There Has Been Much Talk Recently About the Convergence of Inflation

Essay

There has been much talk recently about the convergence of inflation rates between many of the OECD economies. You want to see if there is evidence of this closer to home by checking whether or not Canada's inflation rate and the United States' inflation rate are cointegrated.
(a)You begin your numerical analysis by testing for a stochastic trend in the variables, using an Augmented Dickey-Fuller test. The t-statistic for the coefficient of interest is as follows: $\begin{array}{|c|c|c|c|c|}\hline \text { Variable with } & \text { InfCan } & \Delta \operatorname{InfCan} & \text { InfUS } & \Delta \operatorname{Inf} U \mathrm{~S} \\\text { lag of } 1 & & & & \\\hline \text { t-statistic } & -1.93 & -5.24 & -2.20 & -4.31\\\hline\end{array}$ where InfCan is the Canadian inflation rate, and InfUS is the United States inflation rate. The estimated equation included an intercept. For each case make a decision about the stationarity of the variables based on the critical value of the Augmented Dickey-Fuller test statistic.
(b)Your test for cointegration results in a EG-ADF statistic of (-7.34). Can you reject the null hypothesis of a unit root for the residuals from the cointegrating regression?
(c)Using a working hypothesis that the two inflation rates are cointegrated, you want to test whether or not the slope coefficient equals one. To do so you estimate the cointegrating equation using the DOLS estimator with HAC standard errors. The coefficient on the U.S. inflation rate has a value of 0.45 with a standard error of 0.13. Can you reject the null hypothesis that the slope equals unity?
(d)Even if you could not reject the null hypothesis of a unit slope, would that have been sufficient evidence to establish convergence?