Bank behavior, incomplete interest rate pass-through, and the cost channel of monetary policy transmission

Economic Modelling 26 (2009) 1310–1327

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Economic Modelling j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c m o d

Bank behavior, incomplete interest rate pass-through, and the cost channel of monetary policy transmission Oliver Hülsewig a,1, Eric Mayer b,2, Timo Wollmershäuser c,⁎ a b c

Ifo Institute for Economic Research, Poschingerstr. 5, 81679 München, Germany University of Würzburg, Department of Economics, Sanderring 2, 97070 Würzburg, Germany CESifo and Ifo Institute for Economic Research, Poschingerstr. 5, 81679 München, Germany

a r t i c l e

i n f o

Article history: Accepted 1 June 2009 JEL classification: E44 E52 Keywords: Bank behavior Cost channel Interest rate pass-through Minimum distance estimation

a b s t r a c t This paper employs a New Keynesian DSGE model to explore the role of banks within the cost channel of monetary policy transmission for shaping the interest rate pass-through from money market rates to loan rates. Banks extend loans to firms in an environment of monopolistic competition by setting their loan rates in a staggered way, which means that the adjustment of the aggregate loan rate to a monetary policy shock is sticky. We estimate the model for the euro area by adopting a minimum distance approach. Our findings exhibit that (i) financial costs are an important factor for price changes, (ii) frictions in the loan market have an effect on the propagation of monetary policy shocks as the pass-through from a change in money market rates to loan rates is incomplete, and (iii) the strength of the cost channel is mitigated as banks shelter firms from monetary policy shocks by smoothing loan rates. © 2009 Elsevier B.V. All rights reserved.

1. Introduction The cost channel assigns banks a pivotal role in the transmission of monetary policy, which stems from the notion that firms depend on credit to pre-finance production (Barth and Ramey, 2000; Ravenna and Walsh, 2006). Firms relate their price decisions to credit conditions as their marginal production costs are directly affected by interest rates. As a consequence, a monetary contraction induces upward pressure on prices by deteriorating credit conditions through higher interest rates. Christiano, Eichenbaum, and Evans (2005) and Ravenna and Walsh (2006) present a New Keynesian DSGE model that incorporates the cost channel besides the interest rate channel — i.e. the traditional aggregate demand channel — which presumes that prices decline immediately after a monetary contraction due to a pro-cyclical drop in output and unit labor costs. As the cost channel is counteracting the interest rate channel, this implies that the reaction of prices to a monetary policy shock is mitigated, while the response of output is amplified. Although, banks are embedded in this context explicitly the scope of their behavior is limited as they only act as neutral conveyors of monetary policy. This paper employs a New Keynesian DSGE model to explore the role of banks in the cost channel of monetary policy. Banks are assumed to

⁎ Corresponding author. Tel.: +49 89 9224 1406. E-mail addresses: [email protected] (O. Hülsewig), [email protected] (E. Mayer), [email protected] (T. Wollmershäuser). 1 Tel.: +49 89 9224 1689. 2 Tel.: +49 931 312948. 0264-9993/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2009.06.007

extend loans to firms in an environment of monopolistic competition by setting their loan rates as in Calvo (1983) in a staggered way. In this setup, only a fraction of banks adjust their loan rates to a change in the policy rate, while the remaining fraction leaves their loan rates unchanged, which means that the reaction of the aggregate loan rate to a monetary policy shock is sticky. This is in contrast to Christiano, Eichenbaum, and Evans (2005) and Ravenna and Walsh (2006), who focus on banks operating costlessly under perfect competition with the consequence that the loan rate always equals the policy rate. Our motivation stems from the evidence presented by Ehrmann et al. (2001), which shows for the Euro area that the degree of imperfections in the loan market is distinctive. Moreover, de Bondt (2005), de Bondt, Mojon, and Valla (2005), Hofmann and Mizen (2004), Mojon (2001) and Sander and Kleimeier (2002) document that loan rates immediately react sluggishly to a change in money market rates, which implies that the interest rate pass-through is limited. So far, a number of studies have shown that the cost channel is empirically relevant. For the U.S., Barth and Ramey (2000) find that prices set by firms in several industries increase after a monetary contraction. Since the shift in prices occurs relative to wages this implies the existence of a cost-push shock. Likewise, Dedola and Lippi (2005) document that price changes by firms in different European countries are affected by the development of interest rates.3 For the euro area, Fabiani et al. (2006) reach similar results.

3 This finding is also supported by Gaiotti and Secchi (2006), who show for a large number of Italian firms that financial costs are a driving force for price changes.

O. Hülsewig et al. / Economic Modelling 26 (2009) 1310–1327

Christiano, Eichenbaum, and Evans (2005) conclude that the cost channel in the U.S. matters for the transmission of monetary policy because it contributes to explain inflation inertia, which emerges after a monetary policy shock.4 Ravenna and Walsh (2006) estimate a New Keynesian Phillips curve that explicitly incorporates the cost channel, and find that the dynamics of inflation is positively related to changes in interest rates. In a similar vein, Chowdhury, Hoffmann, and Schabert (2006) conclude that the cost channel is relevant in the U.S. and the U.K., but not in Germany and Japan, which suggests that the structure of the financial system — a market-based system versus a bank-based system — has an impact on the consequences of monetary policy actions. By contrast, Kaufmann and Scharler (2009) find in a cross region comparison between the US and the euro area that differences in the financial system are largely irrelevant to account for differences in the transmission of monetary shocks. Following Christiano, Eichenbaum, and Evans (2005) and Rotemberg and Woodford (1998), we estimate the DSGE model for the euro area by using a minimum distance approach, which consists of two steps. In the first step, we specify a VAR model to generate empirical impulse responses to a monetary policy shock. In the second step, we estimate the model parameters by matching the theoretical impulse responses as closely as possible to the empirical impulse responses. Our results exhibit that (i) price decisions by firms are affected by loan rates, (ii) frictions on the loan market play an important role in the propagation of monetary policy shocks as the immediate pass-through from a change in money market rates to loan rates is incomplete, and (iii) the cost channel contributes to generate an inertial response of inflation to a monetary policy shock, but its effect is mitigated because of a disproportionate adjustment of loan rates to changing money market rates. Overall, our results imply that the strength of the cost channel is mitigated since banks refrain from transmitting monetary policy shocks neutrally. Although, firms base their price decisions on credit conditions, the impact on inflation dynamics arising through a change in loan rates is partly suspended by an incomplete interest rate passthrough. The paper is structured as follows. In Section 2, the DSGE model is set out. Section 3 presents the empirical results that are obtained from the minimum distance estimation. In Section 4, the implications for the cost channel of monetary policy arising through an incomplete loan rate pass-through is discussed. Section 5 summarizes the main findings and concludes. 2. The model We employ a New Keynesian DSGE model that consists of firms, households and banks. Firms are partitioned into final good producers and a continuum of intermediate good producers, which each produce a differentiated type of good by using capital and labor services. Intermediate good producers have some monopoly power over prices that are set in a staggered way as in Calvo (1983). Households obtain utility from consumption and leisure, they supply a differentiated type of labor, own the capital stock and make investment decisions. They decide on their wages, which are also set in a staggered way. Finally, banks extent loans to firms in an environment of monopolistic competition. They face frictions when changing their loan rates, which implies that the aggregate loan rate reacts stickily to a monetary policy shock. The model builds on the framework of Christiano, Eichenbaum, and Evans (2005), Smets and Wouters (2003), Galí, Gertler, and

4 Moreover, Christiano, Eichenbaum, and Evans (2005) find that the cost channel contributes to assessing the average duration of price contracts. In a model with the cost channel they obtain an average price duration of 2.5 quarters, while the exclusion of the cost channel leads to an average duration of price contracts equal to 2.5 years, which appears implausible in the light of available microeconomic evidence (see e.g. Bils and Klenow, 2004).

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López-Salido (2001) and Erceg, Henderson, and Levin (2000) by sharing the same kind of nominal and real rigidities. Following Rabanal (2007) we account for a cost channel by assuming that a fraction of firms require loans from banks as they are obliged to pay their wage bill in advance of selling their product. An addition is the inclusion of a limited interest rate pass-through.5 2.1. Final good producers Final good producers operate under perfect competition. The technology to produce the aggregate final good is given by: Z Yt =



−1
−1
ðiÞdi ;

1

ð1Þ

Yt

0

where Yt is the final good, Yt(i) are the intermediate goods indexed by i ∈ [0, 1], and
N 1 is the elasticity of substitution between the different types of goods. Profit maximization by the final good producers leads to the following demand equation for each intermediate good: 

 Pt ðiÞ −
Yt ; for all ia½0; 1; ð2Þ Pt hR i1 −1
1 is the price of the final good and Pt(i) is where Pt = 0 Pt1 −
ðiÞdi

Yt ðiÞ =

the price of the intermediate goods. 2.2. Intermediate good producers Firms indexed by i ∈ [0, 1] operate in an environment of monopolistic competition. Each firm i has access to the technology: α

Yt ðiÞ = K˜ t ðiÞNt

1− α

ðiÞ;

ð3Þ

where K̃t(i) denotes capital services, which is the effective utilization of the capital stock given by: K̃t(i) = utKt − 1(i), with ut describing the capital utilization rate, Nt(i) denotes labor services and α is the capital share of output. Nominal profits by firm i are given by: firm

Πt

firm

ðiÞ = Pt ðiÞYt ðiÞ − Q t

ðiÞ;

ð4Þ

where Q firm t (i) denote nominal production costs. The firm rents effective capital input in a perfectly competitive market and chooses a composite labor input. For the mass of firms i ∈ [0, ν], which are required to take up loans Lt(i) from banks to pay their wage bill Wt Nt(i), nominal production costs are determined by: Q firm (i) =R Lt Wt Nt(i) +R KtK̃t(i), where the t wage index Wt, the gross loan rate R Lt and the rental rate of capital R Kt are taken as given. For the remaining mass of firms nominal production costs are given by: Q firm (i) =Wt Nt(i) +R Kt Kt̃ (i). Loan repayment by t firms occurs at the end of each period. Firm i ∈ [0, ν] holds a loan portfolio, which is diversified over all types of loans k offered by banks that are aggregated the following way: Z Lt ðiÞ =

1 f−1 0

Lt

f

 f f−1 ði; kÞdk ;

ð5Þ

where Lt(i) denotes the demand for loans by firm i, which is equal to the wage bill Wt Nt(i), and ζ N 1 is the elasticity of substitution between the different types of loans k. Each firm obtains the optimal mix of

5 As the theoretical framework surrounding the cost channel usually neglects problems arising from informational frictions (see e.g. Christiano et al., 2005), we refrain from considering any problems arising from possible loan default.

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differentiated loans by choosing its loan demand schedules. Aggregating across all firms gives the demand for loans of type k: Lt ðkÞ =

!−f L Rt ðkÞ Lt ; RLt

ð6Þ

where Lt(k) =∫01Lit(k)di denotes the demand for loans of type k, Lt =∫ 1 0 hR i 1 Lt(i)di is the aggregate loan volume, RLt = 01 RLt ðkÞ1 − f dk 1 − f is the aggregate gross loan rate and RLt (k) denotes the gross loan rate of loan type k. Firms have some market power for their own product. They maximize expected profits using a stochastic discount factor Λ t,t + l that is equal to the intertemporal marginal rate of substitution of a representative household. Profits are distributed to households at the end of each period. We assume that firms make all their decisions prior to the realization of any time t disturbances.6 Firms face price frictions as in Calvo (1983), which implies a staggered price setting. The price level Pt is determined in each period as a weighted average of a fraction of firms 1 −θp that resets their prices and a fraction of firms θp that leaves their prices unchanged: Pt =

  1  1 −
1−
1−
1− θp Pt4 + θp ðPt − 1 Þ ;

ð7Þ

where P ⁎t is the reset price. Firms that reset their prices are further decomposed into a fraction 1 − ωp that re-optimize their prices and a fraction ωp that set their prices by applying an indexation rule to past inflation (Galí et al., 2001). Profit maximization by firms that are allowed to set their price optimally leads to the following first-order condition: Et − 1

∞ X

l

θ Λ t;t

h

+ l Yt + l ðiÞ

l=0

f

Pt ðiÞ −


P
−1 t

i

+ l ut + l ðiÞ

= 0;

ð8Þ

where P tf (i) is the optimal price, Et − 1 denotes the expectation operator, conditional on the set of information available at time t − 1, and φt(i) are real marginal costs that are given by: 8 ! !1 − α K α L > R t Wt > > 1 Rt > for ia½0; m > < Φ Pt Pt ; ut ðiÞ = !  > K α > Wt 1 − α > > 1 Rt > for iam; 1 :Φ P Pt t

ð9Þ

with Φ = α α(1 − α)1 − α. The optimal price is related to the expected real marginal costs, i.e. P tf(i) is a mark-up over the weighted expected real marginal costs. Finally, the fraction of firms ωp that reset their prices in each period by adopting an indexation rule to past inflation, are assumed to set their prices as in Galí, Gertler, and López-Salido (2001) according to: P tb= P ⁎t − 1(Pt − 1/Pt − 2), which implies that the evolution of reset prices is given by: P ⁎t = (P tf)1 − ωp(P tb)ωp.

There is a continuum of households indexed by j ∈ [0, 1]. Household j maximizes its expected lifetime utility: ∞ X

l

β Ut

+ l ð jÞ;

1 + η

Ut ð jÞ =

ðCt ð jÞ− Ht Þ1 − σ N ð jÞ ; − t 1+η 1− σ

ð10Þ

l=0

6 This implies that the decisions made by firms at time t are predetermined, which is consistent with the identification restrictions of the empirical VAR model considered in the next Section in which output and inflation are prevented from responding contemporaneously to a monetary policy shock.

ð11Þ

where Ct(j) denotes consumption expenditures, σ is the coefficient of relative risk aversion, Nt(j) denotes labor supply and η is the elasticity of marginal disutility of labor. Ht describes external habits, which depend positively on consumption of the aggregate household sector in period t − 1, Ht = hCt − 1. Household j maximizes its expected lifetime utility subject to the intertemporal budget constraint: h i Pt Ct ð jÞ + Pt It ð jÞ + dt ð jÞ = Wt ð jÞNt ð jÞ + RKt ut ð jÞ − Pt Wðut ð jÞÞ Kt − 1 ð jÞ + Rdt − 1 dt − 1 ð jÞ + Divt ð jÞ:

ð12Þ Every household decides on consumption Ct( j) and investment It( j) expenditures, holds deposits Dt( j) offered by banks at the gross deposit rate RtD and receives income from supplying labor Wt( j)Nt( j), from renting capital services to firms, which is equal to the return on the capital stock R Ktut( j)Kt − 1( j) net of the costs arising from changes in the degree of capital utilization PtΨ(ut( j))Kt − 1( j), and from obtaining dividends Divt( j) from firms and banks that are distributed at the end of each period. Since capital is predetermined at the beginning of the period, the income from renting out capital services depends on the level of capital Kt − 1( j), which was installed at the end of the last period, and the capital utilization rate ut( j). The costs of capital utilization are assumed to equal zero when the capital utilization rate is one, i.e. Ψ(1)=0 (Smets and Wouters, 2003). The capital accumulation equation is described by:    It ð j Þ Kt ð jÞ = ð1 − δÞKt − 1 ð jÞ + 1 − S It ð jÞ; It − 1 ð jÞ

ð13Þ

where δ denotes the capital depreciation rate. The evolution of the capital stock accounts for the existence of capital adjustment costs that are introduced through the function S(·), which is increasing and convex. In ̅ ̅ 0 (Christiano et al., 2005). steady state it holds that S ̅ =S ′=0 and S ″N We assume that every household faces the same initial conditions and that the state contingent claims markets are complete. This ensures a symmetric equilibrium for all control variables except for Wt(j), which allows us to drop the index j except for the wage and the labor demanded at that wage. Moreover, we assume that households make all their decisions — similar to firms — prior to the realization of any time t disturbances. 2.3.1. Consumption and savings decision Maximizing the objective function (10) subject to the intertemporal budget constraint (12) with respect to consumption and savings delivers the well-known first-order conditions: λt = ðCt −hCt − 1 Þ

2.3. Households

Et − 1

where Et − 1 is the expectation operator, conditional on the information set available at time t − 1, and β ∈ (0, 1) is a discount factor. Period utility of household j is described by:

−σ

" λt = βEt − 1

# Rdt Pt λt + 1 ; Pt + 1

ð14Þ

ð15Þ

where λt is the Lagrange multiplier associated with the intertemporal budget constraint that equals marginal utility of consumption. 2.3.2. Staggered wage setting Following Erceg, Henderson, and Levin (2000), we assume that households set their wages in a staggered way at random intervals. Only a fraction of households 1 − θw resets their nominal wages in

O. Hülsewig et al. / Economic Modelling 26 (2009) 1310–1327

each period, while the remaining fraction θw leaves their nominal wages unchanged. The aggregate nominal wage satisfies:

 Wt ð jÞ − η Nt ; Wt 

where Nt =

R1 0

ð17Þ

η −η 1 hR i1 −1 η η−1 Nt η ð jÞdj denotes aggregate labor, Wt = 01 Wt1 − η ð jÞdj

is the aggregate nominal wage. The first-order condition associated with the maximization problem is: Et − 1

∞ X l=0

ð23Þ

ð16Þ

where Wt⁎ is the newly set wage. Households that reset their wages in each period are further decomposed into a fraction 1 − ωw that reoptimize their nominal wages and a fraction ωw that adjust their nominal wages by applying an indexation rule to past inflation. Optimizing households choose their wages so as to maximize their objective function subject to the intertemporal budget constraint and the demand for their type of labor, which is given by: 

For each bank the balance sheet constraint is: Lt ðkÞ = dt ðkÞ + Bt ðkÞ;

  1  1 − / 1−/ 1−/ + θw Wt − 1 ; Wt = ð1 −θw Þ Wt4

Nt ð j Þ =

1313

# / Wtf ð jÞλt + l η = 0; N ðβθw Þ Nt + l ð jÞ ð jÞ − /−1 t+l Pt + l

which relates the loan volume to the level of deposits and the net position on the money market.8 Deposits and money market credits are assumed to represent perfect substitutes for refinancing, which implies that the deposit rate always equals the money market rate, i.e. M RD t = R t (Freixas and Rochet, 1997). Bank k maximizes profits Eq. (22) subject to the balance sheet constraint (23) and the downward sloped loan demand Eq. (6). In a flexible loan market, each bank would set its loan rate R L,flex (k) as a t mark-up over nominal marginal costs: R L;flex ðkÞ = f −f 1 RM t t . Since banks are exposed to identical marginal costs it holds that: RL,flex (k) =R L,flex . t t However, banks face frictions when setting their loan rates. Following Calvo (1983), we assume that only a fraction of banks 1 −τ re-optimizes their loan rates in each period, while the remaining fraction τ keeps their loan rates unchanged. Profit maximization by the banks that are allowed to set their loan rates optimally leads to the following first-order condition:

"

l

ð18Þ

Et

∞ X

l

τ Λ t;t

 L Rt 4 ðkÞ −

+ l Lt + l ðkÞ

l=0

 f M R t + l = 0; f−1

ð24Þ

where W tf(j) denotes the optimal nominal wage. Households that reset their nominal wages by adopting an indexation rule to past inflation are assumed to set their wages according to: W bt=W t⁎− 1(Pt − 1/Pt − 2). The dynamics of newly set wages is then given by: W ⁎t = (Wtf )1 − ωw(W bt)ω w.

where R tL⁎(k) is the optimal loan rate and Λ t,t + l is the stochastic discount factor. Using the loan demand Eq. (6) and solving Eq. (24) for the optimal loan rate gives:

2.3.3. Capital and investment decision The first-order conditions for the real shadow value of capital, investment and the choice of capital utilization are:

L Rt 4 ðkÞ

h Q t = Et − 1 Λ t;t

+ 1

 Qt

+ 1 ð1 −

   It Qt 1 − S + Et − 1 Λ t;t + 1 Q t It − 1    I It = 1 + Q t SV t ; It − 1 It − 1 K rt

K

δÞ + r t

+

+ 1 ut + 1

 It SV 1

+ 1

It

 − W ut

 It

+ 1

It

i + 1

; ð19Þ

2 ð20Þ

= WVðut Þ;

In the long-run the loan rate converges to a deterministic steadystate, as shown in Eq. (25), which is equal to the flexible loan market L L M equilibrium: R ðkÞ = R = f −f 1 R , where barred variables denote steady-state values. 2.5. Inference to the interest rate pass-through

Banks indexed by k ∈ [0, 1] extend loans to firms in an environment of monopolistic competition.7 Profits by bank k are given by: L

d

M

ðkÞ = Rt ðkÞLt ðkÞ − Rt dt ðkÞ − Rt Bt ðkÞ;

To gain an insight in the interest rate pass-through, we linearize the Eqs. (25) and (26) by a first-order Taylor-series expansion, which gives:

ð22Þ L

Rt = where Lt(k) is the loan volume, RtL(k) is the gross loan rate, Dt(k) is the level of deposits, RD t is the gross deposit rate, Bt(k) is the net position on the money market and R tM is the gross money market rate, which is controlled by the central bank. Profits are distributed to households at the end of each period.

We assume that banks offer differentiated loans and compete in their loan rates. The differentiation of loans may emerge from specialization in certain types of lending (e.g. small/large firms or to different sectors) or in certain geographical areas (Carletti et al., 2007).

βτ τ ð1 − βτ Þð1 − τÞ M L L E t Rt + 1 + Rt − 1 + Rt : ð27Þ 1 + βτ 2 1 + βτ 2 1 + βτ2

The evolution of the loan rate depends on the relevance of the Calvo parameter τ and the degree of monopolistic competition in the loan market ζ. To keep the analysis analytically traceable, suppose for the moment that the money market rate evolves according to: M

7

ð26Þ

ð21Þ

2.4. Banks

bank

ð25Þ

which is identical for all banks, R tL⁎(k) = R tL⁎. Banks are assumed — in contrast to firms and households — to re-optimize their loan rates in each period after the realization of any disturbances. Finally, the aggregate loan rate evolves according to:  1  1 − f  1 − f 1 − f L L L Rt = ð1− τÞ R t 4 + τ Rt − 1 :

where Qt denotes the real shadow value of installed capital, i.e. Tobin's Q, Λ t,t + l describes the stochastic discount factor given by: Λ t,t + l = βl(λt + l/λt), and rtK denotes the real rental rate of capital.

Πt

hP  f i ∞ l L M l = 0 τ Δt;t + l Rt + l Lt + l Rt + l f Et h i ; =  L f l f − 1 E P∞ t l = 0 τ Δt;t + l Rt + l Lt + l

Rt = R

M

M

+ ut ;

ð28Þ

8 Notice that Bt(k) can either be positive or negative depending on whether the bank borrows or lends on net on the interbank money market.

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O. Hülsewig et al. / Economic Modelling 26 (2009) 1310–1327

9 where uM t is an uncorrelated white-noise monetary policy shock. Eqs. (27) and (28) form a system of expectational difference equations, whose minimum state variable (MSV) solution (McCallum, 1983) has the following error-correction representation:10

L

ΔRt = ð1 − τ Þð1 − βτ Þ  − ð1 − τÞ βτ

f M ΔR f−1 t

ð29Þ

 M f f L M Rt − 1 : R + Rt − 1 − ð1 − βτ Þ f−1 f−1

This type of representation corresponds to an Autoregressive Distributed Lag (ADL) model in which the immediate pass-through — that refers to the pass-through in the period when the monetary policy shock hits the banking industry — is depicted by the first coefficient on the right-hand-side, f ðf; τÞ = ð1 − τÞð1 − βτ Þ f −f 1, whereas the longrun pass-through is defined by the last coefficient in brackets, gðζ; τ Þ = ð1 − βτ Þ ζ −ζ 1. For both dimensions of the pass-through, the degree of loan rate stickiness τ and the degree of monopolistic competition operate in opposite directions. While τ ∈ [0; 1[ implies an incomplete pass-through as both, (1−τ)(1−βτ) and (1−βτ) are smaller than one, ζ ∈ ]1; ∞[contributes to a more-than-complete passthrough as the mark-up f −f 1 is greater than one. In principle, the error-correction representation Eq. (29) is rich enough to accommodate parameter constellations that imply an incomplete, complete, or more- than-complete pass-through, depending on whether f(ζ, τ) ⪋ 1 and g(ζ, τ) ⪋ 1. Solving both conditions for the elasticity of substitution yields ζ ⪌ (βτ+τ(1−βτ))− 1 for the short-run pass-through and ζ ⪌ (βτ)− 1 for the long-run pass-through. Thus, only combinations of low elasticities of substitution ζ (high degree of monopolistic competition in the banking industry) and low degrees of loan rate stickiness τ result in a more-than-complete pass-through. For the degree of interest rate pass-through two main conclusions are drawn. Concerning the impact of the Calvo parameter τ on the pass-through from changes in the money market rate to the loan rate, the following Proposition can be formulated: Proposition 2.1. Both, the immediate and the long-run pass-through of a monetary policy shock to the loan rate become more incomplete, when the fraction of banks τ that stick to last period's loan rates rises. Proof. The partial derivative of the immediate pass-through coefficient with respect to τ; fτ ðf; τÞ = f −f 1 ð2βτ − 1 − βÞ, and the partial derivative of the long-run pass-through coefficient with respect to τ; gτ ðζ; τÞ = − β ζ −ζ 1, are strictly negative for τ ∈ [0; 1[, ζ ∈ ]1; ∞[, and β ∈ ]0; 1[. □ Thus, according to Proposition 2.1, the effect of an increase in τ on the immediate pass-through is unambiguously negative. As an increasing fraction of banks τ abstains from changing the loan rate, the evolution of the loan rate will become more incomplete. If, by contrast, τ = 0, the model collapses towards a flex-price regime, where loan rates are exclusively determined by the degree of competition in the loan market as depicted by the markup f −f 1. Concerning the role of the competitive structure in the loan market for the pass-through from changes in the money market rate to the loan rate, the following Proposition can be formulated: Proposition 2.2. Both, the immediate and the long-run pass-through of a monetary policy shock to the loan rate becomes more incomplete, when the degree of monopolistic competition as measured by the markup f −f 1 decreases.

9 Notice that we introduce a reaction function of the central bank that relates the money market rate to inflation, the future expected output gap and the lagged money market rate in the later part of the paper, which allows us to present a numerical solution for the more complex relationship between the money market rate and the loan rate. 10 See Appendix A for a derivation of the MSV solution.

Proof. The partial derivative of the immediate pass-through coefficient with respect to f; ff ðf; τÞ = − ð1 − τÞð1 −2 τβÞ, and the partial derivative of ðf − 1Þ

the long-run — pass-through coefficient with respect to f; gζ ðζ ;τÞ = −1−

βτ , ðf − 1Þ2

are strictly negative for τ ∈ [0; 1[, ζ ∈ ]1; ∞[, and β ∈ ]0; 1

[. Moreover, when the elasticity of substitution between differentiated loan varieties ζ rises, the degree of monopolistic competition, and □ hence the markup f −f 1, decreases. Thus, according to Proposition 2.2, a more competitive banking industry reduces the impact of f −f 1, which is greater than one and hence contributes to a more-than-complete pass-through, on both, the immediate and the long-run pass-through coefficient. For the limiting case of τ = 0 and ζ → ∞, the interest rate pass-through becomes complete (Ravenna and Walsh, 2006), which means that the loan rate R tL always equals the money market rate R tM.11 2.6. Final goods market equilibrium The equilibrium in the final goods market is characterized by the equality of production and demand by households for consumption and investment adjusted for the resource costs attached to variable capital utilization: Yt = Ct + It + Wðut ÞKt − 1 :

ð30Þ

The market clearing conditions in the capital rental market, the loan market and the labor market require that supply equals demand at the prevailing market prices. 2.7. Model solution The solution of the model is derived by taking a log-linear approximation around the non-stochastic steady state of the economy with zero inflation. Appendix B summarizes the relevant log-linearized relationships. We close the model by specifying the reaction function of the central bank, which is described by the following log-linearized interest rate rule: M M M Rˆ t = μ 1Rˆ t − 1 + μ 2Rˆ t − 2 + ð1 − μ 1 − μ 2 Þ " # ð31Þ 3  μˆ  μ X ˆ + zM ; × π πt − s + Y Et Yˆ t + 1 + Yˆ t + 2 + μ Δ Yˆ Δ Yt t 4 s=0 2

where a variable X̂t denotes the log-linear deviation from the steady state value, Xt̂ = ln(Xt) − ln(X ̅). The parameters μ1 and μ2 capture the degree of interest rate smoothing, μπ and μŶ are the reaction coefficients with respect to the present and past inflation rate π̂t and the expected future output gap Ŷt, μΔŶ is the coefficient of the change of the output gap and zM t is the monetary policy shock. The specification of the reaction function is purely empirical, as it delivers interest dynamics that are very close to those observed in the data.12 3. Empirical results Following Christiano, Eichenbaum, and Evans (2005) and Rotemberg and Woodford (1998), we estimate the New Keynesian DSGE model for the euro area — the log-linearized relationships — by using a minimum 11 This case can be viewed as describing a market-based financial system where financial disintermediation plays a dominant role (Chowdhury et al., 2006). For bankbased systems with 1 b ζ b ∞, banks have pricing power as they supply differentiated credit varieties shaped towards the needs of their clients. 12 This specification is similar to the one chosen by Smets and Wouters (2003) and Boivin and Giannoni (2006). Instead of determining the policy rule parameters by a minimum distance estimation, we also tried to directly implement the policy rule implied by the estimated VAR model (see for example Christiano et al., 2005; Giannoni and Woodford, 2005). Such a rule, however, was very prone to indeterminacy.

O. Hülsewig et al. / Economic Modelling 26 (2009) 1310–1327

distance approach that comprises two steps. In the first step, we specify a VAR model to generate empirical impulse responses to a monetary policy shock. In the second step, we estimate the parameters of the DSGE model by matching the theoretical impulse responses as closely as possible to the empirical impulse responses. As in Boivin and Giannoni (2006), we focus on monetary policy shocks only. Obviously, more efficient estimates of the parameters could be derived by exploiting the impulse responses of the economy to additional shocks (as for example in Altig et al., 2005). However, this potential efficiency gain must be charged up against the cost of imposing further identifying assumptions that would be required. Moreover, to the extent that the model is unable to explain all the characteristics of the data, the estimation on the basis of impulse responses to a monetary shock allows us to focus the estimation on the relevant empirical characteristics of the data that we wish to highlight. In this case, the estimation approach is robust to the identification of additional shocks and to the specification of parts of the model that are not attached to the impulse response functions that we are interest in (Boivin and Giannoni, 2006, p. 453). 3.1. Empirical impulse responses We employ a VAR model for the euro area of the form: Zt = AðLÞZt − 1 + μ + εt ;

ð32Þ

where Zt is a vector of endogenous variables, A(L) describes parameter matrices, μ is a vector of constant terms and εt is a vector of error terms that are assumed to be white noise. The vector Zt comprises the variables: Zt = ðGDPt ; INFLt ; WINFLt ; CPINFLt ; RMt ; RLt Þ V; where GDPt stands for real output, INFLt for the inflation rate, WINFLt for nominal wage inflation, CPINFLt for commodity price inflation, RMt for the policy rate of the central bank, which is approximated by a shortterm money market rate, and RLt for the short-term loan rate. Following Sims (1992) we include CPINFLt as an indicator of nascent inflation in order to avoid a priori any possible problems of misspecification. The VAR model is estimated by using quarterly data over the period from 1990Q1 to 2002Q4.13 The output level is expressed in logs, while the inflation rate, nominal wage inflation, commodity price inflation and the interest rates are in percent. The vector of constant terms comprises a linear trend and a constant. Choosing a lag length of two ensures that the error terms dismiss signs of autocorrelation and conditional heteroscedasticity.14 On the basis of the VAR model (32) we generate impulse responses of the variables in Zt to a monetary policy shock, which is identified by imposing a triangular orthogonalization. The ordering of the variables implies that real output, the inflation rate, nominal wage inflation and commodity price inflation are affected by an innovation in the policy rate with a lag of one quarter, while the loan rate is affected within the same quarter. Fig. 1 displays the impulse responses of the variables to a one standard deviation monetary policy shock (0.29 percentage points). The simulation horizon covers 20 quarters. The solid lines denote impulse responses, which are calculated as the Hall mean derived from a bootstrap procedure with 2000 replications (Hall, 1994). The shaded areas are 95% Hall percentile confidence intervals of the bootstrapped impulse responses. Real output is expressed in percent terms, while all other variables are expressed in units of percentage points at an annual rate. 13 Appendix C provides a description of the data. The end of our sample period is determined by the switch to the new MFI interest rate statistic of the European Central Bank (ECB), which entails a structural break in the loan rate data. 14 We run a variety of tests for misspecification and stability, which are not reported here, but which are available upon request.

1315

The impulse responses show that real output declines by degrees following the monetary policy shock, reaching a trough after four quarters, and returns to the baseline value subsequently. The inflation rate initially increases before it falls significantly after five quarters. The primary shift of inflation reflects a price puzzle, which emerges although commodity price inflation — as an indicator of nascent inflation — is explicitly incorporated. The inflation rate reaches a trough after around eight quarters before it gradually reverts to baseline. Nominal wage inflation declines slowly following the monetary policy shock, getting to a trough after four quarters, and returns to the baseline value subsequently. Commodity price inflation drops instantaneously and recovers afterwards. The money market rate initially increases, then declines temporally and returns to the baseline value subsequently. The loan rate follows a similar pattern as the money market rate, but the reaction is less pronounced. The immediate response of the loan rate is significantly lower than the impulse coming from the money market rate. Thus, the immediate pass-through from shortterm money market rates to short-term loan rates is incomplete and amounts to 48%. Empirical findings by de Bondt (2005), de Bondt, Mojon, and Valla (2005), Hofmann and Mizen (2004), Mojon (2001), Sander and Kleimeier (2002) and Toolsema, Sturm, and de Haan (2001) are consistent with this result by documenting that changes in money market rates are not fully reflected in short-term loan rates after one to three months. Overall, the immediate pass-through at the euro area aggregated level is found to vary between 25% and 75% (for a survey see Table 1, p. 25 in de Bondt et al., 2005). 3.2. Methodology The estimation of the DSGE model in log-linearized form is based on the following matrix representation: Ξ0 Xt = Ξ1 Xt − 1 + Xz zt + Xϑ ϑt ;

ð33Þ

where Xt is the state vector, zt is a vector of shocks and ϑt is a vector of expectational errors that satisfy Etϑt + 1 = 0 for all t. The matrices Ξ0, Ξ1, Ωz and Ωϑ contain the structural parameters of the model (Sims, 2001). The closed loop dynamics of the model, which serves as a starting point to generate the theoretical impulse responses, is given by: Xt ð.Þ = ΘX ð.ÞXt − 1 + Θz ð.Þzt ;

ð34Þ

where the rational expectations equilibrium is solved by using the method developed by Sims (2001).15 For the matching of the impulse responses, we estimate the following set of parameters:   . = hS″ψθp ωp mθw ωw τμ 1 μ 2 μ π μ Yˆ μ Δ Yˆ ; by minimizing a distance measure between the theoretical impulse responses and the empirical impulse responses. The remaining parameters are calibrated according to values typically found in related work (see for example Smets and Wouters, 2003; Del Negro et al., 2005; Leith and Malley, 2005, for estimations of DSGE models of the euro area). The discount factor β is fixed to 0.99, implying a 4% steady-state real interest rate in a quarterly model. The elasticities of the households' utility function σ and η are both assumed to equal 2. The parameter capturing the mark-up in wage setting ϕ is fixed to 3, which implies a 50% steady state mark-up. The share of capital in production α is set to 0.3. The depreciation rate δ is set to 0.025 per quarter, which implies an annual depreciation of capital equal to 10%. The steady-state mark-up of intermediate good producers over nominal marginal costs is set at 10%, implying that
= 11 (see Table 1 for a summary).

15 We use the MATLAB files gensys.m, gensysct.m, qzdiv.m, qzdivct.m, and qzswitch. m, which can be downloaded from Chris Sims's web page.

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O. Hülsewig et al. / Economic Modelling 26 (2009) 1310–1327

Fig. 1. Empirical impulse responses to a monetary policy shock. Notes: Orthogonalized impulse responses to a monetary policy shock. The solid lines denote impulse responses, which are calculated as the Hall mean derived from a bootstrap procedure with 2000 replications (Hall, 1994). The shaded areas are 95% Hall percentile confidence intervals of the bootstrapped impulse responses. Real output is expressed in percent terms, while all other variables are expressed in units of percentage points at an annual rate. The horizontal axis is in quarters.

The need for calibrating a sub-set of parameters is typically encountered in the literature when DSGE models are estimated. One reason for this is that in an unconstrained estimate these parameters are not identified. The decision of which parameters to calibrate, however, is rarely discussed and varies from paper to paper. We therefore propose to distinguish calibrated from estimated parameters by their role for the dynamics of the economy. While the calibrated parameters fully determine the evolution of the flexible price equilibrium of the economy (which takes into account the monopoly power of firms in the intermediate goods market and of households in the labor market), the estimated parameters reflect the inefficiencies resulting from real rigidities (h, S ̅″, ψ), nominal frictions (θp, ωp, θw, ωw, τ) and the cost channel (ν), and the related policy response (μ1, μ2, μπ, μ Y ,̂ μΔY )̂ . The estimator of . minimizes the following distance function (Christiano et al., 2005):     ˆ Cð.Þ VV − 1 Cˆ − Cð.Þ ; J = C−

ð35Þ

where Γ ̂ denotes the empirical impulse responses, Cð.Þ describes the mapping from . to the theoretical impulse responses and V is the Table 1 Calibrated parameters. Parameter Discount factor Risk aversion Labor supply elasticity Monopoly power of households (wage-setting) Depreciation rate Production function Monopoly power of firms (price-setting)

Calibration β σ η 1/ϕ δ α 1/


0.99 2.00 2.00 1/3 0.025 0.3 1/11

weighting matrix with the sample variances of Γ ̂ on the diagonal. The weighting matrix assures that those point estimates with a smaller standard deviation are given a higher priority.16,17 3.3. Minimum distance estimation We estimate the DSGE model — the log-linearized equations — by matching impulse responses to a monetary policy shock.18 The impulse responses are shown in Fig. 2 together with the 95% error bands. The model replicates the empirical impulse responses reasonably well as all theoretical impulse responses lie within the error bounds. However, two main differences are notable: (i) The inflation rate initially exhibits a concave reaction, but the adjustment is negative. While the reaction is consistent with the cost channel, its presence is not strong enough to replicate the price puzzle. (ii) The reaction of nominal wage inflation departs in the degree of inertia, 16 An efficient estimate of . would require the use of the inverse of the complete variance– covariance matrix W of impulse responses as a weighting matrix. However, as in Giannoni and Woodford (2005) and Boivin and Giannoni (2006), such a weighting matrix appears to hinder the convergence of the optimization routine. 17 We use the MATLAB optimization routine fmincon, which attempts to find a constrained minimum of a scalar function of several variables, starting at an initial estimate. This is generally referred to as constrained nonlinear optimization. A limitation of the algorithm, which uses a sequential quadratic programming method, is that it might only give local solutions. In Appendix D we check whether our estimates are robust against the choice of the initial conditions .0 = ð0:5 2:5 50 0:5 0:5 0:5 0:5 0:5 0:5 1:5 − 0:5 1:51:5 1:5Þ, which is the mean of the lower . − = ð0:01 0:01 0 0:01 0:01 0 0:01 0:01 0:01 1:00 − 1:00 1:05 0:00 0:00ÞÞ and the upper boundary . − = ð0:99 5:00100 0:99 0:99 1 0:99 0:99 0:99 2:00 0:00 2:00 3:00 3:00ÞÞ of the constrained optimization. As a further prerequisite for the reliability of the estimates we take care that the optimization algorithm converges and that the solution of the rational expectations model exists and is unique. 18 As commodity prices are neglected in the DSGE model, their impulse response function is excluded from the minimum distance estimation.

O. Hülsewig et al. / Economic Modelling 26 (2009) 1310–1327

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Fig. 2. Model impulse responses to a monetary policy shock. Notes: For the estimated impulse responses see notes to Fig. 1.

which is clearly more pronounced in the theoretical adjustment than in the empirical adjustment. Table 2 presents the point estimates for the parameters in the vector . and the related standard errors, which are computed by means of the delta function method.19 As the point estimates for ψ and ν coincide with the upper boundary of the constrained optimization, we add them to the group of calibrated parameters and therefore do not report standard errors.20 In the consumption Euler equation the estimated degree of habit formation is substantial and indicates that the response of consumption to an interest rate shock is largely driven by habits. This estimate appears to validate the claim of Rudebusch and Fuhrer (2005) that the degree of forward-looking behavior in consumption is limited (see also Giannoni and Woodford, 2005; Nelson et al., 2005). Given a calibrated coefficient of relative risk aversion σ = 2 our estimate implies that an expected one percentage point increase in the real short-term interest rate for four quarters has an impact on consumption of round about 0.045%. The estimate of the adjustment cost parameter in investment dynamics is somewhat smaller than the value reported by Smets and Wouters (2003) who estimate a value of 5.9. Our estimate of 3.18 implies that investment increases by 0.31% following a 1% increase in the current price of installed capital. Calibrating the elasticity of capital utilization with respect to the rental rate of capital ψ to 100 is in line with the calibration of Christiano, Eichenbaum, and Evans (2005) and the estimate reported by Rabanal (2007).

19 See Altig et al. (2005) for further details. For the calculation of the standard errors we used modified versions of the MATLAB files ComputeStdErrors.m, g1g2Func.m, and MomentFunction.m, which can be downloaded from Lawrence Christiano's web page. 20 In Appendix D we show that the estimated parameters are properly identified in the constrained parameter space. In order to take into account the uncertainty surrounding the concrete values of the calibrated parameters, we also check the robustness of the estimates for . against variations of the calibrated parameters (see Appendix E).

The supply side of the model exhibits a considerable degree of stickiness in prices, and additionally reveals a prominent role for backward-looking behavior in price-setting decisions. For price setters the estimate of θp = 0.56 implies that prices are fixed on average for 2.3 quarters. This result is at the lower end of estimates reported in other studies for the euro area. Del Negro et al. (2005) estimate an average price duration of 3 quarters using full information Bayesian techniques; Galí, Gertler, and López-Salido (2001) report values of around 4 quarters using a single equation GMM approach; Welz (2006) who also applies Bayesian techniques to a DSGE model estimates a duration of 6.5 quarters. On the upper end Smets and Wouters (2003) find evidence that price contracts last on average for

Table 2 Parameter estimates. Parameter Habit formation Investment adjustment costs Capital utilization variability Price stickiness Rule-of-thumb prices Share of cost channel firms Wage stickiness Rule-of-thumb wages Loan rate stickiness Taylor rule: smoothing Taylor rule: smoothing Taylor rule: inflation Taylor rule: output gap Taylor rule: output gap growth rate

h S ̅″

Ψ

θp ωp ν θw ωw τ μ1 μ2 μπ μ Ŷ μΔY ̂

Estimate

Standard error

0.91 3.18 100 0.56 0.71 1.00 0.61 0.38 0.41 1.32 − 0.52 1.16 0.57 0.58

0.09 0.40 – 0.19 0.05 – 0.14 0.12 0.03 0.13 0.11 0.11 0.19 0.12

Notes: The value of the distance function J is 53.70 with a probability of 0.9948. The probability is calculated by employing a χ2-distribution with 85 degrees of freedom. The degrees of freedom are calculated as the difference between the total number of estimated observations on the impulse response functions (97) and the number of estimated parameters (Eq. (12)). As the value of the distance function falls below the 1% critical value of the χ2-distribution, the imposed overidentifying restrictions cannot be rejected.

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ten quarters.21 Empirical work on price setting in the euro area using micro consumer price data also reports relatively low price durations with a median of around 3.5 quarters (see Álvarez et al., 2006, for a summary of recent micro evidence). Comparable studies for the U.S. like Altig et al. (2005) report much lower average price durations of just 1.6 quarters, which they claim to be more consistent with recent evidence drawn from US micro-data. Our results additionally indicate that backward-looking price setting behavior plays a prominent role as 71% of all price adjusters reset their prices in each period by complete indexing to past inflation. The empirical evidence on the degree of partial indexation of prices to past inflation rates in the euro area varies from 0.29 to 0.75. Leith and Malley (2005) estimated a value of 0.29, while Coenen, McAdam, and Straub (2007) propose to calibrate the degree of indexation to a value of 0.75. The share of cost channel firms is 1, implying that all firms consider short-term financial costs to be relevant for price setting. This value is significantly higher than in Rabanal (2007) who estimated the share of cost channel firms in the U.S. to be 0.15 (with a standard error of 0.13). The significance of the cost channel is supported by microevidence for the euro area that underlines the relative importance of financial costs as a driving factor for price changes. In the surveys conducted by the ECB's Inflation Persistence Network (see Fabiani et al., 2006) firms in major euro area countries were asked to assign scores between 4 (greater importance) and 1 (minor importance) to cost factors according to their importance for price adjustments. Financial costs received an average score of 2.1. With 2.6 the average score of labor costs was only slightly higher. Wages seem to be as sticky as prices in the euro area with an average wage duration of 2.6 quarters. Rabanal and Rubio-Ramirez (2008) report a smaller estimate with an average duration of 1.2 quarters, while Smets and Wouters (2003) and Leith and Malley (2005) propose values of 4.1 and 7.7, respectively.22 Our estimate for ωp indicates that the share of backwardlooking agents among those who adjust wages is 38%. Leith and Malley (2005) who also apply the complete indexation framework report a share of 17%. Using a partial indexation model, Smets and Wouters (2003) estimate the degree of wage indexation to be 0.66, while Rabanal and Rubio-Ramirez (2008) report a value of 0.34. Evidence for a limited interest pass-through is reflected by the significant estimate for τ. The degree of loan rate stickiness was estimated to be 0.41, which implies that loan rates are fixed on average for 1.7 quarters. Thus, stickiness in financial markets is substantially lower than in goods and labor markets. The immediate pass-through from the money market rate to the loan rate is 54%, and thus slightly higher than in the empirical impulse responses.

21 Note that the estimates of Smets and Wouters (2003) and Del Negro et al. (2005) are not strictly comparable to our estimates. While we have specified the Phillips curve as in Galí, Gertler, and López-Salido (2001), Smets and Wouters (2003) and Del Negro et al. (2005) follow the specification as proposed by Christiano, Eichenbaum, and Evans (2005). In this framework all price setters adjust prices in every period. Thus there is no price stickiness in a strict sense. The parameter 1 − θp in their framework denotes the share of optimizers while θp denotes the share of price setters that partially index prices to last periods inflation rate. This means that all price setters adjust prices, and only a fraction of 1 − θp adjusts optimally. Therefore, the average price duration indicates how long it takes on average before being allowed to reoptimize. In the framework applied by Galí, Gertler, and López-Salido (2001) we have true price stickiness in the sense that a fraction of θp of price setters is not allowed to change prices at all. The remaining mass of 1 − θp is divided into two subgroups: a fraction ωp that adjusts prices according to a complete indexation rule, and a fraction 1 − ωp that optimizes. The main reason for applying the framework of Galí, Gertler, and López-Salido (2001) instead of the partial indexation framework of Christiano, Eichenbaum, and Evans (2005) is that the former better fits the data. Replacing Eqs. (B.8) and (B.10) with their partial indexation counterparts (see Eqs. (32) and (33) in Christiano et al., 2005) results in a 10% higher value of the distance function J. 22 Note that for the same reasons as laid out in the previous footnote the estimates are not directly comparable as Smets and Wouters (2003) and Rabanal and Rubio– Ramirez (2008) aggregate wage setters as proposed by Christiano, Eichenbaum, and Evans (2005), while we apply the aggregation framework of Galí, Gertler, and LópezSalido (2001).

Finally, the Taylor rule coefficients display the familiar values. The estimate of the inflation coefficient is 1.16 and the output gap coefficient is 0.57. In addition we also find evidence for a significant response to the change in the output gap. This finding is in line with Smets and Wouters (2003) and theoretical suggestions of Walsh (2003). The autoregressive interest rate coefficients sum up to 0.80, indicating a substantial degree of interest rate smoothing, which is reported in most of the literature. 4. Relevance of the cost channel and incomplete interest rate pass-through The cost channel appears to matter for the transmission of monetary policy since it contributes to explain inflation inertia after a monetary policy shock. As shown in Fig. 2, the fall of inflation is retarded in the first quarters, sliding along on a concave path, which follows from the primary shift in real marginal costs induced by the increase of the loan rate. As Chowdhury, Hoffmann, and Schabert (2006) point out, the relevance of the cost channel depends on (i) the reliance of firms on credit, and (ii) the preferences of banks to smooth loan rates, which determines the degree of interest rate pass-through. In the following, we discuss the implications of these issues by simulating impulse responses to a monetary policy shock using different parameter constellations. The results are summarized in Fig. 3, where the benchmark impulse responses are shown by the solid lines. The effects of the cost channel can be isolated by setting the share of firms that depend on credit to ν = 0, while leaving the estimated values for the remaining parameters unchanged. The simulated impulse responses are depicted by the dotted lines. The outcome shows that inflation drops immediately following a monetary policy shock, reaching a through after around eight quarters, which is however less pronounced. Inflation still displays inertia, but the fall evolves along on a convex path — as predicted by the interest rate channel — and is triggered by the instant decline in real marginal costs, which results from the drop in both the real wage and the real rental rate of capital. The reaction of real output is only slightly more pronounced, while the response of nominal wage inflation is nearly identical. Next, we seek to explore the effects of the cost channel that arise in consequence of a varying degree of interest rate pass-through. We compare the impulse responses of a complete pass-through, i.e. τ = 0, 23 which implies that R ̂Lt = R ̂M with the impulse responses of the t , benchmark specification, i.e. τ = 0.41. The simulated impulse responses for a complete pass-through are depicted by the dashed– dotted lines. Again the estimated values for all remaining parameters are left unchanged. The outcome shows that the reaction of inflation to a monetary policy shock becomes temporarily positive under a complete interest rate pass-through. The raise in inflation stems from the considerable hike of real marginal costs that emerges when the loan rate follows exactly the money market rate given that the responses of both the real wage and the real rental rate of capital remain almost unchanged. Monetary policy anticipates the shift in inflation and reacts even more aggressively in terms of increasing the money market rate. The reaction of real output is identical under a complete interest rate pass-through, although the initial hike in the money market rate is more pronounced.24 The response of nominal wage inflation is slightly mitigated. While the primary shift in inflation diminishes when the loan rate becomes more sticky, i.e. τ N 0, a complete interest rate pass-through reveals that a price puzzle can be rationalized.

23

See Appendix B expression (B.12). This notwithstanding, real output is determined — inter alia — by the discounted expected future development of the real money market rate. 24

O. Hülsewig et al. / Economic Modelling 26 (2009) 1310–1327

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Fig. 3. Simulated impulse responses to a monetary policy shock. Notes: Simulated impulse responses to a monetary policy shock under different parameter constellations. Benchmark specification (τ = 0.41): solid lines; cost channel shut-off (ν = 0): dotted lines; complete interest rate pass-through (τ = 0): dashed–dotted lines. Estimated values of all remaining parameters are kept unchanged.

Overall, the simulation indicates that the effect of the cost channel on the transmission mechanism of monetary policy is minor, but it helps to explain the delayed adjustment of inflation to a monetary policy shock. Price decisions by firms depend on credit conditions with the result that real marginal costs are related to movements in the loan rate. The intensity of the reaction of the loan rate however is determined by the degree of interest rate pass-through. 5. Conclusion We used a New Keynesian DSGE model to explore the role of banks in the cost channel of monetary policy. Banks are assumed to extend credit to firms in an environment of monopolistic competition by setting their loan rates — as in Calvo (1983) — in a staggered way. Only a fraction of banks adjust their loan rates to a change in the policy rate, while the remaining fraction keeps the loan rate unchanged, which means that the reaction of the aggregate loan rate to a monetary policy shock is sticky. We estimated the DSGE model for the euro area by adopting a minimum distance approach. Our findings display that (i) price changes by firms are affected by movements in loan rates, (ii) frictions on the loan market play an important part in the transmission of monetary policy shocks as the pass-through from a change in money market rates to loan rates is incomplete, and (iii) the cost channel contributes to explain a delayed reaction of inflation to a monetary policy shock, but its effect is mitigated because the adjustment of loan rates to changes in money market rates is sluggish. Overall, our results suggest that the strength of the cost channel is alleviated since banks refrain from transmitting monetary policy shocks neutrally. Although, firms relate their price decisions to credit conditions, the effects on inflation dynamics arising through a change in loan rates are partly suppressed by a limited interest rate passthrough.

Acknowledgements The research project was funded by the Leibniz-Community Pact for Innovation and Research. We are grateful to Helge Berger, Michael B. Devereux, Steffen Henzel, Oliver Holtemöller, Martin Kukuk, Mario Larch, Andreas Schabert, Tomohiro Sugo, and Klaus Wälde for their valuable suggestions and comments on an earlier draft. We also thank Alessandro Calza, Barbara Roffia and Silvia Scopel for kindly providing us the loan rate data. The usual disclaimer applies. Appendix A. Derivation of the MSV solution Eqs. (27) and (28) can be reduced to the following expectational difference equation for RtL: L

Rt =

M ð1 − βτÞð1 − τ Þ f βτ L R + Et Rt + 2 f − 1 1 + βτ 1 + βτ2

+

τ L Rt − 1 + βτ2

1

+

1

ðA:1Þ

ð1 − βτÞð1 − τÞ f M u ; f−1 t 1 + βτ 2

where uM t is an uncorrelated white-noise monetary policy shock. Let us posit a fundamental (minimum state variable) solution of the following generic form (McCallum, 1983): L

L

Rt = /0 + /1 Rt

− 1

M

+ /2 ut ;

ðA:2Þ

where the coefficients ϕ0, ϕ1 and ϕ2 remain to be determined. Taking expectations of Eq. (A.2), EtRLt + 1 = ϕ0 + ϕ1R tL, and replacing RtL by Eq. (A.2), yields L

Et Rt

2 L

+ 1

= /0 + /0 /1 + /1 Rt

− 1

M

+ /1 /2 ut ;

ðA:3Þ

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which can be used to eliminate the endogenous variable Et R tL+ 1 in Eq. (A.1). Applying the method of undetermined coefficients and ignoring the unstable solution for ϕ1, gives /0 = ð1 − τÞ

f M R f−1

ðA:4Þ

/1 = τ

Kˆ t = ð1 − δÞKˆ t − 1 + δ Iˆt ;

ðB:5Þ

ðA:5Þ

/2 = ð1 − βτÞð1 − τ Þ

f : f−1

ðA:6Þ

M M ̅ Inserting Eq. (A.4)–(A.6) into Eq. (A.2) and using uM t = Rt − R gives:

L

It depends positively on the expected future real shadow value and the expected future real rental rate of capital, Et − 1r ̂Kt + 1, and negatively on the ex ante expected real interest rate. The capital accumulation equation is standard:

Rt = βτð1 − τ Þ

f M L R + τRt − f−1

1

+ ð1 − βτ Þð1 − τÞ

f M R ; f−1 t ðA:7Þ

which, after some algebra, can be reformulated as an error-correction model: M f f M ΔR R + ð1 − τ Þð1 − βτÞ f−1 t f−1   f L M Rt − 1 : −ð1 − τÞ Rt − 1 − ð1 − βτÞ f−1

ΔRLt = ð1 − τÞβτ

ðA:8Þ

implying that the capital stock evaluated at the end of the current period is determined by the previous capital stock and investment expenditures. The real rental rate of capital is determined by: K ˆ t: rˆt = Yˆ t − uˆ t − Kˆ t − 1 + u

For the capital utilization equation it holds that: K uˆ t = ψ rˆ t ;

ðB:7Þ

where ψ = Ψ′(1) / Ψ″(1), assuming that the utilization rate equals one in steady state. The evolution of inflation is described by a hybrid New Keynesian Phillips curve, which is given by: π t = γ f Et − 1 π t

+ 1

+ γ b π t − 1 + κ p Et − 1uˆ t ;

ðB:8Þ

where: βθp h i θp + ωp 1 − θp ð1 − βÞ

Appendix B. The linearized model

γf =

We summarize the New Keynesian DSGE model by taking a loglinear approximation of the relevant model equations around the symmetric equilibrium steady state with zero inflation. In the following a variable X t̂ denotes the log-linear deviation from the steady-state value, X ̂t = ln(Xt) − ln(X ̅), where X ̅ represents the steady-state value. The dynamics of real output is described by the goods market equilibrium that can be stated as:

i θp + ωp 1 − θp ð1 − βÞ     1 − θp 1 − βθp 1 − ωp h i : κp = θp + ωp 1 − θp ð1 − βÞ

  1 Yˆ t = γ C Cˆ t + ð1 − γC ÞIˆt + α 1 − uˆ ;
t      1 1 −1+δ . where γ C = 1 − αδ 1 −
β

ðB:6Þ

ðB:1Þ

=

h

γb =

ωp

For the parameters γf and γb it holds that γf + γb = 1, for β → 1. The parameter κ measures the sensitivity of inflation with respect to real marginal costs. Real marginal costs are given by:   K ˆ − Pˆ + mRˆ L : uˆ t = α rˆt + ð1 − α Þ W t t t

ðB:9Þ

The consumption equation with external habit formation h is given by: Cˆ t =

1 E Cˆ 1 + h t −1 t

+ 1

+

 M h ˆ 1− h Ct − 1 − Et − 1 Rˆ t − π t ð1 + hÞσ 1+h

+ 1

 ;

ðB:2Þ where the inflation rate πt is defined as πt = P t̂ − P t̂ − 1. The investment equation is given by: Iˆt =

β E Iˆ 1 + β t −1 t

+ 1

+

1 ˆ 1 I E + PW Qˆ ; 1 + β t −1 S ð1 + βÞ t − 1 t

ðB:3Þ

ˆ = βρ E ˆ ˆ ΔW t 1 t − 1 Δ W t + 1 + ωw ρ1 Δ W t − 1 − βθw ρ2 Et − 1 π t + ρ2 π t − 1 h i ˆ − Pˆ : + κ w Et − 1 ˆ MRSt − W t t ðB:10Þ

where Q̂ t is the real shadow value of installed capital (Tobin's Q), and S ̅″ are investment adjustment costs. The real shadow value of capital evolves according to: K Qˆ t = βð1 − δÞEt − 1 Qˆ t + 1 + ½1 − βð1 − δÞEt − 1 rˆt + 1  M  − Et − 1 Rˆ t − π t + 1 :

The dependency of real marginal costs on the gross loan rate implies that — as emphasized by the cost channel of monetary policy — cyclical movements in the inflation process arise — inter alia — from deviations of the nominal gross loan rate from its steady state. The development of nominal wage inflation is determined by the wage setting behavior of households, which implies the following expression:

ðB:4Þ

where: ρ1 =

θw ωw + θw ½1 − ωw ð1 − βθw Þ

ρ2 =

ωw ð1 − θw Þ ωw + θw ½1 − ωw ð1 − βθw Þ

κw =

ð1 − θw Þð1 − βθw Þð1 − ωw Þ : ωw + θw ½1 − ωw ð1 − βθw Þð1 + η/Þ

O. Hülsewig et al. / Economic Modelling 26 (2009) 1310–1327

The marginal rate of substitution is described by: ˆ MRSt =

  η ˆ αη  σ ˆ Y − uˆ + Kˆ t − 1 + C − hCˆ t − 1 : 1− α t 1− α t 1− h t ðB:11Þ

Nominal wage inflation is determined by future expected and past nominal wage inflation, by the current and past inflation rate and by the gap between the marginal rate of substitution and the real wage. The evolution of the gross loan rate is governed by the following expression: L L L M Rˆ t = βf1 Et Rˆ t + 1 + f1 Rˆ t − 1 + f2 Rˆ t ;

ðB:12Þ

where: f1 =

τ 1 + βτ2

ð1 − βτÞð1 − τÞ f2 = : 1 + βτ 2 The loan rate is determined by the expected future loan rate, the past loan rate and the money market rate. The immediate passthrough from changes in the money market rate to changes in the loan ̂t . rate becomes complete, if τ goes to zero, which implies that R L̂ t = R M We close the model by adding the reaction function of the central bank as presented in the text. Appendix C. Data base The data is taken from the Euro Area Wide Model (AWM, update 5, 1970Q1–2003Q4) — see Fagan, Henry, and Mestre (2001) and www.

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ecb.org — except for the loan rate data, which has been kindly provided by the ECB. Our sample covers the period from 1990Q1 to 2002Q4 due to the limited availability of a continuous time series for the loan rate. 1. GDP: Log of real GDP, seasonally adjusted (AWM code: YER). 2. INFL: Inflation rate, annualized quarterly change of GDP deflator in percent, seasonally adjusted (AWM code: YED). 3. WINFL: Nominal wage inflation, annualized quarterly change of wage rate in percent (AWM code: WRN) 4. CPINFL: Commodity price inflation, annualized quarterly change of commodity prices in percent (AWM code: COMPR) 5. RM: Short-term nominal interest rate, in percent (AWM code: STN). 6. RL: Retail bank lending rates for loans to enterprises with maturities up to one year, nominal in percent. Appendix D. Identification of the parameters Identifiability is a crucial condition needed for any empirical methodology to deliver sensible estimates and meaningful inference. The parameters are identified if the objective function has a unique minimum and displays sufficient curvature in all relevant dimensions. In a recent paper Canova and Sala (2005) provide some diagnostic tools to detect identification problems related to moment estimators when the objective function measures the distance between empirical and model impulse responses. For each parameter Fig. 4 plots the shape of the objective function in the close neighborhood of the optimum. The horizontal axis depicts the difference between the value of the objective function J as a function of the parameter shown on the top of each graph, conditional on the other parameters being fixed at their baseline estimates, and

Fig. 4. Shape of the objective function. Notes: The vertical axis depicts the difference between the value of the objective function J as a function of the parameter shown on the top of each graph, conditional on the other parameters being fixed at their baseline estimates, and the baseline value of the objective function (J = 53.70). The horizontal axis indicates the range, within which the parameters were varied in steps of 0.01 (0.2 in the case of ψ).

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Fig. 5. Distribution of estimates. Notes: The histograms show the density of estimates obtained starting the optimization routine 500 times from different initial conditions uniformly drawn within the ranges considered on the horizontal axis. The figure on the top of each graph is the mode of the distribution of the estimated parameters.

Fig. 6. Ordered distribution of estimates. Notes: The vertical axis depicts the draws ordered by the value of the distance function, starting with the lowest value. The horizontal axis depicts the parameter estimates. The figure on the top of each graph is the parameter estimate corresponding to the draw with the lowest value of the distance function.

O. Hülsewig et al. / Economic Modelling 26 (2009) 1310–1327

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Fig. 7. Robustness of the estimates against variations of σ.

the baseline value of the objective function (J = 53.70). For most of the structural parameters the curvature of the objective functions is sufficient to identify a minimum. Therefore, we can conclude that the responses to monetary policy shocks are very informative in that they can be used to identify most of the structural parameters. The only exceptions are the shapes of the objective function with respect to the capital utilization parameter ψ and the share of cost channel firms ν. As both estimates hit the upper boundary of the constrained optimization, the objective function is falling in the neighborhood of the boundary. While the upper boundary of ν is binding as it defines a share of firms that cannot exceed 1, the upper boundary for ψ is less stringent. Theoretically, ψ may go to infinity, implying that the rental rate of capital is fixed.25 Investigating the curvature of the objective function in one dimension is insufficient to guarantee that the optimization routine detects a global minimum in the constrained parameter space. If the objective function has ridges, flat regions or local minima, the vector of ˆ the parameter estimates . may depend on the vector of initial values .0 . In order to properly identify the parameters we started the optimization routine 500 times from different initial conditions uniformly drawn within the ranges defined by the bounds of the constrained optimization. The histograms in Fig. 5 show the densities of estimates, which are obtained after eliminating the 185 cases where either convergence failed, or the estimated parameters produced imaginary or indeterminate solutions. The figure on the top of each graph is the mode of the distribution of the estimated parameters.26 25 Setting ψ = 1000 reduces the value of the distance function from 53.70 to 53.68, without changing any of the remaining parameter estimates. 26 Here the mode is defined as the center of the bin of the histogram that contains the most frequently occurring estimate. In each histogram we set the number of bins equal to 50. The bin width can be calculated as the difference between the upper and lower range divided by the number of bins. Hence, for a bin size of 50 the most frequently occurring estimate for h is in the range of 0.92 ± 0.01, implying a bin width of 0.02.

There are two interesting results that can be drawn from the histograms. First, the great majority of the estimates for ψ and ν hit the upper boundary. Second, for the remaining parameters the distributions are very peaked with modes that are close to the baseline estimates of the structural parameters shown in Table 2. Such a distribution can be regarded as further evidence for properly identified parameters. To gain further insight we ordered the vector of parameter estimates by the value of the distance function, starting with the lowest value. The lower right graph in Fig. 6 shows that 251 out of 315 draws of initial values result in a value of the distance function equal to 53.70. The horizontal lines that can be found in all graphs indicate that these parameter estimates are associated with the minimum of the distance function. The figures on the top of each graph, which are the parameter estimates corresponding to the draw with the lowest value of the distance function, are identical with the parameter estimates shown in Table 2. The graphs for ψ and ν further show that in the constrained parameter space, the upper boundary is indeed associated with the minimum of the distance function. Appendix E. Robustness against variation of calibrated parameters When a subset of model parameters is calibrated, an important matter is whether the estimates of the remaining model parameters are robust against changes in the calibrated parameters. Figs. 7–12 show the estimation results when one calibrated parameter was altered, conditional on the other calibrated parameters being fixed at their baseline values shown in Table 1. The horizontal axes indicate the range, within which the calibrated parameter under consideration was varied. The range has been chosen so as to best represent the uncertainty about the parameters found in the literature (see Table 3). As initial values we took the parameter estimates of the baseline estimation (see Table 2).

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Fig. 8. Robustness of the estimates against variations of η.

Fig. 9. Robustness of the estimates against variations of ϕ.

O. Hülsewig et al. / Economic Modelling 26 (2009) 1310–1327

Fig. 10. Robustness of the estimates against variations of δ.

Fig. 11. Robustness of the estimates against variations of α.

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O. Hülsewig et al. / Economic Modelling 26 (2009) 1310–1327

Fig. 12. Robustness of the estimates against variations of
.

Except for some graphs in Fig. 7 the parameter estimates depend monotonically on the calibrated parameters. If the degree of risk aversion σ increases, the estimate of the investment adjustment costs S ″̅ falls and the central bank becomes more sensitive to movements in the inflation rate. The largest impact of the two parameters describing the households' supply of labor, η and ϕ, is on the wage setting rigidities, θw and ωw, which are decreasing functions of η and ϕ. Moreover, if η increases, the estimate for the investment adjustment costs S ″̅ and for the degree of price stickiness θp increases, whereas the central bank's response to inflation μπ decreases. The depreciation rate δ basically influences the ̅ which become larger for estimate of the investment adjustment costs S ″, a higher value of δ. The production function parameter α has the broadest impact on the parameter estimates. The higher the capital share of output is, the lower is the estimated degree of habit formation h, the price rigidity parameters θp and ωp and the central bank's response to output gap growth μΔY̑, and the higher is the investment adjustment ̅ the wage setting rigidities θw and ωw, and the central bank's costs S ″, response to inflation μπ and the output gap μY .̂ Variations of the inverse of the monopoly power of firms
only affect the estimate of the ̅ which become larger for a higher value investment adjustment costs S ″, of
. Table 3 Values for calibrated parameters in the literature.

Smets and Wouters (2003) Del Negro et al. (2005) Leith and Malley (2005) Rabanal (2003) Rabanal and Rubio-Ramirez (2008)

β

σ

η

ϕ

δ

α




0.99 0.99 0.93 0.99 0.99

1.61 1 2.02 3.85 5.88

1.19 2.20 1.5 1 1.64

3 4.3 11 6 6

0.025 0.025 – – –

0.3 0.17 0.31 0.36 0.36

– 4.3 11 6 6

Notes: All the papers cited in the Table estimated a DSGE model for the euro area with Bayesian techniques. The figures in the Table show the value of the calibrated parameters. If figures are in bold, the parameters have been estimated.

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