Unobserved Heterogeneity in Multiple-Spell Multiple-States Duration Models

In survival analysis a large literature using frailty models, or models with unobserved heterogeneity, exist. In the growing literate on multiple spell multiple states duration models, or multistate models, modeling this issue is only at its infant phase. Ignoring unobserved heteogeneity can, however, produce incorrect results. This paper presents how unobserved heterogeneity can be incorporated into multistate models, with an emphasis on semi-Markov multistate models with a mixed proportional hazard structure. First, the aspects of frailty modeling in univariate (proportional hazard, Cox) duration models are addressed and some important models with unobserved heterogeneity are discussed. Second, the domain is extended to modeling of parallel/clustered multivariate duration data with unobserved heterogeneity. The implications of choosing shared or correlated unobserved heterogeneity is highlighted. The relevant differences with recurrent events data is covered next. They include the choice of the time scale and risk set which both have important implications for the way unobserved heterogeneity influence the model. Multistate duration models can have both parallel and recurrent events. Incorporating unobserved heterogeneity in multistate models, therefore, brings all the previously addressed issues together. Although some estimation procedures are covered the emphasis is on conceptual issues. The importance of including unobserved heterogeneity in multistate duration models is illustrated with data on labour market and migration dynamics of recent immigrants to The Netherlands.multiple spell multiple state duration, mixed proportional hazard, multistate model, unobserved heterogeneity, frailty

Unemployment duration among immigrants and natives: unobserved heterogeneity in a multi-spell duration model

This paper studies whether the unemployment dynamics of immigrants differ from those of natives, paying special attention to the impact of accounting for unobserved heterogeneity among individuals. Using a large administrative data set for Spain, we estimate multiple-spell discrete duration models which disentangle unobserved heterogeneity from duration dependence. Specifically, we estimate random effects models assuming that the distribution of the effects is discrete with finite support, and fixed effects models in which the distribution of the unobserved effects is left unrestricted. Our results show the importance of accounting for unobserved heterogeneity and that mistaken policy implications can be derived due to improper treatment of unmeasured variables. We find that lack of control for unobserved heterogeneity leads to the conclusion that immigrant males have a higher probability of leaving unemployment than natives and that the negative effect of unemployment benefits for immigrants lasts longer than for natives. Nonetheless, the estimates which do control for unobserved heterogeneity show the opposite results

Estimating Learning Models with Experimental Data

We study the statistical properties of three estimation methods for a model of learning that is often tted to experimental data: quadratic deviation measures without unobserved heterogeneity, and maximum likelihood with and without unobserved heterogeneity. After discussing identi cation issues, we show that the estimators are consistent and provide their asymptotic distribution. Using Monte Carlo simulations, we show that ignoring unobserved heterogeneity can lead to seriously biased estimations in samples which have the typical length of actual experiments. Better small sample properties are obtained if unobserved heterogeneity is introduced. That is, rather than estimating the parameters for each individual, the individual parameters are considered random variables, and the distribution of those random variables is estimated

Unemployment Duration among Immigrants and Natives: Unobserved Heterogeneity in a Multi-Spell Duration Model

This paper studies whether the unemployment dynamics of immigrants differ from those of natives, paying special attention to the impact of accounting for unobserved heterogeneity among individuals. Using a large administrative data set for Spain, we estimate multiple-spell discrete duration models which disentangle unobserved heterogeneity from duration dependence. Specifically, we estimate random effects models assuming that the distribution of the effects is discrete with finite support, and fixed effects models in which the distribution of the unobserved effects is left unrestricted. Our results show the importance of accounting for unobserved heterogeneity and that mistaken policy implications can be derived due to improper treatment of unmeasured variables. We find that lack of control for unobserved heterogeneity leads to the conclusion that immigrant males have a higher probability of leaving unemployment than natives and that the negative effect of unemployment benefits for immigrants lasts longer than for natives. Nonetheless, the estimates which do control for unobserved heterogeneity show the opposite results.Duration models; Discrete choice; Multiple spells; Unobserved heterogeneity; Unemployment; Immigration.

Unemployment duration among immigrants and natives: unobserved heterogeneity in a multi-spell duration model

This paper studies whether the unemployment dynamics of immigrants differ from those of natives, paying special attention to the impact of accounting for unobserved heterogeneity among individuals. Using a large administrative data set for Spain, we estimate multiple-spell discrete duration models which disentangle unobserved heterogeneity from duration dependence. Specifically, we estimate random effects models assuming that the distribution of the effects is discrete with finite support, and fixed effects models in which the distribution of the unobserved effects is left unrestricted. Our results show the importance of accounting for unobserved heterogeneity and that mistaken policy implications can be derived due to improper treatment of unmeasured variables. We find that lack of control for unobserved heterogeneity leads to the conclusion that immigrant males have a higher probability of leaving unemployment than natives and that the negative effect of unemployment benefits for immigrants lasts longer than for natives. Nonetheless, the estimates which do control for unobserved heterogeneity show the opposite results.Duration models, Discrete choice, Multiple spells, Unobserved heterogeneity, Unemployment, Immigration

A simple GMM estimator for the semi-parametric mixed proportional hazard model

Ridder and Woutersen (2003) have shown that under a weak condition on the baseline hazard, there exist root-N consistent estimators of the parameters in a semiparametric Mixed Proportional Hazard model with a parametric baseline hazard and unspeci�ed distribution of the unobserved heterogeneity. We extend the Linear Rank Estimator (LRE) of Tsiatis (1990) and Robins and Tsiatis (1991) to this class of models. The optimal LRE is a two-step estimator. We propose a simple one-step estimator that is close to optimal if there is no unobserved heterogeneity. The e¢ ciency gain associated with the optimal LRE increases with the degree of unobserved heterogeneity.

Unobserved Heterogeneity in the Binary Logit Model with Cross-Sectional Data and Short Panels: A Finite Mixture Approach

This paper proposes a new approach to dealing with unobserved heterogeneity in applied research using the binary logit model with cross-sectional data and short panels. Unobserved heterogeneity is particularly important in non-linear regression models such as the binary logit model because, unlike in linear regression models, estimates of the effects of observed independent variables are biased even when omitted independent variables are uncorrelated with the observed independent variables. We propose an extension of the binary logit model based on a finite mixture approach in which we conceptualize the unobserved heterogeneity via latent classes. Simulation results show that our approach leads to considerably less bias in the estimated effects of the independent variables than the standard logit model. Furthermore, because identification of the unobserved heterogeneity is weak when the researcher has cross-sectional rather than panel data, we propose a simple approach that fixes latent class weights and improves identification and estimation. Finally, we illustrate the applicability of our new approach using Canadian survey data on public support for redistribution.binary logit model; unobserved heterogeneity; latent classes; simulation

The (mis)specification of discrete duration models with unobserved heterogeneity: a Monte Carlo study

Empirical researchers usually prefer statistical models that can be easily estimated using standard software packages. One such model is the sequential binary model with or without normal random effects; such models can be adopted to estimate discrete duration models with unobserved heterogeneity. But ease of estimation may come at a cost. In this paper we conduct a Monte Carlo simulation to evaluate the consequences of omitting or misspecifying the unobserved heterogeneity distribution in single-spell discrete duration models.discrete duration models, unobserved heterogeneity, Monte Carlo simulations