There has been much talk recently about the convergence of inflation rates between many of the OECD economies

Question

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:

Variable with lag of 1 InfCan ?InfCan InfUS ?InfUS
t-statistic -1.93 -6.38 -2.37 -5.63

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?
What will be an ideal response?

Answer 1

Answer:
(a) The critical value for the ADF is (-2.57) at the 10% significance level for the sample period. Therefore you cannot reject the null hypothesis that there is a unit root for both inflation rates. However, given the critical value for the ADF statistic of (-3.43) you can reject the null hypothesis for the difference or the acceleration in the inflation rates at the 1% significance level. Both price levels appear to be I(2) variables.
(b) Given the critical value of (-3.96) for the EG-ADF statistic, you can reject the null hypothesis of a unit root in favor of the two inflation rates being cointegrated.
(c) The DOLS estimator allows for statistical inference on the coefficient using the standard normal distribution. Since 0.45 is more than two standard deviations from unity, you can reject the null hypothesis of that regression coefficient being one.
(d) Finding a unit slope would not be sufficient for convergence, since it would allow for a constant difference between the two inflation rates. To have convergence you would need that difference to be zero.