Optimal Monetary Policy with an Uncertain Cost Channel [forthcoming: Journal of Money, Credit, and Banking] Peter Tillmann1 Swiss National Bank May 21, 2009

Abstract: The cost channel of monetary transmission describes a supply side effect of interest rates on firms’ costs. Previous research has found this effect to vary, both over time and across countries. Moreover, the cyclical nature of financial frictions is likely to amplify the cost channel. This paper derives optimal monetary policy in the presence of uncertainty about the true size of the cost channel. In a minmax approach, the central bank derives an optimal policy plan to be implemented by a Taylor rule. It is shown that uncertainty about the cost channel leads to an attenuated interest rate setting behavior. In this respect, the Brainard (1967) principle of cautious policy in the face of uncertainty continues to hold in both a Bayesian and a min-max framework.

Keywords: parameter uncertainty, minmax, cost channel, optimal monetary policy, Taylor rule JEL classification: E52, E31

1

Swiss National Bank, Börsenstrasse 15, CH-8022 Zurich, [email protected].

I am grateful to the editor of this journal as well as two anonymous referees for very insightful comments. Moreover, I thank Henrik Jensen for fruitful discussions and Andreas Schabert and Michael Evers for comments on an early draft of the paper. I am indebted to seminar participants at the Universities of Bonn and Dortmund, the 2nd Oslo Workshop on Monetary Policy, and the SCE 2007 conference in Montreal for inspiring discussions. The DFG network "Quantitative Macroeconomics" provided financial support. The views expressed in this paper do not necessarily reflect those of the Swiss National Bank.

1

Introduction

Monetary policymakers typically face uncertainty about key relationships describing the economy. Uncertainty potentially disguises the true economic model that governs the economy, disturbs parameters, and introduces noise into the data series available to the policymaker. This paper focuses on the consequences of uncertainty about the supply side effect of monetary policy. Firms rely on borrowing working capital from financial intermediaries. As a consequence, credit conditions affect firms’ cost side. The impact of interest rate changes on the cost of acquiring and holding working capital is referred to as the cost channel. Recently, Ravenna and Walsh (2006) derive optimal monetary policy in the presence of a cost channel. To the extent that deregulation, financial integration, and, most importantly, the cyclical nature of financial frictions affect the credit conditions for firms, the central bank is likely to not be perfectly informed about the true size of the cost channel. Complete knowledge would require a full understanding of how commercial banks pass-through interest rate changes to their customers and how credit conditions in general change after, say, a monetary tightening. In particular, the recent banking turmoil in 2007/08, that evolved into a full-blown financial crisis, raised concerns about firms’ access to credit markets and their ability to borrow working capital to finance ongoing production. This uncertainty is relevant for interest rate setting. As an FOMC member, Evans (2007) argues that "uncertainty surrounds the impact of the change in credit conditions on real economic activity." This paper introduces uncertainty about the true size of the cost channel into the model of Ravenna and Walsh (2006). We solve for optimal discretionary monetary policy that is robust to model misspecifications drawing on the recent work on optimal monetary policy under uncertainty, e.g. Giannoni (2002), Onatski and Stock (2002), and Onatski and Williams (2003). The policymaker acts under discretion, i.e. the central bank does not internalize the effect of current actions on future expectations, and determines optimal policy before the uncertainty about the cost channel is resolved. The central bank follows a minmax approach and seeks to minimize the worst possible loss that could occur due to parameter misspecification.2 Actual policymaking appears to obey this principle. For example, Evans (2007) further explains that 2

See Hansen and Sargent (2008) for an in-depth analysis of the robust control approach to decision

making.

2

"some risks relate to ... extreme macroeconomic outcomes that are not very likely to occur, but whose cost in terms of output and inflation could be quite large. In such cases, it is prudent to adjust policy to be more or less accommodative than we otherwise would as insurance against the highly adverse outcome." This paper analyzes these normative consequences for optimal policy under cost channel uncertainty. We seek to contribute to the ongoing debate as to whether uncertainty makes interest rate setting less or more aggressive. A recent strand of the literature derives consequences of uncertainty for interest rate setting. Giannoni (2002) models uncertainty about key parameters and derives a robust minmax policy that is implemented by a simple instrument rule. His results imply that the policymaker responds more strongly to inflation than under certainty. Likewise, Stock (1999), Onatski and Stock (2002), and Onatski and Williams (2003) deduce optimal Taylor rules under uncertainty. The literature typically finds that uncertainty is likely to lead to more vigorous interest rate setting behavior. Policy no longer obeys the "Brainard principle" (Brainard, 1967), stating that multiplicative parameter uncertainty should motivate a cautious policy stance, i.e. an attenuated interest rate adjustment.3 A crucial result of the paper is that uncertainty about the cost channel can motivate an attenuated policy stance. An uncertain policymaker should overestimate the quantitative importance of the cost channel when setting interest rates. Hence, the larger the degree of uncertainty about the cost channel, the smaller the interest rate response to inflation. In this sense, the policymaker is less aggressive than under certainty. Monetary policy under multiplicative uncertainty, as in Brainard’s (1967) classical result, is generally less aggressive than under certainty while interest rate setting under minmax policy is generally more aggressive as in Giannoni (2002). The presence of a cost channel bridges these opposing views. Cost channel uncertainty attenuates interest rate adjustment even under minmax policy. Thus, the paper provides a counter-example to the conventional view about the size of the responses in a min-max versus a Bayesian policy rule. The remainder of this paper is organized as follows. Section two integrates uncertainty about the cost channel of monetary transmission into an otherwise standard New Keynesian model and derives implications for optimal minmax monetary policy under parameter uncertainty. In section three, the instrument rule that implements the 3

The results of Tetlow and von zur Mühlen (2001) show that the effect of uncertainty on interest

rate setting might be less clear-cut than the distinction between attenuation and anti-attenuation. Kimura and Kurozumi (2007) explicitly derive the cross-equation restrictions implied by parameter uncertainty. They strongly document the anti-Brainard result.

3

optimal minmax equilibrium is derived and interpreted. Section four compares the results to those obtained under a Bayesian approach to parameter uncertainty. Section five finally concludes.

2

Robust monetary policy with an uncertain cost channel

We draw on recent work of Christiano, Eichenbaum, and Evans (2005), Ravenna and Walsh (2006), and Chowdhury, Hoffmann, and Schabert (2006) by introducing costs of holding working capital into an otherwise standard general equilibrium model.4 Assume that firms have to pay their factors of production before they receive revenues from selling their products and thus need to borrow working capital from financial intermediaries. A monetary contraction, for instance, raises the interest rate charged by banks for working capital loans and eventually leads to a decline in output through an adverse supply-side effect.

2.1

The model

The model consists of households, firms, banks, and a central bank. Households and firms. Households consume goods, provide labor, and hold deposits. Firms set prices under monopolistic competition and are subject to a Calvo (1983) scheme of staggered price adjustment. The forward-looking Phillips curve (1) and the IS curve (2) represent log-linearized equilibrium conditions o n π t = βEt π t+1 + κ (σ + η) xt + δilt xt = Et xt+1 − σ −1 (it − Et π t+1 − rtn )

(1) (2)

where π t is the inflation rate, xt the output gap, it the risk-free nominal interest rate controlled by the central bank, and Et is the expectations operator. All variables are expressed in percentage deviations from their respective steady state values. The discount factor is denoted by β < 1, σ is the coefficient of relative risk aversion, η is the elasticity of labor supply, and κ, the slope coefficient of the Phillips curve, depends negatively on the degree of price stickiness and is assumed to be unknown by the central bank. Shocks to the Wicksellian natural real rate of interest are described by the autoregressive process n + εt rtn = ρrt−1

(3)

with 0 ≤ ρ < 1 and εt ∼ N (0, 1). 4

See Woodford (2003) for a deeper analysis and the complete derivation of this family of models

based on optimizing households and firms under monopolistic competition and nominal rigidities.

4

The only departure from the standard New-Keynesian model is the restriction that firms hold working capital borrowed from banks. Let Nt denote employment and Wt the nominal wage rate. Firms must borrow an amount Lt = Nt Wt from financial intermediaries at the nominal lending rate ilt in order to pay the wage bill in advance. If δ = 1, i.e. if the cost channel is present, the linearized Phillips curve (1) contains the lending rate as a driving force of firms’ costs. In the following, we set δ = 1. Banks. Suppose there is a continuum of banks of measure one that behave competitively. Banks take deposits Dt from households at the risk-free rate it and grant one-period riskless loans at a rate ilt . The bank faces unspecified costs of intermediation of Ψ (Lt ) with 1 > Ψ0 (Lt ) > 0. Costs of intermediation increase in the amount of borrowing. This could be motivated by increasingly costly monitoring efforts. The objective is to maximize profits taking it and ilt as given n o max ilt [Lt − Ψ (Lt )] − it Dt Dt

subject to the constraint Dt = Lt . Optimality requires ilt = ψit with ψ ≡

1 1−Ψ0 (Dt )

> 1.

Thus, the coefficient ψ reflects the interest rate pass-through from central bank rates to loan rates. Assume for simplicity that Ψ (Dt ) = ωDt with 1 > ω > 0. Then Ψ0 (Dt ) = ω. It

follows that 1 it (4) 1−ω Costs of financial intermediation introduce a spread between the lending rate and the ilt =

policy-controlled interest rate. Substituting (4) into (1) shows that ψ measures the effect of the risk-free interest rates on firms’ costs and, thus, the strength of the cost channel. The intermediation cost is unobservable to the central bank.5 The central banker only knows that ψ

[ψ l , ψ h ]. Thus, uncertainty about this financial friction translates

into uncertainty about the effect of the policy-controlled interest rate on firms’ cost of holding working capital. In other words, the size of the cost channel becomes uncertain. Policy. Monetary policy is assumed to set interest rates in order to minimize the welfare loss due to sticky prices which is described in terms of inflation volatility and output gap volatility weighted by the parameter λ ≥ 0 min Lt = it

¢ 1¡ 2 π t + λx2t 2

(5)

When formulating optimal policy, the policymaker does not know the true values of the parameter vector ϑ = (κ, ψ) with ϑ Θ. The only information the central bank has 5

The central bank is uncertain about the cost-function of banks. This could be because the central

bank is separated from the banking supervisory authority.

5

available is that the coefficients lie in a range of parameters. In particular, the interval from which nature draws these parameters is given by κ

[κl , κh ]

and

ψ

[ψ l , ψ h ]

where κh > κl > 0 and ψ h > ψ l > 0. Uncertainty about κ reflects imperfect information about the true degree of nominal rigidity. Uncertainty about ψ reflects the uncertain nature of financial conditions for firms that want to borrow working capital. The sources of cost channel uncertainty warrant some explanations, which are provided in the next subsection.

2.2

The uncertain size of the cost channel

Uncertainty of the central bank about the coefficient ψ can be motivated based on several empirical findings. First, empirical estimates of the cost channel vary substantially across countries as well as over time. Using the GMM estimator, Ravenna and Walsh (2006) obtain an estimate for ψ of 1.276 for the U.S. An interval of one standard error around their estimate spans a range of plausible cost channel coefficients of ψ [0.77, 1.77]. Castelnuovo (2007) employs Bayesian estimation techniques and presents a range of posteriors of [0.28, 1.78] for U.S. data. Gabriel et al. (2008), however, find a cost channel coefficient in the U.S. of only 0.33. Moreover, Chowdhury, Hoffmann, and Schabert (2006) obtain a ψ coefficient ranging from about 0.2 for France to 1.5 for Italy based on the GMM estimator.6 Two papers ask whether the cost channel can explain the price puzzle in vector autoregressive studies, i.e. the increase in inflation after a restrictive policy shock. One the one hand, Rabanal (2007) finds only limited evidence for the existence of a cost channel within a Bayesian DSGE model. However, using a very similar model enriched by an incomplete interest rate pass-through and estimated using the minimum-distance estimator, Henzel et al. (2008) support a cost channel coefficient of unity. Tillmann (2008) sheds light on the stability of the cost channel. He estimates the augmented Phillips curve given in (1) in a rolling-window regression and obtains a series of cost channel coefficients over the last 25 years. It is shown that ψ follows a U-shaped pattern. The cost channel was most important in the pre-Volcker period and less important in the Volcker-Greenspan era. Recently, however, the cost channel regained quantitative importance. Second, the spread between the loan rate faced by firms and the short-term interest rate controlled by the central bank varies over the cycle. The spread of U.S. commercial loan 6

Adolfson et al. (2007) calibrate a cost channel coefficient of unity to match the dynamics of the

Euro are business cycle within a DSGE framework.

6

rates over the federal funds rate, for example, exhibits substantial cyclical variation.7 The central bank is likely to be uncertain about the true tightness of credit market conditions. Uncertainty about the spread between loan rates and policy rates translates into uncertainty about the size of the cost channel.8 Frictions on financial markets potentially amplify the impact of interest rate movements on the cost-side of firms. In the following, we do not take a particular stand on the determinants of variation in the size of the cost channel. As a bottom line, however, it is clear that the policymaker faces uncertainty about the wedge between retail rates and policy-controlled rates and, consequently, about the true nature of the cost channel. Whatever the source, uncertainty about the cost channel might be an important factor behind actual monetary policy implementation.

2.3

A minmax approach to parameter uncertainty

In this model, the policy maker plays a zero sum game against a fictitious evil agent who sets the parameter vector such that the welfare loss is maximized. The order of events is as follows: First, the demand shock realizes and is observed by the central bank and the private sector. Second, the central bank designs the optimal policy plan while being uncertain about the parameter vector and private sector expectations are formed. Third, uncertainty is resolved. Fourth, the equilibrium inflation rate, the output gap, and the interest rate are realized. After observing the shock, the central bank commits to a policy f F before the parameter vector ϑ Θ is known. Note that this policy does not imply a commitment to an entire path of future policy. Instead, policy takes expectations of future variables as given. The class of rules F contains the feasible set of non-inertial policies, i.e. policies that do not imply interest rate inertia. The central bank wants to set policy such as to minimize the worst possible loss that can occur due to parameter perturbations. This optimal robust policy is denoted by f ∗ (ϑ∗ ) and is defined by ¾ ½ min max E [Lt (f (ϑ) , ϑ)] f F

ϑ Θ

(6)

We denote the resulting minmax equilibrium by π t (f ∗ (ϑ∗ ) , ϑ∗ ), xt (f ∗ (ϑ∗ ) , ϑ∗ ), and it (f ∗ (ϑ∗ ) , ϑ∗ ), where f ∗ (ϑ∗ ) F is the robust monetary policy plan and ϑ∗ Θ maxi7

The data is available from the Federal Reserve Survey of Terms of Business Lending under

http://www.federalreserve.gov/releases/e2/. 8 Moreover, a vast amount of literature documents the imperfect and asymmetric nature of the interest rate pass-through from policy-controlled rates to lending rates. Hofmann and Mizen (2004), de Bondt (2005), and others show this incompleteness of the pass-through. Moreover, ECB (2006) argues that not only the instantaneous pass-through differs across Euro area countries, but also the level of retail loan rates differs substantially.

7

mizes the welfare loss. This equilibrium is also known as the worst-case equilibrium. If the central bank pursues the optimal robust policy plan f ∗ (ϑ∗ ), but the concern for robustness is unwarranted because the undistorted reference model turns out to be the true model, the outcome is referred to as the approximating equilibrium. This is denoted by π t (f ∗ (ϑ∗ ) , ϑ), xt (f ∗ (ϑ∗ ) , ϑ), and it (f ∗ (ϑ∗ ) , ϑ). The steps towards the solution are the following: First, derive the policy plan f (ϑ) that is optimal for a given parameter vector ϑ. Second, find the parameter vector ϑ∗ that does maximum damage to the representative agent’s utility. Finally, choose an optimal instrument rule that implements the resulting equilibrium π t (f ∗ (ϑ∗ ) , ϑ∗ ), xt (f ∗ (ϑ∗ ) , ϑ∗ ) and it (f ∗ (ϑ∗ ) , ϑ∗ ).

2.4

Deriving optimal policy

The central bank’s task is to derive the optimal policy plan f (ϑ) and the corresponding optimal instrument rule to implement this plan. To solve this problem, we will compute the optimal policy given the central bank’s reference parameter set. Given this policy, we then determine the parameter set that maximizes the welfare loss. We know that an optimal non-inertial policy plan links output and inflation as follows xt = −f (ϑ) π t

(7)

where f (ϑ) > 0 is a function of the model parameters. Given the policy plan, the output variance is therefore given by var(xt ) = f 2 (ϑ) var(π t )

(8)

We analyze discretionary policy which takes expectations about future variables as given. Setting all expectation terms to zero, the IS curve therefore implies it = −σxt + rtn , which can be inserted into the inflation adjustment equation (1) to obtain ∙ ¸2 κψ var(rtn ) var (π t ) = (1 + κf (ϑ) (σ + η) − κσf (ϑ) ψ)

(9)

Hence, the objective function can be compactly written as a function of the policy plan f (ϑ)

¸2 ¤ £ κψ (10) 1 + λf 2 (ϑ) var(rtn ) Lt = 1 + κf (ϑ) (σ + η) − κσf (ϑ) ψ A robust control approach to policy under model uncertainty as advocated in Hansen ∙

and Sargent (2008) focuses on the maximum loss for a given policy f (ϑ). In a first step, we determine f (ϑ). Given the parameter vector ϑ, the central banker formulates optimal policy by minimizing the welfare loss ½ ¾ ¢ ¡ κ2 ψ 2 2 min 1 + λf (ϑ) f (1 + κf (ϑ) (σ + η) − κσf (ϑ) ψ)2 8

(11)

The first order condition is given by f ∗ (ϑ) = f ∗ (κ, ψ) κ [σ (1 − ψ) + η] = λ

(12)

where f ∗ (κ, ψ) is the optimal non-inertial policy plan that minimizes the welfare loss.9 The parameterization chosen below guarantees that f ∗ (κ, ψ) > 0. If ψ = 0, the plan collapses to the standard optimality condition for discretionary monetary policy. The second step pertains to the determination of the worst-case parameter constellation. The central bank faces uncertainty about the true realization of the cost channel coefficient ψ and the slope coefficient κ. Given a particular policy f ∗ , the central bank must find the worst-case realization which optimal robust policy wants to account for. The decision maker solves the problem ½ ¾ ¡ ¢ κ2 ψ 2 ∗2 1 + λf max κ,ψ (1 + κ (σ + η) f ∗ (ϑ) − ψκσf ∗ (ϑ))2

(13)

Proposition 1 If the policy maker is uncertain about κ and ψ, a robust policy should be based on κ = κh and ψ = ψ h . Proof. (i) The first order condition for the choice of κ is given by ¡ ¢ 2κψ 2 1 + λf ∗2 ∂Lt = ∂κ (1 + κ (σ + η) f ∗ (ϑ) − ψκσf ∗ (ϑ))3 For all parameter values, ∂Lt /∂κ > 0. Let κ∗ be the value of κ that maximizes (13). It follows that κ∗ = κh . (ii) The first order condition for the choice of ψ is given by ¡ ¢ 2κ2 ψ 1 + λf ∗2 (1 + κ (σ + η) f ∗ (ϑ)) ∂Lt = >0 ∂ψ (1 + κ (σ + η) f ∗ (ϑ) − ψκσf ∗ (ϑ))3 For any value of f ∗ (ϑ) considered in this paper, ∂Lt /∂ψ > 0. Let ψ ∗ be the value of ψ that maximizes (13). It follows that ψ ∗ = ψ h . The worst case beliefs of the central bank are therefore given by ϑ∗ = (κ∗ , ψ ∗ ) = (κh , ψ h ). This is the parameter perturbation that the central bank considers the worst possible misspecification against which policy should shield the economy. In order to stabilize demand shocks, the central bank must contract the economy. If κ is high, the required output adjustment has large inflationary consequences. An ambiguity-averse central banker should deliberately overestimate the true size of the cost channel and set policy accordingly in order to minimize the welfare consequences 9

The policy plan is identical to the one derived in Ravenna and Walsh (2006).

9

of cost channel misspecification. As in Giannoni (2002) and other papers, the worstcase parameter set corresponds to the boundaries of the constrained parameter set [κl , κh ] and [ψ l , ψ h ]. To summarize, the candidate worst-case beliefs of the central bank are given by ϑ∗ = (κ∗ , ψ ∗ ) = (κh , ψ h ) and the robust policy plan is given by f ∗ (ϑ∗ ) = f ∗ (κh , ψ h ) =

κh [σ (1 − ψ h ) + η] λ

(14)

In equilibrium, the three endogenous variables will be linear functions of the state variable rtn , a solution will have the form π t = Ωπ rtn , xt = Ωx rtn , and it = Ωi rtn . Given these relationships, the expectational terms can be calculated, e.g. Et π t+1 = Ωπ ρrtn . With the optimal plan, the equilibrium responses of output, inflation, and the interest rtn , xt (f ∗ (ϑ∗ ) , ϑ∗ ) = rate in the worst-case model are given π t (f ∗ (ϑ∗ ) , ϑ∗ ) = Ωworst π rtn , and it (f ∗ (ϑ∗ ) , ϑ∗ ) = Ωworst rtn with Ωworst x i = Ωworst π Ωworst = x Ωworst = i

κh ψ h ∗ ∗ 1 + κh (σ(1 − ψ h ) + η)f (ϑ ) + ρ (kh σψ h f ∗ (ϑ∗ ) − kh ψh −κh ψ h f ∗ (ϑ∗ ) 1 + κh (σ(1 − ψ h ) + η)f ∗ (ϑ∗ ) + ρ (kh σψ h f ∗ (ϑ∗ ) − kh ψh 1 + (σ + η) κh f ∗ (ϑ∗ ) − βρ 1 + κh (σ(1 − ψ h ) + η)f ∗ (ϑ∗ ) + ρ (kh σψ h f ∗ (ϑ∗ ) − kh ψh

− β)

(15)

− β) − β)

The respective outcomes in the approximating equilibrium are given by π t (f ∗ (ϑ∗ ) , ϑ) = rtn , xt (f ∗ (ϑ∗ ) , ϑ) = Ωappr rtn , and it (f ∗ (ϑ∗ ) , ϑ) = Ωappr rtn with Ωappr π x i = Ωappr π Ωappr = x Ωappr = i

2.5

κψ 1 + κ(σ(1 − ψ) + η)f ∗ (ϑ∗ ) + ρ (kσψf ∗ (ϑ∗ ) − kψ

− β)

(16)

−κh ψ h f ∗ (ϑ∗ ) 1 + κ(σ(1 − ψ) + η)f ∗ (ϑ∗ ) + ρ (kσψf ∗ (ϑ∗ ) − kψ − β) 1 + (σ + η) κh f ∗ (ϑ∗ ) − βρ 1 + κ(σ(1 − ψ) + η)f ∗ (ϑ∗ ) + ρ (kσψf ∗ (ϑ∗ ) − kψ − β)

The effects of uncertainty

How do equilibrium inflation, output gap, and interest rate dynamics respond to changes in parameters and, in particular, to a change in the degree of uncertainty? To gauge how the reactions to shocks given in (15) change when the potential parameter misspecification increases, we calibrate the model to the U.S. economy as follows. Ravenna and Walsh (2006) obtain an estimate for ψ of 1.276, which serves as a reference value for the cost channel coefficient in this paper. This estimate is surrounded by considerable uncertainty. An interval of two standard errors spans a range of plausible cost channel coefficients of ψ [0.28, 2.26]. With an alternative set of instruments, the authors obtain an estimate for ψ of 1.915. Our measures of ψ h are set to 1.60. Given the empirical findings in Ravenna and Walsh (2006), our worst-case ψ implies a very modest degree of uncertainty. 10

Ravenna and Walsh’s (2006) estimates further imply a value of κ = 0.10, while Christiano, Eichenbaum, and Evans (2005) find κ = 0.2. We follow Surico (2008) and set κ = 0.15. A grave misspecification of the Phillips curve is represented by κh = 0.30, which corresponds to the estimates obtained by Roberts (1995). The inverse of the real interest rate sensitivity of aggregate demand is set to σ = 1. With ρ = 0.35 the demand shock exhibits an intermediate degree of persistence as in Giannoni (2002) and Woodford (2003). Finally, setting η = 1 and λ = 0.25 follows standard practice in the literature. All parameters are summarized in table (1).

κ

κh

0.15

0.30

Table 1: Parameter values σ η ρ ψ

ψh

λ

1.00

1.60

0.25

1.00

0.35

1.276

How does the strength of interest rate adjustment depend on the degree of parameter uncertainty? coefficient is plotted in figure (1) as a function of κh and ψ h . The The resulting Ωworst i results depend on the degree of persistence in the real-rate shock. In the baseline parameterization, the interest rate adjustment after the demand shock becomes stronger as uncertainty about both parameters becomes larger. In this case, the anti-attenuation result found by Giannoni (2002) and others holds. In the case of i.i.d. shocks, see figure (2), however, the interest rate responds less to the demand shock if uncertainty about the cost channel increases and the cost channel is large enough. In this respect, the popular "Brainard principle" holds for the plausible range of ψ h . The central bank fears that interest rate steps have large inflationary consequences and, hence, refrains from aggressive stabilization. Put differently, cost channel uncertainty tends to make interest rate responses more cautions while uncertainty about the degree of price rigidity as represented by uncertainty about κ still leads the policymaker to adjust interest rates more strongly. Monetary policy under multiplicative uncertainty, as in Brainard’s (1967) classical result, is generally less aggressive than under certainty while interest rate setting under worst-case policy is generally more aggressive as in Giannoni’s (2002) paper. Here, cost channel uncertainty attenuates interest rate adjustment even under minmax policy. If the policymaker implements the optimal robust policy but the reference model turns out to be undistorted, the resulting outcome is known as the approximating model. is depicted in figure (3). Again, the central bank responds less The resulting Ωworst i aggressively to the demand shock as the desire for robustness increases. Uncertainty about the slope of the Phillips curve, however, tends to make policy more vigorous.

11

Table (2) shows that uncertainty entails a welfare loss.10 However, the policymaker can partly offset this welfare loss by pursuing an optimal robust monetary policy. Take for example a central bank that sets interest rates to minimize the worst-case outcome κh = 0.3 and ψ h = 1.60 for the case of persistent real-rate shocks. The resulting welfare loss is Lt (f (ϑ∗ ) , ϑ∗ ) = 0.626. Now consider a central bank that does not take

uncertainty into account but sets interest rates as if ϑ∗ = ϑ. The resulting welfare loss would amount to Lt (f (ϑ) , ϑ∗ ) = 0.646. Moreover, compare the case of a central bank

pursuing robust policy when the model turns out to be undistorted, i.e. Lt (f (ϑ∗ ) , ϑ),

with the case of policy under certainty. An unwarranted concern for robustness entails only a small reduction in welfare when compared to policymaking under certainty and can even improve upon the outcome under certainty. This is due to the fact that

deliberately overestimating κ reduces inflation volatility, which in turn partly resolves the stabilization bias and, hence, reduces the welfare loss of discretionary monetary policy.11

3

Implementing optimal policy with a Taylor rule

The equilibrium realizations of output, inflation and the interest rate are only a function of the current value of the demand disturbance. Following Giannoni (2002), this optimal non-inertial policy plan can be implemented by an instrument feedback rule. Importantly, the degree of uncertainty about model parameters affects the coefficients of this instrument rule. When designing optimal robust policy, the central bank commits to implementing the non-inertial policy plan f (θ) by setting the interest rate, its policy instrument, according to a simple contemporaneous interest rate rule of the form proposed by Taylor (1993).12 This rule is characterized by φπ ≥ 0 and φx ≥ 0, with it = φπ π t + φx xt

(17)

The central bank sets interest rates according to that rule in order to realize the optimal policy plan and the resulting equilibrium characterized in (15). Note that the central 10

The welfare loss in the worst case model increases sharply as the degree of uncertainty about

both coefficients increases (not shown). Furthermore, the fact that welfare deteriorates monotonically if κ∗ or ψ ∗ increases, confirms that the minmax equilibrium given in (15) is indeed a global Nash ˆ satisfying Lt (f ∗ (ϑ∗ ) , ϑ∗ ) < Lt (f ∗ (ϑ), ˆ ϑ). ˆ equilibrium, i.e. there is no ϑ 11

In the standard New Keynesian model, discretionary monetary policy results in inflation being

insufficiently stabilized. This bias, which is known as the stabilization bias of monetary policy, becomes larger if ρ increases. See Clarida, Galí, and Gertler (1999) for a discussion. 12 See Kara (2002), Giannoni (2002), Tetlow and von zur Mühlen (2001) and Onatski and Williams (2003) for similar approaches to model optimal minmax policy within a Taylor rule framework.

12

bank derives the Taylor rule implementing the optimal policy plan before uncertainty is resolved. Inserting the equilibrium responses of inflation, output, and the interest rate to the demand shock known from (15) into the Taylor rule gives the feasibility constraint = φπ Ωworst + φx Ωworst Ωworst i π x

(18)

Using (15), the optimal Taylor rule response coefficient to inflation as a function of φx and the distorted parameters can be written as 1 + (κ∗ )2 λ−1 [σ (1 − ψ∗ ) + η] (σ + η) − βρ κ∗ [σ (1 − ψ ∗ ) + η] φx + φπ = κ∗ ψ ∗ λ

(19)

for ψ > 0. Any vector Φ = (φπ , φx ) satisfying (19) implements the non-inertial minmax equilibrium described by (15). How does the interest rate response to inflation, φπ , react if the degree of uncertainty changes? Proposition 2 A central bank that is uncertain about the cost channel responds less aggressively to inflation. Proof. The derivative of φπ with respect to ψ ∗ is given by σ (k∗ )2 φx k ∗ (σ + η) σψ ∗ 1 − βρ (σ + η) f ∗ (ϑ∗ ) ∂φπ − = − − − ∂ψ ∗ λ (ψ ∗ )2 k ∗ (ψ ∗ )2 (ψ ∗ )2 This derivative is negative for all parameters considered in this paper. It follows that φπ (ψ h ) < φπ (ψ). This is a key result of this paper.13 The interest rate response to inflation within an optimal robust Taylor rule decreases when uncertainty about the cost channel of monetary transmission becomes larger. Hence, interest rate setting is attenuated under uncertainty. Therefore, uncertainty about the cost channel is one key candidate evaluated in the next section that can possibly reconcile theoretically derived coefficients (under certainty) with empirically observed behavior. Proposition 3 A central bank that is uncertain about the slope of the Phillips curve responds less aggressively to inflation. 13

This is consistent with Söderström’s (2002) result. He finds that uncertainty about the persistence

properties of inflation, in the absence of a cost channel, gives rise to more aggressive policy, while uncertainty about other parameters might dampen the policy response.

13

Proof. The derivative of φπ with respect to κ∗ is given by 1 ∂φπ φx (σ (1 − ψ ∗ ) − η) 1 − βρ + = [f ∗ (ϑ∗ ) k∗ (σ + η)] − 2 ∗ ∗ ∗ ∂κ σ (κ ) ψ (κ∗ )2 ψ ∗ If ψ ∗ approaches 1 + ησ −1 , the first and the second term become very small and £ ¡ ¢¤−1 < 0. It follows that φπ (κh ) < φπ (κ). ∂φπ /∂κ∗ = − ψ ∗ κ∗2

Figure (4) depicts φπ as a function of ψ h and κh for φx = 0.80. Apparently, a stronger concern about a misspecified cost channel dampens interest rate responses to inflation, Likewise, uncertainty about κ attenuates policy. This is a crucial difference to

Giannoni’s (2002) paper and many other contributions. Uncertainty about the cost channel leads to a less vigorous interest rate adjustment, while these papers show that uncertainty about other parameters (in the absence of a cost channel) generally leads to a more aggressive interest rate setting behavior. In this model, therefore, the Brainard (1967) conservatism principle is obeyed. Uncertainty about the transmission of monetary policy to the economy motivates a cautious policy stance. A common finding is the discrepancy between estimated Taylor rule coefficients and optimal coefficients derived from an underlying economic model. As Rudebusch (2001) forcefully argues, empirical Taylor rule coefficients suggest an attenuated interest rate response to current inflation. As noted by Rudebusch (2001), uncertainty about the slope coefficient of the Phillips curve alone cannot reconcile these numbers. We corroborate these findings here. Uncertainty about the cost channel, in addition to uncertainty about κ, reduces the Taylor rule coefficient further. For reasonable worst-case beliefs, that is, with a modest degree of cost channel uncertainty, we obtain Taylor rule coefficients that lie well in the range of empirical estimates. Thus, we can formulate a second result of this paper. A plausible amount of uncertainty about the cost channel of monetary transmission suffices to replicate actual interest rate setting behavior.14 Due to the fact that the interest rate rule is restricted to respond only to inflation and output, an indeterminacy problem could arise despite the uniqueness of the allocation given in (15). We derive the determinacy properties in the appendix. As a result, the following condition emerges Γ > φπ > 1 +

β + κh ψ h − 1 φ κh (σ + η) x

(20)

This condition corresponds to the conventional Taylor principle requiring interest rates to respond more than one-to-one to inflation. Note that, for reasonable parameters, 14

See Sack (2000) for a similar result. He finds that parameter uncertainty can account for the

observed gradualist policy stance of the Fed. Cateau (2007) also finds that an aversion to model and data-parameter uncertainty can yield an optimal Taylor rule that matches the empirical Taylor rule.

14

Γ is never binding. A cautious central bank sets interest as if ψ equals ψ h > ψ. The lower bound shifts upward the larger the degree of uncertainty, i.e. the higher ψ h . Likewise, the lower bound moves upward if κh becomes larger.

4

A Bayesian perspective

A central result of this paper is that uncertainty about κ and ψ attenuates interest rate setting under robust policy. Robust decision making is based on the assumption that the central bank is unable to formulate a probability distribution over these uncertain parameters. Instead policy takes the worst-case realizations of these parameters into account. An alternative approach to model monetary policy under uncertainty allows the central bank to be able to attach priors to alternative parameter values.15 Let us assume i.i.d. real rate shocks to simplify notation. We follow Walsh (2003a, 2003b) and assume the central bank has a prior on κ and ψ, which is subject to white noise stochastic disturbances. The degree of uncertainty is represented by the variances of these disturbances, i.e. σ2κ and σ 2ψ κ = κ ¯ + εk ¯ + εψ ψ = ψ

¡ ¢ with εk ∼ N 0, σ 2κ ¢ ¡ with εψ ∼ N 0, σ 2ψ

Monetary policy sets the instrument to maximize welfare before uncertainty is resolved. As a consequence, the central bank maximizes the expected welfare loss given in (5). The first-order conditions can be summarized by n o κ Et xt − [σ (1 − ψ) + η] π t = 0 λ

(21)

Using the model equations (1) and (2), this implies, among others, a solution for the rtn with interest rate of the form it = ΩBayes i ¢ ¡ ¡ ¢ ¢ ¡ 2 ¯ +η λ+ κ ¯ + σ 2κ (σ + η) σ 1 − ψ Bayes ³ ´i (22) h Ωi = ¯ 2 + σ2 ¯ − ψσ ¯ 2 − ψσ ¯ (σ + η) + σ 2 ψ λ + (¯ κ2 + σ 2 ) (σ + η)2 − ση ψ κ

ψ

Comparing ΩBayes with Ωappr sheds light on the role of uncertainty under a Bayesian i i

and a min-max approach, respectively. Both approaches coincide if uncertainty is ¯ = ψ = ψ. = Ωappr for σ 2ψ = σ 2κ = 0, κ ¯ = κh = κ, and ψ absent, i.e. ΩBayes h i i It is immediately apparent that a higher uncertainty about ψ attenuates the policy /∂σ2ψ < 0. Some algebra reveals that uncertainty about κ makes stance, i.e. ∂ΩBayes i 15

See Adam (2004) for a general interpretation of these approaches. He argues that robust deci-

sion theory represents the choice of a particular objective function such that Bayesian decisions are insensitive to alternative priors.

15

stabilization policy more aggressive, i.e. ∂ΩBayes /∂σ2κ > 0. If the slope of the Phillips i curve varies itself, the effect of output fluctuations on inflation is reinforced. Therefore, the central bank stabilizes output more strongly in order to prevent inflation from being affected by output gap variability. An uncertain cost channel coefficient, however, implies that the effect of interest rates on inflation is potentially magnified. As a consequence, interest rates are used less vigorously to stabilize the economy. We can therefore conclude that competing approaches to model uncertainty yield the same result: Uncertainty about the size of the cost channel calls for an attenuated interest rate policy.16

5

Conclusions

The cost channel of monetary transmission is present in many general equilibrium models of the business cycle. The size of the cost channel, however, exhibits large variation over time and across countries. As a consequence, the central bank faces uncertainty about the true role of the this transmission channel. Broadly speaking, uncertainty about the cost channel reflects uncertainty about the role of financial markets in transmitting policy shocks to the supply side of the economy. This paper derived the consequences of an uncertain supply-side transmission of policy impulses for the design of optimal monetary policy. It was shown that a central bank that performs a minmax approach under uncertainty, i.e. that sets interest rates such as to avoid particularly bad outcomes, sets interest rates less aggressively to curb inflation than under certainty. In this respect, the Brainard (1967) principle of cautious policy in the face of uncertainty continues to hold. Uncertainty affects the strength of interest rate adjustment. It remains interesting to introduce cost channel uncertainty into a fully specified Dynamic General Equilibrium framework and derive the quantitative implications from Bayesian inference, as proposed by Levin et al. (2005). A richer model with a sophisticated banking system or explicit financial frictions such as the recent work by De Fiore and Tristani (2008) and Faia (2008) would provide additional insights. We leave these issues for future research. 16

Onatski (1999) uses a backward-looking model and shows that the optimal policies under these

alternative approaches to uncertainty are not necessarily too far apart.

16

References [1] Adam, Klaus. (2004) "On the relation between robust and Bayesian decision making." Journal of Economic Dynamics and Control, 28, 2105-2117. [2] Adolfson, Malin, Stefan Laséen, Jesper Lindé, and Mattias Villani. (2007) "Bayesian estimation of an open economy DSGE model with incomplete passthrough.", Journal of International Economics, 72, 481-511. [3] Barth, Marvin J. and Valerie A. Ramey. (2001) "The cost channel of monetary transmission.", NBER Macroeconomics Annual, 16, 199-240. [4] Brainard, William. (1967) "Uncertainty and the Effectiveness of Policy.", American Economic Review, 57, 411-425. [5] Castelnuovo, Efrem. (2007) "Cost Channel and the Price Puzzle: The Role of Interest Rate Smoothing.", unpublished, University of Padua. [6] Cateau, Gino. (2007) "Monetary Policy under Model and Data-Parameter Uncertainty.", Journal of Monetary Economics, 54, 2083-2101. [7] Chowdhury, Ibrahim, Mathias Hoffmann, and Andreas Schabert. (2006) "Inflation Dynamics and the Cost Channel of Monetary Transmission.", European Economic Review, 50, 995-1016. [8] Christiano, Lawrence, Martin Eichenbaum, and Charles L. Evans. (2005) "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy.", Journal of Political Economy, 113, 1-45. [9] Clarida, Richard, Jordi Galí, and Mark Gertler. (1999) "The Science of Monetary Policy: A New Keynesian Perspective.", Journal of Economic Literature, 37, 16611707. [10] de Bondt, Gabe J. (2005) "Interest Rate Pass-Through: Empirical Results for the Euro Area.", German Economic Review, 6, 37-78. [11] De Fiore, Fiorella and Oreste Tristani. (2008) "Optimal Monetary Policy in a Model of the Credit Channel.", unpublished, European Central Bank. [12] ECB. (2006) "Differences in MFI Interest Rates Across Euro Area Countries.", European Central Bank, September 2006. [13] Evans, Charles L. (2007) "Current Economic Outlook.", Speech by Charles L. Evans, President of the Federal Reserve Bank of Chicago at the University of Chicago Graduate School of Business, October 22, 2007. 17

[14] Faia, Ester. (2008): "Optimal Monetary Policy with Credit Augmented Liquidity Cycles.", unpublished, Goethe University Frankfurt. [15] Gabriel, Vasco, Paul Levine, Christopher Spencer, and Bo Yang. (2008) "On the (ir)relevance of direct supply-side effects of monetary policy.", unpublished, University of Surrey. [16] Giannoni, Marc P. (2002) "Does Model Uncertainty Justify Caution? Robust Optimal Monetary Policy in a Forward-Looking Model.", Macroeconomic Dynamics, 6, 111-144. [17] Hansen, Lars P. and Thomas J. Sargent. (2008) Robustness, Princeton: Princeton University Press. [18] Henzel, Steffen, Oliver Hülsewig, Eric Mayer, and Timo Wollmershäuser. (2008) "The price puzzle revisited: Can the cost channel explain a rise in inflation after a monetary policy shock?", forthcoming, Journal of Macroeconomics. [19] Hofmann, Boris and Paul Mizen. (2004) "Interest Rate Pass-Through and Monetary Transmission:

Evidence from Individual Financial Institutions’ Retail

Rates.", Economica, 71, 99-123. [20] Kara, Hakan. (2002) "Robust Targeting Rules for Monetary Policy.", unpublished, Central Bank of Turkey. [21] Kimura, Takeshi and Takushi Kurozumi. (2007) "Optimal monetary policy in a micro-founded model with parameter uncertainty.", Journal of Economic Dynamics and Control, 31, 399-431. [22] Levin, Andrew T. and John C. Williams. (2003) "Parameter Uncertainty and the Central Bank’s Objective Function.", unpublished, Federal Reserve Bank of San Francisco. [23] Levin, Andrew T., Alexei Onatski, John Williams, and Noah Williams. (2006) "Monetary Policy Under Uncertainty in Micro-Founded Macroeconometric Models.", NBER Macroeconomics Annual 2005, 229-287, 2006. [24] Onatski, Alexei. (1999) "Minimax analysis of model uncertainty: comparison to Bayesian approach, worst possible economies, and optimal robust monetary policy.", unpublished, Columbia University. [25] Onatski, Alexei and John H. Stock. (2002) "Robust Monetary Policy Under Model Uncertainty in a Small Model of the U.S. Economy.", Macroeconomic Dynamics, 6, 85-110. 18

[26] Onatski, Alexei and Noah Williams. (2003) "Modelling Model Uncertainty.", Journal of the European Economic Association, 1, 1087-1122. [27] Rabanal, Pau. (2007) "Does inflation increase after a monetary policy tightening? Answers based on an estimated DSGE model.", Journal of Economic Dynamics and Control, 31, 906-937. [28] Ravenna, Federico and Carl E. Walsh. (2006) "Optimal Monetary Policy with the Cost Channel.", Journal of Monetary Economics, 53, 199-216. [29] Roberts, John M. (1995) "New Keynesian Economics and the Phillips Curve.", Journal of Money, Credit, and Banking, 27, 975-984. [30] Rudebusch, Glenn D. (2001) "Is the Fed too timid? Monetary policy in an uncertain world", The Review of Economics and Statistics, 83, 203-217. [31] Sack, Brian. (2000) "Does the Fed act gradually? A VAR analysis.", Journal of Monetary Economics, 46, 229-256. [32] Söderström, Ulf. (2002) "Monetary Policy with Uncertain Parameters.", Scandinavian Journal of Economics, 104, 125-145. [33] Stock, John H. (1999) "Comment.", In Monetary Policy Rules, edited by John B. Taylor, Chicago: The University of Chicago Press. [34] Surico, Paolo. (2008) "The Cost Channel of Monetary Policy and Indeterminacy.", Macroeconomic Dynamics, 12, 724-735. [35] Taylor, John B. (1993) "Discretion vs Policy Rules in Practice.", CarnegieRochester Conference Series on Public Policy, 39, 195-214. [36] Tetlow, Robert J. and Peter von zur Mühlen. (2001): "Robust monetary policy with misspecified models: Does model uncertainty always call for attenuated policy?", Journal of Economic Dynamics and Control, 25, 911-949. [37] Tillmann, Peter. (2008) "The Time-Varying Cost Channel of Monetary Transmission.", forthcoming, Journal of International Money and Finance. [38] Walsh, Carl E. (2003a) Monetary Theory and Policy., Cambridge: MIT Press: [39] Walsh, Carl E. (2003b) "Implications of a Changing Economic Structure for the Strategy of Monetary Policy.", In Monetary Policy and Uncertainty: Adapting to a Changing Economy, Symposium sponsored by the Federal Reserve Bank of Kansas City. 19

[40] Woodford, Michael. (2001) "The Taylor Rule and Optimal Monetary Policy.", American Economic Review, 91, 232-237. [41] Woodford, Michael. (2003) Interest and Prices., Princeton: Princeton University Press.

20

6

Appendix: Determinacy properties

We can substitute the instrument rule (17) into equations (1) and (2) and rearrange the resulting system of equations to obtain " # # " Et xt+1 xt 1 = A + Brtn χ πt Et π t+1 where χ = σ + φx + φπ κ (σ (1 − ψ) + η) and " # σ (1 − κψφπ ) 1 − φπ (β + κψ) A= κσ (σ + η + ψφx ) β (σ + φx ) + κ (σ + η) + κψφx The precise form of B is irrelevant for the stability analysis. In order to ensure determinacy, both eigenvalues of A must lie inside the unit circle. The characteristic polynomial is X 2 + a1 X + a0 , where a1 = −tr(A) χ1 and a0 =

1 χ2

det(A). Here,

σ − κσψφπ + β (σ + φx ) + κ (σ + η) + κψφx σ + φx + φπ κ (σ (1 − ψ) + η) βσ σ + φx + φπ κ (σ (1 − ψ) + η)

a1 = − a0 =

Both eigenvalues are inside the unit circle if and only if both of the following conditions hold (Schur-Cohn criterion) |a0 | < 1

(23)

|a1 | < 1 + a0

(24)

Condition (23) implies the inequality σ (β − 1) < φx + φπ κ (σ (1 − ψ) + η), which is satisfied since β < 1 and (σ (1 − ψ) + η) > 0.

For σ − κσψφπ + β (σ + φx ) + κ (σ + η) + κψφx > 0, condition (24) implies φπ > 1 +

β − 1 + κψ φ κ (σ + η) x

(25)

The threshold on the left hand side of (25) moves upward as ψ = ψ h increases, i.e. as the central bank becomes more uncertain. Moreover, the threshold shifts upward if κh becomes larger. For ψ = 0, this condition collapses to Woodford’s (2001) version of the Taylor principle for the consensus forward-looking model. Under the benchmark parameterization, this condition requires φπ > 1.63. To compare this number to estimates from the data, is is important to note that empirical studies often use annualized rates to estimate φπ and φx . Hence, the derivation of these theoretical thresholds for uniqueness should be based on φx /4 instead of φx . This would lower the determinacy threshold for φπ . See Woodford (2003, p. 245) for this issue. 21

¢ ¡ Note that the condition σ − κσψφπ + β σ + 14 φx + κ (σ + η) + κψφx > 0 imposes an upper bound on the inflation response coefficient. It can be written as φπ <

φx (κψ + β) + κ (σ + η) + σ (1 + β) σκψ

Under the benchmark parameterization, this threshold equals 7.84.

22

1.5

interest rate response

1.4

1.3

1.2

1.1

1 1.6

0.3 0.25

1.4 1.2

0.15

1

0.2

0.1 0.8

worst case ψ

0.05

worst case κ

Figure 1: Interest rate response to real-rate shock as a function of kh and ψ h in the worst-case model

23

1.35

interest rate response

1.3 1.25 1.2 1.15 1.1 1.05 1 1.6

0.3 1.4 1.2 1 0.8

0.05

0.1

worst case ψ

0.15

0.25

0.2

worst case κ

Figure 2: Interest rate response to real-rate shock as a function of kh and ψ h in the worst-case model for ρ = 0

interest rate response

1.3

1.25

1.2

1.15

1.1 0.3

0.8 1

0.25 0.2

1.2 0.15

1.4

0.1 0.05

worst case κ

1.6

worst case ψ

Figure 3: Interest rate response to real-rate shock as a function of kh and ψ h in the approximating model

24

18

inflation coefficient

16 14 12 10 8 6 4 2 0.8 1 1.2 1.4 1.6

0.3

0.25

0.2

0.15

0.1

0.05

worst case κ

worst case ψ

Figure 4: Optimal inflation response coefficient φπ of a robust Taylor rule as a function of κh and ψ h

25

Table 2: Welfare loss under different policy scenarios welfare loss ρ = 0.35 var (π t ) κ = 0.15, ψ = 1.276

var (xt )

ρ = 0.00 L

var (π t )

var (xt )

L

0.087

0.033

0.006

0.035

certainty: Lt (f (ϑ) , ϑ)

0.083

0.016

non robust policy, distorted model: Lt (f (ϑ) , ϑ∗ )

κh = 0.30, ψ h = 1.60

0.615

0.119

0.646

0.208

0.040

0.218

κh = 0.30, ψ h = 1.40

0.417

0.081

0.437

0.151

0.029

0.159

κh = 0.20, ψ h = 1.40

0.185

0.035

0.194

0.071

0.013

0.074

κh = 0.30, ψ h = 1.276

0.323

0.062

0.338

0.122

0.024

0.128

robust policy, distorted model: Lt (f (ϑ∗ ) , ϑ∗ )

κh = 0.30, ψ h = 1.60

0.592

0.136

0.626

0.206

0.047

0.218

κh = 0.30, ψ h = 1.40

0.320

0.166

0.362

0.138

0.072

0.156

κh = 0.20, ψ h = 1.40

0.180

0.041

0.190

0.070

0.016

0.074

κh = 0.30, ψ h = 1.276

0.215

0.163

0.256

0.104

0.078

0.123

robust policy, undistorted model: Lt (f (ϑ∗ ) , ϑ)

κh = 0.30, ψ h = 1.60

0.081

0.019

0.086

0.033

0.008

0.035

κh = 0.30, ψ h = 1.40

0.072

0.037

0.081

0.031

0.016

0.036

κh = 0.20, ψ h = 1.40

0.081

0.019

0.086

0.033

0.008

0.035

κh = 0.30, ψ h = 1.276

0.067

0.051

0.078

0.031

0.023

0.036

26

Optimal Monetary Policy with an Uncertain Cost Channel

May 21, 2009 - bank derives an optimal policy plan to be implemented by a Taylor rule. ..... uncertainty into account but sets interest rates as if ϑ* = ϑ.

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