Estimating labour market transitions and continuations using repeated cross sectional data

doi:10.1016/j.econlet.2011.01.007

Economics Letters

Volume 111, Issue 1, April 2011, Pages 84-87

https://doi.org/10.1016/j.econlet.2011.01.007 Get rights and content

Abstract

This paper proposes a population cohort approach for estimating labour market continuations (or transitions) using repeated cross sectional data. This approach allows for the construction of consistent standard errors that account for the full variability of cross sectional data.

Research Highlights

► I propose a population approach for estimating labour market continuations. ► The approach is applicable to cross sectional data. ► The proposed standard errors account for the full variability of the data. ► Existing methods underestimate the true standard errors.

Introduction

There is a long tradition of exploring labour market transitions in economics. Although the unemployment–employment transition has been the most frequently explored, other transitions or continuations have also been examined, such as the transition out of the labour force (e.g. Jones and Riddell (1999)) and the continuation of a job (job stability, e.g. Brochu (2010), Heisz (2005), Neumark et al. (1999)).

While using panel data to estimate these labour market, transitions is generally the preferred approach, there are circumstances where that approach is problematic. For example, the limited historical coverage (Canadian panels) and data limitations (U.S. panels) make it difficult to differentiate between cyclical and secular changes in job stability.¹ With the absence of this differentiation, one cannot address the real question of interest in the job stability literature: how and why has job stability changed? In such instances, repeated cross sectional data sets offer a valid alternative.

In this paper, I propose a population cohort approach for estimating the continuation (or transition) probability when using repeated cross-section data. The proposed non-parametric approach is empirically tractable, and its identifying assumptions are relatively mild and easy to interpret. Using the proposed population cohort framework, I also re-examine the non-parametric estimator used in the job stability literature. I propose a consistent estimator for its standard errors—one that accounts for the full variability of cross sectional data.

Finally, I use Current Population Survey (CPS) data to show that the existing approaches tend to underestimate the true standard errors. This can lead the researcher to (incorrectly) conclude that job stability has changed.

Section snippets

Existing approach

Following the existing cross sectional literature (e.g. Neumark et al. (1999), Heisz (2005)), one can present the retention rate simply as the fraction of at-risk individuals in the population that remains with the same employer in the next period $R_{t}^{s, c} = \frac{N_{t + 1}^{s + 1, c}}{N_{t}^{s, c}}$ where N_t^s,c is the number of people in the population with time-invariant characteristics c who have been employed for s periods at time t.²

Proposed approach

I start with a population cohort.³ Having a population cohort simply means that there is more than one period of information for each individual in the population. I assume that the repeated cross-sections are drawn from this population cohort, i.e. that each sample (cross-section) be drawn from the same population, but at different

Empirical example

Within a retention rate approach, testing for differences in job stability across time or groups is straightforward—only a single restriction needs to be tested. I focus on time differences; the arguments are similar when testing across groups. The null hypothesis is H₀ : R_j^s,c − R₁^s,c = 0, where R_j^s,c − R₁^s,c is the difference in retention rate over j-1 periods. The t-statistic, t_n, is⁹

References (10)

A. Deaton
Panel data from time series of cross-sections
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R. Moffitt
Identification and estimation of dynamic models with a time series of repeated cross-sections
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M. Baker
Unemployment duration: compositional effects and cyclical variability
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Brochu, P. (2006): “An Exploration in Job Stability”, PhD Thesis, University of British...
Brochu, P. (2010): “The Source of Change of the New Canadian Job Stability Patterns,” Unpublished Manuscript,...

There are more references available in the full text version of this article.

Cited by (1)

The source of the new Canadian job stability patterns
2013, Canadian Journal of Economics

^☆: I would like to thank David Green, Thomas Lemieux, Louis-Philippe Morin and Joris Pinkse for their helpful comments.

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Estimating labour market transitions and continuations using repeated cross sectional data☆