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

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

Empirical Findings

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 backward-bending 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 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 Breusch-Pagan test it is found that the model contains heteroskedasticity, which is the reason why the heteroskedasticity-robust 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 z-score or probit index for a one unit change in the predictor. It is noted that a one unit increase in age increases the z-score by .041 and a one unit increase in agesqrd decreases the z-score 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 z-score increases by .09 and for a one unit increase in expersqrd, the z-score 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 z-score 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 z-score 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 z-score 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 R-squared 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 H0: 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 backward-bending 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”14. “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 well-known that the usual two-stage and maximum likelihood estimators are inconsistent (Adkins and Hill, 2004). Although there are several ways of dealing with this problem15, it is well beyond the scope of this study as of this moment to delve into such complexities.

Quite similar to El-Hamidi (2003), I make two general comments regarding Table 1.9: first, the low R-squared 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 24-60 years of age is too diverse a group to have one labor supply function. Thus, as El-Hamidi (2003) proposes “an analysis of the determinants of labor supply using a disaggregated database should be the focus of further empirical investigations” (El-Hamidi, 2003).

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