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imply that the Slutsky restriction is satisfied for individuals who desire more than -11200 hours of labour supply. In other words, the Slutsky restriction is satisfied for almost all individuals in the sample.
Table 7.7 lists the effects of wage and income on hours, based on the estimates of the quadratic function. These effects are called, from left to right, the
uncompensated response to the wage, the compensated response to the wage, the response to income, the uncompensated elasticity of hours with respect to the wage, the compensated elasticity of hours with respect to the wage, and the total-income elasticity. These terms are explained in Chapter 5.
The first column shows that the uncompensated response to the wage is almost the same as that for the linear function. This is not surprising since the wage effect is almost linear. The third column, however, shows that the response to income is about four times as large as the estimate from the linear function. (Note that the income variables in the regression model are divided by 1000). This means that the linear specification largely underestimates the income effect, perhaps because a few wives who have a very large nonwage income affect the estimates of the income response.
Table 7.7. Wage and Income Effects
dh dw (1) dh' dw (2) dh dm (3) dh w dw h (4) dh" w h (5) dh dm (6) No Child 199.1 323.6 -0.0819 1.088 1.769 -0.6806 One Child Age 199.1 260.6 -0.0819 2.202 2.883 -0.6806 Two Children Age (M 199.1 215.5 -0.0819 8.249 8.929 -0.6806 One ChUd Age 5-9 199.1 300.6 -0.0819 1.334 2.015 -0.6806 Two Children Age 5-9 199.1 272.7 -0.0819 1.840 2.521 -0.6806 Average Wife 199.1 274.8 -0.0819 1.790 2.470 -0.6806 Average Working Wife 198.2 282.7 -0.0642 1.425 2.032 -0.6075
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The fourth column shows that the compensated elasticities differ substantially between the demographic groups. This is because of the large differences in hours worked. The quadratic labour supply function assumes that the uncompensated response to the wage is constant when wage and nonwage income are given. Hence, the elasticity becomes large for people working short hours, and vice versa. In other words, the high elasticity for wives working short hours and the small elasticity for wives working long hours is determined by the specification of the hours worked function, rather than by the estimation. For this reason, the elasticity for a wife who has two children less than five years old is large compared to that for the other demographic groups.
The uncompensated elasticity for an average working wife is 1.43. This value is about the medium value of past studies, of female labour supply using US data, that were listed in Killings worth and Heckman (1986). Seven out of seventeen of the listed suidies estimated elasticities higher than 1.43. In the case of studies using UK data, the uncompensated elasticity is smaller than it is in US studies on average. Two out of fifteen listed studies estimated elasticities higher than 1.43. On the other hand, as we review in Appendix A of this chapter, studies using Australian data report relatively small uncompensated elasticities (see Table A.7.1). Out of five studies listed in Appendix A, only Ross (1986) reported an uncompensated elasticity larger than unity.
The compensated elasticity of hours with respect to the wage is 2.03. Again, about a third of past US studies listed in the survey of Killingsworth and Heckman estimated larger elasticities than this, but no studies in the UK estimated larger elasticities than this. All of the five Australian studies listed in Appendix A reported lower compensated elasticities than that of our estimation.
The total-income elasticity is -0.61. This is large (in absolute terms) compared to the studies listed in the survey of Killingsworth and Heckman and to past Australian
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studies listed in Appendix A. No study presented a larger value than this. However, most of studies defined die nonwage income as wife's nonwage income plus
husband's total income, so we cannot compare our result with the results of the past studies straightforwardly. More discussion about the comparison between our estimation and other Australian studies is in Appendix A of this chapter.
4.4. The Reservation Wage
Table 7.8 lists the estimates of the reservation wage equation. As we discussed before, there are two possible restrictions that can be used to solve the identification problem. One assumption is that one variable in the wage equation does not overlap the equation in the reservation wage equation. The first column of the table assumed that the years of primary and secondary education do not affect the reservation wage rate. Another assumption is that the error term of the market wage equation and the error term of the reservation wage equation are not correlated with each other. The estimation in the second column is based on this assumption.
The standard errors of the reservation wage equation and the participation equation, and the correlation between the market wage equation and the reservation wage equation are calculated by the procedure discussed in Section 2. The coefficient standard errors cannot be calculated, because the correlations between the coefficients in the participation equation and the coefficients in the market wage equation are not available. If the participation equation and the market wage equation were
simultaneously estimated by the maximum likelihood method, it would be possible to calculate the standard errors of the coefficients of the reservation wage equation.
A positive coefficient implies that the variable has a negative effect on
participation and vice versa. When we compare the two equations, we find that the second assumption gives a standard error of the reservation wage equation that is about four times larger. Hence, the coefficients of the variables which are not in the market wage equation, such as the wife's nonwage income, the husband's status
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variables, and the children dummies, are about three times larger (in absolute terms) in the second equation. In both cases tertiary education has a negative effect, but the effect is much larger in the second case.
Table 7.8. Estimates of the Log of the Reservation Wage
Assumption 1 (1) Assumption 2 (2) Constant 1.4922 0.9646 Education ED 0. -0.06838 DIP -0.09579 -0.5136 BACH -0.1613 -1.1716 Age /i30 0.09924 0.2790 /\40 0.1627 0.4676 Country of Birth ASIA -0.09855 0.02944 UK 0.08922 0.2022 EUROPE 0.05025 0.06934 OTHER 0.004278 0.02453 Income NWI/IOOO 0.008812 0.02741 Husband's Status NWI„ /lOOO 0.004907 0.01526 0.001704 0.005301 Children C(M-1 0.4030 1.2539 C(M-2 0.7668 2.3855 CO-4-3 1.0168 3.1632 C5-9-1 0.1965 0.6113 C5-9-2 0.3100 0.9645 C5-9-3 0.4363 1.3575 ClO-14-1 0.1673 0.5204 ClO-14-2 0.1713 0.5329 ClO-14-3 -0.1051 -0.3269
Standard Error of Reservation Wage
Equation (02) 0.3636 1.5143
Standard Error of Participation
Decision Equation (c^ 0.5006 1.5573
Correlation between Market Wage
and Reservation Wage Equations (CT12) 0.08972 0.