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Q4

Economics

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Q4. Answer ALL parts below.

a) Using at least two different plots, how would you detect the presence of
autocorrelation in the residuals? Do you find evidence of autocorrelation? Explain
your reasoning.

b) What are the consequences of autocorrelation on the OLS estimator? Describe this
briefly.

c) Using an appropriate procedure perform a test for autocorrelation in the residuals.

(lO Marks]
QS. Suppose money supply in equation (1) is NOT directly observed and suppose we observe
instead the long run demand for money. Assume the desired level is defined as follows:
inM, — InM,-, = &(inM; — inM;_4) (2)

a) How does the model in equation (1) change in light of (2)?

b) State and estimate the new specification. Interpret the estimation output.

c) Based on your answers to part (b) above, what is the speed of adjustment to the long
run level?

d) Using the new specification, derive the long run static model. How does this compare
to the estimated specification based on equation (1)?

(lO Marks]
Q6. Consider your output to QS b). Using an appropriate procedure, test for autocorrelation
in the residuals.
(5 Marks]
Q?. From the discussion in the lectures, you suspect that the presence of real GDP, inflation,
and lagged dependent variable in the specification in Q5 may lead to an endogeneity issue.

a) Explain and discuss what is the issue of endogeneity in the context of this question.

b) What are the implications of the presence endogeneity for OLS?

c) How would you account for the presence of endogeneity?

(8 Marks]
Q8. Estimate the model in Q5 using Two Stage Least Squares (TSLS). Answer ALL the
following questions:

a) Define the set of instruments used to estimate the model, Justify the reasons for your
selected set of instruments.

b) Compare the qualitative and statistical interpretation of the TSLS estimated model to
that estimated using OLS in Q5. Which model is more consistent and conform to
theory?

c) Using this specification and TSLS estimates, derive the long run static model. How
does it compare to (i) the estimated specification based on equation (1) in Q2 and (ii)
to that derived based on (Q5-d)?

[12 Marks]
3

ata
he Excel file “money.xlsx” (available from SumeyLean/ Coursework) provides a data set to
alyse the demand for money in the US. The data represent a sample observed over the period
150.Q1-2000.Q4. The description of the variables (all seasonally adjusted) in the file is given
slow:
MI = real money supply.
INF = inflation rate.
REALGDP = real GDP.
TBILRATE = treasury bills (proxy for interest rates).
Questions
Use the data to answer the following questions below.
QI. Plot the time series of all the variables paying attention to carefully labelling the graphs.
Describe and discuss the dynamics of the data. How does money supply dynamics compare
to the other three variables? Explain this briefly.

{5 Marks]
Q2. Assuming money supply equals money demand, estimate the static demand for money
equation below:
Im, = Bo + Biinf, + Barly, + Bytbilrate, + uy qa)
where im, is natural log of real money supply, ly;is the natural logarithm of real gdp, ug is
the error term and f is a subscript referring to time.

a) Estimate model (1) above using Ordinary Least Squares. Report the estimation
output.

b) Carefully interpret the estimated coefficients (including the intercept). Are the signs
of the coefficients consistent with economic theory? Explain your reasoning.

c) Test the statistical significance of the coefficients of the independent variables:
inflation, real GDP and interest rates using the critical values corresponding to the #-
distribution and the test p-values. Carefully state the null and alternative hypotheses.
Interpret your results.

[12 Marks]
Q3. Answer ALL parts below.

a) Carry out a joint significance test for the independent variables of the model using
the critical values corresponding to the F-distribution and the test p-values. Carefully
state the null and alternative hypotheses. Interpret your results.

b) Is the model a good fit to the data? Explain.

[5 Marke!
2 oO

 

Q9. Again, from the discussion in the lectures, you suspect the model estimated in Q2 may
be spurious due to the presence of unit roots.

a) Perform the ADF unit root test on all variables in equation (1). State clearly the
hypothesis being tested, the data generating process, the lag length selection criteria
and the critical values. Is there evidence that the data contain a unit root?

b) What is the order of integration of the variables tested in part (a)?

c) Perform the Engle-Granger cointegration test. Are the variables cointegrated? State
clearly hypothesis being tested, the data generating process, the lag length selection
criterion and the critical values.

(15 Marks|
QI0. Imagine you are a policy maker, what policy implications can you draw from this
analysis? In particular, focus on the relationship between real money demand, interest rates,
inflation and real GDP.
(8 Marks]
[End of coursework)
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