Temple University
Department of Economics

Econometrics II
Simultaneous Eqns: Identification, Estimation and Specification

On the web site you can retrieve a file titled MACROMOD.DAT. The file contains data for all of the variables used in this homework. The quarterly data are for the period 1947.1 to 1986.2. Where appropriate they have been deflated.

Consider the following simple Keynesian model of income determination:
Equilibrium:

Consumption:


Investment:


Trade Balance:


The exogenous variables are:
i - interest rate
P - corporate profits
G - government expenditures
T - taxes
ER - exchange rate

1. Is the structural model identified? You must check both the rank and order condition.

2. Derive the reduced form equations for income, Y, and consumption, C.

3. Derive the reduced form equations for investment and net exports.

4. Consider the reduced form equation for income, Y. Collect all variables other than current, once and twice lagged income into a 'constant'. You should have a second order difference equation in income. The coefficients on lagged and twice lagged income should involve unknown parameters. What restrictions on the relevant unknown parameters will guarantee stability of the model? Choose some trial values for the relevant unknowns and plot the time path of income after an initial shock.



In my homepage you will find a file titled MACROMOD.DAT which contains real quarterly data for the period 1947.1 to 1986.2. The model we will be using was specified above

5. Estimate the unknown coefficients of each reduced form using OLS.
a. What is the interpretation of these reduced form coefficients?
b. Evaluate the results on statistical grounds.
c. Do you believe that a correction for autocorrelation in the error term is necessary?

6. Do the coefficients on lagged and twice lagged GNP in the income equation result in a stable time path for equilibrium income?

7. From your OLS results can you compute unique values for the structural coefficients? Show your work.

8. Estimate the parameters of the structural equations by two stage least squares. Discuss the results.

9. Are the new estimates consistent with stability? Show your work.

10. Execute a test of the overidentifying restrictions in the model.

11. Execute a statistical test for the exogeneity of ER, the exchange rate.