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

By Adib J. Rahman
2013, Vol. 5 No. 09 | pg. 2/6 |

The Backward-Bending Labor Supply Model

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)9.

Figure 1.2: Backward-Bending Labor Supply

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.

Literature Review

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)10 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.

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