An Econometric Analysis of the 'Backward-Bending' Labor Supply of Canadian Women

Summary and Conclusion

Past studies on the labor supply of married Canadian women by Alice Nakamura and Masao Nakamura (1981), and Robinson and Tomes (1985) have found that the labor supply schedule of working women is backward bending with elasticity similar in magnitude to typical estimates reported for males. The major goal of this paper was to re-examine the issue with more recent data as of 2009 to provide a better understanding of both hours worked and wage rates. The results of this paper offer strong support for the conclusions reached by them. The markedly backward-bending shape of the labor supply curve of working Canadian women suggests that the income elasticity of demand for leisure is larger relative to the substitution effect for women than for men in Canada.

However, the results reported by Robinson and Tomes (1985) may suggest that the contrasting secular trends observed in the labor supply of men and women are the consequences of the differential responsiveness of male and female labor force participation to opportunities, rather than the hours worked by men and women (Robinson and Tomes, 1985). Additionally, the slope coefficients of the OLS and Heckit estimates do not vary by a large extent in terms of their economic and statistical significance, even though there is evidence of selectivity bias in the OLS hours equation. Furthermore, assortative mating is likely to play a fundamental role in explaining the positive relationship between husband’s income and the woman’s hours of labor that conflicts with the findings of the Nakamuras (1981) and Robinson and Tomes (1985). Lastly, although by ignoring the issue of heteroskedasticity the usual 2-stage Heckit method becomes seriously biased and subsequent t-tests of regression coefficients can suffer from large “size distortion,” the Heckit method is relatively simple to implement in the situations discussed.

References

Angrist, Joshua D. and Alan B. Krueger. (1999). “Empirical Strategies in Labor Economics.” in Orley C. Aschenfelter and David Card, eds. Handbook of Labor Economics Vol 3C, pp 1277-1366.

Becker, G. S. (1973). “A theory of marriage: Part I.” Journal of Political Economy 81 (4), pp 813-846.

Becker, G. S. (1974). “A theory of marriage: Part II.” Journal of Political Economy 82 (2), pp 11-26.

Borjas, G.J. (1980) “The relationship between wages and weekly hours of work: the role of division bias.” Journal of Human Resources 15, pp 409-423.

Borjas, G.J. (1996). labor Economics. 2nd edition. McGraw-Hill.

Boskin, M.J. (1973) “The econometrics of labor supply.” in Cain and Watts eds (1973).

Boulier, B. L. and M. R. Rosenzweig. (1984). “Schooling, search, and spouse selection: Testing economic theories of marriage and household behavior.” Journal of Political Economy 92 (4), pp 712-732.

Burdett, K. and M. G. Coles. (1997). “Marriage and class.” Quarterly Journal of Economics 112 (1), pp 141-168.

Cain, G. G., and H.W. Watts. (1973) “Toward a Summary and Synthesis of the Evidence,” in Cain and Watts, Income Maintenance and labor Supply, New York: Academic Press, pp 328-67.

Carliner, Geoffrey, Christopher Robinson and Nigel Tomes. (Feb., 1980). “Female labor Supply and Fertility in Canada.” Canadian Journal of Economics, 13 (1), pp 46-64.

CCSD Facts & Stats: Fact Sheet on Canadian labor Market: labor Force Rates. CCSD Facts & Stats: Fact Sheet on Canadian labor Market: labor Force Rates. Retrieved 26 Nov, 2012 from Web site: http://www.ccsd.ca/factsheets/labor_market/rates/index.htm.

Chen, Songnian N. & Shakeeb Khan (2003), ‘Semiparametric estimation of a heteroskedastic sample selection model.’ Econometric Theory 19 (6), pp 1040–1064.

Chris Robinson and Nigel Tomes. (1985). "More on the labor Supply of Canadian Women." Canadian Journal of Economics, Canadian Economics Association, Vol. 18(1), pp. 156-63.

Common Menu Bar Links. The Atlas of Canada. Retrieved 26 Nov, 2012 from Web site: http://atlas.nrcan.gc.ca/auth/english/maps/peopleandsociety/population/gender/sex06.

Cross-Section Regression Estimates of labor Supply Elasticities: Procedures and Problems. Retrieved 05 Apr, 2013 from Web site: http://www.econ.ucsb.edu/~pjkuhn/Ec250A/Class%20Notes/B_StaticLSEsts&Heckit.pdf

Connelly, Rachel, Deborah S. DeGraff, and Deborah Levison. (1996). “Women’s employment and child care in Brazil,” Economic Development and Cultural Change 44(3), pp 619–656.

Dasgupta, Purnamita and Bishwanath Goldar. (2005). “Female labor Supply in Rural India: An Econometric Analysis.” E/265.

Donald (1995), “Two step estimation of heteroskedastic sample selection models.” Journal of Econometrics. (65), pp 347–380.

El-Hamidi, Fatma. (2003). “Labor supply of Egyptian married women: participation and hours of work.” Paper presented at the Annual Meeting of the Middle East Economic Association (MEEA) and Allied Social Science Association (ASSA). January 2-5, 2003.Washington, D.C.

Ermisch, J. and M. Francesconi (2002). “Intergenerational social mobility and assortative mating in Britain.” IZA Discussion Papers 465, Institute for the Study of Labor (IZA).

Fernández, R. (2001). “Education, segregation and marital sorting: Theory and an application to UK data.” NBER Working Papers 8377.

Fernández, R., N. Guner, and J. Knowles (2001). “Love and Money: A Theoretical and Empirical Analysis of Household Sorting and Inequality.” NBER Working Paper, No. 8580.

Fernández, R. and R. Rogerson (2001). “Sorting and long-run inequality.” Quarterly Journal of Economics 116 (4), pp 1305-1341.

Gender Discrimination in Canada. NAJCca. Retrieved 26 Nov, 2012 from Web site: http://www.najc.ca/gender-discrimination-in-canada/.

Gronau, R. (1974). “Wage comparisons – a selectivity bias,” Journal of Political Economy, 82, pp 1119-44.

Hall, Robert E. (1973). “Wages, Income, and Hours of Work in the U.S. Labor Force.” in Glen G. Cain and Harold W. Watts, eds. Income Maintenance and Labor Supply, pp 102-162.

Heckman, J.J. (1974). “Shadow prices, market wages, and labor supply,” Econometrica, 42 (4), pp 679-694.

Heckman, J.J. (1979). “Sample selection bias as a specification error,” Econometrica, 47(1), pp 153-161.

Killingsworth, M.R. (1983). Labor Supply, Cambridge: Cambridge University Press.

Killingsworth, M.R. and J.J. Heckman. (1986). “Female labor supply: a survey.” In Handbook of Labor Economics, Vol. I, O. Ashenfelter and R. Layard (eds.). Amsterdam: North-Holland, pp 102-204.

Kremer, M. (1997). “How much does sorting increase inequality?” Quarterly Journal of Economics 112 (1), pp 115-139.

Lewbel, Arthur (2003), “Endogenous selection or treatment model estimation.” Department of Economics, Boston College, 140 Commonwealth Ave., Chestnut Hill, MA, 02467, USA.,

lewbel@bc.edu.

Lewis, H.G. (1974). “Comments on selectivity biases in wage comparisons,” Journal of Political Economy, 82, pp 1145-1157.

Liu, Haoming and Lu Jinfeng. (2006). “Measuring the Degree of Assortative Mating,” Economics Letters, Elsevier, vol. 92(3), pp 317-322.

Mancuso, D. C. (2000). “Implications of marriage and assortive mating by schooling for the earnings of men.” Ph. D. thesis, Stanford University.

Mare, R. D. (1991). “Five decades of educational assortative mating.” American Sociological Review 56 (1), pp 15-32.

Nakamura, M., A. Nakamura, D. Cullen. (1979). “Job opportunities, the offered wage, and the labor supply of married women,” American Economic Review, 69(5), pp 787-805.

Nakamura, A. and M. Nakamura. (1981). “A comparison of the labor force behavior of married women in the United States and Canada, with special attention to the impact of income taxes.” Econometrica 49, pp 451-489.

Nakamura, A. and M. Nakamura. (1983). “Part-time and full-time work behavior of married women: a model with a doubly truncated dependent variable.” The Canadian Journal of Economics 16, pp 229-257.

Pencavel, J. (1998). “Assortative mating by schooling and the work behavior of wives and husbands.” American Economic Review 88 (2), pp 326-329.

Robins, L. (1930). “On the Elasticity of Demand for Income in Terms of Effort.” Economica (29), pp 123-129.

Sharif, M. (1991). “Poverty and the forward-falling labor supply function: a microeconomic analysis.” World Development. 19 (8), pp 1075-1093.

Survey of labor and Income Dynamics (SLID). Retrieved 30 Nov. 2012 from Web site: http://www23.statcan.gc.ca/imdb/p2SV.pl?Function=getSurvey.

Vella, F. (1998). “Estimating models with sample selection bias: a survey,” Journal of Human Resources, 33 (1), pp 127-169.

Wooldridge, Jeffrey. (2008). Introductory Econometrics. United States of America: South- Western College Pub. 4^th edition, pp 606-612 .

Endnotes

1.) The author would like to thank Professor Craig Brett for his invaluable suggestions and comments.

2.) Carliner et al. (1980) in their analysis of 1971 Canadian census data employ three measures of labor supply: labor force participation, hours per week, and weeks per year. Using education as a proxy for potential market wages they found that “greater education of the wife is associated with significantly increased labor supply for all three measures. This suggests that the … substitution effects of an increase in w_f [the wife’s wage] … outweigh the income effect.”

3.) The emphasis of the three papers is quite different. Nakamura, Nakamura, and Cullen (1979) report estimates for Canadian women using the 1971 Canadian census. Nakamura and Nakamura (1981) analyze both Canadian and U.S. census data emphasizing the role of taxes. Nakamura and Nakamura (1983) using these same data sets, distinguish further between full-time and part-time workers.

4.) Robinson and Tomes (1985) used data from 1979 Quality of Life Survey, which is a survey conducted by the Institute for Behavioural Research, York University, to deal against the problems of using census data for their study. The survey contained a direct measure of the hourly wage rate and also presented hours of work directly rather than in intervals for a subset of Canadian women.

5.) Source: http://highered.mcgraw-hill.com/sites/dl/free/0070891540/43156/benjamin5_sample_chap02.pdf.

6.) Source: See http://highered.mcgraw-hill.com/sites/dl/free/0070891540/43156/benjamin5_sample_chap02.pdf for the original table.

7.) Standard hours are usually determined by collective agreements or company policies, and they are the hours beyond which overtime rates are paid. The data apply to non-office worker.

8.) Standard hours minus the average hours per week spent on holidays and vacations.

9.) This supply curve shows how the change in real wage rate affects the amount of hours worked by employees. Source: http://en.wikipedia.org/wiki/Backward_bending_supply_curve_of_labor. See the appendix section.

10.) Although the Heckman sample selection model is written in terms of hours of work H, the same equations

apply equally as well to the wage W.

11.) All the steps of the Heckit method is borrowed from lecture notes: Cross-Section Regression Estimates of labor Supply Elasticities: Procedures and Problems.

12.) See http://www23.statcan.gc.ca/imdb/p2SV.pl?Function=getSurvey&SDDS=3889&lang=en&db=imdb&adm=8&dis=2 for more details on the Survey of labor and Income Dynamics (SLID).

13.) Census data is not used as the limitations of Census data in labor economics is well documented [Killingsworth (1983); Angrist and Krueger (1999)]. Income variables are based on respondents’ memory and willingness to disclose this information that is mostly underreported in the Census.

14.) To check for educational assortative mating, the husband’s education variable was added to the actual data that contains only females. After running a single regression of husband’s education on female’s education, a positive correlation for each level of education was found. Hence, husband’s education was added to the model to see how it affects the results. However, it must be noted that adding husband’s education to the model did not change the Heckit results that much. Most importantly, since adding husband's education to the model still results in a positive coefficient of non-female income in the Heckit, the sorting is not on education even though there is a positive correlation among husband's and wife's education. Therefore, the Heckit results with the inclusion of husband’s education to the model are not reported in this paper. Moreover, the existing literature of labor supply of women doesn't include this kind of variable.

15.) It has been mentioned by Adkins and Hill (2004) that “Donald (1995) has studied this problem and suggested a semiparametric estimator that is consistent in heteroscedastic selectivity models. Chen & Khan (2003) has also proposed a semiparametric estimator of this model. More recently, Lewbel (2003) has proposed an alternative that is both easy to implement and robust to heteroskedastic misspecification of unknown form.” The authors themselves proposed a “simple estimator that is easily computed using standard regression software,” and studied the performance of the estimator in a small set of Monte Carlo simulations.

Appendix

Table 1.2: Variable Descriptions

Table 1.3: Summary Statistics of Canadian women

Table 1.4: Marital Status of Canadian women

Table 1.5: Canadian women living with spouse or not

Table 1.6: Residence of Canadian women

Table 1.7: Highest level of education attained by Canadian women

Table 1.8: Canadian women with or without a child less than six years old 

Table 2.9: OLS Estimates for Canadian Women

* Statistical significance at the 90% level

** Statistical significance at the 95% level

*** Statistical significance at the 99% level

[ ] Heteroskedasticity-robust standard error

Table 2.0: Probit Estimates for Canadian women

* Statistical significance at the 90% level

** Statistical significance at the 95% level

*** Statistical significance at the 99% level

( ) Usual standard error

Table 2.1: Heckit Estimates for Canadian Women

* Statistical significance at the 90% level

** Statistical significance at the 95% level

*** Statistical significance at the 99% level

( ) Usual standard error