Hi! In the book by Gali 2008 p.52 he says “Note that empirical interest rate rules are generally estimated using inflation and interest rate data expressed in annual rates. Conversion to quarterly rates requires that the output gap coefficient be divided by 4.”
I don’t understand why only the coefficient on output gap is divided by 4, but not the coefficient on inflation, in the Taylor rule.
If everything is measured in percentages, then the output gap is special in that it does not accumulate with time. A 1% gap of quarterly GDP for four quarters implies a 1% gap in annual GDP. That is different with inflation and interest rates. 1 percent inflation or interest per quarter implies 4 percent per year.
Following this same logic, if I estimate the coefficients of a Taylor rule, 1.5 for the inflation rate and 0.5 for the output gap, then for biweekly frequency, the inflation coefficient remains the same but that of the output gap changes to 0.5/6 = 0.08, right?