HRDC - Unemployment and Benefit Durations

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5. Further Results: Joint Models of Unemployment and UI Receipt

Although the major results in the preceding two Sections appear quite robust, they are not immune to objection. One potential difficulty with the analysis of unemployment spells reported in Section 3 is that, although there was some investigation of the role played by UI eligibility and by the length of a person's entitlement to UI, these factors were constrained to affect the hazard proportionally. This was true of both the Cox partial likelihood models and the two parametric specifications. However, it may be more natural to envisage such effects as being particularly pronounced in the months and weeks leading up to exhaustion of UI entitlement, so that their effect might rather be to shift the hazard in these periods, or to tilt the overall hazard, relative to the earlier models.¹⁴ Moreover, job finding behaviour might be expected to alter significantly once the unemployment spell is not longer covered by UI (as in Meyer 1990). Relatedly, the analysis that addresses only benefit durations, as in Section 4 above, necessarily fails to capture uncovered spells of unemployment, either because of initial lack of eligibility or because of UI exhaustion. The labour market effects of a change such as C-17 likely extend beyond the durations of UI receipt and, as such, analysis must extend to such overall unemployment and jobless durations.

The purpose of this section is to report the results from two broad sets of models. First, I investigate alternative ways of estimating the determinants of duration with allowance for various time-varying UI effects. Second, as a further check on the earlier results, I also report results from an alternative class of models where the hazard is non-parametrically estimated jointly with the behavioural parameters in a framework due to Prentice and Gloeckler (1978) and extended by Meyer (1990), here termed the PGM model.

Joint models of unemployment and UI receipt

Results from two models that incorporate time-varying UI effects are presented. In the simpler of the two, the base model from Section 3 is augmented by an uninsured dummy variable that takes the value 1 in a period when UI is not received and 0 otherwise. In the alternative specification, three benefit exhaustion effects are studied, using (time-varying) dummy variables that take the value 1 at 1-3, 4-6 and 7-9 weeks until expiry of UI coverage, respectively, and 0 otherwise, to assess the extent to which jobs are found in the weeks prior to the ending of entitlement.

Tables 25-30 give the various results of the insured/uninsured unemployment models, all estimated in the Cox partial likelihood framework, for the full sample and for the VQ/Dis and SW/Oth subsamples, analogous to the ordering in Tables 1-6 of Section 3. The full sample results in Table 25 do not depart greatly from the estimates in the absence of the time-varying coefficient, and the coep effect remains significantly positive and around 0.22 in the models with a full set of controls. The effect on the uninsured dummy variable itself is insignificantly different from zero, although the point estimate is everywhere negative. In Table 26, Model 1 is the only exception in that a significant coep effect is not found for persons not expecting recall. Again, no significant effect of uninsured unemployment on the hazard emerges in those results.

The breakdown by separation reason is given in Tables 27-30. For the VQ/D is group, which represents a fairly small sample overall, the uninsured effect is almost always negative, but the standard error is as large as the point estimate. In contrast, for the SW/Oth group, the Table 29 results give small and positive coefficients on the uninsured variable. However, in view of the insignificance of the estimates, I would not want to make too much of this distinction. With regard to the coep variable, the base models in Tables 27 and 29 yield significant and positive effects which are numerically larger for the VQ/D is group than for the SW/Oth sample. In Table 30, the one point of note is that, for the subsample not expecting recall to the former job, the coep effect is significantly negative at -0.226. This is the only such result in the whole set, however, and I do not attach great importance to this exception. Rather, the results from estimating the determinants of unemployment spells with allowance for an uninsured phase of the unemployment spell clearly echo the earlier findings that the effect of C-17 was significantly to shorten durations. Finally, it is worth noting that the only robust demographic determinant in these results is sex, with men having a significantly higher hazard and hence shorter duration. Although these are some other significant coefficients dotted around Tables 25-30, the overall pattern of the results does not support any other strong conclusions.

A more disaggregated breakdown of time-varying UI effects is reported in Tables 31-34 for the full sample and the SW/Oth group. ¹⁵ For the full sample, there is only a small effect of adding the three benefit exhaustion dummy variables on the estimated coep effect. In Table 31 Model 4, for instance, the point estimate is 0.208, compared with the 0.206 figure obtained in the same model in Table 1. Similarly, the Table 33 results for the SW/Oth group give estimated coep effects of between 0.25 and 0.35. The benefit expiry variables themselves are rather puzzling, with insignificantly positive effects at 7-9 and 4-6 weeks from expiration being replaced by a negative coefficient at 1-3 weeks in Models 2-4 of Table 31. This pattern also occurs, though less pronouncedly, in the Table 32 specifications, and for the SW/Oth subsample in Tables 33 and 34. Since this sign is contrary to what might be expected, and to some related findings in the literature (e.g., Meyer's 1990 analysis of exhaustion effects), these models clearly merit furtherinvestigation.¹⁶ Nonetheless, the clearly positive and significant effect of the coep variable endures throughout these four tables.

PGM models of unemployment durations

The final check on the results reported here is to estimate a variety of alternative models using alternative duration specifications in a PGM framework Prentice and Gloeckler (1978) and Meyer (1990). These models are estimated for the full sample and the VQ/Dis and the SW/Oth groups and incorporate three alternative approaches to duration. First, akin to the Weibull-type models,¹⁷ we introduce log duration in addition to the coep variable. Second, we use a fourth-order polynomial in duration as a flexible means of capturing non-monotonicity. Third, we estimate a fully non-parametric model where each duration in the grid (out to 55 weeks) has its own dummy variable, thereby permitting any pattern to the estimated duration effects.

The results are given in Tables 35-37. For the full sample, the effects are quite consistent across the three duration specifications, with significant log duration effects, significant duration polynomial effects, and a (jointly) significant set of duration dummies. In each case, we estimate a coep effect that is positive and significant, around 0.35 in the absence of other controls, and around 0.26 when those other explanatory variables are added. Moreover, the estimated effects of other variables are quite consistent across models 2, 4 and 6 of Table 35, something that also holds up by and large for Tables 36 and 37. The estimated coep effects are larger for the VQ/Dis group (Table 36) than for the SW/Oth sample, but in all cases the effect is positive and significant. Overall, these results from the PGM method of estimation reinforce our earlier findings and suggest that the conclusions on the effects of C-17 were quite robust.

Note: Standard errors in parentheses with p<0.05 = *, p<0.01 = **. Based on weighted sample from COEP93 and COEP95. Unins is a time-varying covariate that takes the value 1 in the phase of the unemployment spell when UI coverage has been exhausted, and 0 otherwise. Model 1 is for sample reporting that they do not expect return to the reference job; model 2 is for the sample reporting that they expect return to the reference job; and model 3 studies the effects of weeks of UI eligibility for the full sample.

Note: Standard errors in parentheses with p<0.05 = *, p<0.01 = **. — means that a variable was dropped owing to collinearity. Based on weighted sample from COEP93 and COEP95. Unins is a timevarying covariate that takes the value 1 in the phase of the unemployment spell when UI coverage has been exhausted, and 0 otherwise. Model 1 is for sample reporting that they do not expect return to the reference job; model 2 is for the sample reporting that they expect return to the reference job; and model 3 studies the effects of weeks of UI eligibility for the full sample.

Note: Standard errors in parentheses with p<0.05 = *, p<0.01 = **. Based on weighted sample from COEP93 and COEP95. Ben13, Ben46 and Ben 79 are time-varying covariates that respectively take the value 1 in the phase of the unemployment spell when UI benefit exhaustion is 1-3, 4-6 and 7-9 weeks away, and 0 otherwise. Model 1 is for sample reporting that they do not expect return to the reference job; model 2 is for the sample reporting that they expect return to the reference job; and model 3 studies the effects of weeks of UI eligibility for the full sample.

Note: Standard errors in parentheses with p<0.05 = *, p<0.01 = **. Based on weighted sample from COEP93 and COEP95. Prentice-Gloecker-Meyer discrete time proportional hazards estimates are presented with three duration specifications: Models 1 and 2 employ log duration; Models 3 and 4 employ a 4th order polynomial in duration; and Models 5 and 6 employ a full flexible set of dummy variables for each recorded duration (measured in weeks).

Footnotes

¹⁴	Compare the related analysis of hazards that alter with the expiration of a period of advance notice, as in Jones and Kuhn 1995.
¹⁵	Estimates of these particular models for the VQ/Dis sample ran into problems of sample size and collinearity and are not reported here. In each case, however, when the data were suitable aggregated (e.g., using a variable such as Atlantic region, instead of provincial dummy variables), the VQ/Dis results on the coep effect were comparable to those reported in the paper.
¹⁶	One point to bear in mind is that relatively few spells reach the point of benefit exhaustion, as Figures 1-3 reveal. In this respect, these data are similar to those analyzed by Meyer (1990). See also Corak and Jones (1995) for related analysis in the Canadian case.
¹⁷	Weibull models as analyzed above can equally be thought of using a log relative hazard parameterization whereby, scaled by q using our earlier notation, so that the earlier coefficient ß=-qâ, we have ln(t) =ßX + e, and e has an extreme value distribution. Thus, ß*X estimates the logarithm of the duration.

Last Modified: 1998-11-25	Important Notices