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Difference-in-Difference Estimation

The most straightforward means of analyzing the 1987 increase in the flat rate portion of CPP disability benefits is through the "difference-in-difference" framework (Card, 1992; Gruber, 1994). This framework involves a simple comparison of the change in behavior outside of Quebec, where benefits increased, with the change in behavior inside Quebec, where benefits did not increase.¹⁷ This comparison can be implemented in a straightforward manner by estimating logistic regressions of the form:¹⁸

where NP_i is a dummy variable specification for non-participation in the labour force by person i

CPP is an indicator for whether the individual lives in CPP province

AFTER is an indicator for whether the year is after the policy change

X_i is a set of covariates for person i (age, married, education, number of children)

With this regression framework, location is controlled for by including a dummy for whether an individual lives in a CPP province or in Quebec. Time is controlled for by including a dummy for whether each observation is before or after the policy change. The coefficient of interest (B₃) therefore measures the effect of being covered by the CPP, relative to being covered by the QPP, after the benefits increase, relative to before.

The dependent variable is a dummy for whether the 45 to 59 year old man was not working during the week of the SCF survey. Thus, the coefficient B₃ measures the effect of the policy change on labour force non-participation, defined as non-work. The regression equation also includes variables for education, age, marital status, and number of children to control for any observable differences between workers that might confound the analysis. Education is measured by four dummy variables for less than 9 years of education, 9 to 10 years of education, 11 to 13 years of education, and some post-secondary education. Age is measured by a set of dummies for single years of age from 45 to 59. There are separate dummies for each number of co-residing children under age 18 (up to a maximum of 8 children).

This approach is attractive because it can cleanly identify the effects of the benefit change. However, it does have two limitations. First, it does not directly measure the elasticity of response to the change in DI benefits, since it measures only the numerator of the elasticity (the change in labour supply) and not the denominator (the change in potential benefits). Second, this approach uses a very rough categorization of the data that does not fully take advantage of the policy change - particularly the further variation available in potential benefits within provinces at a point in time. Since only the flat rate portion was increased by the CPP, the percentage point increase in the replacement rate is much larger for those with a low lifetime level of earnings, as the flat-rate portion is a larger share of their DI benefits. This fact can be used to further identify the effect of the benefit change, by exploiting the differential impact of the benefits change across workers of different lifetime earnings levels.

Parameterized Models

To address both of these points, one must measure the change in potential benefits for each person in the SCF sample. In theory, calculating potential DI benefits requires longitudinal information on workers' earnings since 1966, which is not available in the SCF (an annual snapshot of earnings). Thus, "synthetic earnings histories" are calculated for groups of workers in order to impute their potential DI benefits. This is done in several steps. The first step is to create a database using each of the individual SCF's for April 1982-1989, and using data on the male heads of families from the family SCF for April 1976, 1978, and 1980. In each of these data sets, workers are then divided into cohort cells according to their age, location (four regions: Quebec, Ontario, the Atlantic Provinces, and the remainder of Canada), and their educational attainment (the four groups described above). Next, the median earnings are tabulated in each cohort cell for each year.¹⁹By stringing together the median earnings in each cohort cell through time, one can form a proxy for the earnings history of a worker in that cohort cell.

These surveys contain annual earnings data for the years 1981-1988, with the exception of 1983 when no survey was carried out, and biannual data from 1975-1979. For the missing years, earnings are imputed as an average of the surrounding years. To backcast from 1975 to 1966, before cross-sectional survey data is available, cross-sectional age-earnings profiles are estimated by education group in the 1975 survey. Next, these estimates are applied to "un-age" the workers in the 1975 survey back to 1966. Finally, these pre-1975 profiles are deflated by average wage growth by region, using data from Gruber and Hanratty (1995).

With these synthetic earnings histories in hand, it is then straightforward to compute potential DI benefits using the legislative rules in place in CPP and QPP in a given year. The key regressor, the replacement rate, is this potential benefit over the synthetic earnings for the cell in the year before the survey. This measure does not vary individual-by-individual, but rather only cell-by-cell, where the cells are defined by each education/region/year group.²⁰

The regression models are estimated in the form of:

where RR is potential replacement rate

ED is a set of dummies for education categories (four categories)

s_j is set of region dummies (four regions)

t_t is set of year dummies

This model controls for fixed effects for year, for each of the 16 education*region cells in each year, and for education*year. The first of these is included to capture secular trends in labour market opportunities in Canada, as in equation (1). The second of these is included to account for the fact that there is a potential spurious correlation between the labour supply choices of these 16 groups and their potential replacement rate. This is just a restatement of the criticism leveled by Bound (1989) against the U.S. literature. By taking out fixed effects for each group, only changes in each group's potential replacement rate over time are used to identify the effect of DI. Finally, the set of education*time interactions are included because there is a potential concern about identification from changes in the return to education over this period, which would affect both the replacement rate and the decision to work.

Conditional on this set of controls, the model is identified by two sources of variation: changes over time in the CPP provinces relative to Quebec (region*time), and how those changes evolve differentially across these 16 groups (region*education*time). The first of these is the difference-in-difference variation that was used to identify model (1). The second is additional variation from the differential impact of this policy change across groups. This additional variation is potentially useful in pinning down the elasticity of labour supply. Moreover, the resulting coefficient B₁ is now directly interpretable as the benefit semi-elasticity of labour supply.

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Footnotes

17	Note that the analysis assumes that there is not migration across the Quebec border in response to DI benefits differences. Under CPP or QPP rules, if a worker moves from a CPP region to Quebec and immediately files for benefits, he receives the benefits he was entitled to under the CPP (similarly QPP benefit rules apply for moves from inside to outside Quebec). If, however, this worker moved and then worked in Quebec before applying, he would be eligible under the QPP rules. Therefore, workers would have to anticipate a future application need for there to be a migration incentive.
18	A logistic function is used. The results are similar when either probit models or linear probability models are used.
19	That is, for 45 to 59 year old cohort in 1989, the 44 to 58 year old cohort in 1988, 43 to 57 year old cohort in 1987, and so on back through time is used. when the mean was used to compute benefits, the results were quite similar.
20	The worker's potential child benefits are not included in the computation of the replacement rates, for two reasons. First, this preserves the variation in potential benefits only at the cell level, which is important for the identification strategy used in the analysis. Second, it is not clear how ot combine child benefits, which for these older workers will only be paid for the presumably small number of years until the child turns age 17, with the other benefit components, which will be paid until age 65 (at which point all disabled are shifted to the retirement income system). In practice, this is not a very important consideration, as only 1/3 of my sample has any children. adding child benefits to the computed benefit total, based on the actual number of children, raises the level of the replacement rate somewhat, but not the relative change; and the estimated elasticities reported below are similar whether or not child benefits are accounted for in calculating replacement rates.