دستاوردهایی از هموار سازی نرخ بهره در یک اقتصاد باز کوچک با گریز از حد صفر

We extend the Monacelli [Monacelli, T. (2005). Monetary policy in a low pass-through environment. Journal of Money, Credit and Banking, 37(6), 1047–1066] model to allow for a central bank that penalizes nominal interest rate paths that are too close to the zero lower bound. We analytically derive the optimal interest-rate policy rule in each equilibrium under four policy regimes: (i) benchmark commitment to an ex-ante optimal monetary-policy plan; (ii) benchmark discretionary policy; (iii) optimal delegation to a discretionary policy maker with similar preferences to society; and (iv) optimal delegation to a discretionary policy maker with an additional taste for interest-rate smoothing. Under the commitment benchmark, the optimal interest-rate rule is proved to be intrinsically inertial, whereas this property is non-existent under discretionary policy. In the absence of commitment, there are gains to delegating policy to an interest-rate smoothing central banker. We show that while the endogenous law of one price gap in the model exacerbates the optimal policy trade-off that arises under discretionary policy, the latter feature of interest-rate smoothing acts to weaken it, by mimicking intrinsic inertia under the commitment policy.

Empirically, the level of nominal interest rates for many industrialized small open economies tend to be highly and positively autocorrelated. For example, Espinosa-Vega and Rebucci (2003) document first-order autocorrelations for nominal interest rates in these countries that are near random walk. Furthermore, these rates are perfectly correlated with the respective countries’ monetary policy rates. Often this feature is rationalized as central banks’ preference for interest-rate smoothing. It may also be the case that such persistence in policy rates arise naturally out of monetary policy that is ex-ante optimal, without any explicit desire for smoothing policy (see Woodford, 1999 and Woodford, 2003b). The former hypothesis then raises the question of whether, and when, such explicit preference for interest rate smoothing has any gain for society in a small open economy. In a closed economy model without any endogenous monetary policy trade off, Woodford (1999) showed there are gains to society for an explicit interest-rate smoothing objective to be incorporated into the central bank’s objective when it cannot commit to an ex-ante optimal monetary policy plan. This is because the interest rate smoothing component of the objective in the latter regime induces an optimal policy that approximates the commitment policy more closely. While Rogoff (1985) considered the delegation of monetary policy to a conservative central banker as a solution to the well-known average inflation bias problem, Woodford (1999) advocated hiring an interest-rate-smoothing central bank delegate as a solution to the stabilization bias problem which arises from lack of commitment by the policy maker. This latter result will be conveniently labeled as the Woodford proposition below. In this paper, we extend the Monacelli (2005) model to consider the case where the monetary policy maker penalizes domestic nominal interest rate paths that are too close (from above) to zero. This not unrealistic assumption, as in Woodford (2003b, see Chapter 4.2), is used as a reduced-form way of bounding the stochastic paths of the interest rate above zero. This has an interpretation of aversion to the zero-interest-rate lower bound by policy makers.1 While we could explicitly model occasionally binding zero-lower-bound constraints (see e.g. Adam and Billi, 2007 and Adam and Billi, 2006) that is not the purpose here in this paper. Instead, we apply the approach of Woodford (2003b) which allows us to analytically derive the optimal interest-rate policy rule in the equilibria for four policy regimes. To that end, we consider notions of optimal policy under the following policy regimes: (i) benchmark commitment to an ex-ante optimal monetary-policy plan; (ii) discretion, or ex-post lack of commitment to (i); and a Rogoff-style delegation of discretionary policy to an independent policy maker that either (iii) shares the same family of loss functions as society, or (iv) has an additional interest-rate smoothing term in its objective function. Under the commitment benchmark, the optimal interest-rate rule is proved to be intrinsically inertial, whereas this property is non-existent under discretionary policy. Analytical and numerical results show that under discretion, there are gains to delegating policy to an interest-rate smoothing central banker. Specifically, we show that in this Monacelli (2005) economy, endogenous deviations from the law of one price exacerbates the optimal CPI inflation and output-gap trade-off in discretionary monetary policy. However, we also show that by delegating policy to an explicit interest-rate smoothing policy maker, this trade-off can be weakened. This weakening of the trade-off can be interpreted as a forced encoding of history dependence in the policy decision that approximates policy under commitment. Our result is robust to alternative degrees of exchange rate pass through, the types of shocks impinging the natural rate, and minor departures from optimal pricing behavior. One might expect the important insight on the value of interest-rate smoothing of Woodford (1999) to carry through to small-open-economy monetary theory and policy. This would indeed be true in the case of typical small-open-economy models with complete exchange-rate pass through in the style of Clarida, Galí, and Gertler, (2001) and Galí and Monacelli (2002). Clarida et al. (2001) showed that the small-open-economy optimal monetary policy rule and resulting equilibrium is qualitatively the same as its closed economy counterpart.2 However, such a conclusion may not be warranted in many small open economies that experience incomplete exchange rate pass through, and this question has not been theoretically analyzed for such economies. In fact, Monacelli (2005) shows that because of incomplete pass through, monetary policy via the interest rate path also affects the paths of CPI inflation (i.e. both domestic and imported goods price inflation) and output gap via the channel of the exchange rate and the deviation from the law of one price. Monacelli (2005) showed that it is no longer optimal to just achieve flexible domestic producer prices (which would have been sufficient in the closed-economy case), but there is a trade off between stabilizing domestic producer prices on the one hand, and stabilizing either the output gap or the law-of-one-price gap on the other. We thus address the unanswered question of whether the Woodford proposition survives in a more general case of a small open economy with incomplete exchange-rate pass through where the optimal monetary policy is clearly one that cannot merely stabilize domestic goods inflation. This question is important since a large number of advanced industrialized countries, for instance Canada, Australia, the United Kingdom, and New Zealand, are small open economies that face exactly this kind of problem where exchange rate pass through is less than complete. The remainder of the paper is organized as follows. We describe the New Keynesian (NK) model of Monacelli (2005) briefly in Section 2. We then motivate why, in the small open economy that we employ, optimal interest-rate smoothing or not can be crucial, in Section 2.2. Optimal monetary policy under commitment is considered and contrasted with alternative optimal discretionary policies in Section 3. In Section 3, we also prove and derive the intuition behind how the Woodford proposition helps to weaken the effect of the endogenous law-of-one-price gap on the equilibrium policy trade-off. We provide numerical examples showing that the Woodford proposition carries through to this economy as well in Section 4. We conclude in Section 5.

In this paper, the role of optimal interest-rate smoothing is considered in the context of a small open economy model that exhibits an endogenous monetary-policy trade-off between inflation and output gap, as a result of imperfect exchange rate pass through to domestic prices. It was shown that the Woodford (1999) conclusion about optimal monetary policy inertia still carries through in the small-open-economy setting that breaks the isomorphism between the closed- and open-economy monetary policy models. The paper proceeded from the benchmark of assuming that the central bank can solve a pre-commitment policy problem. However, if the central bank cannot commit to that policy and thus acts in discretion, this creates too much stabilization on the central bank’s part. Such a stabilization bias manifested itself in the form of greater uncertainty around the macroeconomic variables in the model. The bias is also measured as a larger loss in terms of the social loss function. A possible solution, as was proposed by Woodford (1999), is to hire a central banker whose preferences include interest-rate smoothing even though this is not shared by society’s preferences. It was shown in the paper that allowing for interest-rate smoothing under discretion results in a difference rule for the interest rate. That is, optimal (discretionary) policy in such a case involves setting the change in interest rate in response to CPI inflation and output gap. The reason for having an interest-rate smoothing central banker is that it tends to introduce intrinsic inertia into the interest rate process, thus approximating the desired commitment policy. We showed analytically that the effect of this is to force history dependence in policy decisions under discretion, and that this acts to soften the equilibrium endogenous monetary policy trade-off. This result was verified in various numerical examples. Finally, there is no reason to accept the assumption of a central bank committing to an ex-ante optimal policy plan without explicit modeling of incentives that enforce commitment. If so, then it may well be that observed strong and positive autocorrelation in small-open-economy nominal interest rates could be explained by an optimal social delegation of discretionary policy to an interest-rate smoothing central bank. Such a hypothesis could potentially be empirically tested. For example, the Bayesian structural estimation approach in Kam, Lees, and Liu (2008) could be used, and posterior-odds model comparisons can be made across alternative policy regimes to determine which assumption on policy regimes is more probable, given the data for each small open economy. We leave this suggestion to future explorers.