Banks’ leverage behaviour in a two-agent new Keynesian model

Journal of Economic Behavior and Organization 162 (2019) 347–359

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Banks’ leverage behaviour in a two-agent new Keynesian modelR Andrea Boitani∗, Chiara Punzo Department of Economics and Finance, Università Cattolica del Sacro Cuore, Via Necchi, 5, Milan 20123, Italy

a r t i c l e

i n f o

Article history: Received 22 December 2017 Revised 10 August 2018 Accepted 17 December 2018 Available online 25 December 2018 JEL classification: E3 E5 G1 Keywords: Leverage Procyclicality Two-agent model Risk-aversion

a b s t r a c t We study the distributive effects of a negative shock to banks assets in a saver-capitalist model. We analyze how this kind of heterogeneity affects macroeconomic variables and the distribution between savers and capitalists through banks leverage procyclicality. The distributive effects are non-favourable to savers and long lasting. Lower risk aversion of capitalists strengthens and lengthens the procyclicality of leverage, leading to a lower decrease of savers’ income and consumption. Whilst stricter regulatory requirements are favourable to savers, a tougher inflation targeting is unfavourable to savers. The model is robust to the combined introduction of labour market frictions and hysteresis, which together generate an amplification and lengthening of the recessionary and distributive effects unfavourable to savers. © 2018 Elsevier B.V. All rights reserved.

1. Introduction In the aftermath of the 2007 financial crisis, the high level of leverage of financial intermediaries has commonly been identified as the main weakness of ailing advanced economies and, consequently, as one of the major causes of the crisis (Financial Stability Forum, 2009). Many observers pointed at leverage procyclicality – i.e. the increase (decrease) of leverage following an increase (decrease) of total assets value - as an amplification mechanism of business cycles upturns and downturns (Adrian and Shin, 2010), despite the presence of mildly stabilizing monetary policy. Several empirical studies find that the financial-induced propagation mechanism of exogenous shocks may even become self-reinforcing if banks let their leverage be procyclical, which happens (for instance) if banks target their capital to a fixed proportion of their Value at Risk (VaR)1 . The procyclicality of leverage may indeed fuel a supply side financial accelerator complementing (or substituting for) the demand side financial accelerator pioneered by Bernanke and Gertler (1989) and Kiyotaki and Moore (1997) in explaining business cycle’s booms and recessions. During downturns asset prices fall and – for a given value of debt - the leverage of banks goes up. However, if banks target their leverage, the sale of assets will

R We thank Fabrice Collard, Salvatore Nisticò, Lorenza Rossi and two anonymous referees for their helpful comments and suggestions. We are also grateful to all the participants in the Conference on “Finance and Economic Growth in the Aftermath of the Crisis” held at the University of Milan and the 5th Macro Banking and Finance Workshop held at Università Cattolica del Sacro Cuore in September 2017. ∗ Corresponding author. E-mail addresses: [email protected] (A. Boitani), [email protected] (C. Punzo). 1 See Peek and Roesengren (1997, 20 0 0), IMF (2010), Ciccarelli et al. (2011), Fornari and Stracca (2011), Baglioni et al. (2013) and Beccalli et al. (2015).

https://doi.org/10.1016/j.jebo.2018.12.016 0167-2681/© 2018 Elsevier B.V. All rights reserved.

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A. Boitani and C. Punzo / Journal of Economic Behavior and Organization 162 (2019) 347–359

lead to reducing debt (deposits) in order to restore the targeted leverage. Such a mechanism may also work in the reverse, whenever there is a positive shock to asset prices. Following Jakab and Kumhof (2015), the recent literature on financial frictions in macroeconomics can be divided into three groups. In the first group, all lending is direct and banks are absent. It includes one of the workhorse models of the modern literature, Kiyotaki and Moore (1997), where patient lenders extend direct credit against the real collateral offered by impatient borrowers. Iacoviello (2005) also belongs to this group. In the second group, banks are present but banks’ net worth and balance sheets play no material role in the analysis, and the emphasis is on loans pricing. This group includes another of the workhorse models of the modern literature, Bernanke et al. (1999). In this model, which is also used in Christiano et al. (2014), risk-neutral bankers make zero profits on their loans at all times. Capital adequacy regulation is therefore redundant, and bank net worth is absent. The main function of banks is in generating an external financing premium for borrowers, which means that the focus of the analysis is on the balance sheet and leverage of the borrower, not of the bank. Similar considerations apply to Curdia and Woodford (2010) and Boissay et al. (2016). In the third group of models, which includes (Adrian and Boyarchenko, 2013; Gerali et al., 2010; Gertler and Karadi, 2011; Gertler and Kiyotaki, 2011) and (Clerc et al., 2014), the balance sheet and the net worth of banks do matter, either through an incentive constraint under moral hazard or through a regulatory constraint, in the attempt at exploring the real effects of a supply side financial accelerator. Once again this strand of literature introduces heterogeneity among households by differentiating between patient households and impatient ones. Rannenberg (2016) tries to combine the second and the third group, by developing a Dynamic Stochastic General Equilibrium (DSGE) model with leverage constraints both in the banking and in the non-financial firm sector. Our model contributes to the literature of the third group by introducing a different kind of heterogeneity among households. The distributive consequences of (patient) savers versus (impatient) borrowers heterogeneity in DSGE models with banks are well explored, whilst heterogeneous risk aversion that leads to distinguish between savers and capitalists has not yet been examined. We advance the hypothesis that winners and losers (in the words of Auclert (2017)) in banking booms and crisis are mainly to be found among shareholders/capitalists and depositors/savers as their incomes display markedly different sensitivities to financial shocks (Coibion et al., 2017). In fact, the present paper shows that a negative shock to the value of bank’s assets is non-favourable to savers and it is long lasting. In our model, the two agents differ in their degree of risk aversion and they are both intertemporal maximizers. Capitalists consume and hold the shares of banks but do not work. Savers consume, work, hold depositsand benefit from lump-sum transfers out of firms’ profits (Albonico and Rossi, 2015). We employ a New-Keynesian model with imperfectly competitive goods markets and sticky prices, following Schmitt-Grohé and Uribe (2004) in considering a closed production economy populated by a continuum of monopolistically competitive producers. Each firm produces a differentiated good by using as an input the labour services supplied by savers. The prices of consumption goods are assumed to be stickyà la (Rotemberg, 1982). Two types of one-period financial instruments, supplied by banks, are available: saving contracts (deposits) and borrowing contracts (loans). The banking sector is monopolistically competitive: banks set interest rates on deposits and on loans so as to maximize their profits. The amount of loans issued by each intermediary can be financed through deposits and bank capital, which is accumulated out of profits. The contribution of the paper can be summarized in four main results. First, a negative shock to bank’s asset leads to leverage procyclicality and implies a distributive effect non-favourable to savers and long lasting. Second, lower risk aversion of capitalists strengthens and lengthens the procyclicality of leverage, leading to a lower decrease of savers’ income and consumption. Third, stricter regulatory requirements reduce the non favourable distributive effects on savers. Fourth, a more “conservative” Central Bank, implementing a stricter inflation targeting, appears to have more unfavourable effects on savers. Finally, in order to analyse some crucial real world features interact with our model, we introduce in turns labor market frictions and hysteresis. We show that the presence of hiring costs slightly enhances the recessionary and distributive effects of a negative shock to bank’s assets. The combination of labour market frictions with hysteresis generates a remarkable amplification and lengthening of the recessionary and distributive effects unfavourable to savers. The key drivers of these results are as follows. The consumption of savers is negatively impacted by the reduction in employment (which is demand driven), in deposits and the interest rate, all ignited by the negative shock to bank’s assets. Hence the contractionary effects on aggregate output and consumption are strengthened. On the other hand, the negative impact of the shock on bank’s profits is short lived - thanks to leverage rapidly turning procyclical – and thus unable to modify the expectations of capitalists about future dividends. As a consequence, the consumption of capitalists is only marginally affected by the financial shock. The transmission mechanism just sketched is at work in all our experiments and highlights the role of heterogeneity assumed in this paper. The remainder of the paper is organized as follows. Section 2 spells out the model economy. After calibration, Section 3 analyzes the dynamics of the benchmark model and the impacts that different values of the key parameters have on the model dynamics. The key parameters on which we experiment are the degree of risk aversion of capitalists (related to households behaviour); the regulatory (Basel) leverage coefficient (as representative of macroprudential policies); and, as for the monetary policy rule, alternative inflation and output targeting coefficients. Section 4 explores the interactions among different real world frictions, in order to gauge how much the aggregate and distributive dynamics of a negative financial shock is strengthened and prolonged. More specifically, we embed the labour market frictions into the baseline model introduced in the previous sections. At the end of the section we also consider an extension of the model allowing for the presence of hysteresis. Section 5 summarizes the main findings and concludes.

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2. The model The economy is populated by two groups of households (savers, S, and capitalists, C). The key difference among agent types is the degree of risk aversion: the risk aversion of capitalists (σ c ) is lower than the risk aversion parameter of savers (σ s ). Capitalists consume and hold the shares of banks but do not work2 . Savers consume, work, hold deposits and get lump-sum transfers out of firms profits. This implies that capitalists only maximize their utility with respect to consumption and bank’s profits, whilst savers maximize with respect to deposits and consumption. As for work, savers only match the existing demand for labour, which out-of-equilibrium is determined by the actual dynamics of loans. We consider a NewKeynesian model with imperfectly competitive goods markets and sticky prices. We follow (Schmitt-Grohé and Uribe, 2004) and consider a closed production economy populated by a continuum of monopolistically competitive producers. Each firm produces a differentiated good by using as an input the labour services supplied by households. The prices of consumption goods are assumed to be sticky à la (Rotemberg, 1982). Two types of one-period financial instruments, supplied by banks, are available: saving contracts (deposits) and borrowing contracts (loans). The banking sector is monopolistically competitive: banks set interest rates on deposits and on loans so as to maximize profits. The amount of loans issued by each intermediary can be financed through deposits and bank capital, which is accumulated out of profits. 2.1. Households There is a continuum of households [0,1] indexed by j, all having the same utility function: 1 −σ j

U (C j,t , N j,t ) =

C j,t

1 − σj

.

The agents differ in their risk aversion coefficient σ j . Specifically, we assume that there are two types of agents, j = s, c, with σ s > σ c . All households (regardless of their discount factor) consume an aggregate basket of individual goods k ∈ [0, 1], with 1 ε ε−1 constant elasticity of substitution ε : Ct = [ 0 Ct (k ) ε dk] ε−1 , ε > 1. Standard demand theory implies that total demand for

each good is Ct (k ) = [ PtP(k ) ]−ε Ct , where Ct (k) is total demand of good k, PtP(k ) its relative price and Ct aggregate consumption3 . t t 1 1−ε The aggregate price index is Pt1−ε = 0 Pt (k ) dk. A share (1 − λ ) of households is less risk-averse. Consistent with the equilibrium outcome (discussed below) we impose that less risk-averse capitalists (indexed by c) also hold the shares of banks. Each capitalist chooses consumption and shareholdings of banks, solving the standard intertemporal problem:



max Et

∞ 



βU (Cc,t+i ) ,

i=0

subject to the sequence of constraints:



Cc,t + bc,t Vtb ≤ bc,t−1 Vtb + tb



where Et is the expectations operator and Cc, t is consumption by the less risk-averse agent. Vtb is the real market value of shares in banks at time t, tb are banks profits and bc,t are banks’ shareholdings. The Euler equation - for bank shareholdings is as follows:



Vtb = β Et

Cc,t Cc,t+1

σc



b b Vt+1 + t+1

 

.

(1)

The rest of the households on the [0, λ] interval are more risk-averse (and will save in equilibrium, hence we index them by s for savers). They face the intertemporal constraint:

Cs,t + Ds,t ≤

1 + it−1

πt

Ds,t−1 + wt Ns,t +

tf . λ

(2)

f

where t are real profits of monopolistic firms . Firms profits accrue to savers as lump-sum transfers, involving no choice about their holdings (see also Albonico and Rossi, 2015). The Euler equation for deposits, Ds, t , is as follows: −σs Cs,t =β

2 3



1 + it

πt+1



−σs Cs,t+1 .

As Adrian and Boyarchenko (2015), we allow households to invest via financial intermediaries, a feature strongly supported by the data. This equation holds in aggregate because the same static problem is solved by both types of households.

(3)

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2.2. Firms There are infinitely many firms indexed by k on the unit interval [0, 1], and each of them produces a differentiated variety of goods with a constant return to scale technology4 :

Yt (k ) = zt Nt (k )

(4)

Following Rotemberg (1982), we assume that firms face quadratic adjustment costs:

γ



2

Pt (k ) −1 Pt−1 (k )

2

expressed in the units of the consumption good and γ ≥ 0.The benchmark of flexible prices can easily be recovered by setting the parameter γ = 0. The present value of current and future profits reads as:



Et

∞ 





Qt ,t +i

Pt+i (k )Yt+i (k ) + Pt+i Ltd (k ) − Wt+i Nt+i (k ) d − 1+πρtt−1 Lt−1 (k ) − Pt+i γ2

i=0

Pt+i (k ) Pt+i−1 (k )

−1

,

where Qt ,t +i is the discount factor in period t for nominal profits i periods ahead. Assuming that firms are risk-averse at a

rate which is the average between the risk aversion of the two different households (Qt ,t +i = β ( CCt )σ ), which is assumed to be strictly higher than σ s and lower than σ c . Each firm faces the following demand function:



Yt (k ) =

Pt (k ) Pt

t+1

−ε

Ytd ,

where Ytd is aggregate demand and it is taken as given by each firm k. Firms choose prices Pt (k), the desired amount of labour input Nt (k), loans demand Ltd so as to maximise nominal profits subject to the production function and the demand  function, while taking as given aggregate prices and quantities Pt , Wt , Ytd . Let the real marginal cost be denoted by: t≥0

mct =

(1 + ρt )wt

(5)

zt

Notice that, as in Ravenna and Walsh (2008), real marginal costs depend directly on the nominal interest rate. This introduces the so called cost channel of monetary transmission into the model. If firms’ costs for external funds rise with the short-run nominal interest rate, then monetary policy cannot be neutral, even in the presence of flexible prices and flexible interest rates. At a symmetric equilibrium, where Pt (k ) = Pt and Nt (k ) = Nt for all k ∈ [0, 1], profit maximisation and the definition of the discount factor imply that:

πt (πt − 1 ) = β Et



  Ct σ 2 εz N πt+1 (πt+1 − 1 ) + t t mct − Ct+1 γ

ε − 1 ε

(6)

which is the standard Phillips curve according to which current inflation depends positively on expected future inflation and current marginal cost. The aggregate f.o.c. across firms with respect to the demand for loans is:

1 + ρt =

1

β



Et

πt+1

C

t+1

σ 

Ct

.

(7)

The firm profit function in real terms is given by:

tf = Yt + Ltd − wt Nt −

1 + ρt−1

πt

d Lt−1 −

γ 2

(πt − 1 )2

(8)

which, together with (7) implicitly defines a loan demand function such as:

LD = b(ρt , Ct+1 , Ct , πt ) where bρt < 0; i.e. the demand for loans is a decreasing function of the interest rate on loans, all else being equal. Related to Rannenberg (2016), we assume that, out of equilibrium, firms have to pay in advance a fraction ψ L of their labour expenses, hence they have to borrow from banks. This assumption, together with the assumed behaviour of savers/workers as regards labour supply, implies that labor demand deviations from the steady-state level are related to the deviation of loan demand from its steady state level:

Ltd (k ) − Ld (k ) = ψL [wt Nt (k ) − wN (k )]. 4

In our benchmark model, we assume zt = z = 1. We will relax this hypothesis when we introduce hysteresis in the following Section.

(9)

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2.3. Banks Banks play a central role in our model as they intermediate all financial transactions between agents in the model. The only saving instrument available to risk-averse households (savers) is bank deposits. Firms may borrow only by applying for a bank loan. Following Gerali et al. (2010), the banking sector in our model has three distinctive features: a) monopolistically competitive banks set interest rates on deposits and loans in order to maximise profits; b) the rates chosen by banks are adjusted only infrequently (i. e. they are sticky); c) banks accumulate capital (out of retained earnings), as they try to maintain a capital-to-assets ratio as close as possible to a regulated target level κ (i.e. the inverse of leverage). Deviations from such a level imply a quadratic cost. In particular, the bank pays a quadratic cost (parameterized by a coefficient υKb and proporEb

tional to the outstanding bank capital) whenever the capital-to-assets ratio Lt moves away from the target value κ . t Hence, banks enjoy market power in conducting their intermediation activity, which allows them to adjust rates on loans and deposits in response to shocks or to the cyclical conditions of the economy. The optimal level of leverage might derive from a mandatory requirement (explicitly set forth in the Basel framework as forward-looking buffers to be built up in periods of buoyant growth for use in downturns). Banks make optimal decisions subject to a balance-sheet identity, which forces assets to be equal to deposits plus capital:

Lts = Dtd + Etb stating that banks can finance their loans supply Lts using either deposits Dtd or bank equity Etb . Hence, factors that affect the impact of banks capital on the capital-to-assets ratio force banks to modify their leverage. Thus, the model captures the basic mechanism described by Adrian and Shin (2008), a mechanism which has arguably played a major role in the recent crisis. Given these assumptions, bank capital will have a key role in determining credit supply, since it potentially generates a feedback loop between the real and the financial side of the economy. As macroeconomic conditions deteriorate, banks profit and capital might be negatively hit; depending on the nature of the shock hitting the economy, banks might respond to the ensuing weakening of their financial position by reducing lending, hence exacerbating the original contraction. This way of modeling banks à la (Gerali et al., 2010) accounts for the type of “credit cycle” observed in the 2008 recession, with a weakening real economy, a reduction of bank profits and capital and the ensuing credit restrictions. Modeling bank leverage position and interest rate setting allows one to introduce a number of shocks that originate from the supply side of credit and to study their effects on the real economy. For a commercial bank, the leverage is thus the ratio between its loans and equity (κ is the inverse of leverage).

1

κ

=

Lts Lts

− Dtd

Bank capital is accumulated out of retained earnings:

Etb =

Eb,t−1

πt

b + t−1

(10)

The problem for the bank is to choose its loan supply and deposit demand so as to maximize the discounted sum of (real) cash flows:

max E0 Lts ,Dtd

∞ 



Q0

t=0

s d πt+1 + Dt+1 πt+1 − (1 + it )Dtd (1 + ρt )Lts − Lt+1 2  b  υKb Etb Et+1 πt+1 − Eb,t − 2 Ls − κ Etb



t

subject to the balance-sheet constraint (Lts = Dtd + Etb ) and taking ρ t (the net loan rate) and it (the net deposit rate is equal to the policy rate5 ) as given. The first-order conditions deliver a condition linking the spread between rates on loans and on deposits to the degree of leverage Ltb , that is, Et

ρt = it − υKb



Etb −κ Lts



Etb Lts

2 .

(11)

The objective of the analysis below is to determine the consequences of a negative assets’ value shock and, as in our simple model banks assets are made only of loans, this shock can also be interpreted as a sudden increase in non-performing loans.

Lts + utb = Dtd + Etb

(12)

5 According to Gerali et al. (2010), to close the model, we assume that banks have access to unlimited finance at the policy rate it from a lending facility at the Central Bank; hence by aribitrage the deposit rate is equal to the policy rate.

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A. Boitani and C. Punzo / Journal of Economic Behavior and Organization 162 (2019) 347–359 Table 1 Baseline calibration. Parameter

Description

Value

ϕ β σc σs φπ ε α κ λ ψL υKb φb

Curvature of labour disutility Discount factor Capitalist’s risk aversion coeff. saver’s risk aversion coeff. Inflation targeting coefficient Elasticity of substitution (goods) Index of price rigidities Inverse of leverage ratio Savers’ share Share of firm’s labor costs paid in advance Cost of deviating from target leverage Persistence of the shock

5 0.99 2 4 1.5 6 0.75 0.09 0.7 1 10 0.9

where: b utb = ρb ut−1 − εtb ,

(13)

and ρb ∈ [0, 1 ) is a measure of the persistence of the shock. 2.4. Monetary policy and equilibrium As for the monetary authority, in our baseline model we assume the Central Bank sticks to a pure inflation targeting rule, i.e. it sets the nominal interest rate in response to fluctuations in inflation (we assume for simplicity that target inflation is one):

log

1 + it = φπ log 1+i

πt π

(14)

In an equilibrium of this economy, all agents take as given the evolution of exogenous processes. A rational expectations equilibrium is then as usual a sequence of processes for all prices and quantities introduced above such that the optimality conditions hold for all agents and all markets clear at any given time t. Specifically, labour market clearing requires that labour demand equals total labour supply:

Nt = λNs,t .

(15)

Equity market clearing implies that banks shareholdings of each capitalist are:

bc,t = bc,t−1 =

1 . 1−λ

(16)

Finally, by Walras’ Law the goods market also clears. The aggregate resource constraint reads as follows:

Yt = Ct +

γ 2

(πt − 1 ) + 2

υKb Etb 2

Lts

2

−κ

Etb ,

(17)

where:

Ct = λCs,t + (1 − λ )Cc,t

(18)

is aggregate consumption. All loans issued by the banks will be demanded by firms. Market clearing for loans implies:

Ltd = Lts .

(19)

Finally, all deposits demanded by the banks will be supplied by the savers. Market clearing for deposits implies:

Dtd = λDts .

(20)

3. Model dynamics 3.1. Calibration We solve the model by taking a first order approximation around the steady state. Before showing our results, we briefly describe the baseline calibration of the model’s parameters. This calibration is summarized in Table 1. We assume the following settings for the household related parameters. A finding based on PSID (and HRS) data is that people show very high risk aversions. According to the parameters’ estimates, there are very few individuals whose risk aversion parameter is below 1, with the average CRRA being 4.2. More in detail, 11.4% of the population has σ ≤ 1, 22.9% has

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353

Fig. 1. The effects of a negative shock to bank’s assets.

σ ≤ 1.5, 34.1% has σ ≤ 2, and 74% has σ ≤ 5 (Cozzi, 2013). According to these estimates, we set σc = 2 and σs = 4, while we set λ = 0.7. The parameters pertaining to the banking sector are in line with Gerali et al. (2010), that is: a leverage coefficient κ = 0.09 and the coefficient measuring the cost of deviating from targeted leverage υKb = 10. The parameters not pertaining to households and financial frictions are calibrated according to the consensus values used in the literature. We assume the elasticity of substitution among goods ε = 6 and the curvature of labor disutility ϕ = 5. The model’s main frictions are given, not only by financial frictions, but also by price stickiness and market power in goods market. We assume a baseline setting of α = 0.75 , an average price duration of four quarters, a value consistent with much of the empirical micro and macro evidence, according to which we calibrate the Rotemberg parameter γ following α ε−1 Y the formula γ = (1−α()(1−()αβ )) (Ascari and Rossi, 2012). We proceed by also assuming that firms have to fully prefinance the deviation of labor costs from the SS level via working capital loans, ψL = 1. We focus on a deterministic steady state where inflation is one, i.e. the Central Bank target. To simplify the analysis, we make the further assumption that savers supply a fixed amount of labour in steady state: Ns = 1. This assumption is consistent with the view of a constant employment for risk-averse households, as well as a consumption level proportional to the real wage (Galìet al., 2004). As for the persistence of the shock, we choose φb = 0.9. 3.2. The dynamics of the benchmark model Figs. (1) and (2) show the impulse response functions (IRFs) implied by a negative shock to banks assets in our baseline model. Fig. (1) displays the IRFs of selected aggregate variables to a one percent decrease in bank’s assets, while Fig. (2) shows the distributive effects of the same negative shock. In this simple model, the distributive effects can be gauged by the C-ratio - the ratio between the consumption of a saver and the consumption of a capitalist. The negative shock leads to an impact decrease in lending which brings about an increase in the spread between the lending rate and the policy rate. A simultaneous (mechanical) increase in leverage occurs. Lower loans restrains output. Hence, the CB decreases the interest rate to prevent future deflation. In the third period the leverage of banks goes below the steady state regulatory level and shows a persistent procyclicality (approx. 32 periods) before converging to the regulatory level6 . The distributive effect is non-favourable to savers and long lasting. Indeed savers’ consumption (income) is negatively

6 Leverage is the result of maximizing decisions of banks over time and the channel through which in our model economy a financial shock is endogenously transmitted to real variables. It is thus relevant to look at the whole of the evolution of leverage through time and up to its final convergence to the steady state.

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Fig. 2. The distributive effect of a negative shock to bank’s assets.

impacted by the reduction in employment (which is demand driven), in deposits and the interest rate, all ignited by the negative shock to banks assets. Hence the contractionary effects on aggregate output and consumption are strengthened. On the other hand, the negative impact of the shock on banks profits is short lived – thanks to leverage turning procyclical and thus unable to modify capitalists expectations of future dividends. As a consequence the consumption of capitalists is only marginally affected by the financial shock. The asymmetric effects on savers and capitalists explain the shown dynamics of the C-ratio. 3.3. The impact of capitalists’ risk aversion In this paper, one of the key parameters is the degree of risk aversion. It is then relevant to inquire how the dynamics after the shock is affected by different attitudes towards risk of, at least, one type of agent. Figs. (3) and (4) compare the IRFs implied by our benchmark model (blue solid line) with those implied under lower (black dashed lines) and higher (red dotted line) capitalists’ risk aversion. Fig. (3) displays the IRFs of selected aggregate variables to a one percent decrease in bank’s assets, while Fig. (4) shows the distributive effects of a negative shock to bank’s assets. The degree of risk aversion of capitalists mainly drives the banking sector leverage dynamics. Intuitively, the less risk averse are capitalists (i.e. banks owners) the higher and more persistent is the increase in leverage after a negative shock to banks assets. However, lower risk aversion of capitalists (lower σ c ) strengthens and lengthens the procyclicality of leverage. This behaviour of leverage related to capitalists’ risk aversion has two effects on real variables: (i) the after-shock higher leverage lowers the reduction in the demand for labour and consequently in savers income and consumption; (ii) as leverage goes below target (due to stronger procyclicality), loans are reduced more than equity and the spread goes down. Thus firms profits increase by more and savers income and consumption will decrease by less, explaining the observed dynamics of the C-ratio. In sum, a lower risk aversion of capitalists reduces the destabilizing and the distributive effects of a negative financial shock. 3.4. The impact of regulatory requirements The macroeconomic impact of changing regulatory requirements has long been debated (e.g. IIF, 2011). Hereafter, we  examine the role played by changing leverage targets κ1 . Fig. (5) compares the IRFs implied by our benchmark model (blue solid line) with those implied under lower (black dashed lines) and higher (red dotted line) regulatory leverage. Fig. (5) shows that a stricter Basel requirement - that is a lower regulatory leverage (higher κ ) - implies actual leverage is less volatile: it increases less on impact and becomes less procyclical later on. As labour demand is less unstable, savers consumption decreases less after impact. Consequently, aggregate output bounces back more rapidly and the distribution (as measured by the C-ratio) turns to be less unfavourable to savers already one period after the shock. This result confirms the findings of Boissay et al. (2018) based on a model calibrated on US data, according to which macroeconomic stability is enhanced by relatively high capital requirements. We add that stricter regulatory requirements also reduce the non favourable distributive effects on savers.

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Fig. 3. The effects of a negative shock to bank’s assets with different capitalists’ risk aversion.

3.5. The impact of alternative monetary policy rules In the previous sections the Central Bank is assumed to implement an inflation targeting (IT) rule. With the purpose of benchmarking, in this section we explore the dynamics of our economy after the usual shock under three alternative monetary policy rules: (i) the baseline inflation targeting rule of the previous section, where φπ = 1.5, (ii) an even stricter inflation targeting, where φπ = 2 , (iii) a standard Taylor rule (TR)7 . Fig. (6) shows that if inflation targeting is substituted by a Taylor rule our model economy displays a remarkably stable behaviour. Most of all aggregate output, consumption and the consumption ratio are less influenced by leverage. Also the distributive effects are milder under a Taylor rule. A more conservative Central Bank, implementing a stricter inflation targeting, appears to be destabilizing. By reducing abruptly the policy rate when the negative shock hits, the Central Bank induces banks to push their leverage to a peak (as the cost of funding plunges). The ensuing deleveraging is stronger and longer lasting. The distribution coefficient (C-ratio) shows much more unfavourable effects on savers under a stricter inflation targeting (φπ = 2) than in our benchmark case (φπ = 1.5). By jointly considering the results of this section with those of the previous one, it can be shown that the combination of stricter regulatory requirements and softer monetary policy rules enhances the stabilization of the aggregate model economy and of the distribution of income between savers and capitalists. 4. Model variations 4.1. Labour market frictions In this section we want to explore the interactions among different real world frictions in our model economy, in order to show how much the aggregate and distributive dynamics of a negative financial shock are strengthened and prolonged. We shall introduce in two steps labour market frictions that allow for unemployment equilibria and hysteresis in output. We capture labor market frictions through hiring costs increasing in labor market tightness, defined as the ratio of hires to the unemployment pool (Abbritti et al., 2012; Blanchard and Galì, 2010). More specifically, we embed the labor market frictions into the model introduced in the previous sections. At the end of the section we also consider an extension of the model allowing for the presence of hysteresis. Following Engler and Tervala (2016), we shall assume a simple learning-bydoing mechanism where demand-driven changes in employment can permanently affect the level of productivity, leading to hysteresis in output. 7

log

1+it 1+i

= φπ log ππt + φy log

Yt Y

, where φy = 0.125 and φπ = 1.5.

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Fig. 4. The distributive effect of a negative shock to bank’s assets.with different capitalists’ risk aversion.

Next we describe the key features of the benchmark model with unemployment. Employment in firm k evolves according to:

Nt (k ) = (1 − δ )Nt−1 (k ) + Ht (k ),

(21)

where δ ∈ (0, 1) is an exogenous separation and Ht (k) represents the measure of workers hired by firm k in period t. Note that new hires start working in the period they are hired. At the beginning of period t there is a pool of jobless available for hire, and whose size we denote by Ut . We refer to the latter variable as beginning-of-period unemployment (or just unemployment, for short). We make assumptions below that guarantee full participation, i.e., at all times all individuals are either employed or willing to work, given the prevailing labour market conditions. Accordingly, we have: rate8 ,

Ut = 1 − Nt−1 + δ Nt−1 = 1 − (1 − δ )Nt−1 ,

(22)

1

where Nt ≡ 0 Nt (k )dk denotes aggregate employment. We introduce an index of labour market tightness, tt , which we define as the ratio of aggregate hires to unemployment:

tt ≡

Ht . Ut

(23)

This tightness index tt will play a central role in what follows. It is assumed to lie within the interval [0, 1]. Only agents in the unemployment pool at the beginning of the period can be hired (Ht ≤ Ut ). In addition and given positive hires in the steady state, shocks are assumed to be small enough to guarantee that desired hires remain positive at all times. Note that, from the viewpoint of the unemployed, the index tt has an alternative interpretation. It is the probability of being hired in period t, or, in other words, the job finding rate. Below we use the terms labour market tightness and job finding rate interchangeably. Hiring labour is costly. The cost of hiring for an individual firm is given by gt Ht (k), expressed in terms of the CES bundle of goods. gt represents the marginal cost per hire, which is independent of Ht (k) and taken as given by each individual firm. While gt is taken as given by each firm, it is an increasing function of labour market tightness. Formally, we assume:

gt = zt Ktt ,

(24)

where K is a positive constant9 . The relevance of gt in our model economy is strictly related to the extensive margin hypothesis: each firm may adjust its optimal amount of labour by recruiting additional workers and thus paying the hiring cost; the relevance of hiring costs emerges even in more general models, where extensive margin adjustments are accompanied by intensive margin adjustments, provided the first kind of adjustment does not play a trivial role. Firms may bear 8 9

In particular, we set δ = 0.08 in line with Blanchard and Galì (2010). We set K = 0.12, following Blanchard and Galì (2010). It implies that Eq. (5) becomes mct = (1+ρt )z(twt +gt ) .

A. Boitani and C. Punzo / Journal of Economic Behavior and Organization 162 (2019) 347–359

Fig. 5. The effects of a negative shock to bank’s assets with different capital requirement.

Fig. 6. The effects of a negative shock to bank’s assets with different monetary policy rules.

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Fig. 7. Unemployment cum Hysteresis.

advertising, screening, and training costs and may incur in firing costs when protection legislation imposes legal restrictions. Vacancies are assumed to be filled immediately by paying the hiring cost, which is a function of labour market tightness. 4.2. Labour market frictions cum hysteresis We now introduce hysteresis in output, due to complementarity between past employment and present TFP. Following Tervala (2013) and Engler and Tervala (2016), we hereafter assume that the level of productivity accumulates over time according to past employment, as follows10 :

zt = φz zt−1 + μNt−1

(25)

where 0 ≤ φ z ≤ 1 and μ are parameters (φz = 0.9, μ = 0.11). Eq. (25) highlights that a change in the current labour supply changes the level of productivity in the next period, with an elasticity of μ. Fig. (7) compares the IRFs in response to a negative shock to bank’s assets implied by our benchmark model (blue solid line) with those implied by the model with unemployment (dashed black line) and by the model with unemployment and hysteresis (black solid line). Fig. (7) shows that the presence of hiring costs slightly enhances the recessionary and distributive effects of a negative shock to bank’s assets. Due to the assumed labour market friction, the negative financial shock, by reducing employment, increases unemployment (Ut ) more than hiring (Ht ), and this leads to a reduction in employment in the following period. The combination of labour market frictions with hysteresis generates a remarkable amplification and lengthening of the recessionary effect and the distributive effects unfavourable to savers. 5. Conclusion In this paper we consider a NK-DSGE model with two agents: savers (more risk averse) and capitalists (less risk averse). This is the distinctive heterogeneity on which the paper is built and from which the distributive consequences of financial shocks stem in our model-economy. In line with the literature following (Adrian and Shin, 2010), the leverage of banks turns out to be procyclical after an exogenous negative shock hits the value of banks assets. The focus of the paper is on the distributive effects between savers and capitalists which are endogenously determined by leverage procyclicality after a

10 (Tervala, 2013) and (Engler and Tervala, 2016) build on Chang et al. (2002), which assumes a simple skill accumulation mechanism through learning by doing, in which the skill level accumulates over time depending on past employment and the skill level raises the effective unit of labour supplied by the household.

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shock. We measure the distributive effect in terms of the ratio between the consumption of savers and that of capitalists. Our finding is that the distributive effect is always non-favourable to savers and long lasting. Risk aversion of capitalists in our model runs against savers. Indeed we find that the distributive effect unfavourable to savers is greater when capitalists are more risk averse. As for the impact of macroprudential policies, it turns out that lower regulatory requirements amplify the non favourable distributive effects on savers. Hence stricter regulatory requirements unambiguously favour savers. However, stricter or more “conservative” monetary policy rules adopted by the Central Bank – such as tougher inflation targeting – appear to have more unfavourable effects on savers than softer rules (such as the Taylor rule). There is also complementarity between softer monetary rules and stricter regulatory rules. 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