New estimates of labour supply elasticities for married women in Canada 1996–2005

Abstract

In this article, we estimate income and substitution labour supply and participation elasticities for Canadian married women using data from the Survey of Labour and Income Dynamics 1996–2005. We use the Canadian Tax and Credit Simulator (CTaCS) and detailed information on the structure of income at the household level to compute the marginal tax rates faced by each individual. We then use these marginal tax rates to compute net own-wage, spouse-wage, and nonlabour income. We show how the magnitude of the estimated elasticities varies depending on whether net or gross wages and income are used in the estimation procedure, and quantify biases caused by using average tax rates instead of marginal tax rates. Finally, because marginal tax rates vary significantly over the sample, we use quantile regressions to compare elasticities at different points of the hours distribution. Overall, our results show that public policies now have, on average, less scope for influencing hours of work than 10 years ago. However, the quantile results show that wives working fewer hours per week are more sensitive to changes in their own or spouses’ wages.

Keywords:

• labour supply
• elasticities
• labour force participation
• taxes
• Canada

JEL Classification:

• C25
• H31
• J22

View correction statement:

Erratum

Notes

1. Another branch of the literature focuses on the impact of cost to work on the labour force participation decision, for example, the cost of child daycare (Cleveland et al., 1996; Powell, 1997; Michalopoulos and Robins, 2000; White, 2001; Powell, 2002; Lefebvre and Merrigan, 2008). Chaykowski and Powell (1999) summarize this literature and conclude that diminishing the cost of daycare by 1% will increase labour force participation by 0.38%.

2. A finding confirmed and expanded upon by Nakamura and Nakamura (1981, 1983, 1985).

3. The hours wage elasticity dropped by 60% (0.36 to 0.14), the hours income elasticity by 70% (–0.053 to –0.015), the participation wage elasticity by 95% (0.66 to 0.03) and the participation income elasticity by 60% (–0.13 to –0.05). One suggested explanation is that preferences towards work have changed across birth cohorts.

4. Over the period 1980 to 2000, married women’s own-wage elasticity decreased by 50–56% and their cross-wage elasticity fell by 38–47%.

5. Larger elasticities are obtained for countries where women labour force participation is lower. Estimated decreases in estimated labour supply elasticities over time for a subset of countries seem to coincide with increases in participation.

6. The only available information in the census data are the individual’s contributions to the Canada/Quebec Pension Plans and to Employment Insurance and the type of income (employment income, investment income, self-employed income) received by the individuals.

7. Nakamura and Nakamura (1981) summarize by saying that differences in the respective values of the estimated coefficients of the wage and income variables may simply reflect inter-country differences in the relationship of gross to disposable income.

8. If one was interested only in estimating labour supply elasticities (and not on how they vary over time), there are a number of natural experiments from which to infer the causal impact of wages and income on hours of work that could be used over the period 1996 to 2006. In particular, at the federal level, the government increased the number of tax brackets from three to four in 2001. There have also been a number of reforms at the provincial level. For example, see Sand (2005) for an examination of the 2001 reforms in British Columbia and Alberta.

9. The LFS is akin to the Current Population Survey (CPS) in the US and the SLID is akin to the Panel Study of Income Dynamics (PSID). See Heim (2007) and Blau and Kahn (2007) for recent studies using the CPS to estimate labour supply elasticities.

10. Tax information is missing for about 7% of our sample. These observations are dropped from our analysis.

11. Usual wage or salary before taxes and other deductions. This includes tips, commissions and bonuses but explicitly excludes paid overtime.

12. The number of hours of work is larger than those reported in Morissette and Hou (2008). For 2000, we observe an average of 1584 hours, whereas Morissette and Hou (2008) obtain 1366. Their measure of hours of work is the product of weeks worked and usual weekly hours in May or June. This implies a difficult imputation problem for wives who reported working full-time during the year but not usual hours for these two months. Our measure of nonwage income is also higher, possibly due to individuals underreporting income in census data. Morissette and Hou (2008) do not report average wages.

13. In the US, net money amounts are usually computed with the National Bureau of Economic Research (NBER) TAXSIM model (e.g. see Meyer, 2002; Saez and Veall, 2005; or Heim, 2007) or directly from tax table data (see Devereux, 2004). This last study is one example in which a robustness check is done comparing pre-tax and post-tax results, and they are found not to differ significantly. However, relying on tax tables makes it difficult to take into account itemized deductions so that the computed marginal tax rate faced by the individual is just an estimate of the true marginal tax rate faced.

14. We provide the simulator with very detailed information on the income of the individual from his/her tax form, including (1) union dues, (2) daycare expenses, (3) medical expenses, (4) other deductions, (5) other provincial credits, (6) Registered Pension Plan (RPP) contributions, (7) employment or wage earnings, (8) self-employment income, (9) Registered Retirement Savings Plan (RRSP) income, (10) pension income, (11) Old Age Security (OAS) income, (12) Canada Pension Plan/Quebec Pension Plan (CPP/QPP) income, (14) employment insurance benefits, (15) capital gains income, (16) interest income, (17) social assistance, (18) workers compensation income, (19) other income and (20) amount for spousal equivalent/eligible dependant. These computations also take into account the age, gender, province of residence and year.

15. Standard errors of the estimated elasticities are bootstrapped to account for the sampling process and the multistage nature of the estimation method.

16. Some authors (e.g. Morissette and Hou 2008) use a quantile wage of the employed women. We tried out many different imputation methods from quantile wages over regression imputation to multiple imputation by chained equations. While it made a noticeable difference going from quantile wages to regression imputation, the more advanced method did not change our results significantly. For this reason, we chose to use regression imputation.

17. We note that a constant semi-elasticity implies an elasticity that will be mechanically decreasing in hours.

18. Note that we only include in our sample wives of working husbands. In the case of Canada, there are very few nonworking husbands. If we add these few couples back in the sample (while imputing the husband’s wage), the results are virtually identical.

19. The results for the year 2000 can be directly compared to those from Morissette and Hou (2008) for the same year (see Table 2). We obtain an own-wage elasticity of 0.27 compared to their own estimates varying between 0.03 and 0.17 depending on the wage imputation procedure used for nonworking wives. They also report spouse-wage elasticities varying between –0.11 and –0.14 (compared to our –0.09) and nonlabour income elasticities of –0.00.

20. The issue of whether declining over-time elasticities could be due to changes in the composition of married women has been investigated by Bishop et al. (2009). For example, it could be the case that high-elasticity women married younger in 1996 than in 2005. However, since they find decreasing over-time elasticities for single women as well, they conclude that the sample selection story cannot explain why women’s elasticities fell.

21. The smallest group has 13 observations and the biggest group has 702. The average size is 129 observations.

22. Devereux (2007b) points out the increased likelihood of small-sample biases in EWALD when applied to synthetic cohort models of labour supply, and Devereux (2007a) suggests alternative estimators including Unbiased Error-in-Variables Estimator (UEVE). As an additional robustness check, we also estimated this model and found similar results as with EWALD.

23. The instrumental variables are strongly correlated with the endogenous variables (F-test with p-value 0.00), but since our model is not over-identified we cannot run further specification checks.

24. Nonlabour income elasticities show less variation. After average and marginal tax elasticities are very close and, even though they are lower at the low end of the hours of work distribution, they quickly move up to zero between the fourth and fifth decile.