This question asks you to study the so-called Beveridge Curve from the perspective of cointegration analysis. The U.S. monthly data from December 2000 through February 2012 are in BEVERIDGE.

(i) Test for a unit root in urate using the usual Dickey-Fuller test (with a constant) and the augmented DF with two lags of curate. What do you conclude? Are the lags of curate in the augmented DF test statistically significant? Does it matter to the outcome of the unit root test?

(ii) Repeat part (i) but with the vacancy rate, vrate.

(iii) Assuming that urate and vrate are both I(1), the Beveridge Curve,

urate_t = α = βvrate + u_t,

only makes sense if urate and vrate are cointegrated (with cointegrating parameter β < 0). Test for cointegration using the Engle-Granger test with no lags. Are urate and vrate cointegrated at the 10% significance level? What about at the 5% level?

(iv) Obtain the leads and lags estimator with cvratet, cvratet₂₁, and cvrate_t–1 as the I(0) explanatory variables added to the equation in part (iii). Obtain the Newey-West standard error for β using four lags (so g 5 4 in the notation of Section 12-5). What is the resulting 95% confidence interval for b? How does it compare with the confidence interval that is not robust to serial correlation (or heteroskedasticity)?

(v) Redo the Engle-Granger test but with two lags in the augmented DF regression. What happens? What do you conclude about the robustness of the claim that urate and vrate are cointegrated?lemp232_t