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Monetary Policy Rules

Empirical Applications Based on Survey Data

Series:

Dirk Bleich

This work provides different studies of how econometric evaluation of monetary policy based on forward-looking Taylor rules is conducted. The first part discusses theoretical results regarding the Taylor principle and can be used as a guideline for the evaluation of the following three empirical applications based on survey data of Consensus Economics. The first application deals with the question whether the introduction of inflation targeting affects monetary policy. The second application investigates the consequences of oil price movements for monetary policy. The third application analyzes monetary policy conditions in Spain before and after the changeover to the Euro by estimating forward-looking Taylor rules.

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Appendix B E-Stability of a Forward-Looking Taylor Rule

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In a first step we derive the minimal state variable (MSV) solution (McCal- lum, 1983) for the system of difference equations (A.1) for the REE by using the method of undetermined coefficients. With y = ( xt πt )′ and B = [A1]−1 we rewrite (A.1) as (B.1) yt = AEtyt+1 +Bvt. We guess a solution of the form (B.2) yt = c¯vt, where c¯ is a 2 x 2 matrix that has to be determined. Because of (B.1) and (2.3) and (2.4) we can set up the following conditions (B.3) Etyt = c¯vt, (B.4) Etyt+1 = c¯vt+1 = c¯Fvt = Fyt. Plugging (B.4) into (B.1) and rearranging gives (B.5) yt = (I − FA)−1Bvt, 106 Appendix where I denotes a 2 x 2 identity matrix. It is easy to see that with c¯ = (I − FA)−1B, (2.34) gives the MSV solution for the REE. Suppose the PLM is given by (B.6) yt = a+ cvt. Note that we allow for a structural deviation of (B.6) from the MSV solution for the REE (B.2) in form of an intercept a = 0. Moreover, it is pos- sible that c = c¯. Based on the PLM economic agents form their expectations according to (B.7) E∗t yt+1 = a+ cFvt. Plugging (B.7) into (B.1) gives the ALM (B.8) yt = Aa+ (AcF +B)vt. Now we can carry out the mapping from the PLM (B.6) to the ALM (B.8): (B.9) T ( a c ) = ( Aa AcF +B ) . To obtain the conditions for E-stability we set up the following differential equation:...

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