The individual labor supply curve, relating desired hours of work to the wage rate can be derived by tracing out the labor supply choices (tangencies) in response to different wages. labor supply is zero until the wage equals the reservation wage. For higher wages, the slope of the labor supply function depends on the relative magnitudes of the income and substitution effects (Figure 1.2).
Figure 1.2: Backward-Bending Labor Supply
Figure 1.2 suggests that if real wages were to increase from W1 to W2 then the worker will obtain a greater utility, due to their higher income. Therefore, he/she would be willing to increase their hours worked from L1 to L2. Note that this may be hours worked per day, month, year or even lifetime. Over this section of the curve the substitution effect is positive while the income effect is negative. The substitution effect is greater than the income effect giving rise to a positive price effect. Therefore, the increase in the real wage rate will cause an increase in the number of hours worked.
However, if the real wage increased from W2 to W3, then the number of hours worked would fall from L2 to L3. This is because the income effect has now become greater than the substitution effect. In addition, the utility gained from an extra hour of leisure is greater than the utility gained from the income earned working. Most importantly, beyond the wage of W2 we see that the worker is being paid enough to sustain their current lifestyle without having to work more hours, therefore creating the backwards bend in the curve.
According to El-Hamidi (2003), a vast number of studies on the labor supply of women in developed economies were carried out. However, these studies have produced a wide-range of conflicting estimates of labor supply elasticities with respect to wages and income. In their comprehensive survey of the literature, Killingsworth and Heckman (1986) concluded that estimates of women labor supply elasticities in these contexts are large, both in absolute terms and relative to male elasticities. The wage elasticity estimates vary widely from –0.85 to over 14, depending on the data source, the sub-populations studied (which vary by age group, marital status, and race) and the statistical methodology used. Killingsworth and Heckman (1986) list a wide range of positive estimates of wage elasticities while Nakamura, Nakamura, and Cullen (1979) obtained negative uncompensated wage elasticity. Killingsworth (1983) primarily attributes this result to excluding the schooling variable from the hours of work equation.
Another possible source of this result is the lack of a work experience variable in the wage equation, and/or the selection terms: Connelly, DeGraff and Levison (1997) compared the determinants of participation in employment with the determinants of hours worked for urban Brazilian women using 1985 household survey data. Because there are large proportions of households headed by unmarried women in Brazil, the authors divided their sample into single and married women heads of households. They found that the unobservable factors that increase the likelihood of employment of single women heads caused their hours of work to decrease, once employed. For women with spouses, unobservable factors worked in the same direction for both participation and hours worked.
The classical theory of labor supply states that a woman’s labor force participation decision is dependent upon a comparison of the market wage a woman can obtain and her reservation wage. The reservation wage is the lowest wage rate at which a worker would be willing to accept a particular type of job. It is related to the opportunity cost of a woman’s time at home (or in unpaid work), her unearned income, as well as other factors that may affect her preference for paid work, relative to other time uses. Thus, the labor supply function may be written as a function of the wage rate, other earnings and preferences. While an increase in the wage rate clearly increases the probability of labor force participation, the effect on the number of hours supplied is not as obvious, since both income and substitution effects come into play. The final decision depends on the marginal utility of consuming market goods and services purchased with wage income, relative to that derived from additional “leisure” time (El-Hamidi, 2003).
Killingsworth (1983) categorizes the empirical studies into first generation studies (FGS) and second generation studies (SGS). According to Killingsworth, FGS empirical studies were chiefly concerned with estimating the parameters of ad-hoc labor supply functions that were not derived from a formal model of utility maximization subject to constraints. Different aspects of labor supply (e.g. participation vs. hours of work) were dealt with in a piecemeal manner. On the other hand, SGS work is typically concerned with estimating the parameters of labor supply functions by maximizing an explicitly specified utility function subject to explicitly specified budget constraints.
In estimation, FGS generally assumed that the error term is randomly distributed and did not take into consideration the problem of selection into the workers’ sample according to unobservable characteristics, which became an important issue in SGS. To ignore such problems of participation response may result in not only a loss of information about some aspects of labor supply but also in biased estimates of the parameters that govern labor supply. SGS attempts to deal with these problems by taking into account the fact that individuals are not randomly selected into the working sample, and that a large number of observations have exactly zero hours of labor supply (Killingsworth, 1983).
Long years of research on sample truncation by Cain and Watts (1973) and sample selectivity by Gronau (1974) and Lewis (1974), and Heckman (1974) show that employed workers are those who are offered higher market wages than their reservation wages. Hence, the sub-sample being used for the assessment of determination of wages and hours of work is a non-random sample of the population [El-Hamidi (2003)]. According to Vella (1998), selectivity bias is a result of the unobservable characteristics that is correlated in both wages and hours of work equations. To correct for selectivity bias in econometric models of labor supply, Heckman (1976) suggested a two-stage estimation method. The two-stage estimation method is known as the Heckman correction or the Heckit method that involves a normality assumption and provides a test for sample selection bias and formula for the bias corrected model.Continued on Next Page »
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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.
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lewbel@bc.edu.
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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