1. Using (Qt) = 0 + 1ln(Pt) + 2ln(Yt) + ut ,

where Qt and Pt are the quantity (number) and price of haircuts obtained in Harvard in year t and Yt is mean income in Harvard in year t. Determine the price elasticity of demand in terms of the coefficients, and In (Yt).

2. If the equation of interest is Yi = 0 + 1X1i + 2X2i + ui , where E(u|X)=0 and E(u 2 |X)= 2 and X1 and X2 are uncorrelated in your model. Will the bivariate regression of Y on Xi have a similar coefficient estimate and standard error for 1 as the multivariate regression of Y on X1 and X2?

3. Given the regression equation yt = yt1 + t, t = ..., 2, 1, 0, 1, 2, ...,

where t = ut + 1ut1 + 2ut2,

and where ut is i.i.d. with mean 0 and variance 2u, and both 1 and 2 are unknown parameters that are not equal to 0. You have observations on the y process from period t = 1 through t = T, that is, {yt}Tt=1. Each yt is measured as a deviation from the sample mean over the period 1, ..., T, so that PTt=1 yt = 0.

The Ordinary Least Squares (OLS) estimator of in this sample of size T is

T = PT t=2 yt1yt /PTt=2(yt1)2.

Show that T is not consistent, that is,

plim T T