Question

Consider the a model of the U.S. labor market where the demand for labor depends on the real wage, while the supply of labor is vertical and does not depend on the real wage. You could argue that the supply of labor by households (think of hours supplied by two adults and two children) has not changed much over the last 60 years or so in the U.S. while real wages more than doubled over the same time span. At first that seems strange given the higher participation rate of females over that period, but that increase has been countered by a lower male participation rate (resulting from earlier retirement), an increase in legal holidays, and an increase in vacation days.

a. Write down two equations representing the labor supply and labor demand function, allowing for an error term in each of the demand and supply equation. In addition, assume that the labor market clears.

b. How would you estimate the labor supply equation?

c. Assuming that the error terms are mutually independent i.i.d. random variables, both with mean zero, show that the real wage and the error term of the labor demand equation are correlated.

d. If you find a non-zero correlation, should you estimate the labor demand equation using OLS? If so, what are the consequences?

e. Estimating the labor demand equation by IV estimation, which instrument suggests itself immediately?

Answer 1

a. labour demand and supply equation and attains equilibrium (labour market clear)

labour demand = L_d = c_d + b_d R_w + u_d

where, c_d is the constant or intercept term. Indicating the labour demand when the real wage rate is zero.

b_d is the coefficient of real wage rate (R_w). Indicating the rate of change in labour demand when real wage rate changes.

u_d is the error term.

Note: If the wage rate of women and men vary, it is better to design 'real wage' as two variables: one each for men and women.

Labour supply: seems to be unaffected by real wage rate. but definetly it is variable to be considered. Other variables can be labour hours supplied by men (L_sm) and (L_sw); Real wage rate of men and women (R_wm and R_ww); Number of holidays and Vacations availed by men and women (H_m and H_w) and finally an error term u_s.

Ls = c_s + b_s1 R_w + b_s2 L_sm + b_s3 L_sw + b_s4 R_wm + b_s5R_ww + b_s6 H_m + b_s7 H_w + u_s

b. The labour supply equation can be estimated by OLS

c. If the error term is correlated with real wage rate. then the estimate of labour demand equation is not valid. The R² value will be poor. When the error term is correlated with the independant variable it violates the CLRM assumption of OLS. This could be over by adding few more co-founding variables into regreesion equation.

d. If there is non-zero correlation, then we cannot estimate this equation through OLS.

e. A 2-stage least square model will suggest itself. It is because, a non-zero correlation is sign of endogenity problem, which could be overcome by designing a 2-stage least square model.