Testing for time-invariant unobserved heterogeneity in generalized linear models for panel data

Recent literature on panel data emphasizes the importance of accounting for time-varying unobservable individual effects, which may stem from either omitted individual characteristics or macro-level shocks that affect each individual unit differently. In this paper, we propose a simple specification test of the null hypothesis that the individual effects are time-invariant against the alternative that they are time-varying. Our test is an application of Hausman (1978) testing procedure and can be used for any generalized linear model for panel data that admits a sufficient statistic for the individual effect. This is a wide class of models which includes the Gaussian linear model and a variety of nonlinear models typically employed for discrete or categorical outcomes. The basic idea of the test is to compare two alternative estimators of the model parameters based on two different formulations of the conditional maximum likelihood method. Our approach does not require assumptions on the distribution of unobserved heterogeneity, nor it requires the latter to be independent of the regressors in the model. We investigate the finite sample properties of the test through a set of Monte Carlo experiments. Our results show that the test performs well, with small size distortions and good power properties. We use a health economics example based on data from the Health and Retirement Study to illustrate the proposed test.     

Do Labour Market Programmes Speed up the Return to Work?*

We evaluate the impact of labour market programmes on unemployment durations in Norway, by means of a distribution‐free mixed proportional competing risks hazard rate model. We find that programme participation, once completed, improves employment prospects, but that there is often an opportunity cost in the form of a lock‐in effect during participation. The average net effect of programme participation on the length of the job search period is found to be around zero. For participants with poor employment prospects, the favourable post‐programme effects outweigh the negative lock‐in effects.     

Testing for Hysteresis in Unemployment in OECD Countries: New Evidence using Stationarity Panel Tests with Breaks*

This paper tests hysteresis effects in unemployment using panel data for 19 Organization for Economic Co‐operation and Development (OECD) countries covering the period 1956–2001. The tests exploit the cross‐sectional variations of the series, and additionally, allow for a different number of endogenous breakpoints in the unemployment series. The critical values are simulated based on our specific panel sizes and time periods. The findings stress the importance of accounting for exogenous shocks in the series and support the natural‐rate hypothesis of unemployment for the majority of the countries analysed.     

Testing for structural stability of factor augmented forecasting models

Mild factor loading instability, particularly if sufficiently independent across the different constituent variables, does not affect the estimation of the number of factors, nor subsequent estimation of the factors themselves (see e.g.  Stock and Watson (2009)). This result does not hold in the presence of large common breaks in the factor loadings, however. In this case, information criteria overestimate the number of breaks. Additionally, estimated factors are no longer consistent estimators of “true” factors. Hence, various recent research papers in the diffusion index literature focus on testing the constancy of factor loadings. However, forecast failure of factor augmented models can be due to either factor loading instability, regression coefficient instability, or both. To address this issue, we develop a test for the joint hypothesis of structural stability of both factor loadings and factor augmented forecasting model regression coefficients. Our proposed test statistic has a chi-squared limiting distribution, and we are able to establish the first order validity of (block) bootstrap critical values. Empirical evidence is also presented for 11 US macroeconomic indicators.     

Marginal Effects for Competing Risks Models with Piecewise Constant Hazards*

In the competing risks context, the effect of a covariate on the hazard function for a particular cause may be very different from its effect on the likelihood of exiting due to that cause. The latter probability is a function of all cause‐specific hazards, and thereby potentially affected by indirect effects via hazards for competing causes. We consider the effects of covariates on the cumulative probability of exiting from a particular cause. These ‘marginal effects’ are decomposed into direct effects via the hazard of interest and indirect effects via the hazards for competing causes. For the piecewise constant hazard specification we derive simple closed‐form expressions for the marginal effects that can be computed from the standard hazard function estimates. An empirical application illustrates that the marginal effects provide a useful and coherent way of summarizing the results of competing risks analysis.     

Estimating dynamic local interactions models

This paper presents empirical methods for studying a class of local interactions models in which agents’ transitions are affected by their neighbors’ states. We consider an application to urban unemployment and social networks in job search using publicly available cross-section and retrospective data. Most links in our model are local, but some span an entire metropolitan area. Our methods are designed to accommodate the presence of strong cross-sectional dependence arising from these few cross-metro-area links. We also present simple methods to compare data and model spell distributions and to illustrate the model's dynamic properties.     

A Complete Decomposition of Unemployment Dynamics using Longitudinal Grouped Duration Data*

In this paper, we study the unemployment dynamics in the Belgian regions, Flanders and Wallonia, on the basis of aggregate stratified data covering the period 1973–93. We decompose the aggregate exit probability from unemployment into calendar time and, both observed and unobserved, compositional effects. We find that changes in the inflow composition affect the cyclical fluctuations in unemployment duration only marginally. However, the long‐run improvement in the quality of entrants into unemployment, notably in terms of educational attainment, mitigates the strong upward trend in this duration. This is a new result as none of the existing studies purges the trend in the aggregate outflow rate of the variation in its composition. We also conclude that in Belgium, incidence explains as much as 45% of the evolution of unemployment. Finally, the diverging evolution of unemployment across Flanders and Wallonia predominantly results from a stronger decline in the exit rates from unemployment in Wallonia.     

Testing for Multicointegration in Panel Data with Common Factors*

This paper addresses the concept of multicointegration in a panel data framework and builds upon the panel data cointegration procedures developed in Pedroni [Econometric Theory (2004), Vol. 20, pp. 597–625]. When individuals are either cross‐section independent, or cross‐section dependence can be removed by cross‐section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes. The paper also deals with the issue of cross‐section dependence using approximate common‐factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating an inventories, sales and production relationship for a panel of US industries.     

Unemployment Experiences of Young Men: on the Road to Stable Employment?*

This study examines the unemployment experiences of young men in the United Kingdom over the period 1982.IV–1998.I. The empirical results show that repeated unemployment is a dominant feature of the UK labour market and that individual heterogeneity affects mainly the incidence of unemployment and only to a much lesser extent the duration of unemployment. We estimate that about 73% of the young unemployed find stable employment before the age of 35. The remaining 27%, concentrated among the lower‐skilled, keep returning into unemployment, suggesting structural employment instability. These findings imply that a labour market programme targeted at increasing the employability of the young unemployed would yield long‐term benefits by not only getting them out of unemployment but also keeping them out of unemployment.     

How do extended benefits affect unemployment duration? A regression discontinuity approach

This paper studies a targeted program that extends the maximum duration of unemployment benefits from 30 weeks to 209 weeks in Austria. Sharp discontinuities in treatment assignment at age 50 and at the border between eligible regions and control regions identify the effect of extended benefits on unemployment duration. Results indicate that the duration of job search is prolonged by at least 0.09 weeks per additional week of benefits among men, whereas unemployment duration increases by at least 0.32 weeks per additional week of benefits for women. This finding is consistent with a lower early retirement age applying to women.     

Testing for Fractional Integration Versus Short Memory with Structural Breaks*

Although it is commonly accepted that most macroeconomic variables are non‐stationary, it is often difficult to identify the source of the non‐stationarity. Integrated processes and short‐memory models with trending components, possibly affected by structural breaks, imply similar features in the data and, accordingly, are hard to distinguish. The goal of this article is to extend the classical testing framework of I(1) versus I(0) + trends and/or breaks by considering a more general class of models under the null hypothesis: fractionally integrated (FI) processes. The asymptotic properties of the proposed tests are derived and it is shown that they are very well‐behaved in finite samples. An illustration using US inflation data is also provided.     

Testing for weak identification in possibly nonlinear models

In this paper we propose a chi-square test for identification. Our proposed test statistic is based on the distance between two shrinkage extremum estimators. The two estimators converge in probability to the same limit when identification is strong, and their asymptotic distributions are different when identification is weak. The proposed test is consistent not only for the alternative hypothesis of no identification but also for the alternative of weak identification, which is confirmed by our Monte Carlo results. We apply the proposed technique to test whether the structural parameters of a representative Taylor-rule monetary policy reaction function are identified.     

Goodness-of-fit tests for conditional models under censoring and truncation

The problem of specification tests for conditional models is studied when the data are subject to left truncation and right censoring. A general method is applied to derive tests for the polynomial regression, the proportional hazards, the additive risks and the proportional odds models. Bootstrap versions to approximate the critical values of the test are introduced and proved to work both from a theoretical viewpoint as well as in a small simulation study.     

On the cyclicality of unemployment: Resurrecting the participation margin

This paper considers a real business cycle model with search frictions in the labor market and labor supply which is elastic along the participation margin. Previous authors have found that such models generate counterfactually procyclical unemployment and a positively sloped Beveridge curve. This paper presents a calibrated model which succeeds at generating countercyclical unemployment and a negatively sloped Beveridge curve, despite the presence of a participation margin.     

Testing for structural breaks in dynamic factor models

In this paper we investigate the consequences of structural breaks in the factor loadings for the specification and estimation of factor models based on principal components and suggest procedures for testing for structural breaks. It is shown that structural breaks severely inflate the number of factors identified by the usual information criteria. The hypothesis of a structural break is tested by using LR, LM and Wald statistics. The LM test (which performs best in our Monte Carlo simulations) is generalized to test for structural breaks in factor models where the break date is unknown and the common factors and idiosyncratic components are serially correlated. The proposed test procedures are applied to datasets from the US and the euro area.     

Distribution-free tests for time series models specification

We consider a class of time series specification tests based on quadratic forms of weighted sums of residuals autocorrelations. Asymptotically distribution-free tests in the presence of estimated parameters are obtained by suitably transforming the weights, which can be optimally chosen to maximize the power function when testing in the direction of local alternatives. We discuss in detail an asymptotically optimal distribution-free alternative to the popular Box–Pierce when testing in the direction of AR or MA alternatives. The performance of the test with small samples is studied by means of a Monte Carlo experiment.     

Are Short‐lived Jobs Stepping Stones to Long‐Lasting Jobs?*

This article assesses whether short‐lived jobs (lasting one quarter or less and involuntarily ending in unemployment) are stepping stones to long‐lasting jobs (enduring 1 year or more) for Belgian long‐term unemployed school‐leavers. We proceed in two steps. First, we estimate labour market trajectories in a multi‐spell duration model that incorporates lagged duration and lagged occurrence dependence. Second, in a simulation we find that (fe)male school‐leavers accepting a short‐lived job are, within 2 years, 13.4 (9.5) percentage points more likely to find a long‐lasting job than in the counterfactual in which they reject short‐lived jobs.     

Impacts of Prime‐age Adult Mortality on Labour Supply: Evidence from Adolescents and Women in South Africa*

This paper examines the impact of prime‐age adult mortality on the transition made by adolescents from school to the labour market and on female adult labour force participation decisions in South Africa. We find, first, that deaths of prime‐age adults significantly increase both male and female adolescents’ labour force participation as they stop their schooling. Secondly, the death of prime‐age adults in general also decreases school enrolment ex ante. Thirdly, female adults tend to join the labour force following the death of prime‐age adult males. These findings imply that prime‐age adult mortality increases labour supply and disrupts human capital formation.     

Distribution and determinants of lifetime unemployment

The empirical literature on unemployment almost exclusively focuses on the duration of distinct unemployment spells. In contrast, we use a unique administrative micro data set for the time span 1975-2004 to investigate individual lifetime unemployment — defined as the cumulative length of all unemployment spells over a 25-year period. This new perspective enables us to answer questions regarding the long-term distribution and determinants of unemployment for birth cohorts 1950-1954. We show that lifetime unemployment is highly concentrated on a small part of the population. With censored quantile regressions we investigate the long-lasting influence of bad luck early in the professional career: Controlling for individual and firm characteristics we find that choosing at a young age what turns out to be an unfavorable occupation significantly increases the predicted amount of lifetime unemployment.     

Testing for ARCH in the presence of nonlinearity of unknown form in the conditional mean

Tests of ARCH are a routine diagnostic in empirical econometric and financial analysis. However, it is well known that misspecification of the conditional mean may lead to spurious rejection of the null hypothesis of no ARCH. Nonlinearity is a prime example of this phenomenon. There is little work on the extent of the effect of neglected nonlinearity on the properties of ARCH tests. We investigate this using new ARCH testing procedures that are robust to the presence of neglected nonlinearity. Monte Carlo evidence shows that the problem is serious and that the new methods alleviate this problem to a very large extent. We apply the new tests to exchange rate data and find substantial evidence of spurious rejection of the null hypothesis of no ARCH.