ECB Working Paper No. 12
نویسندگان
چکیده
The optimal weights on indicators in models with partial information about the state of the economy and forward-looking variables are derived and interpreted, both for equilibria under discretion and under commitment. An example of optimal monetary policy with a partially observable potential output and a forward-looking indicator is examined. The optimal response to the optimal estimate of potential output displays certainty-equivalence, whereas the optimal response to the imperfect observation of output depends on the noise in this observation. JEL Classification: E37, E47, E52, E58 Keywords: Partial information, Kalman filter, monetary policy, discretion and commitment Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Optimization under discretion . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1 Optimal ltering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Optimal policy with commitment . . . . . . . . . . . . . . . . . . . . . . 8 3.1 Optimal ltering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4 Optimal weights on indicators: General remarks . . . . . . . . . . . . . . 11 5 Example: Optimal monetary policy with unobservable potential output 15 5.1 Equilibrium under discretionary optimization and under an optimal commitment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 5.2 An optimal targeting rule . . . . . . . . . . . . . . . . . . . . . . . 18 5.3 Ideal indicators and optimal ltering . . . . . . . . . . . . . . . . . 20 5.4 An optimal instrument rule . . . . . . . . . . . . . . . . . . . . . . 23 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 A Optimization under discretion and certainty-equivalence . . . . . . . . . 28 B The Kalman gain matrix and the covariance of the forecast errors . . . . 31 C The Kalman gain matrix in the example of section 5 . . . . . . . . . . . 33 D The Kalman lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
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NOTE: This Working Paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the author and do not necessarily reflect those of the ECB. In 2011 all ECB publications feature a motif taken from the €100 banknote. Fax +49 69 1344 6000 All rights reserved. Any reproduction, publication and reprint in the form of a different publicat...
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