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

By Adib J. Rahman
2013, Vol. 5 No. 09 | pg. 6/6 |

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 .

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.


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

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