I am investigating if the policy of inflation targeting lowers the volatility of inflation.
I have estimated an AR(2)-GARCH(1,1) model, where the conditional mean equations is
$$ Inflation_t = C + Inflation_{t-1} + Inflation_{t-2} + Error_t. $$
and $Error_t$ follows a GARCH(1,1) model. I am unsure of how exactly to conclude if the model estimated on the subsample after inflation targeting does indeed show a reduction in the volatility of inflation as compared with the model estimated on the subsample before inflation targeting.
Is it possible to reach a conclusion by comparing the significance of the GARCH(-1) coefficients before and after inflation targeting or comparing the significance of the RESID(-1)^2 coefficient before and after inflation targeting, or both, or some other way?
Best Answer
GARCH is more appropriate for forecasting volatility. Here, you can use $F$ test to compare the inflation volatility before and after the inflation targeting. It involves lesser assumptions and is more appropriate.
Let $X_1, \dotsc, X_n$ and $Y_1, \dotsc, Y_m$ be independent and identically distributed samples from two populations which each have a normal distribution. The expected values for the two populations can be different, and the hypothesis to be tested is that the variances are equal. Let
$$\overline{X} = \frac{1}{n}\sum_{i=1}^n X_i\text{ and }\overline{Y} = \frac{1}{m}\sum_{i=1}^m Y_i$$
be the sample means. Let
$$ S_X^2 = \frac{1}{n-1}\sum_{i=1}^n \left(X_i - \overline{X}\right)^2\text{ and }S_Y^2 = \frac{1}{m-1}\sum_{i=1}^m \left(Y_i - \overline{Y}\right)^2 $$
be the sample variances. Then the test statistic
$$ F = \frac{S_X^2}{S_Y^2} $$
has an $F$-distribution with $n − 1$ and $m − 1$ degrees of freedom if the null hypothesis of equality of variances is true. Otherwise it has a non-central $F$-distribution. The null hypothesis is rejected if $F$ is either too large or too small.