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.

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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 wf [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.

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Appendix

Table 1.2: Variable Descriptions

hours	total hours paid all jobs during 2009
wage	composite hourly wage all paid jobs in 2009
wagesqrd	the square of composite hourly wage all paid jobs
age	female's age, 2009, external cross-sec file
agesqrd	the square of female's age
marst	marital status of female as of December 31 of 2009 1 – female is married 2 – female is in a common-law relationship 3 – female is separated 4 – female is divorced 5 – female is widowed 6 – female is single (never married)
fslsp	female is living with spouse in 2009 1 – Yes 2 - No
province	Province of residence group, household, December 31, 2009 10 - Newfoundland and Labrador 11 – Prince Edward Island 12 – Nova Scotia 13 – New Brunswick 24 – Quebec 35 – Ontario 46 – Manitoba 47 – Saskatchewan 48 – Alberta 59 – British Columbia
exper	number of years of work experience, full-year full-time
expersqrd	the square of number of years of work experience, full-year full-time
alimo	Support payments received
educ	Highest level of education of female, 1st grouping 1 - Never attended school 2 - 1-4 years of elementary school 3 - 5-8 years of elementary school 4 - 9-10 years of elementary and secondary school 5 - 11-13 years of elementary and secondary school (but did not graduate) 6 - Graduated high school 7 - Some non-university postsecondary (no certificate) 8 - Some university (no certificate) 9 - Non-university postsecondary certificate 10 - University certificate below Bachelor's 11 - Bachelor's degree 12 - University certificate above Bachelor's, Master's, First professional degree in law, Degree in medicine, dentistry, veterinary medicine or optometry, Doctorate (PhD)
nonfemaleincome	income of non-female in the household
kidslt6	female with a child less than six years old
working	total hours paid all jobs greater than zero

Table 1.3: Summary Statistics of Canadian women

Variable	Observations	Mean	Standard Deviation	Minimum	Maximum
puchid25(id)	32065	4012858	7414.513	4000001	4025693
province	31819	33.74845	14.69714	10	59
agyfm	32065	38.72475	25.07988	0	80
agyfmg46	32065	5.924965	2.56457	1	9
alimo46	32065	263.0711	1860.065	0	45000
earng46	31745	51132.91	63660.3	0	1387250
age	17042	43.26998	10.50669	24	60
marst	28264	2.8629	2.118468	1	6
fslac	28325	1.907326	.2899806	1	2
fslsp	28325	1.406884	.4912616	1	2
hours	24009	1129.835	922.4242	0	5200
wage	16371	19.89017	11.81493	6	142
exper	24864	14.9928	13.18434	0	50
alimo	28325	249.0071	1825.297	0	45000
earng42	28108	20899.72	28372.56	0	539000
mtinc42	28179	25065.66	30446.84	0	680000
oas42	28325	1210.796	2430.963	0	7750
ogovtr42	28325	33.60018	181.1052	0	2400
ottxm42	28325	561.278	4202.446	0	120000
prpen42	28325	2120.96	7977.688	0	185000
sapis42	28325	406.2242	2022.65	0	25000
uccb42	28325	139.9682	495.2109	0	7800
uiben42	28325	757.8279	2789.844	0	31000
wgsal42	28325	19643.28	27591.65	0	525000
wkrcp42	28325	130.5137	1279.867	0	32000
educ	28204	7.580946	2.599754	1	12
totalfemincome	28179	50174.48	56331.64	0	1110900
nonfemincome	28067	29301.02	32393.06	0	680000
wagesqrd	16371	535.2028	918.9231	36	20164
agesqrd	28325	2642.723	1801.337	256	6400
expersqrd	24864	398.6038	528.935	0	2500
kidslt6	32065	.0902542	.28655	0	1
working	32065	.8051458	.3960946	0	1

 

 

Table 1.4: Marital Status of Canadian women

Marital Status	Frequency	Percent	Cumulative
1 – female is married	13,841	48.97	48.97
2 – female is in a common-law relationship	2,485	8.79	57.76
3 – female is separated	982	3.47	61.24
4 – female is divorced	1,900	6.72	67.96
5 – female is widowed	2,776	9.82	77.78
6 – female is single (never married)	6,280	22.22	100.00
Total	28,264	100.00

 

Table 1.5: Canadian women living with spouse or not

Living with spouse or not	Frequency	Percent	Cumulative
1 - Yes	16,800	59.31	59.31
2 - No	11,525	40.69	100.00
Total	28,325	100.00

 

Table 1.6: Residence of Canadian women

Province	Frequency	Percent	Cumulative
10 - Newfoundland and Labrador	1,390	4.37	4.37
11 – Prince Edward Island	870	2.73	7.10
12 – Nova Scotia	1,877	5.90	13.00
13 – New Brunswick	1,849	5.81	18.81
24 – Quebec	6,136	19.28	38.10
35 – Ontario	8,976	28.21	66.31
46 – Manitoba	2,124	6.68	72.98
47 – Saskatchewan	2,304	7.24	80.22
48 – Alberta	3,172	9.97	90.19
59 – British Columbia	3,121	9.81	100.00
Total	31,819	100.00

Table 1.7: Highest level of education attained by Canadian women

Highest level of education	Frequency	Percent	Cumulative
1 - Never attended school	111	0.39	0.39
2 - 1-4 years of elementary school	227	0.80	1.20
3 - 5-8 years of elementary school	2,025	7.18	8.38
4 - 9-10 years of elementary and secondary school	2,037	7.22	15.60
5 - 11-13 years of elementary and secondary school (but did not graduate)	1,869	6.63	22.23
6 - Graduated high school	4,449	15.77	38.00
7- Some non-university postsecondary (no certificate)	2,037	7.22	45.22
8 - Some university (no certificate)	1,584	5.62	50.84
9 - Non-university postsecondary certificate	8,548	30.31	81.15
10 - University certificate below Bachelor's	617	2.19	83.34
11 - Bachelor's degree	3,447	12.22	95.56
12 - University certificate above Bachelor's, Master's, First professional degree in law, Degree in medicine, dentistry, veterinary medicine or optometry, Doctorate (PhD)	1,253	4.44	100.00
Total	28,204	100.00

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

Child less than six years old or not	Frequency	Percent	Cumulative
1 - Yes	29,171	90.97	90.97
2 - No	2,894	9.03	100.00
Total	32,065	100.00

 

Table 2.9: OLS Estimates for Canadian Women

Dependent Variable: hours of work
Independent Variables	Coefficient
composite hourly wage of all paid jobs	-1.42 [2.70]
the square of composite hourly wage of all paid jobs	-.065** [.0327]
female's age	39.23*** [5.01]
the square of female's age	-.49*** [.06]
1 - Never attended school (base group)	---
2 - 1-4 years of elementary school	-104.7 [201.5]
3 - 5-8 years of elementary school	65.4 [115.8]
4 - 9-10 years of elementary and secondary school	90.5 [110.1]
5 - 11-13 years of elementary and secondary school (but did not graduate)	21.25 [111]
6 - Graduated high school	117.3 [105.5]
7 - Some non-university postsecondary (no certificate)	4.36 [106.9]
8 - Some university (no certificate)	-14.6 [107.8]
9 - Non-university postsecondary certificate	85.8 [105.2]
10 - University certificate below Bachelor's	61.8 [109.1]
11 - Bachelor's degree	48 [106.2]
12 - University certificate above Bachelor's, Master's, First professional degree in law, Degree in medicine, dentistry, veterinary medicine or optometry, Doctorate (PhD)	51.84 [107.8]
female is living with spouse (base group)	---
female is not living with spouse	77.14 *** [28]
income of non-female in the household	.008*** [.0007]
1 – female is married (base group)	---
2 – female is in a common-law relationship	29.3 [15.98]
3 – female is separated	18.8 [35.14]
4 – female is divorced	20.65 [33.11]
5 – female is widowed	-78.7 [54.71]
6 – female is single (never married)	-23.2 [29.9]
Support payments received	-.013*** [.003]
female without a child less than six years old (base group)	---
female with a child less than six years old	-193.2*** [17.73]
constant	606.7 [149.9]
Sample size	12469
R-squared	0.143

* 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

Independent Variables	Coefficient	∆P(working) per unit ∆independent variable
female's age	.041*** (.012)	.0164
the square of female's age	-.001*** (.0001)	-.0004
number of years of work experience, full-year full-time	.09*** (.004)	.036
the square of number of years of work experience, full-year full-time	-.001*** (.0001)	-.0004
1 - Never attended school (base group)	---	---
2 - 1-4 years of elementary school	.61 (.441)	.244
3 - 5-8 years of elementary school	.87** (.35)	.348
4 - 9-10 years of elementary and secondary school	1.11*** (.351)	.444
5 - 11-13 years of elementary and secondary school (but did not graduate)	1.16*** (.354)	.464
6 - Graduated high school	1.36*** (.35)	.544
7 - Some non-university postsecondary (no certificate)	1.25*** (.35)	.5
8 - Some university (no certificate)	1.34*** (.35)	.536
9 - Non-university postsecondary certificate	1.56*** (.35)	.624
10 - University certificate below Bachelor's	1.64*** (.36)	.656
11 - Bachelor's degree	1.8*** (.35)	.72
12 - University certificate above Bachelor's, Master's, First professional degree in law, Degree in medicine, dentistry, veterinary medicine or optometry, Doctorate (PhD)	1.96*** (.353)	.784
10 - Newfoundland and Labrador (base group)	---	---
11 – Prince Edward Island	.301*** (.108)	.1204
12 – Nova Scotia	-.1 (.082)	-.04
13 – New Brunswick	-.001 (.083)	-.0004
24 – Quebec	-.08 (.07)	-.032
35 – Ontario	-.146 (.07)	-.0584
46 – Manitoba	.044 (.081)	.0176
47 – Saskatchewan	.0454 (.081)	.0182
48 – Alberta	.052 (.076)	.0208
59 – British Columbia	-.106 (.076)	-.0424
constant	-1.22 (.427)	---
Pseudo R-squared	0.17	---
Proportion of women who worked	0.42	---
Final value of log of likelihood function	-5637.7	---

* 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

Dependent Variable: hours of work
Independent Variables	Coefficient
composite hourly wage of all paid jobs	-9.1*** (1.41)
the square of composite hourly wage of all paid jobs	-.006 (.015)
female's age	19.8*** (5.13)
the square of female's age	-.235*** (.061)
1 - Never attended school (base group)	---
2 - 1-4 years of elementary school	-84.8 (334.3)
3 - 5-8 years of elementary school	-18.02 (280)
4 - 9-10 years of elementary and secondary school	-50.34 (278.3)
5 - 11-13 years of elementary and secondary school (but did not graduate)	-148.6 (279.2)
6 - Graduated high school	-67.43 (277.2)
7 - Some non-university postsecondary (no certificate)	-188.9 (277.7)
8 - Some university (no certificate)	-202.9 (278.2)
9 - Non-university postsecondary certificate	-125.9 (277.1)
10 - University certificate below Bachelor's	-183.8 (279.1)
11 - Bachelor's degree	-171.1 (277.4)
12 - University certificate above Bachelor's, Master's, First professional degree in law, Degree in medicine, dentistry, veterinary medicine or optometry, Doctorate (PhD)	-174.3 (278.1)
female is living with spouse (base group)	---
female is not living with spouse	60.9** (25.6)
income of non-female in the household	.01*** (.0003)
1 – female is married (base group)	---
2 – female is in a common-law relationship	19.5 (17)
3 – female is separated	24.6 (34.52)
4 – female is divorced	20.3 (31.3)
5 – female is widowed	-73.3 (50.9)
6 – female is single (never married)	-7.3 (27.8)
Support payments received	-.013*** (.003)
female without a child less than six years old (base group)	---
female with a child less than six years old	-172.2*** (17.3)
constant	1292.3 (299.2)
(Selectivity bias)	-314.8 (18.12)
Sample size	13515

* Statistical significance at the 90% level

** Statistical significance at the 95% level

*** Statistical significance at the 99% level

( ) Usual standard error