Using data on the Maltese economy, Apap and Gravino \({ }^{19}\) estimate a number of versions of Okun's Law. Their quarterly data run from 1999Q1 to 2012Q4 and can be found in the data file apap. The variables used in this exercise are \(D U_{t}=U_{t}-U_{t-4}\) (the change in the unemployment rate relative to the same quarter in the previous year) and \(G_{t}\) (real output growth in quarter \(t\) relative to quarter \(t-4\) ).

a. Estimate the Okun's Law equation \(D U_{t}=\alpha+\beta_{0} G_{t}+e_{t}\). Find both conventional and HAC standard errors and comment on the results.

b. Check the correlogram of the residuals \(\hat{e}_{t}\) from the equation estimated in part (a). Is there evidence of autocorrelation?

c. Create the variable \(q_{t}=G_{t} \times \hat{e}_{t}\), and examine its correlogram. Use this correlogram and equation (9.63) to suggest a reason why the conventional and HAC standard errors for the estimate of \(\beta_{0}\) are similar in magnitude.

d. Estimate the finite distributed lag model

Use HAC standard errors. Is there evidence of a lagged effect of growth on unemployment? Using HAC standard errors in both cases, find a 95\% interval estimate for the total multiplier and compare it with a \(95 \%\) interval for the total multiplier from the model in part (a).

e. Estimate ARDL models \(D U_{t}=\delta+\sum_{s=1}^{p} \theta_{s} D U_{t-s}+\sum_{r=0}^{q} \delta_{r} G_{t-r}+e_{t}\) for \(p=1,2,3\) and \(q=0,1,2\). Use HAC standard errors. Select and report the model with the largest number of lags whose coefficients are significantly different from zero at a \(5 \%\) level.

f. For the model selected in part (e), find estimates for the total multiplier, the impact multiplier, and the first three delay multipliers of the infinite distributed lag representation.
g. For the model selected in part (e), find \(95 \%\) interval estimates for the total multiplier and the two-period interim multiplier. How do they compare with the interval obtained in part (d)?

Transcribed Image Text:

DU, = a + BoG, + BG + BG + e