Question

Q3. Suppose we have the following Demand and Supply equations. Here ut are IID (0,02) Q1 = B1 +B2P+ +U1t...eqn(1) Q = a1 + a2P+ + U2t....eqn(2) a. Write down the estimator for B2 (called it B2) and explain in a few words if OLS estimate of B2 is biased/unbiased and consistent/inconsistent? b. Write down the estimator for 22 (called it az) and explain in a few words if OLS estimate of a2 is biased/unbiased and consistent/inconsistent?

Answer 1

Let X1Y1,X2Y2.......XnYn be a sample of size 'n'taken from the popoulation.The suggested relation between X&Y is given as Y1=+ui for i=1,2,3..n.Therefore,x is independent ,Y is dependent.

80 + 81.ci

Ui=Yi-

80 – 81.ri

Here,Ui=Observed value -estimated value,which ids the error ue for i=1,2,3...n.

The sum of the sqaures of equation is known as E.

The method of ordinary least squares (OLS)states the best values of
B0and81
are those values of
B0and81
which is minimise E.

$\partial$E/$\partial \beta 0$=0 and =0

дЕә31

a /a 80 = Oanda E/a81 = 0

$\varepsilon$XiYi=

B0€ri + Bleri