Leaning Against Windy Bank Lending*
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Contributor Notes

Author’s E-Mail Address: gmelina@imf.org; stefania.villa@unifg.it

Using an estimated dynamic stochastic general equilibrium model with banking, this paper first provides evidence that monetary policy reacted to bank loan growth in the US during the Great Moderation. It then shows that the optimized simple interest-rate rule features no response to the growth of bank credit. However, the welfare loss associated to the empirical responsiveness is small. The sources of business cycle fluctuations are crucial in determining whether a “leaning-against-the-wind” policy is optimal or not. In fact, the predominant role of supply shocks in the model gives rise to a trade-off between inflation and financial stabilization.

Abstract

Using an estimated dynamic stochastic general equilibrium model with banking, this paper first provides evidence that monetary policy reacted to bank loan growth in the US during the Great Moderation. It then shows that the optimized simple interest-rate rule features no response to the growth of bank credit. However, the welfare loss associated to the empirical responsiveness is small. The sources of business cycle fluctuations are crucial in determining whether a “leaning-against-the-wind” policy is optimal or not. In fact, the predominant role of supply shocks in the model gives rise to a trade-off between inflation and financial stabilization.

1 Introduction

The role of central banks in promoting financial stability, in addition to inflation stability, has been debated well before the Great Recession. The so-called “Greenspan doctrine”, which objects to the policy of leaning against the wind blowing from asset-prices, greatly influenced the central banking world before the crisis. However, in the aftermath of the Great Recession, the need to protect the banking sector from periods of unduly high or excessively low credit growth has led to a renewed interest in the “lean” versus “clean” role for monetary policy, with an emphasis on credit conditions.1

Indeed, the important role of credit markets in affecting business cycle fluctuations emerges also from the Basel III framework, aiming at protecting the financial sector from periods of excessive credit growth, often associated with an increase in systemic risk. On this aspect, Jordà et al. (2013) document that, in a sample of 14 countries and a period between 1870 and 2008, more credit-intensive expansions tended to be followed by deeper recessions and slower recoveries. Their measure of “excess credit” build-up during expansions is the rate of change of bank loans to GDP, in deviation from its mean. Furthermore, Bordo and Haubrich (2016) provide empirical evidence that bank lending significantly affects GDP fluctuations in the United States.

This paper focuses precisely on bank lending and it investigates whether monetary policy responded and should respond to credit exuberance. Figure 1 reports the intended changes in the Federal Funds Rate (FFR) around all meetings of the Federal Open Market Committee (FOMC) taken place during the Great Moderation, and whether, in the minutes of each meeting, credit was (i) not a particular concern; (ii) judged to be expanding; or (iii) judged to be weak or tight. 2 As reported in Table 1, in the vast majority of FOMC meetings (79%) in which the FFR was intended to be held constant, credit was not a particular concern. In most cases (79%) in which the FOMC intended to raise the FFR, an expansion in credit was mentioned; while in the greatest part of FOMC meetings (78%) in which the FFR was intended to be lowered, weak or tight credit was mentioned.3

Figure 1:
Figure 1:

Intended federal funds rate changes around FOMC meetings and concerns on credit conditions raised in FOMC minutes (1984Q1-2008Q2; shaded areas indicate NBER recessions)

Citation: IMF Working Papers 2017, 179; 10.5089/9781484312674.001.A001

Table 1:

Descriptive statistics on intended changes in the Federal Funds Rate (FFR) and credit conditions mentioned in minutes of FOMC meetings (1984Q1-2008Q2)

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This narrative analysis motivates an empirical investigation on the extent to which monetary policy had a concern on credit conditions beyond their implications for inflation and economic activity. To this end, we provide Bayesian estimates of a Dynamic Stochastic General Equilibrium (DSGE) model in which frictions in the bank loan market arise due to the presence of lending relationships,4 and monetary policy is set according to a credit-growth-augmented Taylor-type rule.

The estimated parameter representing the interest-rate response to nominal credit growth is statistically positive and economically important within various alternative monetary policy rules. Therefore, estimates point to the evidence that, during the Great Moderation, monetary policy leaned against the wind blowing from the loan market beyond its concern for price and output stability. To our knowledge, this is a novel result. In fact, in a model with financial frictions as in Bernanke et al. (1999). Christiano et al. (2010b) estimate a significant degree of “leaning against credit exuberance” in the euro area monetary policy framework, while Belke and Klose (2010) perform a similar analysis within a reduced-form GMM estimation. However, as far as estimated DSGE models for the US economy are concerned, the literature has so far offered contributions focusing on the reaction of the monetary policy rate to stock prices (for which we also control), but not to credit conditions (see Castelnuovo and Nisticò, 2010, among others).5

Is this the welfare-optimal policy? The answer to this question heavily depends on the sources of business cycle fluctuations. We perform a welfare comparison of alternative interest-rate rules, relative to the Ramsey policy, imposing an approximate zero-lower-bound constraint in a way similar to Levine et al. (2008). We find that optimal monetary policy features almost-zero responses both to the output gap and to credit growth. While the former result is in line with the findings of Schmitt-Grohe and Uribe (2007) in a model with perfect credit markets, the latter is a novel contribution.6 The explanation of such a finding lies in the fact that supply shocks – technology, price and wage mark-up – turn out to be the main drivers of output, lending and inflation fluctuations in the estimated model. These shocks imply a trade-off between inflation and output stabilization. In other words, there is no “divine coincidence” (Blanchard and Galí, 2007) for the two targets. Given the pro-cyclical behavior of lending in the model, a monetary policy that responds also to financial variables should respond more aggressively to inflation. As a result, it turns out to be optimal for monetary policy to respond exclusively to inflation.

The remainder of the paper is structured as follows. Section 2 presents the DSGE model. Section 3 outlines the estimation strategy, discusses empirical results and investigates the dynamic properties of the estimated model. Section 4 examines the welfare implications of alternative interest-rate policies. Finally, Section 5 concludes. An online appendix complements the paper by providing (a) the narrative assessment of the minutes of FOMC meetings; (b) the full set of equilibrium conditions; (c) the detrended model; (d) the deterministic steady state; (e) the derivation of the Ramsey equilibrium; (f) details on the construction of the dataset; (g) additional estimation results; and (h) robustness exercises for optimal policy.

2 Model

The model features standard frictions and a deterministic growth rate γ à la Smets and Wouters (2007) and is augmented with a banking sector that exploits lending relationships. This section outlines the optimization problem of each agent in the model and discusses some important equilibrium conditions. The full set of equilibrium conditions, detrending, and the deterministic steady state are reported in appendices B, C and D, respectively.

2.1 Households

Households are infinitely-lived and solve an inter-temporal utility maximization problem. The economy is populated by a continuum of households indexed by j ϵ (0,1). Each household’s preferences are represented by the following inter-temporal utility function:

Utj=EtΣs=0et+sBβt+s[(Xt+sj)φ(1Ht+sj)1φ]1σc1σc,(1)

where β ϵ (0,1) is the discount factor, etB is a preference shock, Xtj is habit-adjusted consumption, Htj is labor supply in terms of hours worked, σc is the relative risk aversion parameter and ϕ is a preference parameter affecting labor supply. Total time available to households is normalized to unity, thus 1Htj represents leisure time. As in Fuhrer (2000), Xtj is given by

Xtj=CtjθSt1c,(2)
Stc=ρSt1c+(1ρ)Ct,(3)

where Ctj is the level of consumption, Stc is the stock of external habit formation, θ ϵ (0,1) is the degree of habit formation, and ρ ϵ (0,1) is the persistence of the stock of habit.

Each household j is a monopolistic provider of a differentiated labor service and supplies labor Htj to satisfy demand,

Htj=(wtjwt)etWηWHt,(4)

where wtj is the real wage charged by household j, wt is the average real wage in the economy, ηW is the intra-temporal elasticity of substitution across labor services, etW is a wage mark-up shock, and Ht is average demand of labor services by firms. Similarly to Zubairy (2014), the households’ budget constraint also includes a Rotemberg quadratic cost of adjusting the nominal wage, Wtj, which is zero at the steady state. This cost is proportional to the average real value of labor services as in Furlanetto (2011), ξW2(WtjγWt1jΠ)2wtHt=ξW2(wtjγwt1jΠtΠ)2wtHt, where ξW is the wage adjustment cost parameter, Πt = Pt/Pt-1 is the gross inflation rate of price index Pt, and Π is the steady state value of inflation.

The representative household enters period t with Dt1j units of real deposits in the bank. During period t, the household chooses to consume Ctj; supplies Htj hours of work; receives real wage wt, profits of financial and non-financial firms Pt, bears the wage adjustment cost, pays lump-sum taxes Tt, and allocates savings in deposits at the bank, Dtj, that pay the net nominal interest rate RtD one period ahead. Therefore, the budget constraint reads as

Ctj+Dtj+ξW2(wtjγwt1jΠtΠ)2wtHtwtjHtj+1+Rt1DΠtDt1j+PtTt.(5)

Each household maximizes inter-temporal utility (1) with respect to Ctj,Dtj,wtj subject to (2), (3), (4) and (5).

2.2 Entrepreneurs

Entrepreneurs are distributed over a unit interval and indexed by e ϵ (0, 1). They borrow from banks to produce a differentiated output, Yte, sold in a imperfectly competitive market at price Pte. Firms solve two optimization problems: an intra-temporal problem – that can be thought of being solved by the financial department and gives rise to lending relationships – which determines the composition of their loan demand; and an inter-temporal problem in which they maximize the flow of discounted profits by choosing the quantity of factors for production and the price level.

Entrepreneurs minimize their borrowing costs by choosing their demand for each variety of loans and exhibit deep habits in lending.7 The literature has employed this feature to incorporate the effects of informational asymmetries on borrowers’ creditworthiness that lead to lending relationships into a DSGE model (see Aliaga-Diaz and Olivero, 2010; Aksoy et al., 2013; Melina and Villa, 2014 and Ravn, 2016, among others).8 The optimization problem consists in the following:

minLbteEt[011+RbtLΠt+1Lbtedb],(6)
s.t.[01(LbteθLSbt1L)11ηLdb]1/(11ηL)=(XtL)e,(7)
SbtL=ϱLSbt1L+(1ϱL)Lbt,(8)

where RbtL is the net lending rate, Lbte is the demand by firm e for loans issued by bank b, θL is the degree of habit in lending, SbtL is the stock of (external) habit in lending, ηL is the elasticity of substitution across varieties of loans, (XtL)e is the demand for loans by firm e augmented by lending relationships and ϱL is the persistence of lending relationships. Equation (6) represents overall lending expenditure, equation (7) imposes deep habits in lending, while equation (8) imposes persistence in the stock of habit.

The deep-habit-adjusted Dixit-Stiglitz aggregator in equation (7) captures two important findings in empirical finance literature: (i) banks differentiating loan products;9 and (ii) firms holding multiple bank relationships (see e.g. Ongena and Smith, 2000). Solving the cost minimization problem yields a downward-sloping demand for loans, which becomes a constraint in the banks’ profit maximization problem (equation 15).10

Entrepreneur e faces also an inter-temporal problem by solving which she chooses employment, Hte, capital, Kt+1e, investment, Ite, capital utilization, Ute, and the price level, Pte, to maximize the expected discounted value of its lifetime profits. Recalling that in this economy firms are owned by households, the stochastic discount factor of the former, Λt,t+1, is given by the inter-temporal marginal rate of substitution of the latter. The inter-temporal optimization problem is summarized by the following:

maxHte,Kt+1e,Ite,Ute,PteEtΣs=0Λt,t+s{Pt+sePt+sYt+sewt+sHt+seIt+seΨ(Ut+se)Kt+seξ2(Pt+sePt+s1eΠ¯)2Yt+s+(Xt+sL)e+Ξt+sΦt+s01(1+Rbt+s1L)Pt+s+1Pt+sLbt+s1edb},(9)
s.t.Kt+1e=Ite[1S(IteIt1e)]etI+(1δ)etKKte,(10)
LteζIte,(11)
Yte=(PtePt)etPηYt=F(etA,etK,Ute,Kte,Hte).(12)

Equation (9) is the sum of discounted profits expressed in terms of net cash flows, in which wtHte is the wage bill; Ite is the expenditure in investment goods; using capital at rate Ute entails a cost of Ψ(Ute)Kte, where Ψ(Ut)=γ1(Ut1)+γ22(Ut1)2;11 ξ2(Pt+sePt+s1eΠ¯)2Yt+s is a Rotemberg convex cost of adjusting prices; (XtL)e is the deep-habit-adjusted aggregate of loans; ΞtθL011+RbtL1+RtLSbt1Ldb is a deep-habit-specific term analogous to that of Ravn et al. (2006); Φt is a lump-sum cost, not affecting the firms’ behavior, needed to ensure that in equilibrium the amount of financing firms actually receive is given by the pure sum of all loans, i.e. (XtL)e+ΞtΦt=01Lbtedb;12 while 01(1+Rbt+s1L)Pt+s1Pt+sLbt+s1edb represents what they repay to banks. Equation (10) is a standard law of motion of capital, which depreciates at rate δ, and investment is subject to adjustment costs, where S(γ) = S’(γ) = 0 and S”(γ) > 0. In particular, following Smets and Wouters (2007), we assume that investment adjustment costs are quadratic: S(ItIt1)=ψ2(ItIt1γ)2,ψ>0, where ψ represents the elasticity of the marginal investment adjustment cost to changes in investment. The term etI represents a shock to the investment-specific technology process, while etK is a capital quality shock that enters the model as in Gertler and Karadi (2011) and represents a source of exogenous variations in the value of capital.13 We take constraint (11) from Aliaga-Diaz and Olivero (2010). This makes it necessary for firms to borrow from banks in order to finance a fraction ζ ϵ (0,1) of investment expenditures, i.e. it represents a financing constraint needed for external credit to play a role in the model.14 Without the imposition of this constraint, firms would always find it optimal to satisfy their financing needs via internal funds, given the presence of market power in the banking sector. Thus constraint (11) holds with equality in equilibrium and defines the total amount of loans demanded by firm e. Lastly, expression (12) equates the firm-specific Dixit-Stiglitz demand, with intra-temporal elasticity of substitution η and subject to price mark-up shock etP, to firm’s production, which we assume to obey to a Cobb-Douglas technology, F(etA,Ut,Kt,Ht)=etA(Ht)α(etKUtKt)1α, with α being the labor share of income and etA being a total factor productivity shock.

2.3 Banks

Each bank b chooses its demand for deposits, Dbt, the supply of loans to firms, Lbt, and the loan rate, RbtL, to maximize the expected discounted value of its lifetime profits.15 Banks are owned by households as well; therefore, their stochastic discount factor, Λt,t+1, is given by the inter-temporal marginal rate of substitution of households. The optimization problem is summarized by the following:

maxDbt,Lbt,RbtLEtΣs=0Λt,t,+s{1+Rbt+s1LΠt+sLbt+s11+Rt+S1DΠt+sDbt+s1},(13)
s.t.Lbt=Dbt,(14)
Lbt=(1+RbtL1+RtL)ηLXtL+θLSbt1L.(15)

Equation (13) represents the profit of the bank in each period, given by the difference between earnings on assets and interest payments on liabilities. Equation (14) represents the bank’s balance sheet, where loans on the asset side are equal to deposits on the liabilities side. Equation (15) represents the bank-specific demand for loans and arises from the solution to entrepreneurs’ intratemporal problem.

By substituting the balance sheet constraint (14) in the profit function, the maximization problem simplifies to choosing the supply of loans and the loan rate, without the need of introducing a Lagrange multiplier associated to constraint (14). In the symmetric equilibrium, the first order condition with respect to Lbt is

νt=EtΛt,t+1[(RtLRtDΠt+1)+θL(1ϱL)νt+1],(16)

where νt is the Lagrange multiplier associated with constraint (15). Equation (16) states that the shadow value of lending an extra unit in period t is equal to the benefit from the spread earned on this transaction, plus the benefit of expected future profits arising from a share θL of lending being held up at time t + 1.

The first order condition with respect to RbtL yields

Et[Λt,t+sLt+11+RtLΠt+1]=νtηLEt[Xt+1L].(17)

Equation (17) states that the marginal benefit of increasing the loan rate should be equal to its marginal cost given by the reduced demand for loans evaluated at νt.

2.4 Central bank

A central bank conducts monetary policy by following a Taylor-type rule,

log(RtnRn)=ρrlog(Rt1nRn)+(1ρr)[ρπlog(ΠtΠ)+ρylog(YtYtf)+ρΔy(log(YtYtf)log(Yt1Ytf1))+ρslog(LtγLt1ΠtΠ)]+εtR,(18)

where Rtn1+RtD is the gross nominal interest rate, and ρr, ρπ, ρy, ρΔy and ρs are policy parameters referring to interest-rate smoothing, the responsiveness of the nominal interest rate to inflation deviations, the output gap, output gap growth, and nominal credit growth (as e.g. Christiano et al., 2010a,b, among others), respectively, while εtR is a mean zero, i.i.d. random shock with standard deviations σR. Equation (18) represents an augmented version of the monetary policy rule employed by Smets and Wouters (2007). In particular the output gap is computed as the deviation of output from its potential level, Ytf, obtained in a flexible-price and flexible-wage version of the model. Various alternative rules are explored in Subsection 3.5.16

2.5 Equilibrium

The government is assumed to run a balanced budget, i.e. Tt=etG, where etG is government spending. In the symmetric equilibrium all markets clear.

The model is closed by the resource constraint,

Yt=Ct+It+etG+ξ2(ΠtΠ)2Yt+ξW2(ΠtWγΠ)2wtHt+Ψ(Ut)Kt,(19)

and a set of AR(1) processes,

log(etϰeϰ)=ρϰlog(et1ϰeϰ)+εtϰ,(20)

where ϰ={A,B,G,I,P,W,K},e¯ϰ are steady-state values, ρϰ are auto-regressive parameters, and εtϰ are mean zero, i.i.d. random shocks with standard deviations σϰ.

3 Estimation

This section reports the results of the Bayesian estimation. Subsection 3.1 discusses the data and the estimation strategy. Subsection 3.2 presents parameter estimates and a marginal likelihood comparison confirming the leaning-against-the-wind policy from an empirical viewpoint. Subsection 3.3 discusses estimated impulse responses of key macroeconomic and financial variables to the structural shocks of the model and disentangles the stabilization properties of a credit-growth-augmented Taylor rule. Subsection 3.4 presents the analysis of the variance decomposition to assess the importance of the exogenous structural shocks. Finally, Subsection 3.5 checks the robustness of the empirical results to an array of alternative Taylor-type rules.

3.1 Data and estimation strategy

The model is estimated with Bayesian methods (see An and Schorfheide, 2007; Smets and Wouters, 2007, among others). The Kalman filter is used to evaluate the likelihood function of the observable variables. The likelihood function and the prior distribution of the parameters are combined to calculate the posterior distributions. The posterior Kernel is then simulated numerically using the Metropolis-Hasting algorithm with two chains of 150,000 draws each. This Markov Chain Monte Carlo method generates draws from the posterior density and updates the candidate parameter after each draw.

The model is estimated for the US over the Great Moderation period, 1984Q1−2008Q2, using a set of macroeconomic and financial variables. In particular, we use the following nine observable variables: GDP, consumption, investment, wage, lending, hours worked, GDP deflator inflation, the FFR and the lending rate.17 Although observations on all variables are available at least from 1955 onwards, we focus on the above-mentioned period because it is characterized by a single monetary policy regime. Extending the sample period to include the Great Recession may yield biased estimates due to the nonlinearities induced by the fact than the nominal interest rate in the US reached the zero lower bound (on this see e.g. Galí et al., 2011). The following set of measurement equations show the link between the observables in the dataset and the endogenous variables of the DSGE model:

[ΔYtoΔCtoΔItoΔWtoΔLtoHtoπtortn,ortL,o]=[γ¯γ¯γ¯γ¯γ¯h¯π¯r¯nr¯L]+[Y^tY^t1C^tC^t1I^tI^t1W^tW^t1L^tL^t1H^tΠ^tR^tnR^tL]+[0000ɛLtme000ɛRLtme],(21)

where variables on the left-hand side are the observables, γ¯ is the common quarterly trend growth rate of GDP, consumption, investment, wages and lending; h¯ is average hours worked; π¯ is the average quarterly inflation rate; r¯n is the average quarterly nominal interest rate; and r¯L is the average quarterly lending rate. A hat over a variable indicates the log-deviation from its own steady state. The term ɛLtme represents a measurement error in the equation for lending, while ɛRLtme is the measurement error in the equation for the lending rate. These measurement errors account for a possible mismatch between the financial variables in the model and those in the data, analogously to what Castelnuovo and Nisticò (2010) do for stock prices, among others.

Our general estimation and calibration strategy follows the standard procedure proposed by Smets and Wouters (2007). Table 2 shows the calibration of the parameters which could not be identified in the dataset and/or are related to steady-state values of the variables. The time period in the model corresponds to one quarter in the data. The discount factor, β, is equal to the conventional value of 0.99, implying an annual steady-state real interest rate of 4%. The capital depreciation rate, δ, is equal to 0.025, amounting to an annual depreciation of 10%. As standard, the labor share of income, α, is equal to 0.67. The elasticity of substitution across different varieties, η, is equal to 6 in order to target a steady state gross mark-up equal to 1.20. The elasticity of substitution in the banking sector, ηL, is set in order to match a spread between the bank prime loan rate and the 3-month Treasury bill rate of 304 basis points per year - given the estimated value of lending relationship parameter θL – consistently with US data during the Great Moderation.18 The elasticity of substitution in the labor market, ηW is set equal to 11 as in Del Negro et al. (2011), implying a steady-state gross mark-up of 1.10. The preference parameter, ϕ, is set to target steady-state hours of work equal to 0.33. The government-output ratio, G/Y, is calibrated at 0.19, in line with the data. The steady state fraction of investment financed by bank loans, ζ, is equal to 0.63, again in line with our dataset.

Table 2:

Calibrated parameters

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The remaining parameters governing the dynamics of the model are estimated using Bayesian techniques.19 The locations of the prior means correspond to a large extent to those in previous studies on the US economy, e.g. Smets and Wouters (2007).20 We use the Inverse Gamma (IG) distribution for the standard deviation of the shocks and we set a loose prior with 2 degrees of freedom. We use the Beta distribution for all parameters bounded between 0 and 1. For the unbounded parameters we use the Normal distribution. In addition, we set the prior means of the constants in the measurement equations equal to average values in the dataset. As regards the parameters measuring lending relationships we choose prior means close to the values estimated by Aliaga-Diaz and Olivero (2010), equal to 0.70 for θL and to 0.80 for ρL, and we set a standard deviation of 0.125 for both. The prior distribution of the parameter measuring the response of the nominal interest rate to nominal credit growth, ρs, is on purpose loose. In fact, as shown in Figure 2, a prior mean of zero and a standard deviation of 0.30 enable the prior distribution to encompass a broad range of values around zero. This allows us to be agnostic on whether monetary policy leaned against the wind or not. Table 3 summarizes the prior distributions chosen to estimate the deep structural parameters and the shock processes.

Figure 2:
Figure 2:

Prior and posterior probability densities of the Taylor rule parameters

Citation: IMF Working Papers 2017, 179; 10.5089/9781484312674.001.A001

Table 3:

Prior and posterior distributions of estimated parameters (90% confidence intervals are in square brackets)

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3.2 Estimation results

Table 3 reports the posterior mean with 90% probability intervals in square brackets and the marginal log-likelihood of the model computed as in Geweke (1999). There is evidence of both habit in consumption and habit persistence, with statistically positive parameter values, the mean of which equals 0.57 and 0.66 respectively. The degree of deep habits in banking is close to 0.58 with a persistence of 0.72. The degree of price stickiness implies that firms adjust prices about every three quarters and a half, while the estimate of the Rotemberg parameter for wage stickiness is higher, in line with Zubairy (2014). Technology and government spending shocks are more persistent than the other shocks.

As regards the Taylor rule parameters, in line with many other studies, estimates capture nominal interest rate inertia and that, during the Great Moderation, monetary policy was aggressive on inflation, with an estimated coefficient of 2. Similarly to Smets and Wouters (2007), there is evidence of a weak response to the output gap, with an estimated coefficient of 0.03, and of a stronger response to changes in the output gap, with a posterior estimate of 0.16.

A novel result is that the monetary authority is found to respond to nominal credit growth with a point estimate for coefficient ρs of 0.25 and a confidence interval of [0.16,0.34].

Figure 2 shows the prior and posterior densities of the Taylor rule parameters, which are well identified by the data. This is particularly important for ρs, i.e. the responsiveness of the nominal interest rate to credit growth, exhibiting a posterior distribution entirely located around positive values, with the probability density tightly gathered around the posterior mean, despite the loose prior.

This last result is confirmed also by a race between Geweke (1999) marginal log-likelihoods of the baseline model and a restricted model featuring a standard Taylor rule, i.e. with ρs = 0. Table 4 reports the Bayes factor (BF) and the statistics by Kass and Raftery (1995) (KR).21 Subsection 3.5 reports the estimated Taylor rule parameters and likelihood races for models featuring alternative monetary policy rules. Results turn out to be robust. With a BF well above 100, we find “decisive evidence” in favor of a model featuring a credit-growth-augmented Taylor rule over a standard one. The KR statistics is computed as twice the log of the BF. In this case this amounts to 22.94 and points to “very strong” evidence in favor of the unconstrained baseline model versus the restricted model featuring a standard Taylor rule.22 In other words, these results point to evidence that, during the Great Moderation, monetary policy leaned against the wind blowing from the loan market. So far the literature has focused more on the response of monetary policy to asset prices. For instance, on the empirical side, Castelnuovo and Nisticò (2010) argue that a model where the monetary authority has an active concern towards stock-market fluctuations is supported by US data (as we also verify in Subsection 3.5). Christiano et al. (2010b) estimate a significant degree of “leaning against credit exuberance” in the euro area monetary policy framework for the period 1985Q1-2008Q2. Hence, the first novel contribution of our paper to this literature is to provide an analogous empirical result for the US economy, albeit with a different model.

Table 4:

Marginal log-likelihood comparison

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3.3 Dynamic properties of the estimated model

In this section we disentangle the effects of the estimated leaning-against-the-wind policy versus a standard Taylor rule via the analysis of the responses of key macroeconomic variables to all eight structural shocks in the model. In Figure 3 we report impulse responses to shocks of size one percent that determine a fall in real output.

Figure 3:
Figure 3:

Impulse responses of selected variables to structural shocks of size 1 percent in the estimated model featuring a Taylor rule augmented with a response to credit growth and in a restricted model with a standard Taylor rule

Citation: IMF Working Papers 2017, 179; 10.5089/9781484312674.001.A001

The solid line represents responses within the estimated model featuring the credit-growth augmented Taylor rule, whereas the dashed line represents responses of a counterfactual model with ρs = 0.

In particular, the model features five aggregate demand shocks (preference, investment-specific, capital quality, government spending, monetary policy), in which output and inflation move in the same direction, and three aggregate supply shocks (technology, wage mark-up and price mark-up), in which output and inflation move in opposite directions.

A number of noteworthy results emerge from the inspection of Figure 3. First, while the sign of impulse responses is preserved across the two Taylor rule specifications, the severity of the economic downturn generated by each shock varies. Second, with the exception of the preference and government spending shocks, lending positively comoves with real output and the bank spread exhibits a counter-cyclical behavior. This is a feature of lending relationships: in the simulated contractions, future profits are expected to be low (indeed real output persistently remains below steady state), hence banks find it optimal to exploit current lending relationships by charging higher bank spreads and enhancing current profits.

As far as the preference shock is concerned, this generates a shorter-lived output contraction and an overshooting. The explanation is in the fact that such a shock determines a fall of future marginal utility of consumption relative to the current one, and this leads to a fall in consumption and an increase in savings.

The subsequent greater availability of financial funds makes banks willing to supply more loans, which in turn boost future economic activity and profits. The latter are anticipated by banks, which find it optimal to charge a lower spread and lock in new customers into bank-firm lending relationships. Similar arguments apply to the contractionary government spending shock, which crowds in private investment.

In the presence of a credit-growth-augmented Taylor rule, the central bank partially counteracts fluctuations of lending. In the model lending, has real effects because it is instrumental for the acquisition of capital. Therefore, for those shocks in response to which lending exhibits a pro-cyclical behavior, the contraction of output is more severe in the absence of a credit-growth-augmented Taylor rule. On the contrary, for the preference shock and the government spending shock - which yield a counter-cyclical lending response - such a Taylor rule leads to a slightly more severe output contraction. The presence of lending relationships consistently generates responses of the bank spread of opposite sign relative to those of lending. Thus, the general lesson to be learned from the inspection of impulse responses is that leaning against the wind has a stabilizing effect on output for those shocks that imply a pro-cyclical response of lending and a counter-cyclical response of the bank spread.

3.4 Variance decomposition

Movements in output, lending, bank spread and inflation are now decomposed into parts caused by each shock at different time horizons. Table 5 reports both the conditional and the unconditional variance decomposition.

Table 5:

Variance decomposition

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While, on impact, demand shocks play a dominant role in affecting output dynamics, in the medium-to-long term the technology shock together with the other two supply shocks - wage and price mark-up - are its main drivers. These three shocks together account for about 30% of output fluctuations on impact, 62% at a one-year horizon and almost 70% at a two-year horizon, with demand shocks having a more muted effect. The role of government and monetary policy shocks decay over time. Price and wage mark-up shocks are also the dominant factors behind both short-run and medium-run movements in inflation. These results are in line with Smets and Wouters (2007).

The variance decomposition of lending shows that the three supply shocks accounts for more than 60% of long-term variation in lending. However, differently from output dynamics, the investment-specific technology and the capital quality shocks play a stronger role: on impact they dominate – explaining 57% of lending fluctuations – and in the longer term they account for around 30% of the variation in lending. This result is not surprising as the investment-specific technology shock affects the investment Euler equation – lending being used to finance purchases of capital goods – and the capital quality shock affects the law of motion of capital. It is worth noticing that all dominant shocks in the variance decomposition of lending are those that foster a pro-cyclical response of lending itself (see Subsection 3.3).

Results on the variance decomposition of the bank spread show that, on impact, the investment-specific technology shock and, to a minor extent, the capital quality shock are the main exogenous sources of its variation. Price and wage mark-up shocks also play an important role. As the model features a tight (negative) relationship between the bank spread and lending, those shocks playing a key role in explaining the dynamics of lending are likely to play a quantitatively similar role in accounting for the variation of the bank spread.

On this point it is important to note that the shocks that are dominant sources of movements in the spread are those implying a counter-cyclical response of the spread itself. Figure 4 depicts the model-implied spread (one-step-ahead forecast) along with three (demeaned) proxies: (i) Bank Prime (BP) rate minus FFR; (ii) Moody’s Baa minus long-term Treasury constant maturity rate (TCMR); and (iii) the series of the spread constructed by Gilchrist and Zakrajšek (2012).23 Unsurprisingly, the model generates a forecast of the spread of an order of magnitude and behavior closest to the BP-FFR, given that both rates are used as observables in the estimation, and it represents the closest data counterpart of the theoretical definition of the spread in the model. Realistically the spread exhibits rapid surges during recessions. It shows a reasonable comovement also with the other two measures, which, however, are more volatile.24 In addition, the model indeed captures the low lending rates of the late 1990s, the burst of the dot-com bubble and the picking-up of the spread in correspondence to the end-of-sample crisis.

Figure 4:
Figure 4:

Demeaned credit spreads in the US economy v.s. the model-implied measure (shaded areas indicate NBER recessions)

Citation: IMF Working Papers 2017, 179; 10.5089/9781484312674.001.A001

3.5 Robustness to alternative Taylor-type interest-rate rules

This subsection investigates whether our evidence in favor of a leaning-against-the wind policy is robust to different specifications of the Taylor rule. In particular, we consider the six formulations reported in Table 6.

Table 6:

Alternative Taylor-type interest-rate rules

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Formulation (I) is a so-called simple and implementable rule, which includes output in deviation from steady state, Y, instead of a latent variable such as the output gap, so that the central bank responds only to observable variables (see e.g. Faia and Monacelli, 2007; Schmitt-Grohe and Uribe, 2007).

Formulation (II) is an augmented version of implementable rule (I) featuring not only a response to the deviation of output from its steady state, but also a response to output growth.

Formulation (III) is our baseline specification augmented with a response to the stock-price gap. In line with Castelnuovo and Nisticò (2010), this is defined as the gap between the stock price prevailing in the model with price and wage stickiness, Qt, and the stock price that would prevail in a model without nominal stickiness, Qtf.

Formulation (IV) includes a second-order autoregressive interest rate smoothing as proposed by Coibion and Gorodnichenko (2012), and applied also by Ascari et al. (2011), to investigate whether the richer persistence structure might wipe out the response to nominal credit growth.

Formulation (V) combines both an AR(2) interest-rate smoothing structure and a response to stock prices, in addition to the response to nominal credit growth.

Lasly, formulation (VI) corresponds to the same baseline specification of equation (18), but with one important difference: the potential output (Y˜tf) used to compute the output gap is the level that would prevail not only in the absence of price and wage stickiness (as standard in the literature), but also in the absence of financial frictions.

In estimating the models with formulation (III) and (V) for the Taylor rule we include an additional observable variable (stock prices). The corresponding additional measurement equation is given by:

ΔQto=Q¯+Q^tQ^t1+ɛQtme(22)

where Q¯ is the average quarterly growth rate of the stock price index and ɛQtme is a measurement error.25

Table 7 reports the prior distributions and posterior estimates of the Taylor rule parameters in the six cases, while the estimates of all structural parameters are reported in Appendix G. In all cases the point estimate of the interest-rate response to credit growth (ρs) is in the vicinity of 0.25. In addition, the credible sets of parameter ρs are well above zero across models, and the parameter itself is well identified in the data, as can be seen by inspecting prior and posterior probability densities reported in Appendix G. In sum, a credibly positive and economically important estimate of ρs survives six alternative monetary policy formulations.

Table 7:

Prior and posterior distributions of estimated parameters of alternative Taylor-type interest-rate rules (90% confidence intervals are in square brackets)

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Moreover, the estimates of the parameters of the AR(2) interest-rate smoothing formulation (ρ1 and ρ2) exhibit the same signs and comparable magnitudes of those of Ascari et al. (2011), while the responsiveness to stock-prices (ρq) is close to that of Castelnuovo and Nisticò (2010).

Table 8 reports the Geweke (1999) marginal log-likelihoods, the Bayes factor, and the statistics by Kass and Raftery (1995) for the models estimated with Taylor rules (I)-(VI) versus the corresponding constrained versions obtained by setting ρs = 0. For all specifications considered, the Bayes factor is always well above 100 and the Kass-Raftery statistics is always greater than 10, pointing to decisive evidence that during the Great Moderation monetary policy in the US leaned against the wind blowing from the loan market.

Table 8:

Marginal log-likelihood comparisons for alternative Taylor-type interest-rate rules

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4 Optimized simple monetary policy rules

The analysis so far has brought a general equilibrium model with banking frictions to the data and has provided evidence that US monetary policy did lean against the wind blowing from the market for loans during the Great Moderation. The presence of the financial friction, making the bank spread countercyclical, implies that lending is more volatile than optimal over the business cycle. This would in principle create room for central bank intervention. Therefore, in this section, we pose a normative question: should the monetary policy rate react to developments in the loan market? To answer this question we compute optimized simple interest-rate feedback rules (in similar fashion to Schmitt-Grohe and Uribe, 2007; Levine et al., 2008) responding to macro-financial indicators that, we show, are able to closely mimic the Ramsey rule from a welfare perspective.

4.1 Design of simple monetary policy rules

To design simple monetary policy rules, we rewrite the Taylor-type interest-rate feedback rule (18) as

log(RtnR¯n)=ρrlog(Rt1nRn)+απlog(ΠtΠ)+αylog(YtYtf)+αΔy[log(YtYtf)log(Yt1Yt1f)]+αslog(LtγLt1ΠtΠ),(23)

where απ ≡ (1 − ρr)ρπ, αy ≡ (1 − ρr)ρy, αΔy ≡ (1 − ρr)ρΔy and αs ≡ (1 − ρr)ρs. This re-parametrization allows for the possibility of integral rules with a unitary persistence parameter (ρr = 1). These are effectively price-level rules that make the price level trend-stationary as shown in Woodford (2003). Superinertial rules (ρr > 1) are examined in Appendix H.5.26 Then we numerically search for those feedback coefficients in rule (23) to maximize the present value of life-time utility, which reads

Ωt=Et[Σs=0βsU(X˜t+s,1Ht+s)],(24)

where X˜t is the stationarized consumption composite, given the equilibrium conditions of the model. Given the numerous frictions in the model, we refrain from deriving the welfare-based quadratic loss function and, more simply, rewrite equation (24) in recursive form as, e.g., Gertler and Karadi (2011):

Ωt=U(X˜t,1Ht)+βEt[Ωt+1].(25)

In addition, as established by Schmitt-Grohe and Uribe (2007), while more stylized models allow for a first-order approximation to the equilibrium conditions to be sufficient to accurately approximate welfare up to a second order, the presence of the frictions requires taking a second-order approximation both of the mean of Ωt and of the model’s equilibrium conditions around the deterministic steady state.27 In particular, we take the approximation around the steady state of the Ramsey equilibrium, outlined in Appendix E. Similarly to many other NK models in the literature (see e.g. Schmitt-Grohe and Uribe, 2004; Levine et al., 2008, among others), the steady-state value of the gross inflation rate in the Ramsey equilibrium turns out to be very close to unity (Π = 1.002), which implies an almost zero-inflation steady state.

As we approximate the solution to the equilibrium using perturbation methods and these do not easily allow incorporating non-negativity constraints, in similar fashion to Levine et al. (2008), we approximate the zero lower bound (ZLB) constraint on the nominal interest rate by introducing a penalty term in an auxiliary definition of welfare. While in Levine et al. (2008) the penalty term is a symmetric function, we adopt a specification meant to capture the inherent asymmetry implied by the zero lower bound. This is achieved by replacing our objective function (24) with modified welfare,

Ωt*=Et{Σs=0βs[U(X˜t+s,1Ht+s)Θ(Rt+sn)]},(26)

where term Θ(Rt+sn)wr(RtnRn)2exp[wr(Rtn1)] combines a quadratic with an exponential function, and represents a convex penalty for deviations of Rtn from its steady state. With weight parameter wr > 0 sufficiently large, this penalty increases exponentially if the nominal interest rate falls below zero (Rtn<1).28 Hence, the imposition of the approximate ZLB constraint translates into appropriately choosing the weight wr to achieve an arbitrarily low per-period probability of hitting the ZLB, Pr(ZLB)Pr(Rtn<1), which we set at 0.01, i.e. once every 25 years.

We use the modified welfare specification for the sole purpose of imposing the ZLB constraint. In fact, we perform all welfare comparisons by using Ωt and computing the consumption-equivalent welfare loss with respect to the Ramsey equilibrium, as in Schmitt-Grohe and Uribe (2007). For a particular regime associated to a given Taylor-type interest rate rule A, the welfare loss is implicitly defined as

Et{Σs=0βs[U((1ω)X˜t+sR,1Ht+sR)]}=Et{Σs=0βs[U(X˜t+sA,1Ht+sA)]},(27)

where ω × 100 represents the percent permanent loss in consumption that should occur in the Ramsey regime (R) in order agents to be as well off in regime R as they are in regime A.

4.2 Optimal monetary policy results

Table 9 first shows the results arising from the computation of the Ramsey policy. Increasing the penalty parameter wr delivers a lower per-period probability of hitting the ZLB and small welfare losses (less than 0.1% in consumption-equivalent terms). 29 With the penalty parameter equal to 5, the probability of hitting the ZLB is once every four years. It takes a wr = 18 for the probability of hitting the ZLB to decline to once every 15 years, as in the estimated monetary policy rule. A wr = 22 implies a probability of hitting the ZLB equal to 0.01, which corresponds to once every 25 years. A higher penalty translates into a higher welfare loss.

Table 9:

Optimized monetary policy rules

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We then move to optimized Taylor-type rules in which the nominal interest rate features inertia and reacts to inflation, output gap, changes to the output gap and nominal credit growth, (Lt/ (γLt−1))Πt/Π-as in Christiano et al. (2010b,a) and Ozkan and Unsal (2014), among others-for the same probabilities of hitting the ZLB as those in the Ramsey policy. As wr increases, the optimal response to the output gap approaches zero. Irrespective of the value of wr, it is always optimal not to respond to changes in the output gap, while a higher penalty wr delivers a lower optimal an. As far as the main normative question of the paper is concerned, we find a zero optimal responsiveness to nominal credit growth for any value of wr. In the table we compute the consumption equivalent welfare change w relative to the Ramsey regime with wr = 5 (first row). With wr = 22 the welfare loss is equivalent to a permanent loss in consumption of 0.63% - 0.05% = 0.58%.

The estimated monetary policy rule implies Pr (ZLB) = 0.017, i.e. that the nominal interest rate hits the ZLB once every 15 years and implies a consumption-equivalent welfare loss of 1.15% = 1.10%, relative to the Ramsey policy associated to the same probability of hitting the ZLB.

Appendices H.1, H.2 and H.3 check the robustness of the results to (i) Taylor-type rules with potential output defined as the level that would prevail in the absence of price stickiness, wage stickiness and financial frictions; (ii) interest rate rules reacting to alternative financial variables, such as lending and the bank spread, similarly to Cúrdia and Woodford (2010) and Aksoy et al. (2013); and (iii) the implementable specification of the Taylor rule as in Schmitt-Grohe and Uribe (2007), allowing also for a response to output growth.

4.3 Welfare implications and counterfactual experiments

To check the extent to which the welfare loss suffered from employing the empirical rule is due to the presence of the responsiveness to nominal credit growth, in Subfigure 5a, we isolate its effect on welfare by keeping ρr, απ and αy fixed at their optimal values obtained with wr = 22 and by changing αs in the interval [0, 0.5]. The estimated value of αs = 0.041 implies a small consumption-equivalent loss of around 0.06%. In addition, this exercise unveils also a positive relationship whereby the economy suffers an approximately double welfare loss if αs doubles.

Figure 5:
Figure 5:

Welfare implications of leaning against the wind and counterfactual experiments

Citation: IMF Working Papers 2017, 179; 10.5089/9781484312674.001.A001

In a nutshell the second contribution of this paper is showing that it is not optimal for monetary policy to respond to credit growth, that the estimated responsiveness implies a small welfare loss (equivalent to a permanent loss in consumption of less than 0.1%), and that bolder responses to financial conditions may represent a substantial detriment to welfare.

These findings can be rationalized by noticing that supply shocks (technology, price mark-up and wage mark-up) explain the largest share of business cycle fluctuations of lending and inflation. Indeed, Subsection 3.4 shows that the three supply shocks together explain around 63% and 72% of the unconditional variance of lending and inflation, respectively. A, say, contractionary shock of such a kind causes lending to decrease and inflation to rise. A monetary policy that leans against windy bank lending is more accommodative towards inflation in an attempt to boost lending (as shown in Subsection 3.3). But this turns out not to be optimal. In fact, in Subfigure 5b, for a wr = 22, we show that, if we fix αr = 1, αy = 0 (i.e. their optimal values), we let αs vary in the interval [0, 0.1], and we optimize over απ, the optimal value of this last coefficient monotonically increases when as increases, while welfare (not shown) attains virtually the same level for any combination of the two parameter values. In other words, if monetary policy is forced to react more to a(n) tightening (expansion) of lending growth, it is optimal for it to react more also to the increase (decrease) in inflation. As the two objectives are conflicting, there is no “divine coincidence” (Blanchard and Galí, 2007) in this case and the nominal interest rate achieves a better outcome if it only stabilizes inflation. This result, on one hand, is in line with Faia and Monacelli (2007), who find that the presence of only one policy instrument - the nominal interest rate - cannot simultaneously neutralize both financial frictions and price stickiness and that a strong anti-inflationary stance always leads to the highest level of welfare.

To show the importance of the sources of business cycle fluctuations on the optimality of monetary policy responses, Subfigure 5c presents a counterfactual experiment in which we artificially change the volatility of capital quality shocks to match a double and triple standard deviation of output growth compared to the baseline estimated model – by keeping ρr, απ, αy and αΔy at their optimal values when wr = 22, and by changing αs in the interval [0; 0.5].30 For the capital quality shock a form of “trinity” (in analogy to Justiniano et al., 2013) holds: inflation, the output gap and credit growth can be stabilized at the same time. This demand shock is important because it accounts for 38% of the unconditional variance of output and for 30% of that of lending. Such a counterfactual exercise shows that it would be indeed optimal to lean against windy bank lending, with an optimal αs around 0.1 in the scenarios with higher volatility driven by capital quality shocks.31 In contrast, in Appendix H.4 we show that, if the increase in volatilty is due to a proportional increase in the standard deviations of all shocks, it remains optimal not to lean against windy bank lending.

This point can be also verified by suppressing a quantitatively relevant supply shock. Subfigure 5d displays how the optimal αs changes in the absence of wage mark-up shocks (again keeping ρr, an, αy and αΔy at their optimal values when wr = 22). These shocks are the most prominent shocks in the unconditional variance decomposition of inflation and they play an important role for explaining fluctuations in output and lending.32 This exercise is important as (i) it shows that, in the absence of such shocks, it would be indeed optimal to lean against windy bank lending, with an optimal αs around 0.2; and (ii) it allows reconciling our results with the literature. In fact, Aksoy et al. (2013) and Gambacorta and Signoretti (2014), in similar but simpler calibrated models with no wage mark-up shocks, find a leaning-against-the-wind policy to be optimal. Moreover, Cúrdia and Woodford (2010) and Nisticò (2012) show that the optimality of a leaning-against-the-wind-type of monetary policy is very sensitive to the source of business cycle fluctuations. Our research strategy entails first bringing a canonical model augmented with banking to the data; next, estimating a set of standard shocks; and last, on the estimation results, basing optimal policy computations.

Appendix H.5 investigates the robustness of the results also to superinertial rules. We find that superinertial responses of the interest rate have negligible effects on welfare relative to price level rules, and also in the superinertial case it is optimal not to lean against windy bank lending.

5 Concluding remarks

In recent times credit booms and busts have dramatically affected business cycle fluctuations. This has called for a deeper understanding of credit market conditions and the role of central banks in ensuring financial stability. This paper examines whether interest-rate policy has reacted and whether it should indeed react to bank lending growth in the US economy.

We first estimate a DSGE model in which banking frictions arise due to the presence of lending relationships and monetary policy is set according to a credit-growth-augmented Taylor-type rule. The empirical results provide evidence that during the Great Moderation monetary policy leaned against the wind blowing from the loan market. Such findings survive various specifications of the monetary policy rule, including when this features also a response to asset prices.

We then compare the welfare implications of estimated and optimized interest-rate rules. Results unveil that the estimated responsiveness of monetary policy to credit growth delivers a small welfare loss, but the higher such a responsiveness the higher is the detriment to welfare. Such a finding can be rationalized by noticing that supply shocks are the main medium-to-long run drivers of output, lending and inflation fluctuations in the estimated model and that these shocks imply a trade-off between inflation and output stabilization. Given the pro-cyclical behavior of lending, it turns out to be optimal for monetary policy to respond entirely to inflation. On this aspect, the paper highlights that the optimality of a leaning-against-the-wind policy is sensitive to the sources of business cycle fluctuations.

The findings of this paper agree with the recent tendency in central banking to move towards macroprudential instruments as tools to promote financial stability. Indeed, a bolder research effort is necessary to identify effective instruments and design rules that achieve the goal of reducing financial instability without conflicting with the objective of inflation stabilization.

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