If We Take Lagged Interest Rates Into Account, We Should Estimate the Following Equation (3)

Methodology

In order to forecast monetary policy, we should have some guidance on the way the different central banks react on changes in the economic climate. Taylor (1993) argues that the reaction function of the central bankers can quite accurately be described in a rule in which inflation and output (and their deviations from the target) are the key determinants of the interest rate. He defends this proposal by showing that equation (1) gave a good picture of interest rate movements in the U.S during the period 1987-1992.

it = r +Πt + α(Πt-Π*) + βyt

In which i stands for current nominal short term interest rate, Π represents inflation and y measures the output gap. This original rule has some drawbacks however. First of all, it does not take expectations into account. It is well documented that central banks are not targeting current inflation, but are more concerned with expected inflation. The reason is of course that prices are sluggish and do not respond immediately to changes in the economic conditions. Therefore, equation (2) is often estimated:

it = r + Πt + α(E(Πt+n) -Π*) + βyt

This is a forward looking rule, which takes expected inflation in period t+n into account. The determination of n cannot be done in a mechanical way. We set n equal to 2. A next modification to this rule is to introduce lagged interest rate. This is done because it is observed that interest rates are largely persistent. This is due to the tendency of central bankers to smoothen the evolution of interest rate and change the rates only by 25 or 50 basis points.

If we take lagged interest rates into account, we should estimate the following equation (3)

it = (1-ρ)(r + Πt + α(E(Πt+n) -Π*)+βyt) + ρ it-1

ρ stands for the adjustment factor. It measures the importance of past interest.

Now we move to the issue of estimation these rules. The original Taylor rule (equation (1)) can easily be estimated by OLS. However, this is no longer the case for the second equation. On the one hand, we assume that the current interest rate is influenced by the expected inflation. On the other hand, predictions on expected inflation include the current stance of the monetary policy. In other words, we face an endogeneity problem. This problem can be tackled by using GMM estimation techniques. As instrumental variables, we then use lagged values of our independent variables.

In the next section, we report the results of our estimations. We estimated two different models, both equation (2) and (3). Since our measure of expected inflation only starts in 1991, we have to restrict our sample to the first quarter of 1991 as starting point and the last quarter of 2003 as ending point. When interpreting the results, we should bear in mind that the coefficient estimates on inflation and output gap should be adjusted for the adjustment factor.