Economics 170Final Exam
Spring 1991
Answer each of the following equally weighted questions.
1) Econometric models are described as stochastic rather than deterministic. The stochastic nature of the models comes from the error term which we have labeled µ. Describe the sources of this error term and the assumptions we make about it in deriving the ordinary least squares estimator.
2) Suppose the true model is Yi = a + Xib1 + Zib2 + ei where
ei = Xivi and v satisfies all the usual assumptions we make about the error. Which, if any, of the ordinary least squares assumptions are violated by the true model? Explain how you would correctly estimate the model.
3) Suppose you are given the three equation model:
Y1 = a0 + a1X1 + a2Y2 + a3Y3 + #181 1
Y2 = b0 + b1X2 + #181 2
Y3=X1 + X3 + Y1
where Y's are endogenous variables and X's are predetermined or
exogenous variables. Find the reduced form equations and, if
possible, the structural parameters. Describe how you would
estimate the first equation via two stage least squares.
4) Suppose you have the following model of the demand for money, Mt as a function of income It and the expected interest rate rt:
Mt = a + b1It + b2rt + #181
Following the adaptive expectations model, expectations are formed in the following way:
r(t) - r(t-1) = d(r(t) - r(t-1)).
Find the equation to be estimated and discuss any problems there might be in applying ordinary least squares.
5) Your estimate of a quarterly consumption model on 40 observations is:
Consumption = -48.7 + .68Income - .04intrate
R2 = .75, dw = 1.55
Is autocorrelation present? What is the magnitude of the correlation between the errors. If autocorrelation is present what can be said about the results of the estimation?
6) Suppose that you have the following true model:
Y = 35 + 1X1 -.33X2 + 2X3 + #181
If you estimate X3 against the other X's you obtain the following results:
X3=-15 + .75X1 -.10X2
Find the values of the coefficients of the model estimated by omitting the variable X3. What can be said about coefficients estimated from a model omitting a relevant variable?
7) Specification errors often show up as either autocorrelation or heteroskedasticity. Explain.
8) You have estimated the following demand functions for tv dinners (hd stands for hot dogs):
D=150.83-.75PD + .37PHD -.65Income + .23White + .17Highsc + .78Age
D=168.19 - .63PD + .46PHD -.83 Income + .75Age
based on 200 observations. The mean price is $2.50, the mean quantity is 75. Find the price elasticity of demand. The residual sum of squares from the first equation is 756, and for the second equation is 930. Test the restriction that the coefficients on white and highschool are simultaneously zero. Interpret the coefficient on income; suppose average income is 150, if this helps.
_______________________________