Download Debt, Equity and Monetary Policy∗

Debt, Equity and Monetary Policy
Daria Finocchiaroy
Caterina Mendicino
June 2013
Abstract
This paper studies the optimal conduct of monetary policy in an economy subject to changes in the
…nancing conditions of …rms. The model features credit and equity …nancing as well as nominal price
rigidities. Firms face two types of …nancial frictions: a collateral constraint, and rigidities in their capital
structure. In the face of adverse shocks, entrepreneurs who are limited in their capital holding by the
existence of an occasionally binding collateral constraint may partly raise external funds via a reduction in
their equity payout. However, since adjusting their capital structure is costly, …rms cut both employment
and investment. Two sources of macroeconomic ‡uctuations are introduced into the model: a productivity
shock, and a shock originating in the credit market. Welfare analyses show that, in addition to in‡ation,
an interest-rate response to credit is optimal. In contrast, a response to asset prices is welfare detrimental.
Credit shocks account for most of the gains from a policy response to credit.
Keywords: Interest-rate Rules, Financial frictions, Loan-to-Value Ratio, Penalty Functions
JEL codes: E44, E52,G32
Finocchiaro: Sveriges Riksbank, Research Division SE103-37 Stockholm, Sweden, daria.…[email protected]. Mendicino: Banco de Portugal, Department of Economic Studies R. Francisco Ribeiro, N. 2, Lisboa, 1150-165, Portugal, [email protected]. The views expressed in this paper are solely the responsibility of the authors and should not be
interpreted as re‡ecting the views of the Executive Board of Sveriges Riksbank or of the Bank of Portugal. Any errors or omissions
are the responsibility of the authors
y Corresponding author.
1
1.
Introduction
Economic history has made clear the existence of important macro-…nancial linkages. The crucial role of
…nancial markets in the ampli…cation and propagation of shocks or as a source of business cycle ‡uctuations
is now almost unanimously recognized. Going beyond Modigliani and Miller (1958)’s irrelevance result, the
seminal contributions of Bernanke and Gertler (1989) and Kiyotaki and Moore (1997) have sprouted a new
branch of literature in which these linkages are more seriously taken into account. Among others, Jermann and
Quadrini (2012) and Covas and Denhaan (2011) highlight the importance of properly incorporating …rms’debt
and equity ‡ows into otherwise standard macro models. The former also documents the real e¤ects of …nancial
shocks in the US business cycles.
On the normative side, the role of …nancial variables in the conduct of monetary policy has recently received
a great deal of attention. As a result, models with …nancial frictions have become increasingly popular in the
analysis of optimal monetary policy. Some authors (e.g., Cecchetti et al., 2002) have argued that monetary policy
should take into account the information content of asset price movements or other …nancial indicators. However,
this view is controversial. Other studies have documented that a positive interest-rate policy response to …nancial
variables induces negligible stabilization gains (e.g., Bernanke and Gertler, 1999) or is even detrimental (e.g.,
Faia and Monacelli, 2007).
Previous attempts to investigate the optimality of monetary policy response to …nancial variables have mainly
relied on models that incorporate …nancial market frictions through the assumption of limited enforcement or
information asymmetry in the credit market. Additionally, most of the previous literature assumes that debt
is the only source of external funding. It is also common to neglect macroeconomic ‡uctuations originating in
the …nancial sector.1
In this paper, we depart from the previous literature and investigate the potential bene…ts of a policy interestrate response to …nancial variables in a model where …rms can …nance their activity with debt and equity. We
assume that …rms face two types of …nancial frictions: a borrowing constraint originating from an enforcement
problem in the credit market, and rigidities in their choice of …nancial structure. Further, the …nancial sector is
a source of macroeconomic ‡uctuations. We document that rigidities a¤ecting the …nancial structure of …rms
and shocks originating in the credit market are key to assessing the optimality of an interest-rate response to
movements in …nancial variables.
In the baseline version of our model, …nancial rigidities a¤ect the decisions of households and …rms in various
ways. The enforcement constraint distorts capital accumulation and exerts an e¤ect on both short-run dynamics
1 Two exceptions are both Carlstrom et al. (2010)’s and Cúrdia and Woodford (2009)’s studies on optimal monetary policy in
response to …nancial shocks.
2
and the steady state of the economy. On the contrary, rigidities in …rms’…nancial structures have only short-run
implications through their e¤ect on the labor wedge. Consider the case of an adverse shock. Entrepreneurs,
limited in their capital holding by the existence of an occasionally binding collateral constraint, may reduce
production or partly raise external funds throughout a reduction in their equity payout. However, since either
changing prices or changing their …nancial structure is costly, …rms cut both employment and investment.
Our main …nding is that an interest-rate response to credit, in addition to in‡ation, is welfare improving.
In contrast, a response to asset prices is detrimental. Credit shocks account for most of the gains from a policy
response to credit.
Our results are robust to the alternative assumptions regarding the borrowing constraint. First, following
most of the literature on credit frictions, we also solve a version of the model with a collateral constraint that
binds at any time. Secondly, we allow for an alternative assumption regarding the liquidation value of capital.
In both cases, a monetary policy response to credit is welfare improving.
Our work is related to the growing literature addressing macro-…nancial linkages. Bernanke and Gertler
(1989) propose a …nancial accelerator model of the entrepreneurial sector. The key friction in the model is a
costly state veri…cation problem between borrowers and lenders which create a premium on external …nance.
The link between the premium and borrowers’ net worth acts as a powerful transmission mechanism for exogenous shocks. Kiyotaki and Moore (1997) propose a di¤erent approach which relies on the existence of
enforcement problems in credit markets. If borrowers cannot pre-commit to repaying their debts, lenders can
protect themselves by requiring some collateral. The dynamic interactions between credit limits and collateral
values might generate ampli…cation. Jermann and Quadrini (2012) subsequently develop a model with debt
and equity …nancing in which the …nancial sector is an important source of business cycle ‡uctuations. In their
model, employers need working capital. As a result, …nancial frictions have a direct impact on both capital
accumulation and employment demand. Our framework follows theirs by introducing two sources of …nance
for …rms, debt and equity. However, unlike Jermann and Quadrini (2012), we do not assume the existence of
intra-period loans to …nance working capital. Moreover, we explicitly take into account asset price feedbacks
on borrowing limits by embedding the model with an enforcement constraint à la Kiyotaki and Moore (1997).
We show that, in the presence of price stickiness, the credit channel also works through labor demand even
without the working capital assumption. Moreover, asset-price feedback e¤ects on the borrowing constraint
exacerbate the welfare losses of not responding to …nancial variables. In this paper we also depart from most
of the previous literature by allowing for the …nancial constraint to be occasionally binding and exploring the
role of non-linearity for the optimal conduct of monetary policy.
Several papers have studied optimal monetary policy in the presence of …nancial market imperfections. In
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a version of Carlstrom and Fuerst (1997) that is modi…ed to generate a countercyclical …nance premium, Faia
and Monacelli (2007) conclude that, in comparison with an interest-rate response to asset prices, a strong antiin‡ationary stance is welfare maximizing. In their model, productivity is the only source of uncertainty. We
contribute to their …ndings by documenting that …nancial shocks are crucial for the optimality of responding
to …nancial variables. In particular, we show that responding to credit, rather than to movements in asset
prices, turns out to be welfare improving. Carlstrom et al. (2010) study a stylized economy without capital
accumulation in which agency costs distort labor markets. They show that, although there exist a tension
between stabilizing in‡ation, the output gap and the risk premium, stabilizing in‡ation is near optimal. Our
setup di¤ers from theirs in that …nancial frictions a¤ect both investment and employment decisions in our
model.
Another branch of literature has emphasized the role of information frictions in justifying a monetary policy
reaction to credit conditions (see e.g., Gilchrist and Saito, 2008, Christiano et al., 2010). We depart from that
literature by focusing on a model with full information in which movements in asset prices are only driven by
fundamentals.
Finally, the recent …nancial crisis has prompted central banks to use less conventional monetary policy
tools. As a result, there is a growing literature studying the e¤ects of direct interventions in credit markets by
central banks (e.g., Gertler and Karadi, 2011, Cúrdia and Woodford, 2010). This paper, however, focuses on
conventional monetary policy.2
The remainder of the paper is organized as follows. Section 2. describes of the baseline model. Section 3.
presents the solution method and the calibration strategy. Section 4. illustrates the interactions of …nancial
frictions on the model dynamics. Section 5. studies the welfare implications of di¤erent monetary policy rules.
Section 6. through 8. analyze the results and their sensitivity to our modelling assumptions. Section 9. presents
the conclusions.
2.
The Model
Consider a discrete time in…nite horizon economy populated by …rms and households. Firms combine labor and
capital to produce intermediate inputs to the …nal good production. They can …nance their activity with both
debt and equity, but debt is preferred over equity because it produces a tax advantage. There are three sources
of …nancial frictions. First, …rms’ability to borrow is limited by a collateral constraint as in Kiyotaki and Moore
(1997). Second, the sources of funds can only be adjusted slowly, i.e. equity payout is subject to quadratic costs,
2 Other
studies on optimal monetary policy in the presence of …nancial friction include Monacelli (2008), Cúrdia and Woodford
(2009) and Lambertini et al. (2011). All of these focus on household borrowing.
4
as in Jermann and Quadrini (2012). Third, the model features a …nancial shock that captures credit disruptions
originating in …nancial markets. Households are shareholders, consume the …nal good, provide work and hold
non-contingent bonds issued by the …rms. A central bank conducts monetary policy following a Taylor-type
rule.
2.1
Firms
There is a continuum of monopolistic competitive …rms in the [0; 1] interval. Each …rm produces intermediate
goods, Yt (i) ; using capital (k) and labor (l) according to a constant returns-to-scale technology:
Yt (i) = zt kt (i) lt (i)
1
;
where z follows an exogenous stochastic process. The intermediate good is then used as an input in the …nal
good production:
3""1
2 1
Z
" 1
:
Yt = 4 Yt (i) " di5
0
Pro…t maximization implies the following demand function:
Yt (i) =
Pt (i)
Pt
"
Yt ;
(1)
where Pt (i) is the nominal price set by the single …rm and Pt is the aggregate nominal price index. Firms’
borrowing capacity is limited to a fraction
of the liquidation value of capital:
bt (i)
1 + rt
t Et qk;t+1 kt
(i) ;
(2)
where bit (i) and kt (i) are the individual borrowing and capital holding, respectively, for the current period
and rt is the nominal interest rate paid on debt. Equation (2) stems from an enforcement problem in credit
markets. If …rms cannot pre-commit to repaying their debts, lenders can protect themselves by collateralizing
…rms’ capital. However, in case of default, only a fraction
of the collateral can be recovered by the lender,
i.e. the liquidation value of capital is equal to
(i) : It is further assumed that
t Et qk;t+1 kt
can ‡uctuate.
The introduction of this collateral shock aims at capturing variations over time in the degree of credit market
tightness.
In addition to using debt, …rms can also …nance their activity with equity. The substitution between these
two sources of funds is not frictionless. Speci…cally, …rms are subject to a quadratic equity payout cost:
(dt ) = dt +
5
2
dt
d
2
;
where dt is the equity payout, d is the steady-state payout target and
can be interpreted, as the degree of
rigidity in a …rm …nancial structure.
Each …rm maximizes its future discounted value:
V (bt
1
(i) ; kt
1
(i) ; Pt
1
(i) ; It
1
(i)) =
max
dt ;lt ;bt ;kt ;It
fdt (i) + Et
t+1 V
(bt (i) ; kt (i) ; Pt (i) ; It (i))g
(3)
subject to the demand for the …rm’s product (Eq. (1)), the borrowing constraint (Eq. (2)), and the budget
constraint:
Pt (i)
bt (i)
Y (i)t +
Pt
Rt
bt (i)
wt lt (i)
t (d)
t
It (i)
where wt lt (i) represents payments to workers, Rt = 1 + rt (1
…rm, and
'
2
Pt (i)
Pt 1 (i)
2
1
Yt = 0
) is the e¤ective gross rate on debt paid by the
represents the tax advantage of using debt: Capital evolves according to:
kt (i) = (1
where % (It ; It
1)
=
1
It
1
(i) + % (It (i) ; It
1
(i))
2
It
2
) kt
1
1
It
1
is a function capturing investment adjustment costs. Nominal
rigidities are introduced assuming adjustment costs à la Rotemberg (1982):
'
2
Pt (i)
Pt 1 (i)
2
1
Yt :
Consistently with the households’problem described below, the stochastic discount factor is de…ned as:
t+1
Uct+1
:
Uct
=
In our analysis, we focus on aggregate rather than idiosyncratic uncertainty and we study symmetric equilibria. Appendix A. summarizes the …rst order conditions of the optimization problem solved by the representative
…rm.
2.2
Households
Households hold both equity shares (s) and non-contingent bonds (b) issued by the …rms. They choose consumption (c) and labor (l) in order to maximize their lifetime utility subject to a budget constraint:
V H (bt 1 ; st 1 ) = U (ct ; lt ) + E V H (bt ; st )
bt
bt 1
+ st 1 (dt + qt )
st qt ct
st : wt lt +
1 + rt
t
where Tt =
ln ct + v ln (1
bt
1+rt (1
)
lt ) and V
bt
1+rt
H
Tt = 0
represents a lump-sum tax to …nance the subsidy to …rms’ debt, U (ct ; lt ) =
the value function associated to this dynamic program: Appendix 1.2 reports the
…rst order conditions for this optimization problem.
6
2.3
Monetary policy
The monetary authority manages the short-term nominal interest rate. As a baseline case, we assume the
following Taylor-type rule:
1 + rt
1 + rss
where
t
=
;
(4)
ss
is the responses of the nominal interest rate to changes in in‡ation and the subscript ss refers to
steady state variables.
In equilibrium, households’and …rms’…rst order conditions are satis…ed and prices clear all markets. Appendix A and Appendix B report, respectively, the equations and steady state conditions.
3.
Solution Method and Calibration
In the numerical implementation of the model, we approximate the inequality constraint using a di¤erentiable
penalty function, P (ki;t ; bi;t ), that enters utility of the borrowers:
P (kt ; bt ) =
1
e[
0
(
Et [
t qt+1 kt ]
bt
1+rt
)] :
0
The penalty term,
0,
discourages the agents from violating the constraint, i.e. large values of
0
ensure that
the agents’indebtedness does not exceed the limit.3 In equilibrium, the derivative of the penalty function with
respect to bt replaces the shadow price of the occasionally binding borrowing constraint, . Thus, we can set
equal to
term,
0,
1
such that the two versions of the model are equivalent. In the baseline economy, we set the penalty
equal to 100.
Table 1 summarizes our parametrization. The model’s period is one quarter. We assign standard values
to preference and technology parameters. We assume separable log-utility and calibrate the utility weight on
leisure (v) by …xing steady-state hours worked at 0:3: The discount factor ( ) is equal to 0.9825, implying an
annual return from equity equal to 7:32 percent. We follow Jermann and Quadrini (2012) and calibrate the
tax bene…t on debt ( ) at 35 percent. Capital share in the production for intermediate goods ( ) is set to 0.36
and the depreciation rate of capital ( ) equals 0.025. The elasticity of substitution across intermediate good
varieties (") is 6 and price adjustment costs are calibrated in order to match a frequency of price adjustment of
about 3 quarters, a value in the range of Nakamura and Steinsson (2008) …ndings for non-sale prices. Steady
state in‡ation is assumed to be zero.4
3 The same approach has already been used to solve models with non-negativity constraints by, among others, Preston and Roca
(2007), Haan and Ocaktan (2009) , Jinill Kim and Kim (2010) and Kim and Ruge-Murcia (2011)
4 Alternatively, one could think of the model as already detrended by long-term in‡ation.
7
We parametrize the technology shock (z) by constructing a capital series as described in Jermann and
Quadrini (2012) and extracting the Solow residuals. The collateral shock ( ) and the payout cost ( ) are key
model parameters for which there is less consensus in the literature. The mean of the …nancial shock ( ) is set to
0:35 to match the debt over GDP ratio for the non …nancial business sector according to the data from the Flow
of Funds. The persistence of the …nancial shock equals 0.96 as in Liu et al. (2013).5 The payout cost parameter
( ) ; the standard deviation of the credit shock (
) and the investment adjustment cost parameter ( ) are
jointly calibrated to minimize the distance between the unconditional standard deviation of debt repurchase,
net equity payout, and investment produced by the model and those computed from the data. We conduct
some sensitivity analysis on these values in Section 7..
4.
Model’s Dynamics
In the model, …nancial ‡ows are linked to the real side of economy through di¤erent channels. On the one
hand, both the enforcement constraint and rigidities in …rms’ …nancial structures can amplify the e¤ect of
exogenous disturbances. On the other hand, the …nancial sector per se is a source of business cycle ‡uctuations
as exogenous variations in the loan-to-value (LTV) ratio have an impact on real variables. In this section, we
elucidate the e¤ects of these channels.
The enforcement constraint a¤ects capital and investment accumulation both in the short and in the longrun. It is straightforward to show that the steady state level of capital positively depend on the lagrange
multiplier on the credit constraint;
and on the LTV ratio,
kss
lss
=
"
1
"
1
(1
)
:
(1
)
#1 1
To understand the e¤ect of , it is useful to recall that in steady state:
=
(
(1
)
)+
:
In the model, the tax deductibility of interest payments from corporate earnings generates a preference of
debt over equity and makes the enforcement constraint binding in steady state. In an economy with higher
interest rate deductibility the shadow value of the constraint is higher; …rms accumulate more debt, pay higher
dividends and invest more in capital. A similar argument follows if the enforcement problem is less sever, i.e.
is higher.
5 For
the speci…cation of the collateral constraint as in (2) see Liu et al. (2013) Appendix ?? .
8
On the contrary, rigidities in the adjustment of sources of funds, ; distort …rms employment decisions only
in the short run:
M P L = M RS h
("
"
1)
t
d t Yt
i;
(5)
where the left hand side of the equation represents the marginal product of labor , M RS is the marginal
rate of substitution between leisure and consumption and the residual term is a measure of deviation from
optimality, i.e. a labor wedge.6 Equation (5) shows that in the presence of price stickiness (
frictions
dt
t
> 0), …nancial
enter the wedge, i.e. distort labor markets in the short run. Thus, the credit channel has a direct
e¤ect on labor demand even without postulating the need for working capital.
In the following, we shed further light on how …nancial distortions impact on the model’s dynamics. Figures
1 and 2 plots the impulse responses of some key variables to negative productivity and …nancial shocks in two
cases the benchmark model and a "frictionless" economy, i.e. an economy where there are no rigidities in …rms’
…nancial structure. In both …gures it is assumed that the monetary authority follows a simple Taylor type rule
as described in Eq. (4). In the frictionless economy
is set to zero and
= 0:00035.7 For this parameter
con…guration, changes in …rms’…nancial conditions have no e¤ects on the real sector, as made clear from Figure
2.
Figure 1 displays the e¤ects of a negative productivity shock. The …gure shows that when the initial driving
force of movements in economic activity is a non …nancial factor, the presence of a collateral constraint together
with rigidities in …rms’ …nancial structure ampli…es the initial e¤ect of the shock on output and economic
activity. This mechanism is in force in our model although its e¤ects are quantitatively limited.
Figure 2 depicts the impulse responses of some selected variables to a negative …nancial shock in the benchmark and the frictionless economy. If …rms can freely change their …nancial structure, they respond to the
deterioration in the credit market by cutting on equity payouts. Thus the credit shock has an impact on …nancial ‡ows, leaving the real sector una¤ected. In contrast, …rms cut on both employment and investment in
response to credit market disruptions when adjusting their capital structure is costly.
"
6 In steady state, M P L = M RS
: Monopolistic competion distorts the steady state of the model while …nancial frictions
[(" 1)]
do not enter the wedge.
7 The tax advantage on debt , ; is not set to zero for numerical reasons. The "frictionless" model still features a preference for
debt of equity, so that in steady state the borrowing constraint is binding and debt level is determined. However, the tax advantage
is now small enough to make …rms "almost" indi¤erent between debt and equity. In this model, productivity becomes the only
drive of business cycle ‡uctuations, as in a standard RBC model
9
5.
Optimal Simple Rules and Welfare
Our notion of optimal monetary policy is con…ned to the set of simple rules that maximizes agents’welfare, i.e.
the expectation of lifetime utility as of time t. Speci…cally, we focus on interest-rate rules that in addition to
in‡ation and output also respond to …nancial variables, such that,
1 + rt
1 + rss
where xt = fbt ; qt g and
x
y
yt
yss
=
ss
x
xt
xss
;
(6)
0. On methodological grounds we follow Schmitt-Grohe and Uribe (2007). To
assess the optimality of di¤erent rules based on welfare evaluations and to deal with the non-linearity induced
by the borrowing constraint, we solve for the recursive law of motion by relying on a second order approximation
around the non-stochastic steady state of the economy. Then, we conduct a grid search on the parameters in
Eq. (6) to maximize the asymptotic mean of agents’welfare.8
Table 3 (panel A) reports the coe¢ cients of the welfare-maximizing interest-rate rules and the resulting
welfare levels. To evaluate the performance of di¤erent monetary policy rules, we also compute consumptionequivalent welfare measures. Table 3, column 2 reports the welfare gains of responding to credit with respect
to alternative rules, i.e. the percentage increase in consumption,
a
; that a household would need under a set
of alternative rules in order to get the same unconditional expected utility as in the stochastic economy under
rule (i).9
Our main result is that the simple rule that achieves the highest welfare level features a moderate response
to in‡ation, a mute response to output and a small positive response to deviation of credit from the steady state
target (rule (i)). In contrast, responding to asset prices is welfare detrimental. Indeed, the optimal response to
asset prices in rule (ii) is nil. Notice that rule (ii) is equivalent to a constrained optimal rule that …xes
zero and reoptimizes over the other two coe¢ cients (
and
y ).
that, in the absence of a positive response to …nancial variables (
x
at
Thus, another way of reading the results is
b
=
q
= 0), the optimized interest-rate rule
requires a positive response to output and an aggressive response to in‡ation. Notice that the optimal response
to in‡ation takes the largest possible value in the grid.10
We also consider rules that respond to the growth in …nancial variables rather than to deviations from
steady state targets. The rule that targets credit growth features a positive response to output growth and
reacts aggressively to both credit growth and deviations of in‡ation from the steady state target (rule (iii)).
8 We
employ a three dimensional grid. The parameters ranges are [1.1,4] for
, [0,2] for y , and [0,2] for x . The grid step for
each parameter is 0.1.
P1 t
a
a
9 Thus, a satis…es: W = E
U (ca
); lta ), where ca
t (1 +
t and lt denote consumption and hours under the alternative
t=0
interest-rate rule and W the unconditional level of welfare achieved under the optimized rule (i).
1 0 Removing the upper bound on the in‡ation response parameter would imply a much larger response to in‡ation, though,
without yielding signi…cant improvements in terms of welfare.
10
However, responding to changes in the level of credit yields higher results in terms of welfare with respect to an
interest-rate response to changes in credit growth. In line with the results presented above, responding to asset
prices is not optimal (rule (iv)).
We compute the welfare gains of the best optimized rule (rule (i)) with respect to non-optimized rules.
First, we consider a rule that deviates from the optimal response to credit while maintaining the coe¢ cients
of in‡ation and output at their optimal levels (rule (v)). Then, we consider two other cases: standard values
under a Taylor-rule (see rule (vi)); a policy regime that completely stabilizes in‡ation (rule (vii)). All three
experiments show that the cost of not responding to credit can be large, especially if monetary policy has a
positive response to output (see rule (vi)) or if in the absence of a response to credit, it does not react aggressively
to in‡ation (rule (v)). Finally, in our framework, a complete stabilization of in‡ation is also costly.
5.1
Stabilization E¤ect
We now investigate the stabilization e¤ ects of the welfare-maximizing rule. Table 4 panel (A) reports the standard deviations of some key variables under the optimized rule (i), whereas panel (B) reports the di¤erences
with respect to the standard deviations implied by alternative interest rate policies. Overall, an optimal response to the deviation of credit from the steady state target stabilizes the economy. The stabilization e¤ect
is particularly pronounced in …nancial variables. The largest reduction in volatility is in terms of the debt
repurchase. The optimal interest-rate rule also delivers lower variability of consumption and investment. In
contrast the volatility of output is somewhat larger under the rule that optimally responds to credit. This is
mainly due to the larger volatility of hours worked. The same result holds for in‡ation. Thus, for such a policy
to be welfare improving it means that the welfare gains driven by the stabilization of …nancial variables more
than compensate the costs of a higher degree of in‡ation and output volatility.
6.
Financial Shocks and Frictions
6.1
On the Importance of Financial Shocks.
The results presented in the previous section show that an interest rate response to credit delivers non-negligible
gains in terms of welfare. The analysis conducted in this paper does not aim to design interest-rate rules that
are optimal conditional on some particular shocks but, instead, is based on the assumption that various sources
of ‡uctuations can a¤ect the economy. Hence, we do not target the complete smoothing out of either …nancial
shocks ( t ) or productivity shocks (zt ). However, we are interested by the relationship between the welfare
gains of the best welfare-maximizing rule (rule (i)) and the occurrence of …nancial shocks in the economy.
11
Table 5 evaluates the performance of di¤erent interest-rate rules under three cases: only …nancial shocks, only
productivity shocks, both shocks. The welfare gains of the optimal rule with respect to alternative rules are
evaluated using the same metric described in Section 5..
Under the occurrence of …nancial shocks only (column a), an interest-rate response to credit generates welfare
gains of similar magnitude as in the benchmark case (column c). In contrast,when productivity shocks are the
only source of business cycle ‡uctuations (column b), the welfare gains of an interest rate response to credit are
substantially reduced. When the economy is only hit by productivity shocks, the welfare gains of the optimal
rule over a strict in‡ation targeting regime that completely stabilize in‡ation at all times also turn out to be
negligible. Thus, we can conclude that the welfare gains of an interest-rate response to credit growth are mainly
linked to the occurrence of …nancial shocks.
6.2
Frictionless Economy
To get further insights, we consider the special case in which the …nancial shock has no e¤ects on the real sector.
As shown in Section 4., when the cost of equity payout ( ) and the tax bene…t of debt, ( ) are close to zero,
the economy is almost equivalent to a frictionless economy. See Figures 1 and 2.
Table 3 (panel B) reports the reports the coe¢ cients of the welfare-maximizing interest-rate rules in the
frictionless economy. In this special case, the simple rule that achieves the highest welfare level features an
aggressive response to in‡ation and a mute response to both output and credit (rule (i.a)). Comparing such the
optimized interest-rate rule with a policy that completely stabilizes in‡ation we do not …nd signi…cant di¤erences
(rule (iv.a)). In contrast responding to other variables, such as output or credit, is welfare detrimental. Thus,
in the absence of real e¤ects of …nancial shocks responding to …nancial variables is not optimal.
7.
Key Modelling Features: Robustness
Two modelling features make our framework di¤erent from most New Keynesian models: (1) rigidities in the
substitutability between debt and (2) the occasionally binding nature of the borrowing constraint. In the
following, we conduct sensitivity analyses with respect to these two features as summarized by the payout cost
parameter ( ) and the penalty term parameter (
0 );
respectively.
First, we investigate how the degree of ‡exibility that …rms have in adjusting their capital structure a¤ects
the results. We compare the baseline case ( = 1:7463) with two alternative values of
= f0:5; 2:5g: A higher
indicates a higher cost of new equity issuance and, thus, lower ‡exibility in the choice of the …rms’…nancial
structure.11 Table 6 reports the coe¢ cients of the welfare-maximizing interest-rate rules in economies featuring
1 1 Notice
that
does not a¤ect the deterministic steady state of the model and, thus, the welfare level in the non-stochastic
12
alternative degrees of ‡exibility in the substitution between debt and equity. Further, it also reports the welfare
gains of such a rule with respect to a standard Taylor rule and a strict in‡ation targeting regime.
As for the optimized rule, we …nd that a lower
imply a larger value of the optimal response to in‡ation.
However, a higher degree of …nancial rigidity, does not a¤ect the optimality of responding to credit. In contrast,
a higher
does not have any e¤ect on the optimimized coe¢ cients of the rule. The welfare levels implied by
the optimized rule are, however, larger for higher . Most importantly, in economies with a lower degree of
‡exibility in the …nancing of …rms, the welfare gains of responding to credit are more sizeable.
In the baseline case, we use a barrier approach to deal with the occasionally binding constraint. Thus, to
ensure that the agents never borrow more than the debt limit, we introduce a large cost in terms of utils. In the
following, we consider the case in which the cost of violating the limit is reduced, though still large. Reducing
the penalty term,
0;
has no substantial e¤ect on the optimality of the response to the variables considered in
the rule. The only di¤erence with the benchmark calibration of
0
is a somewhat more aggressive response to
in‡ation. Note that a higher penalty cost of deviating from the credit limit implies larger gains from responding
to credit. See Table 6, Panel (B).
8.
Insights from the Collateral Constraint
In this section, we conduct sensitivity analyses of our results with respect to di¤erent speci…cations of the
collateral constraint (Eq. (2)). First, following most of the credit friction literature, we assume that the
collateral constraint is always binding.12 Secondly, we consider a version of the collateral constraint without
asset-price feedback e¤ects. In each of the alternative speci…cations the payout cost parameter ( ) ; the standard
deviation of the credit shock (
) and the investment adjustment cost parameter ( ) are calibrated to match
the same moments as in the benchmark model. The results below show that an interest-rate response is optimal
under the two alternative speci…cations of the collateral constraint. However, both the occasionally-binding
nature of the collateral constraint and the asset price feedback e¤ects are important features to assess the
welfare gains of responding to credit deviations from the steady state target.
8.1
Binding Collateral Constraint
A common practice in the DSGE literature is to assume that the …nancial constraint is always binding. In the
analysis above, we depart from this assumption by allowing agents to borrow less than the credit limit in a
steady state is unchanged.
1 2 See, among others, Iacoviello (2005) and Jermann and Quadrini (2012).
13
neighborhood of the steady state. Then, we conduct welfare analysis in a version of the model where Eq. (2)
holds with equality at any time.
The optimality of responding to credit is robust to the alternative assumption of a collateral constraint that
binds at any time (see Table 7, Panel (A)). Regarding the optimized coe¢ cients, the response to credit is also
somewhat larger. Additionally, the interest rate optimally responds to output, and the response to in‡ation
is more aggressive. The response to in‡ation takes the largest possible value in the grid. However, in the
presence of an always binding credit constraint, responding to credit generates somewhat lower welfare gains
compared to alternative policy regimes, such as a standard Taylor-rule and a strict in‡ation targeting regime.
Thus, neglecting the occasionally binding nature of the borrowing constraint underestimate the e¤ectiveness of
responding to credit in improving the households’welfare.
8.2
Asset Price Feedback E¤ect
To investigate the implications for optimal policy of the dynamic interaction between credit limits and asset
prices, we solve a version of the model in which the valuation of the borrowers’current capital holdings is done
at steady-state prices, so that expectations about future prices do not enter the collateral constraint:
bt
(1 + rr )
qss kt ;
where the subscript ss refers to steady state values. Table 7 , Panel (B) reports the coe¢ cients of the optimized
rule that allow for a response to credit.
In the absence of an asset-price feedback e¤ect in the collateral constraint, the welfare maximizing interestrate rule requires a much larger response to in‡ation, whereas the optimal response to credit is only slightly
larger. However, the welfare gains of such a rule with a strict in‡ation targeting regime are less sizeable.
Thus, the dynamic e¤ect of asset prices on the borrowing limit is important for capturing the welfare gains of
responding to credit.
9.
Conclusions
Our paper investigates optimal interest-rate rules in a model that features debt and equity …rms’ …nancing
and nominal price rigidities. We assume that …rms face two types of …nancial frictions. First, …rms’ability to
borrow is limited by a collateral constraint. Second, the sources of funds can only be adjusted slowly, i.e. equity
payout is subject to quadratic costs. The enforcement constraint distorts capital accumulation, while rigidities
in …rms’…nancial structures have short-run e¤ects on the labor wedge. Further, the …nancial sector is a source
14
of macroeconomic ‡uctuations. Relying on this framework, we evaluate alternative policy regimes in terms of
welfare.
Our …ndings show that an interest-rate rule that responds directly to credit is welfare maximizing. We show
that most of the gains from responding to this …nancial variable are due to the occurrence of …nancial shocks.
15
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17
A
First Order Conditions
1.1
Firm
E
1
Yk;t+1
t+1
1
d;t+1
1 = Et
wt "1
Yl;t = h
("
1
"
1)
t
d;t Yt
1 t+1
" Yt+1 (i)
d;t
t+1 qk;t+1
+ (1
i
)
qk;t+1
=
d;t+1
qk;t
t t qk;t+1
d;t
%2 (It+2 ; It+1 ) + qk;t %1 (It+1 ; It )
d;t+1
Et
d;t Rt
+
t+1
d;t+1 t+1
Et
t+1
Yt +
Pt+1
Pt
bt+1
Rt
1 Yt+1
bt
Pt+1
Pt
w t lt
dt
=
dt+1
t (d)
t
d;t
It
bt+1
1 + rt
t qk;t+1 kt
Rt t
=1
1 + rt
Pt
Pt 1
'
2
1 Yt
Pt
Pt 1
Pt
+
Pt 1
d;t t
2
1
Yt = 0
0
Yt = zt kt lt1
where
1.2
t
is the lagrange multiplier associated to the demand for the …rm’s product.
Household
Et
Uc;t+1
t+1
Ul;t
Uc;t
Uc;t
(1 + rt )
= Uc;t wt
Uc;t+1 (dt+1 + qt+1 )
=
Et
qt
=
18
B
Steady State
=
0
qk
=
1
d
=
1
=
1
l
= :3
=
1+r
=
R
=
=
"
1 + r (1
(
(1
=
k
l
ss
(1
)
)+
)
(1
k
l
)
"
k=
1
"
k
l
F =
#
)
1
"
1
w = (1
)
l
k
l
l
b = k (1 + r)
c=F
d=c+
1
R
q=
1
19
k
1 b
d
wl
1
1
Tables and Figures
Table 1: Parameters’Values
v
Production technology
.36
Discount factor
.9825
Utility parameter
"
Elasticity of substitution
6
k
Investment adjustment costs
0.268
1.563
z
Technology shock, persistence
.95
Depreciation rate
0.025
z
Technology shock, volatility
.0047
Tax advantage
.35
Financial shock, persistence
.96
Equity payout costs
1.746
Financial shock, volatility
.0136
Price adjustment costs
35.18
Financial shock, mean
.35
Table 2: Target moments used in the calibration
Data
Model
Std
Equity Payout
GDP
1.39
1.39
Std
Debt Repurchase
GDP
1.88
1.88
5.72
5.72
Std(log(Investm ent))
Std(log(GDP))
20
−3
−3
−3
Output
x 10
0.5
−4
Debt Repurchase
x 10
4
−4
Inflation
x 10
5
Policy Rate
x 10
4
−3.5
Benchmark
Frictionless
0
3
−0.5
2
3
−4
2
−4.5
−1
1
−5
−1.5
0
−5.5
−2
−1
1
0
−1
−2
−6
0
5
−3
0.5
10
15
20
−2.5
5
−3
Hours worked
x 10
0
−2.7
10
15
20
−2
0
5
Consumption
x 10
10
15
20
−3
0
5
−3
Investment
−0.002
0.5
10
15
20
15
20
Equity Payout
x 10
−0.004
−2.8
0
0
−0.006
−2.9
−0.5
−0.008
−0.5
−3
−0.01
−1
−3.1
−1
−0.012
−3.2
−1.5
−0.014
−3.3
−1.5
−0.016
−2
−2
−3.4
−2.5
0
5
10
15
20
−3.5
−0.018
0
5
10
15
20
−0.02
0
5
10
15
20
−2.5
0
5
10
Figure 1: Responses to a negative technology shock: benchmark vs frictionless model
21
−3
0
Output
x 10
−3
Debt Repurchase
0.005
0.5
−3
Inflation
x 10
0.5
0
−1
Policy Rate
x 10
0
0
−0.005
−2
−0.5
−0.5
−0.01
−1
−3
−0.015
−1
−1.5
−4
−0.02
Benchmark
Frictionless
−5
−0.025
−0.03
0
5
−3
2
−2.5
−2
−6
−7
−2
−1.5
10
15
20
−0.035
0
5
−3
Hours worked
x 10
−3
3
10
15
20
−2.5
0
5
Consumption
x 10
10
15
20
−3.5
0
5
Investment
10
15
20
15
20
Equity Payouts
0.01
0.005
0
0
−0.01
−0.005
−0.02
−0.01
−0.03
−0.015
−0.04
−0.02
−0.05
−0.025
2.5
0
2
−2
1.5
1
−4
0.5
−6
0
−0.5
−8
−1
−10
−1.5
−12
0
5
10
15
20
−2
0
5
10
15
20
−0.06
0
5
10
15
20
−0.03
0
5
10
Figure 2: Responses to a negative …nancial shock: benchmark vs frictionless model
22
Table 3: Optimized Interest-Rate Rules
Welfare Measures
Level
Welfare Gains (
(A) Financial Frictions
Optimized Interest rate Rules
(i)
= 1:7; y = 0; b = 0:1
(ii)
= 4; y = 0:3; q = 0
(iii)
= 4; y = 0:6; b = 1:5
(iv)
= 4; y = 1:3; q = 0
Ad Hoc Rules
(v)
(vi)
(vii)
= 1:7; y = 0
= 1:5; y = 0:5
Strict In‡ation Targeting
47:2512
47:3582
47:3493
47:3659
0:1874
0:1718
0:2007
47:3892
47:4688
47:3597
0:2414
0:3803
0:1899
(B) Frictionless Economy
Optimized Interest rate Rules
(i.a)
= 4;
Ad Hoc Rules
(ii.a)
(iii.a)
(iv.a)
y=
= 1:7;
= 1:5;
0;
b=
0
47:965
b=
0:1
=
0:5
y
Strict In‡ation Targeting
48:0017
48:2446
47:9649
0:06420
0:48810
0:00018
Welfare gains of the best optimal simple rule (i) w.r.t. alternative rules:
23
a
.
a
)
Table 4: Stabilization E¤ect
(A) Std.
(B) Di¤erences w.r.t. Alternative Rules
rule(i)
rule(ii)
rule(v)
rule(vii)
rule(vi)
0.53
0.93
0.51
1.88
1.04
0.19
0.95
4.59
0.22
-0.16
0.25
-0.25
-0.35
-0.25
0.11
0.13
-0.18
-0.05
-0.16
0.25
-0.25
-0.35
-0.25
0.11
0.13
-0.18
-0.05
-0.13
0.24
-0.23
-0.3
-0.24
0.19
0.07
-0.45
0
-0.34
0.14
-0.37
-0.04
-0.3
-0.25
0.43
0.04
-0.33
Consumption
Hours worked
Asset prices
Debt repurchase
Equity payout
In‡ation
Output
Investment
Policy rate
Table 5: Financial Shocks and Optimal Interest-Rate Rules
Welfare Gains a
Financial shocks Productivity shocks
(ii)
= 4;
y=
(iv)
= 1:5;
(v)
0:3;
b=
=0
Both shocks
0.18659
0.00076
0.18735
0.13920
0.24144
0.38030
= 1:7
0.24813
-0.00670
0.24143
In‡ation Targeting
0.19865
-0.00875
0.18992
a
y=
0:5
q
= Welfare gains of the best optimal simple rule (i) w.r.t. alternative rules.
24
Table 6: Robustness: Degree of Financial Flexibility and Penalty function
Welfare levels and gains
(A) Degree of Financial Flexibility
= 0:5
Optimized Rules
Welfare level
y
2:5
0
= 2:5
b
0:1
-47.3104
(B) Penalty Parameter
y
1:7
0
0=
b
0:1
y
1:8
-47.2158
Welfare gains
= 1:5;
0=
b
0:1
y
1:8
0
75
b
0:1
-47.2926
-47.2748
a
0:5
0.2436
0.3076
0.2880
0.3305
In‡ation Targeting
0.0241
0.1273
0.0851
0.1350
a
y=
0
50
= Welfare gains of the best optimal simple rule (i) w.r.t. alternative rules.
25
Table 7: Alternative Model Speci…cations and Optimal Interest-Rate Rules
Welfare levels and gains
Binding Constraint
Optimized Rules
4
Welfare level
y
b
0:2
0:2
y=
0:5
Optimal Taylor
y
4
0.2853
0.0713
0
0.0120
26
b
0:2
a
b
0:4
0
-47.3153
0.222
0.08936
In‡ationTargeting
a
y
2:7
-47.3686
Welfare gains
=1.5
No Financial accelerator
y
4
0:3
0.0691
b
0