Assume the Following Model of the Labor Market:
N^d = $\frac { W } { P }$

Essay

Assume the following model of the labor market:
N^d = ?₀ + ?₁
$\frac { W } { P }$ + u
N^s = ?₀ + ?₁
$\frac { W } { P }$ + v
N^d = N^s = N
where N is employment, (W/P)is the real wage in the labor market, and u and v are determinants other than the real wage which affect labor demand and labor supply (respectively). Let
E(u)= E(v)= 0; var(u)= $\sigma _ { u } ^ { 2 }$ ; var(v)= $\sigma _ { v } ^ { 2 }$ ; cov(u,v)= 0
Assume that you had collected data on employment and the real wage from a random sample of observations and estimated a regression of employment on the real wage (employment being the regressand and the real wage being the regressor). It is easy but tedious to show that $\left( \hat { \beta } _ { 1 } - \beta _ { 1 } \right) \xrightarrow{p} \left( \gamma _ { 1 } - \beta _ { 1 } \right) \frac { \sigma _ { u } ^ { 2 } } { \sigma _ { u } ^ { 2 } + \sigma _ { v } ^ { 2 } }$ > 0
since the slope of the labor supply function is positive and the slope of the labor demand function is negative. Hence, in general, you will not find the correct answer even in large samples.
a. What is this bias referred to?
b. What would the relationship between the variance of the labor supply/demand shift variable have to be for the bias to disappear?
c. Give an intuitive answer why the bias would disappear in that situation. Draw a graph to illustrate your argument.