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Means

Table 1 presents the means of the data set, divided into the CPP regions and the QPP region, before the law change and afterwards. The final column of the table shows a first pass difference-in-difference estimate of the policy effect. There are two findings of interest from Table 1. First, as the first two rows show, the policy change was associated with a significant increase in benefits. While the replacement rate was roughly constant in Quebec, it rose substantially in the rest of Canada. The relative rise in CPP disability benefits was 8.8 percentage points, or 36 percent of the baseline average replacement rate.

Second, there is strong evidence of a labour supply response to the benefits increase. Non-participation raises from before to after in the CPP regions, and falls in the QPP regions. The latter finding reflects the underlying improvements in the Canadian economy over this period. As a result, there is a large relative rise in non-participation in the CPP regions of 2.7 percentage points.

Difference-In-Difference Regression Results

The next table formalizes the inferences from the table of means in a regression model, including as well the set of covariates in (1). Recall that the regression also includes a full set of dummies for age and number of children which are not reported in the table. The regression is estimated as a logistic model. The last row shows the effect of the difference-in-difference interaction on the probability of being non-employed, which is the average effect across the sample on the predicted probability of non-participation.

These findings confirm the conclusion from Table 1 that there is a response to the policy change. The effect is slightly smaller than in Table 1, with a relative rise in non-employment in the CPP regions of 2.3 percent and it is statistically significant. This is still a quite sizeable response, indicating that the 36 percent benefits rise led to a rise in non-employment of 11.5 percent, for an implied elasticity of labour force non-participation of 0.32. Thus, this straightforward difference-in-difference estimate is very supportive of a strong labour supply response to the benefits increase. The control variables in the regression have their expected effects, with married and more educated workers less likely to be non-participants. The age dummies (not shown) have the expected upwards trend, while there is no clear pattern from the dummies for number of children (also not shown).

Parameterized Model

As noted above, these difference-in-difference estimates do not fully exploit the available variation in potential benefits across workers in Canada. To do so, Table 3 presents estimates of the replacement rate model (2). For each model, Table 3 shows the coefficient of interest, the implied effect of the 8.8 percentage point replacement rate rise, and the implied elasticity of labour force non-participation.

The first row presents the basic model. There is a sizeable and significant effect of the potential replacement rate. The estimate implies that this policy change raised the non-employment rate by 1.2 percentage points, which is substantially below the difference-in-difference estimate, but is more precisely estimated. The implied elasticity of labour force non-participation with respect to benefits is 0.17.

One potential concern about the identification of this model, however, is that the variation in benefits does not arise solely from the policy change, as it impacts the 16 different education*region groups, but rather also from year to year changes in replacement rates within the before and after periods. Some of this year to year variation is legislative, arising from evolving system parameters over time (i.e., changes in the flat rate). But some of it also arises from year to year differences in earnings across education*region cells, which induce changes in the potential replacement rate, but which might also be independently correlated with the labour supply decisions of individuals in those cells. Moreover, this year to year variation may reduce the signal to noise ratio in my key regressor, since the true variation of interest comes from the policy change only.

In order to purge the model of these year to year changes and focus solely on the before/after comparison, the next row of Table 3 presents instrumental variables estimates of the model. The instruments are a set of interactions of education* region*AFTER, where as in equation (1) AFTER is an indicator for being after the policy change. When instrumented in this way, the only variation in benefits that is used by the regression model is the before/after difference in benefits, on average and as it impacts differentially these 16 education*region groups. That is, this IV strategy provides the means of extending the difference-in-difference estimation to account for variations in the impact of the policy by education and region.²¹ The first stage fit is excellent and the F statistic is 5500.

In fact, this instrumental variables approach raises the estimates substantially, consistent with the notion that noise in the year to year replacement rate changes was biasing the estimate downwards. At this new point estimate, the implied effect on labour force non-participation from the policy change, 1.8 percentage points, is close to the difference-in-difference estimate. The implied elasticity of labour force non-participation with respect to CPP disability benefits rises to 0.25. This is higher than the post-Parsons literature in the U.S., but is only half of the lower bound of Parsons' estimates.²²

Addressing Alternative Hypotheses

The fundamental identification assumption embodied in the estimation thus far is that there was no other change in the CPP provinces, relative to Quebec, that was correlated with the labour supply decisions of older workers. This section considers the two natural alternatives to this identifying assumption. The first is that the policy was itself responding to a trend in relative labour supply across the provinces. That is, perhaps there was an underlying trend towards lower labour force participation among men in the CPP provinces, relative to Quebec, and the policy was passed in response to this trend.

It is possible to test for this underlying trend by pursuing a falsification exercise: reestimating the model on data around a year when there was no significant change in DI policy. For this purpose a new sample was constructed of men age 45 to 59, with data from April 1982 and 1983 as the "before" period, and April 1985 and April 1986 as "after". There was no significant change in DI policy around 1984. Thus, if I estimate the difference-in-difference model on this data set, and there is a significant positive effect on non-participation, then it suggests that there was a pre-existing trend. If there is no effect, however, it demonstrates that labour supply was moving in parallel in Quebec and the rest of Canada in this pre-policy change period, and that the break in the series arose only when the benefits were increased under the CPP.

The result of this falsification exercise are presented in the first row of Table 4. In fact, there is a small and insignificant positive coefficient. As the second column shows, this coefficient indicates that non-participation rose by 0.3 percentage points in the CPP (relative to the QPP) before the policy change, as opposed to the roughly 2 percentage point increase around the time of the policy change. That is, there was no relative trend before the policy change; the differential between the CPP and QPP grew only after 1987. This timing evidence supports the contention that the policy change caused the relative growth in labour force non-participation, and not the other way around.

Moreover, this finding provides a means of confirming that the contemporaneous change in the early retirement age under the CPP is not driving the main results presented in this report. The effect of this change in retirement age on 45 to 59 year olds is testable because there is a "reverse experiment" arising from the fact that Quebec first lowered its retirement age from 65 to 60 in 1984, without changing QPP disability benefits. As a result, if the early retirement age change is driving the behavior that we see for 45-59 year olds, there should be a similar change in behavior for this group in Quebec, relative to the rest of Canada, around 1984. But this is exactly the hypothesis that is tested, and rejected, by the falsification exercise. There is no relative change in labour supply across these regions around 1984. This rules out the early retirement age change as an explanation for the main findings presented in this report.

The second alternative is that there was some other contemporaneous change in the relative labour market prospects of older workers in Quebec and the rest of Canada, perhaps due to a relatively faster recovery from the recession of the early 1980s in Quebec. It is possible to assess the importance of contemporary economic conditions in driving the results by making use of a within-region control group: workers aged 25 to 39. This younger age group should be subject to the same economic shocks that affected older workers, but is unlikely to be affected in an important way by changes in DI policy, since the incidence of DI is so much lower for young workers.²³ Thus, by rerunning the basic models for this group, it is possible to assess whether there are omitted variables driving the findings.

In fact, as the next two rows of Table 4 show, there is little correlated change in behavior among younger workers. The difference-in-difference coefficient is positive, but it is fairly small relatively to the magnitude for older workers. In the next row, the (instrumental variables) parameterized model is re-estimated for this population, assigning to younger workers the benefits for 45 to 59 year olds in that region/education/year cell. In fact, applying this method to younger workers yields a negative and insignificant coefficient.

Thus, the two specification checks indicate that there was a relative change in labour supply of older workers in the CPP provinces, relative to Quebec, that arose only after benefits increased, and that was present only for the older workers to which the program primarily applies (and not for younger workers). That is, the only potential factors which could be confounding the main findings of this report are sudden changes in the relative economic opportunities or tastes for work of older workers (relative to younger workers), in the CPP provinces (relative to Quebec), around January, 1987.

In fact, there is one further test that can even rule out alternatives in this category. A CPP*AFTER interaction can be explicitly included in the parameterized model, and then used to estimate a "difference-in-difference-in-difference" model (Gruber, 1994) which is identified solely from differences in the effects of this policy change across these 16 groups of workers. That is, this model controls for any changes on average in the economic circumstances or tastes for work of older workers in the CPP regions relative to Quebec, ruling out most plausible alternative explanations for the results. After controlling for average relative changes in labour supply across Quebec and the rest of Canada, this model asks whether the groups that saw the largest replacement rate increase were the groups that increased their labour force non-participation the most.

The results of this estimation are presented in the final row of Table 4, for the IV model (instrumented once again by region*education*AFTER). In fact, the estimated effect here is somewhat larger than in Table 3, indicating an elasticity of 0.32, and the coefficient is marginally significant. Taken together with the findings for younger workers, this result suggests that other general changes in the CPP provinces relative to Quebec are not driving the main estimates. Overall, the findings in Tables 2 to 4 suggest a fairly elastic labour supply response of older workers to changes in DI benefits, with the elasticity of labour force non-participation with respect to these benefits being in the range of 0.25 to 0.32.

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Footnotes

21	In terms of the discussion above, in this model the identification comes solely from region *AFTER and region *education *AFTER.
22	Note also that these estimates are consistent with aggregate relative movement in the DI rolls over this period. From 1984 to 1989, the number of persons on the CPP program, relative to the QPP program, rose by 56,576. Unfortunately, only aggregate enrollment data over time for both provinces was available, so it was not possible to distinguish the share of this increase due to 45 to 59 year old men. But assume that this group represented the share of the increase that they represent of the 1993 CPP rolls (30 percent); the rise for this group was then 16,973 workers. 1.8 percent of the 45-59 year old male population in the CPP provinces, times a 68 percent average acceptance rate, is 16,340 workers, which is quite close to this administrative figure.
23	The incidence of DI among make workers age 25 to 39 in is less than 0.2 percent.