This suggests that fine-tuning the model may be required in order to identify optimal approaches. For instance, Gionnani and Woodford add that, "It is only if we ask whether the same policy continues to be optimal when we vary the statistical properties of the disturbances that we can hope to find an advantage of one representation of the policy rule over the other (1427).
Gionnani points out that rather than restricting the analysis to the Taylor rules component of the new Keynesian model, an optimal model should determine a robust optimal monetary policy rule within a larger family of rules that is sufficiently flexible to implement the optimal plan in those cases where the parameters are known with certainty. A study by Leeper reports that optimal monetary policy behavior in the simplest forward-looking version of the popular class of dynamic stochastic general equilibrium models with nominal rigidities. Woodford (2003) exhaustively examines many variants on this model. An important variant arises when both prices and wages are sticky (Leeper 2005).
A study by Jondeau and Le Bihan estimated two small macroeconomic models with forward-looking components, one for the U.S. economy and another for the German economy. The models, which include a Phillips curve, an I-S curve and a monetary policy rule, are estimated using the full-information maximum-likelihood procedure. They are shown to have some robustness with respect to the Lucas critique. These researchers then computed optimal monetary policy rules in the class of dynamic Taylor rules. Based on their findings, Jondeau and Le Bihand report that optimal policies imply a strong degree of interest-rate smoothing. Moreover, German optimal policy was determined to require a more persistent and slightly stronger response to inflation and output than the U.S. optimal policy.
Finally, according to Sarno and Taylor, "Some support for significant portfolio balance effects is provided by Ghosh (1992). Ghosh's approach is to use a forward-looking monetary model of the exchange rate in order to capture signaling effects. Since the monetary model implies that the exchange rate is a function of expected future monetary fundamentals, the monetary policy signaling effects must be captured" (225). Following this step, it is possible to test for the effects of sterilized intervention through channels besides the signaling channel (Sarno and Taylor 225).
The issue of "divine coincidence"
The property described in the assumptions section above is termed the divine coincidence; this property differs from the popular views concerning the undesirability of policies that attempt to completely and always stabilize inflation irrespective of the costs involved in terms of output (Blanchard and Gali 35). In this regard, Blanchard and Gali notes that, "That consensus underlies the medium-term orientation adopted by most inflation targeting central banks" (Blanchard and Gali 35). The divine coincidence is closely associated with a specific aspect of the standard New Keynesian model with respect to the fact that the gap between the efficient (first-best) level of output and the natural level of output is constant and remains unchanged in response to shocks (Blanchard and Gali 35). This aspect suggests that stabilizing the output gap (e.g., the gap that exists between actual and natural output) is comparable to also stabilizing the welfare-relevant output gap (e.g., the gap that exists between actual and efficient output), and it is this equivalence that represents the basis for the so-called divine coincidence. According to Blanchard and Gali, "The New Keynesian Phillips curve implies that stabilization of inflation is consistent with stabilization of the output gap. The constancy of the gap between natural and efficient output implies in turn that stabilization of the output gap is equivalent to stabilization of the welfare-relevant output gap" (36).
This property can likewise be attributed to the lack of nontrivial real imperfections in the standard New Keynesian model, but the New Keynesian model contains one such real imperfection which is real wage rigidities (Blanchard and Gali 35). In this regard, Blanchard and Gali note that, "The existence of real wage rigidities has been pointed to by many authors as a feature needed to account for a number...
Once the New Keynesian model is extended in this way, the divine coincidence disappears" (Blanchard and Gali 37). The reason for the disappearance of the divine coincidence in this area relates to the fact that the gap that exists between efficient output and natural output is no longer invariant and is susceptible to shocks (Blanchard and Gali 35).
Despite these differences, though, stabilizing the output gaps is still the same as stabilizing inflation; however, it is not equivalent to stabilizing the welfare-relevant output gap and, as a result, from a welfare perspective, it is no longer desirable (Blanchard and Gali 35). As these economists point out, "Stabilization of inflation and stabilization of the welfare-relevant output gap now present the monetary authority with a trade-off. In the face of an adverse supply shocks, in particular, the monetary authority must decide whether to accommodate a higher level of inflation or, instead, keep inflation constant but allow for a larger decline in the welfare-relevant output gap" (Blanchard and Gali 37).
The implementation of the optimal monetary policy
Optimal monetary policy analysis can be viewed as a constrained optimization problem: the policymaker chooses a competitive equilibrium allocation that maximizes social welfare among the set of all feasible competitive equilibrium allocations. Part of the solution to this problem is a monetary policy rule that determines how variables that are under direct control of the policymaker -- the monetary policy instruments-are set. An optimal policy rule is said to implement the optimal allocation if, conditional on the policy rule, the allocation is the unique rational expectations equilibrium of the economy. For a simple monetary model, we study the implementation of full-commitment and Markov-perfect policies when the policymaker uses a money-stock instrument. For a local approximation of the economy, we show that both policy rules implement the respective optimal allocations. We also show that the results for local approximations do not necessarily extend to a global analysis of the economy: the Markov-perfect policy rule is not implementable, and there is no proof that the full-commitment policy rule is implementable (Dotsey and Hornstein 113).
The study by Dotsey and Hornstein considered optimal monetary policy as the solution to both full-commitment and time-consistent Markov-perfect planning problems. The solutions were found to be consistent with rational expectations competitive equilibria. The optimal solution to the planning problem implies a rule for the assumed policy instrument which in the Dotsey and Hornstein study was a money supply instrument. These researchers also verified that, for local approximations to the solution of the optimal policy problem, the implied policy rules implement the planning allocations, that is, the planning allocation is the unique rational expectations equilibrium conditional on the implied policy rule; however, these researchers also examined whether the implied policy rules also implement the allocation globally. Based on their analysis, Dotsey and Hornstein determined that a money supply rule that is Markov-perfect does not implement the planning solution.
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Blanchard, Olivier and Jordi Gali. (2007). "Real Wage Rigidities and the New Keynesian
Model." Journal of Money, Credit & Banking 39(1): 35-7.
Dotsey, Michael and Andreas Horstein. (2006, Spring). "Implementation of Optimal Monetary
Policy." Economic Quarterly 113-34.
Ghosh, A.R. (1992). "Is it signaling? Exchange intervention and the Dollar-Deutschmark rate."
Journal of International Economics 54: 439-53 in Sarno and Taylor at 57.
Giannoni, M.P. (2006, February). "Robust Optimal Monetary Policy in a Forward-Looking
Model with Parameter and Shock Uncertainty." Journal of Applied Econometrics 22:
Jondeau, Eric and Herve Le Bihan. (2002). "Evaluating Monetary Policy Rules in Estimated
Forward-Looking Models." Annals of Statistics and Economics 67/68: 357-363.
Knoop, Todd A. Recessions and Depressions: Understanding Business Cycles. Westport, CT:
Leeper, Eric M. (2005, May 12). "Optimal monetary policy in simple models." Indiana
University and NBER. [Online]. Available: http://mypage.iu.edu/~eleeper/Bundesbank/
Roberts, John M. (1995). "New Keynesian Economics and the Phillips Curve." Journal of Money, Credit & Banking 27(4): 975-77.
Rotheim, Roy J. New Keynesian Economics/Post Keynesian Alternatives. London: Routledge,
Sarno, Lucio and Mark P. Taylor. The Economics of Exchange…
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