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·	From Theory To Practice

It has become customary to follow Cox (1972) and to specify a so-called proportional hazard function. Let

The term on the left-hand side, , is the individual exit rate at time t. The first term on the right-hand side, , is the baseline hazard, i.e. the hazard common to all individuals. The second term captures the effect of the explanatory variables whose values may, or may not, change over time, and ß is an appropriately dimensioned vector of parameters to be estimated. The exponential term constrains the hazard rate to be positive. This model is said to be proportional since the exogenous variables simply multiply the baseline hazard.⁹
Intuitively, this model states that the individual hazard rate can be written as the product of a component that is identical for each individual [] and a person specific component (exp(x_i(t)B)). It is assumed that individual circumstances, as captured by x_i(t) (age, benefits during the spell, unemployment rates during the spell, etc.), are responsible for differences in hazard rates for individuals within the same socio-demographic group.

This econometric model allows for right censoring, i.e. the existence of ongoing spells at the end of the sample period. The main difficulty in specifying a statistical model lies in the choice of a particular functional form for the baseline hazard. There are essentially three ways to model . First, one can rely on well-known parametric models (Weibull, log-logistic, etc.). Second, one can approximate non-parametrically to avoid having to choose a particular functional form. Third, one can turn to Cox’s partial likelihood model and avoid having to specify a function for altogether. This remarkable result implies that the B coefficients can be estimated without having to specify any functional form for . In what follows, we will use Cox’s partial likelihood estimator to assess the impact of Bill C-12.

The econometric assessment of the new Employment Insurance (EI) legislation can be conducted on the basis of two different indicators: (1) duration of unemployment spells following job separation; (2) Unemployment Insurance (UI) recipiency durations. Both indicators provide different insights into the adjustments to the legislation. Furthermore, when studying both indicators the analyst must keep in mind that the samples at his disposal are not representative of the same underlying population. Indeed, some unemployed individuals may or may not qualify for benefits, while others may qualify but elect not to claim benefits. Thus, the analysis of unemployment durations is more relevant within the context of a theoretical job-search model. The analysis of the recipiency durations, on the other hand, rests on individuals that both qualify for benefits and have elected to claim benefits. The main interest for studying recipiency durations relates to the budgetary implications of policy changes. Because they rely on fundamentally different samples, both indicators have very little in common and are thus of interest for their own sake.¹⁰ Results for both indicators will be presented in turn. We first start with the duration of unemployment spells.

3.1 Results for Unemployment Spells

A common feature of conducting quasi-experimental evaluations of policy change is to start by specifying the simplest model possible, i.e. by incorporating a single dummy variable that captures the treatment effect (“After Bill C-12” period in our case). To the extent the samples in both the “Before” and “After” periods are homogeneous, and to the extent the economic environment has remained stable over time, the parameter estimate can be interpreted as a pure treatment effect. The empirical strategy consists of gradually introducing explanatory variables into the model to study the robustness of the initial estimate. This is precisely the strategy we follow in this research.

As there are numerous tables in the appendix, it is perhaps worthwhile to explain at this stage how the results are structured. In all, there are eight separate socio-demographic groups that are studied separately. These groups were deemed more likely to be affected by the new EI legislation or to be of particular interest. These groups are: women, men, youths, adults, part-time workers, full-time workers, seasonal workers and non-seasonal workers. In addition, the first set of results concerns the entire sample. There are thus nine different sets of results pertaining to unemployment durations. Each set of results contains three different tables. The first table looks at the impacts of Phase I and Phase II separately. The second and third tables provide estimates of the total impact of Bill C-12. The second table uses data from Q97/04 and Q95/04, while the third uses data from Q97/02 and Q96/02. Finally, the first column of each table presents a “pure” quasi-experimental estimate and additional columns simply introduce additional explanatory variables into the model to investigate the robustness of the “pure” estimate.

It would be unreasonable to discuss each single table in turn. Instead, we will highlight the most salient results in each set and underline regularities that are found across most tables.

• Complete Sample

Tables 3–5 report results for the entire sample. The variable C-12 is a dummy indicator that equals 1 in the period after Bill C-12 and 0 in the period before. As mentioned previously, the effects of Phase I are estimated with cohorts from Q96/04 and Q95/04. The dummy indicator is thus equal to 1 for spells that occurred during Q96/04 and 0 for those that occurred during Q95/04. The significantly positive coefficient of 0.115 on the C-12 variable in the first column of Table 3 means that the hazard rate out of unemployment is higher in Q96/04 than Q95/04. Recall that the explanatory variables operate on the baseline hazard rate through exp(x'B ). The point estimate thus implies that the baseline increased by a proportion of exp(0.115)= 1.1218, i.e. a 12.18 percent increase between quarters. Recall from Table 1 that a simple comparison of mean durations between Q96/04 and Q95/04 yielded a decrease of 0.8 of a month, equivalent to 5.1 percent. The difference between 5.1 percent and 12.18 percent is entirely attributable to the fact that the latter accounts for censored spells whereas the former does not.

The second column adds a series of demographic control variables. Eligibility is a dummy variable whose value is 1 if the individual is entitled to benefits. Entitlement represents the number of weeks of benefits entitlement. Minority is a dummy indicator equal to 1 if the individual is part of a “visible” minority. Unemployment rate refers to the rate in the individual’s region of residence. Next is a series of nine provincial dummy variables. Ontario has been omitted from the list.¹¹ Consequently, the parameter estimates must be interpreted with respect to Ontario. Finally, the table contains a series of six school dummy indicators. The omitted group is “less than high-school”. The parameter estimates must be interpreted accordingly. The inclusion of demographic variables slightly decreases the magnitude of the C-12 coefficient even though few control variables are statistically significant. Being part of a visible minority decreases the hazard rate considerably. Being married also decreases the exit rate, although the parameter is only marginally significant. Interestingly, individuals living in PEI, Saskatchewan or Alberta have higher exit rates than those living in Ontario. None of the parameter estimates on the school dummy variables come out statistically significant.

In the third column four additional dummy variables are added to the model. These variables investigate whether men behave differently than women and whether there are any differences between youths (25 years of age or less) and adults, part-time workers and full-time workers, and seasonal versus non-seasonal workers. As mentioned above, these four categories were chosen because of their expected sensitivity to the new EI legislation or for their intrinsic interest. Note that the introduction of the additional variables brings the parameter estimate of C-12 to its original value in the first column. All new four variables are statistically significant. The results indicate that, all else being equal, men have much higher exit rates than women, youths exit faster than adults, full-time workers have higher exit rates than part-time workers, and finally, seasonal workers have much higher exit rates than non-seasonal workers. According to the parameter estimate, seasonal workers have exit rates that are 62 percent higher than non-seasonal workers (=1-exp(0.483)).

The specification in column 4 investigates whether the exit rates are sensitive to the number of entitlement weeks left in a claim. Exhaust (8,4,2) are time-varying dummy indicators that equal 1 whenever there are between 4-8, 2-4, or less than 2 weeks of entitlement left, respectively. These variables are meant to capture the “exhaustion” effect found in the literature.¹² Although none of the variables are statistically significant, they all bear a negative sign, which is somewhat surprising.¹³

Finally, the fifth column of the table presents the full specification. Most parameter estimates are relatively robust and in particular, the parameter estimate of C-12 is nearly identical to the quasi-experimental estimate in column 1. One notable result concerns the school dummy variables. In the full specification, some are now statistically significant and have the expected sign. In particular, those who have some college or university training have systematically higher exit rates.

The lesson to be drawn from so far is that the provisions of Bill C-12 that were implemented in Phase I seem to have affected the exit rates in the expected direction but the order of magnitude is relatively modest. We now turn to the next five columns of the table, which focus on the provisions implemented under Phase II. The results show little evidence that Phase II has had any impact on the exit rates. The parameter estimate of C-12 ranges between 0.05 and 0.08 and its statistical significance is sensitive to the choice of a particular specification. Note that most explanatory variables are not statistically significant. On the other hand, the parameter estimates associated with PEI, Nova Scotia, and New Brunswick are significant and are quite sensitive to the inclusion of dummy indicators for men, youth, full-time, and seasonal workers. Given the prevalence of seasonal work in these provinces, once this is controlled for, these provinces are not much statistically different from Ontario.¹⁴

The next table provides estimates of the total impact of Bill C-12 based on cohorts 1997/04 and 1995/04. The cohort 1995/04 is sufficiently remote from the implementation of Phase I to assume that no strategic claims occurred during that quarter. Furthermore, cohort 1997/04 is sufficiently far from Phase II to assume that all behavioural adjustments have taken place and that individuals experiencing unemployment spells have fully integrated the new provisions of the EI legislation. Consequently, the comparison of these cohorts should provide the best possible estimate of the total impact of Bill C-12.

The first column in Table 4 shows that the total impact of Bill C-12 was to raise the exit rates considerably. Not surprisingly, this is roughly equal to the sum of the corresponding parameter estimates of Phase I and Phase II. The parameter estimate is highly significant and translates into an overall increase of 18.4 percent (=1-exp (0.169)).¹⁵ The set-up of the next four columns is identical to that of the previous table. Notice that the parameter estimate of C-12 is very robust and hardly varies across specifications. As before, the dummy indicator for PEI is sensitive to the inclusion of the seasonal dummy and the parameter estimate of Saskatchewan is large and significant. Interestingly, once we control for men, youth, full-time and seasonal work, the parameter estimates associated with schooling variables all become statistically significant.

Table 4 shows that Bill C-12 has had some impact on the exit rates. As mentioned previously, given the timing of the COEP surveys it is possible to obtain a second estimate of the impact of Bill C-12. For this second estimate, the “Before” cohort includes spells that occurred during 1996/02 while the “After” cohort includes those that occurred during 1997/02. In theory, the two estimates should be similar.¹⁶ Yet, given the proximity of the “Before” cohort and Phase I it is conceivable that the estimate will be contaminated by unusual behavioural adjustments. Indeed, recall that the tracking of benefits for both the “Clawback” and the “intensity rule” start with Phase I. To the extent that some individuals are likely to experience future unemployment spells (insured or not), they may elect to extend their spell as much as possible before the tracking is implemented. As a result, some of the claims that occurred during 1996/02 may be unusually lengthy, and the quasi-experimental estimate may be biased downward.

Table 5 presents the results based on the 1997/02-1996/02 cohorts. The first five columns of the table are identical to that of the previous table. The last four columns introduce an additional time-varying covariate. The Remain (8,4,2) variable is a time-varying indicator that equals 1 whenever there are between 4-8, 2-4, or 0-2 weeks left before the implementation of C-12, respectively. We will first focus on the first five columns. A striking feature of these columns is that the parameter estimate of Bill C-12 is not statistically different from zero. Hence, using these cohorts it appears that Bill C-12 has had no impact whatsoever on the duration of unemployment spells. These results are also consistent with those reported in Table 1. The remaining parameters are qualitatively similar to those of the previous table. Indeed, the parameter estimate associated with PEI is sensitive to the inclusion of the seasonal variable and individuals living in Saskatchewan (and Alberta) appear to have much shorter spells than any one else in Canada. Note also that the schooling variables have the expected sign and most are statistically significant.

On the whole, the results of Table 5 are relatively similar to those of Table 4, except for the parameter estimate of interest, C-12. We now turn to the last four columns of the table. The various specifications of these columns investigate the robustness of the parameter estimates of C-12 to the inclusion of different sets of explanatory variables. The striking feature of these columns is that the C-12 parameter is now statistically significant and very close to the one obtained using the two previous cohorts. The change in the parameter estimates of Bill C-12 is entirely due to the inclusion of the Remain (8,4,2) covariates. The table indicates that all three parameter estimates are negative, although only Remain-2 is ever statistically significant. In other words, it appears as though the individuals who entered a claim near the implementation of Bill C-12 may have purposely postponed their exit so as to claim as much benefits as possible without incurring future penalties. The remaining parameter estimates of the last four columns are remarkably similar to those of the first five columns and to those of the previous table.¹⁷

The conclusions to be drawn from the results presented so far are twofold. First, it seems that the provisions implemented under Phase I have had more impact than those implemented under Phase II. This should not be surprising since the benefits tracking for both the “Clawback” and the “intensity rule” were implemented under Phase I. Second, it appears that some claimants may have the ability to postpone their exit from unemployment in order to benefit as much as possible from the older UI legislation. These results pertain to the whole population of claimants. As such, the parameter estimates of all socio-demographic groups are constrained to be identical. In what follows, we will present results for each group separately. Doing so will allow us to determine which group has been most affected by the new EI legislation.

• Women and Men

Tables 6–11 present the results pertaining to women and men separately. Each set of three tables is set up in the same manner as the tables pertaining to the whole sample. We will start by discussing the results for women.

The impact of Phase I is presented in the first five columns of Table 6. All five columns indicate that the provisions implemented under Phase I have had no statistical impact on their exit rates. The results for PEI and Saskatchewan are qualitatively similar to those of the whole sample. Very few parameter estimates are statistically significant. As before, being young (Youth) or being a seasonal worker (Seasonal) increases significantly the exit rates. The last five columns provide some evidence that Phase II has had some impact on the exit rates. The parameter estimates are all statistically significant at 5 percent, except for the pure quasi-experimental estimate which turns out not to be significant.

Table 7 provides estimates of the total impact of Bill C-12 for women using cohorts 1997/04 and 1996/04. The C-12 parameter estimates are all statistically significant and very similar to those concerning Phase II. This is not surprising given that Phase I was found not to have any impact. Table 8 provides an alternative estimate of the total impact using cohorts 1997/02 and 1996/02. The first five columns indicate that Bill C-12 has had no impact on the exit rates of women. This result is very similar to the one obtained for the complete sample. The specifications of the last four columns include the Remain (8,4,2) variables. It turns out that their inclusion has a direct impact on the parameter estimates of C-12. Indeed, both Remain-4 and Remain-2 are negative and statistically significant. Hence, it must be concluded that some female claimants managed to postpone their exit from unemployment in the weeks preceding the implementation of C-12. Consequently, a comparison of the two cohorts that does not account for such behavioural adjustment will yield a downward biased estimate of the true impact of Bill C-12. As it turns out, both Tables 7 and 8 yield very similar estimates of the impacts of Bill C-12 on women’s exit rates.

Tables 9–11 concern men. Table 9 shows that Phase I has had a considerable impact on men’s exit rates. The parameter estimates are robust with respect to various specifications. On the other hand, Phase II appears not to have had any impact on their exit rates. Not a single parameter estimate is significant at conventional levels. The total impacts reported in Table 10 are sizeable and approximately correspond to the compounded impacts of Phase I and Phase II reported in the previous table. There is no contradiction in the fact that the total impact is significant while that of Phase II is not. What is more puzzling on the other hand, is that the measure of Bill C-12 obtained from cohorts 1997/02 and 1996/02, as reported in Table 11, is not significant even when accounting for weeks remaining prior to implementation. The parameter estimate of Remain-2 is statistically significant and its inclusion in the model increases the parameter estimate of C-12, but the significance level of the latter remains very weak.

The overall conclusions of these results are that men have been impacted somewhat more than women from the new EI legislation, and that women have reacted more to Phase II while men seem to have reacted more to Phase I.

• Seasonal and Non-Seasonal Workers

Our next set of results concerns seasonal and non-seasonal workers and is presented in Tables 12–17. The first column of Table 12 indicates that Phase I has increased the exit rates of seasonal workers. Once we control for various explanatory variables the impact is reduced somewhat and loses some of its statistical significance (P-value = 0.071). Consequently, it must be concluded that the economic environment of seasonal workers has changed sufficiently between cohorts so as to affect their overall exit rates upwardly. Although the evidence is statistically weak, Phase I still has had a small, albeit not very significant, impact. As an indication that seasonal workers were responsible for PEI having a large parameter estimate, notice that when we focus on the sample of seasonal workers the PEI parameter estimate is small in absolute value and no longer significant.

Phase II also appears to have had little impact on the exit rates of seasonal workers. Indeed, not a single parameter estimate associated with Bill C-12 is statistically significant. Table 13 reports that the overall impact of Bill C-12 has increased the exit rates of seasonal workers by approximately 17 percent (1-exp(0.16)). This is roughly equal to the compound impact of Phases I and II. The result is robust and highly statistically significant. Turning to the alternate estimate in Table 14, we notice once again that the total impact is not statistically different from zero in the first five columns. When controlling for weeks remaining before implementation, the total impact of Bill C-12 is roughly equal to that of Table 12 but is not statistically significant.

The results pertaining to non-seasonal workers are presented in Tables 15–20. The impact of Phase I, as reported in Table 15, is relatively weak and imprecise. The statistical significance of the C-12 parameter estimate is sensitive to the choice of a particular specification. As for seasonal workers, the parameter estimate decreases somewhat once we control for various explanatory variables. Phase II, on the other hand, appears not to have had any impact on the exit rates. The total impact measured by cohorts 1997/04 and 1995/04 is reported in Table 16. The parameter estimate is large, significant and corresponds to the compounded effects of Phases I and II. The alternate estimate reported in Table 17 is equal to zero when no account is made of time remaining before implementation of Phase I. When controlled for, the total impact is significant and closely matches the impact of Phase I. Once again it must be concluded that non-seasonal workers have somehow managed to postpone their exits from unemployment in the weeks prior to Phase I.

• Young and Older Workers

The samples are next broken down according to age groups. The “younger” workers include those that were 25 years of age or less while unemployed and the “older” workers include those that were aged more than 25. The results for these two groups are included in Tables 18–23.

The results in Table 18 clearly indicate that Phase I has had no impact on young workers’ exit rates. Notice also that apart from Men and Seasonal, not a single parameter estimate is statistically significant. In particular, PEI and Saskatchewan are no longer significant. The other panel of the table also indicates that Phase II has had no statistically significant impact on their exit rates. It should thus come as no surprise that the total impact, as measured by cohorts 1997/04 and 1995/04 in Table 19, is also not statistically significant. On the other hand, the total impact measured by cohorts 1997/02 and 1996/02 (Table 20) is marginally statistically significant when we control for weeks remaining prior to Bill C-12.

Older workers, on the other hand, appear to have been more sensitive to the new EI legislation. As reported in Table 21, Phase I has had a significant impact on their exit rates, but not Phase II. The total impact measured by cohorts 1997/04 and 1995/04 in Table 22 is large and statistically significant. When measured with cohorts 1997/02 and 1996/02, the total impact is not significant, even when controlling for weeks remaining before implementation.

• Part-Time and Full-Time Workers

The last set of results concern part-time and full-time workers and is presented in Tables 24–29. An individual is considered a part-time worker if the average weekly number of hours on the last job before separation was less or equal to thirty. The first panel of Table 24 shows that Phase I has had no statistically significant impact on the exit rates of part-time workers. On the other hand, Phase II has had a significant impact that is relatively robust across specifications. The parameters associated with the explanatory variables behave as they did for the other demographic groups. The next table provides estimation of the total impact of Bill C-12 based on quarters 1997/04 and 1995/04. Not surprisingly, the results essentially replicate those of Phase II in the previous table. Finally, Table 26 provides an alternative estimate of the total impact based on quarters 1997/02 and 1996/02. As before, the first five columns do not take into account the possibility of strategic behaviour. It is thus found that Bill C-12 has had no impact on exit rates of part-time workers. Surprisingly, once we do control for strategic behaviour, the parameter estimates still indicate that Bill C-12 has had no impact.

The results pertaining to full-time workers are presented in Tables 27–29. The impacts of Phase I and Phase II are opposite to those of part-time workers. Indeed, Phase I appears to have had a significant impact on their exit rates, whereas Phase II appears not to have had any. The total impact of Bill C-12, as reported in the next table, is naturally approximately equal to that of Phase I, since Phase II was found to have no effect. Finally, the last table reports the total impact of Bill C-12 based on the quarters 1997/02 and 1996/02. The results of the first five columns, in which we do not control for strategic behaviour, indicate that Bill C-12 has had no impact on the exit rates of full-time workers. When we do control for the latter, we find the total impact to be approximately equal to the one obtained from quarters Q97/4 and Q95/04. This is strong evidence of strategic behaviour.

3.2 Results for Recipiency Durations

We have conducted the same analysis as above for recipiency durations. The results are contained in Tables 30–56. It would be rather tedious to discuss all the results in detail. Given that they are qualitatively similar to those concerning unemployment spells, we will instead focus on what follows in broad results.

As a general rule, the impact of the new EI legislation on recipiency durations is smaller in absolute value than its impact on the duration of unemployment spells. Given smaller sample sizes, the results are also usually less precise than previously.

Phase II has had no impact on the exit rates of any of the demographic groups considered, except for seasonal workers. In the latter case, Phase II has significantly increased their exit rates. Interestingly, Phase I has had a noticeable impact on the exit rates of men, adult workers, full-time workers, and seasonal workers, but none on women, young workers, part-time workers, and non-seasonal workers. These results are relatively robust. The total impact of Bill C-12 measured by the Q97/04 and Q96/04 quarters are consistent with these findings. On the other hand, the results based on quarters Q97/02 and Q96/02 perform relatively poorly, even when accounting for strategic behaviour. Indeed, only for seasonal workers do both estimators yield sensibly similar results.

Footnotes

9	In fact, the model is said to be proportional because the hazard for any individual is a fixed proportion of the hazard for any other individual. To see this, take the ratio of the hazard for two individuals i and j:
10	The two groups are very different because of the presence of a large number of job losers who are not eligible for EI, and of a large group of workers who are eligible, but do not claim (see Bertrand, Duclos and Van Audenrode (1999) for example). Looking at recipients allows us to better insulate the effects of the reform conditional on being eligible, but misses potential changes in eligibility and take-up decisions caused by the reform.
11	The samples include no observations from the Territories or Yukon.
12	Meyer (1990) was the first to investigate the impact of exhaustion on the exit rates from unemployment in the U.S.
13	Jones (1998) has found a similar result using Canadian Out of Employment (COEP) data.
14	This is based on regression results not reported here for the sake of brevity.
15	This is slightly larger than the result obtained from a simple comparison of the mean durations reported in Table 1. Again, the difference is entirely attributable to the fact that the latter does not account for censored spells.
16	The impact of Bill C-12 is a parameter estimate and is thus a random variable. Hence, the two estimates cannot be identical. But they should be close to each other in the statistical sense, i.e. we should not reject the null assumption that they are equal.
17	We have also included the variables Remain (8,4,2) when investigating the impact of Phase II alone. Recall that the entrance requirements have changed dramatically starting with Phase II. These changes may have made it easier for some workers to qualify for benefits. Thus, these workers could have delayed their exit in the weeks prior to Phase II knowing they would qualify for benefits. For the sake of brevity, we have not reported these results in the tables. When statistically significant, the parameter estimates indicate that the exit rates increase rather than decrease in the weeks before Phase II. They are thus consistent with the fact that the (insured or uninsured) unemployed workers are adversely affected by the “intensity rule”.