Interpretation of OLS Estimates for Canadian Women
The OLS results of the multiple regression model (1) for hours of work on the independent variables is for women in the labor force (Table 1.9, Appendix). Based on the results, wage has a significant positive effect on hours of work until a turning point of negative $10.9/hour is reached, and beyond this value wage has a negative impact on hours of work. This means that hours of work increase with wage at a decreasing rate and this relation gives a backwardbending supply of labor for Canadian women. The elasticity at the mean hours and wage is 0.02.
The effect of age on hours of work is significantly positive until a woman reaches a turning point of 40 years of age, and beyond this value age has a negative impact on hours of work. This means that hours of work increase with age at a decreasing rate. In addition, husband’s income surprisingly has a very significant positive effect of .008 hours per year on females’ hours of work, however, this effect is economically insignificant. Regarding the support payments received by the individual female, the effect is negative effect on hours of work by .013 hours per year and although the effect is statistically significant, it is not economically significant. On the other hand, if a female is living with a child less than six years old then not surprisingly this will have a negative effect on her hours of labor compared to a female who does not have a child less than six years old. This effect is both economically and statistically significant. The effects of indicator variables of the individual female on her hours of work such as the highest level of education she attained and her marital status do not appear statistically significant, although some of their categories are economically significant.
However, most importantly, if a female is not living with a spouse then her hours of labor would increase by 77.14 hours per year compared to a female who is living with a spouse. This effect is statistically and economically significant. Moreover, if a woman is living with a child less than six years old then her hours of work reduces by 193.2 hours per year compared to a woman not living with a child less than six years old. This effect is statistically and economically significant.
Note that this multiple regression model does not include variables such as experience and province which may affect a woman’s hours of work. Besides, by running the BreuschPagan test it is found that the model contains heteroskedasticity, which is the reason why the heteroskedasticityrobust standard errors are reported (Table 1.9). Furthermore, the model suffers from functional form misspecification as discovered after running a Ramsey Regression Equation Specification Error Test (RESET). Moreover, we only observe the hours equation for the individual females who worked in 2009 and not for the ones who did not work. Hence, we have a selection bias problem (Gronau, 1974; Lewis, 1974). Therefore, in order to test and correct for sample selection bias due to unoberservability of the wage offer for nonworking women we need to estimate a probit model for labor force participation.
Interpretation of Probit Estimates for Canadian Women
The probit estimates of the first step of the Heckman procedure is reported first. In the probit model, female’s age, years of experience, highest level of education she attained, and the province in which she lives have a strong effect on her labor force participation.
In Table 2.0, the probit regression coefficients give the change in the zscore or probit index for a one unit change in the predictor. It is noted that a one unit increase in age increases the zscore by .041 and a one unit increase in agesqrd decreases the zscore by .001. These coefficients are significant at 99% confidence interval. The scaled probit coefficients for educ and educsqrd are roughly .4(.041) ≈ .02 and .4(.001) ≈  0.0004 respectively, meaning that a one unit increase in edu roughly increases the likelihood of a woman’s labor force participation by .02. And, on the other hand, a one unit increase in edusqrd roughly decreases the likelihood of a woman’s labor force participation by 0.0004. Likewise, for a one unit increase in exper, the zscore increases by .09 and for a one unit increase in expersqrd, the zscore decreases by 0.001. Both of the coefficients are very statistically significant. The scaled probit coefficients for exper and expersqrd are roughly .036 and 0.004 respectively, indicating that a one unit increase in exper increases the likelihood of woman’s labor force participation by approximately .036 and on the other hand, a one unit increase in expersqrd decreases her labor force participation with a probability of roughly.0004.
In addition, the indicator variables for educ also appear statistically significant suggesting that for example, a female having graduated high school versus no years of schooling (base group), increases the zscore by 1.36. The marginal effect for each of the highest level of education attained by the female individual has a positive effect on her probability of working, although with diminishing returns with higher levels of education.
In terms of the residence of the female affecting her labor participation, most of the indicators of province appear statistically insignificant without the exception of the female residing in P.E.I and Ontario. It is noted that a one unit increase in the female living in P.E.I, increases the zscore by .301 compared to the female living in Newfoundland (base group). On the other hand, a one unit increase in the female living in Ontario, decreases the zscore by .146 compared to the female living in Newfoundland. Furthermore, if a woman is residing in P.E.I then this increases her probability of working by approximately 0.1204 compared to a woman living in Newfoundland. On the contrary, a woman living in Ontario decreases her probability of working by approximately .06. The change in the probability of working per unit change in each independent variable of the probit regression is reported, and the pseudo Rsquared for the probit equations is 0.17 (Table 2.0). Therefore we cannot use these estimated equations to make accurate predictions about whether any particular woman will choose to work.
Interpretation of Heckit Estimates for Canadian Women
The estimated probit coefficients were used to compute the normal probability of working for each female which in turn was used for the Heckit estimates (Nakamura and Nakamura, 1981). From the Heckit results in Table 2.1, there is evidence of a sample selection problem in estimating the hours of work equation (1). The coefficient of the inverse Mill’s ratio (has large t statistic, so we fail to reject H_{0}: ρ = 0. Just as importantly, there are no practically large differences in the estimated slope coefficients in Table 2.1, other than female’s age which differs by 19.4 years. In addition, the factors that appear statistically significant on hours of work in the OLS results also appear statistically significant in the Heckit results.
The wage has a significant positive effect on hours of work until a turning point of negative $758.33/hour is reached, and beyond this value wage has a negative impact on hours of work. This means that hours of work increase with wage at a decreasing rate and this relation gives a backwardbending supply of labor for Canadian women. The elasticity at the mean hours and wage is 0.16.
Very similar to the OLS results, the effect of age on hours of work is significantly positive until a woman reaches a turning point of 40 years of age, and beyond this value age has a negative impact on hours of work. Hence, hours increase with age at a decreasing rate. Husband’s income and support payments received by a woman are economically insignificant, while the indicator variables of a woman living with a spouse and a woman having a child less than six years old respectively are economically significant in Heckit results.
A possible explanation of the puzzling positive relationship between husband’s income and woman’s hours of labor that conflicts with the findings of the Nakamuras (1981) and Robinson and Tomes (1985) may be due to “assortative mating”. “Assortative mating” is a term widely used to refer to the positive correlation between the traits of husbands and wives (Liu and Lu, 2006). Becker (1973, 1974) investigated the reasons for assortative mating, and its effects on various social issues and his work has motivated many researchers such as Boulier and Rosenzweig (1984); Burdett and Coles (1997); Kremer (1997); Fernandez (2001); Fernandez, Guner, and Knowles (2001); Fernandez and Rogerson (2001); Pencavel (1998); Ermisch and Francesconi (2002) to study the mechanisms that relate assortative mating with inequality and their quantitative importance. Liu and Lu say that “these studies (of or related to assortative mating) are accompanied by a few empirical papers (Mare 1991; Mancuso 2000) that document the evolution of assortative mating, particularly educational assortative mating” (Liu and Lu, 2006). For example, it is more likely that a “successful” woman will marry a man who is “successful” because of social norms and other reasons, say a female doctor marrying another male doctor not only because of security reasons but also because of common interests, lifestyle choice, etc.
However, note that the slope coefficients for the highest level of a female’s education are all negative in Heckit results compared to its slope coefficients in probit results. This could mean that the more educated the female is the less she works, i.e., education gets people in the labor force but does not influence their hours once they are already in. There is not a strong correlation between education and preference for leisure. On the other hand, marital status for most type has a positive effect on hours compared to the female being married (base group). Although, a widow works less than a married woman by 73.3 hours per year, none of the effects of types of marital status are statistically significant even though they can be considered economically significant.
An important issue regarding the Heckit model addressed: If the errors of the selection equation, the regression equation, or both are heteroskedastic, it is wellknown that the usual twostage and maximum likelihood estimators are inconsistent (Adkins and Hill, 2004). Although there are several ways of dealing with this problem, it is well beyond the scope of this study as of this moment to delve into such complexities.
Quite similar to ElHamidi (2003), I make two general comments regarding Table 1.9: first, the low Rsquared value of 0.143 implies that there is still a wide range of unidentified determinants explaining the decision to work extra hours or not. Second, these results suggest that the category of 2460 years of age is too diverse a group to have one labor supply function. Thus, as ElHamidi (2003) proposes “an analysis of the determinants of labor supply using a disaggregated database should be the focus of further empirical investigations” (ElHamidi, 2003).Continued on Next Page »
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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 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 fulltime and parttime 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.mcgrawhill.com/sites/dl/free/0070891540/43156/benjamin5_sample_chap02.pdf.
6.) Source: See http://highered.mcgrawhill.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 nonoffice 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: CrossSection 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 nonfemale 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 crosssec 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 commonlaw 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, fullyear fulltime

expersqrd

the square of number of years of work experience, fullyear fulltime

alimo

Support payments received

educ

Highest level of education of female, 1st grouping
1  Never attended school
2  14 years of elementary school
3  58 years of elementary school
4  910 years of elementary and
secondary school
5  1113 years of elementary and
secondary school (but did not
graduate)
6  Graduated high school
7  Some nonuniversity postsecondary (no certificate)
8  Some university (no certificate)
9  Nonuniversity 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 nonfemale 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 commonlaw 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  14 years of elementary school

227

0.80

1.20

3  58 years of elementary school

2,025

7.18

8.38

4  910 years of elementary and
secondary school

2,037

7.22

15.60

5  1113 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 nonuniversity postsecondary (no certificate)

2,037

7.22

45.22

8  Some university (no certificate)

1,584

5.62

50.84

9  Nonuniversity 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  14 years of elementary school

104.7
[201.5]

3  58 years of elementary school

65.4
[115.8]

4  910 years of elementary and
secondary school

90.5
[110.1]

5  1113 years of elementary and
secondary school (but did not
graduate)

21.25
[111]

6  Graduated high school

117.3
[105.5]

7  Some nonuniversity postsecondary (no certificate)

4.36
[106.9]

8  Some university (no certificate)

14.6
[107.8]

9  Nonuniversity 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 nonfemale in the household

.008***
[.0007]

1 – female is married (base group)



2 – female is in a commonlaw 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

Rsquared

0.143

* Statistical significance at the 90% level
** Statistical significance at the 95% level
*** Statistical significance at the 99% level
[ ] Heteroskedasticityrobust 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, fullyear fulltime

.09***
(.004)

.036

the square of number of years of work experience, fullyear fulltime

.001***
(.0001)

.0004

1  Never attended school (base group)





2  14 years of elementary school

.61
(.441)

.244

3  58 years of elementary school

.87**
(.35)

.348

4  910 years of elementary and
secondary school

1.11***
(.351)

.444

5  1113 years of elementary and
secondary school (but did not
graduate)

1.16***
(.354)

.464

6  Graduated high school

1.36***
(.35)

.544

7  Some nonuniversity postsecondary (no certificate)

1.25***
(.35)

.5

8  Some university (no certificate)

1.34***
(.35)

.536

9  Nonuniversity 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 Rsquared

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  14 years of elementary school

84.8
(334.3)

3  58 years of elementary school

18.02
(280)

4  910 years of elementary and
secondary school

50.34
(278.3)

5  1113 years of elementary and
secondary school (but did not
graduate)

148.6
(279.2)

6  Graduated high school

67.43
(277.2)

7  Some nonuniversity postsecondary (no certificate)

188.9
(277.7)

8  Some university (no certificate)

202.9
(278.2)

9  Nonuniversity 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 nonfemale in the household

.01***
(.0003)

1 – female is married (base group)



2 – female is in a commonlaw 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