Rethinking capital regulation : the case for a dividend prudential target.
Date: 2019-06-05
Institutions: European Systemic Risk Board
Subjects: bank, economic model, financial regulation, financial risk, financial stability, investment income, venture capital

Working Paper Series 

No 97 / June 2019 

Rethinking capital regulation: 
the case for a dividend  
prudential target 

by 
Manuel Muñoz 

Abstract

The paper investigates the e¤ ectiveness of dividend-based macroprudential rules in com-

plementing capital requirements to promote bank soundness and sustained lending over the

cycle. First, some evidence on bank dividends and earnings in the euro area is presented.

When shocks hit their pro…ts, banks adjust retained earnings to smooth dividends.This gener-

ates bank equity and credit supply volatility. Then, a DSGE model with key …nancial frictions

and a banking sector is developed to assess the virtues of what shall be called dividend pru-

dential targets. Welfare-maximizing dividend-based macroprudential rules are shown to have

important properties: (i) they are e¤ ective in smoothing the …nancial and the business cycle

by means of less volatile bank retained earnings, (ii) they induce welfare gains associated to a

Basel III-type of capital regulation, (iii) they mainly operate through their cyclical component,

ensuring that long-run dividend payouts remain una¤ ected, (iv) they are ‡exible enough so

as to allow bank managers to optimally deviate from the target (conditional on the payment

of a sanction), and (v) they are associated to a sanctions regime that acts as an insurance

scheme for the real economy.

Keywords: macroprudential regulation, capital requirements, dividend prudential target,

…nancial stability, bank dividends

JEL classi…cation: E44, E61, G21, G28, G35

1 Introduction

The recent …nancial crisis has highlighted the importance of counting with a comprehensive pru-
dential regulatory framework that includes macroprudential tools to smooth the …nancial cycle and
prevent the endogenous build-up of systemic risk (see, e.g., Galati and Moessner 2013, Constâncio
2017). Regulatory capital ratios remain a central element of such toolkit. Some of the key objec-
tives …nancial regulators pursue with this policy instrument are to ensure soundness of banks and
normal lending activities during economic downturns. However, the attainment of such objectives
cannot be taken for granted since macroeconomic e¤ects of meeting capital requirements heavily
depend on the channel through which banks adjust their capital ratios.1

In order to increase its regulatory capital ratio, a bank can either raise capital (numerator)
or decrease total risk-weighted assets (denominator).The denominator can be reduced either by
shrinking total assets - in many cases via cutting back on lending - or by reducing their assets’
risk weighted average (substitution of riskier assets for safer ones). The main caveat of the latter
is that a risk shift of this kind may not necessarily contribute to sustained lending. For instance,
the replacement of "risky" loans for public debt is an alternative way of restricting credit supply
to the private sector.

Perhaps, one of the most powerful mechanisms to meet capital requirements while enhancing
bank solvency and lending to the real economy is to directly raise capital. There are two main
options in this regard: to issue new equity or to retain earnings. The issuance of new equity can be
e¤ective but it has a number of disadvantages that make it one of the least attractive strategies to
raise capital on a regular basis: (i) it is costly, (ii) the desire of attracting new shareholders often
pushes banks to increase their dividend payout ratios (retained earnings decreases), and (iii) it is
the least attractive option for existing bank shareholders as a new share issue tends to reduce the
market value of the existing shares.

Alternatively, the bank can opt to retain more earnings. Retained earnings represent the core
component of high quality regulatory capital and a source of regular capital accumulation at a
low direct cost. The bank can target higher retained earnings either by boosting total pro…ts or
by reducing its dividend payout ratio. The direct way of increasing pro…ts is by enlarging the
lending spread. Yet, competition in lending markets can even deter big banks from choosing this
option. Beyond the fact that non bank lending has constantly gained weight since the outbreak
of the recent crisis, small banks themselves can improve their market share (against big banks) by
compressing their margins.

1According to the evidence, bankers internally set their own target capital ratio. This ratio usually includes a
bu¤er above the regulatory capital requirement. To the extent that such bu¤er is directly related to the capital
requirement, I indistinctly use expressions "meeting capital requirements " and "adjusting capital ratios" to make
reference to the action by which bankers adjust their regulatory capital ratio towards their internal target.

2Regarding the alternative of cutting back dividends, the challenge is that markets (share-
holders) immediately react to dividend announcements and penalize lower-than-expected dividend
payments. Nevertheless, in this case there is a strong, economic theory-based reason that may
justify public intervention. According to the evidence, large, established corporations (including
banks) distribute a signi…cant percentage of their pro…ts in the form of dividends and they tend
to smooth them over the cycle. There is a vast theoretical and empirical literature focused on the
analysis of the various market frictions that may be behind this pattern. See Lintner (1956), Miller
and Rock (1985), Dewenter and Warther (1998), La Porta et al. (2000), Allen and Michaely (2003),
DeAngelo et al. (2009), and Leary and Michaely (2011), among others. There is, however, little
agreement on why corporations really smooth dividends and what determines their propensity to
smooth.

The joint consideration of several recent empirical studies points to the existence of a potential
link between the dividend policies of euro area banks and the adjustment mechanisms through
which they improved their capital ratios in the aftermath of the Great Recession. Based on the
statement that retained earnings is the most important source of banks’own funds, Shin (2016)
documents on the accumulated dividends and retained earnings during 2007-2014 for a sample
of 90 euro area banks, to conclude that for certain eurozone countries, "retained earnings would
have been more than double what it was at the end of 2014, had pro…ts been ploughed back into the
bank."

In addition, Cohen and Scatigna (2016) show that for the period 2009-2013 the euro area
banking sector was boosting regulatory capital ratios, foremost via asset shrinking, while virtually
the rest of the world was doing so, primarily by means of capital increases. This evidence is
aligned with the main …ndings in Gropp et al. (2018). Taking the EBA 2011 capital exercise
as a quasi natural experiment, these authors show that European banks which had to raise their
core tier 1 capital ratios in response to the mentioned exercise did it by reducing their levels of
risk-weighted assets rather than by increasing their levels of capital. More precisely, they engaged
in asset shrinking rather than in risk reduction. A reduction in total assets that has been mainly
attributed to a reduction in outstanding customer loans, with e¤ects on the real economy.

The objective of this paper is to evaluate the e¤ectiveness of dividend-based prudential reg-
ulation for banks in complementing the existing capital regulation in its aim of improving bank
soundness, …nancial stability, and social welfare.2

The proposal for regulating bank dividends as a complement of capital requirements is not a
new one. As argued in Acharya et al. (2012), "The erosion of common equity was exacerbated by

2Basel III regulation states that credit institutions face no restrictions on their dividend policies provided that
they comply with the minimum capital requirement plus the conservation bu¤er (10.5% of risk-weigthed assets).
Existing regulation says little about the adjustment mechanisms through which banks should meet their capital
requirements.

3large scale payments of dividends, in spite of widely anticipated credit losses. Dividend payments
represent a transfer from creditors (and potentially taxpayers) to equity holders in violation of the
priority of debt over equity..Thus, an early imposition of regulatory sanctions against the paying
of dividends (for instance, as part of an increasing “ladder of sanctions” that are based on market
or common-equity based notions of bank leverage) may have an important place in the agenda for
reform of the regulatory system".3 Moreover, Goodhart et al. (2010) follow a two-period modeling
approach to assess the impact of imposing dividend restrictions on the functioning of the interbank
market. Acharya et al. (2017) provide theoretical rationale for the use of dividend restrictions for
banks. Similarly, Admati et al. (2013) advocate dividend restrictions and capital conservation in
bad times.

To the best of my knowledge, there hasn’t been developed any work in which a DSGE modeling
approach is adopted to asses the relevance of bank dividend regulation as a macroprudential tool in
a world of capital requirements. Existing theoretical work on bank dividend-based macroprudential
regulation is limited and usually tends to focus on the particular case in which regulated institutions
do not comply with capital legislation, disregarding the potential bene…ts of regulating bank payout
policies, even when …nancial institutions meet their capital requirements.

On these grounds, and based on the available evidence, this paper attempts to contribute to
…ll this gap in the literature by developing a …nancial business cycle model which incorporates the
following key features: (i) bank capital accumulation out of retained earnings, (ii) endogenous bank
dividend policies, and (iii) a set of …nancial frictions that makes bankers to optimally adjust capital
ratios through the retained earnings and credit supply channel in order to smooth dividends. Such
imperfections impede aggregate …nancial and economic ‡uctuations to be optimal from a social
welfare point of view.

Absent a broad consensus on this front, I opt to remain agnostic about the underlying causes
behind dividend smoothing and only attempt to reproduce this pattern in a standard but simple
manner. In particular, I allow for two mechanisms through which bank dividend smoothing can
potentially take place in the model: (i) bankers’ preferences (which are represented by a CES
utility function), and equity payout adjustment costs, in the spirit of Jermann and Quadrini
(2012). These are, probably, two of the most widely followed approaches to generate a pattern
of dividend smoothing in a simple DSGE model (see, e.g., Jermann and Quadrini 2012, Iacoviello
2015, and Begenau 2019).4

The …rst mechanism is consistent with a strand of literature arguing dividend smoothing relates

3These authors carry out an empirical analysis based on U.S. banking data for the period 2007-2009 to draw

some general conclusions and give speci…c recommendations on capital regulation.

4In this regard, it is relevant to highlight the aim of this model is not to carefully microfound dividend smoothing
but rather to reproduce this pattern at an aggregate level, in order to focus the analysis on the e¤ects of dividend-
based macroprudential regulation.

4to managers’preferences (see, e.g., Fudenburg and Tirole 1995 and Wu 2017). The second one is
aligned with recent evidence suggesting payout policies based on dividend smoothing strategies are
costly to corporations (Brav et al. 2005). Whether the pattern of dividend smoothing is generated
by the banker’s preferences or by the dividend adjustment cost function heavily depends on the
parameterization of the two. As it will be discussed further, due to empirical and theoretical
reasons, the model has been calibrated such that dividend smoothing is induced by bankers’
preferences, implying the role played by the dividend adjustment cost function in this model is
mostly limited to the speci…cation and transmission of the proposed prudential regulation (and
that its corresponding coe¢ cient can be basically interpreted as a policy parameter).

In the same way Angelini, Neri and Panetta (2014) specify a target for dynamic capital re-
quirements, the model incorporates a dynamic regulatory target for bank dividends. The main
di¤erence between their approach and the one followed in this paper is that, in this case, the extra
cost bankers can incur when deviating from what shall be called the "dividend prudential target"
(henceforth "DPT") is not taken as a deadweightloss. Rather, the paper assumes such cost takes
the form of a penalty payment or sanction that is collected by the prudential authority and directly
transferred as a net subsidy to the non …nancial sector of the economy. As it will be shown, under
certain conditions this sanctions regime can be interpreted as an insurance scheme for the real
economy.

The rest of the model builds on a number of recent contributions to the macro-…nance literature
which have been essential to shed light on the macroeconomic implications of …nancial interactions.
The main role of the banking sector in this model is to allow for resource transfers between
savers and borrowers. In the spirit of Bernanke et al. (1999), the presence of certain frictions
enables …nancial intermediation activities to endogenously propagate and amplify shocks to the
macroeconomy. As in Gertler and Karadi (2011) and Gertler and Kiyotaki (2010), bankers face a
balance sheet constraint when obtaining deposits. In the tradition of Kiyotaki and Moore (1997),
borrowers are constrained in their capacity to borrow by the value of their real estate collateral.
Based on Iacoviello (2015), …nancial intermediaries face a similar type of borrowing constraint
which can be interpreted as a capital adequacy restriction.5 This assumption is important in order
to focus the attention on the e¤ects of a possibility not considered in the Basel III Accord. To
regulate bank dividend policies even when credit institutions comply with capital requirements.
The general structure of the model has its similarities to Gerali et al. (2010).

In a …rst stage, a stylized version of the model is presented to clearly identify the transmission

5This capital adequacy constraint can be interpreted as the overall regulatory capital ratio bankers target inter-
naly. According to the evidence, such target ratio typically includes a bu¤er bankers maintain above the minimum
capital requirement imposed by the …nancial regulator. Some of the factors that determine such bu¤er are prof-
itability, risk, size and loan loss provisions.

5channel through which the proposed policy rule complements capital ratios in the attainment of
their goals. A quantitative exercise is carried out to show that simple dividend prudential targets
which react to deviations of the credit-to-GDP gap call for procyclical, relatively more volatile
bank dividends in order to smooth the …nancial cycle.

Then, the model is extended as in Iacoviello (2005).

Incorporating an additional type of
borrower (impatient households), physical capital and various types of exogenous shocks helps to
improve the dynamics of the model and its matching to quarterly euro area data. As in Clerc et al.
(2015), households own all existing …nancial and non-…nancial corporations in the economy. That
allows me to carry out a sensible welfare analysis that restricts to households without neglecting any
consumption capacity generated in the economy. Welfare-maximizing dividend prudential targets
are shown to have important properties: (i) they are e¤ective in smoothing …nancial and business
cycles by means of less volatile bank retained earnings, (ii) they induce welfare gains associated to
a Basel III-type of capital regulation6, (iii) they mainly operate through their cyclical component,
ensuring that long-run dividend payouts remain una¤ected, (iv) they are ‡exible enough so as
to allow bank managers to optimally deviate from the target (conditional on the payment of a
sanction), and (v) they are associated to a sanctions regime that acts as an insurance scheme for
the real economy.

The paper is organized as follows. Section 2 presents empirical evidence on bank dividends
and earnings in the euro area. Section 3 describes the basic model and identi…es the transmission
mechanism through which a dividend prudential target improves bank soundness and …nancial
stability. Section 4 presents the extended model to improve the matching of the model to the
data. Section 5 develops a quantitative exercise to asses the welfare e¤ects of the proposed policy
and its interactions with regulatory capital ratios. Section 6 concludes.

2 Patterns of Bank Dividends in the Euro Area

Figure 1 describes some of the key patterns of euro area bank dividends and their link with equity
developments. Plotted …nancial data is at quarterly frecuency and has been seasonally adjusted by
means of the Tramo/Seats method. Financial data is from the Euro Stoxx Banks Index, SX7E.7

6Countercyclical dividend prudential targets complement Basel III capital regulation through two main channels:
(i) They tend to compensate the negative welfare e¤ects induced by hikes in the regulatory capital ratios (through
a more restrictive and relatively more volatile credit supply), and (ii) they reinforce the e¤ectiveness of the CCyB
in smoothing the business and the …nancial cycle.

7The Euro Stoxx Banks Index, SX7E, is a capitalization-weighted index. The largest stocks in the EMU banking
sector are selected to weigh in the index according to their free-‡oat market capitalization. As of October 31,2018,
the top ten components of the index (and their corresponding weights) were Banco Santander (16.42%), BNP
Paribas (12.90%), ING Group (9.89%), BBVA (7.90%), Intesa Sanpaolo (7.73%), Societe Generale Group (6.36%),
Unicredit (5.81%), Deutsche Bank (4.01%), KBC Group (3.87%), and Credit Agricole (3.41%).

6Given the purpose of the paper, such composite index has been selected as a representative group of
the euro area banking system for several reasons. First, it captures relatively well the performance
of the sector since it is composed of large, listed banks that are leaders in their industry in terms
of market capitalization. Second, given the size and interconnectednes of its members, it is a fairly
good sample of banks to carry out systemic risk analysis. Third, the signalling power of dividends
is more evident for the case of large, listed companies. Fourth, the constructed series are from
data that is available and updated by Bloomberg.

Figure 1(a) plots the euro area annual GDP growth rate (secondary y-axis) and the dividend
payout ratio of the SX7E for the period 2002:I-20018:II. The dividend payout ratio is de…ned as
the total net dividend payout (including all cash type of dividends and excluding returns of capital
and in-specie dividends) as a percentage of net pro…ts. The payout ratio is notably countercyclical
and it becomes more volatile in times of severe …nancial stress and economic downturn (2009 and
2012). According to the data reported by Bloomberg, in 2009:II, distributed earnings represented
about 82.5% of net pro…ts while they exceeded 100% of total earnings in 2012II and 2012III.

Figure 1(b) sheds light on the main underlying drivers of such pattern. Especially from 2009:I
onwards, bank managers opted to smooth dividends over the cycle, paying high and stable amounts
of dividends in cash even if net income for the period was negative. Overall, both variables are
procyclical, while earnings are relatively more volatile than dividends. Earnings (net pro…ts) have
been represented according to two di¤erent measures of adjusted net income. However, both of
them are based on the de…nition of operating income after provisions.8 Due to certain events
and regulatory changes, loan-loss provisioning increased in the aftermath of the …nancial crisis.
Such provisions are crucial to understand the aggregate net losses incurred in certain quarters
between 2011 and 2014.9 Note that the spike of the dividend payout ratio in 2012:III relates to the
July 2012 …nancial turmoil. Relying on the signalling role attributed to dividend policies, bankers
maintained dividend payouts roughly stable despite the severe fall in earnings.10

Such a dividend policy has tangible implications for the composition and performance of bank

8See Appendix A for details on data construction.

9Due to auditing purposes, banks tend to record an important part of their annual loss provisions in the fourth

quarter. That becomes more obvious when looking at raw rather than seasonally-adjusted data on net income.

10The series presented in …gure 1(b) may not necessarily coincide with the time series on the dividend payout
ratio plotted in …gure 1(a). Due to data availability, the former have been constructed as a simple sum of the SX7E
members whereas the latter is a capitalization-weighted sum of the same group of banks. In additon, quarterly
aggregate data on payout ratios should be taken with caution for at least two reasons: (i) For each quarter, the
index can only incorporate information on members whose net pro…ts for the period are strictly positive. Otherwise
the payout ratio cannot be computed. (ii) The adjustments made to raw data on net income (denominator of
the payout ratio) often vary across analysts. These adjustments can be quantitatively important, especially when
considering a time series that accounts foar a period of severe …nancial crisis and deep regulatory changes (in
loan-loss provisioning rules, etc).

7equity over the cycle and for the available adjustment mechanisms to meet the target capital ratio.
Figure 1(c) plots total equity and retained earnings of the SX7E for the same period.11 Not
surprisingly, both aggregates are procyclical and highly correlated. Nonetheless, retained earnings
are relatively more volatile, especially during economic downturns. Given that retained earnings
is a core component of total equity, these patterns can be interpreted as suggestive evidence of
two important …ndings. First, the adjustment in the face of shocks that a¤ect banks’net pro…ts
is mainly borne by retained earnings (i.e., dividend smoothing). Second, retained earnings are an
important driver of bank equity (and, hence, credit supply) falls during economic recessions.

All in all, these patterns suggest that bank managers assign a prominent signaling role to
dividends. This becomes particularly clear in periods of …nancial stress. Consequently, retained
earnings have to adjust severely. This evidence deserves especial attention from the policymaker.
To the extent that issuing new equity in times of market stress and economic downturn can be
particularly costly, this art of dividend policies may be crucial to understand the preference of euro
area banks for meeting capital requirements through asset shrinking.

3 The basic model

Consider three types of agents who interact in a real, closed, decentralized and time-discrete
economy in which all markets are competitive. Households work, consume, accumulate housing
and invest their savings in one-period bank deposits. Entrepreneurs demand real estate capital and
labor to produce an homogeneous …nal good. Due to a discrepancy in their discount factors, in the
aggregate households are net savers whereas entrepreneurs are net borrowers. There are …nancial
‡ows in equilibrium. Bankers intermediate …nancial resources by borrowing from households and
lending to entrepreneurs. They devote the resulting net pro…t to do both; pay dividends (bankers’
consumption) and meet the capital requirement by retaining earnings. For each type of agent,
there is a continuum of individuals in the [0; 1] interval.

In the spirit of Iacoviello (2005), entrepreneurs and bankers are assumed to face borrowing
constraints that are binding in a neighborhood of the steady state. Consequently, the …rst best is
unattainable in equilibrium. Moreover, the presence of credit and equity payout adjustment costs
potentially generates additional ine¢ ciencies over the cycle. Such …nancial imperfections play two
important roles: (i) they amplify the e¤ects of exogenous shocks through the …nancial sector, and
(ii) they open up the possibility of a welfare-improving public intervention.

The aim of this section is to identify the transmission mechanism through which the considered

11As made available by Bloomberg, each of these time series is presented as the capitalization weigthed sum of

the SX7E members after having normalized individual data by the number of shares outstanding.

8policy operates. In doing so, the paper evaluates its e¤ectiveness in favouring …nancial stability
by smoothing the credit cycle.

3.1 Main Features

3.1.1 Households (net savers)

Let Ch;t, Hh;t and Nh;t represent consumption, housing demand and hours worked by households
in period t. The representative household seeks to maximize the objective function

E0

1

(cid:12)t
h

t=0
X

"

log Ch;t + j log Hh;t

N 1+(cid:30)
h;t
(1 + (cid:30))#

(cid:0)

subject to the sequence of budget constraints

Ch;t + Dt + qt(Hh;t

Hh;t

(cid:0)

(cid:0)

1) = Rh;t

1Dt

(cid:0)

(cid:0)

1 + Wh;tNh;t

where Dt denotes the stock of deposits, Rh;t is the gross interest rate on deposits, qt is the price
(0; 1) is the households’
of housing and Wh;t the wage rate. Housing does not depreciate. (cid:12)h 2
subjective discount factor, j is the preference parameter for housing services and (cid:30) stands for the
inverse of the Frisch elasticity. Each period, the representative household allocates its resources
in terms of wage earnings, properties in the housing market and gross returns on total deposits
between …nal consumption and investment in deposits and housing. The standard intertemporal
and intratemporal optimality conditions can be derived from the …rst order conditions of the
problem.

(cid:18)

1
Ch;t+1 (cid:19)
qt+1
Ch;t+1 (cid:19)

1
Ch;t

= (cid:12)hRh;tEt

qt
Ch;t

=

j
Hh;t

+ (cid:12)hEt

(cid:18)

Wh;t
Ch;t

= N (cid:30)
h;t

(1)

(2)

(3)

Expression (1) is the Euler equation for consumption, which in this model determines the
equilibrium interest rate on deposits. Equation (2) refers to the optimality condition for intertem-
poral substitution between consumption and housing demand. Expression (3) is the labor supply

9schedule, relating real wages to the marginal rate of substitution between consumption and hours
worked.

3.1.2 Entrepreneurs (net borrowers)

The representative entrepreneur chooses the trajectories of consumption Ce;t, housing He;t, demand
for labor Nh;t and bank loans Bt that maximize

subject to the sequence of budget constraints

t=0
X

1

E0

(cid:12)t

e log Ce;t

Ce;t + Re;tBt

(cid:0)

1 + qt(He;t

He;t

(cid:0)

(cid:0)

1) + Wh;tNh;t + (cid:8)e(Bt) = Yt + Bt

(Bt

(cid:30)e
2

where Bt stands for bank loans, Re;t is the gross interest rate on loans, and (cid:8)e(Bt) =

Bt
(cid:0)
Bss
is a quadratic loan portfolio adjustment cost, assumed to be external to the entrepreneur as in
Iacoviello (2015). This cost discourages the entrepreneur from changing their credit balances too
quickly, thereby contributing to match the empirical fact that bank credit varies slowly over time.
Yt is …nal output. Bss is the steady-state value of Bt and (cid:30)e is the loans adjustment cost para-
(0; 1) is the subjective discount factor of the entrepreneur, which is assumed to be
meter. (cid:12)e 2
strictly lower than (cid:12)h, implying that, in equilibrium, households are net savers and entrepreneurs
are net borrowers. Each period, the representative entrepreneur devotes her resources in terms of
produced …nal output and loans to consume, repay its debt, remunerate productive factors and
adjust credit demand.

(cid:0)

The homogeneous …nal good is produced by using a Cobb-Douglas technology that combines

labor and commercial real estate as follows:12

In addition, entrepreneurs are subject to

Yt = H (cid:29)
e;t

(cid:0)

1N 1
(cid:0)
h;t

(cid:29)

Bt

(cid:20)

mH

t Et

qt+1
Re;t+1

He;t

(cid:18)

(cid:0)

(cid:19)

mN Wh;tNh;t

(4)

(5)

12The speci…cation of a production function in which real estate enters as an input has become common practice
in the macro-…nance literature. See, e.g., Iacoviello (2005 and 2015), Andrés and Arce (2012) and Andrés et al.
(2013).

1)2

10Expression (5) dictates that the borrowing capacity of entrepreneurs is tied to the value of their
collateral. In particular, they cannot borrow more than a possibly time-varying fraction mH
t of the
expected value of their real estate stock. More precisely, mH
is the exogenously time-
varying loan-to-value ratio, where mH
[0; 1] and "mh
follows a zero-mean AR(1) process with
autorregressive coe¢ cient equal to (cid:26)mh and i.i.d innovations emh;t that are normally distributed
and have a standard deviation equal to (cid:27)mh. Moreover, the borrowing constraint indicates that a
fraction mN
[0; 1] of the wage bill must be paid in advance, as in Neymeyer and Perri (2005).13
As in Iacovielllo (2015), entrepreneurs are assumed to discount the future more heavily than
1

t = mH"mh

2

2

t

t

households and bankers. Formally, (cid:12)e =

, an assumption that ensures the bor-

rowing constraint is binding in a neighborhood of the steady state.14

(cid:13)

1
(cid:12)h

+ (1

(cid:13))

(cid:0)

1
(cid:12)b

The optimality conditions for housing and labor demand can be obtained from the …rst order

conditions

1
qt
Ce;t (cid:20)

1

(cid:0)

(cid:0)

(cid:18)

@(cid:8)e(Bt)

@Bt (cid:19)

mH

t Et

qt+1
Re;t+1 (cid:19)(cid:21)

(cid:18)

= (cid:12)eEt

1
Ce;t+1 (cid:20)

qt+1(1

(cid:26)

mH

t ) + (cid:29)

(cid:0)

Yt+1
He;t (cid:19)(cid:21)(cid:27) (6)

(cid:18)

1
Ce;t (cid:20)

Wh;t + mN Wh;t

1

(cid:0)

(cid:18)

@(cid:8)e(Bt)

@Bt (cid:19)

(cid:0)

(cid:29))

(1

(cid:0)

Yt
Nh;t (cid:21)

= (cid:12)eEt

1
Ce;t+1

(cid:20)

mN Wh;tRe;t

(7)

(cid:21)

Equations (6) and (7) inform about the optimal intertemporal substitution schemes between
consumption and demand of the corresponding productive factor. The way mH
t and mN enter in
each of the optimality conditions shows that the collateral constraint introduces a wedge between
the marginal productivity of the input and its price. Whereas credit adjustment costs only distort
entrepreneurs’decisions in the transition dynamics, the presence of a borrowing constraint of the
type (5) does not only generate ine¢ ciencies in the transition but also in the steady state itself. To
have a clear account of this phenomenon, the steady state expressions of (6) and (7) are presented

Y
He (cid:19)
13Whitout loss of generality, this assumption is made for quantitative analysis-related reasons. It helps in shaping
the steady state levels and transition dynamics of aggregate …nancial variables, particularly in a reduced form model
of this kind.

q =

(cid:29)
(cid:17)

(cid:18)

14As it will be shown later, (cid:12)b is the discount factor of bankers and (cid:13)

expressed in terms of banks’total assets.

[0; 1] refers to their borrowing capacity

2

11Wh =

(cid:29))

(1

(cid:0)

Y
Nh

where (cid:17) =

1
1
(cid:12)e (cid:20)

mH
Re (cid:0)

(cid:0)

(cid:12)e(1

(cid:0)

mH)
(cid:21)

, and   =

1 + mN [1

(cid:12)eRe]

. It could be shown

(cid:0)

that, given the considered lower and upper bounds for mH and mN and the range of values
typically proposed in the literature for the discount factors of borrowers and bankers, the following
inequalities always hold in the steady state of this economy: (cid:17) < 1 and,   > 1. Compared to
a frictionless economy, in the long-run equilibrium the commercial real estate-to-labor ratio is
ine¢ ciently low.

(cid:8)

(cid:9)

3.1.3 Bankers

Let db;t represent bank dividends (which are fully devoted to …nal consumption by bankers) in pe-
riod t; (cid:27) > 0 be the elasticity of intertemporal substitution (EIS), and (cid:12)b < (cid:12)h. The representative
banker seeks to maximize

subject to

1

E0

t=0
X

(cid:12)t
b

(1

1

(cid:0)

1
(cid:27) )

1

(cid:27) )

(1
b;t

d

(cid:0)

Bt = Kb;t + Dt

db;t + Kb;t

(1

(cid:0)

(cid:0)

(cid:14))Kb;t

(cid:0)

1 = re;tBt

(cid:0)

1

(cid:0)

rh;t

(cid:0)

1Dt

(cid:0)

1

(cid:0)

(cid:8)b(Bt)

(cid:0)

'(db;t)

Dt

(cid:20)

(cid:13)Bt

(8)

(9)

(10)

(11)

Where equations (9), (10) and (11) denote the balance sheet identity, the sequence of cash ‡ow

restrictions, and the borrowing constraint of the banker, respectively.

According to (9), bank assets are …nanced by the sum of bank equity Kb;t (also referred to as
bank capital) and debt. There is only one type of bank assets; one-period loans which are extended
to entrepreneurs. Bank debt is entirely composed of funds borrowed by households in the form
of homogeneous one-period deposits. The model assumes full inside equity …nancing, in the sense
that bank equity is solely accumulated out of retained earnings. Formally, the law of motion for
bank capital is similar to that of Gerali et al. (2010)

12 
Kb;t = Jb;t

db;t + (1

(cid:14))Kb;t

(cid:0)

1

(cid:0)

(cid:0)

(12)

where Jb;t stands for bank net pro…ts and (cid:14)

[0; 1] denotes the fraction of own resources the
2
banker can no longer accumulate as bank capital in period t due to exogenous factors. Rearranging
in expression (12), bank net pro…ts can be decomposed into three parts:

Jb;t = (Kb;t

Kb;t

1)

(cid:0)
reinvested pro…ts

(cid:0)

+ (cid:14)Kb;t

(cid:0)

+

1

db;t

eroded equity

distributed earnings

(13)

(cid:0)

{z

| {z }

|
Kb;t
|

retained earnings
}
{z

where the term (Kb;t

|{z}
1) refers to the part of pro…ts made in period t which are reinvested
(cid:0)
in the …nancial intermediation business, and (cid:14)Kb;t
1 is the fraction of bank own resources which,
due to exogenous factors, cannot be further accumulated as bank capital into the next period.
The term (cid:14)Kb;t
1 can be interpreted in several manners: (i) own resources the banker devotes to
manage bank capital and to play its role as …nancial intermediary, or (ii) equity that erodes due
to a variety of factors which are not explicitly accounted for in the model and which may relate to
speci…c characteristics of capital such as its quality or its value.

}

(cid:0)

(cid:0)

The de…nition of bank equity as a stock variable that accumulates over time out of retained
earnings is a crucial assumption due to empirical factors. First, an important proportion of total
bank equity is accumulated out of retained earnings in practice (see …gure 1c).15 Second, equation
(12) allows to map the model to …rst and second moments of data on bank dividends and earnings
(see section 5).

Equation (10) is a ‡ow of funds constraint which states that in each period the banker has to
distribute net pro…ts Jb;t between dividend payouts db;t and retained earnings. In the basic model,
bank net pro…ts are de…ned as the di¤erence between net interest income and the corresponding
credit and equity payout adjustment costs.16 re;t and rh;t denote the net interest rates on loans and
deposits, respectively. As in Jermann and Quadrini (2012), the model assumes an equity payout
adjustment cost of the type

'(db;t) =

(cid:20)
2

(db;t

(cid:0)

b )2
dss

(14)

where (cid:20)

(cid:21)

0 is the payout adjustment cost parameter, and dss
b

the long-run payout target

15In fact, it is the availability of (cumulative) retained earnings what allows bankers to pay dividends even when

earnings for the period are non-positive.

16As in the case of the entrepreneur, (cid:8)b(Bt) =

is assumed to be external to the banker. (cid:30)b (cid:21)

(Bt

(cid:30)b
2

1)2
(cid:0)

Bt
(cid:0)
Bss

is a quadratic loan portfolio adjustment cost and

0 is the credit adjustment cost parameter.

13!1

(steady state). Given the preferences of the representative banker (i.e., represented by a CES
utility function), there are two standard cases which can be labelled as representative of the two
main alternative ways of accounting for the empirical regularity of dividend smoothing, under this
u (db;t) = db;t and (cid:20) > 0, the modeling device represented by expression (14)
set-up. When lim(cid:27)
generates a pattern of dividend smoothing.17 Lintner (1956) found that managers have a dividend
payout target and a …xed rate at which dividends should converge towards that target. While
remaining agnostic about the underlying factors of dividend smoothing, assuming '(db;t) allows
to capture the main macroeconomic implications of such phenomenon in a simple manner. At the
individual level, bank managers face costs from deviating from a pre-determined payout target.18
At the social level, it generates ine¢ ciencies over the cycle.

By way of contrast, when lim(cid:27)

1 u (db;t) = log db;t, bankers’preferences already account for the
empirical fact of dividend smoothing and the main role played by function (14) basically limits
to allow for the proposed dividend-based regulatory scheme.19 20 Importantly, given the aim and
scope of this paper, the calibration of the model presented in sections 3 and 5 of this paper falls
within this general case.21

!

Expression (11) stipulates that bankers are constrained in their ability to issue liabilities. For a
[0; 1] of total assets. Given this expression
(cid:13)) can be interpreted as the target capital

given period t, deposits cannot exceed a proportion (cid:13)
is binding in a neighborhood of the steady state, (1
ratio internally set by bankers.

2
(cid:0)

The optimality condition for this maximization problem can be obtained after having re-

arranged and substituted in its three …rst order conditions.

(cid:13)) +

(1

(cid:0)

@(cid:8)b(Bt)
@Bt

1
(cid:27)

b;t [1 + (cid:20)(db;t
d

dss
b )]

(cid:0)

= (cid:12)bEt 8
<

(Re;t+1

(cid:14))

(cid:0)

(cid:0)

(cid:13) (Rh;t

b;t+1 [1 + (cid:20) (db;t+1
d

1
(cid:27)

(cid:0)

(cid:14))
(cid:0)
b )] 9
dss
=

(15)

Expression (15) stands for the optimality condition for intertemporal substitution between the

:

;

17see, e.g., Jermann and Quadrini (2012), for a simple DSGE model with a …nancial friction, and Begenau (2019)
for a DSGE model with a banking sector and capital requirements. See Brav et al. (2005) for some recent evidence
suggesting payout policies based on dividend smoothing strategies are costly to corporations.

18An important empirical fact is that markets react negatively (positively) to announcements of dividend decreases

(increases). See Allen and Michaely (2003).

19See, e.g., Iacoviello (2015), for a DSGE model in which bankers’preferences are modeled in this fashion. See, e.g.,
Fudenburg and Tirole (1995) and Wu (2017), for theoretical and empirical studies suggesting dividend smoothing
relates to managers’preferences.

20The social costs of dividend smoothing can potentially take two forms in this model. First, the direct cost
in terms of the resources devoted by bankers to deviate from the dividend target, which in the aggregate may be
non-negligible (this type of ine¢ ciency only emerges when (cid:27) is su¢ ciently small and (cid:20) > 0). Second, the implicit
social welfare cost in terms of increased volatility in …nancial aggregates (loans, deposits, etc) induced by forcing
retained earnings to act as the main adjustment variable in the face of shocks that hit bank pro…ts.

21See section 5 for a detailed discussion on the reasons underlying this approach.

141

1
(cid:27)

d
b;t [1 + (cid:20)(db;t

dss
b )]

part of net income devoted to the dividend payout policy (denominator) and that dedicated to the
…nancial intermediation activity (numerator). The engine of the intertemporal activity of bankers
is earnings retention. Importantly, bankers endogenously manage the size of their balance sheet
and set the growth path of future expected pro…ts (and, thus, of expected dividends) by controlling
for retained earnings.

From the perspective of the banker as a consumer, expression (15) can be interpreted as the

standard Euler equation for intertemporal substitution of consumption.22The term

(cid:0)
refers to the marginal utility of resources devoted to consumption in period t:23 The terms in the
numerator of each side of the equation account for all the di¤erent components involved in the
expected gross return on marginal savings (via earnings retention) in period t. Recall from equa-
(cid:13)) units, automatically implies the borrowing of
tions (9) and (11) that increasing equity by (1
(cid:0)
additional (cid:13) units of debt and the extension of an extra unit of loans. The latter implies paying

(cid:14)) is the marginal revenue of lending, (cid:13) (Rh;t

a marginal cost for having adjusted the loan portfolio of

@(cid:8)b(Bt)
@Bt
(cid:14)) the marginal cost of issuing debt,
that (Re;t+1
(cid:13)) the marginal opportunity cost of equity (in terms of foregone marginal utility of div-
and (1
idends). In the optimum the banker is indi¤erent between devoting an extra unit of pro…ts to
paying dividends today and postponing such payment to the next period.

in period t. Then, it follows

(cid:0)

(cid:0)

(cid:0)

From the lens of the banker as a manager, it is optimal to invest (via earnings retention) up
to the point in which the marginal cost of retaining an additional unit of net pro…ts equalizes
the marginal revenue of such investment. Expressed in terms of the opportunity cost (foregone
marginal utility of dividends), the right-hand side of expression (15) informs about the discounted
marginal gross lending spread the banker expects to obtain tomorrow as a consequence of having
invested (1

(cid:13)) units of retained earnings today.24

(cid:0)

(cid:0)

Given the interest rate on deposits, expression (15) determines the equilibrium interest rate on

loans. Hence, the assumption by which (cid:12)b < (cid:12)h ensures that in the steady state, (Re;t+1
(cid:13) (Rh;t

(cid:14)) > 0.

(cid:14))

(cid:0)

(cid:0)

Equation (15) synthesizes the information of a powerful mechanism for transmission and am-
pli…cation of shocks that hit bank pro…ts. Absent the possibility of raising capital by issuing new
equity (equation 12), the strong preference for dividend smoothing implicit in expressions (8) and
(14) implies that the bulk of the adjustment to shocks that hit pro…ts is going to be made via
retained earnings. Due to the strong link between equity, loans and deposits (equations 9 and 11),

22Recall that in the basic model bankers are both, owners and managers of the bank. As owners, in each period

they receive a dividend payout which is fully devoted to …nal consumption within the same period.

23Which include the dividend payment and the equity payout adjustment cost.
24Again, by equations (9) and (11), such decision automatically involves borrowing additional (cid:13) units of deposits

and lending an extra unit of assets.

15such ‡uctuations in retained earnings are going to have an impact on the welfare of savers and
borrowers through volatile deposits and loans, respectively.

3.1.4 Macroprudential Authority

In the baseline scenario, the only policy instrument the prudential authority has at hand is the
constant capital requirement implied by equation (11). The regulator is assumed to have full
control over the capital adequacy parameter (cid:13) from equation (11).

Consider an alternative policy scenario in which the capital requirement (cid:13) is complemented by

a simple prudential rule on bank dividends

d(cid:3)t = (cid:26)d + (cid:26)(cid:31)(

xt
xss (cid:0)

1)

(16)

where d(cid:3)t is what shall be called the dividend prudential target. This rule comprises a micro-
prudential component, (cid:26)d; which is the equity payout targeted by the prudential authority in the
absence of …nancial ‡uctuations, and a macroprudential component, (cid:26)(cid:31)(
1), that adjusts to
tame the …nancial cycle. xt is an aggregate the prudential authority closely monitors to detect
potential signs of systemic risk and …nancial instability (e.g., the credit-to-output ratio), and xss
its steady state value. Thus, (cid:26)(cid:31) is the policy parameter that measures the degree of responsiveness
of d(cid:3)t to deviations of xt from its steady state level (e.g., reaction to the so called credit-to-output
gap).

xt
xss (cid:0)

As in Angelini, Neri and Panetta (2014), the macroprudential policy rule enters in the corre-

sponding equity adjustment cost function (equation 14) as follows

'(cid:3)(da

b;t) =

(cid:20)
2

(cid:0)

da
b;t (cid:0)

d(cid:3)t

2

(cid:1)

(17)

where da

= da

b;t refers to the bank dividend payout in the alternative policy scenario. In period t,
the following inequalities may hold: db;t
b;t). Given
that such adjustment cost di¤erential would be triggered by policy intervention, the corresponding
resources shouldn’t be considered as a deadweight loss, but rather as a penalty bankers must
pay to the public authority for having deviated from d(cid:3)t . In the model, such public resources are
transferred within the same period to the non …nancial sector of the economy. The net subsidy
under consideration can be de…ned as follows

= d(cid:3)t , implying '(db;t)

b;t and dss
b

= '(cid:3)(da

Tt =

(cid:20)
2

h(cid:0)

da
b;t (cid:0)

d(cid:3)t

2

(cid:0)

(db;t

(cid:0)

b )2
dss

(cid:1)

i

(18)

166
6
6
As it will become more evident in the quantitative exercise, the net subsidy (18) can be positive
or negative over the cycle and its size is proportional to the deviation of the representative banker,
da
b;t, from the dividend prudential target, d(cid:3)t .

Importantly, the transmission of macroprudential dividend regulation in this model mainly

takes place through the optimality condition of the representative banker, which now reads

@(cid:8)b(Bt)
@Bt

(1

(db;t)

(cid:13)) +

(cid:0)
1
(cid:27) [1 + (cid:20)(db;t

d(cid:3)t )]

(cid:0)

= (cid:12)bEt

(Re;t+1

(

(db;t+1)

1
(cid:27)

(cid:14))

(cid:0)

(cid:0)
1 + (cid:20)

(cid:13) (Rh;t

db;t+1

(cid:14))

(cid:0)
d(cid:3)t+1

(cid:0)

(19)

)

Absent a dynamic dividend target, the banker …nds optimal to react to exogenous shocks mostly
by readjusting the variables that take part in the …nancial intermediation activity (numerator on
each side of equation 15).25 Under a dividend prudential target within the class (16), the regulator
aims at discouraging bankers from making the adjustments via credit supply by means of more
responsive bank dividends (denominator on each side of equation 19).

(cid:2)

(cid:0)

(cid:1)(cid:3)

Without prejudice of the merit alternative speci…cations of dividend regulation may have,
the regulatory scheme comprised of equations (16), (17), and (18) has been selected due to its
properties, which will be commented upon in the quantitative exercise of this section.26

Dividend prudential targets are aimed at mitigating the potential negative macroeconomic
e¤ects of adjusting regulatory capital ratios and at enhancing the e¤ectiveness of capital regulation
as a macroprudential tool. Thus, it is reasonable to consider an additional policy scenario to asses
the functioning of dynamic capital requirements in this model. In order to do so, the debt-to-assets
ratio, (cid:13), is augmented with a cyclical component

(cid:13)t = (cid:13) + (cid:13)x(

xt
xss (cid:0)

1)

(20)

where (cid:13)x is the macroprudential policy parameter associated to the regulatory capital ra-
tio implied by equation (20), (1
is the same macroeconomic indicator chosen for
policy rule (16). Note that equations (11) and (15) are directly a¤ected by this new policy
environment.

(cid:13)t). xt

(cid:0)

25In equations (17) and (18), variables under the alternative policy scenario have been denoted with superscript
b;t, for t = 0; 1; 2; ::For simplicity, such superscript

"a" to make clear that the following inequality may hold; db;t
has been omitted in other equations in which it would be applicable, such as expression (19).

= da

26Alternatively, a regulatory scheme on bank dividends could be based either on distributed earnings taxation or
on a linear restriction on dividend payouts (generally de…ned as an upper bound for dividend payments in terms of
net pro…ts).

176
3.1.5 Aggregation and market clearing

In equilibrium, all markets clear. In the case of the …nal goods market, the aggregate resource con-
straint dictates that the income generated in the production process is fully expended in the form
of …nal private consumption, and banking expenditure devoted to adjust key …nancial aggregates
and to manage the capital position of the bank, (cid:14)Kb;t

1 (also interpretable as eroded equity).27

(cid:0)

Yt = Ct + (cid:14)Kb;t

(cid:0)

1 + '(db;t) + (cid:30)b(Bt) + (cid:30)e(Bt)

(21)

where Ct denotes the aggregate consumption of the three agent types. Formally, Ct = Ch;t +
Ce;t + db;t. Similarly, aggregate demand for housing equalizes supply. Housing supply is speci…ed
as a …xed endowment that is normalized to unity.

H = Hh;t + He;t

3.2 Quantitative Exercise

Do dividend prudential targets contribute to …nancial stability by smoothing the …nancial cycle?
To gain some insights into this matter, this paper analyzes the economy’s response to a …nancial
shock under alternative policy scenarios. In particular, the aim of this section is twofold. First,
to clearly identify the transmission mechanism through which the proposed policy rule works.
Second, to quantitatively assess the potential of dividend prudential targets to tame the credit
cycle in the face of collateral shocks.

In order to do so, the paper follows Angelini, Neri and Panetta (2014), who assume the macro-
prudential authority seeks to minimize an ad hoc loss function with respect to the parameters of
the policy rule. In following that approach, there is no attempt in presenting such an objective
function as a welfare criterion, but rather as a measure of the potential the proposed policy rule
has to prevent the build-up of macro-…nancial imbalances.

A utility-based welfare analysis will be carried out in section 5 for the extended model.

3.2.1 Calibration

The calibration is largely based on Gerali et al. (2010) and Iacoviello (2015). The households’
discount factor is set to 0.9943, implying a steady-state interest rate on deposits slightly above 2

27This speci…cation of the resource constraint guarantees that the …nal goods market clears. The moments of
the distribution function of …nal output, Yt, as de…ned in expression (4) are identical to those of the same variable
as de…ned in identity (21). The omission of any of the terms in the latter, including (cid:14)Kb;t
1, would likely yield an
excess supply in the mentioned market. See the technical appendix of Gerali et al. (2010) for a model in which
bank capital evolves according to a similar law of motion as equation (12) and markets clearing requires (cid:14)Kb;t
1 to
be interpreted as …nal expenditure and included in the resource constraint.

(cid:0)

(cid:0)

18percent (2.3%). The discount factor of the entrepreneur is …xed to 0.94, within the range typically
suggested in the literature for constrained consumers. The banker’s discount factor, (cid:12)b, is chosen
to ensure that the steady-state annualized lending rate to the private sector is roughly 5.6 percent,
implying an annualized lending spread of 3.4%.

As in Iacoviello (2015), the weight of housing in the household’s utility function is set to 0.075,
the elasticity of production with respect to commercial housing, (cid:29), at 0.05, the loan portfolio
adjustment cost parameter of entrepreneurs and bankers to 0.25, and the leverage parameter for
the bank to 0.9. The latter implies a capital-asset ratio of 0.1, implying a positive capital bu¤er
(over the minimum capital requirement of 0.08), as the evidence suggests. As in Jermann and
Quadrini (2012), the dividend adjustment cost parameter, (cid:20), is …xed to 0.426.

The loan-to-value ratio on housing, mH, the intertemporal elasticity of substitution for con-
sumption of bankers, (cid:27), and the inverse of the Frisch elasticity of labor, (cid:30), are set to standard
values of 0.7, 1, and 1.5, respectively.

The bank capital depreciation rate is calibrated at 0.034 so as to ensure the steady state
dividend payout ratio is in the vicinity of 0.6, as the evidence for the SX7E index suggests. mN is
…xed to 0.5, implying a loan-to-output ratio of 1.9, as in the model estimated for the euro area in
Gerali et al. (2010). The autocorrelation coe¢ cient and the standard deviation associated to the
housing collateral shock are obtained from the structural estimation of the same paper.

3.2.2 The Transmission Mechanism of Dividend Prudential Targets

Figure 2 plots the response of some key banking and …nancial aggregates to a unitary negative
collateral shock.28 Impulse responses are de…ned in terms of percentage deviations from the steady
state and the solid line refers to the baseline scenario. The shock triggers a credit crunch that
negatively a¤ects bank net pro…ts . In line with the evidence shown in section 2, dividends and
retained earnings fall during the bust (i.e., they are procyclical), being the former relatively less
volatile than the latter. The dividend payout ratio is notably countercyclical since the adjustment
is mainly borne by retained earnings.

The starred and dotted lines correspond to an economy in which the macroprudential authority
solves the following problem with respect to the policy parameters of the dividend prudential target
and the dynamic capital requirements, respectively

arg min

(cid:2)

Lmp = (cid:20)z(cid:27)2
z

(cid:20)z > 0

(22)

where (cid:2) refers to the vector of policy parameters with respect to which the policymaker solves

28See Andrés et al. (2013) and Iacoviello (2015) for a detailed description and presentation of the macroeconomic
e¤ects of housing collateral shocks faced by entrepreneurs in similar set-ups of the economy. Section 5 of this paper
discusses the main macroeconomic e¤ects of the proposed prudential instrument to a variety of shocks.

19(cid:0)

(cid:0)

1
g

150)

(
(cid:0)

150
g

; (cid:26)x f

the optimization problem and (cid:27)2
z is the asymptotic variance of a macroeconomic indicator of the
choice of the regulator. Due to its relevance in macroprudential policy decision-making , zt has
been chosen to be the loans-to-output gap. Based in the literature, the preference parameter (cid:20)z is
…xed to 1. In order to identify the optimal simple rule within the class (16) that solves (22), it has
been searched over a multidimensional grid of parameter values, which can be de…ned as follows.
(cid:26)d f
0
. The choice of the search grid deserves a thorough explanation.
First, (cid:26)d refers to the dividend payout targeted by the prudential authority in the steady state.
Taking that into account and normalizing the values for (cid:26)d by expressing them in terms of steady
state bank pro…ts, it is reasonable to assume that its optimized value will lie somewhere between
0 and 1 (0 refers to the case in which all pro…ts are retained and 1 to that in which steady state
pro…ts are fully distributed). Second, a wide grid of values for (cid:26)x has been chosen for several
reasons. Firstly, the dynamics of this policy rule is largely unknown. Secondly, the combination of
two potential drivers for dividend smoothing (log utility of bankers and equity adjustment costs)
and a somewhat low baseline value for structural parameter (cid:20), suggests the rule will have to be
considerably responsive for bankers to optimally deviate from their long-run target.

There has been searched within the baseline calibration model. The values that correspond to
the optimized policy rule are the following: (cid:26)d = 0:56, (cid:26)x = 67:84. The optimal simple rule within
the class (16) that solves (22) under full commitment calls for a countercyclical (i.e., (cid:26)x > 0) and
highly responsive dividend prudential target and a steady state dividend payout slightly lower than
the one targeted by bankers absent any dividend regulation.29

As …gure 2 makes clear, such rule calls for highly procyclical, relatively more volatile bank
dividends. Importantly, now bank dividends adjust more gradually towards its steady state level.
The in‡uence credit adjustment costs have on the prudential tool through the credit-to-output
ratio account for this e¤ect. As a result of this, retained earnings and bank capital are less volatile
than in the baseline scenario. As retained earnings, dividends are now a key adjustment variable
as well. Thus, the hike in the dividend payout ratio becomes less pronounced during the bust
phase. Given the linear relationship between equity and loans implied by equations (9) and (11),
the policy is e¤ective in taming the credit cycle.

For the sake of comparison between the workings of prudential policy rules (16) and (20),
consider a third scenario in which the macroprudential authority solves (22), but this time with
respect to the parameters of policy rule (20), (cid:13) and (cid:13)x (dotted line). The selected grid of parameter
values can be de…ned in the following manner. (cid:13)
. The grid for (cid:13)
implies a sensible range of values for the capital ratio between the minimum capital requirement
(i.e., 0.08) and a regulatory capital ratio of 0.15. The grid for (cid:13)x is based upon the Basel III Accord
and has been chosen to asses whether the optimized capital bu¤er in this model is countercyclical

; (cid:13)x f
(
(cid:0)

0:92
g

0:85

1
g

1)

(cid:0)

(cid:0)

f

29Recall that the baseline calibration implies a dividend payout ratio of roughly 0.6.

20(i.e., (cid:13)x < 0) or not. The optimized policy rule within the class (16) that solves (22) under full
0:380.30 As shown in …gure 3, this policy (dotted
commitment corresponds to: (cid:13) = 0:895; (cid:13)x =
line) smooths credit supply and the loans-to-output gap.31

(cid:0)

However, the mechanisms triggered by each of the two macroprudential rules under exami-
nation are di¤erent. Under an optimized dynamic capital requirement, bankers have to meet a
lower target capital ratio. Hence, the adjustment in retained earnings to smooth dividends is even
more pronounced than in the baseline scenario. Loans volatility is reduced by the relative substi-
tution of equity for debt induced by the countercyclical capital bu¤er (CCyB).32 In contrast, the
credit smoothing attained through the optimized dividend prudential target builds on less volatile
retained earnings and bank equity.

Table 1 summarizes the results of the solution to problem (22), for a variety of arguments
for the loss function, (cid:27)2
z. Part (i) of the table presents the prudential losses for a variety of loss
functions, under the baseline scenario. Part (ii) reports the results of the solution to the mentioned
problem when optimizing with respect to (cid:26)d and (cid:26)x. Part (iii) presents the results of the solution
to the same problem but only when having optimized with respect to (cid:26)x. Several conclusions are
worth mentioning. First, the kind of dividend-based macroprudential rule that promotes …nancial
stability is robust across macroeconomic indicators, zt . The optimized rule within the class (16)
that smooths the …nancial cycle is countercyclical and notably responsive.33 Second, dividend
prudential targets aimed at promoting …nancial stability mainly operate through their cyclical
component.34

The quantitative exercise helps to identify several properties of the optimized dividend pruden-
tial target. (i) It is e¤ective in smoothing the credit cycle by means of a countercyclical, highly
responsive dividend prudential target that ensures the main burden of the adjustment is no longer
borne by retained earnings. (ii) It is ‡exible in the sense that it allows bankers to optimally deviate
from the target.35 As noted in …gure 3, bankers optimally choose dividends to be considerably
less volatile than the dividend prudential target. (iii) It is associated to a sanctions regime that

30In order to ensure that I have found a global minimum in each of the two optimization problems, I have selected

di¤erent tuples of initial conditions. Optimized parameter values remain the same regardless of the initial guess.

31Given the objective of the prudential authority (i.e., to solve (22)), the optimized rule within the class (20)

mainly operates through its cyclical component, (cid:13)x.

32Note that in this model, during the bust phase, the action of the CCyB by which the target capital ratio

descends, automatically implies an increase in the leverage ratio.

33Interestingly, when optimizing only with respect to (cid:26)x, the parameter value that solves problem (22) coincides

for most of the considered macroeconomic indicators, zt, ((cid:26)x = 54:96).

34Note that the di¤erences in terms of macroprudential losses between solving the optimization problem with

respect to (cid:26)d and (cid:26)x, and solving it only with respect to (cid:26)x are small.

35In the model, this property is important to ensure that a balance between the social bene…ts from credit
smoothing and the cost for bankers of higher dividend volatility is optimally stricken.
In practice, this kind of
‡exibility could be decisive in order for the regulatory scheme to be implementable. Allowing for deviations permits
bankers to manage additional risks which are not considered in this model (e.g., the risk of a severe fall in the equity
price in response to a regulatory induced cut in dividends).

21acts as an insurance scheme for the real economy.36 (iv) It mainly operates through its cyclical
component, allowing for tangible e¤ects without having to a¤ect long-run dividend payouts. 37
(v) As shown in …gure 3, it is more e¤ective than a standalone optimized capital rule of the type
(20) in smoothing the credit cycle (measured by the asymptotic variance of the credit gap and the
credit-to-output gap), as well as in promoting bank soundness (proxied by the asymptotic variance
of bank equity).

4 Extended Model

In order to improve the dynamics of the model and its mapping to the data, the model is extended
in three main directions. First, a second type of household with a lower subjective discount factor
is incorporated into the model. Thus, two types of households coexist, one being net savers (patient
households) and the other one being net borrowers (impatient households). In equilibrium bank
loans are now extended to credit constrained households and entrepreneurs. Second, the model
allows for physical variable capital. Capital-good-producers sell their output to entrepreneurs, who
use it as an input in the productive process. Third, additional shocks are considered to allow for
a more comprehensive analysis of dividend prudential targets.

Importantly, in this version of the model households are the owners of all existing …rms: …nal-
good-producing …rms (entrepreneurs), banks and capital-good-producing …rms. As in Clerc et
al. (2015) and Mendicino et al. (2018), this approach permits to restrict the welfare analysis to
households without neglecting any consumption capacity generated in the economy.

The speci…cation of preferences has also been revised for all types of agents: (i) Households in
the extended model are assumed to have GHH preferences (see Greenwood et al. 1988). This type
of preferences has been extensively used in the business cycle literature as a useful device to match
several empirical regularities. Their main di¤erence when compared to log preferences, as assumed
in the basic model, is that consumption and leisure are non-separable and wealth e¤ects on labor
supply are arbitrarily close to zero.38 (ii) By generalizing log utility functions of entrepreneurs and

36As noted in …gure 2, the net subsidy (equation 18) associated to the optimized dividend prudential target is
countercyclical. That is to say, their recipients (households and/or entrepreneurs) bene…t from a positive payment
when the marginal utility of their consumption is relatively high.

37This result has important implications. Optimizing (regulating) only with respect to the cyclical component of
the dividend-based rule ensures that in the steady state: (i) the dividend payout and the welfare of bankers are not
negatively a¤ected, and (ii) equations (17) and (18) are equal to zero.

38See Jaimovich and Rebelo (2009) for a generalization of GHH preferences and Galí (2011) for a similar spec-
i…cation of individual preferences that permits to control for the size of wealth e¤ects. Schmitt-Grohé and Uríbe
(2012) present evidence suggesting that wealth e¤ects on labor supply are practically zero. As in this paper, GHH
preferences have been formulated by other authors when evaluating macroprudential policies, in order to prevent a
counterfactual increase in labor supply during crises (see, e.g., Bianchi and Mendoza 2018).

22bankers to CES utility functions, corresponding elasticities of intertemporal substitution can be
calibrated to match the second moments of dividends.

This section only discusses the main changes the extended model incorporates, with respect to
the basic version under the baseline scenario. The full set of equilibrium equations that includes
the policy block, can be found in Appendix B.

4.1 Overview of the Model

4.1.1 Households

Impatient households discount the future more heavily than patient ones, implying (cid:12)i < (cid:12)p. In
the extended model the representative household maximizes

(cid:12)t

{ 2

1

1

(cid:0)

C{;t

(cid:27)h  

(cid:0)

(cid:27)h

(cid:0)

1

N 1+(cid:30)
{ ;t
(1 + (cid:30))!

1

E0

t=0
X

4

+ "h

t j log H{;t3
5

(23)

where { = p; i denotes the type of household the problem refers to. (cid:27)h stands for the risk
aversion parameter of households and "h
is an exogenous preference shock for housing demand.
t
Shocks in the extended model have the same properties as the one presented in the basic version.

Patient households (net savers)

In the case of patient households, the maximization of (23)

is restricted to the sequence of budget constraints

Cp;t + Dt + qt(Hp;t

Hp;t

(cid:0)

(cid:0)

1) = Rd;t

(cid:0)

1Dt

(cid:0)

1 + WtNp;t + !bdb;t + (cid:31)Tt + !ede;t

(24)

where de;t refers to earnings distributed by entrepreneurs. !b is the fraction of banks owned by
patient households and !e the proportion of entrepreneurial …rms owned by the same agent type.
(cid:31) is the fraction of net subsidy they receive from the prudential authority, which is considered to
be equal to the stake of banks they own (i.e., (cid:31) = !b). That is, the degree of "insurance" received
by households is assumed to be proportional to their exposure to the increased bank dividend
volatility triggered by the dividend prudential target. This is relevant for the alternative policy
scenario, in which the following inequality may hold, Tt

= 0.

Impatient households (net borrowers) As a net borrower, the representative impatient

household is restricted not only by a sequence of budget constraints but also by a borrowing
limit.

236
Ci;t + Ri;t

(cid:0)

1Bi;t

(cid:0)

1 + qt(Hi;t

(cid:0)

Hi;t

(cid:0)

1) + (cid:8)i(Bi;t)

= Bi;t + WtNi;t + (1

!b)db;t + (1

(cid:31))Tt + (1

!e)de;t

(cid:0)

(cid:0)

(cid:0)

Bi;t

(cid:20)

mH

i;tEt

qt+1
Ri;t

(cid:20)

Hi;t

(cid:21)

(25)

(26)

Each period, impatient households devote their available resources in terms of wage earnings,
loans, distributed earnings, and the corresponding net subsidy; to consume, repay their debt,
demand housing real estate and adjust their loan portfolio. As it was the case for entrepreneurs
in the basic model, the borrowing capacity of impatient households is tied to the expected value
of their housing property. Such collateral is hit by an exogenous shock, mH
i;t.

4.1.2 Entrepreneurs

(cid:21)p
t+1
(cid:21)p
t
t and (cid:21)i

Let (cid:3)e

+ (1

!e(cid:12)p
(cid:20)

0;t =
agers), with (cid:21)p
optimization problems, respectively. Then, the representative entrepreneur maximizes

t being the Lagrange multipliers of the patient and impatient households’

be the stochastic discount factor of entrepreneurs (man-

!e)(cid:12)i

(cid:0)

(cid:21)i
t+1
(cid:21)i
t (cid:21)

1

E0

(cid:3)e
0;t

t=0
X

1

(cid:0)

(1

1
(cid:27) )

(1
e;t

d

(cid:0)

1

(cid:27) )

(27)

subject to the sequence of budget constraints, the available technology and the corresponding

borrowing limit

de;t + Rb;tBe;t

(cid:0)

1 + qk
t

Ke;t

(1

(cid:0)

(cid:0)

(cid:14)k
t )Ke;t
(cid:0)

1

+ qt(He;t

He;t

(cid:0)

(cid:0)

1) + WtNt + (cid:8)e(Be;t) = Yt + Be;t

(28)

(cid:2)

(cid:3)

Yt = At(utke;t

(cid:0)

1)(cid:11)H (cid:17)
e;t

(cid:0)

1N (1

t

(cid:0)

(cid:11)

(cid:0)

(cid:17))

Bt

(cid:20)

mH

e;tEt

qt+1
Re;t+1

He;t

(cid:18)

(cid:0)

(cid:19)

mN Wh;tNh;t

(29)

(30)

Note the three di¤erences of this optimization problem compared to the one presented in the

24previous section. First, Owners and managers of …nal-good-producing …rms are no longer the same
agent. Second, entrepreneurs also face a technology shock, At. Third, in order to produce …nal
goods, the available technology does not only combine labor and commercial real estate but also
variable physical capital. As in Schmitt-Grohé and Uribe (2012), the depreciation rate of physical
capital is an increasing and convex function of the rate of capacity utilization. In particular:

t (ut) = (cid:14)k
(cid:14)k

0 + (cid:14)k

1(ut

1)2 +

(cid:0)

(cid:14)k
2
2

1)2

(ut

(cid:0)

(31)

4.1.3 Bankers

Similarly, (cid:3)b

!b(cid:12)p
(cid:0)
(cid:20)
Bank managers seek to maximize

0;t =

+ (1

(cid:21)p
t+1
(cid:21)p
t

!b)(cid:12)i

(cid:21)i
t+1
(cid:21)i
t (cid:21)

stands for the stochastic discount factor of bankers.

1

E0

t=0
X

(cid:3)b
0;t

(1

1

(cid:0)

1
(cid:27) )

(1
b;t

d

(cid:0)

1

(cid:27) )

(32)

subject to a balance sheet identity, a sequence of cash ‡ows restrictions, and a borrowing

constraint, respectively

Bit + Be;t = Kt + Dt

(33)

db;t+Kb;t

(1

(cid:0)

(cid:0)

(cid:14)t)Kb;t

(cid:0)

1 = re;tBe;t

(cid:0)

1+ri;t

(cid:0)

1Bi;t

(cid:0)

rd;t

(cid:0)

1

(cid:0)

1Dt

(cid:0)

1

(cid:0)

(cid:8)be(Be;t)

(cid:0)

(cid:8)bi(Bi;t)

(cid:0)

'(db;t)

(34)

Dt = (cid:13)iBi;t + (cid:13)eBe;t

(35)

As for the case of entrepreneurs, in the extended model there is a separation between ownership
and management of banks. The loan portfolio is composed of two types of assets, Bi;t and Be;t,
which may di¤er in two aspects: (i) their associated capital requirements, (cid:13)i and (cid:13)e, and (ii) their
respective adjustment cost parameter. (cid:14)t = (cid:14)"kb
t denotes a possibly time-varying erosion rate of
is an exogenous shock.39 As it will be discussed in section
bank equity, where (cid:14)

[0; 1] and "kb
t

2

39"kb
is a bank capital shock similar to the one considered in Gerali et al. (2010). However, in this paper I assume
t
that "kb
t hits eroded bank equity, (cid:14)tKb;t
1. Since the term
1, rather than uneroded bank capital,
(cid:14)tKb;t
1 enters in the resource constraint, this is an important consideration in order to ensure that all statistical
moments of output as de…ned in equation (29) are identical to those of the same variable as de…ned in identity
(40) and, thus to guarantee that the model is "properly closed".

(cid:14)t)Kb;t

(1

(cid:0)

(cid:0)

(cid:0)

(cid:0)

255, combined with that of the preference parameter (cid:27), the calibration of the size of this shock is
important to match the empirical relative volatilities of bank earnings and dividends.

Importantly, the solution to this optimization problem yields two optimality conditions analo-

gous to expression (15), one for each asset class.

4.1.4 Capital goods producers

At the beginning of each period, capital producers demand an amount It of …nal good from
entrepreneurs, which combined with the available stock of capital, allows them to produce new
capital goods. Capital producers choose the trajectory of net investment in variable capital, It,
that maximizes

1

E0

(cid:3)e

0;t (qk;t(cid:1)xt

t=0
X

It )

(cid:0)

xt = xt

(cid:0)

1 + It

1

"

(cid:0)

 I
2

It
It

(cid:0)

(cid:18)

1 (cid:0)

2

1
(cid:19)

#

subject to

where (cid:1)xt = Ke;t

(1

(cid:0)

(cid:0)

(cid:14)k
t )Ke;t
(cid:0)

1

is the ‡ow output. S

It
It

(cid:18)

1 (cid:19)

(cid:0)

=

 I
2

It
It

(cid:0)

(cid:18)

1 (cid:0)

1
(cid:19)

investment adjustment cost function, whose formulation has become standard in the literature
(see, e.g., Christiano et al. 2005 and Schmitt-Grohe and Uribe 2012) due to empirical reasons.
The maximization of (36) permits to derive a market price for capital, qk;t

(36)

(37)

2

is an

1 = qk;t

1

"

(cid:0)

 I
2

It
It

(cid:0)

(cid:18)

1 (cid:0)

2

1
(cid:19)

 I

(cid:0)

It
It

(cid:0)

(cid:18)

1 (cid:0)

It
It

(cid:0)

1
(cid:19)

1 #

(cid:3)e

0;tqk;t+1 I

+ Et

"

It+1
It (cid:0)

2

It+1
It (cid:19)

#

1
(cid:19) (cid:18)

(cid:18)

The usual law of motion for physical capital holds

Ke;t = (1

(cid:14)k
t )Ke;t
(cid:0)

1 + It

(cid:0)

1

"

(cid:0)

 I
2

It
It

(cid:0)

(cid:18)

1 (cid:0)

2

1
(cid:19)

#

(38)

(39)

264.1.5 Aggregation and market clearing

By the Walras’law, all markets clear . The aggregate resource constraint of the economy represents
the equilibrium condition for the …nal goods market.

Yt = Cp;t + Ci;t + qk

t It + (cid:14)tKb;t
(cid:0)

1 + Adjt

(40)

where the term Adjt corresponds to the sum of all resources dedicated in the economy to adjust

loans and bank dividends in period t. Similarly, in equilibrium labor demand equals total labor
supply,

Even if loans to impatient households and to entrepreneurs may be related to some external

di¤erences, they are homogeneous across agents. Thus, in equilibrium

Nt = Np;t + Ni;t

(41)

In equilibrium, the housing market clears

Bt = Bi;t + Be;t

H = Hp;t + Hi;t + He;t

(42)

(43)

5 Quantitative Analysis

5.1 Calibration

I follow a three-stage strategy in order to calibrate the model to quarterly euro area data for the
period 2002:I-2018:II. 40In a …rst step, I pre-set some parameter values that have become standard
in the business cycle literature (table 2A). Then, I calibrate a second group of parameters by using
key steady state ratios and …rst moments of the data (table 2B). Lastly, I simulate the model to
calibrate a third group of parameters so as to match certain second moments of the data (table
2C).

First, several parameters are set following convention. Some of them are standard in the
literature. Some others are based on papers in the …eld of macro-…nance. The inverse of the
Frisch elasticity of labor is set to a value of 1, whereas the risk aversion parameter of household

40All time series expressed in Euros are seasonally adjusted and de‡ated. With regards to second moments
matching, the log value of de‡ated time series has been linearly detrended before computing standard deviation
targets. All details on data description and construction are available in Appendix A.

27preferences is …xed to a standard value of 2. Loan-to-value ratios on housing (for both, households
and entrepreneurs) are set equal to 0.7. These values are based on data of the big four euro
area economies and coincide with those presented in Gerali et al. (2010), and Quint and Rabanal
(2014), among others. Regarding the dynamic depreciation rate of physical capital (cid:14)k
0 is …xed to
a standard value of 0.025 while, following convention, (cid:14)k
2 are de…ned as speci…c fractions of
the steady state interest rate on physical capital. As in Jermann and Quadrini (2012), the equity
payout cost parameter (cid:20) is set to 0.426. The adjustment cost parameter value for corporate loans
coincides with that obtained in the structural estimation by Iacoviello (2015).

1 and (cid:14)k

t ; (cid:14)k

Second, another group of parameters is calibrated by using steady state targets. The patient
households’discount factor, (cid:12)p = 0:9943; is chosen such that the annual interest rate equals 2.3%.
The impatient households’discount factor is set to 0.95, in order to generate an annualized bank
spread of 3.4%.41 Household weights on housing utility, jp and ji, have been calibrated to match
the savers-to borrowers housing ratio and the household loans-to-GDP ratio, respectively. Patient
households are assumed to own all the entrepreneurial and capital-producing …rms of the economy,
!e = 1, while impatient households own all the banks, !p = 0. This assumption is based on the
following reasons. (i) They are chosen to match a corporate loans-to-GDP ratio of 175.3% and
(ii) It permits to limit the
a weight of corporate loans on total credit of 0.451, respectively.
welfare analysis to two types of agents (henceforth referred to as savers and borrowers) while
fully separating by agent types the two key sources of business cycle costs triggered by optimized
dividend prudential targets.42 43 44 The shares in …nal-good-production of physical capital (cid:11) and
commercial real estate (cid:17) are set to match an investment-to-GDP ratio of 21.19% and an aggregate
real estate wealth-to-annual output of 280.2%, respectively.

With regards to bank parameters, it shall be proceeded as follows. The depreciation rate of
bank capital (cid:14) is set to 0.041, which is consistent with a payout ratio of 0.563, in line with the

41In order to compute the annualized bank spread, (rss

b has been de…ned as the average of the steady
b (cid:0)
state rates on household and corporate loans, each of them weighted by the proportion of total loans it represents.
Steady state interest rates are the only targets that have not been obtained from updated euro area data but from
the constructed series in Gerali et al. (2010).

rss
d ), rss

42As it will be discussed in the welfare analysis that follows, two negative welfare e¤ects induced by dividend-
based rules have to be weighted with the positive e¤ects derived from …nancial smoothing. On the one hand, bank
owners su¤er from an increased volatility in bank dividends. On the other hand, entrepreneurial-…rm owners face
a "loan portfolio readjustment e¤ect" by which supply for corporate loans tends to be partially substituted for
household loans due to the higher capital requirement they are associated to.

43Importantly, the assumption by which borrowers are allowed to own part of the entrepreneurial …rms and banks
in the model rests on empirical evidence con…rming that a fraction of the households holding shares are indebted.
44In addition, the proposed set up does not allow for savers to own all entrepreneurial …rms and banks. Were
they owners of all banks, the relationship between (cid:12)p and (cid:3)b
0;t would be such that there would not be positive
…nancial ‡ows in equilibrium. Alternative set ups have been proposed in the literature to allow savers to be owners
of all …rms in the economy (see, e.g., Gertler and Kiyotaki 2010, Gertler and Karadi 2011, and Clerc et al. 2015).
However, in order for these approaches to be applicable, these authors have to make assumptions implying that
dividend payout ratios are constant and (usually) very low. A result that is sharply at odds with reality and which
does not permit to carry out the type of analysis proposed in this paper.

28evidence of the SX7E banks’index presented in section 2. Note that after having rearranged in
the steady state expression of equation (12)

db
Jb

= 1

(cid:14)Kb
Jb

(cid:0)

from which the in‡uence parameter (cid:14) has on the steady state payout ratio becomes evident.
The calibrated values of the complementaries of capital requirements on household loans (cid:13)i and
corporate loans (cid:13)e are obtained by solving a system of two linear equations

0:895 = (cid:13)i

Bi
B

+ (cid:13)e

Be
B

(1

(cid:0)

(cid:13)e) = 2:1176(1

(cid:13)i)

(cid:0)

(44)

(45)

Equation (44) is the result of equating the steady state leverage ratio to 0.895 after having
normalized expression (35) to total loans. Its interpretation is straightforward. The equilibrium
(cid:13)e) and
capital requirement is a weighted average of the two sectorial capital requirements, (1
(cid:13)i), and it has been set to 0.105. Such value has been chosen for empirical and regulatory
(1
reasons. (i) It is similar to the pre-crisis historical average of regulatory capital ratios. (ii) Accord-
ing to existing capital legislation, in general terms, the authority cannot impose any restriction
on dividend payouts as long as the bank meets the minimum capital requirement (0.08) plus a
conservation bu¤er of 0.025.

(cid:0)

(cid:0)

Expression (45) indicates that the capital requirement on corporate loans is slightly more than
two times that on household loans. This is exactly the same proportion held by these two sectorial
ratios according to the IRB-based calibration presented in Mendicino et al. (2018). For simplicity,
a 100% risk weight has been assumed for each of the two asset types.45 Table 3 o¤ers an overview
of selected target ratios that have been considered when calibrating the model.

Third, the size of shocks and certain adjustment cost parameters are calibrated to improve the
…t of the model to the data in terms of relative volatilities (see tables 2C and 4). The investment
adjustment cost parameter  I is set to target a relative standard deviation of investment of 2.642
%. The adjustment cost parameter on household loans (cid:30)i is …xed to a value of 0.504, thereby: (i)
favoring corporate loans to be relatively more volatile than household loans, as supported by the
evidence in the euro area (recall that corporate loans parameter (cid:30)e has been pre-set to 0.06), and
(ii) roughly matching the relative volatility of bank assets.

I have matched the second moments of bank dividends and earnings (and, thus, accounted

45This assumption is reasonable. As the Capital Requirements Regulation (EU) stipulates, exposures to corpo-
rates with an "average" credit rating or for which no credit assesment is available, shall be assigned a 100% risk
weight. Unless certain conditions are met, exposures fully secured by a mortgage on immovable property shall also
be assigned a risk weight of 100 %.

29for the phenomenon of dividend smoothing) mostly by calibrating the elasticity of intertemporal
substitution (EIS) of bankers and the size of the bank capital shock. Several important consid-
erations are worth noting in this regard. First, I have targeted the relative standard deviation of
bank dividends by calibrating bankers’EIS rather than adjustment cost parameter (cid:20) for various
reasons: (i) I have found substantially more di¢ cult to match such second moment with the latter
than with the former.46 (ii) Although a careful microfoundation of dividend smoothing is beyond
the scope of this paper, assuming the origin of dividend smoothing to be related with individual
preferences seems more reasonable than associating it to an external adjustment cost parameter.
(iii) Given the values to which (cid:27) and (cid:20) have been …xed, dividend adjustment costs basically do
not a¤ect the dynamics of bank dividends or any other aggregates under the baseline scenario.
Therefore, the role played by function '(db;t) under this calibration is basically limited to being
an important part of the proposed regulatory scheme.47 Second, calibrating the size of the bank
capital shock is relevant to allow for dividends and earnings to be su¢ ciently volatile, while …xing
the value of (cid:27) permits to create a wedge between the standard deviation of earnings and that of
dividends.

As in the basic model, the autoregressive parameters of the …ve shocks that are present in the

extended model correspond to the estimates proposed in Gerali et al. (2010).

5.2 Welfare Analysis

This section analyzes the main welfare consequences of complementing capital requirements with
a dividend prudential target. Consider the expected life-time utility of savers and borrowers as the
welfare criterion

1

V {
0 = E0

(cid:12)t
{U (C{;t; H{;t; N{;t)

(46)

with { = p; i. The model is solved by using second-order perturbation techniques in Dynare
(Adjemian et al. 2011). Unconditional lifetime utility is computed as the theoretical mean based
on …rst order terms of the second-order approximation to the nonlinear model, resulting in a

t=0
X

46Other authors have recently targeted second moments of aggregate dividends by calibrating parameter (cid:20) in a
set up in which the objective function (i.e., bankers’preferences) is linear in dividends. Two examples are Jermann
and Quadrini (2012), who calibrate (cid:20) by targeting the relative volatility of the dividends-to-GDP ratio (rather
than dividends themselves), and Begenau (2019), who targets the relative standard deviation of US bank dividends,
themselves.

47As a consequence, parameter (cid:20) could well be interpreted as an additional policy parameter. This is important
to rule out a modeling of the economy in which the increased relative volatility of bank dividends induced by
dividend prudential targets a¤ets the value of parameter (cid:20). Nevertheless, the welfare e¤ects of the proposed rule
are evaluated for alternative values of (cid:20) in the robustness checks exercise presented at the end of this section.

30second-order accurate welfare measure (see e.g. Kim, Kim, Schaumburg, and Sims 2008). This
approach ensures that the e¤ects of aggregate uncertainty are taken into account.

Figure 3 plots the welfare e¤ects of changing the value of parameter (cid:26)x in a policy rule of
the type (16) while keeping (cid:26)d …xed at its baseline value.48 There is a considerable range of (cid:26)x
(positive) values for which both types of agents are better-o¤ than under the baseline scenario.
Interestingly, …gure 3 makes clear that each agent class face a di¤erent trade-o¤, when being
exposed to changes in (cid:26)x. Higher values of (cid:26)x are associated to less volatile …nancial aggregates
(including deposits and aggregate loans), which improves welfare of savers and borrowers.

However, increasing (cid:26)x is not free of charge. A more responsive dividend prudential target leads
to a higher bank dividend volatility, that negatively a¤ects borrowers’welfare (as bank owners).
In addition, changes in (cid:26)x modify the optimal composition of the representative banker’s loan
portfolio. Given that corporate loans are subject to higher capital requirements, a countercyclical
dividend prudential target yields a "loan portfolio readjustment e¤ect" by which bankers tend to
increase the weight of household loans (in their balance sheet) at the expense of corporate ones.
Such e¤ect has a negative impact on savers’welfare (as owners of entrepreneurial …rms).

Next, a normative approach is adopted to de…ne a measure of social welfare and maximize
it with respect to (cid:26)x in order to quantify the welfare gains of introducing an optimized dividend
prudential rule. As in Schmitt-Grohe and Uribe (2007), welfare gains of agent type "{" are de…ned
as the implied permanent di¤erences in consumption between two di¤erent scenarios. Formally,
consumption equivalent gains can be speci…ed as a constant (cid:21){, that satis…es

1

E0

(cid:12)t
{U

C a
{;t; H a

{;t; N a
{;t

= E0

1

(cid:12)t
{U

(1 + (cid:21){) C b

{;t; H b

{;t; N b
{;t

(47)

(cid:2)

(cid:0)

(cid:1)

t=0
X

t=0
X
where superscripts a and b refer to the alternative policy scenario (optimized prudential rules)
and the baseline case, respectively. In addition, social welfare is de…ned as a weighted average of
the expected lifetime utility of each agent class. Similar to the approach followed in Mendicino et
al. (2018), social welfare maximization is subject to certain conditions. The solution: (i) must be a
Pareto improvement relative to the baseline scenario, and (ii) it has to yield the same consumption
equivalent gains for savers and borrowers, given a pre-set grid of values for (cid:26)x. Such grid is set as
follows: (cid:26)x f
48Without loss of generality, the macroeconomic indicator xt incorporated in prudential rule (16) has chosen to

.49 Formally, the optimization problem under consideration reads
180
g

(cid:0)

0

(cid:3)

be …nal output, Yt.

49Note in …gure 3 that borrowers su¤er from welfare losses for values of (cid:26)x approximately larger than 180.

31arg max

(cid:2)

V0 = (cid:16)V p

0 + (1

(cid:16))V i
0

(cid:0)

(48)

s:t: (cid:21)p = (cid:21)i

(cid:21)p > 0, (cid:21)i > 0

where (cid:16)

[0; 1] is the weight of patient households’ welfare and (cid:2) is the vector of policy
parameters with respect to which the objective function is maximized. Problem (48) is also subject
to all the competitive equilibrium conditions of the extended model.50

2

The optimized prudential rule within the class (16) that solves (48) is associated to (cid:26)x =
143:741, and (cid:21){ = 0:002604. Table 5 reports the main results of shutting down, one-by-one, each
of the shocks. The di¤erences in welfare gains generated by shutting down a particular shock vary
across shocks. Figure 4 plots the welfare impact of changing (cid:26)x for each agent class under the
di¤erent shock scenarios considered in table 5. Some results are worth commenting. Given the
solution to problem (48), the wedge in welfare gains created between savers and borrowers when
shutting down non …nancial shocks (i.e., housing preference and technology shocks) is relatively
large. The potential the proposed prudential rule has to smooth credit supply is relatively larger
under housing preference shocks (than under any other shock), among other reasons, due to the
relatively large size of these shocks under this calibration (see …gures 9 to 13). That explains why
shutting down this shock considerably deteriorates the welfare trade-o¤ experienced by borrowers
under a countercyclical dividend prudential target (i.e., (cid:26)x > 0). By way of contrast, shutting down
technology shocks notably improves the welfare trade-o¤ faced by borrowers under this regulatory
scheme, since bank dividend volatility induced by countercyclical DPTs in the face of these shocks
is notably larger than under any other shock. This strong response of dividend prudential targets
triggers a smoothing e¤ect on certain aggregates to the point that the correlation of output with
some other variables (e.g., NFC loans) experiences a change in its sign. Savers bene…t from the
benchmark optimized DPT (i.e., (cid:26)x = 143:741), especially when the economy is hit by technology
shocks; credit supply to entrepreneurs expands when …nancing is needed the most, during the
downturn. Thus, shutting down this shock worsens the welfare trade-o¤ faced by non-…nancial
corporations’owners (i.e., savers).

The wedge in welfare gains created between savers and borrowers when shutting down …nancial

50In particular, the only di¤erence between the approach followed in Mendicino et al. (2018) and the one followed
in this paper is that they search over the grid (cid:16)
[0; 1] to …nd the value of the savers’ welfare weight that solves the
problem while this paper maximizes with respect to the policy parameter, (cid:26)x . By construction, given the approach
followed here, social welfare gains are going to coincide with those of savers and borrowers regardless of the value
(cid:16) takes.

2

32shocks is more moderate. The proposed policy rule leads to positive welfare e¤ects for both types
of agents under …nancial shocks, although these e¤ects tend to be quantitatively larger for the case
of borrowers since they directly bene…t from credit smoothing (while savers only indirectly bene…t
from that e¤ect through their ownership of non-…nancial corporations).

5.2.1 Welfare E¤ects and Capital Requirements

Angeloni and Faia (2013), analyze optimized monetary policy rules under alternative Basel regimes.
Inspired in their approach, this paper examines the welfare e¤ects of optimized dividend-based
macroprudential rules under alternative capital scenarios.

Microprudential Capital Regulation Absent a countercyclical dividend prudential target
(baseline scenario), in this model an increase in the capital requirement a¤ects welfare through
two main transmission channels. On the one hand, non …nancial corporations and impatient
households su¤er from a more restrictive credit supply. From optimality condition (15), it follows
(cid:13)) in the left-hand side of the equation has to go hand
that a higher capital requirement (1
in hand with an increase in the discounted marginal lending spread. The implied reduction in
the debt-to-assets ratio does not account for the entire adjustment and bankers optimally reduce
their credit supply to induce an increase in their loans rate. On the other hand, in a higher capital
requirements scenario, bankers retain more earnings and bene…t from an increased marginal lending
spread. That allows them to attain a higher and smoother dividend payout (at the expense of a
more volatile and restricted credit supply).

(cid:0)

From the above explanation, it follows that an increase in capital requirements unambiguously
leads to a negative welfare e¤ect on savers (as owners of entrepreneurial …rms), while borrowers
have to face a welfare trade-o¤ resulting from two con‡icting e¤ects. Sub…gures in the left and
right columns of …gure 5 plot the welfare e¤ects of changing the value of parameters (cid:13)i and (cid:13)e in
a policy rule of the type (20), respectively. The range of (cid:13)i and (cid:13)e values for which the welfare
functions of both agent classes have been plotted are based on the Basel III Accord as well as on
results presented in the literature (see, e.g., Mendicino et al. 2018 and Begenau 2019). Ceteris
(cid:13)i ), that maximizes borrowers’welfare
paribus, the risk-adjusted capital ratio on HH loans, (1
corresponds to a value of 6.72%, which is close but below the one calibrated in the baseline
(cid:13)e ), that
scenario (7.05%). Ceteris paribus, the risk-adjusted capital ratio on NFC loans, (1
maximizes borrowers’welfare corresponds to a value of 13.68%, which is also close but below the
one calibrated in the baseline scenario (14.92%).

(cid:0)

(cid:0)

Table 6(i) reports the welfare gains from increasing the capital ratio by 1 percentage point
(from 10.5% to 11.5%) under two di¤erent scenarios in terms of dividend regulation. In the …rst

33case, the hike in the capital ratio occurs absent any dividend regulation. Savers and borrowers
su¤er welfare losses induced by a more restrictive and volatile credit supply. Note, however, that
the losses experienced by savers are considerably larger than those su¤ered by borrowers. As bank
owners, borrowers bene…t from higher and smoother dividend payouts, an e¤ect that partially
compensates the impact of the mentioned decline in loans supply. In the second case, the increase
in the capital requirements is combined with the adoption of the dividend prudential target that
solves (48) under the baseline capital scenario (i.e., scenario in which (cid:13) = 0:895). The loans and
deposits smoothing e¤ect generated by the dividend-based rule helps in moderating the welfare
losses experienced by savers. The combination of a higher dividend payout and a smoother credit
supply ensures that borrowers bene…t from the macroprudential policy mix.

The remainder of table 6 reports the welfare gains generated by the proposed policy rule under
alternative capital scenarios, with and without reoptimizing with respect to (cid:26)x.51 In particular,
table 6(ii) evaluates the welfare implications of solving problem (48) for two capital scenarios
alternative to the baseline (i.e., (cid:13) = 0:895).52 Not surprisingly, the optimized countercyclical
responsiveness of the dividend prudential target increases with the capital requirement. Higher
capital ratios are associated to lower and more volatile credit supply. Thus, they increase the
potential of dividend prudential targets to improve welfare. As noted in table 6(iii), this is par-
ticularly true for the case of borrowers. Given a pre-set value for (cid:26)x that implies a countercyclical
and su¢ ciently responsive dividend prudential target (e.g., (cid:26)x = 143:741), increases in the capital
ratio have particularly positive e¤ects on the welfare of impatient households. This is so because
they bene…t from an improved trade-o¤. Given that the dividend-based rule is responsive enough
so as to notably smooth loans, higher capital ratios induce higher dividend payouts and contribute
to o¤set the dividend volatility generated by the policy rule under consideration.

Figure 6 plots the welfare e¤ects of changing the value of parameter (cid:26)x in a policy rule of
the type (16) while keeping (cid:26)d …xed at its baseline value, for the three above mentioned capital
scenarios and for each of the two types of agents. The …gure allows to di¤erentiate between the
welfare gains potentially attainable by means of a countercyclical DPT, for each capital scenario,
and the welfare level associated to each capital scenario, for a given value of (cid:26)x. There are at least
two considerations which deserve some discussion: (i) Even if savers’ welfare level decreases in
capital requirements, the shape of their welfare function remains approximately unchanged across
capital scenarios, implying that su¢ ciently responsive, countercyclical DPTs are welfare increasing

51There is an important di¤erence between part (i) and parts (ii) and (iii) of table 6 which may not be noticeable
in terms of reporting. In part (i) the capital ratio di¤ers between the "alternative" and the "baseline scenario",
whereas in parts (ii) and (iii) do not.

52The three considered capital scenarios (including the baseline) are inspired in the Basel III Accord. 0.08 refers
to the minimum capital requirement. Adding the conservation bu¤er (0.025) to it yields a capital ratio of 0.105. As
of November 2018, all euro area G-SIBS were required a surcharge lying between 0.01 and 0.02. For that reason,
the paper considers a third scenario whith a capital adequacy ratio of 0.12.

34for the case of savers (regardless of the capital scenario). (ii) With respect to borrowers, …gure 6
suggests that their maximum attainable welfare level (by means of a countercyclical DPT) is related
to a capital ratio similar to the one calibrated in the baseline scenario. At the same time, however,
higher capital requirements are associated to higher attainable welfare gains as well as to a larger
range of (cid:26)x values for which countercyclical DPTs are welfare increasing. That is, countercyclical
DPTs have the potential to complement existing capital regulation and to compensate the welfare
costs of capital ratio increases in two main dimensions. First, they moderate the welfare costs
capital increases unambiguously have for savers. Second, they have the potential to more than
o¤set the welfare losses su¤ered by borrowers in the event of a capital requirements hike.

Macroprudential Capital Regulation Given the properties of dividend prudential targets
as a macroprudential tool, it is relevant to also investigate its interactions with the macropruden-
tial component of existing capital regulation, the so-called countercyclical capital bu¤er (CCyB).
Figures 7 and 8 plot the welfare e¤ects of ceteris paribus changes in the value of parameters (cid:13)x
and ((cid:26)x; (cid:13)x), respectively. When solving problem (48) with respect to macroprudential policy pa-
rameter (cid:13)x, there is no solution found such that (cid:21)p = (cid:21)i and (cid:21)p > 0, (cid:21)i > 0. In addition, there
is no interior solution for the problem of maximizing borrowers’ welfare with respect to (cid:13)x (for
a regulatory meaningful range of (cid:13)x). Thus, I maximize savers’ welfare with respect to (cid:13)x, for
alternative values of (cid:26)x.53 Figure 8 and part (i) of table 7 make clear that savers prefer a highly
responsive countercyclical DPT (and a mildly responsive CCyB), whereas borrowers have a pref-
erence for a highly responsive CCyB (and a mildly responsive countercyclical DPT). Part (ii) of
table 7 summarizes the welfare gains from solving problem (48) with respect to macroprudential
policy parameters (cid:26)x and (cid:13)x. The optimized macroprudential toolkit comprises a joint capital-
and-dividend based countercyclical regulation (i.e., (cid:26)x > 0, and (cid:13)x < 0) that can be interpreted as
a compromise between the preferences of the two agent classes, which allows patient and impatient
households to enjoy higher welfare gains than under a policy scenario in which problem (48) is
only solved with respect to (cid:26)x.

Figures 9 to13 plot the impulse-responses of key economic aggregates to the 5 di¤erent shocks
that hit this economy. The solid line refers to the responses under the baseline scenario, while the
diamond, starred, and dotted lines correspond to alternative policy scenarios in which problem
, (cid:26)x, and (cid:13)x, respectively. 54. Several conclusions can
(48) has been solved with respect to
be drawn from the analysis. First, both macroprudential instruments are e¤ective in smoothing

(cid:26)x; (cid:13)xg
f

0; 143:741; 180:0
g

borrowers are worse-o¤ due to the adoption of a countercyclical DPT (when compared to the baseline scenario).

53Such values for (cid:26)x f
54When solved with respect to (cid:13)x, there is no solution to problem (48) such that (cid:21)p = (cid:21)i and (cid:21)p > 0, (cid:21)i > 0.
Thus, in this case, I set (cid:13)x to -0.538 for two reasons: (i) It represents a compromise between the preferences of the
two types of agents, and (ii) it allows for an easy comparison between a world in which only a CCyB applies and
that in which both, the DPT and the CCyB are active (see table 7).

have been chosen to ensure that, ceteris paribus, neither savers nor

35the economic and the …nancial cycles (credit supply, housing prices, etc). Second, for most of the
shocks, the jointly optimized macroprudential rule (diamond line) is more e¤ective in smoothing
the business and the …nancial cycles than any of the two individual macroprudential rules on their
own (starred and dotted lines), suggesting that both rules are mutually reinforcing for economic
stabilization and …nancial stability purposes.

5.3 Robustness Checks

So far, the robustness of the main results associated to the welfare analysis presented in the
previous section has been tested for capital adequacy parameters (cid:13) and (cid:13)x. However, there are
other parameters to which welfare e¤ects may also be sensitive and which may change over time.
First, the introduction of a dividend prudential target can potentially a¤ect certain structural
parameters, especially dividend adjustment cost parameter (cid:20). Given a sensible range of values for
(cid:20), the shape of savers and borrowers’lifetime utility as a function of (cid:26)x are not signi…cantly a¤ected,
although as the value of (cid:20) increases, the welfare trade-o¤ faced by savers under a countercyclical
DPT tends to improve while the one faced by borrowers tends to deteriorate (see …gure 14). This
result does not come as a surprise since bank owners are those who borne the direct cost of adjusting
dividends. Therefore, as (cid:20) increases, the value of (cid:26)x that solves problem (48) and the associated
welfare gains tend to decline.

Second, the fraction of banks owned by savers, !b, (and, thus, by borrowers) may change over
time. As noted in …gure 15, as !b increases, the welfare level of savers goes up while that of
borrowers declines. This is so, because the bank dividend payout received by a given household
increases in the fraction of banks it owns, !b. However, the shape of lifetime utility (as a function
of (cid:26)x) remains basically unchanged for alternative values of !b and for each of the two agent classes.
Third, the public authority may consider to modify the fraction of net transfer that savers
receive according to their bank property, (cid:31). Not surprisingly, regardless of the (cid:26)x value, the
welfare level of borrowers declines (whereas that of savers increases) as the fraction of the net
tranfer received by bank owners (i.e., borrowers) declines (and that received by savers increases).
In a nutshell, although quantitative di¤erences may arise, the main conclusions of this exercise
are very robust across calibrated values of key parameters and across alternative speci…cations of
policy scenarios. Countercyclical dividend prudential targets induce welfare gains for savers and
borrowers through their smoothing e¤ect on …nancial aggregates.

366 Conclusion

Available evidence on euro area bank dividends and earnings suggests there is a potential link
between payout policies and the adjustment mechanisms through which bankers opt to meet their
target regulatory capital ratios. When shocks hit bank pro…ts, managers adjust retained earnings
to smooth dividends. This generates bank equity and credit supply volatility.

This paper develops a DSGE model that features a banking sector and certain …nancial frictions
that account for this empirical phenomenon. Then, it de…nes a dividend-based regulatory scheme
that is shown to be an e¤ective macroprudential complement to capital requirements. In particular,
what shall be called dividend prudential targets: (i) are e¤ective in smoothing the …nancial and the
business cycle by means of less volatile bank retained earnings, (ii) induce welfare gains associated
to a Basel III-type of capital regulation, (iii) mainly operate through their cyclical component,
ensuring that long-run dividend payouts remain una¤ected, and (iv) are associated to a sanctions
regime which acts as an insurance scheme for the real economy and allows bankers to optimally
deviate from the target. The latter is a property that may be crucial to tackle one of the main
potential critiques dividend-based prudential rules may face in practice. The negative impact
dividend regulation could have on market volatility.

The simplicity of the model is instrumental to clearly identify the transmission mechanism
through which the proposed policy rule operates. Yet, it comes at the cost of abstracting from a
number of considerations that potentially constitute promising avenues for future research. Model-
ing one or more of the market imperfections that may be behind bank dividend policies should be
helpful to match the data by means of an improved microfoundation of the macroeonomic model.
Moreover, additional ingredients which are present in reality and that could possibly change
some of the results have been omitted. On the one hand, assuming a positive probability of bank
(2015), should reinforce the argument in favour of this complement
failure, as in Clerc et al.
to the existing macroprudential toolkit. On the other hand, incorporating outside equity in an
environment in which bank owners can substitute their bank shares for alternative assets at a
relatively low cost, may make the policy proposal less attractive. In addition, the literature has
shown that the approach to modeling bank risk taking and systemic risk can notably in‡uence
macroprudential policy prescriptions (see, e.g., Martinez-Miera and Suarez 2014).

Lastly, optimal coordination between this type of prudential regulation and other macroeco-
nomic policies should be considered as well (e.g., monetary policy). Based on the ECB annual
report of 2016, one of the critiques the European Parliament (2017) has recently made to the ECB
relates to this issue. "The European Parliament is concerned that euro area banks did not use the
advantageous environment created by the ECB to strengthen their capital bases but rather, accord-
ing to the Bank for International Settlements, to pay substantial dividends sometimes exceeding

37the level of retained earnings."

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42Table 1: Optimized rules and prudential losses; collateral shock (basic model)

(i) Baseline
(cid:26)d; (cid:26)xg
(ii)

f

(iii)

(cid:26)xg

f

Loss
Loss
Loss Variation(1)
(cid:26)(2)
d
(cid:26)x
Loss
Loss Variation
(cid:26)x

(cid:27)2
B

(cid:27)2

B=Y

(cid:27)2
Kb

(cid:27)2
q

0.002012 0.002232 0.000020 0.000640
0.000394 0.000381 0.000004 0.000416

-34.00
-80.41
0.1684
0.5417
16.9175
67.2409
0.000527 0.000535 0.000005 0.000519

-82.29
0.5598
67.8427

-80.42
0.5443
67.3268

-73.80
54.9622

-76.37
54.9622

-73.80
54.9622

-18.91
29.4588

Note:(1) Percentage changes in the value of the loss function under the policy scenario associated to the

optimized dividend prudential target, with respect to the baseline scenario. (2) Values of the autonomous

component of the policy rule have been normalized by expressing them in terms of steady state bank

pro…ts.

43Parameter

Description

Value

Source/Target ratio

Table 2: Baseline parameter values

A) Pre-set params

2

'
(cid:27)h
mHi; mHe
(cid:14)k
1; (cid:14)k
(cid:14)k
(cid:20)
(cid:30)e
B) First moments
(cid:12)p
(cid:12)i
jp
ji
!e
!b
(cid:11)
(cid:17)
(cid:13)e
(cid:13)i
(cid:14)

C) Second moments

(cid:30)i
(cid:27)
(cid:27)h
(cid:27)kb
(cid:27)mh
(cid:27)mk
(cid:27)A

1
2
0.7

Inverse of the Frisch elasticity
HH Risk aversion param
LTV ratio on HH and NFC housing
Depreciation rate of physical capital 0.025
Endogenous depr. rate params
Dividend adj. cost parameter
NFC credit adj.cost param

ke;0.1*rss
rss
0.426
0.06

Standard
standard
Standard
Standard

ke Gerali et al. (2010)

Savers’discount factor
Borrowers’discount factor
Savers’housing weight
Borrowers’housing weight
Fraction of …rms owned by HHp
Fraction of banks owned by HHp
Capital share in production
Real estate share in production
Debt-to-assets, NFC risk-adjusted
Debt-to-assets, HH risk-adjusted
Depreciation rate of bank capital

Investment adj. cost param
HH credit adj.cost param
Banker EIS
Std. housing pref. shock
Std. bank capital depr. shock
Std. NFC collateral shock
Std. HH collateral shock
Std. productivity shock

0.9943
0.95
0.0805
0.4802
1
0
0.2699
0.0385
0.8522
0.9302
0.041

0.092
0.504
2.76
0.1999
0.0495
0.0024
0.0026
0.0020

Jermann & Quadrini (2012)
Iacoviello (2015)

Rss
h = (1:023)1=4
(rss
rss
d )400 = 3:4
b (cid:0)
H ss
p =H ss
i = 1:3585
Bss
i =(Y ss) = 2:1403
Bss
e =Bss = 0:4510
Bss
e =Y ss = 1:7530
I ss=Y ss = 0:2119
(qssH ss)=(4Y ss) = 2:802
(cid:13)e=(cid:13)i = 2:1176
K ss
dss=J ss

b =Bss = 0:105
b = 0:5625

(cid:27)I=(cid:27)Y = 2:642
(cid:27)B=(cid:27)Y = 6:473
(cid:27)db=(cid:27)Y = 15:050
(cid:27)q=(cid:27)Y = 2:429
(cid:27)Kb=(cid:27)Y = 6:554
(cid:27)Jb=(cid:27)Y = 59:102
(cid:27)C=(cid:27)Y = 0:748
(cid:27)Y = 2:138

Note: Parameters in A) are set to standard values in the literature, whereas those in B) and C) are

calibrated to match data targets. Abreviations HH and NFC refer to households and non-…nancial cor-

porations (entrepreneurs), respectively. HHp stands for patient households.

44 
(1

(cid:0)

Variable
C ss=Y ss
I ss=Y ss
rss
4
b
(cid:2)
rss
4
d
(cid:2)
rss
(rss
d )
b (cid:0)
(cid:13)e)=(1
(cid:0)
b =Bss
K ss
Bss
i =(Y ss)
Bss
e =(Y ss)
Bss
i =Bss
Bss
e =Bss
b =J ss
dss
b
hss
p =hss
i
(qssH ss)=(4Y ss)

Table 3: Steady state ratios

Description

Total consumption-to-GDP ratio
Gross …xed capital formation-to-GDP ratio
Annualized bank rate on loans (per cent)
Annualized bank rate on deposits (per cent)
Annualized Bank Spread (per cent)

Model Data

0.7632 0.7607
0.2196 0.2119
6.020
2.293
3.727

5.6
2.3
3.4

(cid:13)i) Capital requirement of NFC loans-to-mortgage loans 2.1176 2.1176
0.105
0.105
2.1875 2.1291
1.7938 1.7530
0.5494 0.5490
0.4506 0.4510
0.5621 0.5625
1.4763 1.3585
2.6104 2.8018

Capital requirements on mortgage and NFC loans
HH loans-to-GDP ratio
NFC loans-to-GDP ratio
Fraction of HH loans
Fraction of NFC loans
Bank dividend payout-ratio
Savers-to-borrowers housing ratio
Housing wealth-to-GDP ratio

Note: All series in Euros are seasonally adjusted and de‡ated. Data targets have been constructed from

euro area quarterly data for the period 2002:I-2018:II. The exceptions are the following: annualized bank

rates, which have been taken from constructed series presented in Gerali et al. (2010), and the target for

capital requirements, which has been based on the Basel III regime. Data sources are Eurostat, ECB and

Bloomberg.

45Table 4: Second moments

Variable Description

Model Data

Banking data (SX7E)

(cid:27)db / (cid:27)Y
(cid:27)Jb / (cid:27)Y
(cid:27)Kb / (cid:27)Y
(cid:27)B / (cid:27)Y

Std. bank dividends
Std. bank pro…ts
Std. bank capital
Std.bank assets

15.989 15.050
43.428 59.102
6.554
5.959
6.473
6.760

Macro data (EA)

Std. housing prices
Std. investment
Std consumption
Std(GDP)*100

(cid:27)q / (cid:27)Y
(cid:27)I / (cid:27)Y
(cid:27)C / (cid:27)Y
(cid:27)Y

2.123
3.139
0.938
2.138

2.429
2.642
0.748
2.138

Note: All series are seasonally adjusted and de‡ated, and their log value has been linearly detrended

before computing standard deviation targets. Since some observations in the series "bank pro…ts" (i.e.,

earnings) take negative values, in this case a constant has been added to all observations before taking

logs, such that the minimum of the transformed series series is equal to one.The standard deviation (Std)

of GDP is in quarterly percentage points.

Table 5: Welfare Gains

Shocks

All shocks
(i) No …nancial shocks

Savers Borrowers
0.2604
0.2488
0.2487
0.2605
0.2602
(ii) No housing pref shock 0.2824
(iii) No technology shock
-0.0105

*No HH collateral shock
*No NFC collateral shock
*No equity shock

0.2604
0.2201
0.2376
0.2598
0.2436
-0.5189
0.8097

Note: Second-order approximation to the welfare gains associated to the benchmark optimized dividend

prudential target in which none or some of the shocks are shut down. welfare gains are expressed in

percentage permanent consumption.

46Table 6: Welfare Gains and capital regulation

(1

(cid:13))

(cid:26)x

Savers Borrowers

Capital ratio increases

(cid:0)

(i) 1.0 p.p. increase in (1

*0.11.5
*0.11.5

(cid:13))

(cid:0)

Alternative capital scenarios
(ii) Reoptimization wrt. (cid:26)x

*0.08
*0.105
*0.12

(iii) No reoptimization wrt. (cid:26)x

*0.08
*0.105
*0.12

0

-0.3629
143.741 -0.1021

-0.2761
0.2671

71.46
143.741
197.66

0.0694
0.2604
0.3916

0.0694
0.2604
0.3916

143.741
143.741
143.741

0.3367
0.2604
0.2685

-0.5332
0.2604
0.7183

Note: Part (i) highlights the di¤erences in welfare gains between increasing the capital ratio with and

without the introduction of a dividend prudential target, with respect to the baseline scenario.Parts

(ii) and (iii) summarize the welfare e¤ects of dividend-based prudential rules under alternative capital

scenarios. Hence, in this case, the baseline and the policy scenarios are associated to the same capital

ratio. A capital ratio that may no longer coincide with its baseline calibration value.

47Table 7: Welfare Gains and the CCyB

(cid:13)x

-1.345

(cid:26)x

0

Savers Borrowers

0.1716

1.4795

-0.549 143.741 0.3073

0.3567

-0.322

180.0

0.3752

0.0626

V p
0
V p
0
V p
0

(i)

(cid:13)xg
f
*arg max

(cid:13)x

*arg max

(cid:13)x
*arg max

(cid:13)x

(ii)

(cid:13)x; (cid:26)xg
f
V0
*arg max
(cid:13)x;(cid:26)x

-0.538 149.215 0.3175

0.3175

Note: Part (i) presents a second-order approximation to the savers’ welfare gains associated to the op-

timized countercyclical-capital bu¤er (CCyB), for alternative values of the DPT (cyclical parameter).

Part (ii) presents a second-order approximation to the welfare gains associated to the jointly optimized

countercyclical-capital bu¤er (CCyB) and dividend prudential target (cyclical parameter).

48Figure 1: Bank dividends and earnings in the euro area. 2002:I – 2018:II 

Note: SX7E refers to the Euro Stoxx Banks Index. When applicable, the secondary y-axis corresponds to the dashed line. 
See Appendix A for details on data construction. Data sources: Bloomberg, Eurostat, and own calculations. 

-6-4-2024602040608010012014016018020022003200420052006200720082009201020112012201320142015201620172018(a) SX7E Dividend payout ratio (percent) Dividend Payout RatioAnnual Real GDP Growth Rate-20-15-10-5051015202520022003200420052006200720082009201020112012201320142015201620172018(b) SX7E  Dividends and earnings (billion Euros)DividendsEarnings (a)Earnings (b)020406080100120140160-20308013018023028033020022003200420052006200720082009201020112012201320142015201620172018(c) SX7E Equity and retained earnings (million Euros per share)EquityRetained  Earnings49 
 
 
 
 
 
Note: Variables are expressed in percentage deviations from the steady state. The solid line refers to the baseline scenario. 
The  starred  line  corresponds  to  an  alternative  (policy)  scenario  in  which  the  optimized  prudential  rule  is  a  dividend 
prudential  target.  The  dotted  line  relates  to  an  alternative  (policy)  scenario  in  which  the  optimized  prudential  rule  is  a 
dynamic capital requirement. 

Note: Each subfigure represents a second-order approximation to the unconditional welfare of a specific agent type (saver 
or borrower) as a  function of the  cyclical parameter of  the dividend prudential target, ρx,  while  keeping the other policy 
parameter, ρd, to its baseline calibration value.  

50 
 
 
 
 
 
 
 
 
Note:  Second-order  approximation  to  the  unconditional  welfare  of  savers  and  borrowers  as  a  function  of  the  cyclical 
parameter of the dividend prudential target, ρx, while individually shutting down each of the shocks. 

Note: Second-order approximation to the unconditional welfare of savers and borrowers as a function of capital adequacy 
parameters γi and γe. Note that the steady-state capital ratio for NFC loans is (1- γe) whereas the steady-state capital ratio for 
HH loans is (1- γi). 

51 
 
 
 
 
 
 
 
 
 
 
 
Note:  Second-order  approximation  to  the  unconditional  welfare  of  savers  and  borrowers  as  a  function  of  the  cyclical 
parameter of the dividend prudential target, ρx, for three alternative capital scenarios (1-γ). 

Note:  Second-order  approximation  to  the  unconditional  welfare  of  savers  and  borrowers  as  a  function  of  the  cyclical 
parameter of the dynamic capital requirement, γx, for alternative values of the cyclical parameter of the dividend prudential 
target, ρx.   

52 
 
 
 
 
 
 
 
 
 
 
Note:  Second-order  approximation  to  the  unconditional  welfare  of  savers  and  borrowers  as  a  function  of  cyclical 
parameters of the dynamic capital requirement and the dividend prudential target, γx  and ρx. 

Note: Variables are expressed in percentage deviations from the steady state. The solid line refers to the baseline scenario. 
The starred line corresponds to an alternative (policy) scenario in which  welfare has been maximized with respect to the 
cyclical parameter of the dividend prudential target, ρx. The dotted line relates to an alternative (policy) scenario in which 
welfare  has been  maximized  with respect to the cyclical parameter of the  dynamic capital requirement, γx. The diamond 
line makes reference to an alternative (policy) scenario in which welfare has been maximized with respect to cyclical policy 
parameters ρx  and γx . 

53 
 
 
 
 
 
 
 
 
 
 
Note: Variables are expressed in percentage deviations from the steady state. The solid line refers to the baseline scenario. 
The starred line corresponds to an alternative (policy) scenario in which  welfare has been maximized with respect to the 
cyclical parameter of the dividend prudential target, ρx. The dotted line relates to an alternative (policy) scenario in which 
welfare  has been  maximized  with respect to the cyclical parameter of the dynamic capital requirement,  γx. The diamond 
line makes reference to an alternative (policy) scenario in which welfare has been maximized with respect to cyclical policy 
parameters ρx  and γx . 

Note: Variables are expressed in percentage deviations from the steady state. The solid line refers to the baseline scenario. 
The starred line corresponds to an alternative (policy) scenario in which  welfare has been maximized with respect to the 
cyclical parameter of the dividend prudential target, ρx. The dotted line relates to an alternative (policy) scenario in which 
welfare  has been  maximized  with respect to the cyclical parameter of the dynamic capital requirement,  γx. The diamond 
line makes reference to an alternative (policy) scenario in which welfare has been maximized with respect to cyclical policy 
parameters ρx  and γx . 

54 
 
 
 
 
 
 
 
Note: Variables are expressed in percentage deviations from the steady state. The solid line refers to the baseline scenario. 
The starred line corresponds to an alternative (policy) scenario in which  welfare has been maximized with respect to the 
cyclical parameter of the dividend prudential target, ρx. The dotted line relates to an alternative (policy) scenario in which 
welfare  has been  maximized  with respect to the cyclical parameter of the dynamic capital requirement,  γx. The diamond 
line makes reference to an alternative (policy) scenario in which welfare has been maximized with respect to cyclical policy 
parameters ρx  and γx . 

Note: Variables are expressed in percentage deviations from the steady state. The solid line refers to the baseline scenario. 
The starred line corresponds to an alternative (policy) scenario in which  welfare has been maximized with respect to the 
cyclical parameter of the dividend prudential target, ρx. The dotted line relates to an alternative (policy) scenario in which 
welfare  has been  maximized  with respect to the cyclical parameter of the dynamic capital requirement,  γx. The diamond 
line makes reference to an alternative (policy) scenario in which welfare has been maximized with respect to cyclical policy 
parameters ρx  and γx . 

55 
 
 
 
 
 
 
Note:  Second-order  approximation  to  the  unconditional  welfare  of  savers  and  borrowers  as  a  function  of  the  cyclical 
parameter  of  the  dividend  prudential  target,  ρx,  for  alternative  values  of  the  dividend  adjustment  cost  parameter,  κ.  The 
solid line refers to the baseline scenario whereas the dotted and dashed lines relate to alternative parameterization scenarios. 

Note:  Second-order  approximation  to  the  unconditional  welfare  of  savers  and  borrowers  as  a  function  of  the  cyclical 
parameter of the dividend prudential target, ρx, for alternative fractions of banks owned by savers. The solid line refers to 
the baseline scenario whereas the dotted and dashed lines relate to alternative parameterization scenarios. 

56 
 
 
 
 
 
 
 
 
 
 
Note:  Second-order  approximation  to  the  unconditional  welfare  of  savers  and  borrowers  as  a  function  of  the  cyclical 
parameter of the dividend prudential target, ρx, for alternative fractions χ of the net transfer that savers receive according to 
their bank property. The solid line refers to the baseline scenario whereas the dotted and dashed lines relate to alternative 
parameterization scenarios. 

57 
 
 
 
 
 
 
 
 
A Data and Sources

This section presents the full data set employed to present some evidence on euro area bank
dividends and earnings in section 2 and to calibrate the extended model in section 5.

Gross Domestic Product: Gross domestic product at market prices, Chain-linked volumes
(rebased), Domestic currency (may include amounts converted to the current currency at a …xed
rate), Seasonally and working day-adjusted. Source: Eurostat.

GDP De‡ator: Gross domestic product at market prices, De‡ator, Domestic currency, Index
(2010 = 100), Seasonally and calendar adjusted data - ESA 2010 National accounts. Source:
Eurostat.

Final Consumption: Final consumption expenditure at market prices, Chain linked volumes

(2010), Seasonally and calendar adjusted data. Source: Eurostat.

Gross Fixed Capital Formation: Gross …xed capital formation at market prices, Chain

linked volumes (2010), Seasonally and calendar adjusted data. Source: Eurostat.

Households Housing Wealth: Housing wealth (net) of Households and non pro…t institu-
tions serving households sector (NPISH), Current prices, Euros, Neither seasonally adjusted nor
calendar adjusted - ESA 2010. Source: European Central Bank.

Housing Prices: Residential property prices; New and existing dwellings, Residential property
in good and poor condition. Neither seasonally nor working day adjusted. Source: European
Central Bank.

Business Loans: Outstanding amounts at the end of the period (stocks) of loans from MFIs
to Non-Financial corporations (S.11) sector, denominated in
excluding ESCB reporting sector
Euros. Source: MFI Balance Sheet Items Statistics (BSI Statistics), Monetary and Financial
Statistics (S/MFS), European Central Bank.

Households Loans: Outstanding amounts at the end of the period (stocks) of loans from MFIs
excluding ESCB reporting sector
to Households and non-pro…t institutions serving households
(S.14 & S.15) sector, denominated in Euros. Source: MFI Balance Sheet Items Statistics (BSI
Statistics), Monetary and Financial Statistics (S/MFS), European Central Bank.

Dividend Payout Ratio: Fraction of net income payed to shareholders in dividends, in per-
centage. Calculated as: Total Common Dividends*100 / Income Before Extraordinary Items Less
Minority and Preferred Dividends. Capitalization-weighted sum of the SX7E members. Source:
Bloomberg.

Dividends: Dividends paid to common shareholders from the pro…ts of the company. Includes
regular cash as well as special cash dividends for all classes of common shareholders. Excludes
return of capital and in-specie dividends. For the cases in which dividends attributable to the
period are not disclosed, dividends are estimated by multiplying the Dividend per Share by the

58number of Shares Outstanding. Simple sum of the SX7E members. Seasonally adjusted data
(TRAMO/SEATS). Source: Bloomberg.

Earnings (a): Income before extraordinary items and discontinued operation but after mi-
nority interest, preferred dividend, and other adjustments. Calculated as: Pretax Income - Income
Tax - After Tax (Income) Loss from A¢ liates - Minority Interest - Preferred Dividends - Other
Adjustments. Simple sum of the SX7E members. Seasonally adjusted data (TRAMO/SEATS).
Source: Bloomberg.

Earnings (b): Net income available to common shareholders. Calculated as: Net Income
- Total Cash Preferred Dividend - Other Adjustments.55 Simple sum of the SX7E members.
Seasonally adjusted data (TRAMO/SEATS). Source: Bloomberg.

Retained Earnings: Cumulative undistributed earnings. Includes net unrealized gain (loss)
on securities held for sale and other items included in accumulated comprehensive income (net of
tax). Includes deferred compensation to o¢ cers. Retained earnings are decreased by the amount
of treasury stock. Reserves resulting from revaluation of assets in many countries are included as
a part of shareholders’equity and are included. Normalized by the number of shares outstanding.
Capitalization-weighted sum of the SX7E members. Seasonally adjusted data (TRAMO/SEATS).
Source: Bloomberg.

Total Equity: Firm’s total assets minus its total liabilities. Calculated as: Common Equity
+ Minority Interest + Preferred Equity.56 Simple sum of the SX7E members. Seasonally adjusted
data (TRAMO/SEATS). Source: Bloomberg.57

Total Assets: Firm’s total assets. Calculated as: Cash and bank balances + Fed funds
sold and resale agreements + Investments for Trade and Sale + Net loans + Investments held to
maturity + Net …xed assets + Other assets + Customers’Acceptances and Liabilities. Simple sum
of the SX7E members. Seasonally adjusted data (TRAMO/SEATS). Source: Bloomberg.

55"Other adjustments" include any adjustments to bottom-line net income (except for preferred dividends) that
are needed to arrive at Basic Net Income Available for Common Shareholders. Examples of Other Adjustments
are exchangeable preferred membership interest buyback premium, earnings allocated to participating securities,
interest expense for hybrid securities, accretion of preferred stock issuance cost, and net income allocated to general
partners.

56"Common Equity" refers to the amount that all common shareholders have invested in a company. Calculated

as: Share Capital & additional paid in capital (APIC) + Retained Earnings and Other Equity.

57For calibration purposes, total equity has been constructed as the simple sum of all SX7E member’s total equity.
For reporting purposes (see …gure 1), and following investors and Bloomberg’s convention, total equity has been
constructed as the capitalization-weighted sum of the SX7E members, after having normalized raw data by the
number of total shares outstanding (as retained earnings have been constructed).

59B Equations of the Extended Model

This section presents the full set of equilibrium equations of the extended model.

B.1 Patient Households

Patient households seek to maximize (23) subject to the following buget constraint

Cp;t + Dt + qt(Hp;t

Hp;t

(cid:0)

(cid:0)

1) = (Rd;t

(cid:0)

1)Dt

(cid:0)

1 + WtNp;t + !bdb;t + (cid:31)Tt + !ede;t

(B.1)

Their choice variables are Cp;t, Dt, Hp;t and Np;t. The optimality conditions of the problem

read

(cid:21)p
t =

Cp;t

(cid:27)h

(cid:0)

N 1+(cid:30)
p;t
(1 + (cid:30))!

(cid:0)

(cid:21)p
t = (cid:12)pRd;tEt(cid:21)p

t+1

qt(cid:21)p

t =

j"h
t
Hp;t

+ (cid:12)pEt

qt+1qt(cid:21)p

t+1

(cid:0)
Wt = N (cid:30)
p;t

(cid:1)

(B.2)

(B.3)

(B.4)

(B.5)

where (cid:21)p
t

household.

is the Lagrange multiplier on the budget constraint of the representative patient

B.2 Impatient Households

The representative impatient household chooses the trajectories of consumption Ci;t, housing Hi;t,
demand for labor Ni;t and bank loans Bi;t that maximize (23) subject to a budget constraint and
a borrowing limit

Ci;t + Ri;t

(cid:0)

1Bi;t

(cid:0)

1 + qt(Hi;t

Hi;t

1) + (cid:8)i(Bi;t)

(cid:0)

(cid:0)
= Bi;t + WtNi;t + (1

!b)db;t + (1

(cid:31))Tt + (1

!e)de;t

(cid:0)

(cid:0)

(cid:0)

(B.6)

60 
The resulting optimality conditions are

Bi;t

(cid:20)

mH

i;tEt

qt+1
Ri;t

(cid:20)

Hi;t

(cid:21)

(cid:21)i
t =

Ci;t

(cid:27)h

(cid:0)

N 1+(cid:30)
i;t
(1 + (cid:30))!

(cid:0)

Wt = N (cid:30)
i;t

(B.7)

(B.8)

(B.9)

(cid:21)i
t

qt
(cid:20)

1

(cid:0)

(cid:0)

(cid:18)

@(cid:8)i(Bi;t)

@Bi;t (cid:19)

Et

mH
i;t

(cid:18)

qt+1
Ri;t (cid:19)(cid:21)

=

j"h
t
Hi;t

+ (cid:12)iEt

qt+1(cid:21)i

t+1

1

mH
i;t

(cid:0)

(cid:2)

(cid:0)

(cid:1)(cid:3)

(B.10)

where (cid:21)i

t is the Lagrange multiplier on the budget constraint of the representative patient

household.

B.3 Entrepreneurs

Entrepreneurs seek to maximize (27) subject to a budget constraint, the available technology and
the corresponding borrowing limit

de;t + Rb;tBe;t

(cid:0)

1 + qk
t

Ke;t

(1

(cid:0)

(cid:0)

(cid:14)k
t )Ke;t
(cid:0)

1

(cid:2)

(cid:3)

+ WtNt + (cid:8)e(Be;t) = Yt + Be;t

(B.11)

Yt = At(utke;t

(cid:0)

1)(cid:11)H (cid:17)
e;t

(cid:0)

1N (1

t

(cid:0)

(cid:11)

(cid:0)

(cid:17))

Be;t

(cid:20)

mH

e;tEt

qt+1
Re;t+1

He;t

(cid:18)

(cid:0)

(cid:19)

mN WtNt

(B.12)

(B.13)

Their choice variables are de;t, Ke;t, ut, Be;t and Nt. The following optimality conditions can

be derived from the …rst order conditions of the problem

61 
1
d(cid:0)
(cid:27)
e;t

qt
(cid:20)

(cid:0)

(cid:18)

1

(cid:0)

@(cid:8)e(Be;t)

@Be;t (cid:19)

mH

e:tEt

qt+1
Re;t+1 (cid:19)(cid:21)
(cid:18)
= (cid:3)e
0;tEt

1
(cid:27)
e;t+1

d(cid:0)

(cid:26)

qt+1(1
(cid:20)

(cid:0)

mH

e;t) + (cid:17)

Yt+1
He;t (cid:19)(cid:21)(cid:27)

(cid:18)

(B.14)

1
d(cid:0)
(cid:27)
e;t

Wt + mN Wt
(cid:20)

(cid:18)

1

(cid:0)

@(cid:8)e(Bt)

@Bt (cid:19)

(cid:0)

(1

(cid:11)

(cid:0)

(cid:0)

(cid:17))

Yt
Nt (cid:21)

= (cid:3)e

0;tEt

1
(cid:27)

e;t+1mN WtRe;t+1
d(cid:0)

(B.15)

h

i

1
(cid:27)

e;t qk
d(cid:0)

t = (cid:3)e

0;tEt

1
(cid:27)
e;t+1

d(cid:0)

(cid:26)

qk
t+1
(cid:20)

(cid:0)

Yt+1
ke;t (cid:19)(cid:21)(cid:27)

(cid:18)

(B.16)

(B.17)

(cid:14)k
t

1

(cid:0)

+ (cid:11)

(cid:1)
Yt
utke;t

(cid:0)

(cid:18)

1 (cid:19)

1 + (cid:14)k
(cid:14)k

2 (ut

1) = (cid:11)

(cid:0)

B.4 Bankers

The representative banker chooses the trajectories of dividend payouts db;t, loans to households Bi;t,
loans to entrepreneurs Be;t, and deposits Dt that maximize (32) subject to a cash ‡ow restriction
and a borrowing limit (capital adequacy constraint)

db;t + Bit + Be;t

Dt

(1

(cid:14)t) (Bi;t

1 + Be;t

1

Dt

1)

(cid:0)

(cid:0)

(cid:0)
= re;tBe;t

(cid:0)
1 + ri;t

(cid:0)
1Bi;t

(cid:0)

(cid:0)

(cid:0)
rd;t

(cid:0)
1Dt

(cid:0)

1

(cid:0)

(cid:0)

1

(cid:0)

(cid:8)be(Be;t)

(cid:8)bi(Bi;t)

(cid:0)

(cid:0)

'(db;t)

(B.18)

(cid:0)

Dt = (cid:13)i;tBi;t + (cid:13)e:tBe;t

(B.19)

In order to incorporate the information of the balance sheet constraint in the optimization
problem, there has been rearranged in equation (33) to substitute Kb;t in expression (34). The law
of motion for bank equity reads

The resulting optimality conditions read

Kb;t = Jb;t

db;t + (1

(cid:14)t)Kb;t

(cid:0)

1

(cid:0)

(cid:0)

(B.20)

62(1

(cid:0)
1
(cid:27)

(cid:13)i;t) +

@(cid:8)bi(Bi;t)
@Bi;t

b;t [1 + (cid:20)(db;t
d

d(cid:3)t )]

(cid:0)

ri;t

= (cid:3)b

0;tEt 8
<

(cid:0)

(cid:13)i;trd;t

+ (1

(cid:0)
(cid:0)
1
b;t+1 [1 + (cid:20) (db;t+1
d
(cid:27)
(cid:1)

(cid:13)i;t) (1

(cid:14)t)

(cid:0)
d(cid:3))]

(cid:0)

(1

(cid:0)
1
(cid:27)

(cid:13)e;t) +

@(cid:8)be(Be;t)
@Be;t

d
b;t [1 + (cid:20)(db;t

d(cid:3)t )]

(cid:0)

:

re;t+1

= (cid:3)b

0;tEt 8
<

(cid:0)

(cid:13)e;trd;t

+ (1

(cid:0)
d
b;t+1 [1 + (cid:20) (db;t+1
(cid:1)

(cid:0)

1
(cid:27)

(cid:13)e;t) (1

(cid:14)t) "kb
t

(cid:0)
d(cid:3))]

(cid:0)

:
B.5 Capital Goods Producers

(B.21)

(B.22)

9
=

;

9
=

;

Capital-good-producing …rms seek to maximize (36) with respect to net investment in physical
capital, It. The resulting optimal condition is

1 = qk;t

1

"

(cid:0)

 I
2

It
It

(cid:0)

(cid:18)

1 (cid:0)

2

1
(cid:19)

 I

(cid:0)

It
It

(cid:0)

(cid:18)

1 (cid:0)

It
It

(cid:0)

1
(cid:19)

1 #

(cid:3)e

0;tqk;t+1 I

+ Et

"

It+1
It (cid:0)

2

It+1
It (cid:19)

#

1
(cid:19) (cid:18)

(cid:18)

As standard in the literature, the law of motion for physical capital reads

Ke;t = (1

(cid:14)k
t )Ke;t
(cid:0)

1 + It

(cid:0)

1

"

(cid:0)

 I
2

It
It

(cid:0)

(cid:18)

1 (cid:0)

2

1
(cid:19)

#

B.6 Macroprudential Authority

As in the basic model, the dividend prudetial target is speci…ed as follows

d(cid:3)t = (cid:26)d + (cid:26)(cid:31)(

xt
xss (cid:0)

1)

(B.23)

(B.24)

(B.25)

Bank dividend deviations from such target are penalized with a proportional payment that
takes the form of a sanction. Such penalty payments are transfered within the same period to
bank owners. The corresponding net subsidy reads

Tt =

(cid:20)
2

h(cid:0)

da
b;t (cid:0)

d(cid:3)t

2

(cid:0)

(db;t

(cid:0)

b )2
dss

(cid:1)

i

(B.26)

63The prudential authority has full control over the banker’s regulatory capital ratio (1

through the leverage ratio imposed by the borrowing limit (35)

(cid:13)t)

(cid:0)

(cid:13)t = (cid:13) + (cid:13)x(

xt
xss (cid:0)

1)

(B.27)

where (cid:13) = (cid:13)i

Bi
B

+ (cid:13)e

Be
B

.

B.7 Aggregation and market clearing

Market clearing is implied by the Walras’s law, by aggregating all the budget constraints. The
aggregate resource constraint of the economy represents the equilibrium condition for the …nal
goods market.

Yt = Cp;t + Ci;t + qk

t It + (cid:14)tKb;t
(cid:0)

1 + Adjt

(B.28)

where the term Adjt corresdonds to the sum of all resources dedicated in the economy to adjust

loans and bank dividends in period t.

In equilibrium, the housing market clears. The endowment of housing supply is …xed and

normalized to unity

B.8 Shocks

H = Hp;t + Hi;t + He;t

(B.29)

The following zero-mean, AR(1) shocks are present in the extended model: "mh
These shocks follow the processes given by:

t

, "mk
t

, "kb

t , "h

t , At.

log "mh

t = (cid:26)mh log "mh
t
(cid:0)

1 + emh;t; emh;t s N (0; (cid:27)mh)

log "mk

t = (cid:26)mk log "mk
t
(cid:0)

1 + emk;t; emk;t s N (0; (cid:27)mk)

log "kb

t = (cid:26)mk log "kb
t
(cid:0)

1 + ekb;t; ekb;t s N (0; (cid:27)mk)

log "h

t = (cid:26)h log "h
t
(cid:0)

1 + eh;t; eh;t s N (0; (cid:27)h)

(B.30)

(B.31)

(B.32)

(B.33)

64log At = (cid:26)A log At
(cid:0)

1 + eA;t; eA;t s N (0; (cid:27)A)

(B.34)

65Imprint and acknowledgements 

The views expressed in this paper are those of the author and do not necessarily reflect the views of the 
institutions he is affiliated to. I am indebted to Javier Andrés and Luis A. Puch for invaluable support and 
guidance. I also thank Jorge Abad, Pablo Aguilar, Jordi Caballé, Eudald Canadell, Ángel Estrada, María José 
Fernández, Jordi Galí, Samuel Hurtado, Laura Mayoral, Galo Nuño, Johannes Pfeifer, Jesús Saurina, Javier 
Suárez, Dominik Thaler and Carlos Thomas for very helpful comments and suggestions, as well as participants 
at various seminars and conferences, including those kindly organized by the National Securities Market 
Commission (CNMV) and the Bank of Spain. I am responsible for all remaining errors. 

Manuel Muñoz 
Spanish Ministry for Economy and Business, Madrid, Spain; e-mail: manuel.munoz@mineco.es 

© European Systemic Risk Board, 2019 

Postal address 
Telephone 
Website 

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source is acknowledged. 

Note: 
The views expressed in ESRB Working Papers are those of the authors and do not necessarily reflect 
the official stance of the ESRB, its member institutions, or the institutions to which the authors are 
affiliated. 

ISSN 
ISBN 
DOI 
EU catalogue No 

2467-0677 (pdf) 
978-92-9472-111-2 (pdf) 
10.2849/88629 (pdf) 
DT-AD-19-011-EN-N (pdf)