Finance as a barrier to entry:
U.S. bank deregulation and volatility∗
Viktors Stebunovs†
Boston College
November 10, 2006
Abstract
Banks are the largest suppliers of debt capital to small firms, which produce half of U.S. output.
In the data, lower bank concentration and branching deregulation are associated with more firms in
operation and smaller average firm size. The period of drastic bank deregulation, which started in
1977, coincides with a decline in firm level and aggregate volatility. I examine whether deregulation
can account for this volatility decline by reducing bank local monopoly power. In my dynamic,
stochastic, general equilibrium model bank market power determines firm concentration. The model
predicts an increase in the number of firms and a decrease in firm size after deregulation. Over the
business cycle, weaker banking competition implies more vigorous firm entry, more countercyclical
firm markups, and stronger substitution effects in labor supply decision. As a consequence, firm entry
and output, labor supply, consumption, investment, and aggregate output are all less volatile after
deregulation.
∗ I thank my advisors, Fabio Ghironi, Peter Ireland, and Matteo Iacoviello for advice and support; Ingela Alger, Fabio
Schiantarelli, Susanto Basu, Andrea Raffo, Jonathan Willis, Jordan Rappaport, Giovanni Lombardo, John Leahy, Stephanie
Schmitt-Grohe, and Phillip Strahan for helpful conversations. I also thank participants in the thesis and R@BC workshops
at Boston College, and in seminars at the Monetary Policy Strategy division at the ECB and at the Economic Research
department at the Federal Reserve Bank of Kansas City. I gladly acknowledge the hospitality of Economic Research
department at the FRB of Kansas City (Summer 2006) and the the Monetary Policy Strategy division at the ECB (Summer
2005).
† Department of Economics, Boston College, 140 Commonwealth Avenue, Chestnut Hill, MA 02467, email address:
[email protected], the URL: <www2.bc.edu/~stebunov>
1
1
Introduction
Small firms, that produce half of U.S. economy’s output, tend to depend on local external sources of
finance.1 Commercial banks are the largest suppliers of debt capital to these firms.2 The empirical
evidence shows that in U.S. local markets with concentrated banking, potential entrants face greater difficulty gaining access to credit than in markets where banking is more competitive. For example, Cetorelli
and Strahan (2006) find that lower local bank concentration and looser restrictions on geographical expansion are associated with more firms in operation and smaller average firm size.3 Hence, the exercise of
monopoly power by banks has the potential to influence a large fraction of U.S. GDP through bank-firm
interactions. In turn, I focus on the bank market power as a determinant of firm concentration and its
implications for business cycle dynamics in general equilibrium framework.
U.S. banking system was once extremely fragmented. Every state in the country barred banks from
other states, so instead of one national banking system there were 50 small banking systems, one per
state. Most states also prohibited branching into other cities within the state, so there were countless
small banking systems, one per city (Morgan et al, 2004). A period of dramatic state-level deregulation
started in 1977. The deregulation of restrictions on banks’ ability to expand across local markets was
completed with the passage of the Riegle - Neal Interstate Banking and Branching Efficiency Act in 1994.
Since then it becomes increasingly less plausible to view banking markets as local, both because of the
deregulation and the onset of new lending technologies that allow long distance lending (Cetorelli and
Strahan, 2006).
The deregulation of restrictions on bank expansion, both within and across states, has been shown to
limit bank market power. Jayarante and Strahan (1998) and Dick (2006) find that loan prices and bank
spreads declined after deregulation. Black and Strahan (2002) find that the rate of new incorporations increased following deregulation of branching restrictions, and that deregulation reduced the negative effect
of concentration on new incorporations. They also find the formation of new incorporations increased as
1 The research on bank market power suggests that the relevant geographical market for banking services, especially for
small firms or potential entrepreneurs, is local. See, for example, Berger et al (1999).
2 Based on the Survey of Small Business Finances, Berger and Udell (1998) show that commercial banks provide on
average over 18% of total equity plus debt and other financial intermediaries provide additional 6%. There are considerable
differences across firms though. For example, commercial banks alone provide over 30% of total equity plus debt for 3-4
year old firms. Turning to particular kinds of credit, commercial banks supply more than 80% of lending in the credit line
market and more than 50% in other markets, such as commercial mortgages and vehicle, equipment, and other loans (U.S.
Small Business Administration).
3 They find no effect of changes in banking competition, however, on the largest firms, which is reasonable given that
these firms have access to nationwide securities markets. The non-financial sector is represented by a panel data set from
the County Business Patterns of manufacturing establishments in operation across U.S. states between 1977 and 1994.
2
the share of small banks decreased, suggesting that diversification benefits of size outweighed the possible comparative advantage small banks might have had in forging lending relationships. Correa (2006)
finds that the interstate bank integration decreased financing constraints, with small firms benefiting the
most.4
In what follows I concentrate on privately held firms, that tend to depend on local external sources of
finance.5 The number of privately held firms increased by over 34% between 1980 and 2000 (Davis et al,
2006). Their share of employment in total employment increased by nearly 3 percentage points to 74%.
The average firm size, measured by average firm employment scaled by GDP, declined by about 36%.6
Contrary to the earlier studies, that focused solely on publicly traded firms, recent research finds that
U.S. firms became significantly more stable in the past 25 years.7 Davis et al (2006) find opposing trends
in the volatility of publicly traded and privately held firms. Their results show that while the rise in
volatility among publicly traded firms is significant, it is not large enough to offset the decline in volatility
among privately held firms, which is of the magnitude of either 18% or 50% depending on the measure
used.8 An important factor in the decline in volatility is the slow down in the pace of business entry
and exit by more than 40%. The decline in firm level volatility coincides with the ”great moderation” in
aggregate volatility, see Table 6 in Appendix. The decline in volatility of GDP can be traced to a number
of causes, including the decrease in volatility of personal consumption expenditures and non-residential
fixed investment. The decline in volatility of total private hours and in net firm entry is also remarkable.9
Precisely how financial deregulation affects volatility, that is, by what channel, is far from obvious.
In this paper I investigate just one possible channel linking the reduction in bank monopoly power to
economic fluctuations. I examine whether Cetorelli and Strahan (2006) finding can be explained in
general equilibrium framework, whether financial deregulation can account for the decline in firm level
and aggregate volatility by reducing bank local monopoly power.10
4 This
paper uses data on publicly-traded firms in the U.S. though.
realize that there are few large privately held firms in U.S. economy, for example family-controlled S.C. Johnson Co.,
that compete on national rather than local market and have access to national securities market. Nevertheless, small firms
with fewer than 500 employees represent 99.7% all employer firms, employ half of all private sector employees, pay more
than 45% of total U.S. private payroll, have generated 60 to 80% of net new jobs annually over the last decade, and produce
more than 50% of non-farm private GDP (U.S. Small Business Administration).
6 The average firm size, measured by average firm employment, increased from 14.6 to 17.7 employees (Davis et al, 2006).
The average firm size scaled by U.S. population declined by 2.7%.
7 Comin and Mulani (2003) or Comin and Philippon (2005) report the rise in publicly traded firm volatility.
8 The first measure includes short lived firms, the second measure includes firms with the lifespan of 10 years or more.
9 Net firm entry is defined as the difference of new business incorporations and business failures. See Table 7 in Appendix
for details.
1 0 Philippon (2003) stresses the role of competition in goods market behind the increase in volatility for publicly traded
firms. In his model, an unexplained change in competition pressure leads to a higher frequency of price adjustments and
hence higher sales volatility. In turn, more frequent price adjustments dampen the economy response to aggregate demand
5I
3
I develop a flexible-price, dynamic, stochastic general equilibrium (DSGE) model of the macroeconomy
with a monopolistic banking sector. The model is based on the framework of Ghironi and Melitz (2005)
and Bilbiie et al (2006), where monopolistic firm entry is subject to sunk cost and time-to-build lag.
The number of firms is an endogenous state variable, consistent with the notion that the number of
producing firms is fixed in the short run.11 In the model investment is accounted for by the creation
of new firms. The model incorporates the premise, proposed by Cestone and White (2003), that entry
deterrence takes place through financial rather than product markets. In the model banks with market
power erect a financial barrier to firm entry to protect the profitability of their existing borrowers. The
bank concentration is exogenous to the business cycle.12
The model predicts that bank deregulation generates an increase in the long run number of firms, a
decrease in firm size, an increase of the investment share in the economy, an increase in labor supply, and
a decrease in firm and bank markups. The model generates procyclical firm entry and countercyclical
firm and bank markups.13 Over the business cycle, driven by a favorable aggregate productivity shock,
bank monopoly power implies more vigorous firm entry, more countercyclical firm markups, and stronger
substitution effects (and weaker income effects) in labor supply decision.14
As a consequence, firm
entry and output, labor supply, consumption, investment, and aggregate output are less volatile after
deregulation. I do not attempt to replicate exactly the levels of second moments, just the changes in
second moments. The channel identified in the context of the tractable DSGE model appears to be
sufficiently powerful to merit serious empirical investigation in future research.
I emphasize that I do not discount the role of other explanations of the volatility decline observed in
the data, such as the run of good luck in stochastic shocks (Stock and Watson, 2002). There might be
alternative structural explanations of the decline in firm and aggregate volatility as well. For example, an
alternative channel might work through the interplay of a collateral requirement for firm start-up loans
and labor supply.15 Financial deregulation might lead to a decline in labor supply volatility by lowering
the collateral requirement, and hence lead to a decline in firm level and aggregate volatility.
shocks. Having the business cycle driven by demand shocks is crucial in his setup, as nominal rigidities tend to dampen
supplies shocks.
1 1 This is in contrast to other recent contributions, such as Comin and Gertler (2006) and Jaimovich (2006), whose entry
mechanisms allow instantaneous variation in the number of producing firms.
1 2 As shown in Stebunovs (2007), there is some indication that the bank market structure became endogenous to the
business cycle. In the late 1970s bank branch movement turned from acyclical to countercyclical.
1 3 In the data firm entry is procyclical, see Chatterjee and Cooper (1993) or Devereux et al (1996), and bank loan markups
are countercyclical, see Dueker and Thornton (1997).
1 4 Domowitz et. al. (1988) document more countercyclical markups in concentrated industries.
1 5 This channel is similar to the one studied by Campbell and Hercowitz (2006) in the case of household borrowing.
4
The remainder of the paper is organized as follows. Section 2 presents the benchmark model. Section
3 discusses some key properties of the model and solves for its steady state. Section 4 shows dynamic
properties of the model for transmission of an aggregate productivity shock by computing impulse responses and second moments. Section 5 discusses the extended model, computes impulse responses and
changes in second moments, and suggests the complementary collateral channel. Section 6 concludes. A
section in Appendix gives more details on the effects of branching deregulation, including the effects on
loan prices, deposit rates, and bank spreads.
2
Benchmark model
There are three classes of agents in the economy: households, banks, and firms. There are several
exogenously given locations with a number of banks and a continuum of firms at each of them.16 Each
location bears some similarity to Salop (1979) circle commonly used in the banking literature. Figure 1
illustrates the representative location setup.
i th bank
*
*
ω th firm
)
local
goods
market
*
*
Figure 1: Representative location with H = 4 banks and a local goods market.
Each firm is monopolistic, produces one consumption variety, competes in a local market, has no
collateral to pledge except a stream of future profits, and its entry is subject to a sunk entry cost. The
model reflects the notion that small firms tend to patronize a local bank.17 Unspecified financial frictions
1 6 In the model the boundaries of product markets and lending markets coincide. However, in reality some larger firms
may span multiple banking markets. In such cases, a bank could still have an impact on entry within its area of influence.
1 7 This assumption rules out bundling the entry loan amount over several banks, and thus precludes risk sharing among
5
force a prospective entrant to borrow the amount necessary to cover the sunk entry cost from a nearby
bank rather than to raise funds directly in an equity market. I assume that sufficiently high ”switching”
cost inhibit prospective entrants from borrowing from a distant bank at the same location.18 Before
deregulation borrowing at a different location is prohibited altogether. Firm entry reduces the stream of
future profits of both incumbents and entrants and thus the amount pledgeable for entry loan repayments.
Each bank, being a local monopolist, is able to extract all the profits from a prospective entrant, holds
a portfolio of firms and decides on the number of loans to be issued (that is, on the number of entrants).19
Each bank trades the increase in revenue from expanding its firm portfolio (portfolio expansion effect)
against the decrease in revenue from all firms in its portfolio due to stronger firm competition (profit
destruction effect). The profit destruction effect gives rise to credit rationing on the extensive margin
as not all of the prospective entrants will be funded. Thus, there is an intrinsic inefficiency built into
the model due to the presence of monopolistic banks.20 Each bank supplies real one-period deposits to
households in a perfectly competitive national market. The bank then uses the deposits to fund firm
entry. Thus, the cost that each bank faces is the deposit interest rate.
Since the completion of financial deregulation in 1994, it becomes increasingly less plausible to view
banking markets as local. Banks’ ability to expand across local markets and new technologies, that allow
banks to lend to distant borrowers, limited incumbent banks’ local monopoly power.21 Consequently,
I model bank deregulation as lifting the restriction on borrowing from a bank at a different location.
The number of banks in the economy might stay the same or decrease. However, the number of banks
represented locally increases. In what follows, for expositional simplicity, I present the economy with one
location only.22
banks. The bundling might function similarly to loan syndication that became widespread in the early 1990s.
1 8 Modelling switching costs explicitly is not necessary. I assume that firms borrow only once to cover the entry cost.
Banks are symmetric, price entry loans the same way, there is no room for arbitrage and hence entry loan refinancing is not
possible.
1 9 Banks compete in the number of entrants in Cournot fashion as in the static partial equilibrium model of GonzalezMaestre and Granero (2003).
2 0 If one interprets the number of firms as the number of production lines in the economy, then a bank might be thought as
of a multi-production line company that produces a set of goods that compete within this set and also with goods produced
by other multi-production line companies. Then each multi-production line company internalizes only its own ”product
cannibalization.”
2 1 Black and Strahan (2002) argue that after deregulation, the effects of concentration ought to have been mitigated by
the threat of entry. That is, banking concentration no longer signals market power when barriers to entry from regulations
have been eliminated. And, in fact, they find that the effect of concentration on the rate of creation of new incorporations
does fall significantly with deregulation.
2 2 I conjecture that the predictions will remain the same in the multi-location model.
6
2.1
Households
The economy is populated by a unit mass of atomistic households. All contracts and prices are written
in nominal terms, prices are flexible, and money is just a unit of account for contracts. Each household
supplies l units of labor inelastically and maximize expected intertemporal utility from consuming the
basket C,
Et
∞
X
β s−t
s=t
Cs1−γ
1−γ
where β ∈ (0, 1) is the discount factor and γ > 0 is the inverse of the intertemporal elasticity of substitution, subject to a budget constraint.
Households enjoy variety. Households consume the basket of goods at time t, Ct , defined over a
continuum of goods Ω,
Ct =
µZ
ct (ω)
θ−1
θ
ω∈Ω
dω
θ
¶ θ−1
,
where θ > 1 is the symmetric elasticity of substitution across goods. At any given time t, only a subset
of goods Ωt ⊂ Ω is available. Let pt (ω) denote the nominal price of a good ω ⊂ Ωt . The consumption
based price index is then given by
Pt =
µZ
pt (ω)1−θ dω
ω∈Ωt
1
¶ 1−θ
,
(1)
and the household’s demand for each variety ω is
ct (ω) =
µ
pt (ω)
Pt
¶−θ
Ct = (ρt (ω))−θ Ct ,
(2)
where ρt (ω) = pt (ω)/Pt is the relative price of variety ω.
Households hold two types of assets: shares in a mutual fund of H banks, st , and one-period deposits,
Bt . The mutual fund pays a total profit in each period (in units of currency) equal to the total profit
P
of all banks, Pt i∈H π t (i), where πt (i) denotes the profit of bank i. During period t, the representative
household buys st+1 shares in the mutual fund of H banks. The date t price in units of currency of a
claim to the future profit stream of the mutual fund of H banks is equal to the nominal price of claims
P
to future bank profits, Pt i∈H vt (i), where vt (i) is the price of claims to future profits of bank i. Hence,
7
the period budget constraint in units of consumption is:
Bt + st
X
vt (i) + Ct = (1 + rt−1 )Bt−1 + st−1
i∈H
X
(π t (i) + vt (i)) + wt l,
(3)
i∈H
where rt−1 is the consumption based interest rate on deposits between t − 1 and t (known with certainty
as of t − 1), and wt is the real wage.
The Euler equations for deposits and share holdings are, respectively:
1 = β(1 + rt )Et
and
vt = βEt
where vt =
P
i∈H
vt (i) and πt+1 =
P
"µ
i∈H
Ct+1
Ct
"µ
¶−γ
Ct+1
Ct
¶−γ #
,
#
(π t+1 + vt+1 ) ,
(4)
πt+1 (i). Forward iteration of the Euler equation for shares
holdings gives the value of the mutual fund, vt , in terms of a stream of bank profits, π t .
2.2
Firms
There is a mass of monopolistic firms, Nt , in each period t; Nt is the mass of the set Ωt ∈ Ω. Each firm
produces one different variety, ω ⊂ Ω, with a linear production function,
yt (ω) = Zt lt (ω)
where Zt is exogenous aggregate productivity, and lt (ω) is labor demand. The unit cost of production
(marginal cost), in units of the consumption good is wt /Zt . Exogenous aggregate productivity follows an
autoregressive process of order one, AR(1), with the persistence parameter ϕZ .
Each firm ω faces demand given by equation (2) and sets its price in a flexible fashion as a constant
markup over marginal cost. In units of consumption, firm ω’s price is
ρt (ω) =
wt
θ wt
= µF .
θ − 1 Zt
Zt
(5)
where ρt (ω) is the relative firm ω price, and µF = θ/ (θ − 1) is the firm markup over the marginal cost.
8
The period profit in units of consumption is given by
dt (ω) =
1
ρ (ω)1−θ Ct .
θ t
Firm prices, quantities, and profits follow from the post entry firm’s problem after imposing symmetry.
There are no idiosyncratic shocks, all firms face the same marginal cost and the same demand. Hence,
equilibrium prices and quantities are identical across firms: pt (ω) = pt , ρt (ω) = ρt , lt (ω) = lt , dt (ω) = dt .
The firm price under symmetry is such that:23
1
ρt = Nt θ−1 .
An increase in the number of firms implies necessarily that the relative price of each good increases.
When there are more firms, households derive more welfare from spending a given nominal amount,
ceteris paribus, the price index decreases, and the relative price of each good must rise.
A potential entrant faces a sunk entry cost and has to borrow from a bank to cover this cost. An
entrant can pledge up to dt in entry loan repayments post entry in each period t,
dt =
1 1−θ
1 Ct
Ct =
.
ρ
θ t
θ Nt
(6)
Since the bank has all the bargaining power, it sets the periodic entry loan repayment at dt to extract
all the profit, and the entrant accepts that.24 Entrants are sufficiently small and take the aggregate
consumption, Ct , as given. Hence, the expression (6) yields an inverse relationship between the mass of
incumbent firms in the economy, Nt , and the loan repayment, dt . The resulting firms’ willingness to pay
for entry depends on the mass of firms.
2 3 This
equation follows from the price index under symmetry, see the equation (1).
modelling strategy precludes interpreting the financial contract as debt, as the entry loan repayments are not firm
state dependent. Although the assumption that banks have bargaining power and are able to extract all the profit may be
unrealistic, it simplifies the model solution substantially. It is not necessary to keep track of outstanding loan amounts for
each firm generation, and firms of different vintages can be treated equally. This modelling strategy also allows the model
to reproduce the apparent absence of pure profits in U.S. industries despite the presence of market power (even in the short
run).
2 4 The
9
2.3
Banks
The fixed number of banks, H, competes in Cournot fashion in each period t.25 Each bank i acts on the
expectation that its own decision will not affect decisions of its rivals. The bank i decides simultaneously
with other banks on the number of entrants to be funded, kt (i), taking into account: (1) limited liability
— periodic repayments of the entry loan are at most equal to firm profits; (2) goods market clearing — all
firms compete in the local market, where firm prices, quantities, and profits are determined; and (3) post
entry firm profit maximization — each firm sets an optimal price for its variety.
In every period t, there is a mass of firms, Kt (i), in each bank i’s portfolio, a mass Nt of firms in the
economy, and an unbounded number of prospective entrants around each bank i. Each bank i takes the
aggregate variables, Ct , wt , and rt , as given. The bank correctly anticipates expected future firm profit,
ds , in every period s ≥ t + 1, and takes into account the exogenous probability δ of the firm exit inducing
shock. Entrants at time t only start producing at time t + 1, which introduces a one period time-to-build
lag in the model. The exogenous exit shock occurs at the end of each period. Therefore, a proportion δ of
period t entrants will never produce and will exit within the period.26 The assumed timing of entry and
production implies that the number of producing firms in period t, Nt , is an endogenous state variable
that behaves like physical capital in standard real business cycle (RBC) models.
The household’s Euler equation for shares, equation (4), implies the objective function for each bank
i:
max
{Ks+1 (i),ks (i)}∞
s=t
Et
∞
X
s=t
β
s−t
µ
Cs
Ct
¶−γ
π s (i).
Bank i’s profit, π t (i), is given by
πt (i) = Kt (i)dt + BtS (i) −
wt
S
kt (i) − (1 + rt−1 ) Bt−1
(i),
Zt
(7)
where dt Kt (i) is the return from bank i’s portfolio of Kt (i) incumbent firms, BtS (i) is the amount of household deposits in period t into bank’s i,
wt
Zt kt (i)
S
is the amount lent to k(i) entrants, and (1 + rt−1 ) Bt−1
(i)
is the principal and interest on the period’s deposits. Equation (6) gives the periodic entry loan repayment, dt . Each bank i accrues portfolio returns after firm entry has been funded and then rebates its
2 5 As will become clear later, this is not exactly the Cournot model as not only the value of entrants, but also the value
of incumbents depends on the number of entrants.
2 6 In the data business failures are countercyclical (Cooper and Chatterjee, 1993, and Devereux et al, 1996). Although,
an endogenous exit rate would help explain the slow down in firm turnover reported by Davis et al (2006), introducing it
would complicate the model considerably, see Stebunovs (2007).
10
profits to the mutual fund owned by households in each period t. Thus, bank i’s balance sheet constraint
is:
BtS (i) =
wt
kt (i).
Zt
I assume that the sunk entry cost per entrant in units of effective labor is one, and hence the sunk entry
cost in units of consumption is wt /Zt , which varies with the business cycle.
The law of motion of the firm portfolio of bank i is:
Kt (i) = (1 − δ)(Kt−1 (i) + kt (i)),
(8)
Aggregation across banks gives the overall mass of incumbent firms in the economy in a period t, Nt =
P
P
i∈H Kt (i), the overall mass of entrants nt =
i∈H kt (i), and the law of motion of the overall mass of
firms in the economy,
Nt = (1 − δ)(Nt−1 + nt−1 ).
(9)
First order condition with respect to Kt+1 (i) gives the Euler equation for firm value to bank i, qt (i),
and involves a term capturing the internalization of the profit destruction externality (PDE):27



µ C ¶−γ 

∂dt+1 ∂Nt+1



t+1
qt (i) = βEt 
+ (1 − δ)qt+1 (i) .
dt+1 + Kt+1 (i)
 Ct


∂Nt+1 ∂Kt+1 (i)
{z
}
|
internalization of PDE
Firm entry reduces incumbent firms’ size and profits, and hence decreases the repayments to bank i.
Each bank i internalizes only the effects of the competition it funded, thus Kt+1 (i) multiplies the profit
destruction externality,
∂d(Nt+1 ) ∂Nt+1
∂Nt+1 ∂Kt+1 (i) .
First order condition with respect to kt (i) defines a firm entry
condition, which holds as long as the number of entrants, kt (i), is positive. Entry occurs until ex ante
firm value, qt (i), is equalized with the expected, discounted entry cost, which is given by the deposit
principal and the interest to be paid back next period, t + 1,
qt (i) = β
µ
(1 + rt ) wt
(1 − δ) Zt
¶
Et
"µ
Ct+1
Ct
¶−γ #
.
(10)
2 7 Bilbiie et al (2006) work with post entry value of firm, in their notation v , whereas here q is ex ante entry value of
t
t
firms. Assuming the profit destruction externality away, the firm values are related by qt = vt /(1 − δ).
11
The cost of creating a firm to be repaid at t + 1 is known with certainty as of period t. As there is no
difference between marginal and average qt , firm entry drives down not only the value of entering firms,
but also the value of incumbents until all firms’ value is equalized with the sunk entry cost.
Since all banks are identical and there are no idiosyncratic shocks, one can impose symmetry to obtain
the Nash equilibrium. The equation for firm value, qt , becomes:28
qt = βEt
"µ
Ct+1
Ct
¶−γ µµ
¶#
¶
1
1−
.
dt+1 + (1 − δ)qt+1
H
(11)
The parameter H plays in bank market the same role that θ plays in goods market. At one extreme,
H = 1 or absolute bank monopoly, equation (11) says that there is no entry as there is no marginal
(and average) return from funding an entrant: the portfolio expansion effect is totally offset by profit
destruction effect.29 The economy is starved of firm entry and of any activity as well. The model displays
a gradual reduction in market power as the number of banks, H, increases.30 At the other extreme,
H = ∞, the equation simplifies to the usual asset pricing equation.
2.4
Aggregation and data consistent variables
Aggregating the budget constraint across households, and noting that the share holdings in the bank
mutual fund add up to one in equilibrium, yields the aggregate accounting constraint:
Ct + Bt = dt Nt + wt L,
where L is the aggregate labor supply, L =
R
j
(12)
l(j)dj. The aggregate accounting constraint states that
current consumption and deposits must be equal to total income, that is, labor income plus dividend
income. Current household deposits are the measure of current real investment in the economy. Deposit
2 8 Recall
2 9 Under
that qt (i) is ex ante entry value of firm, hence thehentry entry loan repayment,
dt (i), is not multiplied by (1 − δ).
i
H = 1, equation (11) becomes qt = β(1 − δ)Et (Ct+1 /Ct )−γ qt+1 , which is a contraction mapping because
of discounting, and by forward iteration under the assumption limT →∞ (β(1 − δ))T Et qt+T = 0 (there is a zero value of
firms when reaching the terminal period), the only stable solution for firm value is qt = 0, which implies Nt = 0. An
alternative would be to assume that the monopolist bank takes into account its influence on the aggregate consumption
demand, Ct . This channel is reminiscent of ”Ford effect” described in d’Aspremont et al (1996) where a firm-monopolist,
owned by households, internalizes the effects of dividend pay outs, that boost households income, on demand for its output.
In an alternative multi-location setup, where firms compete in a national market rather than in local markets, there is firm
entry under H = 1 at each location as long as there is more than one location in the economy.
3 0 In Salop’s (1979) model of competition on a circle, the addition of one establishment makes all establishment more
substitutable with each other, so markups fall. The same is true for conventional models of Cournot competition.
12
market clearing equates deposits with investment in new firms:
Bt =
wt
nt .
Zt
(13)
Labor market equilibrium requires that the total amount of labor employed in the production of goods
and in creation of new firms must be equal to the aggregate labor supply:
L=
1
Ct
1
(Nt )− θ−1 + nt .
Zt
Zt
As in Bilbiie et al (2006), although the labor supply is fixed, there are labor market dynamics, as labor
reallocates between the two sectors of the economy in response to shocks. The allocation is determined by
banks deciding on firm entry. Thus, the value of a firm to a bank, qt , plays a central role in determining
the labor allocation.31
Although the model does not feature an explicit interest rate markup over the deposit interest rate,
one may define an aggregate ex post markup in banking, µB
t , as the residual concept:
µB
t =
dt Nt
− rt .
qt Nt+1
The modelling strategy of entry loan repayments makes it possible to treat firms of different vintages
symmetrically. There is also no difference between marginal and average qt . Taking into account the
time-to-build lag between the period of a firm entry and the period it starts repaying the entry loan,
one can think of the ratio dt Nt /qt Nt+1 as measuring the relative return from funding a marginal (and
average) firm.
As argued in Ghironi and Melitz (2005), when investigating the properties of the model with endogenous variety in relation to the data, any variable in units of the consumption basket should be deflated
by a data consistent price index. In the model, the average variety price, pt , is closer to actual CPI data
than the welfare-based price index, Pt . Therefore, data consistent counterparts of the model variables
are obtained as follows:
XtR =
3 1 To
Pt
Xt
Xt
Xt =
= 1/(θ−1) .
pt
ρt
Nt
close the model, either the aggregate accounting constraint or the labor market clearing condition is necessary.
13
For example, the expenditure definition of GDP is Yt = Ct + Bt . Then, GDP in data consistent terms is
YtR = CtR + BtR = yt Nt +
nt
,
µF
(14)
where CtR is aggregate consumption and is given by the product of firm level output, yt and the mass
of producing firms in period t, Nt ; and BtR is the amount invested in firm creation evaluated at average
prices and is given by nt /µF .
Table 8 in Appendix summarizes the model equations. The model constitutes of a system of 11 equations in 11 endogenous variables.32 Of these endogenous variables, the mass of firms, Nt , is predetermined
as of time t. The exogenous state variable is the aggregate productivity, Zt . My benchmark model under
perfectly competitive banking nests Bilbiie et al (2006) with inelastic labor supply and Dixit-Stiglitz
preferences, notwithstanding the timing discrepancy in firm entry equation (10).
3
Results
3.1
Calibration
I interpret model periods as quarters. Table 1 shows the calibrated parameter values. For computation of
second moments, I set the parameter H before deregulation such that it implies a bank markup of about
10 percentage points, then the roughly 34% increase in the mass of firms pins down H after deregulation.
The discount factor and the inverse of intertemporal elasticity of substitution are set at standard values
for RBC literature.
Although it implies a fairly high firm markup, I set the elasticity of substitution across goods (θ) at
3.8 for two reasons. First, it fits U.S. plant and macro trade data.33 Second, the model, void of period by
period fixed cost, delivers equal marginal and average cost. Therefore the firm markup, µF , is a measure
of both markup over marginal and average cost.34
Steady state levels of variables are denoted by dropping the time subscript. All exogenous variables,
including aggregate productivity, are constant in steady state. I set steady-state aggregate productivity,
3 2 The model can be reduced to a system of 3 equations in 3 variables: the number of firms, N , aggregate consumption,
t
Ct , and aggregate productivity, Zt .
3 3 See Bernard et al (2003) and Ghironi and Melitz (2005).
3 4 In Bilbiie et al (2006) free entry ensures that firms earn zero profits net of the entry cost, meaning that firms price at
average cost inclusive of the entry cost. In my model, with rationed entry under monopolistic banks, firms price at average
cost partly inclusive of the entry cost.
14
Z, and aggregate labor endowment, L equal to one without loss of generality. These parameters determine
the size of economy, but leave the model second moments, unaffected.
Table 1: Quarterly calibration
Preferences
Discount factor
Elast. of goods subst.
Risk aversion
β
θ
γ
0.99
3.8
1
Economy scale
Agg. productivity
Aggregate labor
Z
L
1
1
Exogenous process
Prob. of exog. exit
Agg. prod. persist.
δ
ψZ
0.025
0.90
Ghironi and Melitz (2005) set the size of the exogenous firm exit shock δ = 0.025 to match the
U.S. empirical level of 10% job destruction per year.35 Using as a guideline the fraction of firm closures
and bankruptcies over the total number of firms, reported by the U.S. Small Business Administration,
consistently around 10% per year over the recent years, gives the same calibration.36
In contrast to a model without entry, the dynamics of firm entry results in responses of aggregate
variables to temporary exogenous shocks that persist beyond the duration of the shocks. I set the
persistence of the aggregate productivity process to 0.90.37 As such, I do not attempt to replicate
exactly U.S. data moments. I illustrate the implications of bank monopoly power for firm and aggregate
volatility by computing changes in second moments induced by deregulation for the standard deviation
of productivity innovations of 1%.
3.2
Steady state
All endogenous variables are constant in steady state. The steady state interest rate is pinned down as
usual by the rate of time preference, 1 + r = β −1 .38 The closed form solution for the steady state mass
3 5 Empirically, job destruction is induced by both firm exit and contraction. In the model the exogenous exit shock induces
firm exit.
3 6 There are two calibration approaches that might suggest an upward revision of the δ calibration. First, one might
interpret δ as a parameter controlling the fraction of non-performing loans. Then the average delinquency rate for commercial
and industrial loans between 1986 and 2006 is 3.34% per quarter (FDIC Charge-off and Delinquency Rates data). Second,
one might look at the survival rates for new firms. Two-thirds (66%) of new employer establishments survive at least two
years, and 44% survive at least four years (Knaup, 2005). Assuming that the number of years that a firm survives follows
geometric distribution with parameter δ, one can calibrate δ at 0.0625 per quarter. In general, higher δ results in a lower
number of firms in steady state and lower persistence of endogenous variables. Setting δ = 0.025 implying expected firm
lifetime of 10 years adjusts for the fact that larger firms tend to survive longer. Since the model here features no firm
heterogeneity, the parameter δ might be thought of as an output weighted probability of exit, making 0.025 a plausible
choice.
3 7 The structure of models with varying product space calls for corrections to the standard formula for of Solow residual
in order to estimate a model consistent productivity process. See Bilbiie et al (2006). For example, Devereux et al (1996)
estimate the persistence parameter of 0.91 for their model with firm entry.
3 8 As in typical DSGE models, the interest rate is pinned down by household time preference, which is kept constant
across simulations. In the data, however, the deposit interest rate increased after the deregulation. Thus, in the model the
15
of firms, N , is
N=
β(1 − δ)(1 − 1/H)
ZL.
(θ − 1)(1 − β(1 − δ)) + δβ(1 − 1/H)
(15)
Given the solution for N it is easy to recover solutions for all other variables. The number of new entrants
makes up for the exogenous destruction of existing firms, n = δ/(1 − δ)N . From equation (15) it is clear
why steady state aggregate productivity, Z, or the labor endowment, L, function as scale parameters.
Figure 2 shows how key variables depend on H given the model calibration described above.
Although some of the model’s dynamic equations are different, my model nests the steady state
solution of Bilbiie et al (2006) with inelastic labor supply as H → ∞. That is, the model nests the
market outcome in the economy with perfectly competitive banking and carries over the properties of
Bilbiie et al’s steady state.
An increase in long-run aggregate productivity results in a larger number of firms, higher consumption
and firm value. The mass of firms, N , tends to zero if θ tends to infinity or if H tends to one. For banks
to find it profitable to let firms enter, the expected present discounted value of the future profit stream
must be positive, so as to cover the sunk entry cost. But profits tend to zero in all periods if firms have
no monopoly power. Marginal (and average) return from firm creation also tends to zero if H tends to
one as the portfolio expansion effect is totally offset by the profit destruction effect. Increasing H from
one shows that the portfolio expansion effect dominates the profit destruction effect up to H marginally
below 2, and the dominance reverses from thereon.39 The interplay of these effects causes the mass of
firms in bank’s portfolio (K) to be a non-monotonic function of H. Nevertheless, the mass of firms in
the economy, N , is a monotonic function of H.40 Firm size, measured by either firm output (y) or firm
level employment (l), and profit (d) are monotonically decreasing functions of H. As H increases, the
mass of firms in the economy increases, eroding each firm’s market share and hence profit. A decline in
bank market power results in more entrants, and hence in an increase in share of investment in aggregate
output, captured by the ratio B/Y.
Bank market power results in low firm valuation (q) due to internalization of the profit destruction
change in bank markup after the deregulation stems only from a decrease in loan price, d/q.
3 9 The inflection point for this particular calibration is H = 1.8933.
4 0 The increase in N induced by a fall in bank monopoly power is welfare improving as it allows households to enjoy more
variety and higher consumption. In a version of this model with elastic labor supply, the increase in N leads to both higher
consumption and labor effort, with the welfare gain of the former dominating the disutility from extra labor.
16
externality. The bank return on firm creation (that might be thought of as the loan price) is
r+δ
d
=
,
q
1 − 1/H
which captures a premium for expected firm destruction (δ) and the effect of bank market power. Hence,
the steady-state banking markup, µB = d/q − r, approaches δ as H → ∞. The banking markup diverges
to infinity as H → 1.
The steady-state predictions of the model are consistent with empirical findings that associate more
vigorous banking competition with a greater number of establishments and a smaller establishment size.
3.3
Impulse responses
Impulse responses highlight the difference between monopolistic and competitive banking in the model’s
dynamics. Figure 3 shows the responses, in percent deviations from steady state to a 1% increase in
aggregate productivity with persistence 0.9 under monopolistic banking (where H = 1.5) and competitive
banking (where H is set to a sufficiently high number, H = 2000). The model is stationary under
temporary shocks. The number of quarters after the shock is on the horizontal axis. Variables with the
superscript R denote variables in data consistent terms.41
The following applies to both scenarios. The aggregate productivity shock makes the business environment more attractive, drawing a higher mass of entrants than in steady state. This translates into a
temporary larger mass of producers with a lag, due to the sunk entry cost and the time to build lag. This
induces marginal cost and the relative price of each product, ρ, to start increasing only in the period after
the shock, when a larger number of producing firms puts pressure on labor demand. Consumption and
GDP, both in data consistent terms, also increase. As in the data the aggregate ex post bank markup is
countercyclical. All variables return to the respective steady states in the long run.
The responses of firm level output, y, and aggregate output in data consistent terms, Y R , underline
the different roles of intensive and extensive margins during expansions. The model predicts that the
expansionary effect of higher productivity takes place initially through the intensive margin. Output
per firm rises, because the aggregate consumption demand is higher and the predetermined number of
producers remains constant on shock impact and then increases slowly. Over time, the increase in ρt
4 1 I show impulse responses of data consistent variables to maintain continuity between this section and the following
section where I compute second moments. The impulse responses of welfare consistent variables are qualitatively similar.
17
Figure 2: The dependence of endogenous variables on H in the steady state.
Figure 3: Impulse responses (in percent deviations from steady state) to a 1% aggregate productivity
shock under monopolistic and competitive banking.
18
pushes firm level output below the steady state level, but the aggregate expansion continues through
the extensive margin, as the mass of producing firms increases. Noteworthy, firm-level output is actually
below the steady-state level during most of the transition, except for a short lived initial expansion. These
predictions are the same as in Bilbiie et al (2006).
During the business cycle, there is a reallocation of the fixed labor supply from production of consumption goods to creation of new firms. The increase in productivity makes some labor redundant in
production of goods (as aggregate consumption demand rises by less than income due to consumption
smoothing) and at the same time boosts entry, as firm profits are higher and the cost of creating new
firms is lower. Over time, the rising cost of effective labor and hence the rising burden of sunk entry cost
redistributes labor back to production of consumption goods. In contrast to a model without entry, the
dynamics of firm entry result in responses of aggregate variables that persist beyond the duration of the
exogenous shock.
Turning to the differences in responses across banking scenarios, the effects of an aggregate productivity shock are amplified in the monopolistic banking economy. Combining the aggregate accounting
constraint (12) with goods pricing (5) and deposit market clearing (13) — all linearized — one obtains,
1 Cb
1C b
ZL b
bt =
Ct −
Nt + n
Zt ,
µF B
θB
n
where percentage deviations from steady state are denoted by variables with hats. All variables on the
bt is the endogenous state that does not respond to period
left-hand side are endogenous. In particular, N
t shocks.
The ratio on the right-hand side, ZL/n, is larger under monopolistic banking. The exogenous scale
parameters, Z and L, are the same for both scenarios. However, monopolistic banks suppress the mass
of firms, N , and hence firm entry, n, is lower in steady state. Sustaining this lower mass of large and
profitable firms requires less resources than under competitive banking. The aggregate productivity
shock then generates much stronger wealth effect that causes a more pronounced boom in consumption,
hence goods production, and investment in new firms.42 This stronger consumption boom then raises
significantly firm-level output and profits. However, the expansion along the intensive margin is short4 2 Firm monopoly power and variety as such are not crucial for this mechanism. For example, in a model with decreasing
returns to labor in production of homogenous goods, firms earn profits as well, hence making firm entry possible. In this
model the implications of monopolistic banking will be the same as in the benchmark model. See Stebunovs (2007) for
details.
19
lived. The incentive to create a large mass of new firms is similarly short-lived, as profit opportunities are
exhausted quickly. The influx of new firms drives firm level output below the steady state in just a few
periods. The short-lived firm investment boom makes firm entry more volatile, which in turn makes firmlevel output more volatile as well. After over 20 quarters, the effects of monopolistic banking vanish and
the impulse responses in the monopolistic and competitive banking economies converge. In the bigger,
competitive banking economy there are more firms and less steady-state profits per firm. An aggregate
productivity shock of the same magnitude does not generate such a strong wealth effect and consumption
— investment boom, leading to lower firm entry and output volatility. Interestingly, the response of GDP
in data consistent terms, Y R , is not significantly amplified before the deregulation. The following section
considers this issue in detail.
3.4
Second moments
In this section I compute changes in model second moments induced by changes in H, that is, before
and after the financial deregulation, keeping other model parameters and the stochastic shock process
the same. The standard deviation of productivity innovations is 1%. I calibrate H as follows. I pick the
value of H before financial deregulation that implies a bank markup of about 10 percentage points.43
Then the roughly 34% increase in the mass of firms pins down the value of H after deregulation. The
resulting H before deregulation is equal to about 1.48, after deregulation H is about 1.815.44
Table 2 shows model second moments under both banking scenarios scaled by standard deviation
of aggregate productivity, σ Z = 1.2833.45 The reduction in bank monopoly power generates significant
declines in volatility of firm entry, firm output, data consistent consumption, and data consistent investment. The model generates firm-level decrease in volatility similar to the data.46 Davis et al (2006)
report two measures of firm volatility. In the spirit of my model, one might consider the measure that
takes into account firm dynamics and hence rely on the 18% decline in firm level volatility between 1980
and 2000 as a benchmark.47 Table 7 in Appendix shows the changes in empirical moments of aggregate
4 3 In the aggregate data, the bank spread in 1980 was around 8 percentage points and in 2000 about 5 percentage points
(see the details in Appendix). The model requires rather strong bank monopoly power to generate large volatility declines.
4 4 The implied bank markup before deregulation is 9.8 percentage points and after deregulation — 6.81 percentage points.
4 5 The theoretical moments are HP filtered with λ = 1600.
4 6 The model ”underestimates” the decline in firm volatility in comparison with Davis et al (2006) as they calculate
growth rates that are symmetric around zero and bounded. They report the volatility of firm growth rate calculated as
γ t = (xt − xt−1 )/(xt + xt−1 )/2, where x is some firm size measure.
4 7 As dictated by data availability Davis et al estimate firm volatility based on firm employment. The preferred measure
of firm volatility here is based on firm output because its contribution to GDP is immediately clear from equation (14). In
the model, firm-level labor and output always move in the same direction. However, the magnitudes of movements might
20
variables between 1980 and 2000.
Table 2: Volatility effects of deregulation
standard deviations
before
after
change, %
firm level
yt
aggregate level
nt
CtR¡(= yt Nt ) ¢
BtR = nt /µF
YtR
0.5861
0.4984
-14.97
8.0458
0.4618
8.0458
0.8610
6.4957
0.4107
6.4957
0.8516
-19.27
-11.06
-19.27
-1.09
As the simulations show, the reduction in volatility of consumption (or goods production) and of
investment do not lead to a significant reduction in the volatility of GDP data consistent terms. GDP
volatility depends on three factors: the volatility of its components, their covariation, and their relative
weights. In order to look at each factor in turn, consider a linearized version of equation (14),
C bR B bR
YbtR = C
+ Bt .
Y t
Y
(16)
Note that the post deregulation weight of goods production in aggregate output is lower and the weight
of investment in new firms is higher (since the ratio B/Y is higher post deregulation). The linearized
equation above implies the variance of Y R given by:
σ2Y R =
µ
CR
YR
¶2
σ 2C R + 2
C RBR
2 σC R BR +
(Y R )
µ
BR
YR
¶2
σ 2B R ,
(17)
where σ X denotes the variance of variable X and σC R B R denotes the covariance between the consumption
and investment in new firms. This decomposition adjusts the variance of each component of GDP for the
share of the component in GDP. A very volatile component may have little effect on overall volatility if
it accounts for a small share of GDP. Table 3 shows the breakdown of the variance of Y R as well as the
break down of component contributions before and after deregulation. The entries in the table are not
scaled by standard deviation of aggregate productivity, σ Z .
The benchmark model predicts significant declines in volatility of firm entry, firm output, and conbe different. Setting θ = 6 generates bigger firm-level labor movements.
21
Table 3: Breakdown of the variance of Y R
³
´2
R
C
σ 2C R
YR
R
2 C(Y RB)2 σ C R B R
³ R ´2
B
σ 2B R
YR
σ 2Y R
R
change, %[1]
comp. contr., %[2]
0.2363
-24.28
-6.21
0.5393
-3.46
-1.58
before
after
0.3121
0.5586
0.3501 0.4188
19.62
1.2208 1.1944
-2.16
2
Note: [1] the percentage change in σ Y R should not be equal
to the sum of percentage changes of σ 2Y R components;
[2] the contribution of each component X, γ cX ,
4σ 2
is calculated as in Blanchard and Simon (2001), γ cX = σ2 X ,
5.63
-2.16
YR
where σ 2Y R is the variance of aggregate output before
the deregulation; γ cX ’s sum up to the percentage change in σ 2Y R
sumption, but does not generate a significant decline in aggregate output volatility. This is the consequence of the compositional change in aggregate output predicted by the model after deregulation.
Although, the variance of investment in new firms (or firm entry) decreases, its weight in GDP increases.48 The decline in the contributions of goods production and the covariance between the latter
and investment are not sufficient to offset significantly the increase in the contribution of investment in
new firms. In the next section, I explore an extension of the model that makes it possible to generate
also lower volatility in GDP.
4
Countercyclical firm markups and endogenous labor supply
The model extension further exploits the implications of endogenous variety.49 This extension separates
taste for variety and firm monopoly power, allows for varying demand elasticity (hence for varying firm
markups), delivers more significant decline in firm volatility, and when combined with elastic labor supply
4 8 Blanchard and Simon (2001) suggest that the composition of GDP changed substantially over the last 50 years and
that the share of non residential fixed investment increased by about 4 percentage points.
4 9 There are other straightforward extension to the benchmark model. The first extension is a step towards standard
business cycle models as it introduces physical capital, although the labor supply is still inelastic. In this 3 sector model an
endogenous number of monopolistic firms produces consumption goods, a perfectly competitive sector with a fixed number
of firms produces capital goods, and monopolistic banks fund firm entry. The difference between the model outlined here
and the model with physical capital in Bilbiie et al (2006) is that the latter is not a 3 sector model as physical capital
and consumption goods are produced by the same firms. The second extension voids the benchmark model of the firm
monopolistic competition, hence of the variety effects, but retains the inelastic labor supply assumption. In this model
homogenous consumption goods are produced by competitive firms under decreasing returns to scale in labor. The steady
state properties of both extensions are similar to that of the benchmark model. Both models predict that aggregate output
volatility is not significantly lower after deregulation. See Stebunovs (2007) for details.
22
also delivers a significant decline in aggregate output volatility. Bank markups remain countercyclical.
In the extended model households maximize expected intertemporal utility from consumption and
the supply of labor hours, Lt :
Et
∞
X
1+1/ϕ
β s−t
s=t
L
Cs1−γ
−χ t
,
1−γ
1 + 1/ϕ
where χ > 0 is the the weight of disutility of labor effort and ϕ > 0 is the Frisch elasticity of labor
supply to wages. Household’s intertemporal optimality conditions remain the same, the only additional
intratemporal condition is the optimality condition for labor supply. Elastic labor supply implies that
households have an extra margin of adjustment to aggregate productivity shocks, as in Bilbiie et al
(2006). This enhances the propagation mechanism of the model by amplifying the responses of endogenous
variables with respect to the benchmark model.
However, elastic labor supply on its own is not sufficient to generate an aggregate volatility decline
after financial deregulation. The wealth effect dominates the substitution effect in labor supply decisions
before deregulation.50 This leads to higher volatility of labor and hence higher aggregate volatility after
deregulation.
One way to break the tight link between aggregate productivity and wages, and hence reverse the
dominance of the wealth effect over the substitution effect without destroying the stronger incentive for
firm entry over the business cycle before the deregulation, is to introduce countercyclical firm markups.51
One obvious mechanism that delivers countercyclical firm markups is to have the elasticity of demand
perceived by the representative firm vary over the business cycle.
To obtain this, I move to a model with a discrete number of firms and separate taste for variety,
measured by the elasticity of substitution between goods, θ, from firm monopoly power, associated with
the perceived elasticity of demand, ε > 0.52 Given an endogenous number of firms, one cannot assume a
priori that this number is sufficiently large for the weight of each producer to be negligible. As suggested
by Yang and Heijdra (1993), each producer then no longer ignores the effects of its price, pt (ω), on the
5 0 The paths of wages before and after deregulation, however, are similar, as wages track the path of aggregate productivity
closely until the mass of firms in the economy increases sufficiently to drive a wedge between the two. Consider a linearized
bt = w
bt . Hence, at shock impact w
bt , and since N moves
version of the goods pricing equation (5), 1/(θ − 1)N
bt − Z
bt = Z
gradually, it takes several periods for N to increase significantly above its steady state level. The increase in N is dampened
by the fraction 1/(θ − 1), hence the substitution effect is weak.
5 1 As discussed in Rotemberg and Woodford (1990), one needs endogenous countercyclical variation in markups to explain
the non countercyclical variation of real wages at business cycle frequencies.
5 2 Jaimovich (2006) follows a similar approach in order to generate varying firm markups. Another way to generate
countercyclical firm markups is to use translog preferences as in Bilbiie et al (2006). Their setup generates varying demand
elasticity from demand side rather than supply side considerations. It allows to work with a continuum of firms, and features
a parameter controlling the pass-through of changes in the mass of firms into firm markups.
23
³
general price index, Pt . The perceived demand elasticity is then εt = θ 1 −
1
Nt
´
. Note that taking into
account this indirect price effect decreases the elasticity perceived by a firm, εt < θ, and hence increases
its monopoly power. The implied firm markup is µF
t =
εt
εt −1 .
Since firm entry is procyclical in the model,
firm markups are countercyclical.53 In turn, countercyclical markups imply that market clearing prices
work to amplify, rather than stabilize, movements in firm output. The necessary model modifications are
shown in Appendix, Table 9.
I examine the model predictions under two calibrations of the Frisch elasticity, ϕ: under low elasticity,
ϕ = 2, and under high elasticity, ϕ = 10.54 I set the weight of disutility of labor, χ, to one in both cases.
The household preference, economy scale, exogenous exit and aggregate productivity process parameters
remain the same as in the benchmark model (see Table 1).55 The calibration strategy of H, the parameter
controlling bank monopoly power, is the same as before as well. I pick the value of H before financial
deregulation that implies a bank markup of about 10 percentage points. Then the roughly 34% increase
in the number of firms post deregulation pins down the value of H after deregulation.56
The extended model predicts more firms, lower firm and bank markups, and higher labor supply in
steady state after deregulation.57 Note that firm markup in the extended model is always higher than
the firm markup in the benchmark model. Given that firm entry is costly, the number of firms is never
sufficiently high to bring the firm markup down to the level implied solely by the elasticity of substitution
between goods, θ. The remaining model steady-state properties carry over from the benchmark model.
Figure 4 shows the responses (in percent deviations from steady state) to a 1% increase in aggregate
productivity with persistence 0.9 before and after deregulation. The amplification mechanism before
deregulation works as follows. As in the benchmark model less vigorous banking competition suppresses
the number of firms in steady state. The aggregate productivity shock then generates firm investment
boom. The influx of a larger number of new firms makes firm markups move in countercyclical fashion.
5 3 The derivative of firm markup, µF , with respect to the number of firms, N , is negative, ∂µF /∂N
t
t =
t
t
−θ/ ((θ − 1) Nt − θ)2 < 0.
5 4 The case in which ϕ → ∞ corresponds to linear disutility of effort and is often studied in the business cycle literature.
5 5 King et al (1988) show that under separable preferences, log utility of consumption ensures that income and substitution
effects or real wage variation on effort cancel out in steady state. This guarantees constant steady state effort and is necessary
for balanced growth under trend productivity growth.
5 6 For Frisch elasticity of 2, before deregulation H is 2.0405, the implied bank markup is 9.8 percentage points, and
after deregulation H is 2.475, the implied bank markup is about 6.1 percentage points. For Frisch elasticity of 10, before
deregulation H is 2.086 and after deregulation — 2.48. The implied bank markup before deregulation is about 9.8 percentage
points and after deregulation is about 6.21 percentage points.
5 7 Although households supply higher labor effort in steady state after the deregulation, they enjoy higher welfare, as the
higher utility of consumption offsets the disutility of labor effort. Hence, the model predicts that the deregulation is welfare
improving.
24
The countercyclical firm markups narrow with one period lag the inefficient wedge between marginal
product and factor prices, hence lower firm price and boost the demand for firm output, and hence make
firm output more volatile under monopolistic banking. The countercyclical firm markups also break the
tight link between wages and aggregate productivity features in the benchmark model.58
Figure 4: Impulse responses (in percent deviations from steady state) to a 1% aggregate productivity
shock under ϕ = 2.
The amplified response of the wage on the one hand and the willingness of households to postpone
consumption on the other hand enable the substitution effect to offset the income effect in household’s
labor supply decisions. The amplified response of labor effort then increases firm level volatility further
and generates higher aggregate volatility. The Frisch elasticity controls the amplification of labor effort
responses. The higher the elasticity, the more amplification less vigorous bank competition generates.59
Table 4 shows model second moments before and after deregulation, scaled by standard deviation
of aggregate productivity, σ Z = 1.2833, for both low and high Frisch elasticities. As anticipated, the
extended model delivers more significant reduction in firm level volatility, measured either by firm output
1 b
bt , or after
Nt = µ
the linearized version of the equation (5) when firm markups are varying: θ−1
bt + w
bt − Z
³
´
µF −1
1
bt . The coefficient of N
bt is larger than in the benchmark model, and it is also
bt = w
bt − Z
substitutions, θ−1 + N −1 N
larger before deregulation. Hence the gradual increase in the number of firms impacts wages more significantly before
deregulation.
5 9 Virtually all models, including RBC and New Keynesian models, work best when this elasticity is high. My model is
not an exception, and requires elasticity above 2 to generate a significant decline in aggregate output.
5 8 Consider
25
or firm employment after deregulation. The extended model also separates the volatility of investment in
new firms from that of firm entry. The volatility of all aggregate variables falls after deregulation.60 The
magnitude of the decline of aggregate volatility is dictated by the Frisch elasticity. Hence, the key to the
reduction of aggregate volatility is the decline in labor supply volatility induced by less countercyclical firm
markups, which in turn are induced by diminished incentives for a firm creation boom after deregulation.
Table 4: Volatility effects of deregulation
low Frisch elasticity, ϕ = 2
before
after
change, %
Standard deviations
firm level
yt
0.8105
0.6549
-19.19
lt
1.1167
0.8759
-21.57
aggregate level
nt
15.8272 11.1665
-29.45
Lt
1.1923
1.0522
-11.75
CtR
0.6061
0.5791
-4.45
BtR
15.8051 11.1570
-29.41
YtR
1.6047
1.5746
-1.87
Contemporaneous Correlations
R
µF
-0.2130 -0.1458
t and Yt
high Frisch elasticity, ϕ = 10
before
after
change, %
1.5775
1.8845
1.1336
1.3851
-28.14
-26.50
35.9137
3.8266
1.1024
35.8479
3.3712
24.1416
3.1709
0.8825
24.1145
3.0467
-32.78
-17.13
-19.95
-32.73
-9.63
-0.1738
-0.0925
As before, in order to look at each factor determining the volatility of GDP, I consider equation (16),
YbtR =
C R bR
C
YR t
+
BR b R
B .
YR t
Table 5 shows the breakdown of the variance of Y R as well as the break down
of component contributions before and after deregulation for ϕ = 2. The decline in the contribution of
goods production and the investment in new firms is sufficient to offset significantly the increase in the
contribution of the covariance between goods production and investment.
I should emphasize that I do not discount the role of other explanations of the volatility decline
observed in the data, such as the run of good luck in stochastic shocks suggested by Stock and Watson
(2002).61 However, the channel identified here in the context of a tractable DSGE model appears to be
sufficiently powerful to merit both empirical and theoretical investigation in future research.
There is an alternative structural explanation of the decline in firm and aggregate volatility that works
6 0 Note
that the extended model over-predicts the ratio of firm entry to aggregate output observed in the data both before
and after the deregulation by a factor of 2.3 - 2.5. However, in terms of percentage changes these ratio declined about the
same magnitude: by 28% in the model and by 22% in the data.
6 1 Interestingly, Stock and Watson’s evidence might be consistent not only with a run of good luck in shocks but also
with a structural change in the economy. As Lubik and Surico (2006) emphasize within the framework of structural DSGE
models (for instance, in the three equation Neo-Keynesian model), a change in policy parameters affects the stability of
both reduced-form coefficients and reduced-form error variances.
26
Table 5: Breakdown of the variance of Y R for ϕ = 2
³
´2
R
C
σ2C R
YR
R R
2 C(Y RB)2 σ C R B R
³ R ´2
B
σ 2B R
YR
σ2Y R
change, %
comp. contr., %[1]
before
after
0.5150
0.4435
-13.87
-1.68
1.2622
1.4270
13.06
3.89
2.4637 2.2131
-10.17
-5.91
4.2408 4.0836
-3.71
-3.71
Note: [1] component contributions are defined in Table 3
through changes in labor volatility induced by financial deregulation and might complement the channel
studied here. Suppose that households supply labor elastically and accumulate physical capital, that
serves as a collateral for firm start-up loans.62 Then shortage of collateral during firm investment booms
might motivate households to work more. Financial deregulation might then lead to a decline in labor
supply volatility by lowering the collateral requirement, reinforcing the decline in aggregate firm output
and therefore the decline in GDP volatility.63 In the data the correlation between net firm entry and
GDP appears to decline after 1980.64 In support of the collateral story, one may argue that better access
to credit can explain the weaker link between GDP and net firm entry. The collateral channel might also
help in reducing the covariance between goods production and investment in new firms predicted by the
extended model.
5
Conclusion
Banks are the largest suppliers of debt capital to small firms, which produce half of U.S. output. In the
data, more vigorous banking competition, that is, lower bank concentration and financial deregulation is
associated with more firms in operation and smaller average firm size. The volatility of small firms has
declined significantly as deregulation proceeded and the financial sector became less localized and more
competitive.
I examine whether lower bank local monopoly power leads to lower firm concentration in general
6 2 Having
the collateral requirement on the firm side might generate data inconsistent predictions. As Philippon (2003)
conjectures, improvements in financial markets will cause firms to select more risky projects (hence increasing firm volatility)
by reducing agency cost, but will also diminish the aggregate financial accelerator (thereby stabilizing the economy).
6 3 This channel is similar to the one studied by Campbell and Hercowitz (2006) in the case of household borrowing. Their
model predicts that the reduction of equity requirements can explain a large fraction of the actual volatility decline in hours
worked, output, household debt, and household durable goods purchases.
6 4 See Stebunovs (2007) for details.
27
equilibrium framework, and whether bank deregulation can account for the decline in firm level and
aggregate volatility by limiting bank local market power. To answer these questions I develop a tractable
DSGE model where finance acts as a barrier to firm entry.
The model predicts that bank deregulation generates an increase in the long run number of firms,
a decrease in firm size, an increase of the investment share in the economy, and a decrease in firm
and aggregate ex post bank markups. The model generates procyclical firm entry and countercyclical
firm and bank markups. Over the business cycle, driven by a favorable aggregate productivity shock,
bank monopoly power implies more vigorous firm entry, more countercyclical firm markups, and stronger
substitution effects (and weaker income effects) in labor supply decision. As a consequence, firm entry and
output, labor supply, consumption, investment, and aggregate output are less volatile after deregulation.
I do not discount the role of other explanations of the volatility decline observed in the data, such as
the run of good luck in stochastic shocks suggested by Stock and Watson (2002). However, the channel
identified here in the context of the tractable DSGE model appears to be sufficiently powerful to merit
both empirical and theoretical investigation in future research.
References
Amel, D. F. and J. N. Liang (1997). Determinants of entry and profits in local banking markets. Review
of Industrial Organization 12 (1), 59—78.
Berger, A. N., R. S. Demsetz, and P. E. Strahan (1999). The consolidation of the financial services industry: Cause, consequences and implications for the future. Journal of Banking and Finance 23 (2-4),
135—194.
Berger, A. N. and G. F. Udell (1998). The economics of small business finance: The roles of private
equity and debt markets in the financial growth cycle. Journal of Banking & Finance 22 (6-8),
613—673.
Bernard, A., J. Eaton, J. B. Jensen, and S. S. Kortum (2003). Plants and productivity in international
trade. American Economic Review 93 (4), 1268—1290.
Bilbiie, F., F. Ghironi, and M. J. Melitz (2006). Endogenous entry, product variety, and business cycles.
Working paper, Boston College.
28
Black, S. E. and P. E. Strahan (2002). Entrepreneurship and bank credit availability. Journal of Finance 57 (6), 2807—2833.
Blanchard, O. J. and J. Simon (2001). The long and large decline in U.S. output volatility. Brookings
Papers on Economic Activity 1, 135—174.
Calem, P. S. and L. I. Nakamura (1998). Branch banking and the geography of bank pricing. Review
of Economics and Statistics 80 (4), 600—610.
Campbell, J. R. and Z. Hercowitz (2005). The role of collateralized household debt in macroeconomic
stabilization. NBER Working Paper 11330, National Bureau of Economic Research.
Cestone, G. and L. White (2003). Anticompetitive financial contracting: The design of financial claims.
Journal of Finance 58 (5), 2109—2142.
Cetorelli, N. and P. E. Strahan (2006). Finance as a barrier to entry: Bank competition and industry
structure in local U.S. markets. Journal of Finance 61 (1), 437—461.
Chatterjee, S. and R. Cooper (1993). Entry and exit, product variety and the business cycle. NBER
Working Paper 4562, National Bureau of Economic Research.
Comin, D. and M. Gertler (2006). Medium term business cycles. American Economic Review 96 (3),
523—551.
Comin, D. and S. Mulani (2003). Diverging trends in macro and micro volatility: Facts. Working paper
0306008, EconWPA.
Comin, D. and T. Philippon (2005). The rise in firm-level volatility: Causes and consequences. NBER
Working Paper 11388, National Bureau of Economic Research.
Correa, R. (2006). Bank integration and financial constraints: Evidence from U.S. firms. Working
paper, Columbia University.
d’Aspremont, C., R. D. S. Ferreira, and L.-A. Gerard-Varet (1996). On the Dixit-Stiglitz model of
monopolistic competition. American Economic Review 86 (3), 623—629.
Davis, S. J., J. C. Haltiwanger, R. Jarmin, and J. Miranda (2006). Volatility and dispersion in business
growth rates: Publicly traded versus privately held firms. NBER Working Paper 12354, National
Bureau of Economic Research.
29
Devereux, M. B., A. C. Head, and B. J. Lapham (1996). Aggregate fluctuations with increasing returns
to specialization and scale. Journal of Economic Dynamics and Control 20 (4), 627—656.
Dick, A. A. (2006). Nationwide branching and its impact on market structure, quality, and bank
performance. Journal of Business 79 (2), 567—592.
Domowitz, I., R. G. Hubbard, and B. C. Petersen (1988). Market structure and cyclical fluctuations
in U.S. manufacturing. Review of Economics and Statistics 70 (1), 55—66.
Dueker, M. J. and D. L. Thornton (1997). Do bank loan rates exhibit a countercyclical mark-up?
Working Paper 1997-004, Federal Reserve Bank of St. Louis.
Gale, D. (1992). Branch banking, unitary banking, and competition. Working paper, Boston University.
Ghironi, F. and M. J. Melitz (2005). International trade and macroeconomic dynamics with heterogeneous firms. Quarterly Journal of Economics 120 (3), 865—915.
González-Maestre, M. and L. M. Granero (2003). Industrial loans and market structure. European
Economic Review 47 (5), 841—55.
Guiso, L., P. Sapienza, and L. Zingales (2006). The cost of banking regulation. NBER Working Paper
12501, National Bureau of Economic Research.
Jaimovich, N. (2006). Firm dynamics, markup variations and the business cycle. Working paper, Stanford University.
Jayaratne, J. and P. E. Strahan (1998). Entry restrictions, industry evolution, and dynamic efficiency:
Evidence from commercial banking. Journal of Law & Economics 41 (1), 239—273.
King, R. G., C. I. Plosser, and S. T. Rebelo (1988). Production, growth and business cycles: I. the
basic neoclassical model. Journal of Monetary Economics 21 (2-3), 195—232.
Knaup, A. E. (2005). Survival and longevity in the business employment dynamics database. Monthly
Labor Review 128.
Lubik, T. A. and P. Surico (2006). The Lucas critique and the stability of empirical models. Working
Paper 06-05, Federal Reserve Bank of Richmond.
Mester, L. J. (1987). Multiple market contact between savings and loans. Journal of Money, Credit,
and Banking 19 (4), 538—549.
30
Morgan, D. P., B. Rime, and P. E. Strahan (2004). Bank integration and state business cycles. Quarterly
Journal of Economics 119 (4), 1555—1584.
Petersen, M. A. and R. G. Rajan (2002). Does distance still matter? The information revolution in
small business lending. Journal of Finance 57 (6), 2533—2570.
Philippon, T. (2003). An explanation for the joint evolution of firm and aggregate volatility. Working
paper, New York University.
Rotemberg, J. J. and M. Woodford (1990). Cyclical markups: Theories and evidence. NBER Working
Paper 3534, National Bureau of Economic Research.
Salop, S. C. (1979). Monopolistic competition with outside goods. Bell Journal of Economics 10 (1),
141—156.
Stebunovs, V. (2007). Finance as a barrier to entry in DSGE. Disseration, Boston College.
Stiroh, K. J. and P. E. Strahan (2003). The competitive dynamics of competition: Evidence from U.S.
banking deregulation. Journal of Money, Credit, and Banking 35 (5), 801—828.
Stock, J. H. and M. W. Watson (2002). Has the business cycle changed and why? NBER Working
Paper 9127, National Bureau of Economic Research.
Yang, X. and B. J. Heijdra (1993). Monopolistic competition and optimum product diversity: Comment. American Economic Review 83 (1), 295—301.
31
6
Appendix
6.1
More details on the effects of branching deregulation
The recent financial deregulation of restrictions on bank expansion, both within and across states, has
been shown to limit market power (Jayarante and Strahan, 1998). Besides the actual completion of
deregulation, the advent of new technologies in bank lending might have undermined bank local monopoly
power as well. The new technologies, like availability of detailed credit histories and pervasiveness of credit
scoring in small business lending, allow banks to lend to distant borrowers. Petersen and Rajan (2002)
show that banks during the 1990s are much more likely to lend over long geographic distances than they
were in the 1970s.
Amel and Liang (1997) find that a competitive process is at work in banking markets as high profits
attract new entrants.65 Entry, in turn, directly reduces market profits. This process potentially limits
the ability of above-normal profits to persist over long periods of time. Calem and Nakamura (1998)
show that bank branching tends to mitigate localized market power by broadening the geographic scope
of competition.66
Jayaratne and Strahan (1998) find that following within state branching deregulation loan prices
fell significantly between 1976 - 1992, though deposit rates were not affected.67 Their model without
lags of the dependent variable suggests a declines of loan price of about 0.3 percentage points following
branching deregulation.68 Dick (2006) examines the effects of the passage of the Riegle - Neal Act, which
allowed across state branching, between 1993 - 1999.69 She finds that loan prices decrease throughout
the period, whereas deposit rates increase. While loan rates decrease by 0.2 percentage point following
deregulation, deposit rates increase by 0.3 percentage point. Banking spreads appear to decrease by about
0.6 percentage point as a result of deregulation, that is, the spread fell by about 10%. The decrease in
the spread, driven by the decrease in loan rates and the increase in deposit rates, might be indicative of
6 5 Stiroh and Strahan (2003) find that the increased competition induced by the deregulation lead to reallocation of
market share toward better (more efficient) banks. They conclude that earlier regulation of U.S. banks blunted this market
mechanism and seriously hindered the competitive process.
6 6 The testable implication of their theory, which enjoys strong empirical support, is that branching restrictions are
associated with larger price differentials across banks. Mester (1987) and Gale (1992) argue similarly that branching
increases competitiveness to the extent that the same rivals meet at multiple locations.
6 7 In their paper the unit of observation is a state×time combination.
6 8 Based on the information provided in their paper, it doesn’t seem possible to calculate the exact decline in bank spread.
Based on the mean loan rate of 10.87%, the mean deposit rate of 4.04%, and the decline of loan price of 0.3 percentage
points (the regression coefficient on the deregulation dummy), the decline in bank spread is around 5%, which is likely to
underestimate the actual decline.
6 9 In her paper the unit of observation is a bank×state×time combination.
32
an increase in banking competition.
Figure 5 shows bank spread based on the aggregate data available from FDIC.70 The downward trend
observed in the disaggregated data is less obvious. Bank spread, however, declined by about 3 percentage
points between 1980 and 2000. Since this decline might reflect both changes in bank market power and
changes in loan portfolio risk, I construct a loan risk measure as well.71 Although, the charge-off rate
itself is on upward trend, the spread appears to be less sensitive to the charge-off rate after 1980. This
might be indicative of an increase in bank competition pressure as banks are less selective, but are more
reluctant to pass the loan risk onto borrowers. For example, financial deregulation in Italy brought a
reduction in rates spreads and an increased access to credit at a cost of an increase in bad loans. (Guiso
et al, 2006) Alternatively, loan syndication might allow banks to share risk better. However, the onset of
syndication came much later in the early 1990s.
8.0
7.5
1.6
Bank spread
Charge-off rate
1.4
7.0
1.2
6.5
1.0
6.0
0.8
5.5
0.6
5.0
0.4
4.5
0.2
4.0
3.5
0.0
1947 1953 1959 1965 1971 1977 1983 1989 1995 2001
Figure 5: Bank spread in percentage points and charge-off rate (right axis) in percentages, the shaded
areas represent NBER recessions.
7 0 Bank spread is the difference of ”loan price” and ”deposit price”. I construct loan price as in Jayaratne and Strahan
(1998) or Dick (2006). It is basically the average yield on all loans, constructed by dividing total interest income on loans
and leases by total loans and leases, imputed using the flow data from the income statements and the corresponding stocks
from the balance sheets respectively. Deposit price is defined as the ratio of interest expenditures on deposits in domestic
offices over total deposits, and does not included fees as in Jayaratne and Strahan (1998) or Dick (2006) due to my data
limitations.
7 1 As in Dick (2006) loan portfolio risk is measured by charged-off losses over loans, imputed from the income statements.
33
Another implication of the financial deregulation is related to the integration of once fragmented
banking system across via bank holding companies. In theory, on one hand the integration tends to
dampen the impact of bank capital shocks on state activity, but on the other hand it amplifies the impact
of firm collateral shocks. Apparently bank capital shocks (capital supply shocks) dominate in the data,
as Morgan et al (2004) find that fluctuations in a state’s economic growth fall as its banks become more
integrated with banks in other states and that fluctuations in these states tend to converge. They also
find that the link between economic growth and bank capital within a state weakens with integration,
whereas the link between growth and housing prices (a possible proxy for collateral availability) tends to
increase.
34
6.2
Changes in firm and aggregate volatility
Table 6: Level and volatility changes between 1980 and 2000
change, %
Level
number of firms[1]
average firm size / real GDP
firm turnover[1]
bank spread (in percentage points)[2]
34
-36
-40
-3
firm vol. accounting for firm dynamics[1]
firm vol. not accounting for firm dynamics[1]
net firm entry
personal consumption expenditures
non residential fixed investment
total private hours
real GDP
-18
-50
-44
-28
-24
-23
-32
Volatility
Sources: [1] Davis et al (2006), privately held firms only,
approximate changes; [2] see the section on effects of deregulation in
Appendix; all other changes are based on own calculations for the periods
1947:1979 and 1980:2000, for details see Table 7.
Note: measure of volatility is standard deviation, all changes
are approximate.
6.3
Standard deviations of aggregate variables
Table 7: Standard deviations of aggregate variables
1947:1979 1980:2000 change, %
net firm entry[1]
personal consumption expenditures
non residential fixed investment
total private hours
real GDP
7.3825
1.4328
5.1325
2.9366
1.9281
4.1458
1.0330
3.9188
2.2706
1.3098
-43.84
-27.90
-23.65
-22.68
-32.07
Note: [1] net entry = new business incorporations - business
failures, quarterly series, HP filtered in logs (λ = 1600) over the entire
period 1947:1998; all other series are HP filtered in logs (λ = 1600) over
the entire period 1947:2000
Data source: [1] Dun and Bradstreet Corporation, NBER, Presidential
Reports; all other series - FRED II, Federal Reserve Bank at St.Louis
35
6.4
Benchmark model summary
Table 8: Benchmark model equations
10 endogenous variables: r, w, d, π, q, n, v, N, B, C
(1)
(2)
(3)
Goods pricing
Firm periodic profit
Bank periodic profit
(4)
Firm entry condition
(5)
Euler equation (q equation)
(6)
Number of firms
(7)
Euler equation (deposits)
(8)
Euler equation (shares)
(9)
(10)
Deposit market clearing
Aggregate accounting
t
(Nt )1/(θ−1) = µF w
Zt
1 Ct
dt = θ Nt
t−1
π t = dt Nt − (1 + rt−1 ) w
nt−1
Z
³
´ ·³ t−1´−γ ¸
Ct+1
t wt
qt = β 1+r
1−δ Zt Et
Ct
·³
¸
´−γ ¡¡
¢
¢
1
qt = βEt CCt+1
+
(1
−
δ)q
1
−
d
t+1
t+1
H
t
Nt+1 = (1 − δ)(N
·³ t + n´t ) ¸
−γ
1 = β (1 + rt ) Et CCt+1
t
¸
·³
´−γ
vt = βEt CCt+1
(v
+
π
)
t+1
t+1
t
t
Bt = w
Zt nt
Ct + Bt = dt Nt + wt L
1 exogenous variable: Z ∼ AR(1)
Note: For the analytical solution for steady state N see equation (15) in the text.
6.5
Countercyclical firm markup model
Table 9: Necessary modifications to Benchmark model
3 new endogenous variables: ε, µF , and L
Demand elasticity
Firm markup
Firm periodic profit[1]
Euler equation (q equation)[2]
Labor supply
Aggregate accounting[3]
³
´
εt = θ 1 − N1t
εt
µF
t = εt −1
Ct
dt = ε1t N
t
·³
´−γ ³³
´
´¸
1
1
1
−
d
qt = βEt CCt+1
+
(1
−
δ)q
t+1
t+1
H 1−1/Nt+1
t
1/ϕ
χLt = wt Ct−γ
Ct + Bt = dt Nt + wt Lt
Note: [1] replaces equation (2) in Table 8; [2] replaces equation (5) in Table 8;
[3] replaces equation (11) in Table 8; I solve for steady state N numerically using
guess and verify method.
36