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?

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The Answer of 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?

Consider the a Model of the U