Highlights
Q1.
Using Data Set 1 provided, and positing the following relation
lnC∗ t = lnβ1 +β2 lnYt +εt
where C = consumers’ expenditure in constant prices
Y = disposable income in constant prices
The figures are in GBP billions. and assuming the partial adjustment hypothesis
lnCt −lnCt−1 = δ(lnC∗t −lnCt−1)
1. Estimate the short-run function and obtain the adjustment parameter . What does this adjustment parameter imply?
2. Retrieve the estimated parameter coefficients for the long-run relation. Is the long-run income elasticity greater or less than the corresponding short- run income elasticity and why?
3. Test the hypothesis that there is no serial correlation (of the first order) here using Durbin’s h statistic. Is this conclusion consistent with that given by the Lagrangean
multiplier (LM) test of residual serial correlation (F version)?
4. Is there evidence of correlation between the lagged dependent variable and the error term?
5. Consider the data on Y (disposable income) in Data Set 1 provided. Fit a suitable ARIMA model to these data outlining the steps involved in carrying out this task.
Q2.
Data Set 2 involves quarterly seasonally adjusted data from 1972Q1 through 1989Q4 for the Federal Republic of (West) Germany. It contains series for the narrow money supply (M0) in billions of current Deutsche marks, GNP in billions of current Deutsche marks, a consumer price index (1985 = 100), and the Central Bank discount rate.
The data can be used to model the demand for money. Monetary theory suggests that the real demand for money, M, depends on a ’scale variable’ such as real GNP, Y , and an opportunity cost or rate-of-interest variable, R.
We can form the variable M by deflating the money series by the price index. This gives the money supply in constant 1985 prices. Similarly, we can form Y by deflating the GNP series by the price index. This gives GNP in constant 1985 prices. For the opportunity cost variable, we use
R = 1+ I 100
where I is the discount rate in percentage terms.
We work in terms of ln(M), ln(Y ), and ln(R). Therefore, the demand for money relation is as follows
Mt = αR β1tY β2te εt (0.1)
where Mt=demand for money (real cash balances); Rt=an opportunity cost indicator; Yt=real GNP
For statistical estimation, equation (0.1) may be expressed conveniently in log form
lnMt = lnα+β1 lnRt +β2 lnYt +εt (0.2)
1. Examine the three series and ascertain their order of integration. Your analysis should use time paths (charts), sample autocorrelation functions, and ADF (Augmented DickeyFuller) statistics.
• How many differenced variables are included on the right-hand side of the ADF regression in each case? Explain why?
2. Looking for a possible long-run relationship between lnMt and lnYt; test for cointegration between these variables.
3. Use the Engle-Granger two-step procedure to estimate the short-run relationship between money supply and GNP. That is, estimate an appropriate error correction model (hint: using residuals from the long-run or cointegration regression as estimates of the disequilibrium errors).
• Your analysis should provide t ratios; and statistics for R, autocorrelation, and specification error (RESET). Are the diagnostic statistics satisfactory?
• Also, be sure to interpret the estimated parameter coefficients here. Is the disequilibrium error term ²t−1 correctly signed with a significant t ratio?
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