A semiparametric random effects approach to unobserved heterogeneity in count data models of organizational founding

The paper discusses a semiparametric random-effects approach to the problem of unobserved population heterogeneity in organizational research based on models for pooled cross-sectional time series count data. The analytical value of this approach rests in its ability to produce estimates of the structural parameters that do not depend on any specific assumption about the distribution of the heterogeneity components in the population. The practical value of the method proposed is illustrated in an empirical application to processes of organizational founding, and to the relation between density dependence and unobserved heterogeneity in spatially distributed organizational populations. The empirical evidence produced suggests that future studies of organizational founding at the population level will have to account for variation in observed as well as unmeasured (or unobservable) variables.     

Using frailty models to account for heterogeneity in multistage manufacturing and service processes

Statistical process control has been widely applied to manufacturing and service operations with the aim of monitoring and improving the reliability of products. The existing monitoring procedures were introduced following the assumption that a single-stage process with independent quality characteristic is under consideration. However, in multistage processes with dependent variables, quality characteristics of interest should be optimally monitored only after they have been adjusted for the effect of influential covariates. In general, it is impossible to include all relevant covariates because measuring such values entails great financial costs. The neglect of such covariates results in having unobserved heterogeneity which dampens the detection ability of the monitoring procedure. The more complicated picture arises when the values corresponding to the reliability-related quality variable are censored due to the time and cost constraints. Thus, to deal with the effect of observed and unobserved covariates together with the censoring issue, the frailty and the proportional hazard models are used and some model-based monitoring schemes are devised. The surveillance procedures are proposed in both the presence and absence of a censoring mechanism. The performance analysis shows that the monitoring procedure based on the cumulative sum chart is superior in detecting shifts while the exponentially weighted moving average chart is effective in some cases.     

HETEROGENEITY,EXCESS ZEROS,AND THE STRUCTURE OF COUNT DATA MODELS

This paper demonstrates that the unobserved heterogeneity commonly assumed to be the source of overdispersion in count data models has predictable implications for the probability structure of such mixture models. In particular, the common observation of excess zeros is a strict implication of unobserved heterogeneity. This result has important implications for using count model estimates for predicting certain interesting parameters. Test statistics to detect such heterogeneity-related departures from the null model are proposed and applied in a health-care utilization example, suggesting that a null Poisson model should be rejected in favour of a mixed alternative. © 1997 John Wiley & Sons, Ltd.     

Mixed Hidden Markov Models for Longitudinal Data: An Overview

In this paper we review statistical methods which combine hidden Markov models (HMMs) and random effects models in a longitudinal setting, leading to the class of so‐called mixed HMMs. This class of models has several interesting features. It deals with the dependence of a response variable on covariates, serial dependence, and unobserved heterogeneity in an HMM framework. It exploits the properties of HMMs, such as the relatively simple dependence structure and the efficient computational procedure, and allows one to handle a variety of real‐world time‐dependent data. We give details of the Expectation‐Maximization algorithm for computing the maximum likelihood estimates of model parameters and we illustrate the method with two real applications describing the relationship between patent counts and research and development expenditures, and between stock and market returns via the Capital Asset Pricing Model.     

Correcting for bias in retrospective data

When panel data are not available, retrospective data are used in the estimation of dynamic choice models. However, retrospective data are not reliable. Previous studies of voting choices, for example, have shown that respondents misreport their past choices in order to appear more consistent with their current choice. Such retrospective bias leads to inconsistent estimates, especially when there is state dependence in choices. Specifically, observed persistence in retrospective data may be due to (a) true state dependence, (b) unobserved heterogeneity, and (c) retrospective bias in reporting previous choices. Whereas Heckman in his 1981 study deals with (a) and (b), we introduce a method to estimate true state dependence while accounting for both unobserved heterogeneity and retrospective reporting bias. Our method is based on modeling the reporting behavior and integrating it into the estimation. The identification strategy is based on the correlation between the reported previous choices and current exogenous variables. Using data on Israeli voters, we find that the probability that a respondent whose vote intention in 1991 differed from his or her past voting choices would lie about their past choices is 0.23. Copyright © 2007 John Wiley & Sons, Ltd.     

Measuring state dependence in individual poverty histories when there is feedback to employment status and household composition

This paper argues that the assumption of strict exogeneity, which is usually invoked in estimating models of state dependence with unobserved heterogeneity, is violated in the poverty context as important variables determining contemporaneous poverty status, in particular employment status and household composition, are likely to be influenced by past poverty outcomes. Therefore, a model of state dependence is developed that explicitly allows for possible feedback effects from past poverty to future employment and household composition outcomes. Empirical results based on data from the German Socio‐Economic Panel (GSOEP) suggest that there are indeed such feedback effects and that failure to take them into account may lead to biased estimates of the state dependence effect. Copyright © 2009 John Wiley & Sons, Ltd.     

STATE DEPENDENCE AND HETEROGENEITY IN HEALTH USING A BIAS‐CORRECTED FIXED‐EFFECTS ESTIMATOR

This paper estimates a dynamic ordered probit model of self‐assessed health with two fixed effects: one in the linear index equation and one in the cut‐points. This robustly controls for heterogeneity in unobserved health status and in reporting behavior, although we cannot separate both sources of heterogeneity. We find important state dependence effects, and small but significant effects of income and other socioeconomic variables. Having dynamics and flexibly accounting for unobserved heterogeneity matters for those estimates. We also contribute to the bias correction literature in nonlinear panel models by comparing and applying two of the existing proposals to our model. Copyright © 2012 John Wiley & Sons, Ltd.     

How does the benefit effect vary as unemployment spells lengthen?

This paper investigates how the effect of income while unemployed on the probability of an individual leaving unemployment varies with the length of time that the individual has been unemployed. We examine this question in the context of a variety of alternative econometric models. We extend the Proportional Hazards model with unrestricted baseline hazard to one in which there are unrestricted effects of a subset of the explanatory variables and also consider models that can be estimated as series of binary response models. The proportional hazard restrictions are rejected for the sample of British unemployed men analysed and in the binary sequence framework Logit and Probit models based on symmetric distributions dominate (in likelihood terms) the Extreme Value form model implied by extension of the Proportional Hazards formulation. Logit models with a flexible form for the duration dependence which also incorporate unobserved heterogeneity in a flexible way are estimated. The results for all formulations indicate a rapidly declining effect of unemployment income as a spell lengthens, with no significant effect for the long-term unemployed. The preferred specifications which allow for omitted heterogeneity indicate no significant effect after about 5 months, and this result is robust to the inclusion or exclusion of previous labour-market experience variables and to the choice of mixing distribution.     

Initial Financial Conditions,Unobserved Heterogeneity and the Survival of Nascent Canadian Manufacturing Firms

The firm dynamics literature has stressed productivity, size, and age effects in firm duration. Understanding the implications of financial state has largely been unexplored because of the lack of quality data on private entrant firms. This paper investigates the role of start‐up financial conditions (debt‐to‐asset ratio) on the duration of entrant manufacturing firms using a unique administrative firm‐level database called T2LEAP. The debt‐to‐asset ratio has an economically and statistically significant effect on firm hazard after controlling for usual covariates and unobserved heterogeneity. Further, a non‐monotonic relationship between firm hazard and leverage appears. Firm hazard varies positively with leverage for firms in the top two leverage quintiles, whereas hazard rates fall with leverage in the lower quintiles. Copyright © 2011 John Wiley & Sons, Ltd.     

Variance components models for survival data

Extensions of the Cox proportional hazards model for survival data are studied where allowance is made for unobserved heterogeneity and for correlation between the life times of several individuals. The extended models are frailty models inspired by Y ashin et al. (1995). Estimation is carried out using the EM algorithm. Inference is discussed and potential applications are outlined, in particular to statistical research in human genetics using twin data or adoption data, aimed at separating the effects of genetic and environmental factors on mortality.     

Adjustment and unobserved heterogeneity in dynamic stochastic frontier models

Stochastic frontier models with autocorrelated inefficiency have been proposed in the past as a way of addressing the issue of temporal variation in firm-level efficiency scores. They are justified using an underlying model of dynamic firm behavior. In this paper we argue that these models could have radically different implications for the expected long-run efficiency scores in the presence of unobserved heterogeneity. The possibility of accounting for unobserved heterogeneity is explored. Random- and correlated random-effects dynamic stochastic frontier models are proposed and applied to a panel of US electric utilities.     

A journey home: What drives how long people are homeless?

This paper uses survival analysis to model exits from two alternative forms of homelessness: sleeping on the streets (‘literal homelessness’) and not having a home of one's own (‘housing insecurity’). We are unique in being able to account for time-invariant, unobserved heterogeneity. Like previous researchers, we find results consistent with negative duration dependence in models which ignore unobserved heterogeneity. However, controlling for unobserved heterogeneity, we find that duration dependence has an inverted U-shape with exit rates initially increasing (indicating positive duration dependence) and then falling. Exit rates out of both literal homelessness and housing insecurity fall with age. Women are more likely than men to exit housing insecurity for a home of their own, but are less likely to exit literal homelessness. Persons with dependent children have higher exit rates. Finally, education seems to protect people from longer periods of housing insecurity.     

Semi‐nonparametric competing risks analysis of recidivism

In this paper we specify a semi‐nonparametric competing risks (SNP‐CR) model of recidivism, for misdemeanors and felonies. The model is a bivariate mixed proportional hazard model with Weibull baseline hazards and common unobserved heterogeneity. The distribution of the latter is modeled semi‐nonparametrically, using orthonormal Legendre polynomials on the unit interval, and integrated out to make the two durations dependent, conditional on the covariates. The SNP‐CR model involved corresponds to a Logit model for felony arrest; hence the validity of the SNP‐CR model can be tested by testing the validity of the implied Logit model. The latter will be done by using the integrated conditional moment (ICM) test. In the first instance we have estimated and tested two versions of the SNP‐CR model, without and with fixed state effects. However, the ICM test rejects these models. Therefore, we have estimated and tested the model for each state separately. These state models are not rejected by the ICM test. Indeed, the estimation results vary substantially per state. Copyright © 2007 John Wiley & Sons, Ltd.     

Bias corrections for two-step fixed effects panel data estimators

This paper introduces large-T bias-corrected estimators for nonlinear panel data models with both time invariant and time varying heterogeneity. These models include systems of equations with limited dependent variables and unobserved individual effects, and sample selection models with unobserved individual effects. Our two-step approach first estimates the reduced form by fixed effects procedures to obtain estimates of the time varying heterogeneity underlying the endogeneity/selection bias. We then estimate the primary equation by fixed effects including an appropriately constructed control variable from the reduced form estimates as an additional explanatory variable. The fixed effects approach in this second step captures the time invariant heterogeneity while the control variable accounts for the time varying heterogeneity. Since either or both steps might employ nonlinear fixed effects procedures it is necessary to bias adjust the estimates due to the incidental parameters problem. This problem is exacerbated by the two-step nature of the procedure. As these two-step approaches are not covered in the existing literature we derive the appropriate correction thereby extending the use of large-T bias adjustments to an important class of models. Simulation evidence indicates our approach works well in finite samples and an empirical example illustrates the applicability of our estimator.     

DURATION DEPENDENCE VERSUS UNOBSERVED HETEROGENEITY IN TREATMENT EFFECTS: SWEDISH LABOR MARKET TRAINING AND THE TRANSITION RATE TO EMPLOYMENT

The effect of a treatment on the hazard rate of a duration outcome may depend on the elapsed time since treatment. In addition, treatment effects may be heterogeneous across agents. The former gives rise to duration dependence of the treatment effect, whereas unobserved heterogeneity gives rise to spurious duration dependence of the observable hazard rate. We develop a model allowing for duration dependence and unobserved heterogeneity in the treatment effect. The model incorporates a Timing of Events model and allows for selectivity on unobservables. We prove identification, exploiting variation in the timing of treatment and outcome. In the application we analyze the effects of the Swedish vocational employment training program on the individual transition rate from unemployment to work. We demonstrate the appropriateness of the approach by studying the enrollment process. The data cover the population and include multiple unemployment spells for many individuals. The results indicate a large, significantly positive effect on exit to work shortly after exiting the program. The effect at the individual level diminishes after some weeks. When taking account of the time spent in the program, the effect on the mean unemployment duration is small. Copyright © 2012 John Wiley & Sons, Ltd.     

A two-step approach to account for unobserved spatial heterogeneity

A two-step approach to account for unobserved spatial heterogeneity. Spatial Economic Analysis. Empirical analysis in economics often faces the difficulty that the data are correlated and heterogeneous in some unknown form. Spatial econometric models have been widely used to account for dependence structures, but the problem of directly dealing with unobserved spatial heterogeneity has been largely unexplored. The problem can be serious particularly if we have no prior information justified by economic theory. In this paper we propose a two-step procedure to identify endogenously spatial regimes in the first step and to account for spatial dependence in the second step. This procedure is applied to hedonic house price analysis.     

Wage differentials in the presence of unobserved worker,firm, and match heterogeneity

We consider the problem of estimating and decomposing wage differentials in the presence of unobserved worker, firm, and match heterogeneity. Controlling for these unobservables corrects omitted variable bias in previous studies. It also allows us to measure the contribution of unmeasured characteristics of workers, firms, and worker-firm matches to observed wage differentials. An application to linked employer-employee data shows that decompositions of inter-industry earnings differentials and the male-female differential are misleading when unobserved heterogeneity is ignored.     

Birth-spacing,fertility and neonatal mortality in India: Dynamics,frailty, and fecundity

Using microdata on 30,000 childbirths in India and dynamic panel data models, we analyse causal effects of birth-spacing on subsequent neonatal mortality and of mortality on subsequent birth intervals, controlling for unobserved heterogeneity. Right censoring is accounted for by jointly estimating a fertility equation, identified by using data on sterilization. We find evidence of frailty, fecundity, and causal effects in both directions. Birth intervals explain only a limited share of the correlation between neonatal mortality of successive children in a family. We predict that for every neonatal death, 0.37 additional children are born, of whom 0.30 survive.     

The role of observed and unobserved heterogeneity in the duration of unemployment

This paper studies the degree to which observable and unobservable worker characteristics account for the variation in the aggregate duration of unemployment. I model the distribution of unobserved worker heterogeneity as time varying to capture the interaction of latent attributes with changes in labor-market conditions. Unobserved heterogeneity is the main explanation for the duration dependence of unemployment hazards. Both cyclical and low-frequency variations in the mean duration of unemployment are mainly driven by one subgroup: workers who, for unobserved reasons, stay unemployed for a long time. In contrast, changes in the composition of observable characteristics of workers have negligible effects.     

Identification and estimation of nonlinear dynamic panel data models with unobserved covariates

This paper considers nonparametric identification of nonlinear dynamic models for panel data with unobserved covariates. Including such unobserved covariates may control for both the individual-specific unobserved heterogeneity and the endogeneity of the explanatory variables. Without specifying the distribution of the initial condition with the unobserved variables, we show that the models are nonparametrically identified from two periods of the dependent variable _Yit$Y_{it}$ and three periods of the covariate _Xit$X_{it}$. The main identifying assumptions include high-level injectivity restrictions and require that the evolution of the observed covariates depends on the unobserved covariates but not on the lagged dependent variable. We also propose a sieve maximum likelihood estimator (MLE) and focus on two classes of nonlinear dynamic panel data models, i.e., dynamic discrete choice models and dynamic censored models. We present the asymptotic properties of the sieve MLE and investigate the finite sample properties of these sieve-based estimators through a Monte Carlo study. An intertemporal female labor force participation model is estimated as an empirical illustration using a sample from the Panel Study of Income Dynamics (PSID).