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The framework for the initial analysis of the determinants of unemployment durations is a hazard model of the underlying transitions. As noted above, this means that I studied determinants of the probability that a given unemployment spell will terminate in the next week, conditional on that spell not having yet ended prior to that week. This approach has several statistical advantages over, say, basic regression analysis or the study of average spell lengths alone, particularly in that it permits appropriate correction for spells that are still in progress at the time of study. Within this general framework, I particularly studied a set of models due to Cox (1972), although some alternative specifications that depart from the Cox framework have also been estimated and are reported subsequently.

In this leading approach, usually called the Cox Partial Likelihood Method, the hazard out of unemployment is assumed to factor into two separate components: a baseline hazard b(t, 0) that gives the (conditional) probability of a spell ending at a given time t when all explanatory (or control) variables are set at the value 0; and a set of explanatory (or control) variables that are assumed to act proportionally on this baseline. This latter feature is the reason why these Cox models represent one variety of the class of models known as proportional hazards specifications. The key element in the Cox framework is that, owing to the partial likelihood approach, the baseline may assume any shape and factors out of the likelihood equation; that is, the baseline is not estimated. Thus, the hazard is given by the product of the two components.

h(t,X(t))=b(t,0)e^x(t)B

where X(t) is a vector of explanatory variables and B is the associated vector of coefficients.

I presented the results of this type of Cox proportional hazard model on unemployment durations first (measured since the Record of Employment (ROE) date that is derived from the Canadian Out of Employment Panel (COEP)97 dataset). Specifically, I matched up pairs of cohorts from the COEP96 on a seasonal basis (those with job separation and ROE date in 1995Q3 were matched up with those from 1996Q3, and so on), thereby matching cohorts 1 and 5, cohorts 2 and 6, cohorts 3 and 7, and cohorts 4 and 8 in four separate datasets. The first two of these four datasets provide a quasi-experimental comparison of the UI period before July 1996 with the EI phase-in period in the third and fourth quarters of 1996, while the last two of the four datasets give comparison of UI and EI periods between 1996Q1/Q2 and 1997Q1/Q2 respectively. In addition, with the recent availability of data from the final two cohorts of COEP96, I have also been able to construct datasets that match up cohorts 1 and 9 (both in calendar Q3) and cohorts 2 and 10 (both in calendar Q4). These newer datasets span spells that are two years apart (1995 and 1997, respectively) and can serve as one check on the results from the datasets for cohorts that are only one year apart.

Initially, it is important to allow for the maximum flexibility in the seasonal influence on these durations. This is best performed by permitting the exact match of quarters across calendar years. My earlier work (Jones, 1997) investigating Canadian unemployment insurance data from the 1990s (using the COEP93 and the COEP95) suggested that such seasonal factors were of considerable importance and could easily outweigh program effects if the policy changes involved were comparatively small. However, I also address an alternative empirical strategy below by pooling the datasets, restricting the seasonal effects to be of a particular uniform nature, and thereby gaining the advantages that may accrue to a larger sample size. The sample sizes for the pre-EI period (cohorts 1-4) are now fixed. These samples may be too small for some of the demographic breakdowns one might wish to address (effects on youth, on women, and on different regions, for example). In this regard, there seems to be no alternative but to adopt some sort of parameterized seasonal structure and utilize datasets that pool individuals from different cohorts.

The initial results for unemployment durations are contained in a set of Tables, with three Tables for each pairwise-cohort dataset. Within each paired dataset, the three Tables present the results for the overall sample, for those categorized as having had a separation for reasons of ShortWork/Other, and for those categorized as having had separation reasons of Voluntary Quit/Dismissal. Such heterogeneity in separation reason is potentially very important and is hence investigated by allowing all estimated parameters to vary according to the reason code. The small samples for many of the VQ/Dismissal datasets are noted at the outset. Overall with four year-on-year comparisons, and two two-years- apart comparisons, and with each model having three Tables, these initial results for the hazard models of the determinants of unemployment duration are contained in Tables 1-18.

In each case, four specifications of the explanatory variables were employed. First, I used only a dummy variable that takes the value 1 for an individual in the later cohort, and 0 otherwise. These dummy variables are termed coh05, coh06, ..., coh09 in the respective Tables. Second, I added the local unemployment rate to this dummy variable. Third, I instead added indicators of sex (male=1, 0 otherwise), marital status (married=1, 0 otherwise), age, education (less than [high school], college, university), and four regional indicators (Atlantic, Quebec, Prairies, and British Columbia and the Territories). The omitted (baseline) case thus represents an unmarried female with a high school education living in Ontario. Finally, model 4 in each of these Tables gives the nesting specification that includes all of these demographic variables, the cohort dummy variable, and the measure of local labour market conditions.

6.1 UI and the EI Phase-in Period

I address first the comparison of the UI period and the EI phase-in period by examining Tables 1 and 4 that give the full sample results for the cohorts 1 & 5 and 2 & 6 datasets, respectively. The results in Table 1 display a positive and significant coefficient on the coh05 dummy variable across all four models. This means that the hazard out of unemployment is significantly higher for the cohort 5 (1996Q3) group than for the cohort 1 (1995Q3) group. Since the effect of an explanatory variable X operates on the baseline hazard as exp(X'b), given the above specification, the point estimate from model 1 of 0.185 implies that the baseline hazard is shifted up proportionally by a factor of exp(0.185)=1.20, compared to the case when coh05=0 (i.e., for members of cohort 1). With no other controls, this is the quasi-experimental effect in the context of this Cox specification. Since the hazard is the conditional probability that the spell will end in a given time period, a higher probability of the spell ending implies a small but significant tendency for unemployment durations to fall in the EI phase-in period.

In the other three models reported in Table 1, as the other controls are added sequentially, there is a slight tendency for this estimated cohort coefficient to rise. Model 2 adds the local unemployment rate at the time of the ROE separation, an indicator of overall economic conditions (as well as a factor that affects qualification requirements). Its effect is small, though significant. The coh05 effect is essentially unchanged. Model 3 adds the demographic controls and these tend to raise the cohort effect, with the resulting point estimate of 0.335 implying a proportional hazard shift upwards of 1.40. According to this specification, the two major demographic effects are for the age and the Atlantic provinces variables, both of which tend to lower the estimated hazard and hence raise expected unemployment durations. Nonetheless, only the age variable would be regarded as significantly different from zero at a 5 percent level. The local unemployment rate is added to Model 4. The cohort and age coefficients remain sizeable and significant, although relative to Model 2, the effect from local labour market conditions is less striking (and now no longer significant), given the other regional controls.

Table 4 reports the analogous results for the UI/EI phase-in analysis using the cohorts 2 & 6 dataset, and while there is no a priori reason to favour either set of results over the other, for brevity only the main points and important departures from Table 1 will be discussed. The cohort effect in model 1 (labelled coh06) is now numerically slightly smaller, with the point estimate of .155 implying a hazard shift of 1.17. This effect remains statistically significantly different from zero in the first two models (but not in the final two). The age and Atlantic effects are again clear in models 3 and 4. In addition, there is a pattern of significantly negative coefficients for Quebec. Finally, there is some evidence that being a male raises the hazard out of unemployment, although this effect is only significantly different from zero at a 10 percent confidence level.

Tables 2 and 3 and Tables 5 and 6 report, respectively, the results for these two datasets using the SW/Other and VQ/Dismissal breakdown of the sample by reason code. In each case, however, the SW/Other group comprises the vast majority of the overall sample and the results for this group hence match up closely with those already discussed, while the small VQ/Dismissal samples probably preclude significant results when there are many explanatory variables. Interestingly, though, even when the cohort effect is estimated alone for the VQ/Dis sample (model 1 in Tables 3 and 6), the estimate is small and insignificant. Below, I will investigate whether this effect persists when datasets are pooled in an effort to overcome the very small sample sizes for the VQ/Dis groups.

6.2 UI and Fully-implemented EI

I now turn to the four datasets that compare the final four quarters of experience under UI (1995Q3 to 1996Q2) with the first four quarters of the fully implemented EI system (1997Q1 to 1997Q4). To allow for seasonal comparison, cohorts in the same quarters before and after EI were matched. First, cohorts with initial job separations that are two years apart (cohorts 1 & 9, and cohorts 2 & 10) were matched. Second, cohorts with initial separations that are one year apart (cohorts 3 & 7, and cohorts 4 & 8) were matched. As before, there is no particular reason to favour one set of these results over another — their overall pattern is of much greater importance than any one result or coefficient — so I present the full results in each case. With the breakdown by reason for job separation as before, the relevant results are given in Tables 7-9 (cohorts 1 & 9), Tables 10-12 (cohorts 2 & 10), Tables 13-15 (cohorts 3 & 7), and Tables 16-18 (cohorts 4 & 8).

The basic quasi-experimental effects in Tables 7 and 10 are estimated as 0.192 and 0.174 respectively, both effects being significant at the 5 percent level. This implies that the proportional hazard shifts upward by 1.21 in Table 7 and by 1.19 in Table 10. In both cases, this effect remains positive and significant across the four estimated model specifications, with the coefficient on the later cohort dummy variable (coh09 and coh10, respectively) tending to rise as the other controls are added in Table 7 but not in Table 10. Local unemployment conditions play some role, tending to lower the hazard and hence lengthen unemployment spells. However, these effects are greatly diminished by the presence of other regional variables. As before, age plays a significant role, with a small but significant coefficient in models 3 and 4 in both cases.

The breakdown by reason for job separation given in Tables 8 and 9 and in Tables 11 and 12 once again illustrates the dominance of the SW/Oth group which accounts for the vast majority of the overall sample in both cases. The VQ/Dis results are based on small samples and are largely insignificantly different from zero, with some point estimates (e.g., models 3 and 4 in Table 12) even having the "wrong" sign relative to the pattern of results to date.

When we turn to the set of results for the cohorts with job separations only one year apart, as reported in Tables 13-15 (cohorts 3 & 7) and Tables 16-18 (cohorts 4 & 8), a different pattern in the results emerges. If we begin by examining the basic quasi-experimental effect (model 1 in each case) for the full sample, we see that in both Table 13 and Table 16 the estimated coefficient is negative, is numerically small, and is insignificantly different from zero, even at a 10 percent confidence level. Moreover, this pattern of small and insignificant coefficients holds up across the four estimated models in each Table; the sign changes in the coh07 estimate for models 3 and 4 of Table 13 are unimportant, given their insignificance. In aggregate, this framework implies little or no overall effect in the initial period of full EI implementation, relative to that in the matching quarter of the previous calendar year (that is, in the six months preceding the change). The patterns of the other estimated coefficients are somewhat inconsistent between the two datasets, with some local labour market effects in Table 13 but not in Table 16, and with some other differing demographic effects. As before, the reason code subsample results in Tables 14 and 15 and in Tables 17 and 18 largely confirm the full sample results for the SW/Other group and suggest acute sample size problems for the VQ/Dismissal subsample.

Overall, to give the initial conclusions from these results, the determinants of unemployment duration contained in Tables 1-6 suggest a small effect of the UI/EI move in the phase-in period, raising the hazard and hence lowering expected unemployment durations. However, sample sizes definitely hamper our ability to sort out any differential effects according to the reason for the past job separation. The results fail to confirm the existence of such an effect for the fully implemented EI system. While the estimated effects were in line with those for the phase-in period using the sample of cohorts two years apart (Tables 7-12), these same estimated effects were small and insignificant for the sample of cohorts that are only one calendar year apart (Tables 13-18). If anything, one would prefer the latter estimates. Since the plausibility of the quasi-experimental framework is greater when the two groups being considered are closer, one would prefer to obtain significant results for the latter estimates. In other words, more factors that are not being fully controlled for may change between calendar quarters two years apart than between calendar quarters only one year apart. Thus, the failure of the results from the Cox model for cohorts 3 & 7 and cohorts 4 & 8 is important, and probably outweighs the previous results based on cohorts 1 & 9 and cohorts 2 & 10. Certainly, one would initially conclude that the evidence of clear and consistent behavioural effects of the move from UI to EI is not present.