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Short- and long-term unemployment
a b,c ,
*
Pedro Portugal , John T. Addison
a
Research Department, Banco de Portugal, Av. Almirante Reis 71, 1150 Lisboa, Portugal b
Department of Economics, University of South Carolina, Columbia, SC 29208, USA c
Department of Commerce, University of Birmingham, Birmingham B15 2TT, UK
Received 8 March 1999; accepted 15 July 1999
Abstract
This paper estimates a semi-parametric hazard model for unemployment duration that accommodates time-varying covariate effects. For both baseline hazard functions selected, some dramatic changes are detected in the regression coefficients. The results are robust to the incorporation of unobserved heterogeneity. 2000 Elsevier Science S.A. All rights reserved.
Keywords: Unemployment duration; Semi-parametric hazard model; Time-varying coefficients; Unobserved heterogeneity
JEL classification: J64; J65
1. Introduction
Despite the importance of the empirical distinction between short- and long-term unemployment, few micro-econometric studies have attempted explicitly to differentiate between the jobless experience of those who find a job shortly after entering unemployment and that of others who take a very much longer time to locate a job. The search behavior of unemployed workers is conventionally approached through the definition of a hazard function that specifies the influence of covariates on the instantaneous escape rate from unemployment as shifting the baseline hazard function depicting duration dependence. Unobserved individual heterogeneity is incorporated via an error term. In this framework, longer durations are simply the outcome of observed factors, chance, and unobserved unfavorable characteristics (a compositional effect).
The notion that effect of the covariates on the baseline hazard may not be constant — the proportionality assumption — is well developed in the biometrics literature (e.g., Cox and Oaks,
*Corresponding author. Tel.: 11-803-777-4608; fax: 11-803-777-6876.
E-mail address: [email protected] (J.T. Addison)
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1984), wherein a number of tests of proportionality have been offered. In economics, although proportional hazard models do seem to be the natural choice as a first approximation, there are actually no theoretical reasons to assume proportionality (Lancaster, 1990). Indeed, there are several instances where nonproportionality is actually implied. Apart from the fairly transparent example of
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benefit exhaustion (Mortensen, 1977; Moffitt and Nicholson, 1982), other factors pointing to nonproportionality include human capital depreciation, stigmatization, expectations of recall, as well as the provision of various forms of job search assistance.
2. Measurement and data
Our identification of time-varying covariate effects proceeds by estimating a semi-parametric piecewise-constant hazards model that can incorporate discrete changes in the regression coefficients. This type of model is especially useful for the grouped duration displaced worker data used here (see Prentice and Gloeckler, 1978).
In implementing the model, we use just two different specifications for the baseline hazard. The first assumes that there is just one interval, that is, a constant baseline hazard. The second specification uses 33 intervals. While our unemployment data are top coded at 99 weeks, the choice of 33 intervals rather than 99 is dictated by the relative frequency of the observations within each (weekly) cell. The intervals comprise weekly observations up to and including week 22, then seven intervals of 4 weeks each up to and including week 50, followed by three intervals of 12 weeks duration, and a final
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interval encompassing the balance of the observations.
In identifying the structural break in the effects of the covariates, our choice was guided by median jobless duration. Experimentation with alternative breakpoints revealed that 8 weeks was most appropriate. Alternative knot points of 4, 6, 10, 12 and 26 weeks produced similar results — with time-varying effects that eroded the further their location from this breakpoint.
Finally, we accommodated unobserved individual heterogeneity via the inclusion of a multiplicative error term. For this purpose, we used both the standard gamma and inverse Gaussian distributions.
The dataset used is the nationally representative, 5-year January 1988 Displaced Worker Survey (DWS). The data are well described elsewhere (e.g., Farber, 1993, 1997). The unemployment data refer to the single completed spell of unemployment (strictly joblessness) in the wake of the displacement event. This information is supplemented by data from the parent Current Population Survey (CPS) for those workers who never found work after job loss and who were seeking work as of the survey date. There are thus two sources of right censoring that have to be accommodated in the likelihood function: first, as noted earlier, the DWS data are top coded at 99 weeks; second, since the CPS information refers to ongoing spells, the latter are necessarily right-censored.
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McCall (1994) proposes a test of proportionality for grouped data in a specification test that incorporates unobserved individual heterogeneity.
2
Meyer (1990) takes the time-varying effect of benefit exhaustion into account, while Nickell (1979), Fallick (1991), and Narendranathan and Stewart (1993) estimate the changing effects of unemployment insurance benefits on unemployment duration.
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Our regressors include two measures of human capital, namely, the number of years of schooling completed (School ) and low skill endowments (Unskilled ). Reservation wages are proxied by tenure on the lost job (Tenure) and the natural logarithm of earnings on that job (lnOldwage). If reservation wages are not constant, each argument might be expected to have effects that vary over the jobless spell. Similarly, reason for displacement may have time-varying effects insofar as those laid off by reason of plant closing (Close) should initially, if not subsequently, have better re-employment prospects than workers displaced via mass layoffs (the omitted category). This is because they typically receive a larger volume of search assistance, including advance notice. A second category of displaced workers, separated by reason of the abolition of their shift or position (Abolish), should also have initially better re-employment prospects than mass layoffs as they too should harbor no illusions of recall. Although they are important determinants of unemployment duration, we have no such firm priors for the balance of our regressors, namely, race, age, marital status, and state unemployment rates at the time of displacement (respectively, White, Age, Married, and Unrate).
The standard restrictions were applied. Thus, we excluded those employed part time and in
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agriculture at the point of displacement, as well as those aged above 61 years. Our sample is further restricted to males (n52345).
3. Findings
Benchmark equations allowing us to assess the effects on the regression estimates of the two baseline hazard specifications are given in the first two columns of Table 1. From the log-likelihood
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values at the base of the table, we can clearly reject the exponential vis-a-vis the 33-segment piecewise constant hazard specification (PCH-33). Otherwise, the effects of the covariates are quite conventional, and conform with those reported in the literature (e.g., Addison and Portugal, 1987).
The third and fourth columns of the table allow for changes in covariate effects after 8 weeks for the two baseline specifications. Based on a likelihood ratio test we can reject the null hypothesis of unchanged regression coefficients. This result holds irrespective of the baseline hazard specification. Looking at the individual coefficients, one can discern a number of fairly dramatic changes in coefficient magnitudes as between the first 8 weeks of unemployment and thereafter. The clearest examples are School, Age, Tenure, Unskilled, and Close. Interestingly, the pattern of changes in the point estimates is similar across specifications of the baseline hazard. For all these variables, apart from the schooling argument, the results accord with our priors, that is, the effects erode through time. For School, however, the anticipated effect of the variable on hazard rates is observed only in the second interval; prior to that, greater schooling is associated with lower escape rates. This result might suggest that search intensity among more educated workers may be comparatively low in the first few weeks of the jobless spell. In any event, our results suggest that time-varying effects are real and should not be ignored in duration analysis.
To what extent are these results mediated by unobserved individual heterogeneity? To ascertain the potential bias, we experimented with both a standardg representation of the error term and the inverse Gaussian, each of which is nested in the Hougaard (1984, 1986) distribution. Heckman and Singer
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Table 1
a Benchmark equations and discrete change in covariate effects specifications
Variable Baseline hazard function
Constant effects specification Discrete effects specification
Exponential PCH-33 Exponential PCH-33
#8 weeks .8 weeks #8 weeks .8 weeks
School 0.0006 0.0002 20.028 0.032 20.023 0.028
(0.007) (0.009) (0.013) (0.013) (0.014) (0.014)
Age 20.020 20.016 20.022 20.011 20.021 20.011
(0.002) (0.003) (0.004) (0.004) (0.004) (0.004)
Tenure 20.017 20.015 20.027 20.006 20.025 20.008
(0.004) (0.004) (0.006) (0.005) (0.006) (0.006)
1nOldwage 20.022 20.017 0.039 20.071 20.017 20.017
(0.039) (0.049) (0.050) (0.049) (0.068) (0.075)
White 0.460 0.386 0.366 0.441 0.364 0.411
(0.060) (0.075) (0.108) (0.099) (0.112) (0.108)
Married 0.133 0.108 0.157 0.066 0.152 0.062
(0.040) (0.051) (0.068) (0.070) (0.071) (0.076)
Unrate 20.118 20.091 20.105 20.079 20.101 20.076
(0.009) (0.011) (0.015) (0.015) (0.015) (0.016)
Unskilled 20.211 20.175 20.241 20.121 0.241 20.109
(0.040) (0.051) (0.068) (0.068) (0.071) (0.074)
Close 0.114 0.135 0.234 0.008 0.229 0.024
(0.040) (0.050) (0.066) (0.070) (0.069) (0.075)
Abolish 0.095 0.107 0.157 0.036 0.156 0.043
(0.059) (0.073) (0.098) (0.102) (0.102) (0.110)
Log2likelihood 27870.34 27336.67 27727.13 27321.75
a
Asymptotic standard errors in parentheses. The equations also include three metropolitan statistical area dummies and three regional dummies.
(1984) have suggested that regression coefficients are highly sensitive to the precise heterogeneity distribution, while Ridder (1987) contends that misspecification of unobserved heterogeneity is not material if the duration distribution (baseline hazard) is reasonably flexible to begin with.
Summary results of incorporating our two heterogeneity controls are given in Table 2. (Full results for the regression parameters, which mimic those reported in Table 1, are available on request.) If one uses the more flexible specification for the baseline hazard function — namely, PCH-33 — then irrespective of the type of covariate effects, the log-likelihood values are to all intents and purposes unaffected. If, on the other hand, the baseline hazard is not flexible — the exponential — one is indeed likely to obtain an indication of unobserved individual heterogeneity. It seems to make little difference whether one selects the standard gamma or the inverse Gaussian to represent the heterogeneity distribution provided the baseline hazard is flexible.
Table 2
a The effect of incorporating unobserved individual heterogeneity
Hazard function Type of covariate effect
Constant effect Discrete change after 8 weeks
Exponential 27870.34 27727.13
Exponential plusg 27756.59 27718.91
Exponential plus inverse Gaussian 27744.26 27718.43
PCH-33 27336.67 27321.75
b
PCH-33 plusg 7335.95 –
b PCH-33 plus inverse Gaussian 7335.95 –
a
The cells contain log-likelihood values for the benchmark and unobserved individual heterogeneity augmented specifications.
b
The unobserved individual heterogeneity parameter converged to a boundary solution.
heterogeneity controls. In sum, our results better accord with Ridder’s simulations than with Heckman and Singer’s experimentation using actual unemployment data.
4. Conclusions
The evidence on time-varying coefficients reported here points, first, to dramatic changes in the magnitudes of the point estimates — and, in one case, a sign reversal. This evidence contrasts sharply
with the duration literature, which typically assumes proportionality. Vulgo: the proportionality assumption should in future be routinely tested in duration analyses. Second, our results are not an artifact of inability to use a flexible representation of the baseline hazard or to control for unobserved individual heterogeneity, that is, they appear to be robust to definition of the baseline hazard and to unobserved heterogeneity. Third, once one deploys a flexible specification for the duration dis-tribution, the use of a mixing distribution to account for unobserved heterogeneity does not appear to affect either the regression coefficients or the shape of the baseline hazard function.
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