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Article Excerpt
IN THE RECENTLY POPULAR CLASS of dynamic stochastic general equilibrium (DSGE) models, private economic agents such as consumers and firms are often modeled as optimizing decision makers. However, central bank behavior is typically described by a reduced-form monetary policy rule rather than a set of deeper monetary policy objectives often institutionally defined. Empirical estimates obtained from reduced-form monetary policy rules are functions of both the underlying structure of the economy and policy objectives. Characterizing policy from the level of policy objectives allows one to distinguish changes in the policy rule that result from changes to structural parameters in the economy, from, changes in policy objectives.
Modeling the deeper central bank objectives enables us to empirically infer the importance a central bank places on particular institutionally defined monetary policy objectives such as inflation stabilization and output stabilization. In this paper, we apply this simple idea to a new empirical problem for small open economies. We treat the central bank as an optimizing agent, thus placing the central bank on the same footing as the other optimizing agents in the model economy. We identify the macroeconomic objectives of three of the earliest explicit small-open-economy inflation targeters--Australia, Canada, and New Zealand, over the period 1990Q1-2005Q3. We estimate the same DSGE model for each country and reverse engineer stabilization objectives that are conditioned on the structure of each economy.
Contributions. A considerable number of studies utilize loss function parameters for optimal monetary policy experiments (e.g., Rudebusch and Svensson 1999, Levin and Williams 2003, Del Negro and Schorfheide 2005). However, Dennis (2006) argues that typical loss function parameterizations may be inconsistent with the data. In particular, these yield aggressive policy rules that are inconsistent with the observed interest-rate-smoothing behavior documented in the literature (see Lowe and Ellis 1997).
This paper contributes to this debate by explicitly identifying the loss function parameters for three microfounded small open economies conditioned on historical data. In particular, we ask the questions of (i) whether our sample central banks explicitly care about stabilizing the real exchange rate and (ii) whether their policy preferences are similar overall. In doing so, our approach yields a slightly deeper insight into institutionally defined policy preferences. This is in contrast to empirical analyses (e.g., Lubik and Schorfheide 2007) that inquire into the behavioral responses of central banks. We also provide the link between our empirical analysis of uncovering what central bank preferences are and the resulting implication for policy behavior. We argue and show that it is straightforward to derive the mapping from preferences to equilibrium behavior (i.e., reduced-form policy rules) for the central banks, but the converse is not the case, if we begin the analysis from an ad hoc behavioral rule.
The results from our analysis will help inform monetary policy experiments seeking optimal policy rules for open economy inflation targeters. Estimates of macroeconomic policy objectives can potentially enhance both the transparency and accountability of the practical implementation of monetary policy. Most inflation-targeting central banks describe themselves as "flexible" in their approach to inflation targeting, implying central banks objectives embody factors beyond simply inflation. However, while central banks are often explicit about the macroeconomic variables they are concerned with, the trade-offs across these macroeconomic objectives are never elucidated. We believe transparency is enhanced by providing explicit statements of how alternative stabilization objectives are weighted (see Svensson 2005) and our analysis provides such statements.
Finally, historical estimates of stabilization objectives (conditioned on an explicit structural and microfounded model) provide a framework for central bank boards or government agencies tasked with assessing central bank performance. For example, clause 4(b) of New Zealand's 2002 Policy Targets Agreement (PTA), the agreement between the Governor of the Reserve Bank of New Zealand and the Minster of Finance, states: "In pursuing its price stability objective, the Bank shall seek to avoid unnecessary instability in output, interest rates and the exchange rate." Simply observing the unconditional volatilities of the goal variables in the PTA cannot provide an examination of monetary policy, since these volatilities are also affected by nonpolicy structural features of the economy.
Another contribution from our exercise is to provide alternative full-information Bayesian estimates on a popular class of open economy New Keynesian model parameters under the assumption of optimal monetary policy. Our Bayesian posterior estimates may be used for comparison with existing estimation strategies that condition on simple policy rules, or simply for users who wish to calibrate their models for policy simulations.
Main findings. We find that none of the central banks show a concern for stabilizing the real exchange rate. However, all three central banks share a concern for minimizing the volatility in the change in the nominal interest rate. According to our analysis, the Reserve Bank of Australia (RBA) places the most weight on minimizing the deviation of output from trend. In contrast to existing applications of Bayesian econometrics to the evaluation of DSGE models, we also compare the posterior distributions of the central banks' preference parameters. Tests of the posterior distributions of these policy preference parameters suggest that the central banks have very similar preferences.
We also show that the resulting optimal policy rule still responds to exchange rate movements, even in the case where the central banks do not explicitly care about exchange rate stabilization. We also estimate a class of simple rules, as in Lubik and Schorfheide (2007), as an alternative representative of central bank behavior, and this exercise also corroborates the exchange rate response result in the optimal policy. The former optimal rules may be comparable to the simple rules estimates. The latter, as we show, may be misleading when used in empirical exercises to infer what central banks really care about.
Related literature. Several authors report empirical estimates of the objectives of the U.S. Federal Reserve system. Salemi (1995) provides the earliest estimates based on a vector autoregressive (VAR) model. In contrast to the mandate of the Federal Reserve, Favero and Rovelli (2003), Castelnuovo and Surico (2004), and Dennis (2006) find either small or insignificant weights on output stabilization over the Volcker--Greenspan period. In addition, Ozlale (2005) and Dennis find a significant weight on interest rate smoothing in the context of aggregate empirical models without explicit optimizing firms and households. Furthermore Cecchetti, McConnell, and Perez-Quiros (2001) present cross-country estimates from a nonstructural model that has little dynamic structure. Nimark (2006) provides estimates of macroeconomic objectives for both the RBA and the Federal Reserve that suggest the RBA puts more weight on output stabilization and interest smoothing than the U.S. Federal Reserve. However, Nimark's paper uses a closed economy model that is silent on any preference for mitigating exchange rate volatility. Given Australia's degree of openness and the focus of this paper, an open economy model appears necessary to approximate the constraint the RBA faces in implementing monetary policy.
In contrast to Nimark (2006), we estimate central bank preferences for Australia, Canada, and New Zealand within an open economy DSGE model. Furthermore, the DSGE model provides an incomplete exchange rate pass-through channel in import prices such that deviations from the law of one price (or alternatively real exchange rate deviations) matter for the economies. Such a model provides a rationale for incorporating central bank preferences over exchange rate movements, as indicated in practice by New Zealand's PTA, for example.
Our DSGE model extends Monacelli (2005) by introducing endogenous persistence on both the aggregate demand and supply sides of the model and has similarities with Justiniano and Preston (Forthcoming). This feature is crucial for bringing the model closer to the data, as shown in Fukac and Pagan (Forthcoming). Thus, for example, a simpler purely forward-looking model used in Lubik and Schorfheide (2007) may be misspecified.
We use Bayesian methods to estimate the model and apply an identical prior to each of the countries in our sample. We make inferences regarding central bank preferences using Bayesian posterior distributions on the model parameters. Our Bayesian methodology closely follows related papers in the literature (see, e.g., Smets and Wouters 2003, Rabanal and Rubio-Ramirez 2005). Although we focus on policy objectives, the estimates from our DSGE model should also help inform a growing empirical open economy literature (see, e.g., Justiniano and Preston Forthcoming, Lubik and Schorfheide 2005, 2007).
The paper is organized as follows. Section 1 sets out the model. Section 2 outlines the empirical methodology and describes the data we use. Sections 3 and 4 contain our main results. We make concluding comments in Section 5.
1. THE MODEL
1.1 The Average Household
The stylized economy is similar to the open economy model in Monacelli (2005) and Justiniano and Preston (Forthcoming). The economy has identical households with a total population of measure 1. We assume the functional form for period utility
U([C.sub.t] - [H.sub.t], [N.sub.t]) = [(C.sub.t] - [H.sub.t.sup.1-sigma]] / 1 - [sigma] - [N.sup.1+[phi].sub.t] / 1 + [phi], (1)
where [C.sub.t] is an index of consumption goods, [H.sub.t] = h[C.sub.t-1] is an external habit stock, with h [member of] (0, 1) capturing the degree of habit persistence, and [N.sub.t] is labor hours. Define the prices for each differentiated home and foreign good of type i [member of] [0, 1] and j [member of] [0, 1], respectively, as [P.sub.H,t](i) and [P.sub.F,t](j). Let [B.sub.t] be an Arrow security that pays out contingent on the state of the world and [W.sub.t][N.sub.t] be the total wage income. The stochastic discount factor is [E.sub.t] [Q.sub.t,t+1] such that it will be inversely related to the gross return on a nominal riskless one-period bond, [E.sub.t][Q.sub.t,t+1] = [R.sup-1.sub.t].
The price-taking average household solves a Bellman equation problem
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
subject to the sequence of budget constraints
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
with [B.sub.0] given.
The consumption index Ct is linked to a continuum of domestic, [C.sub.H,t](i), and foreign goods, [C.sub.F,t](j), which exist on the interval of [0, 1] where
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
and
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
The elasticity of substitution between home and foreign goods is given by [eta] > and the elasticity of substitution between goods within each goods category (home and foreign) is [epsilon] > 0. Optimal allocation of the household expenditure across each good type gives rise to the demand functions
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
for all i, j [member of] [0, 1], where the aggregate price levels are defined as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
and optimal consumption demand of home and foreign goods can be derived, respectively, as
[C.sub.H,t] = (1 - [alpha]) [([P.sub.H,t]/[P.sub.t]).sup.-[eta]] [c.sub.t] [C.sub.F,t] = [alpha] [([P.sub.H,t]/[P.sub.t]).sup.-[eta]] [C.sub.t].
Substitution of these demand functions into (4) yields the consumer price index as
[P.sub.t] = [[(1 - [alpha]) [P.sup.1-[eta].sub.H,t] + [alpha][P.sup.1-[eta].sub.F,t]].sup.1/1-[eta]]. (8)
The intratemporal condition relating labor supply (the marginal rate of substitution between consumption and leisure) to the real wage (the marginal product of labor) must also be satisfied
[([C.sub.t] - [H.sub.t]).sup.[sigma]] [N.sup.[sigma].sub.t] = [W.sub.t]/[P.sub.t]. (9)
Finally, intertemporal optimality for the household decision problem must satisfy
[beta] [([C.sub.t+1] - [H.sub.t+1]/[C.sub.t] - [H.sub.t]).sup.-[sigma]] ([P.sub.t]/[P.sub.t+1]) [[mu].sub.t]([h.sup.t+1] | [h.sup.t]) = [Q.sub.t,t+1] (10)
for all dates and state t [member of] N, and [[mu].sub.t]{[h.sup.t+1] | [h.sup.t]) denotes the probability measure on the continuation history (or state, in the Markovian case), conditional on the realized history. Taking conditional expectations yields the familiar stochastic Euler equation
[beta][R.sub.t][E.sub.t] {[([C.sub.t+1] - [H.sub.t+1]/[C.sub.t] - [H.sub.t]).sup.[sigma]] ([P.sub.t]/[P.sub.t+1])} = 1.
1.2 International Risk Sharing and Relative Prices
The rest of the world, denoted by variables and parameters with an asterisk, solves a similar problem to the small open economy. Specifically, the rest of the world is the limiting case of a closed economy, where [alpha]* [right arrow] 1. First-order conditions for optimal labor supply and consumption, analogues of (9 ) and (10), also hold for the rest of the world, also hold. Given identical global preferences and complete international markets, we obtain perfect risk sharing,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
for all dates and states, and where [[??].sub.t], is the nominal exchange rate. We also define conventionally the real exchange rate as
[Q.sub.t] = [[??].sub.t][P.sup.*.sub.t]/[P.sub.t]. (12)
Assuming ex ante identical countries, and no preference shocks to the rest of the world, this implies that
[C.sub.t] - h[C.sub.t+1] = v* ([Cs.up.*.sub.t] - h[C.sup.*sub.t+1]) [Q.sup.1/[sigma].sub.t], (13)
where v* = 1 imposes ex ante symmetry of countries and zero net foreign asset holdings.
Let [c.sub.t] := ln([C.sub.t]/[C.sub.ss]), [y.sup.*.sub.t] := ln([Y.sup.*.sub.t]/ [Y.sup.*.sub.ss]) = ln([C.sup.*.sub.t]/ [C.sup.*.sub.ss]), and [q.sub.t] := ln([Q.sub.t]/[Q.sup.*.sub.t]),denote the percentage deviation of home consumption, foreign output, and real exchange rate from their respective steady states, where [X.sub.ss] is the deterministic steady...
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