t distribution with an unknown number of degrees of freedom. The ß-expectaion tolerance region obtained in this paper is optimal in the sense of having minimum enclosure among all such tolerance regions that guarantees that it would cover any preassigned proportions, namely, ß×100 percent of the future responses from the model.     

On characterizations and variance bounds of discrete α-unimodality

Characterizations of α-unimodality for integer-valued random variables about a specific mode are established in terms of their probability mass functions, distribution functions and characteristic functions. Using these characterizations variance lower bounds in terms of α and the mode are derived. For α=1 all these results are reduced to ordinary unimodality. The new variance lower bounds for discrete unimodality is sharper than its continuous counterpart. An upper bound for the variance of discrete unimodal distribution defined on a finite support is discussed.     

Parametric link modification of both tails in binary regression

Common binary regression models such as logistic or probit regression have been extended to include parametric link transformation families. These binary regression models with parametric link are designed to avoid possible link misspecification and improve fit in some data sets. One and two parameter link families have been proposed in the literature (for a review see Stukel (1988)). However in real data examples published so far only one parameter link families have found to improve the fit significantly. This paper introduces a two parameter link family involving the modification of both tails of the link. An analysis based on computationally tractable Bayesian inference involving Monte Carlo sampling algorithms is presented extending earlier work of Czado (1992, 1993b). Finally, the usefulness of the two tailed link modification will be demonstrated in an example where single tail modification can be significantly improved upon by using a two tailed modification.     

Consistency,asymptotic unbiasedness and bounds on the bias of s2 in the linear regression model with error component disturbances

The OLS estimator of the disturbance variance in the linear regression model with error component disturbances is shown to be weakly consistent and asymptotically unbiased without any restrictions on the regressor matrix. Also, simple exact bounds on the expected value of s² are given for both the one-way and two-way error component models.     

Application of Stein-type estimation in combining regression estimates from replicated experiments

This paper considers the application of Stein-type estimation procedure for the coefficients in a linear regression model when data are available from replicated experiment. Two families of estimators characterized by a single scalar are proposed and their large sample asymptotic properties are derived. These are utilized for comparing the performances of the two estimators along with the conventional estimator and conditions for the superiority of one estimator over the other are deduced.     

Distributional aspects in latent variable models

For observable indicators with ordered categories one can assume underlying latent variables following certain marginal distributions. Transforming the latent variables changes its marginal distributions but not the observable qualitative indicators. The joint distribution of the latent variables can be constructed from the marginal distributions. There is a broad class of multivariate distributions for which the observable indicators are equivalent. By choosing the multivariate normal distribution from this class we can analyse a linear relationship between the transformed latent variables. This leads to latent structural equation models. Estimation of these latter models is therefore more general than the distributional assumption might initially suggest. Robustness of the estimation procedure is also discussed for deviations from this distribution family. Using ordinal business survey data of the German Ifo-institute we test the efficiency of firms' price expectations implied by the rational expectation hypothesis.     

Partial residuals in cumulative regression models for ordinal data

We are concerned with cumulative regression models for an ordered categorical response variable Y. We propose two methods to build partial residuals from regression on a subset Z₁ of covariates Z., which take into regard the ordinal character of the response. The first method makes use of a multivariate GLM-representation of the model and produces residual measures for diagnostic purposes. The second uses a latent continuous variable model and yields new (adjusted) ordinal data Y^*. Both methods are illustrated by a data set from forestry.     

Jackknife variances and confidence intervals of the Mantel-Haenszel estimator

In the situation of stratified 2×2 tables, consitency of two different jackknife variances of the Mantel-Haenszel estimator is discussed in the case of increasing sample sizes, but a fixed number of strata. Different principles for constructing confidence limits for the common odds ratio are investigated from a theoretical point of view with regard to the position and the length of the resulting intervals. Monte Carlo experiments compare the finite sample performance of the consistent jackknife variance with that of other noniterative variance estimators. In addition, the properties of these variance estimators are investigated when used for confidence interval estimation.     

Estimation for 3-parameter lognormal distribution with unknown shifted origin

A new reparameterization of a 3-parameter lognormal distribution with unknown shifted origin is presented by using a dimensionless parameter. We avoid, in this article, the application of logarithmic and exponential transformations to a value which has a physical dimension. The distribution function contains two dimensional parameters and one dimensionless parameter. Modified moment estimators and maximum likelihood estimators are presented. The presented modified moment estimators and maximum likelihood estimators are confronted with some actual data.     

Producing Monthly Estimates of Unemployment and Employment According to the International Labour Office Definition

Monthly unemployment statistics are available in Britain from a monthly count of the number of people claiming unemployment-related benefits. There has been considerable debate on the appropriateness of this measure. Unemployment and employment statistics are available quarterly from the Labour Force Survey (LFS), using International Labour Office (ILO) definitions. In this paper various options for producing monthly unemployment estimates according to the ILO definition are examined. Methods considered are a monthly LFS, calculating rolling averages from the quarterly LFS, and methods which combine LFS and claimant count data. It is proposed that a monthly LFS of 60 000 households be introduced which can produce monthly estimates of total unemployment and more detailed estimates quarterly. Such a survey would also fill an important gap by providing monthly employment statistics which are needed to provide a complete picture of the labour market.     

Comparison of location parameters of two exponential distributions when scale parameters are different and unknown

Letx _i(1)≤x _i(2)≤…≤x _i(r_i) be the right-censored samples of sizesn _i from theith exponential distributions $\sigma _i^{ - 1} exp\{ - (x - \mu _i )\sigma _i^{ - 1} \} ,i = 1,2$ where μ_i and σ_i are the unknown location and scale parameters respectively. This paper deals with the posteriori distribution of the difference between the two location parameters, namely μ₂-μ₁, which may be represented in the form $\mu _2 - \mu _1 \mathop = \limits^\mathcal{D} x_{2(1)} - x_{1(1)} + F_1 \sin \theta - F_2 \cos \theta $ where $\mathop = \limits^\mathcal{D} $ stands for equal in distribution,F _i stands for the central F-variable with [2,2(r _i?1)] degrees of freedom and $\tan \theta = \frac{{n_2 s_{x1} }}{{n_1 s_{x2} }}, s_{x1} = (r_1 - 1)^{ - 1} \left\{ {\sum\limits_{j = 1}^{r_i - 1} {(n_i - j)(x_{i(j + 1)} - x_{i(j)} )} } \right\}$ The paper also derives the distribution of the statisticV=F ₁ sin σ?F ₂ cos σ and tables of critical values of theV-statistic are provided for the 5% level of significance and selected degrees of freedom.     

The effects of vocational training programmes on the duration of unemployment in Eastern Germany

Summary Vocational training programmes have been the most important active labour market policy instrument in Germany in the last years. However, the still unsatisfying situation of the labour market has raised doubt on the efficiency of these programmes. In this paper, we analyse the effects of the participation in vocational training programmes on the duration of unemployment in Eastern Germany. Based on administrative data for the time between the October 1999 and December 2002 of the Federal Employment Administration¹, we apply a bivariate mixed proportional hazards model. By doing so, we are able to use the information of the timing of treatment as well as observable and unobservable influences to identify the treatment effects. The results show that a participation in vocational training prolongates the unemployment duration in Eastern Germany. Furthermore, the results suggest that locking-in effects are a serious problem of vocational training programmes. The authors thank Heinz Galler and an anonymous referee for valuable comments. The paper has also benefited from fruitful discussion at the annual meeting of the German Statistical Society in 2004, Frankfurt, and in IZA seminar, Bonn. All remaining errors are on our own. Financial support of the IAB, Nuremberg, is gratefully acknowledged.     

Small area estimates of labour force participation under a multinomial logit mixed model

Summary.  A new methodology is developed for estimating unemployment or employment characteristics in small areas, based on the assumption that the sample totals of unemployed and employed individuals follow a multinomial logit model with random area effects. The method is illustrated with UK labour force data aggregated by sex–age groups. For these data, the accuracy of direct estimates is poor in comparison with estimates that are derived from the multinomial logit model. Furthermore, two different estimators of the mean-squared errors are given: an analytical approximation obtained by Taylor linearization and an estimator based on bootstrapping. A simulation study for comparison of the two estimators shows the good performance of the bootstrap estimator.     

THE UNEMPLOYMENT RATE WHEN THE LABOUR MARKET IS MODELLED BY A MARKOV CHAIN

Assuming a Markov chain model for the labour market flow, we study it in its equilibrium state, We compare the observed and the theoretical unemployment rates. It is found that the observed unemployment rate approximates very closely the theoretical one. The mean and variance of the observed unemployment rate are computed. It is shown that its asymptotic distribution is normal.     

Adapting the optimal job search model for active labour market policy

Summary.  The structural theoretical framework for the analysis of duration of unemployment has been the optimal job search model. Recent advances in computational techniques in Bayesian inference now facilitate the analysis of incomplete data sets and the recovery of structural model parameters. The paper uses these methods on a UK data set of the long-term unemployed to illustrate how the optimal job search model can be adapted to model the effects of an active labour market policy. Without such an adaptation our conclusion is that the simple optimal job search model may not fit empirical unemployment data and could thus lead to a misspecified econometric model and incorrect parameter estimates.     

Choosing between alternative classification criteria to measure the labour force state

Summary.  Labour force counting relies on general guidelines that are set by the International Labour Office to classify individuals into three labour force states: employment, unemployment and inactivity. However, the resulting statistics are known to be sensitive to slight variations in operational definitions which are prima facie consistent with the general guidelines. We consider two interpretations of the general guidelines, operationalized by the criterion that is currently followed by Eurostat and a criterion that was followed by the Italian Statistical Office up to 1992. After showing that the labour force statistics resulting from the two criteria differ considerably, we compare individuals whose classification depends on the criterion that is adopted with individuals whose classification is common between criteria to study the boundary between unemployment and inactivity. An application of our strategy is presented using data from the Italian Labour Force Survey, painting a picture neatly against the criterion that is currently followed by Eurostat.     

A Poisson geometric process approach for predicting drop-out and committed first-time blood donors

A Poisson geometric process (PGP) model is proposed to study individual blood donation patterns for a blood donor retention program. Extended from the geometric process (GP) model of Lam [16 Y. Lam, Geometric process and replacement problem, Acta Math. Appl. Sin. 4 (1988), pp. 366–377. doi: 10.1007/BF02007241[Crossref] , [Google Scholar]], the PGP model captures the rather pronounced trend patterns across clusters of donors via the ratio parameters in a mixture setting. Within the state-space modeling framework, it allows for overdispersion by equating the mean of the Poisson data distribution to a latent GP. Alternatively, by simply setting, the mean of the Poisson distribution to be the mean of a GP, it has equidispersion. With the group-specific mean and ratio functions, the mixture PGP model facilitates classification of donors into committed, drop-out and one-time groups. Based on only two years of observations, the PGP model nicely predicts donors’ future donations to foster timely recruitment decision. The model is implemented using a Bayesian approach via the user-friendly software WinBUGS.     

Multilevel and Multi-index Monte Carlo methods for the McKean–Vlasov equation

We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity. This problem is equivalent to estimating the weak solution of the limiting McKean–Vlasov SDE. To that end, our approach uses systems with finite numbers of particles and a time-stepping scheme. In this case, there are two discretization parameters: the number of time steps and the number of particles. Based on these two parameters, we consider different variants of the Monte Carlo and Multilevel Monte Carlo (MLMC) methods and show that, in the best case, the optimal work complexity of MLMC, to estimate the functional in one typical setting with an error tolerance of \(\mathrm {TOL}\), is Open image in new window when using the partitioning estimator and the Milstein time-stepping scheme. We also consider a method that uses the recent Multi-index Monte Carlo method and show an improved work complexity in the same typical setting of Open image in new window . Our numerical experiments are carried out on the so-called Kuramoto model, a system of coupled oscillators.     

Unemployed and their caseworkers: should they be friends or foes?

Summary.  In many countries, caseworkers in public employment offices have dual roles of counselling and monitoring unemployed people. These roles often conflict, which results in important caseworker heterogeneity: some consider providing services to their clients and satisfying their demands as their primary task. However, others may pursue their own strategies, even against the will of the unemployed person. They may assign jobs and labour market programmes without the consent of the unemployed person. On the basis of a very detailed linked jobseeker–caseworker data set for Switzerland, we investigate the effects of caseworkers' co-operativeness on the probabilities of employment of their clients. Modified statistical matching methods reveal that caseworkers who place less emphasis on a co-operative and harmonic relationship with their clients increase their chances of employment in the short and medium term.     

Unemployment duration and the length of entitlement periods for unemployment benefits: do the IAB employment subsample and the German Socio-Economic Panel yield the same results?*

Summary: We compare information on the length of unemployment spells contained in the IAB employment subsample (IABS) and in the German Socio-Economic Panel (GSOEP). Due to the lack of information on registered unemployment in the IABS, we use two proxies of unemployment in the IABS as introduced by Fitzenberger/Wilke (2004). The first proxy comprises all periods of nonemployment after an employment spell which contain at least one period with unemployment compensation transfers. The second proxy includes all episodes between two employment spells during which an individual continuously received unemployment benefits. Estimation of standard duration models indicates that conclusions drawn from the IABS and the GSOEP differ in many cases. While the GSOEP suggests that the hazard rate has a maximum at about 12 months of unemployment, the IABS results suggest that this maximum is at about 20 months. Contrary to our GSOEP results and contrary to many results based on the GSOEP found in the literature, we find a statistically significant association between longer maximum entitlement periods of unemployment benefits (‘Arbeitslosengeld’) and longer unemployment durations for men in the IABS. The results for women do not show such clear patterns. The large sample size of the IABS also allows to trace out statistically significant effects of characteristics such as regional and industry indicators, which is generally not possible in the relatively small GSOEP. * Acknowledgements: We would like to thank the editors of this special issue, Joachim M?ller and Bernd Fitzenberger, two anonymous referees, the participants of the ‘Statistische Woche 2004’ in Frankfurt (in particular Reinhard Hujer, Olaf Hübler and Gerd Ronning), seminar participants at the ZEW Mannheim (especially Fran?ois Laisney and Alexander Spermann) and Jennifer Hunt for their many helpful comments and suggestions. All remaining errors are our own. Financial support of the Deutsche Forschungsgemeinschaft (DFG) through the research project ‘Microeconometric modelling of unemployment durations under consideration of the macroeconomic situation’ is gratefully acknowledged. The data used in this paper were made available by the Institute for Employment Research (IAB) at the Federal Labour Office of Germany, Nürnberg, and the German Socio Economic Panel Study (GSOEP) at the German Institute for Economic Research (DIW), Berlin.