The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
WHY DO FINANCIAL SYSTEMS DIFFER?
HISTORY MATTERS
Cyril Monnet
Erwan Quintin
Center for Latin American Economics
Working Paper 0304
Center for Latin American Economics
Working Paper 0201
December 2004
FEDERAL RESERVE BANK OF DALLAS
Why do Financial Systems Differ? History Matters.
Cyril Monnet
Erwan Quintin∗
European Central Bank
Federal Reserve Bank of Dallas
December 1, 2004
Abstract
We describe a dynamic model of financial intermediation in which fundamental characteristics of the economy imply a unique equilibrium path of bank and financial market
lending. Yet we also show that economies whose fundamental characteristics have converged may continue to have very different financial structures. Because setting up
financial markets is costly in our model, economies that emphasize financial market
lending are more likely to continue doing so in the future, all else equal.
Keywords: Financial Systems, Financial Markets, Financial Institutions, Banks, Convergence.
JEL Classification: L16, G10, G20, N20.
∗
This project was undertaken when Erwan Quintin was a research visitor at the European Central Bank,
which he wishes to thank for its hospitality. The views expressed in this paper are not necessarily the one
of the European Central Bank, the Eurosystem, the Federal Reserve Bank of Dallas or the Federal Reserve
System. cyril.monnet@ecb.int and erwan.quintin@dal.frb.org
1
Why do Financial Systems Differ? History Matters.
Abstract
We describe a dynamic model of financial intermediation in which fundamental characteristics of the economy imply a unique equilibrium path of bank and financial market lending.
Yet we also show that economies whose fundamental characteristics have converged may continue to have very different financial structures. Because setting up financial markets is costly
in our model, economies that emphasize financial market lending are more likely to continue
doing so in the future, all else equal.
2
1
Introduction
Financial systems vary greatly even among nations at similar stages of economic development.1 For instance, bank lending is the leading source of funds for most German firms,
while financial markets play a larger role in the U.S., as illustrated in figure 1. In this paper,
we describe a model in which two economies can continue to have very different financial
systems long after their fundamental characteristics have converged.
Specifically, we embed the adverse selection model of Bolton and Freixas (2000) in a
dynamic, general equilibrium framework. Every period, a continuum of borrowers need to
fund a two-stage, risky project. The likelihood of a positive payoff at the end of the first
stage is public information, but only the borrower knows the likelihood of a positive payoff
at the end of the second stage of his project. Other agents simply know that projects more
likely to succeed in the first stage are also more likely to succeed in the second stage. Lenders
can make their funds available to borrowers directly on a financial market, or, instead, via
a bank. Bank intermediation is costly, but the bank learns the quality of the project at the
end of the first stage. In the financial market, lenders discover the quality of the project after
funding its second stage. Entry into the financial market carries an initial fixed cost, but no
further cost until lenders choose to exit and revert to using the bank.
In competitive equilibrium, agents take the gross surplus lenders can expect on the financial market as given, and the market for each type of financing clears every period. As
in Bolton and Freixas (2000), borrowers whose project is too risky receive no funding, while
safe projects are funded on the financial market. Projects of intermediate risk level obtain
funding from the bank. One key result we establish is that given a sequence of fundamental
characteristics (that is, for each period, the cost of bank intermediation, the cost of entry
on the financial market, and the distribution of project characteristics) and given an initial
size of the financial market, a unique equilibrium sequence of financial market sizes exists.
Put another way, fundamentals fully explain financial systems. Yet we also establish that
convergence in fundamentals does not imply financial convergence. Economies with different
initial financial systems may continue to differ even if their fundamental characteristics be1
Allen and Gale (2000) provide a comprehensive survey of financial structures in several developed countries.
3
come forever identical. The intuition for this result is simple. Current fundamentals may not
justify entry into the financial market for lenders who have yet to pay the fixed cost, but it
may be profitable for incumbent lenders to stay put. The financial market can remain persistently large in an economy where past fundamentals led a high number of lenders to enter
the financial market. It follows that to understand an economy’s current financial structure,
one needs to take account of past fundamentals. In other words, history matters.
In appendix A we briefly document the well-known fact that institutional environments
used to differ greatly between Germany and the U.S. Our theory suggests that despite the
fact that these differences have been fading, the U.S. and German financial systems could
continue differing for a long time. That the U.S. developed large financial markets early is
not surprising given its institutional history. According to our model, this head-start could
explain why the U.S. continues to emphasize financial markets today. Similarly, the fact banks
have played a large role historically in Germany could explain why they are still a prominent
form of finance today.
By rationalizing differences in financial structures even in observably similar economies,
our theory differs from those of Dewratipont and Maskin (1995), Holmstrom (1996), or Bolton
and Freixas (2000), among others. In effect, we show that embedding those theories in a standard framework of firm dynamics can help us understand the persistence of financial structures. Furthermore, we obtain persistence without resorting to multiple equilibria. Baliga and
Pollak (2004), for instance, find that their static model of monitored versus non-monitored
financing can support both German and Anglo-saxon equilibria that are robust to individual
deviations. In our model, the equilibrium is unique and Pareto efficient. As in Allen and Gale
(2000), financial outcomes cannot be Pareto ranked. More generally, ours is a step towards
thinking about financial systems in the context of a dynamic, general equilibrium environment
in which the impact of policy choices can be studied.2
2
See also De Fiore and Uhlig (2004) who however concentrate on a steady state analysis.
4
2
The environment
Time is discrete and infinite. The economy we study is populated by three classes of riskneutral agents: borrowers, lenders, and a bank. Lenders have mass > 1. They are infinitely
lived, discount future flows at rate β ∈ (0, 1), and are endowed with two units of the consumption good at the beginning of each period. A mass one of borrowers are born every period.
They live for one period and are not endowed with any consumption good. They are however endowed with a productive technology described by parameters p1 ∈ (0, p̄], p2 ∈ {0, 1}
and R > 0. This technology transforms one unit of the consumption good invested at the
beginning of the period into R units after half a period with probability p1 . With probability
1 − p1 , this first investment yields nothing. Borrowers can then invest another unit of the
consumption good with proceeds R with probability p2 , 0 with probability 1 − p2 . Borrowers
also enjoy non-monetary benefits B for each half-period in which their project is implemented.
While R is common across borrowers, p1 and p2 vary. Borrowers know the characteristics
of their own technology, but other agents only know p1 . We will refer to borrowers with p2 = 1
as good borrowers, while other borrowers will be termed bad borrowers. The distribution of
borrower characteristics at the beginning of the period is known by all agents. Agents also
know that p1 and p2 are correlated in the following specific sense: E[p2 |p1 ] = g(p1) where g
is a strictly increasing, continuous, g(0) = 0 and g(p̄) < 1. That is, they know that fraction
g(p1 ) of borrowers with initial likelihood of success p1 are good borrowers.3 Safe projects are
more likely to be good projects. Like Bolton and Freixas (2000), we restrict parameters so
that in an environment with full information bad projects would not be implemented.
Assumption 2.1. p̄R < 1
On the other hand, some good projects are profitable in the sense that for p1 large enough,
expected returns exceed the opportunity cost of the funds a project requires:
Assumption 2.2. p̄R + g(p̄)R > 2
Like lenders, the bank is infinitely lived. It can store deposits on behalf of lenders during
3
Notice that we do not make any assumption of independence of outcome across projects. We simply
assume no aggregate uncertainty.
5
the period with a net return normalized to zero.4 It can also lend funds to borrowers. In that
case, the bank incurs a cost ρt ≥ 0 for each unit of good it lends to borrowers at date t, and
discovers whether each project is good or bad at the end of the first stage of production.
Instead of depositing their endowment at the bank, lenders can make it available directly
to a borrower. If at date t − 1 a lender chose the bank option, choosing the direct lending
option at date t entails cost ct > 0. Lenders who already chose to lend their endowment
directly at date t − 1 can do so once again at date t at no cost. We will refer to lenders
who lend their funds directly to borrowers and the borrowers who obtain funds directly from
lenders as the financial market. By size of the financial market we will mean the mass of
projects so funded. Unlike banks, lenders on the financial market only find out whether a
project is good or bad after funding its second stage.
3
Contracts
Consider a borrower who seeks funding from the bank given a current cost ρ ≥ 0 of intermediation. A contract between the borrower and the bank stipulates a transfer x1 ≤ R from the
borrower to the bank if the project succeeds in the first half-period, and a transfer x2 ≤ R
at the end of the period if the borrower turns out to be good. Because they enjoy private
benefit B when and only when their project is financed, bad borrowers want their projects
to be implemented in both half-periods. Since bad projects are never profitable (assumption
2.1), bad borrowers have no choice but to mimic the behavior of good borrowers. Therefore,
all borrowers of a given publicly observable type p1 receive the same terms from the bank.
We will assume that the bank behaves competitively so that among the contracts that cover
the bank’s expected costs, the most favorable borrowers prevails. That is, the bank offers
borrowers of type p1 a contract x1 , x2 that solves:
max p1 (R − x1 ) + R − x2 + 2B
x1 ,x2 ≤R
4
Alternatively, we could assume that the bank has access to a foreign capital market where a one period
risk-free security pays zero interest.
6
subject to the bank’s participation constraint:
p1 x1 + g(p1)x2 ≥ 1 + ρ + g(p1 )(1 + ρ)
Indeed, good borrowers are successful with probability p1 in the first half-period, in which
case their net income is R − x1 , and are successful with probability 1 in the second half-period
and earn R − x2 . They also enjoy non-monetary benefits 2B since the project is implemented
in both subperiods. The bank’s expected return and cost depend on whether the borrower
is good or bad. They earn x1 during the first stage with probability p1 , and x2 during the
second stage if the borrower proves good, which occurs in fraction g(p1) of the projects. The
bank’s cost per unit loaned is the sum of the monitoring cost ρ and the gross return (1) on
risk-free investments. The bank’s cost, therefore, is 1 + ρ for the first half-period, and 1 + ρ
again for the second half period when the borrower turns out to be good. Note that the bank
can cover its expected cost if and only if p1 R + g(p1 )R ≥ 1 + ρ + g(p1)(1 + ρ). Denote by
pB (ρ) the value of p1 for which this condition holds as an equality. The optimal contract is
easy to characterize:
Proposition 3.1. Optimal bank contracts for borrowers with projects of type p1 ≥ pB (ρ), are
x1 = R and x2 =
1+ρ+g(p1 )(1+ρ)−p1 R
.
g(p1 )
The bank offers no contract to projects of type p1 < pB (ρ).
Proof. First write the objective function as (p1 + 1)R − (p1 x1 + g(p1 )x2 ) − (1 − g(p1 ))x2 + 2B.
Then note that at a solution, the bank’s participation constraint is binding since the objective
function is strictly decreasing in x1 and x2 . So we may rewrite the problem as
min (1 − g(p1))x2
x1 ,x2 ≤R
subject to
p1 x1 + g(p1 )x2 = 1 + ρ + g(p1 )(1 + ρ).
1 )(1+ρ)−p1 R
)
Since 1−g(p1 ) > 0, making x2 as low as possible is optimal. This implies that (R, 1+ρ+g(pg(p
1)
is optimal. Indeed, assumption 2.1 says that setting x1 = R does not suffice to cover the bank’s
costs. Together with the fact that p1 ≥ pB (ρ), it implies that
1+ρ+g(p1 )(1+ρ)−p1 R
g(p1 )
∈ (0, R]. To
prove the second part of the proposition, simply note that the participation constraint is
7
violated even if x1 = x2 = R if p1 < p(ρ).
Turning now to the financial market, assume that contracts on the financial market currently give at least gross surplus q M to lenders. We assume that borrowers and lenders behave
competitively in the financial market in the sense that they take this surplus as given. We
will refer to q M as the price of financial market contract. Then the optimal contract for good
borrowers with success probability p1 solves:
max p1 (R − x1 ) + R − x2 + 2B
subject to the lenders’ participation constraint:
p1 x1 + g(p1 )x2 ≥ q M
Denote by pM (q M ) the unique value of p1 such that p1 R + g(p1 )R = q M . As in the case of
banking contracts, optimal contracts on the financial market for projects of type p1 ≥ pM (q M )
satisfy x1 = R, and x2 =
q M −p1 R
,
g(p1 )
while no contracts are offered to other types of borrowers.
Notice that since competition prevails on both financial sectors, the surplus borrowers
enjoy in each type of contract is a monotonic function of the right hand side of the participation
constraint. Borrowers of a given type simply choose the financial option associated with the
weakest participation constraint. As a corollary, all the equilibrium results we establish below
continue to hold as long as borrowers have preferences representable by a strictly increasing
utility function. Assuming that they are risk-averse, for instance, would not change any
of our conclusions. The dynamic results we establish in the remainder of this paper are
also independent of the theory of financial intermediation one has in mind. We rely on the
framework of Bolton and Freixas (2000) because it is a simple static model in which banks and
direct intermediation co-exist. One could rely instead on any other model in which different
borrowers choose different financial options.
8
4
Equilibrium
Our goal is to study financial market development in an economy with a given sequence
{ct , ρt , Ft }+∞
t=0 of financial market entry costs, intermediation costs and distributions of observable project characteristics.5 Like Lucas and Prescott (1971), we will study equilibria in
which all agents know and take as given the sequence {qtM }+∞
t=0 of prices of financial market
contracts. We will require that when agents behave optimally given those prices, the market
for each type of financing clears every period.
Recall that at a given date t > 0, a lender’s opportunities to invest his endowment depend
on their investment decision at date t − 1. If at date t − 1 they supplied their endowment
on the financial market, they can choose to do the same at no cost at date t. We will denote
by VtM the expected present value of future income as of date t for lenders who were in the
financial market at date t − 1. Other lenders must bear cost ct if they choose to enter the
financial market. Let VtB be the expected present value of future income as of date t for those
lenders.
In each period, lenders decide whether to deposit their endowment in the bank, or lend
it on the financial market. They choose the option that maximizes their future income.
Formally, for all t ≥ 0,
M
B
.
; 2 + βVt+1
VtM = max qtM + βVt+1
(4.1)
Indeed, lending on the financial market yields qtM in the current period and expected income
M
as of date t + 1. Bank deposits on the other hand yield zero net return (since the bank
Vt+1
B
behaves competitively) and give the lender expected income Vt+1
as of period t + 1. Similar
considerations for lenders who were not in the financial market at date t − 1 yield:
M
B
.
; 2 + βVt+1
VtB = max qtM − ct + βVt+1
(4.2)
Denote by et the mass of lenders who enter the financial market at date t while xt is the fraction
of lenders who exit the financial market. Because there are more lenders than borrowers
M
B
≤ 2 + βVt+1
for all
( > 1) in each period, it is necessary in equilibrium that qtM − ct + βVt+1
5
By Ft we mean the distribution of borrowers’ observable success types. We assume for notational simplicity
that R and g are constant across projects and across time.
9
t > 0, with equality if et > 0. But this implies
B
VtB = 2 + βVt+1
for all t or, for short and for all t,
VtB = V B ≡
2
.
1−β
M
B
≥ 2 + βVt+1
, or more
As for exit, xt > 0 in equilibrium for some t will imply qtM − ct + βVt+1
M
≥ V B . In passing, note as a result of these observations, xt > 0
succinctly, qtM − ct + βVt+1
implies et = 0. Entry into and exit from the financial market cannot coincide in equilibrium.6
We now turn to the problem solved by borrowers in equilibrium. We need to calculate
the mass of borrowers who obtain funding on the financial market in each period. Recall
first that borrowers whose project is too risky, specifically borrowers whose p1 is such that
p1 < pM (qtM ) at a given date t ≥ 0, cannot get any funding on the financial market. Borrowers
whose p1 exceed this threshold expect utility p1 R + R + 2B − (1 + ρt + g(p1)(1 + ρt )) from the
bank, while on the financial market they expect p1 R + R + 2B − qtM . Therefore, a borrower’s
expected utility is higher on the financial market if qtM ≤ 1 + ρt + g(p1 )(1 + ρt ). It follows
that borrowers on the financial market at date t have mass 1 − Ft (p∗1 (qtM , ρt )) where
p∗1 (q, ρ)
M
= max p (q); g
−1
for all q, ρ ≥ 0, with the convention that g −1 is zero if
q − (1 + ρ)
1−ρ
q−(1+ρ)
1−ρ
is negative. It is, in other words,
borrowers with relatively safe projects that opt for the financial market. This is because bank
monitoring is particularly valuable for good borrowers with a low p1 . Our model inherits this
feature from the model of Bolton and Freixas (2000). Note for future reference that p∗1 is
continuous, rises with its first argument, and decreases with its second argument.
We can now define an equilibrium from the vantage point of a reference date t = 0. All
relevant past information is summarized by the mass m−1 of lenders who were on the financial
market at date t − 1, that is, the size of the financial market at date t − 1. Given m−1 , a
6
This feature is no longer present when we introduce exogenous exit in section 6.
10
M +∞
sequence {mt }+∞
t=0 of financial market sizes, a sequence {qt }t=0 of financial market prices, the
+∞
associated value functions {VtM }+∞
t=0 , and a sequence {et , xt }t=0 of entry and exit decisions
constitute an equilibrium if:
M
1. qtM − ct + βVt+1
≤ V B with equality if et > 0,
M
≤
2. qtM + βVt+1
2
1−β
if xt > 0,
3. for all t ≥ 0, mt+1 = mt − xt + et ,
4. for all t ≥ 0, mt = 1 − Ft (p∗1 (qtM , ρt )).
The key result of this section is that the fundamental characteristics {ct , ρt , Ft }+∞
t=0 of the
economy uniquely determine its financial development.
Proposition 4.1. Given an initial size m−1 of the financial sector, a unique equilibrium
sequence {m∗t } of financial market sizes exists.
Proof. From a technical standpoint, our economy resembles the framework of Hopenhayn,
1992,7 and like Hopenhayn, we will adapt the arguments of Lucas and Prescott, 1971 to
establish that a unique equilibrium exists in our model. For m ∈ (0, 1), define Dt (m) implicitly
by
1 − Ft (p∗1 (Dt (m), ρt )) = m.
Dt (m) is therefore the market price for which m lenders are active in the market. To see
that Dt is well-defined for all t, recall that Ft is continuous and strictly increasing, and
note that for q large enough p∗1 (q, ρt ) = 1, while for q small enough p∗1 (q, ρt ) = 0. Then let
Dt (0) = limm↓0 Dt (m) and Dt (1) = limm↑1 Dt (m). Because p1 + g(p1) converges to zero as p1
falls, we have Dt (1) = 0. Furthermore, Dt is strictly decreasing on [0, 1] for all t, because Ft
is strictly increasing. Now let
S(m, t) =
0
7
m
Dt (i)di
Our environment differs from Hopenhayn’s in one important respect. The demand for funds on the
financial market depends not only on the price of the funds, but also on time varying intermediation and
entry costs, and characteristics of the distribution projects.
11
for all m ∈ [0, 1] and t ≥ 0, and extend S on [1, ] by S(m, t) = S(1, t) if m > 1. Since
limm↑1 S(m, t) = Dt (1) = 0, S(•, t) is differentiable on [0, ]. Now consider the following
surplus maximization problem:
v(m, t) = max S(m + e − x, t) − ect − 2(m + e − x) + βv(m + e − x, t + 1)
e,x
x ≥ 0
subject to :
x ≤ m
e ≥ 0
e ≤ −m
Our goal is to show that solutions to the surplus maximization problem and competitive
equilibrium allocations coincide. A standard appeal to dynamic programming arguments
shows that for all t ≥ 0, v(•, t) is well-defined, concave, and differentiable on [0, ], and that
v1 (m, t) = 0 if m ≥ 1 (since exit is free.) Let λ, µ, η and γ be the non-negative multipliers
associated with the first three constraints, respectively. Necessary and sufficient8 conditions
for a solution to the above maximization program at date t are:
−S1 (m + e − x, t) + 2 − βv1 (m + e − x, t + 1) + λ − µ = 0
(4.3)
S1 (m + e − x, t) − ct − 2 + βv1 (m + e − x, t + 1) + η − γ = 0
(4.4)
λx = 0
(4.5)
µ(m − x) = 0
(4.6)
ηe = 0
(4.7)
γ( − m − e) = 0
(4.8)
Observe that e > 0 implies x = 0. Indeed, if η = 0 then (4.3) and (4.4) imply that λ > 0.
Conversely, x > 0 implies e = 0. Also note that γ = 0. To see this, suppose γ > 0 so that
8
These conditions are sufficient because S(•, t) is strictly concave for all t on [0, 1] since Dt is strictly
decreasing.
12
e = − m > 0 by (4.8). Then x = 0 and µ = 0 by (4.6). What’s more, since S1 (1, t) = 0
and v1 (m, t) = 0 if m ≥ 1, (4.3) implies that λ < 0, a contradiction. Now let {xt , et }+∞
t=0 be a
solution to the surplus maximization problem. Then together with
mt = mt−1 + et − xt
VtM = v1 (mt , t) + V B ,
and
qtM = S1 (mt + et − xt , t),
for all t, (4.3 − 4.8) imply that {xt , et , mt }+∞
t=0 satisfy the four defining conditions of a competitive equilibrium. We need only check that {VtM }+∞
t=0 so defined satisfies equation (4.1). The
envelope theorem gives
v1 (mt , t) = S1 (mt + et − xt , t) − 2 + βv1 (mt + et − xt , t + 1) + µt
for all t, where µt ≥ 0 is the value of the multiplier associated with the second constraint at
date t. But then (4.3) implies v1 (mt , t) = λt . So v1 (mt , t) ≥ 0. If λt happens to be positive,
xt = 0, hence µt = 0 by (4.6). Then λt = S1 (m + e − x, t) − 2 + βv1 (m + e − x, t + 1), by
M
− V B ). It follows that,
(4.3), or , λt = qtM − 2 + β(Vt+1
M
− V B ), 0 ,
VtM − V B = v1 (mt , t) = max qtM − 2 + β(Vt+1
which is equation (4.1) with VtB = V B = 2/(1 − β) for all t. So we have shown that solutions
to the surplus maximization problem are competitive equilibria. That competitive equilibria
are solutions to the surplus problem is established similarly.
To see that an equilibrium exists, observe that the surplus maximization problem is the
maximization of a continuous function on a compact subset of IR∞ equipped with the product
topology. As for uniqueness, note that the set of feasible sequences {xt , et }+∞
t=0 is convex, and
that S(•, t) is strictly concave for all t because Dt is strictly decreasing. This completes the
proof.
13
Proposition 4.1 is not merely of technical interest. It implies that our theory for why
financial structures vary in apparently similar economies is not one of multiple equilibria.
Given an initial size of the financial sector, economies with the same sequence of fundamental
characteristics have the same equilibrium sequence of financial structures. Fundamentals fully
explain financial structures. Put another way, if two economies reach two different financial
systems, their fundamental characteristics must have differed at some point. This, however,
does not imply that two economies whose fundamental characteristics converge will converge
to similar financial systems. We now turn to establishing this result.
5
Fundamental vs. financial convergence
In this section we compare the equilibrium sequence of financial structures of economies with
different sequences of fundamental characteristics. Formally, let i ∈ {1, 2} index two distinct
economies. Denote by (cit , ρit , Fti) the financial market entry cost, the bank intermediation cost,
and the distribution of observable project characteristics in economy i at date t. By economy
i’s fundamental characteristics at date t we mean (cit , ρit , Fti ). A sequence {cit , ρit , Fti }+∞
t=0 of
fundamentals together with an initial distribution mi−1 of financial market lenders in economy
i imply a unique equilibrium sequence {mit } of financial structures, by Proposition 4.1. The
question we ask in this section is whether convergence (in some sense) of {ρ1t , c1t , Ft1 }+∞
t=0 to
1 +∞
2 +∞
1
2
{ρ2t , c2t , Ft2}+∞
t=0 implies that {mt }t=0 converges to {mt }t=0 , for any pair (m−1 , m−1 ) of initial
conditions.
We will show that, convergence in fundamentals does not imply convergence in financial
structures unless entry into the financial market is free. To emphasize the key role of entry
costs, we first show that if, eventually, c1t = c2t = 0, then convergence in fundamentals imply
financial convergence. In this case, financial market entry is eventually costless and lenders
solve a static problem as past financial decisions do not matter. The supply of funds on the
financial market, therefore, only depends on current fundamental characteristics. If those
characteristics converge, so must the size of the financial sector. For concreteness, we will
1
2 +∞
say that two economies converge in fundamentals if {ρ1t − ρ2t }+∞
t=0 and {ct − ct }t=0 converge
to zero with t in the usual sense, while {Ft1 − Ft2 }+∞
t=0 converge to zero uniformly on [0, 1]. To
14
avoid the usual convergence technicalities, we will also assume that {Ft1 − Ft2 }+∞
t=0 is a normal
family of functions:9
Assumption 5.1. {Ft1 − Ft2 }+∞
t=0 is equicontinuous on [0, 1].
Under that assumption, we obtain:
Proposition 5.2. If c1t = c2t = 0 for t large enough, convergence in fundamentals implies
convergence in financial structures.
Proof. When c1t = c2t = 0 from t on, VsM = V B for all s ≥ t in both economies and the
supply of funds on the financial market in a given period is independent of the previous
size of the financial sector. Specifically, when qs = 2 at date s ≥ t, lenders are indifferent
between the bank and the financial market. The supply of fund, in that case, is any number
in [0, ]. Demand, on the other side is 1 − Fsi (p∗1 (2, ρis )) in economy i, which is contained is
[0, 1]. Therefore qs = 2 clears markets for all s ≥ t. Since the equilibrium sequence of market
sizes is unique, we must have mis = 1 − Fsi (p∗1 (2, ρis )) for i = 1, 2 and s ≥ t. To complete the
argument, note that we can assume without loss of generality that {ρ1t , ρ2t }+∞
t=0 is bounded.
Indeed, whenever ρ > 1, p∗1 (2, ρ) = p∗1 (2, 1). Therefore, p∗1 is uniformly continuous. Because
1
2
{Ft1 − Ft2 }+∞
t=0 is equicontinuous, mt − mt converges to zero in the standard sense as t rises,
as claimed.
But, in general, fundamental convergence does not imply financial convergence. To see
this, we consider an extreme case of fundamental convergence by assuming that, for both
i ∈ {1, 2}, (cit , ρit , Fti ) = (c, ρ, F ) for all t. We further restrict parameters so that if c = 0 the
financial sector is active in every period. Without such an assumption, the two economies
would jump to the same degenerate (banks only) financial structure immediately. Formally,
Assumption 5.3. 1 − F (p∗1 (2, ρ)) > 0.
When, as is now the case, fundamentals are constant, it is natural to inquire about invariant values for the size of the financial sector, that is, set of initial conditions m∗ such that
if m−1 = m∗ , mt = m∗ for all t in equilibrium. Let Γ be the set of such initial values. A
To obtain a generic convergence result assuming that {Ft1 −Ft2 }+∞
t=0 has a small Julia set suffices. Potential
problems only arise in the proof of proposition 5.2 if p∗1 lands in the Julia set of {Ft1 − Ft2 }+∞
t=0 infinitely often.
9
15
necessary condition for economies with the same sequence of constant fundamentals to always
converge to the same financial structure is that Γ be a singleton. Otherwise, two economies
whose initial conditions are two distinct points of the invariant set would remain at those
distinct points at all dates. The following remark records the fact that Γ is a singleton when
entry into the financial market is costless.
Remark 5.4. If c = 0, Γ is a singleton.
Proof. When c = 0, mt = 1 − F (p∗1 (2, ρ)) for all t in equilibrium, regardless of m−1 .
In fact, when c = 0 and all fundamentals are identical in the two economies, both
economies jump to the unique invariant size of the financial sector immediately and remain
there. They trivially converge to the same financial structure. When c > 0 however, there are
many invariant distributions and, therefore, convergence in fundamentals in any sense does
not imply convergence in financial structures.
Proposition 5.5. If c > 0, Γ is a closed interval of strictly positive diameter.
Proof. Let m∗ = 1 − F (p∗1 (2, ρ)) and assume that c > 0. If qt = 2 for all t then et = 0 for all
t since lenders are just willing to enter markets if qt = 2 for all t when c = 0. In particular,
m∗ remains invariant when c > 0. Now choose q so that if qt = q for all t, VtM − c = V B for
all t. Then q > 2 and for all q ∈ (2, q ), qt = q for all t implies VtM − c < V B for all t so that
et = 0 for all t. But since q > 2 we also have xt = 0 for all t. It follows that for q ∈ [2, q ],
m = 1 − F (p∗1 (q, ρ)) is invariant. Because F is strictly increasing and continuous, the set of
such size of the financial market is a closed interval of positive mass.
The intuition for this result is simple. Fundamentals imply a unique sequence of prices of
financial contracts. Those prices can be such that it is profitable for lenders who have borne
the entry cost to remain on the financial market, but not high enough to cover the entry cost
for lenders who have yet to bear it. If c is high, many such price sequences exist and so,
therefore, do many invariant sizes of the financial market. The fact that the upper bound of
the set of invariant distribution is the unique element (m∗ = 1 − F (p∗1 (2, ρ)) of Γ in economies
where entry costs are zero should also be intuitive. It is finally easy to see that for c large
16
enough or ρ low enough, Γ = [0, m∗ ] so that, in that case, economies that did not develop a
financial market in the past never will.
6
Discussion of our key assumptions
Many of the simplifying assumptions we have made heretofore are easy to relax. For instance,
assuming that borrowers also face a cost when they choose to participate in financial markets
(to ensure symmetry with lenders), or assuming that exit from financial markets is costly,
would add notation without altering any of our results. Similarly assigning more general
preferences, though still monotonic, to borrowers would not affect our results. Two critical
assumptions we make however are that 1) no exogenous exit from financial markets ever occurs
and, 2) that lenders cannot fund more than one project with bounded size. The purpose of
this section is to discuss the role of those two key assumptions.
6.1
Exogenous exit
So far we have assumed that there is no exit from the financial market for exogenous reasons.
Lenders exit when and only when it is profit maximizing for them to do so. Lenders who
entered the financial market in the past because fundamental characteristics justified it may
choose to stay put in equilibrium while given current and future fundamentals lenders who
have yet to pay the fixed cost maximize their income by staying out of the financial market.
To highlight the importance of this feature of our model, we now introduce exogenous exit
by assuming that a fraction δ > 0 of lenders die every period and are immediately replaced
by newly born lenders. Furthermore, all newly born lenders have to pay the fixed cost if they
choose to enter the financial market. For clarity, we state here the equations which the value
functions of lenders must solve when death occurs with positive likelihood. From the point
of view of risk-neutral lenders, this only means that they discount future flows at rate βδ,
instead of β:
M
B
; 2 + βδVt+1
,
VtM = max qtM + βδVt+1
17
while, for lenders who were not in the financial market at date t − 1,
M
B
=
; 2 + βδVt+1
VtB = max qtM − ct + βδVt+1
2
.
1 − βδ
Our definition of an equilibrium changes little. The main difference is that condition 3 becomes, for all t ≥ 0, mt+1 = mt (1−δ)−xt +et , where xt is understood as the mass of surviving
lenders who choose to exit the financial market in period t. One can replicate the arguments
behind proposition 4.1 to show that equilibria continue to exist and that the equilibrium path
of financial market sizes continues to be unique. More importantly, we can also show:
Proposition 6.1. If δ > 0, then Γ is a singleton. Furthermore, if for i ∈ {1, 2} and for all
t ≥ 0 (ctt , ρit , Fti) = (c, ρ, F ), then m1t − m2t is zero after a finite number of periods.
Proof. Let m∗ be an element of Γ. (Γ is not empty because it always contains at least the
unique invariant distribution that prevails when c = 0.) If m∗ > 0, then there must be some
entry in invariant equilibrium in all periods since xt + δm∗ > 0 for all t. This implies that
qt = q̄ for all t where
q̄
1−βδ
− c = V B or, q̄ = 2 + (1 − βδ)c. That is, q̄ is the unique constant
price of financial market contracts such that lenders are just willing to enter the financial
market in each period. But then m∗ = 1 − F (p∗1 (q̄, ρ)) is the only possible element of Γ. Note
that if (and only if) 1 − F (p∗1 (q̄, ρ)) = 0, m∗ = 0 is the only element of Γ.
To see that both economies converge to Γ’s unique element, assume that m∗ > 0 and
that m1t < m∗ for some t. Then qt > q̄ for otherwise we would have too many borrowers on
the financial market in economy 1 since 1 − F (p∗1 (q̄, ρ)) = m∗ > m1t . If qs > q̄ for all s > t
then all lenders would enter the financial market at date t since q̄ is such that, if maintained
for ever, lenders are just willing to enter the financial market. This is incompatible with
equilibrium. So we must have qs < q̄ for some s > t so that, at some s, ms ≥ m∗ . If ms = m∗ ,
we are done. So without loss of generality we can assume that mi−1 > m∗ for i ∈ {1, 2},
that is start both economies above the invariant size of financial market. We will construct a
continuation equilibrium from that point that converges to m∗ in a finite number of period.
Because equilibria are unique from any initial size, the result will then be established.
Let m̃it = mi−1 (1 − δ)t+1 . If, at date t, mi1 (1 − δ)t+1 < m∗ let qt (mi−1 ) = q̄. Otherwise,
let qt (mi−1 ) be such that be such that the financial market clears at size m̃it , i.e. the unique
18
solution to 1 − F (p∗1 (q, ρ)) = m̃it . Let VtM be the corresponding value function for lenders on
the financial market. Note that qt (mi−1 ) ≤ q̄ for all t. Therefore, at those prices, VtM ≤ V B +c
since VtM = V B + c when qs = q̄ for all s ≥ t. Define
m̄ = max{m ∈ [
m∗
, 1] : V0M ≥ V B given prices {qt (m)}}.
1−δ
i
t+1
If mi−1 > m̄ then V0M < V B given prices {qt (mi−1 )}+∞
t=0 . In that case, choose m̃t = m̄(1 − δ)
and construct prices as before. To complete our construction of an equilibrium, we need to
describe a path for entry and exit from the financial market. If mi1 ≤ m̄, set xt = 0 for all t.
If mi−1 ≥ m̄, then set x0 = (1 − δ)(mi−1 − m̄) and xt = 0 for all t > 0. As for entry, set et = 0
if mi−1 (1 − δ)t+1 > m∗ , and et = δm∗ otherwise. One easily checks that we have constructed
∗
m
an equilibrium from initial condition mi−1 . What’s more, mit = m∗ after at most log(1−β)
periods in both economies. In particular, m1t − m2t = 0 after a finite number of periods, as
claimed.
Obtaining convergence, therefore, requires that exit occurs exogenously sufficiently enough,
and that the lenders who replace lenders on the financial market do not inherit their opportunities. Note however that convergence occurs at a rate that depends on the rate of exogenous
exit. While not permanent, differences in financial market can be arbitrarily persistent if the
rate of exogenous exit is low.
6.2
Project size
In our model, participation in the financial market allows lenders to manage exactly one
project for any number of periods after bearing a cost of entry. However, they cannot fund
more than one project. Relaxing this assumption enables lenders to mitigate entry costs. For
instance, lenders could pool resources and delegate a representative in the financial market,
dividing the proceeds equally among members of the coalition.10 If the entry cost borne by the
coalition does not increase with its size, the entry cost per project can be made arbitrarily
10
Lender could also choose to accumulate resources in order to fund several projects. Wealth accumulation
introduces additional technical complications since the evolution of the economy now depends on another state
variable. But as long as setting up more projects is costly for lenders, financial systems should be persistent.
19
small. As a consequence, the set of invariant financial market sizes will shrink. One key
assumption we are making, therefore, is that the total cost of setting up projects rises with
the number of projects, even if the same lender is involved in all projects.
A related assumption we are making is that project size is unique. Under the alternative
assumption that lenders can fund project of various sizes, and that set-up costs increase less
than linearly with size, large projects would be funded first on the financial market. But,
again, as long as funding more projects carries an initial cost, channelling more resources to
the financial market will be more costly. Then, as in our basic model, economies who have
created a large financial market in the past will remain more likely to have a large financial
market in the future, making financial structure persistent. In short, as long as making the
financial market bigger from one period to the next is costly, history will continue to matter.
7
Conclusion
We have presented a dynamic, general equilibrium model in which financial structure differences between two economies can persist even after fundamental characteristics have converged. In simple terms, this occurs in our theory because channelling funds through the
financial market is cheaper in economies that have borne the cost of building large financial
markets in the past.
A possible illustration of these forces at play are the economic histories of Germany and
the United States. Germany used to impose significant legal barriers to entry into financial
markets. Meanwhile, federal laws discouraged bank intermediation in the U.S. As a consequence, early on, banks became heavily involved in corporate lending in Germany, while U.S.
firms learned to rely on other sources of funds. Even though the legal frameworks of the two
nations no longer differ much, the U.S. has a longer history of financial market lending than
Germany, and financial markets remain a more cost effective source of funds for U.S. firms
than for German firms.
Quite importantly, equilibria are unique and Pareto optimal in our model. Financial
structures are efficient given the fundamental characteristics of each economy. While current
fundamentals may not suffice to explain a nation’s current financial structure, together with
20
past fundamentals they fully explain, and justify it.
Finally, our model more generally suggests that basic industrial organization principles
could help us understand why financial structures vary so markedly across nations.
A
Historical Motivation
One motivation for this paper is the fact that, historically, institutional environments have
differed markedly in Germany and the United States. In the U.S., banking activities have
been regulated by states since the end of the Second Bank of the U.S. in 1836. The fear of
concentration in the banking sector prompted most states to impose restrictions on branching.
The National Banking System introduced after the Civil War in 1863 further limited the scale
and scope of banks by restricting their holdings of equities and imposing minimum capital
requirement (see Sylla, 1969.) The importance of local banks, the absence of nationwide banks
and the absence of a central bank created an environment propitious to banking panics.11 In
response, the Federal Reserve System was created in 1913. The poor functioning of the
banking sector until then favored the development of alternative sources of finance, and
the growing role of financial markets. Davis (1965) writes that “a series of new financial
institutions capable of surmounting the barriers raised by distance and by the lack of adequate
branch-banking legislation was innovated. In the period 1870 to 1914, barriers to short-term
mobility were overcome by direct solicitation of interregional funds, by commercial bank
rediscounting, and most important, by the evolution of a national market for commercial
paper.” Unlike the banking sector, financial markets were subject to little regulation in the
U.S. (see Smith and Werner, 1991). Incumbent financial market participants managed to
erect some barriers to entry, 12 but the presence of many competing institutions and large
broking firms mitigated the impact of these barriers. Michie (1986) points out for instance
that “the most serious challenge [to the New York Stock Exchange] came in 1885, when
a number of rival exchanges merged to form the Consolidated Stock Exchange, with 2403
members”, which competed with the New York Stock Exchange until World War I.
While the relative importance of banks steadily declined in the U.S. in the XIXth century,
they became the dominant source of funds for firms in Germany. According to Guinnane
(2002), several institutional factors explain the historical dominance of bank financing in
Germany. Prior to 1871, Germany was a constellation of independent states with local control
over financial regulations. Most states restricted the number of limited liability firms, as they
feared the separation of firm’s ownership and firm’s liabilities would allow entrepreneurs to
11
Panics occurred in 1837, 1857, 1873, 1884, 1893 and 1907.
Davis and Neal (1998) and Michie (1986) review the history of the New York Stock Exchange. The
exchange started operating in 1792 with 24 members and was formally established in 1817. The number of
members reached 1,100 in 1879 and remained there until 1914. Then, a new member had to buy the seat of
an existing member and pay a substantial entry fee ranging between $64,000 and $94,000 in 1910. The fact
that existing members owned the stock exchange enabled them to levy a minimum commission for each trade
and restrict the type of securities they wished to trade. As a result, the average size of each issue from quoted
industrial and commercial companies was $24.7 million by 1914. Minimum commissions and restricted access
created inefficiencies and fragmented the New York securities market.
12
21
escape their debts and because they wanted to extract rents from granting this privilege. The
right to set up a joint stock firm was seldom granted. In 1857, only 203 joint stock firms
existed in Germany. Despite high demand and an improved legal framework under the 1861
Business Code, very few additional firms had obtained joint stock status by 1870. Banks thus
remained the main providers of funds for most industrial firms’ funds in Germany. Guinnane
(2002) and Tilly (1998) also argue that the presence of a lender of last resort made banks
more willing to engage in industrial lending. The Bank of Prussia, founded in 1847, “acted,
to some degree at least, like a lender of last resort. Banks that were in trouble could sell bills
out of their own portfolio to the Bank of Prussia” (Tilly, 1998.) The Bank of Prussia later
became the Reichsbank, and continued to serve this role. In contrast, no lender of last resort
existed in the United States until the Federal Reserve was founded in 1913.
Despite the many institutional barriers they faced, financial markets experienced a shortlived growth spurt after Prussia defeated Austria in the 1866 war and the new North German
Confederation was founded. All trade barriers were abolished and a single currency was established. An economic boom ensued marked by large capital intensive projects such as railroad
expansion. The Berlin Stock Exchange expanded briskly for a few years, but was severely
hit by the 1873 crash. As a response to the ensuing instability, Germany decided to restrict
the Berlin Stock Exchange’s activities in a process that culminated with the 1884 and 1896
company Laws. Although some debate the effects of the companies laws on firms’ finance (see
Fohlin 2001), these laws imposed new constraints on financial markets activities. For instance
Tilly (1982) reports that “only larger firms having a stock exchange listing could tap in that
market for capital without delay and only large firms would not find the minimum issue volume of one million marks and minimum share size of one thousand marks inconvenient. This
gap must have benefited banks who did have access to the stock exchange, but it also must
have excluded many potential users of the capital market.” As far as investors are concerned,
the 1885 stock exchange laws restricted access to the Berlin Stock Exchange. Entrance tickets (“Eintrittskarte”) were only granted to members of the “Korporation der Kaufmannschaft
von Berlin” and owners of firms or corporations that were registered in Berlin.13 Importantly,
it is barriers to access to the stock market, rather than its malfunctioning, that seem to have
limited its development. Fohlin and Gehrig (2004) argue that the Berlin Stock Exchange was
surprisingly efficient for the time.
Although legal differences between Germany, the U.S. and other nations (see e.g Allen and
Gale, 2000) still exist, they are fading. In the U.S. for instance, the Riegel-Neal Interstate
Banking and Branching Efficiency Act of 1994 set up a timetable for relaxing the restrictions
on interstate banking. Also, the restrictions imposed by The Glass-Steagall Act of 1933 on
securities underwriting have been gradually relaxed.14
13
We thank to Martin Uebele and Stefan Volk for providing this information to us. Unfortunately, we could
not obtain the price of these tickets.
14
A firewall preventing the flow of information between subsidiaries and other parts of the banks remains
mandated however. In Germany the underwriting of securities is unrestricted and can be undertaken directly
by the bank. Germany does not mandate any firewalls.
22
References
[1] Allen, F. and D. Gale (2000) Comparing Financial Systems, MIT Press.
[2] Baliga, S. and B. Polak (2004) The emergence and persistence of the Anglo-saxon and
German financial systems. The Review of Financial Studies, Vol. 17, No. 1, pp. 129-163.
[3] Barth, J., D. Nolle and T. Rice (1997) Commercial Banking Structure, Regulation and
Performance: An International Comparison. Economics Working paper 97-6, Comptroller
of the Currency.
[4] Bolton, P., and Freixas X., (2000) Equity, Bonds and Bank Debt: Capital Structure and
Financial Market Equilibrium Under Assymetric Information. The Journal of Political
Economy, Vol. 108, No. 2, April, pp324-351.
[5] Davis, L. E. (1965) The investment market, 1870-1914: The evolution of a national
market. Journal of Economic History, Vol. 25, Issue 3, September.
[6] Davis, L. E. and L. Neal (1998) Micro Rules and Macro Outcomes: The Impact of
Micro Structure on the Efficiency of Security Exchanges, London, New York and Paris,
1800-1914. American Economic Review, Vol. 88, No. 2, 40-45.
[7] De Fiore, F. and H. Uhlig (2004) Bank finance versus bond finance: What explains the
differences between the US and Europe? Mimeo European Central Bank.
[8] Demirguc-Kunt, A. and R. Levine (2001), Financial Structure and Economic Growth: A
Cross-Country Comparison of Bank, Markets, and Development, MIT Press monograph.
[9] Dewatripont, M. and E. Maskin (1995) Credit and Efficiency in Centralized and Decentralized Economies. The Review of Economic Studies, Vol. 62, No. 4, pp. 541-555.
[10] Fohlin, C. (2001) Regulation, Taxation and the Development of the German Universal
Banking System, 1884-1913. European Review of Economic History.
[11] Fohlin, C. and T. Gherig (2004) Price Discovery in Early Securities Markets: The Case
of the Berlin Stock Exchange 1880-1910. Mimeo.
23
[12] Guinnane, T. W. (2002) Delegated monitors, large and small: Germany’s banking system, 1800-1914. Journal of Economic Literature, Vol. XL, March, pp. 73-124.
[13] Holmstrom, B. (1996) Financing of Investments in Eastern Europe: A Theoretical Perspective. Industrial and Corporate Change, Vol 5, No 2.
[14] Hopenhayn, H. A. (1992) Entry, exit, and firm dynamics in long run equilibrium. Econometrica, Vol. 60, No.5, September, pp. 1127-1150.
[15] Lucas, R. E. Jr. and E.C. Prescott (1971) Investment under uncertainty. Econometrica,
Vol. 39, No. 5, September, pp. 659-681.
[16] Michie, R. C. (1986) The London and New York Stock Exchanges, 1850-1914. Journal
of Economic History, Vol. 46, No.1, 171-187.
[17] Smith, S. T. and W. Werner (1991) Wall Street. Columbia University Press, New York.
[18] Sylla, R. (1969) Federal Policy, Banking Market Structure, and Capital Mobilization in
the United States, 1863-1913. Journal of Economic History, Vol. 29, No. 4, 657-686.
[19] Tilly, R. (1982) Mergers, external growth, and finance in the development of largescale enterprise in Germany, 1880-1913. Journal of Economic History, Vol. XLII, No. 3,
September.
[20] Tilly, R. (1998) Universal Banking in Historical Perspective. Journal of Institutional
Theoretical Economics 154:1, pp. 7-32.
24
Figure 1: Bank Lending and Financial Markets in Germany and the U.S.
Private credit by deposit money banks to GDP
1.5
Germany
U.S.
1
0.5
1975
1980
1985
1990
Stock market capitalization to GDP
1995
1985
1990
Private bond market capitalization to GDP
1995
2000
1.5
1
0.5
0
1980
2000
1.5
1
0.5
0
1990
1991
1992
1993
1994
1995
Source: Demirguc-Kunt and Levine, 2001.
25
1996
1997
1998
1999
2000
@FedFRASER