Competition among banks and the pass-through of monetary policy

Economic Modelling 28 (2011) 1891–1901

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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

Competition among banks and the pass-through of monetary policy☆ Jochen H.F. Güntner ⁎ Otto-von-Guericke-University Magdeburg, PO Box 4120, 39016 Magdeburg, Germany

a r t i c l e

i n f o

Article history: Accepted 15 March 2011 JEL classification: C61 E32 E43 E51

a b s t r a c t This paper introduces monopolistically competitive financial intermediaries into the New Keynesian DSGE setting. Modelling bank market power explicitly contributes to understanding two empirical facts: (i) The short-run transmission of changes in money market rates to bank retail rates is far from complete and heterogeneous. (ii) Stiffer competition among commercial banks implies that loan rates correlate more tightly with the policy rate. In my model, the degree of monopolistic competition in the banking sector has a sizeable impact on the pass-through of changes in the policy rate. In particular, a more competitive market for bank credit amplifies the efficiency of monetary policy. © 2011 Elsevier B.V. All rights reserved.

Keywords: Monopolistically competitive banks Collateral External finance premium Inside money premium

1. Introduction The present paper examines the impact of an explicitly modelled banking sector on the transmission of monetary policy shocks. Drawing on Goodfriend and McCallum (2007), I introduce a continuum of monopolistically competitive financial intermediaries whose products are imperfect substitutes. Just like price-setting goods producers, commercial banks can thus determine the retail interest rates on their deposits and loans. There is ample empirical evidence that the pass-through from monetary policy to bank retail rates is incomplete, at least in the short run. Both loan and deposit rates are found to adjust sluggishly to changes in market interest rates (see e. g. Cottarelli and Kourelis, 1994, Berlin and Mester, 1999, and de Bondt, 2005).1 Retail rate adjustment costs are a plausible explanation for this behaviour

☆ I would like to thank Gerhard Schwödiauer, Marvin Goodfriend, Bennett McCallum, Per Krusell, Eduardo Engel, Christiane Clemens, and Henning Weber for many helpful comments and support, and am particularly indebted to an anonymous referee. I furthermore benefitted from productive discussions at the “Doctoral Workshop on Dynamic Macroeconomics” of the University of Konstanz, the “13th ZEI Summer School on Heterogeneity in Macroeconomics” of the University of Bonn, and the ZEW conference “Recent Developments in Macroeconomics” in Mannheim. This paper was revised while the author was a Visiting Scholar at the University of Michigan, Ann Arbor. Financial support by the German Academic Exchange Service (DAAD) is gratefully acknowledged. ⁎ Tel.: + 49 391 67 18816; fax: + 49 391 67 11136. E-mail address: [email protected]. 1 See also Kok Sørensen and Werner (2006) for further euro area evidence and a comprehensive survey of the related literature. 0264-9993/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2011.03.015

(Hofmann and Mizen, 2004), as the long-run pass-through is typically estimated to be higher, or almost complete.2 In spite of the consensus view that the extent of stickiness differs between countries and bank product categories, the causes are still up for debate. Starting from the seminal theoretical contribution of Klein (1971), a strand of the empirical literature has focused on the relationship between bank competition and monetary transmission. Hannan and Berger (1991) find that deposit rates adjust significantly more sluggishly in concentrated markets, especially when money market rates are rising. van Leuvensteijn et al. (2008) analyse the impact of loan market competition on bank rates in the euro area between 1994 and 2004. They find that stronger competition implies lower interest differentials between bank and market rates for most loan products. Moreover, the responsiveness of retail rates to changes in market interest rates is positively correlated with the extent of competition. This agrees with evidence from prior studies using different measures of competition or concentration, including Cottarelli and Kourelis (1994), Borio and Fritz (1995), and de Bondt (2005).3 Empirically, stiffer competition from other banks or the capital market seems to speed up the adjustment of retail rates to changes in money market conditions. According to Lago-González and Salas-Fumás

2 Implicit risk-sharing agreements (Berger and Udell, 1992), where banks shield their customers from fluctuations in market interest rates, and relationship banking (Berger and Udell, 1995) are alternative explanations not considered in this paper. 3 Certainly, monopolistic competition is just one of several explanations for the observed heterogeneity in interest rate pass-through, but a comparatively robust one (see Sørensen and Werner, 2006).

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(2005), a mixture of bank market power and adjustment costs can account for the observed rigidity in retail rates. Introducing monopolistic competition among banks into a New Keynesian DSGE model entails an under-provision of deposits and credit contracts, relative to the perfect competition scenario, in the long run. More importantly, the model replicates the incomplete passthrough from the policy rate to deposit and loan rates. Sluggish adjustment of deposit rates amplifies changes in private households' liquidity premium and thus the fluctuations in output, consumption, and employment at business cycle frequencies. On the contrary, sticky interest rates on loans attenuate the deviations of investment and employment from their steady-states, due to a cost channel for monetary policy. Monopolistic competition in the market for firm credit represents a significant bottleneck in this model, that reduces the efficiency of monetary policy. Goodfriend and McCallum (2007) study the dynamic implications of Goodfriend (2005) in a calibrated DSGE model. In order to provide loans, the financial sector uses collateral and monitoring effort, while bank deposits are a prerequisite for facilitating transactions. The authors identify two opposing effects of corporate banking: On the one hand the well-known “financial accelerator” introduced by Bernanke et al. (1999), which results from a drop in the value of collateral under adverse economic conditions, on the other hand a “banking attenuator” arising from a fall in consumption and the consequent rise in collateral-eligible assets during a recession. Following up on Goodfriend and McCallum (2007), my model evolves from a two-sector economy with goods production and banking. Firms use labour and capital to produce a diversified output which is sold in a monopolistically competitive market. They cannot retain earnings, but accumulate productive capital through investment. Returns accrue at the end of a period, while the wage bill and investment are paid up front. Firms must therefore pre-finance their working capital by a one-period bank loan. Commercial banks provide two types of financial intermediation. They combine collateral, consisting of a borrower's productive capital stock and end-of-period profits, with monitoring effort to produce loans. Since monitoring is costly, banks demand an external finance premium (EFP) on top of the risk-free reference rate. They moreover collect deposits from private households. Due to administrative costs, deposits are an imperfect substitute for high-powered central bank money from a bank's perspective. Accordingly, they yield a return below the monetary policy rate. In line with Stracca (2007), I refer to this interest rate differential as the liquidity or inside money premium (IMP). Heterogeneity of financial contracts generates an imperfectly competitive market pattern, where both the steady states and dynamics of the above spreads are affected by the extent of bank competition as well as standard arguments in the marginal costs of deposit and loan provision. By widening the spreads between policy and retail rates beyond these costs, commercial banks realise a positive expected net profit. This paper attempts to overcome the absence or passivity of financial intermediaries in most models. By allowing banks to set interest rates optimally, subject to quadratic adjustment costs à la Rotemberg (1982), I add a micro-founded imperfection to the transmission mechanism of monetary policy. Recently, a limited number of papers have approached the question of incomplete interest rate pass-through and monopolistic competition among banks in a general equilibrium framework. Among them, the contributions of Scharler (2008), Hülsewig et al. (2009), and Gerali et al. (2008, 2010) are most closely related to my work. Scharler (2008) analyses the implications of limited pass-through from market to both loan and deposit retail interest rates for macroeconomic volatility in a calibrated sticky price model. Incomplete pass-through arises from the introduction of intermediation costs which provide an incentive for banks to smooth retail interest rates even within a perfectly competitive financial sector.

Hülsewig et al. (2009) analyse the role of loan market frictions in the propagation of monetary policy shocks. They combine sticky loan interest rates à la Calvo (1983) with monopolistic competition of the same functional form used in this paper. While the authors comment on the immediate and long-run effects of monopolistic competition on the pass-through of monetary policy shocks in proposition 2.2, the corresponding sensitivity parameter is dropped in the empirical analysis where they focus on the role of incomplete interest rate passthrough for the cost channel of monetary policy transmission. Gerali et al. (2010) develop a financially rich model and estimate it on euro area data. Their banking sector also features interest rate adjustment costs and monopolistic competition in loan and deposit markets. As opposed to my model, their wholesale interest rates will be identical to the monetary policy rate in the long-run equilibrium without shocks.4 As a consequence, the entire steady-state spread between the monetary policy rate and bank retail rates necessarily arises from monopolistic competition. While this comprehensive framework allows the authors to address numerous interesting questions, especially in relation to the recent financial turmoil, the role of monopolistic competition among banks is not tracked down in their analysis. My work contributes to the above line of research by analysing precisely the quantitative importance of imperfect competition in the markets for bank products on the transmission of monetary policy shocks, given a constant degree of interest rate stickiness. For this purpose, I use a calibrated New-Keynesian DSGE model. The rest of the paper is organised as follows. Section 2 describes the model. In Section 3, I derive the intertemporally optimal behaviour of banks and the symmetric equilibrium. The calibration of parameters and steady-state results are presented in Section 4. Section 5 analyses the dynamic implications of bank competition for the responses to an expansionary monetary policy shock. Section 6 concludes. 2. The model The model is set up in discrete time and features a representative private household, a representative final goods producer, a continuum of intermediate goods-producing firms, a continuum of financial intermediaries, and a monetary authority. At the beginning of period t, intermediate goods producers take out a short-term bank loan to hire labour and to invest into new capital which is productive as of period t + 1. By means of the borrowed working capital, firms produce a differentiated intermediate output that is traded in a monopolistically competitive market. Banks produce these loans from two substitutable input factors: collateral and labour to screen and monitor borrowers. Since only monitoring is costly, higher collateral reduces the cost of providing a loan and thus the loan interest rate demanded by the bank. A representative final goods producer merges the continuum of intermediate goods into a final good that can be either invested by firms or consumed by the household. The market for final output is perfectly competitive and yields zero profit. The central bank provides private banks with high-powered money in exchange for risk-free bank bonds which yield a return equal to the central bank-determined policy rate. Monetary policy follows a standard Taylor rule. The representative household supplies two types of homogeneous labour – work and monitoring effort – to firms and banks, respectively. The real wage is identical across sectors. A constraint requires the household to hold bank deposits for transactions. Imperfectly competitive agents extract monopolistic rents which are redistributed to the owner, the representative household, at the end of period. Likewise, the household receives the central bank's 4 Gerali et al. (2010) model each bank as a composition of one “wholesale” branch and two “retail” branches with monopolistic competition in the market for deposits and loans, respectively.

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seignorage proceeds. Resources are either consumed or saved for future periods and to provide liquidity services in the form of deposits.

Intermediate goods producers rely on bank loans in order to finance their working capital up front. In real terms, firm j borrows an amount

2.1. The representative household

lt ð jÞ = wt nt ð jÞ + qt it ð jÞ:

The infinitely-lived representative household derives utility from final goods consumption ct and from the consumption of leisure time. It maximises discounted lifetime utility

For simplicity, the typically pro-cyclical real market price of capital, qt, is fixed at unity. Final consumption and investment goods are identical; so are their prices. This switches off the “financial accelerator” in the sense of Bernanke et al. (1999). Still, the value of collateral, the demand for monitoring effort, and the EFP remain prone to changes in a firm's stock of physical capital and expected profits — two generally procyclical quantities likely to amplify impulse responses. Note that this assumption is not a prerequisite for solving the model. A market price for capital can be derived by adding a representative capital goods producer who transforms the depreciated old capital stock and final output into new productive capital within a costly investment process.6 In equilibrium, default on debt obligations is not an option for firms. Successful screening by commercial banks excludes any wouldbe borrowers from the loan market, right from the start, and avoids cases of bankruptcy among intermediate-goods producers.7 All firms are owned by the representative household. They do not accumulate own funds, apart from the stock of productive capital. At the end of each period, monopolistic profits gt are therefore distributed to the household. The risk-neutral manager of firm j chooses {nt(j), Pt(j), kt(j)} in order to maximise

∞

v

Et ∑ β Ut + v ;

where

v=0

Ut = Inðct −hct−1 Þ + ϕ Inð1−nt −st Þ:

ð1Þ

β is the subjective discount factor, while h N 0 allows for habit formation in consumption. nt and st are the shares of total time endowment, normalised to 1, the household spends working in the firm and the bank, respectively. Presuming asymmetric information in the retail market, final goods producers require an evidence of solvency, i. e. households must guarantee a constant share α of consumption by bank deposits dt. I implement this restriction by means of a deposit-in-advance (DIA) constraint in the sense of a standard cash-in-advance (CIA) constraint.5 Consumption is paid out of labour income, wt(nt + st), and dividends distributed by firms, gt, and banks, gtf, seignorage proceeds transferred by the central bank, gtcb, and previous savings. Households save in terms of deposits, dt, at a commercial bank which yield a gross return of 1 + rtd. By choosing an infinite series of optimal {ct, nt, st, dt}, the representative household maximises lifetime utility subject to the budget constraint,

ct + dt ≤wt ðnt + st Þ +


 d dt−1 1 + rt−1 πt

f

cb

+ gt + gt + gt ;

ð2Þ

and the deposit-in-advance constraint, αct ≤ dt :

ð3Þ

The optimisation problem is formulated in real terms. Accordingly, principal and interest of period t − 1 deposits are divided by the Pt inflation factor πt = Pt−1 . Note that dt should be interpreted as an

∞

v

Et ∑ β λt + v gt + v ð jÞ; v=0

ð4Þ

ð5Þ

where real current firm profits in period t,
 l 1 + rt−1 ½wt−1 nt−1 ð jÞ + it−1 ð jÞ Pt ð jÞ yt ð jÞ− gt ð j Þ = Pt πt  2  2 ϕp Pt ð j Þ ϕ it ð jÞ −1 yt ð jÞ− i −1 it ð jÞ; − 2 πPt−1 ð jÞ 2 it−1 ð jÞ

ð6Þ

aggregate including both sight deposits and cash, in this model, or as a “highly liquid” asset, in general.

are weighted by the household's marginal utility λt and discount factor βt. Accordingly, the manager maximises the present value, in terms of utility, of future expected profits to the household, subject to satisfying the demand for intermediate good j by the final goods producer:

2.2. The intermediate goods sector

kt−1 ð jÞ nt ð jÞ

The continuum of intermediate goods producers is indexed by j ∈ [0,1]. Firm j hires n(j) units of homogeneous labour from the representative household and produces its differentiated intermediate output y(j) using a common constant returns to scale (CRS) technology. Imperfect competition in the market for intermediate goods allows producers to reap a positive expected monopolistic profit. All investment decisions, notably the accumulation of productive physical capital, are in the hands of the firm. As usual, the capital accumulation equation is deterministic: kt(j) = (1 − δ)kt − 1(j) + it(j), where it(j) is the gross investment undertaken by firm j in period t. The Cobb–Douglas production function, yt(j) = kt − 1(j)γnt(j)1 − γ, is not subject to stochastic technology innovations, in this model. Note further that the period t capital stock of a firm, which consists of the depreciated kt − 1 and recently undertaken investment, will not be productive until the beginning of period t + 1. 5 The DIA constraint formalises the notion that bank deposits facilitate transactions. Similarly, it would be possible to include deposits in the utility function (see e. g. Christiano et al., 2009). Note that DIA implies a strict complementarity between consumption and real deposits, as every unit of consumption requires α units of deposits. Although this represents a strong simplifications, all results persist for a deposit-in-the-utility formulation as long as one realistically assumes that consumption and deposits are Edgeworth complements as discussed in Walsh (2003), Chapter 2.

γ

1−γ

  P ð jÞ −μ ≥ t yt = yt ð jÞ: Pt

ð7Þ

The presence of the per-period loan rate rl in the profit function (6) introduces a cost channel of monetary policy into the model. Via marginal costs, optimal firm behaviour is directly affected by changes in the policy rate and thus the loan rate.8 I assume that monopolistically competitive firms face quadratic adjustment costs when resetting prices9 or altering the flow of investment. Note that the presence of investment adjustment costs implies a value of installed productive capital to the firm that may well lie above q = 1. As intuition suggests, both costs are zero in the stationary equilibrium. 6 Another version of the model which includes this extension replicates the financial accelerator, without, however, influencing the conclusions drawn from the introduction of monopolistically competitive banks. I therefore omit it in the present paper. 7 This short cut is adopted from Goodfriend and McCallum (2007) who refer to Kocherlakota (1996). 8 For a theoretical analysis of the cost channel's relevance for monetary policy transmission and an overview of the related literature, see Henzel et al. (2009). 9 The lagged repayment of working capital loans complicates the computation of an expression for real marginal costs. I therefore preferred quadratic price adjustment costs according to Rotemberg (1982) to the more common price stickiness à la Calvo (1983). Both approaches lead to an equivalent optimal price-setting behaviour of monopolistically competitive goods producers (see e. g. Roberts, 1995).

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2.3. The final goods sector The representative final goods producer purchases yt(j) units of intermediate good j at price Pt(j) and combines these inputs in a Dixit–Stiglitz composite good to produce the homogeneous final output

yt =

  μ μ−1 μ−1 1 ∫0 yt ð jÞ μ dj ;

ð8Þ

where μ is the elasticity of substitution between intermediate goods of different producers. The profit-maximising demand of the final goods  Pt ð jÞ −μ yt , producing firm for intermediate good j is thus yt ð jÞ = Pt
 1 with an aggregate price index Pt = ∫10 Pt ð jÞ1−μ dj

1−μ

.

2.4. The financial intermediaries sector Commercial banks – indexed i ∈ [0,1] – provide differentiated financial products. They face a constant finite elasticity of substitution in the market for deposits and loans, respectively, where they compete in their interest rates. In line with Gerali et al. (2008, 2010), I assume that customers demand a Dixit–Stiglitz composite of the above differentiated contracts. Formally, this means that the representative household divides its deposit holdings across the entire continuum of banks, while firms sign a loan contract with each bank in order to raise one unit of external funds. Although the story behind this micro-founded approach is far from realistic, it incorporates the crucial features for analysing the impact of bank competition on the pass-through of monetary policy.10 As a consequence, bank i faces a downward-sloping demand curve !−ηl r l ðiÞ lt for loans and an upward-sloping demand curve lt ðiÞ = t l rt !ηd rd ðiÞ dt for deposit accounts (see also Hülsewig et al., dt ðiÞ = t d rt 2009, Gerali et al., 2008, 2010). The sensitivity of bank i's share in the composite deposit and loan contract to the corresponding interest rate depends inversely on the CES parameters ηd and ηl. When resetting interest rates, banks bear Rotemberg (1982) adjustment costs. Similar to the case of a price-setting firm, the latter should be considered as “menu costs”. In particular, they cover any resource costs related to communicating the new retail rates. Bank i produces loans according to the CRS function σ

1−σ

lt ðiÞ = F ðgt + κkt Þ st ðiÞ

;

ð9Þ

where F is a constant TFP coefficient. Monitoring effort st, supplied by the household, is the only costly input factor. I assume that all banks are of comparable size and have an identical number of clients which are distributed randomly across financial institutions. Subject to these simplifications, the monitoring required to provide a line of credit lt(i) decreases in the level of economy-wide collateral.11

On the one hand, collateral consists of current period profits which are only distributed to the household after a firm has honoured its debt. On the other hand, banks can seize the borrower's capital stock in the event of default, excluded here. Since kt is installed in the firm, only a fraction κ b 1 is considered actually collectible by banks.12 Moreover, bank i provides deposits to the household. The ωdt ðiÞ is linear in the amount of deposits and falling associated cost mt ðiÞ in the bank-specific reserves of high-powered money. A bank can expand its reserves through open market operations, issuing a riskfree bond bt(i) which is bought by the monetary authority in exchange for mt(i). ω represents a constant marginal cost coefficient. In open market operations, private banks may borrow without limit at the central bank determined risk-free rate. They will thus not agree to pay a return on sight deposits above rt less the cost of deposit provision. The difference between the policy rate and rdt is a liquidity premium, termed the inside money premium (IMP) below. The risk-neutral manager of bank i chooses {dt(i), bt(i), st(i), mt(i), rdt (i), rlt(i)} to maximise ∞

v

v=0

f gt ðiÞ


 l lt−1 ðiÞ 1 + rt−1 ðiÞ mt−1 ðiÞ = dt ðiÞ + bt ðiÞ + + −mt ðiÞ−lt ðiÞ πt πt
 d dt−1 ðiÞ 1 + rt−1 ðiÞ b ðiÞð1 + rt−1 Þ ωdt ðiÞ − − t−1 −wt st ðiÞ− πt mt ðiÞ πt !2 !2 ϕrd ϕr l rtd ðiÞ rtl ðiÞ −1 dt ðiÞ− −1 lt ðiÞ; − d l 2 rt−1 2 rt−1 ðiÞ ðiÞ ð11Þ

subject to dt ðiÞ≥

!η !−η l rtd ðiÞ d rtl ðiÞ d and l ð i Þ≥ lt . The constraining t t d l rt rt

demand curves result from an optimal deposit placement of the representative household as well as from a cost-minimising borrowing behaviour of intermediate goods producers. 2.5. The monetary authority Instead of modelling a complete government sector, I only introduce an authority which exercises monetary policy. Its highly stylised balance sheet contains high-powered money, mt, on the liabilities side and bank bonds, bt, on the asset side. Each period, the central bank conducts open market operations to provide commercial banks with their desired amount of highpowered money in exchange for risk-free bank bonds. Since its assets bt yield a return, namely the policy rate, while its liability mt does not, the monetary authority retains a positive seignorage profit from open market operations13: cb

Approaches with a richer economic content are taken e. g. by Andrés and Arce (2008). They use a version of Salop's (1979) circular city to model imperfect competition in the loan market, where borrowers suffer a utility cost when travelling to a bank. Aliaga-Díaz and Oliveiro (2007) introduce switching costs à la Klemperer (1995) as a source of market power. These costs lead to a bank client “lock-in” effect. 11 While an influence of firm-specific collateral on the cost of external funding would be more realistic, I make this simplifying assumption to avoid an additional channel of monetary transmission. Feedback from the loan rate into individual firms' optimal investment and production decisions creates an incentive to exert influence on rlt by accumulating excess capital. In a symmetric equilibrium, the assumption of economywide collateral is entirely unproblematic.

ð10Þ

where instantaneous profits are

gt = mt + 10

f

Et ∑ β λt + v gt + v ðiÞ;

bt−1 ð1 + rt−1 Þ m −bt − t−1 : πt πt

ð12Þ

To avoid that these proceeds are lost to the economy, I assume that they are transferred to the representative household as an additional source of non-labour income. 12 The real market price of uninstalled physical capital would then again equal 1, as it is identical in its characteristics to the final output good. 13 A rise in the policy rate increases thus the financial intermediaries' cost of holding reserves as well as the seignorage profit of the central bank.

J.H.F. Güntner / Economic Modelling 28 (2011) 1891–1901

Monetary policy follows a simple version of the standard Taylor (1993) rule:
 −1 r rt = ð1−ρÞ β −1 + φπ ðπt −1Þ + ρrt−1 + t :

ð13Þ

The risk-free nominal interest rate, rt, adjusts to offset any deviations of current inflation from its target value.14 In a stationary environment, it is reasonable to assume that the central bank targets strict price stability, i. e. a zero inflation rate. Interest rate inertia (0 b ρ b 1) captures the aversion to fluctuations in the policy instrument. The shock rt is beyond the authority's control and prevents an exact pursuit of the policy rule. The Taylor principle for stability is fulfilled, if the central bank raises the real interest rate in response to an inflationary shock. Kwapil and Scharler (2010) emphasise that equilibrium determinacy requires a stronger response than the standard φπ N 1, if the pass-through from monetary policy shocks to bank retail rates which are more relevant for consumption and investment decisions is incomplete in the long run. While retail rate adjustment costs and monopolistic bank competition entail significant interest rate smoothing in the short run, long-run pass-through in my model is always complete. Consequently, the standard Taylor principle is both necessary and sufficient in order to guarantee a determinate equilibrium. 3. Intertemporal optimisation of agents While deriving the first order conditions (FOCs) of households and firms is entirely standard and skipped here for the sake of brevity, the profit maximisation of financial intermediaries deserves to be discussed. 3.1. Optimal bank behaviour In equilibrium, bank i satisfies the following FOCs w. r. t. dt(i), bt(i), st(i), and mt(i):
 d d λt + 1 1 + rt ðiÞ ω λ ðiÞ ϕ d −1 = t − r + βEt mt ðiÞ λt λt 2 πt + 1 1 = βEt

d

rt ðiÞ −1 d ðiÞ rt−1

λt + 1 ð1 + rt Þ πt + 1 λt


 l l ϕl λt + 1 1 + rt ðiÞ λ ðiÞ wt st ðiÞ + r + t −1 = βEt λt ð1−σ Þlt ðiÞ λt 2 πt + 1

!2 ð14Þ

ð15Þ !2 l rt ðiÞ −1 l ðiÞ rt−1 ð16Þ

βEt

λt + 1 1 ωdt ðiÞ = 1− ; λt πt + 1 mt ðiÞ2

ð17Þ

where λd(i) and λl(i) are the multipliers on its deposit and loan demand constraints. Combining Eqs. (14) and (15), we receive an expression for the inside money premium, i. e. the spread between the risk-free interest rate and the return on deposits at bank i. IMPt : Et

d  ϕd β λt + 1
ω λ ðiÞ d − t rt −rt ðiÞ = + r πt + 1 λt mt ðiÞ λt 2

!2 d rt ðiÞ −1 d ðiÞ rt−1

This interest differential is determined by the marginal cost of deposit provision (the first term on the right hand side), the marginal cost in terms of household utility of a loss of clients who dissolve their accounts 14 Alternative Taylor rules, e. g. embedding a reaction to the so-called output gap, change neither qualitative nor quantitative results significantly, provided that parameter values are empirically relevant.

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at the bank (the second term on the right hand side) and quadratic interest rate adjustment costs (the third term on the right hand side). Equivalently, we may substitute from Eq. (15) into the FOC with respect to monitoring, Eq. (16), to obtain an expression for the external finance premium. It quantifies the opportunity cost of firms when relying on external funds, i. e. bank loans. EFPt : Et

l  ϕl β λt + 1
l wt st ðiÞ λ ðiÞ − t rt ðiÞ−rt = + r πt + 1 λt ð1−σ Þlt ðiÞ λt 2

l

rt ðiÞ −1 l rt−1 ðiÞ

!2

The meaning of right hand side terms is accordingly: The marginal cost of an additional unit of monitoring effort, st(i), the change in utility terms of a gain or loss in loan market share, and the quadratic costs of adjusting the loan interest rate. I finally combine Eq. (17) with Eq. (15) to derive an explicit demand for central bank money: β λt + 1 ωdt ðiÞ Et r = ⇔ mt ðiÞ = π t + 1 λt t mt ðiÞ2

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u ωdt ðiÞ u  : u t 1 βrt Et πt + 1

ð18Þ

Commercial banks can neither influence the policy rate rt in open market operations, nor do they face adjustment costs. Bank i accumulates reserves until the marginal product of mt in deposit provision equals the spread between the central bank-determined interest rate and the return on high-powered money. The loan production function and a firm's credit requirement complete the above FOCs and imply that the demand for loans will always be satisfied in equilibrium. These conditions arise in a framework with fully competitive banks in very similar form. Monopolistic competition among private banks adds two new decision variables. Deposit and loan interest rates are set in the face of adjustment costs and a proportional loss or gain of market share. Accordingly, the optimal values of rdt and rlt, respectively, fulfil the following FOCs: !η −1   rtd ðiÞ d dt ω 1− d d mt ðiÞ rt rt !η −1 " # d dt rt ðiÞ d 1 + rtd ðiÞ rtd ðiÞ ηd + d −βEt λt + 1 πt + 1 rtd rtd rt ! !η r d ðiÞ rtd ðiÞ d dt −1 −λt ϕrd d t d rt−1 ðiÞ rtd rt−1 ðiÞ ! !η d d r ðiÞ rt + 1 ðiÞ d rtd + 1 ðiÞ dt + 1 + βEt λt + 1 ϕrd t +d 1 −1 rt ðiÞ rtd+ 1 rtd ðiÞ2 !η −1 !η −1 !2 ϕd rtd ðiÞ rtd ðiÞ d dt rtd ðiÞ d dt d −1 −λt ηd r −λ η =0 t d d 2 rt−1 rtd rtd ðiÞ rtd rtd

λt ηd

ð19Þ

!−η −1 !−η −1 " # l l rtl ðiÞ lt lt rtl ðiÞ 1 + rtl ðiÞ rtl ðiÞ λt ηl −βEt λt + 1 ηl − l πt + 1 rtl rtl rtl rt rtl ! !−η l r l ðiÞ rtl ðiÞ lt −λt ϕrl l t −1 l rt−1 ðiÞ rtl rt−1 ðiÞ ! !−η l l l l r ðiÞ rt + 1 ðiÞ rt + 1 ðiÞ lt + 1 + βEt λt + 1 ϕrl t +l 1 −1 l rt ðiÞ rt + 1 rtl ðiÞ2 !2 !−η −1 !−η −1 l l ϕl rtl ðiÞ rtl ðiÞ lt rtl ðiÞ lt l + λt ηl r + λ η = 0: −1 t l l 2 rt−1 rtl rtl ðiÞ rtl rtl

ð20Þ It is straightforward to simplify these equations, dividing by the marginal utility of household consumption, λt, and by the economywide average levels of sight deposits, dt, and loan contracts, lt, as well as multiplying them by rtd and rtl, respectively.

1896

J.H.F. Güntner / Economic Modelling 28 (2011) 1891–1901

3.2. Symmetric equilibrium The competitive equilibrium is an infinite sequence for the endogenous variables, where all economic agents optimise, the monetary authority follows its Taylor rule, and goods as well as financial contract markets clear. The equilibrium conditions of the household and the central bank replicate their FOCs. The same is true for the monopolistically competitive firms and banks. Although the latter two profit from quantifiable market power which allows each firm j to set its price and each bank i to set its interest rates independently, I assume symmetric behaviour in the following. Facing a common economic state and only aggregate innovations, their factor demand and price-setting decisions will be identical in equilibrium. The symmetric equilibrium is summarised by the system of equations in Appendix A. 4. Calibration and stationary equilibrium From the symmetric equilibrium, it is straightforward to derive the deterministic steady state by dropping time indices and setting the only stochastic disturbance r = 0.15 Wherever possible, I calibrate the parameter set in accordance with the recent literature, as e. g. Christiano et al. (2005). With regard to banking-related parameters, prior sources of reference are rare. My calibration aims thus at empirically relevant steady-state values of key financial variables, in particular of bank interest rates and spreads. 4.1. Choice of parameter values 4.1.1. Stationary equilibrium parameters The household discount factor β is set to a quarterly value of 0.995 to match the average inflation-adjusted Effective Federal Funds Rate between 1985 and 2010, This corresponds to a real annual policy rate of 2%. The utility weight of leisure ϕ is left to adjust so that the representative household spends one third of its total time endowment working in either firms or banks. The household displays significant habit persistence (h = 0.7) and is required to guarantee α = 80% of consumption by bank deposits. I set the income share of capital in goods production to γ = 0.35. Productive capital depreciates at a quarterly rate δ of 2.5%. A price elasticity of demand for intermediate goods μ = 6 implies a steadystate monopolistic mark-up over marginal cost of 20%. Collateral is relatively more productive in banking than in the goods sector. The higher a borrower's guarantee, the less screening and monitoring effort must be employed by banks to provide a certain amount of credit and ensure its repayment. Without collateral, no loans are produced, at all. Similar to Goodfriend and McCallum (2007), I therefore assume σ = 0.6. Installed physical capital is recoverable and marketable only to an extent κ of 20%. A constant TFP F = 6 completes the parameters related to loan production. The latter are calibrated to match Rl to the average US Prime Lending Rate between 1985 and 2010. The stationary equilibrium value of the deposit interest rate is highly sensitive to marginal administration costs. To obtain a reasonable differential, ω is kept very low.16 The interest elasticities of deposit and loan demand, ηd and ηl, are not yet well-established in the New Keynesian literature. Henzel et al. (2009) and Gerali et al. (2010) represent the only sources of reference 15 Due to the highly nonlinear nature of the model, a closed form analytical solution is not admissible. Instead, the steady state is solved numerically by means of the Gauss–Newton method in MATLAB. 16 Higher ω easily leads to a negative real interest rate on household deposits. While this is not unrealistic when considering nominal interest rates on checking or overnight deposit accounts and correcting for inflation, I favour a calibration with positive steady-state real return on all financial assets.

known to the author.17 Setting ηd = 5 and ηl = 7, I assume that banks face a higher elasticity of substitution in the loan market. As a consequence, they demand a lower markup over marginal costs.18 Moreover, banks and firms enjoy comparable levels of market power. Due to the lack of microeconomic evidence, the CES coefficients are the most obvious source of vagueness in my calibration. 4.1.2. Dynamic equilibrium parameters The parameters affecting dynamic bahaviour are frequently identified by “taking models to the data” (see e. g. Ireland, 2003). Accordingly, the business cycle literature provides estimates for at least some of the quadratic adjustment cost coefficients present in this model. Following the results of Christiano et al. (2005) in a sticky price setting without variable capital utilisation, I set the investment adjustment cost parameter ϕi to 1.58. Moreover, the coefficient of price rigidity ϕp is set to 100, a value in the mid range of the corresponding estimates in Ireland (2003). Empirical evidence for the remaining adjustment cost coefficients, ϕrd and ϕrl, is rather limited. It seems reasonable to render it similarly costly for a bank to change its interest rate as it is for a firm to change its price. With regard to the different measures of price – which is a numéraire, here – and interest rates, as well as to the steady-state values of retail rates per quarter, I choose ϕrd = 0.25 and ϕrl = 1.16.19 The Taylor rule is characterised by interest-rate inertia and an exclusive reaction to deviations from the zero target inflation rate. The central bank weights rt − 1 with ρ = 0.75. In order to satisfy the Taylor principle discussed in Section 2.5, I set φπ to 1.5, in line with the author's original proposal. It is common in the literature to specify monetary policy shocks as pure white noise with a quarterly standard deviation, σr, of 25 basis points. An innovation of this magnitude corresponds to a one percentage point change in the policy rate on an annual basis. Table 1 of Appendix C summarises the set of benchmark parameter values used in the following numerical analysis. 4.2. The stationary equilibrium Given these parameters, the model predicts standard values for the capital-output, the consumption-to-GDP, and the investment-to-GDP ratio in steady state. Both banks and firms earn a positive monopolistic rent. Table 2 of Appendix C provides a complete list of steady-state values. The stationary equilibrium applies for a period length of one quarter and zero inflation. Therefore, r, rd, and rl imply an annual real interest on risk-free bonds (the policy rate), sight deposits, and loans of about 2%,1%, and 4.6%. This corresponds to a steady-state annual IMP of 100 basis points and a steady-state annual EFP of 2.6%. While there is no empirical counterpart to which the IMP could be compared directly,20 the EFP matches the empirically observed average spread between the Effective Federal Funds Rate and the US Prime

17 In these, the interest elasticity of loan demand by firms is set to 3.5 and 3.1, respectively. Gerali et al. (2010) choose values of 2.79 for loans to households and − 1.46 for deposits. A negative elasticity of substitution implies a markdown on the deposit rate, due to an upward sloping demand curve. 18 This calibration is motivated by the seemingly stronger ties between commercial banks and private households as depositors (compare e. g. Hannan and Berger (1991) and van Leuvensteijn et al. (2008)). 19 Gerali et al. (2010) estimate quadratic adjustment cost coefficients for bank retail rates, receiving posterior mean values of 3.5 for household deposits and 9.36 for loans to firms. While adjustment costs are not weighted by the respective interest rates in d l my model, the fact that rˆt and rˆt are defined i. t. o. percentage point deviations from steady state allows to take their estimates as a guideline. Calibrating ϕrd and ϕrl somewhat more moderately guarantees that interest rates are not overly sticky. 20 Remember that household deposits dt correspond to an aggregate including both sight deposits and cash or to an imaginary highly liquid asset, in general, for which we lack interest rate data.

J.H.F. Güntner / Economic Modelling 28 (2011) 1891–1901

Lending Rate from 1985 to 2010. This is no surprise, of course, as the corresponding interest rate data were used to calibrate the model. The companion working paper, Güntner (2009), analyses in detail the quantitative effects of imperfect competition among banks on longrun economic activity. Stationary output, investment, and employment are negatively correlated with both the IMP and the EFP, in this model. The smaller ηd and ηl, i. e. the less sensitive the demands for deposits and loans of bank i are to rdt (i) and rlt(i), the higher is the markup, respectively markdown, demanded on marginal costs. The impact of deposit market competition on economic activity is quantitatively small, even for ηd approaching its lower bound of 1, whereas moderate markups over marginal costs of loan production yielding an annual EFP of 6.5 percentage points are sufficient to reduce steady-state output and investment by 1.5% and 2.5% relative to an environment with perfectly competitive banks. In line with the findings of van Leuvensteijn et al. (2008), bank market power leads to an increase in spreads between retail rates and the policy rate, causing an under-provision of agents with liquidity and working capital loans. In an economy with monopolistic competition among financial intermediaries, the model thus predicts a reduction in output, consumption, employment, and investment below their potential steady-state values.

1897

0.05

0

0

−0.05 −0.05 −0.1

ηd=5

−0.15 −0.2 0

5

10

15

The purpose of this dynamic analysis is to assess the impact of monopolistic competition among private banks on the transmission and thus the efficiency of monetary policy.21 For the numerical simulations, the model is loglinearised at the non-stochastic steady state.22 Appendix B contains the transformed system of equilibrium conditions. In the light of recent central bank behaviour, it seems to be of particular interest whether and to what extent the responses to a sudden monetary expansion, i. e. the short-run pass-through from a drop in the policy rate to the real economy, are affected by the degree of competition in the banking sector. 5.1. The degree of deposit market competition

ηd=5

−0.1

50 →∞

20

−0.15

50 →∞

0

Inside Money Premium 0.2

10

15

20

50 →∞

0.1

5

20

High−Powered Money m

ηd=5

ηd=5 50 →∞

10

0 0

−0.1 −0.2 0

5

10

15

20

−10

0

Sight Deposits d

5

10

15

0.2 ηd=5

ηd=5 50 →∞

0.1

0.05

0.05 5

10

15

50 →∞

0.15

0.1

0 0

20

0

0

Output y ηd=5

0.2 0.15

15

0.4

20

0.1

0.05

0 15

ηd=5 50 →∞

0.2

0.1

10

10

0.3

50 →∞

5

5

Employment n

0.25

0 0

20

Consumption c

0.2 0.15

5. Financial intermediation and monetary pass-through

Deposit Interest Rate Rd

Risk−Free Interest R 0.05

20

−0.1

0

5

10

15

20

Fig. 1. Impulse responses to a monetary policy innovation for ηd = 5, 50, and 1 ⋅ 1012.

For the following analysis, the interest elasticity of demand for the deposits provided by a certain bank, ηd, is successively set to 5, 50, and 1 ⋅ 1012. These values are chosen in order to characterise the benchmark, a situation with reduced market power, and perfect competition in the market for deposits. A selection of impulse responses for the first 20 periods following an expansionary monetary policy shock on the scale of one standard deviation is presented in Fig. 1. As expected, the stock of high-powered money soars after a drop in the policy rate. Yet, the magnitude of m's reaction is insensitive to the parameter of interest. I therefore focus on the impulse responses of rd and the corresponding interest differential. Even under perfect competition, the IMP displays some variation which arises from the endogenous costs ωdt of deposit provision, . With ηd=50, demand for bank deposits is still mt elastic enough to trace the previous scenario closely. If, however, the market for deposits is highly monopolistically competitive, the IMP drops by 17.6 basis points in response to the

21 While the subsequent sections focus only on the impulse responses to a “monetary policy shock”, rt , Güntner (2009) shows that a very similar version of the model is reasonably well able to reproduce the empirically observed responses of key variables to standard supply and demand shocks as well as to shocks emerging directly from the banking sector. These disturbances are not discussed here. 22 The dynamic system of linearised equations is solved in DYNARE on MATLAB. All cases are simulated numerically for 10,000 periods in order to extract the policy and transition functions as well as first and second order moments of the model's endogenous variables.

monetary expansion. Private banks find it optimal to adjust the deposit rate with a lag and by only a fraction of the percentage point revision undertaken in a perfectly competitive market. The strict complementarity of deposits and consumption enforced by the DIA constraint implies that a dampened reduction in rd, corresponding to a more pronounced decrease in the liquidity premium, lowers the cost of deposit-secured consumption to the household. Accordingly, the response of consumption and sight deposits which move one-for-one in percentage terms is accelerated by banks' interest rate smoothing. Some qualification is appropriate, at this point. The predicted acceleration hinges on the assumption that consumption and deposits are complements, though not on the strict complementarity imposed by the DIA constraint. As mentioned earlier, the optimisation problem of households can alternatively be set up with deposits in the utility function (DIU). Analogue to the MIU setting (see e. g. Walsh, 2003), consumption and deposits can be either substitutes or complements in a DIU model, depending on the parameterisation of the utility function. The acceleration results we obtain, when households face a DIA constraint, carry over to various alternative formulations with deposits in the utility function, as long as ct and dt are Edgeworth complements, i. e. the marginal utility of consumption increases in the amount of sight deposits held by the household. If instead consumption and deposits are Edgeworth substitutes (ucd b 0), interest rate setting power of banks in the deposit market attenuates the pass-through of monetary policy.

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J.H.F. Güntner / Economic Modelling 28 (2011) 1891–1901

Output, consumption, and employment will then fluctuate less over the business cycle than under perfect competition.23 Monopolistic competition has a sizeable effect on consumption and deposits only in the first year following the change in the policy rate. The percentage deviation from steady state for ηd = 5 exceeds that in the perfect competition case by up to 13%. Due to the larger reduction in the IMP, the representative household increases consumption by more, ceteris paribus, the higher the market power of banks. Similarly, GDP and employment respond more to an innovation in the policy rate, while firm's investment behaviour and the physical capital stock (not shown in Fig. 1) are virtually unaffected. The effects on y and n are quantitatively small, not exceeding 6% in terms of the deviation from steady state even for a low interest-rate elasticity. In this model, limited competition in the market for deposits amplifies the expansion of real economic activity in response to an unforeseen drop in the monetary policy rate. 5.2. The degree of loan market competition The second dynamic analysis examines monopolistic competition in the market for loans. Again, I pick three values for parameter ηl that characterise the benchmark, an increased, and an – at least approximately – infinitely high substitutability between the working capital loans provided by different banks. Fig. 2 displays the impulse responses of key variables to a monetary expansion for ηl = 7, 50, and 1 ⋅ 1012. In response to an unexpected drop in the monetary policy rate, commercial banks lower the loan rate, as well. Yet, how closely rl follows r depends on two aspects: On the one hand, a rising real wage rate and higher need for monitoring effort – due to the increased loan demand – raise the cost of loan production and thus the EFP. On the other hand, banks take into account the adjustment cost and market share effects of their behaviour when setting retail rates. In line with the empirical evidence, monopolistic competition among banks attenuates the pass-through from market to loan interest rates in this model. For a demand elasticity of 7, rl decreases by a maximum of 3 basis points as opposed to 18.5 basis points when ηl → ∞, i. e. the relative short-run pass-through from an innovation in the policy rate to the loan rate amounts to less than one sixth. While the EFP remains largely constant in a competitive loan market, its increase under monopolistic competition is negatively related to the value of ηl, temporarily rising by 17 basis points in the benchmark case. Even with only a modest degree of market power, banks find it optimal to significantly smooth the loan rate in response to a change in r, allowing for a transitory increase in the EFP by more than 10 basis points. Surprisingly, the structural composition of the loan market has a much stronger influence on the transmission of monetary impulses to the real economy variables than that of the market for deposits. As depicted in the bottom half of Fig. 2, the percentage deviations from steady state of output, investment, and employment for ηl = 7 fall well behind their counterparts under perfect competition. If firms rely on working capital loans in order to produce, as in this model, monetary policy also operates through the well-known cost channel (see e. g. Hülsewig et al., 2009). A drop in the relevant interest rate will then reduce marginal costs, which – especially if the shock is expected to be temporary – provides an extra incentive for producers to expand their labour demand and capital investment. If, moreover, retail rates rather than the policy rate are relevant for firms, interest rate smoothing behaviour of monopolistically competitive banks may significantly attenuate the actual expansionary or contractionary effect of a given monetary stimulus. Note that banks are subject to the same interest rate adjustment costs regardless of the value of ηl. 23 A flexible DIU specification along the lines of Walsh (2003), Chapter 2, favours complementarity between c and d for empirically plausible parameterisations of the utility function. For this reason, the further discussion is limited to the acceleration scenario.

Loan Interest Rate Rl

Risk−Free Interest R 0.05

0.05

0

0

−0.05

−0.05

−0.1

−0.1

ηl=7

−0.15 −0.2 0

5

10

15

20

−0.2 0

External Finance Premium 0.3

ηl=7

−0.15

50 →∞

50 →∞

5

10

15

1

ηl=7

ηl=7

50 →∞

0.2

20

Credit Supply l 50 →∞

0.1

0.5

0 −0.1 0

5

10

15

20

0 0

Output y

5

10

15

20

Investment i

0.25

0.8

ηl=7

0.2

50 →∞

0.15

ηl=7 50 →∞

0.6 0.4

0.1 0.2

0.05 0 0

5

10

15

20

0 0

Employment n 0.4

15

20

Bank Employment s ηl=7

2

50 →∞

0.2

10

2.5

ηl=7

0.3

5

50 →∞

1.5 1

0.1

0.5

0 −0.1 0

0 5

10

15

20

−0.5 0

5

10

15

20

Fig. 2. Impulse responses to a monetary policy innovation for ηl = 7, 50, and 1 ⋅ 1012.

Accordingly, any difference in impulse responses to the monetary policy shock arises solely from a change in the degree of bank market power. Intuitively, investment should be most sensitive to monetary policy shocks and thus to interest rate smoothing. On impact, its percentage deviation from steady state lies between + 0.27 and +0.39 — a difference of 45%. The peak expansion ranging from 0.57 to 0.65% is attained after three quarters and one year, respectively. Limited competition among banks costs the economy approximately 3.6, 5.3, and 10.3 basis points of the potential expansion in output, employment, and credit demand. While these figures are small in absolute terms, they correspond to differences of 15.3% for l and around 19% for both y and n, relative to ηl → ∞. The preceding simulations suggest that monopolistic competition in the loan market represents a potential bottleneck for monetary policy. In this respect, the model matches the empirical evidence (see e. g. van Leuvensteijn et al., 2008 who exclusively consider loan market competition, and de Bondt, 2005). The pass-through from policy or market interest rates to bank retail rates is weaker in less competitive markets. Banks as interest rate makers cushion thus the response of real economic variables. 6. Conclusion In the present model, private agents rely on two types of financial services provided by commercial banks. Also, the deposits and loans of

J.H.F. Güntner / Economic Modelling 28 (2011) 1891–1901

different banks substitute imperfectly against each other. The spreads between the risk-free refinancing rate and banks' retail rates, i. e. the inside money and external finance premium, are therefore determined by standard cost arguments of financial intermediation and by the degree of monopolistic competition in the banking sector. In the longrun steady state, when adjustment costs do not play a role, the real effects of market imperfections are small. My findings from the dynamic simulations suggest that bank market power might have a sizeable impact on the pass-through of monetary policy in the short run. Monopolistic competition among the providers of deposits acts as a financial accelerator, in this model. By contrast, the heterogeneity of bank credit attenuates the response of the loan rate to changes in market interest rates and absorbs thus part of the monetary policy shock. While the degree of competition in deposit markets has only marginal influence, the interest sensitivity of loan demand appears to be quantitatively important for the economy's behaviour over the business cycle.

λt =

1 βh − −αξt ct −hct−1 ct + 1 −hct

ðA:1Þ

ϕ 1−nt −st

λt w t =

ðA:2Þ

1 + rtd λt = βEt λt + 1 + ξt πt + 1

ct + dt = wt ðnt + st Þ +

ðA:3Þ


 d dt−1 1 + rt−1

cb

gt = mt +

πt

+ gt +

+

cb gt

ðA:5Þ

αct = dt βEt

 λt + 1
l 1 + rt wt nt = ð1−γÞΞt yt πt + 1

ð1−μ Þ + μ

−βEt

ðA:4Þ

ðA:6Þ

2 ϕp
π t Ξt π2 π −1 = ϕp t2 − t +μ λt 2 π π π

λt + 1 π2 π ϕp t +2 1 − t + 1 λt π π

!

bt−1 ð1 + rt−1 Þ ωdt −mt −lt −wt st − πt mt !2 !2 ϕrd ϕrl rtd rtl − −1 dt − −1 lt d l 2 rt−1 2 rt−1

ðA:7Þ

 2    1 + rtl it 2 i ϕ it + λt ϕi − t −1 + λt i πt + 1 it−1 it−1 2 it−1  3  2  it + 1 i y = βEt λt + 1 ϕi − t +1 + βγEt Ξt + 1 t + 1 it it kt

kt = ð1−δÞkt−1 + it

ðA:9Þ

γ 1−γ kt−1 nt

gt = yt −

ðA:8Þ

ðA:10Þ


 l 1 + rt−1 ðwt−1 nt−1 + it−1 Þ πt



−

2 ϕ ϕp
π t it −1 − i 2 π 2 it−1

2 −1 it

ðA:11Þ mt = bt

ðA:12Þ

ðA:15Þ ðA:16Þ

lt = wt nt + it σ 1−σ

lt = F ðgt + κkt Þ st

ðA:17Þ

d  ϕd β λt + 1
ω λt d Et rt −rt = − + r πt + 1 λt mt λt 2

!2

d

rt

d rt−1

 ϕd β λt + 1
l wt st λl rt −rt = − t + r Et πt + 1 λt ð1−σ Þlt λt 2

−1

rtl l rt−1

ðA:18Þ !2 −1

β λt + 1 ωd ðrt −1Þ = 2t πt + 1 λt mt

λt = βEt λt + 1

−βEt

rtd d rt−1

λt + 1 ϕrd λt

ðA:19Þ

ðA:20Þ

1 + rt πt + 1

ηd −βð1 + ηd ÞEt ϕd −ηd r 2

yt + 1 yt

ðA:14Þ

−

!

βEt λt + 1

yt =

bt−1 ð1 + rt−1 Þ m −bt − t−1 πt πt



 l d lt−1 1 + rt−1 dt−1 1 + rt−1 m gtf = dt + bt + t−1 + − πt πt πt

Et f gt

ðA:13Þ

Eqs. (A.14) and (A.15) are the central bank's and a financial intermediary's profit functions, while Eqs. (A.16) and (A.17) describe the equilibrium loan demand and supply. Eqs. (A.18)–(A.21) are the symmetric IMP, EFP, money demand and bond FOC, respectively. Finally, Eqs. (A.22) and (A.23) represent the optimal interest rate setting of banks in a scenario with monopolistic competition and quadratic adjustment costs.

Appendix A. The symmetric equilibrium The symmetric equilibrium is an infinite time series of the 23 endogenous variables y, c, i, k, n, s, w, g, g f, r, r d, r l, m, d, l, π, g cb, b, λ, ξ, Ξ, λd, and λl given the exogenous path of r that solves the following system of 23 equations. Eqs. (A.1) to (A.13) replicate the household and firm FOCs as well as the corresponding constraints and monetary policy:

1899


 −1 r rt = ð1−ρÞ β −1 + φπ ðπt −1Þ + ρrt−1 + t :

ðA:21Þ

λt + 1 rtd λ β ω −ηd Et t + 1 −ηd mt λt πt + 1 λt πt + 1 !2 −1

2

= ϕrd

rtd

rtd

!

− d d2 rt−1 rt−1 ! 2 rtd+ 1 rtd+ 1 dt + 1 λd − d + ηd t 2 dt λt rt rtd

ðA:22Þ

!2 ϕrl λt + 1 rtl λt + 1 β rtl ηl + βð1−ηl ÞEt −ηl Et + ηl −1 l λt π t + 1 λt π t + 1 2 rt−1 ! ! l2 l l2 l l rt rt λt + 1 rt + 1 rt + 1 lt + 1 λ = ϕrl − ϕ − −ηl t −βE l t 2 r l l l2 l λt lt λt rt−1 rt r rt t−1

ðA:23Þ Appendix B. The model in loglinear form Below, xˆ t stands for the percentage deviation of variable x from its d stationary equilibrium in period t. Note that the denotations rˆt , rˆt , and l rˆt have a slightly different meaning: The interest rates on risk-free bonds, deposits, and loans enter the loglinear system in terms of absolute, i. e. in percentage point deviations from steady states.

1900

J.H.F. Güntner / Economic Modelling 28 (2011) 1891–1901

The order and the meaning of Eqs. (B.1)–(B.17) corresponds to that in Appendix A. ˆ − 0 = λλ t

h
 i 1 2 βhcˆt + 1 − 1 + βh cˆt + hcˆt−1 + ξαξˆ t cð1−hÞ2

ˆt + λ ˆ t− 0=w 0=



1 nnˆ t + ssˆt 1−n−s

ðB:1Þ

ðB:3Þ



 ˆ t + sˆt − d rˆdt−1 ˆ t + nˆ t −ws w 0 = ccˆt + d dˆt −wn w π
 d  1 + r d
f f cb ˆ t −g gˆ t −g gˆ t −g gˆ cb − dˆ t−1 −π t π

ðB:4Þ

0 = dˆt −cˆt

ðB:5Þ


 l ˆ −yˆ ˆ ˆ t + nˆ t −Ξ ˆ t +1 + w 0 = rˆt + Et λ t + 1 −π t t

ðB:6Þ

ˆ t −ϕp π ˆ t + ðμ−1ÞΞ ˆ t + βϕp Et π ˆ t +1 0 = ð1−μ Þλ

ðB:7Þ

l

l rˆt ˆ t +1 −Et π 1 + rl

0 = kˆ t −ð1−δÞkˆ t−1 −δ iˆt ˆ t −yˆ t 0 = γkˆ t−1 + ð1−γÞn wn + i l rˆt−1 π  i 1 + rl h
ˆ ˆt wn wt−1 + nˆ t−1 + i iˆt−1 + ðwn + iÞππ + π

!

ðB:8Þ

0=

 β

 β
d d ˆ t +1 + λ ˆt + ωm ˆ ˆ t + 1 −λ rˆ −rˆ − r−r Et π π t t π m t λd
ˆ d ˆ  + λt − λt λ  β
 
β
l l ˆ t +1 + λ ˆt ˆ t + 1 −λ rˆt −rˆt − r −r Et π π π l  ws
ˆ λ
ˆ l ˆ  − wt + sˆt −lˆt + λt −λt ð1−σ Þl λ

ðB:20Þ

ˆ ˆ t + 1 −λ ˆ t + 1 + Et λ 0 = βrˆt −Et π

ðB:21Þ

  ϕd ϕd β ˆdt+ 1 − ð1 + βÞ r + ð1 + ηd Þ rˆdt + r rˆdt−1 E r t π rd rd rd i
 ωˆ βh d ˆ t+1 + λ ˆt ˆ t + 1 −λ + ηd mt + ð1 + ηd Þr + ηd Et π m π λd
ˆ d ˆ  −ηd λt −λt λ   ϕl ϕl ϕl l β l l 0 = β rl Et rˆt + 1 − ð1 + βÞ rl −ð1−ηl Þ rˆt + rl rˆt−1 π r r r 0=β

ðB:18Þ

ðB:19Þ


 β βr
ˆ t +1 + λ ˆ t − ωd dˆt −2m ˆt ˆ −λ rˆ − E π π t π t t +1 m2

ϕrd

ðB:22Þ

i

l  βh l ˆ t +1 + λ ˆ t + ηl λ λ ˆt ˆ t −λ ˆ t + 1 −λ ð1−ηl Þr −ηl Et π π λ ðB:23Þ l

−

ðB:10Þ

Appendix C. Tables ðB:11Þ

ˆ t −bˆ t 0 =m

ðB:12Þ

ˆ t −rt 0 = rˆt −ρrˆt−1 −ð1−ρÞφπ ππ

ðB:13Þ


 cb cb ˆ − b rˆ − bð1 + r Þ bˆ −π ˆ t + bbˆ t 0 = g gˆ t −mm ðB:14Þ t t−1 π t−1 π  m
ˆ ˆt + mt−1 −π π

 l 1 + rl
 m f f ˆ t−1 −π ˆt − ˆt 0 = g gˆ t + llˆt −ddˆt −bbˆ t − m lˆt−1 −π π
π d  d 1+r
l l d d ˆ t + rˆt−1 − rˆt−1 + dˆ t−1 −π π π π  bð1 + r Þ
ˆ ˆt + bt−1 −π π

 b ˆ t + ws w ˆ t + sˆt + ωd dˆt −m ˆt + rˆt−1 + mm π m ðB:15Þ
 ˆ t + nˆ t −iiˆt ðB:16Þ 0 = llˆt −wn w σg σκk ˆ gˆ − k −ð1−σ Þsˆt g + κk t g + κk t

0=

ðB:9Þ

0 = g gˆ t −yyˆ t +

0 = lˆt −

0=

ðB:2Þ


 1 d ˆ t + 1− 1 ˆ t −ξξˆ t ˆ t + 1 + Et λ rˆt −Et π λλ λ−ξ 1 + rd

1+r 0 = βϕi iˆt + 1 −ϕi ð1 + βÞ iˆt + ϕi iˆt−1 −β π i Ξy h ˆ ˆ ˆ Et yˆ t + 1 −λ + βγ t + 1 + Ξt + 1 − kt λk

loan interest rate, respectively. Note that imperfect competition among banks yields a kind of hybrid Phillips curve in retail interest rates, when they are sticky.

Table 1 Benchmark calibration of all model parameters relevant for the economy's steady state and dynamic behaviour. Parameter Values (benchmark calibration) Coefficient

Value

Coefficient

Value

α β γ δ h ϕ ω σ F κ

0.8 0.995 0.35 0.025 0.7 1.45 0.001 0.6 6 0.20

μ ηd ηl ϕi ϕp ϕrd ϕrl ρ ϕπ σr

6 5 7 1.58 100 0.25 1.16 0.75 1.5 0.25

Table 2 Steady-state results obtained from the benchmark calibration of parameters. Steady-State Values (benchmark calibration)

ðB:17Þ

Eqs. (B.18) and (B.19) are the IMP and EFP equilibrium conditions expressed in percentage deviations from steady state, while Eqs. (B.22) and (B.23) are the loglinearised FOCs w. r. t. the deposit and

y

c

i

k

n

s

1.1222

0.8500

0.2708

10.8306

0.3311

0.0022 f

w

d

m

l

g

g

1.8242

0.6800

0.3085

0.8747

0.2374

0.0024

r

rd

rl

0.0050

0.0025

0.0116

π

IMP

EFP

1.0000

0.0025

0.0065

J.H.F. Güntner / Economic Modelling 28 (2011) 1891–1901

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