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Working Paper Series

Quantifying the Impact of Financial
Development on Economic Development

WP 10-05

Jeremy Greenwood
University of Pennsylvania
Juan M. Sanchez
Federal Reserve Bank of Richmond
Cheng Wang
Iowa State University

This paper can be downloaded without charge from:
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Version: April 2010

Quantifying the Impact of Financial Development on Economic
Development
by
Jeremy Greenwood, Juan M. Sanchez and Cheng Wang
Working Paper No. 10-05

Abstract
How important is …nancial development for economic development? A costly state veri…cation
model of …nancial intermediation is presented to address this question. The model is calibrated to
match facts about the U.S. economy, such as intermediation spreads and the …rm-size distribution
for the years 1974 and 2004. It is then used to study the international data, using cross-country
interest-rate spreads and per-capita GDP. The analysis suggests a country like Uganda could increase its output by 140 to 180 percent if it could adopt the world’s best practice in the …nancial
sector. Still, this amounts to only 34 to 40 percent of the gap between Uganda’s potential and
actual output.
Keywords: costly state veri…cation, economic development, …nancial intermediation, …rm-size distribution, interest-rate spreads, cross-country output di¤erences, cross-country TFP di¤erences
JEL Nos: E13, O11, O16

A- iations: University of Pennsylvania, Federal Reserve Bank of Richmond, and Iowa State University

Introduction

How important is …nancial development for economic development? Ever since Raymond W.
Goldsmith’s (1969) classic book, economists have been developing theories and searching for
empirical evidence connecting …nancial and economic development. Goldsmith emphasized
the role that intermediaries play in steering funds to the highest valued users in the economy.
First, intermediaries collect and analyze information before they invest in businesses. Based
upon this information, they determine whether or not to commit savers’ funds. If they
proceed, then they must decide how much to invest and on what terms. Second, after
allocating funds intermediaries must monitor …rms to ensure that savers’best interests are
protected. Increases in the e¢ ciency of …nancial intermediation, due to improved information
production, are likely to reduce the spread between the internal rate of return on investment
in …rms and the rate of return on savings received by savers. The spread between these
returns re‡ects the costs of intermediation. This wedge will include the costs of gathering
ex-ante information about investment projects, the ex-post information costs of policing
investments, and the costs of misappropriation of savers’s funds by management, unions, etc.,
that arise in a world with imperfect information. An improvement in …nancial intermediation
will not necessarily a¤ect the rate of return earned by savers. Aggregate savings may adjust
in equilibrium so that this return always equals savers’rate of time preference.
Figure 1, left panel, plots the intermediation wedge for the U.S. economy over time. (All
data de…nitions are presented in the Appendix.) The United States is a developed economy
with a sophisticated …nancial system. The wedge falls only slightly. At the same time, it is
hard to detect an upward trend in the capital-to-output ratio. Contrast this with Taiwan,
shown in the right panel. Here, there is a dramatic drop in the interest-rate spread. As the
cost of capital falls one would expect to see a rise in investment. Indeed, the capital-to-output
ratio for Taiwan shows signi…cant increase. The observation that there is only a small drop
in the U.S. interest-rate spread does not imply that there has not been any technological
advance in the U.S. …nancial sector. Rather, it may re‡ect the fact that e¢ ciency in the
U.S. …nancial sector has grown in tandem with the rest of the economy, while for Taiwan it
1

has outpaced it. For without technological advance in the …nancial sector, banks would face
a losing battle with the rising labor costs that are inevitable in a growing economy. The
intermediation spread would then have to rise to cover costs. More on this later.
United States

Taiwan

2.4

spreads
(left axis)

2.0
5

2.0

spreads
(left axis)

1.6

capital/output
(right axis)

1.6

3
1.2

2
capital/output
(right axis)

1
1970

1980

1990

2000

1.2

2
1

0.8
2010

1970

1980

1990

2000

0.8
2010

Years

Figure 1: Interest-rate spreads and capital-to-output ratios for the United States and Taiwan,
1970-2005.

Now, in Goldsmithian fashion, consider the scatter plots presented for a sample of countries in Figures 2 and 3. Take Figure 2 …rst. The left panel shows that countries with lower
interest-rate spreads tend to have higher capital-to-output ratios. The right panel illustrates
that a higher capital-to-output ratio is associated with a greater level of GDP. Dub this the
capital-deepening e¤ect of …nancial intermediation. Next, turn to the left panel in Figure
3. Observe that lower interest-rate spreads are also linked with higher levels of total factor
productivity, TFP. This would happen when better intermediation tends to redirect funds
to the more e¢ cient …rms. The right panel displays how higher levels of TFP are connected
2

with larger GDP. Call this the reallocation e¤ect arising from …nancial intermediation. The
capital deepening and reallocation e¤ects from improved intermediation will play an important role in what follows. While the above facts are stylized, to be sure, it will be noted that
empirical researchers have used increasingly sophisticated methods to tease out the relationship between …nancial intermediation and growth. This literature is surveyed masterfully
by Levine (2005). The upshot is that …nancial development has a causal e¤ect on economic
development; speci…cally, …nancial development leads to higher rates of growth in income

50000

and productivity.

JPN
CHE

40000

LUX

K-to-GDP ratio
2

AUT
ITA
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USA NOR

GDP per capita
20000
30000

FINTHA

.05
.1
Interest-rate spread

.15

2
K-to-GDP ratio

Figure 2: The cross-country relationship between interest-rate spreads, capital-to-output
ratios and GDP.

The impact that …nancial development has on economic development is investigated
here, quantitatively, using a costly state veri…cation model that is developed, theoretically,
3

50000

1500

LUX

IRL

USA

FINITA
ISR
NZL
ESP
PRT

URY
MEX
COL
SLV

MAR
LKA
PHL
THA
PAK BOL
IND

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NLD
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JPN GBR

10000

500

TFP

NOR
BEL
NLD
MUS
GBR
AUT
FRA
AUS
ISR
ITADNK
CAN
SWE
CHE
NZLESP
FIN
JPN
PRT
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TTO
ARG
EGY
PAN

USA
NOR

GDP per capita
20000
30000

1000

40000

LUX

.05
.1
Interest-rate spread

.15

500

TFP

1000

1500

Figure 3: The cross-country relationship between interest-rate spreads, TFP and GDP

in Greenwood et al. (forthcoming). The source of inspiration for the framework is classic
work by Diamond (1984), Townsend (1979), and Williamson (1986). It has two novel twists,
however. First, the e¢ ciency of monitoring the use of funds by …rms depends upon both
the amount of resources devoted to this activity and the state of technology in the …nancial
sector. Second, …rms have ex-ante di¤erences in the structure of returns that they o¤er.
A …nancial theory of …rm size emerges. At any point in time, …rms o¤ering high expected
returns are underfunded (relative to a world without informational frictions), while others
yielding low expected ones are overfunded. This results from diminishing returns in information production. As the e¢ ciency of the …nancial sector rises (relative to the rest of the
economy) funds are redirected away from less productive …rms in the economy toward the
more productive ones. Furthermore, as the interest-rate spread declines, and the cost of
borrowing falls, there will be capital deepening in the economy.
The model is calibrated to match some stylized facts for the U.S. economy, speci…cally
the …rm-size distributions and interest-rate spreads for the years 1974 and 2004. It does
an excellent job replicating these facts. The improvement in …nancial sector productivity
required to duplicate these facts also appears to be reasonable. It does this with little change
in capital-to-output ratio. In the model, improvements in …nancial intermediation account
for 30 percent of U.S. growth. The framework also is capable of mimicking the dramatic
decline in the Taiwanese interest-rate spread. At the same time, it predicts a signi…cant rise
in capital-to-output ratio. It is estimated that dramatic improvements in Taiwan’s …nancial
sector accounted for 50 percent of growth.
The calibrated model is then taken to the cross-country data. It also does a reasonable
job predicting the di¤erences in cross-country capital-to-output ratios. Similarly, it does a
good job matching the empirical relationship between …nancial development and average
…rm size. Financial intermediation turns out to be important quantitatively. For example,
in the baseline model Uganda would increase its GDP by 140 percent if it could somehow
adopt Luxembourg’s …nancial system. World output would rise by 65 percent if all countries
adopted Luxembourg’s …nancial practice.

Still, the bulk (or 64 percent) of cross-country

variation in GDP cannot be accounted for by variation in …nancial systems.
There are other recent investigations of the relationship between …nance and development that use quantitative models. The frameworks used, and the questions addressed,
di¤er from the current analysis. For example, Townsend and Ueda (2006) estimate a version
of the Greenwood and Jovanovic (1990) model to examine the Thai …nancial reform. Their
analysis stresses the role that …nancial intermediaries play in producing ex-ante information
about the state of the economy at the aggregate level. Financial intermediaries o¤er savers
higher and safer returns. They …nd that Thai welfare increased about 15 percent due to …nancial liberalization. Buera et al. (2009) focus on the importance of borrowing constraints
in distorting the allocation of entrepreneurial talent in the economy. This helps explain
TFP di¤erentials across nations.1

Limited investor protection is emphasized by Castro et

al. (2009). They build a two-sector model to explain the positive cross-country correlation
between investment and GDP. They note that the capital-goods sector is risky. This makes
capital goods expensive to produce in poor countries with limited investor production, because of the high costs of …nance. An implication of their framework is that the correlation
between investment and GDP is weaker when measured at domestic vis à vis international
prices. This is true in the data.

The Economy

The analysis focuses on two types of agents; to wit, …rms and …nancial intermediaries.
Firms produce output using capital and labor. Their production processes are subject to
idiosyncratic productivity shocks. The realized value of the productivity shock is a …rm’s
private information. All funding for capital must be raised from …nancial intermediaries.
This is done before the technology shock is observed. After seeing its shock, a …rm hires
labor on a spot market. When …nancing its capital a …rm enters into a …nancial contract
1

Erosa and Cabrillana (2008) also investigate the interplay between …nancial market frictions and the
allocation of managerial talent for explaining cross-country productivity di¤erences, albeit with more of a
theoretical emphasis.

with the intermediary. This contract speci…es the state-contingent payment that a …rm
must make to an intermediary upon completing production. Hidden in the background
are consumer/workers. They supply a …xed amount of labor to the economy. They also
deposit funds with an intermediary that earn a …xed rate of return. Given the focus here
on comparative steady states, an analysis of the consumer/worker can be safely suppressed.
The behavior of …rms and intermediaries will now be described in more detail.

Firms

Firms hire capital, k, and labor, l, to produce output, o, in line with the constant-returnsto-scale production function
o = x k l1

The productivity level of a …rm’s production process is represented by x . It is the product
of two components: an aggregate one, x, and an idiosyncratic one, . The idiosyncratic level
of productivity is a random. Speci…cally, the realized value of
set

= f 1;

Pr( =

2 g,
1

with

and Pr( =

The set

is drawn from the two-point

di¤ers across …rms. Call this the …rm’s type. Let
1.

The probabilities for the low and high states

(1 and 2, respectively) are the same across …rms. The realized value of

is a …rm’s

private information. For now take the aggregate level of productivity, x, to be some known
constant.
Suppose that a type- …rm has raised k units of capital. It then draws the productivity
shock

It must now decide how much labor, li , to hire at the wage rate w. In other words,

the …rm will solve the maximization problem shown below.
R( i ; w)k

maxfx i k li1

wli g:

P(1)

Denote the amount of labor that a type- …rm will hire in state i by li ( ) = li ( 1 ;

2 ).

Substituting the implied solution for li into the maximand and solving yields the unit return
function, R( i ; w), or
ri ( )

R( i ; w) = (1

)(1
7

(x i )1= > 0:

(1)

Think about ri ( ) = R( i ; w) as giving the gross rate of return on a unit of capital invested
in a type- …rm, given that state

occurs.

Financial Intermediaries

Intermediation is competitive. Intermediaries raise funds from consumers and lend them to
…rms. Even though an intermediary knows a …rm’s type, , it cannot observe the state of
a …rm’s business either costlessly or perfectly.2 That is, the intermediary cannot costlessly
observe , o and l. Suppose a …rm’s true productivity in a period is
the intermediary that its productivity is

which may di¤er from

It reports to

The intermediary

can audit this report. It seems reasonable to presume that the odds of detecting fraud are
increasing the amount of labor devoted to verifying the claim, lmj , decreasing in the size of
the loan, k— because there will be more activity to monitor— and rising in the productivity
of the monitoring technology, z. Let Pij (lmj ; k; z) denote the probability that the …rm is
caught cheating conditional on the following: (1) the true realization of productivity is
(2) the …rm makes a report of

(3) the intermediary allocates lmj units of labor to monitor

the claim; (4) the size of loan is k (which represents the scale of the project); (5) the level of
productivity in the monitoring activity is z. The function Pij (lmj ; k; z) is increasing in lmj
and z, and decreasing in k. Additionally, let Pij (lmj ; k; z) = 0 if the …rm truthfully reports
2

Recall that the intermediary knows the …rm’s type, . One could think about this as representing the
activity, industry or sector that a …rm operates within. For instance, Castro et al. (2009, Figure 3) present
data suggesting that the capital-goods sector is riskier than the consumption-goods one. It would be possible
to have a screening stage where the intermediary veri…es the initial type of a …rm. The easiest way to do
this would be to have them pay a cost that varies with loan size to discover . If the …rm’s type can’t be
undercovered perfectly, as in the classic work of Boyd and Prescott (1986), then it may be possible to design
the contract to reveal it.

that its type is

(i.e., when j = i). A convenient formulation for Pij (lmj ; k; z) is3
8
1
>
>
1
< 1; with 0 < ; < 1;
>
(z=k) (lmj )
<
Pij (lmj ; k; z) =
for a report j 6= i ;
>
>
>
: 0;
for a report j = i :
i

(2)

The intermediary makes a …rm a loan of size k. In exchange for the loan the …rm will
make some speci…ed state-contingent payment to the intermediary. The rents that accrue
to a …rm will depend upon the true state of its technology,

the state that it reports,

plus the outcome of any monitoring that is done. Clearly, a …rm will have no incentive to
misreport when the bad state,
good report,

occurs. Likewise, the intermediary will never monitor a

It will just audit bad ones,

If it …nds malfeasance, then

the intermediary should exert maximal punishment, which amounts to seizing everything or
r2 k. If it doesn’t, then it should take all of the bad state returns, or r1 k. These latter two
features help to create, in a least-cost manner, an incentive for the …rm to tell the truth.
The above features are embedded into the contracting problem presented below. A more
formal, step-by-step analysis is presented in Greenwood et al. (forthcoming).
Turn now to the contracting problem. Intermediation is competitive. Therefore, an
intermediary must choose the details of the …nancial contract to maximize the expected
rents for a …rm. Competition implies that all intermediaries will earn zero pro…ts on their
lending activity. Suppose that intermediaries can raise funds from savers at the interest
rate rb. If the depreciation rate on physical capital is , then the cost of supplying capital is
re = rb + . The intermediary’s optimization problem can be expressed as4
v

maxf 2 [1
k;lm1

To guarantee that Pij (ljm ; k; z)
ljm

P21 (lm1 ; k; z)][r2 ( )

r1 ( )]kg;

P(2)

0, this speci…cation requires that some minimal level of labor must
1=

be devoted to monitoring; i.e.,
>
(k=z) . Note that this minimal labor requirement for monitoring
can be made arbitrarily small by picking a large enough value for ". The choice of " can be thought of as
normalization relative to the level of productivity in the production of monitoring services— see Greenwood
et al. (forthcoming) for more detail.
4

This is the dual of the problem presented in Greenwood et al. (forthcoming).

subject to
[ 1 r1 ( ) +

1 r2 (

)]k

2 [1

P21 (lm1 ; k; z)][r2 ( )

r1 ( )]k

1 wlm1

= rek:

(3)

The objective function P(2) gives the expected rents for a …rm. These rents accrue from the
fact that the …rm has private information about its state. Suppose that the …rm lies about
being in the good state. When it doesn’t get caught it can pocket the amount [r2 ( ) r1 ( )]k.
The odds of not getting caught are 1
2.

P21 (lm1 ; k; z). The good state occurs with probability

An incentive compatible contract o¤ers the …rm the same amount from telling the truth

that it can get from lying.5

Equation (3) is the intermediary’s zero-pro…t condition. The

expected return from the project is [ 1 r1 ( ) +
give the …rm
returns is

2 [1

1 wlm1 .

P21 (lm1 ; k; z)][r2 ( )

1 r2 (

)]k. Out of this the intermediary must

r1 ( )]k. The expected cost of monitoring low-state

Represent the amount of labor required to monitor a type- …rm in

state 1 by lm1 ( ) = lm1 ( 1 ;

2 ).

The contract presumes that the intermediary is committed

to monitoring all reports of a bad state. Last, for some types of …rms a loan may entail a
loss. The intermediary will not lend to these …rms.

Stationary Equilibrium

The focus of the analysis is on stationary equilibria. Firms di¤er by type,
1

= ( 1;

with

2
R+
. Suppose that …rms are distributed over

Denote the space of types by T

Let p2 represent the payment that a …rm makes to the intermediary in the good state. The incentive
constraint for the contract will read
[1

P21 (l1m ; k; z)][r2 ( )

r1 ( )]k

r2 ( )k

p2 :

The left-hand side represents what the …rm will get by lying, while the right-hand side shows what it will
receive when it tells the truth. The latter must dominate, in a weak sense, the former. (Recall that upon
the declaration of a bad state the …rm must turn over r1 ( )k to the intermediary. So, it will make nothing
when it truthfully reports a bad state. If the …rm gets caught cheating, then it must make the payment
r2 ( )k, so it will also earn zero rents here.) The incentive constraint will bind. Thus, P(2) maximizes the
…rm’s expected rents, 2 [r2 ( )k p2 ], subject to the zero-pro…t constraint. As in Townsend (1979), it can
be shown that the revelation principle holds, so the focus here on incentive compatible contracts is without
loss of generality.

productivities in accordance with the distribution function
F (x; y) = Pr(

For all …rms …x the odds of drawing state i at Pr( =
be thought of as specifying the mean,

1 1

2 2,

y).

This distribution F can then

and variance,

2
2) ,

1 2( 1

of project

returns across …rms. So, which …rms will receive funding in equilibrium?
To answer this question, focus on the zero-pro…t condition for intermediaries (3). Now,
consider a …rm of type . Clearly, if

1 r1 (

)k +

1 r2 (

incur a loss on any loan of size k > 0. Likewise, if

)k < 0, then the intermediary will
1 r1 k

1 r2 k

> 0, then it will be

possible to make non-negative pro…ts, albeit the loan may have to be very small. Therefore,
a necessary and su¢ cient condition to obtain funding is that

lies in the set A(w)

de…ned by
A(w)

f :

1 r1 (

2 r2 (

)

re > 0g:

(4)

This set shrinks with the wage, w, because ri ( ) is decreasing in w; as wages rise a …rm
becomes less pro…table.
Firms with

2 A(w) will demand li ( 1 ;

units of labor in state i. Should one of these

…rms declare that it is in state 1, then the intermediary will send lm1 ( 1 ;

units of labor

over to audit it. Recall that labor is in …xed supply. Suppose that there is one unit in
aggregate. The labor-market-clearing condition will then appear as
Z
[ 1 l1 ( 1 ; 2 ) + 2 l2 ( 1 ; 2 ) + 1 lm1 ( 1 ; 2 )]dF ( 1 ;

= 1.

(5)

A(w)

It is now time to take stock of the situation thus far by presenting a de…nition of the
equilibrium under study.
De…nition 1 Set the steady-state cost of capital at re. A stationary competitive equilibrium
is described by a set of labor allocations, li and lm1 , a set of active …rms, A(w), together
with a loan size, k, and a value, v, for each …rm, and …nally a wage rate, w, such that:
1. The loan, k, o¤ered by the intermediary maximizes the value of a …rm, v, in line with
P(2), given the prices re and w. The intermediary hires labor for monitoring in the
amount lm1 , as also speci…ed by P(2).
11

2. A …rm is o¤ered a loan if and only if it lies in the active set, A(w), as de…ned by (4).
3. Firms hire labor li , so as to maximize its pro…ts in accordance with P(1), given wages,
w, and the size of the loan, k, o¤ered by the intermediary.
4. The wage rate, w, is determined so that the labor market clears, in accordance with
(5).

Discussion

The analysis focuses on the role that intermediaries play in producing information. Before
an investment opportunity is funded, intermediaries assess its risk and return. In the current
setting, this amounts to knowing a project’s type, . This can be costlessly discovered in
the model here. It would be easy to add a variable cost for a loan that is a function of z.
Doing so would have little bene…t, however. Intermediaries need to put systems in place to
monitor cash ‡ows, or face the prospect of lower-than-promised returns. In yesteryear, banks
required borrowers to keep their funds in an account with them. This way transactions could
be monitored. Now, even a privately funded …rm needs to be monitored, unless the scale
is so small that the owner can operate it himself. Managers and workers tend to siphon o¤
funds from the providers of capital, whether they are banks, bondholders, private owners,
share holders, or venture capitalists. At the micro level, this is what a shirking worker in
a fast food restaurant is doing. And, there is computer surveillance software available for
$200 a month, called HyperActive Bob, designed to catch such a person.6
E¢ ciency of monitoring, z, is likely to depend on the state of technology in the …nancial
sector, both in terms of human and physical capital. Better information technologies allow
for greater quantities of …nancial information to be collected, exchanged, processed and
analyzed. Indeed, the most IT-intensive industry in the United States is Depository and
Nondepository Financial Institutions. Computer equipment and software services accounted
for 10 percent of value added over the period 1995 to 2000, as opposed to 5 percent in
Industrial Machinery and Equipment, or 2.6 percent in Radio and Television Broadcasting.
6

“Machines that can see.” The Economist, March 5th 2009.

Berger (2003) discusses the importance of IT in accounting for productivity gains in the U.S.
banking sector. This is re‡ected in the growth of ATM machines, Internet banking, electronic
payment technologies, and information exchanges that permit the use of economic models
to undertake credit scoring for small businesses, develop investment strategies, create new
exotic …nancial products, etc. Similarly, a more talented work force allows for higher-quality
information workers: accountants, …nancial analysts, and lawyers. Last, the e¢ ciency of
monitoring will depend on the legal environment, which speci…es what information can,
must, or must not be produced. This is separate from regulating the terms of payments,
especially in bankruptcy (here p1 or p12 ) as analyzed in Castro et al. (2004).
Before proceeding on to the quantitative analysis, some mechanics of the above framework
will now be inspected in a heuristic manner. For a more formal analysis see Greenwood et
al. (forthcoming). The presence of diminishing returns to information production leads to a
…nancial theory of …rm size, as will be discussed. In fact, they can be thought of as providing
a microfoundation for the Lucas (1978) span of control model. The framework also speci…es
a link between the state of …nancial development and the state of economic development.
(1) A …rm’s production is governed by constant returns to scale. In the absence of …nancial market frictions, no rents would be earned on production. Additionally, in a frictionless
world only …rms o¤ering the highest expected return would be funded. In this situation,
max [ 1 r1 ( ) +

2 r2 (

for all funded projects
those

2 B(w)

projects—

)] = re— cf (4). With …nancial market frictions,

1 r1 (

2 r2 (

) > re

2 A(w), a fact easily gleaned from (3). Thus, deserving projects—

fx : maxx2T [ 1 r1 (x) +

2 r2 (x)]g—

will be underfunded, while undeserving

2
= B(w)— are simultaneously overfunded. Funded …rms will earn rents, v, as

given by P(2).
(2) What determines the size of a …rm’s loan? By eyeballing the left-hand side of (3),
which details the intermediary’s pro…ts, it looks likely that the …rm’s loan will be increasing
in the project’s expected return,

1 r1 (

1 r2 (

), ceteris paribus. This is true. Recall that

the odds of detecting fraud, P21 (lm1 ; k; z), decrease in loan size, k. Therefore, more labor
must be allocated to monitoring the project in response to an increase in loan size. Since

there are diminishing returns to information production, the size of the loan, k, is uniquely
determined as a function of expected return. Similarly, it appears that a …rm’s loan will
decrease in the project’s risk, as measured by r2 ( )

r1 ( ). This is also true. When the

spread between the high and low states widens, there is more of an incentive for the …rm
to misreport its returns. Recall that the gain from lying is given by the objective function
in P(2). To counter this the intermediary must devote more labor to monitoring. The
diminishing returns to information production imply that loan size is uniquely speci…ed as
a function of risk.
(3) Imagine that aggregate productivity, x, grows over time at the constant rate g 1= .
Will there be balanced growth? Conjecture that along a balanced growth path the k’s, o’s,
and w, will all grow at rate g. Also guess that A(w) and the li ’s, l1m ’s, and ri ( )’s will remain
constant. It is easy to see from the isoelastic forms of P(1) and (1) that the conjectured
solution for balanced growth solution will be satis…ed for the li ’s, l1m ’s, and ri ( )’s. Since the
ri ( )’s remain constant so does the active set, A(w), that is spelled out in (4). Since the li ’s
and l1m ’s remain …xed, if the labor-market clearing condition (5) holds at one point along
the balanced path it will hold at all others. So, the hypothesized solution for w is consistent
with this. What about k? The solution guessed for k is consistent with P(2), if P12 does not
change along a balanced growth path. From (2) it is clear that the odds of getting caught
cheating, P21 , will change over time, however, unless z grows at precisely the rate g. If this
happens, then balanced growth occurs.
(4) Consider the case where x grows at a di¤erent rate than z. Speci…cally, for illustrative
purposes, take the extreme situation where z rises while x remains …xed. Thus, there is only
…nancial innovation in the economy. By inspecting (2) the odds of detecting fraud will rise,
other things equal. The rents that …rms can make will drop, a fact that is evident from
the objective function in P(2). This makes it feasible for …nancial intermediaries to o¤er
…rms larger loans, ceteris paribus, as can be gleaned from (3). The implied increase in the
economy’s aggregate capital stock will then drive up wages. Thus, ine¢ cient …rms will have
their funding cut, as (4) makes clear. Therefore, …nancial innovation operates to weed out

unproductive …rms. The active set of …rms, A(w), thus shrinks. Average …rm size in the
economy is the total stock of labor (one) divided by the number of …rms (or the measure
of the active set). Therefore, average …rm size increases. If z increases without bound,
then the economy will enter into a frictionless world where only …rms o¤ering the highest
expected return, max [ 1 r1 ( ) +
max [ 1 r1 ( ) +

2 r2 (

)], are funded. These …rms will earn no rents; i.e.,

)] = re.

The United States and Taiwan

7.1

Fitting the Model to the U.S. Economy

The quantitative analysis will now begin. To simulate the model, values must be assigned
to its parameters. This will be done by calibrating the framework to match some stylized
facts. Some parameters are standard. They are given conventional values. Capital’s share
of income,

, is chosen to be 0:35, a very standard number.7

Likewise, the depreciation

rate, , is set to 0:06, another very common …gure.8 The chosen value for return on savings
through an intermediary is re = 0:03.9

Nothing is known about the appropriate choice for parameters governing the interme-

diary’s monitoring technology

and . Similarly, little is known about the distribution of

returns facing …rms. Let 1 be the mean across …rms for the logarithm of low shock, 1 ; i.e.,
R
R
ln( 1 )dF ( 1 ; 2 ). Analogously, 2
ln( 2 )dF ( 1 ; 2 ). Likewise, 2j will denote
1
R
the variance over …rms for the low shock; i.e., 2j
[ln( j )
]2 dF , for j = 1; 2. In a
j
similar vein,

will represent the correlation between the low and high shocks, ln( 1 ) and

ln( 2 ), in the type distribution for …rms. Assume that these means and variances of …rm-level
7

Conesa and Krueger (2006) and Domeij and Heathcote (2004) use a capital share of 0.36, close to the
number imposed here.
8

The same number is used, for instance, by Chari et al. (1997).

For the period 1800 to 1990, Siegel (1992) estimates the real return on bonds, with a maturity ranging
from 2 to 20 years, to be between 3.36 percent (geometric mean) and 3.71 percent (arithmetic mean). He
also estimates the real return on 90 day commercial paper to be between 2.95 percent (geometric mean) and
3.13 percent (arithmetic mean).

ln(TFP) are distributed according to a bivariate truncated normal, N (
Normalize

;

2
1

;

2
2

; ).

to be 1. Of course, values for the parameters determining the productivities

of the technologies used in the production and …nancial sectors, x and z, are also needed.
Let Targetsj represent the j-th component of a n-vector of observations that the model
should match. Similarly, M (param) denotes the model’s prediction for this vector. The calibration procedure will minimize the distance between the vectors Targets and M (param) :
The key, then, is to choose targets that will be tightly connected to the model’s parameters.
The technological parameters, x and z, are very important for determining the e¢ ciencies of
the production and …nancial sectors. In particular, the model provides a mapping between
the aggregate level of output (per person), o, and the interest-rate spread, s, on the one
hand, and the state of technology in its production and …nancial sectors, x and z, on the
other. Represent this mapping by (o; s) = O(x; z; p); where p = ( ; ; ;
resents the remaining 7 parameters in param (where

;

2
1

;

2
2

; ), rep-

is normalized to one and hence is

omitted). Now, while the states of the technologies in these sectors are unobservable directly,
this mapping can be used to make an inference about (x; z), given an observation on (o; s),
by using the relationship
(x; z) = O 1 (o; s;p):

(6)

Given the importance of these two parameters, this condition will be used as a constraint
in the minimization of the distance between Targets and M (param). Equation (6) will
also play an important role in the cross-country analysis.
The distribution of returns across …rms will be integrally related to the distribution of
employment across them. Firms with high returns will have high employment, other things
equal. Figure 4 illustrates a …rm’s employment, l, as a function of its capital stock, k, and
the realized value of the technological shock, . A …rm that receives a bigger loan, k, will hire
more labor, l, other things equal. Recall that the size of the loan is determined before the
technology shock is realized. Given the size of its loan, a …rm will hire more labor the higher
is the realized state of its technology shock. Given this relationship, the size distributions of
…rms for the years 1974 and 2004 are chosen as data targets to determine the remaining 8
16

parameters. Seven points on the distribution for each year are picked. As it is well known,
the size distribution of …rms is highly skewed to the right; that is, there are many small …rms,
employing a relatively small amount of labor in total, and a few large ones, hiring a lot. For
instance, in 1974, the smallest 60 percent of establishments employed only 7.5 percent of
the total number of workers, while the largest 5 percent of establishments hired about 60
percent of workers. Using only one target for the size distribution would be insu¢ cient to
capture this fact. It is important that the largest 12 percent of establishments employ 75
percent of the workers, but it is equally important that the truncated distribution inside of
the largest 12 percent of establishments is also very skewed— remember that the largest 5
percent of establishments employed about 60 percent of workers. Therefore, it is useful to
consider the share of employment in the smallest 60, 75, 87, 95, 98, 99.3, and 99.7 percent
of establishments. Thus, there are 7 targets for each of the two years. Denote the jth
percentile target for the year t by eUj;tS and let Mj xUt S ; ztU S ; p give the model’s prediction
for this statistic (all for j = 60; 75; 87; 95; 98; 99:3; 99:7 and t = 1974; 2004).
The mathematical transliteration of the above calibration procedure is
(
)
X wj
X wj
S
US
S
US
min
[eUj;74
Mj xU74S ; z74
; p ]2 +
[eUj;04
Mj xU04S ; z04
; p ]2 ;
p
2
2
j
j

P(3)

subject to
US
(xU74S ; z74
) = O 1 (oU74S ; sU74S ;p);

(7)

US
(xU04S ; z04
) = O 1 (oU04S ; sU04S ;p):

(8)

and

Thus, following this strategy, 18 targets (including the oU S ’s and sU S ’s) are used to calibrate
11 parameters (including the xU S ’s and z U S ’s).
The upshot of the above …tting procedure is now discussed. First, there exists a set of
US
US
technology parameters for the production and …nancial sectors, (xU74S ; z74
; xU04S ; z04
), so that

the model can match exactly interest-rate spreads and per-capita GDP for the years 1974
and 2004. Second, the model does a very good job matching the 1974 and 2004 …rm-size
distributions— see the upper two panels. Across time the size distribution shifts slightly to
17

Labor, l

Productivity, θ

Capital, k

Figure 4: Employment, l, as a function of capital, k, and the realized value of the technological shock, –model

1.0

Employment, Cumulative Share

0.8

1.0

Data 1974
Model 1974

0.8

0.6

0.4

0.2

0.0
0.6
1.0
0.8

0.7

0.8

0.9

0.0
0.6
1.0

1.0

Model 1974
Model 2004
Counterfactual

0.8

0.6

0.4

0.2

0.0
0.6

0.7

0.8

0.9

0.0
0.6

1.0

Data 2004
Model 2004

0.7

0.8

0.9

1.0

0.9

1.0

Data 1974
Data 2004

0.7

0.8

Establishments, Percentile

Figure 5: Firm-size distribution, 1974 and 2004–data and model

the left, as the lower right panel of Figure 5 makes clear. The largest …rms account for
a little less of employment. Last, the parameters obtained from the …tting procedure are
presented in Table 1.

Table 1: Parameter Values
Parameter

De…nition

Basis

= 0:35

Capital’s share of income

Conesa and Krueger (2006)

= 0:06

Depreciation rate

Chari, Kehoe and McGrattan (1997)

re = 0:03

Return to Savers

Siegel (1992)

= 32:57

Pr of detection, constant

Normalization

= 0:95

Pr of detection, exponent

Calibrated to …t targets

= 0:40

Monitoring cost function

Calibrated to …t targets

= 1:0

Mean of ln( 1 )

Normalization

= 3:05

Mean of ln( 2 )

Calibrated to …t targets

= 0:53

Variance of ln( 1 )

Calibrated to …t targets

= 0:61

Variance of ln( 2 )

Calibrated to …t targets

2
1

2
2

0:87

Correlation ln( 1 ) and ln( 2 ) Calibrated to …t targets

x1974 = 0:14; z1974 = 11:5 TFP’s

Calibrated to …t targets

x2004 = 0:20; z2004 = 28:2 "

7.2

The United States, Balanced Growth

It would not be unreasonable to argue, for the purposes of the current analysis, that the U.S.
economy is characterized by a situation of balanced growth. First, there is only a small shift
in the U.S. …rm-size distribution between 1974 and 2004, as was shown in Figure 5 (bottom
right panel). Second, the economy’s interest-rate spread shows only a modest decline— recall
Figure 1. Third, the capital-to-output ratio displays a small increase— again Figure 1.
Finance is important in the model. This can be gauged by undertaking the following
counterfactual question: By how much would GDP have risen between 1974 and 2004 if
there had been no technological progress in the …nancial sector? As can be seen from the
third panel of Table 2, output would have risen from $22,352 to $33,656 or by about 1.4
percent a year (when continuously compounded). This compares with the increase of 2.0
percent ($22,352 to $41,208) that occurs when z rises to its 2004 level. Thus, about 30
20

percent of the increase in growth is due to innovation in the …nancial sector. Likewise, the
model predicts that about 12 percent of TFP growth was due to improvement in …nancial
intermediation. The …nancial system actually becomes a drag on development when z is not
allowed to increase. Wages rise as the rest of the economy develops. This makes monitoring
more expensive. Therefore, less will be done. As a consequence, interest rates rise and the
economy’s capital-to-output ratio drops. Without an improvement in the …nancial system,
the …rm-size distribution actually moves over time in a direction (rightward) that is opposite
to that shown in the data (leftward), as can be seen by comparing the lower two panels of
Figure 5. When there is no technological progress in the …nancial sector there will be a
larger number of small ine¢ cient …rms around. Therefore, the smallest …rms in the economy
(or the left tail) will now account for a smaller fraction for the work force— see the lower left
panel.
Now, monitoring and the provision of …nancial services are abstract goods, so it is dif…cult to know what a reasonable change in z should be. One could think about measuring
productivity in the …nancial sector, as is often done, by k=lm , where k is the aggregate
amount of credit extended by …nancial sector and lm is the aggregate labor that it employs.
By this traditional measure, productivity in the …nancial sector rose by 2.59 percent annually between 1974 and 2004. Berger (2003, Table 5) estimates that productivity in the
commercial banking sector increased by 2.2 percent a year over this same period (which
includes the troublesome productivity slowdown) and by 3.2 percent from 1982 to 2000.

Table 2: The U.S. Economy
Data

Model

Spread, s

3.07%

GDP (per capita), o

$22,352 $22,352

capital-to-output ratio (indexed), k=o

1.00

1974

TFP

1.00
6.63

2004
Spread, s

2.62%

GDP (per capita), o

$41,208 $41,208

capital-to-output ratio (indexed), k=o

1.02

TFP

2.62%

1.10
9.54

US
US
= z1974
2004 Counterfactual, z2004

7.3

Spread, s

2.62

3.87

GDP (per capita), o

$41,208 $33,656

capital-to-output ratio (indexed), k=o

1.02

0.86

TFP

9.12

Yearly growth in …nancial productivity

2.59%

Taiwan, Unbalanced Growth

Return to Taiwan, as shown in Figure 1. In Taiwan there was a large drop in the interestrate spread between 1974 and 2004. This was accompanied by a signi…cant increase in the
economy’s capital-to-output ratio. This is clearly a situation of unbalanced growth. Recall
that model provides a mapping between the state of technologies in the production and
…nancial sectors on the one hand, x and z, and output and interest-rate spreads, o and
s, on the other. This mapping can be inverted to infer x and z using observations on o
and s using (6), given a vector of parameter values, p. Take the parameter vector p that
22

was calibrated/estimated for the U.S. economy and use the Taiwanese data on per-capita
GDPs and interest-rate spreads for the years 1974 and 2004, (oT1974 ; sT1974 ; oT2004 ; sT2004 ), to get
T
T
the imputed Taiwanese technology vector (xT1974 ; z1974
; xT2004 ; z2004
). The results of the …tting

exercise for Taiwan are shown below.
So, how important was …nancial development for Taiwan’s economic development? To
answer this question, compute the model’s solution for 2004 assuming that there had been
T
T
no …nancial development; i.e., set z2004
= z1974
. Almost 50 percent of Taiwan’s 6.1 percent

annual rate of growth between 1974 and 2004 can be attributed to …nancial development. It
also accounts for 20 percent of the growth in Taiwanese TFP. Taiwan had almost a 10 percent
annual increase in the productivity of its …nancial sector, as is conventionally measured.

Table 3: The Taiwan Economy
Data

Model

1974
Productivity, industrial

x1974 =0.0383

Productivity, …nancial

z1974 =0.4214

Spread, s

5.41%

GDP (per capita), o

$2,211

capital-to-output(indexed), k=o

1.00

TFP

1.68
2004

Productivity, industrial

x2004 =0.0897

Productivity, …nancial

z2004 =16.267

Spread, s

1.96%

GDP (per capita), o

$13,924 $13,924

capital-to-output(indexed), k=o

1.847

TFP

1.96%

1.905
4.46

T
T
= z1974
2004 Counterfactual, z2004

Spread, s

1.96%

9.66%

GDP (per capita), o

$13,924 $5,676

capital-to-output(indexed), k=o

1.847

0.630

TFP

3.66

Yearly growth in …nancial productivity

9.89%

Cross-Country Analysis

Move on now to some cross-country analysis. In particular, a sample of 45 countries, the
intersection of all the nations in the Penn World Tables and the Beck, Demirguc-Kunt

and Levine (2000, 2001) dataset, will be studied. For each country j, a technology vector
(xj ; z j ) will be backed out using data on output and interest-rate spreads (oj ; sj ), given
the procedure implied by (6) while setting p to the calibrated parameter vector for the
U.S. economy. Erosa (2001) uses interest-rate spreads to quantify the e¤ects of …nancial
intermediation on occupational choice. It is not a foregone conclusion that this can always
be done; i.e., that a set of technology parameters can be found such that (6) always holds.10
The results are reported in Table 9 in the Appendix. By construction the model explains all
the variation in output and interest-rate spreads across countries.11 Still, one could ask how
well the measure of the state of technology in the …nancial sector that is backed out using the
model correlates with independent measures of …nancial intermediation. Here, take the ratio
of private credit by deposit banks and other …nancial institutions to GDP as a measure of
…nancial intermediation, as reported by Beck et al. (2000, 2001). (Other measures produce
similar results but reduce the sample size too much.) Additionally, one could examine how
well the model explains cross-country di¤erences in capital-to-output ratios.
Table 4 reports the …ndings. The correlation between the imputed state of technology
in the …nancial sector and the independent Beck et al. (2000, 2001) measure of …nancial
intermediation is quite high— see Table 4 and Figure 6. Thus, it appears reasonable to use
10

Theoretically speaking, there is a maximum interest-rate spread that the model can match. When the
…nancial sector becomes too ine¢ cient, it no longer pays to monitor loans. As z falls (relative to x) the
aggregate volume of lending declines. The wage rate will decline along with the economy’s capital stock. As
this happens, the r1 ’s rise–see (1). Take the …rms with the highest value of r1 and denote this by r1 . By
de…nition, r1 = r1 ( ), where = arg max 2T fr1 ( )g. Eventually, r1 will hit re. At this point, a Williamson
(1986)-style credit-rationing equilibrium emerges. In the credit-rationing equilibrium, r1 = re. Here type…rms will pay the …xed interest rate r1 . They will not be monitored. Because r2 > re for these …rms, they
would demand as big a loan as possible. Thus, their credit must be rationed. The interest-rate spread on
these loans will be zero. Note that r1 can never exceed re, because in…nite pro…t opportunities would then
emerge in the economy. Thus, the interest rate spread is a \-shaped function of z. (The interest-rate spread
also approaches zero as z ! 1, or when economy asymptotes to the frictionless competitive equilibrium.
As z ! 0 the fraction of loans that are not monitored will eventually approach one, implying that the
interest-rate spread will drop to zero.) The peak of the \ function is the maximum permissible interest-rate
spread allowed by the model.
11

The model predicts a positive association between a country’s rate of investment and its GDP. Castro
et al. (2009, Figure 1) show that this is true. As was mentioned, it is stronger when investment spending
is measured at international prices, as opposed to domestic ones. This puzzle could be resolved here by
adopting aspects of Castro et al.’s (2009) two-sector analysis.

the constructed values of z for investigating the relationship between output and …nancial
development. Now, the backed-out measure for the e¢ ciency of the …nancial sector correlates
well with a country’s adoption of information technologies, as is shown in Figure 6 (upper left
panel). It also is strongly associated with a country’s human capital (upper right) and the
maturity of its legal system (lower right). These three factors should make intermediation
more e¢ cient, for the reasons discussed in Section 6. Indeed, Figure 6 (lower left panel) also
illustrates how the ratio of overhead cost to assets, a measure of e¢ ciency, declines with
constructed ln(z).
As can be seen, the capital-to-output ratios predicted by the model are positively associated with those in the data. The correlation is reasonably large. That these two correlations
aren’t perfect, should be expected. There are other factors, such as the big di¤erences in
public policies discussed in Parente and Prescott (2000), which may explain a large part
of the cross-country di¤erences in capital-to-output ratios. Di¤erences in monetary policies
across nations may in‡uence cross-country interest-rate spreads. Additionally, there is noise
in these numbers given the manner of their construction— see the Appendix.

Table 4: Cross-Country Evidence
k=o
Corr(model, data)

0.62

ln z with Beck et al (2000, 2001) k=lm with Beck et al (2000, 2001)
0.81

0.82

Interestingly, Sri Lanka and the United States both have an interest-rate spread of about
4.2 percent. The model predicts the United States’ z is about 250 percent higher (when
ln di¤erenced or continuously compounded) than Sri Lanka’s— the former’s ln(z) is 2.28,
compared with 0.013 for the latter; again, see Table 9 in the Appendix. But, recall that
the units for ln(z) are meaningless, since monitoring is abstract good. If one measures
productivity in the …nancial sector by the amount of credit extended relative to the amount
of labor employed in the …nancial sector, as was discussed earlier, then the analysis suggests
that intermediation in the United States is about 214 percent (continuously compounded)
more e¢ cient than in Sri Lanka. Why? The United States has a much higher level of income
26

THA

PRT
ITA
MUS ESP

AUS
NOR
SWE
DNK

CHE
USA

ZAF
URY
CRI LKA
PAK IND
MEX
COL
SLV
PHL
BOL
PER
BRA
GTM NIC
TUR
HND
KEN

-2

ZAF
IND
LKA
PAK
MEXURYCRI
COL
MAR
SLV
PHL
BOL
PER
NIC
BRA
ETH
GTM
TUR
HND
KEN
NGA
UGA

UGA

5
10
15
Average years of school ing of adults (aged 15+), total

20
40
60
Personal computers (per 100 people)

IRL
AUS
FINCHE NZL
JPN
NLD
NOR
BEL
AUT GBR
PRT
SWE
FRA
ISR
ITA
USA
MUS ESP
DNK
THA

IRL
JPNNZLFIN
NLD
BEL
AUT
GBR
ISR FRA

Efficiency in monitoring (ln z)
0
2
4

LUX

IRL

LUX
AUS
CHE
NZL
NLD
NOR
BEL
AUT
GBR
PRTISR SWE
FRA
MUS USADNKITA
THA ESP

Efficiency in monitoring (ln z)
0
2
4

LUX

ETH

LKA
SLVBOL
PHL

ZAF
CRI

MEX

URY
COL

PER
NIC
BRA
TUR GTM

HND

-2

KEN
NGA
UGA

INDPAK
MAR

FIN
JPN

.02
.04
.06
Overhead costs to total assets

.08

THA
ZAF
LKA IND
PAK
MEX
COL
MAR
SLV PHL
BOL
PER
NIC
BRA
ETH
GTM
TUR
HND
KEN
NGA UGA

-1

IRL
AUS
FIN
CHE
JPN
NZL
NLD
NOR
BEL
AUT
GBR
PRT
SWE
FRA
ISR
ITA
USA
MUS
ESP
DNK

URY
CRI

Rule of Law

Figure 6: The relationship between imputed ln(z) on the one hand, and measures of information technology, human capital, overhead costs to assets and the rule of law, on the
other

per worker and hence TFP than does Sri Lanka ($33,524 versus $3,967). Therefore, given
the higher wages, monitoring will be more expensive in the United States. To give the same
interest-rate spread, e¢ ciency in the U.S.’s …nancial sector must be higher. Before proceeding
on to a discussion of the importance of …nancial development for economic development, note
that the …ndings in the next section do not change much if the model is matched up with
overhead costs, perhaps a more direct measure (see Figure 6), instead of the Beck et al.
(2000, 2001) interest-rate spreads.

8.1

The Importance of Financial Development for Economic Development

It is now possible to gauge how important e¢ ciency in the …nancial sector is for economic
development, at least in the model. To this end, let the best industrial and …nancial practices
in the world be denoted by x

maxfxi g and z

maxfzi g, respectively. Represent country

i’s output, as a function of the e¢ ciency in its industrial and …nancial sectors, by oi =
O(xi ; zi )— this is really just the …rst component of the mapping O(x; z; p). If country i could
somehow adopt the best …nancial practice in the world it would produce O(xi ; z). Similarly,
if country i used the best practice in both sectors it would attain the output level O(x; z).
The shortfall in output from the inability to attain best practice is O(x; z)

O(xi ; zi ). The

United States turns out to have the highest value for x, and Luxembourg for z.
The percentage gain in output for country i by moving to best …nancial practice is given
by 100

[ln O(xi ; z)

ln O(xi ; zi )]. The results for this experiment are plotted in Figure 7.

As can be seen, the gains are quite sizeable. On average, a country could increase its GDP by
31 percent, and TFP by 10 percent. The country with the worst …nancial system, Uganda,
would experience a 140 percent rise in output. Its TFP would increase by 30 percent. While
sizeable, these gains in GDP are small relative to the increase that is needed to move a
country onto the frontier for income, O(x; z). The percentage of the gap that is closed by
a movement to best …nancial practice is measured by 100
O(xi ; zi )]

100

[O(xi ; z)

O(xi ; zi )]=[O(x; z)

G(xi ; zi ). Figure 7 plots the reduction in this gap for the countries

in the sample. The average reduction in this gap is only 17 percent. For most countries
the shortfall in output is accounted for by a low level of total factor productivity in the
non-…nancial sector.
Therefore, the importance of …nancial intermediation for economic development depends
on how you look at it. World output would rise by 65 percent by moving all countries to
the best …nancial practice— see Table 5. This is a sizeable gain. Still, it would only close 36
percent of the gap between actual and potential world output. Dispersion in cross-country
output would fall by about 19 percentage points from 77 percent to 58 percent. Financial
development explains about 27 percent of cross-country dispersion in output by this metric.

Table 5: World-Wide Move to Best Financial Practice, z
Increase in world output (per worker)

65%

Reduction in gap between actual and potential world output

35.6%

Increase in world TFP

17.4%

Fall in dispersion of ln(output) across countries

27.2% ( ' 111.4% - 84.2%)

Fall in (pop-wghtd) mean of (cap-wghtd) distortion

20.8% (' 23.4% - 2.6%)

Fall in (pop-wghtd) mean dispersion of (cap-wghtd) distortion 13.5% (' 14.6% - 1.1%)
Restuccia and Rogerson (2008) started a literature about the importance of idiosyncratic
distortions that create heterogeneity in the prices faced by individual producers. Although
they do not identify the sources of those distortions, they show they can generate di¤erences
in TFP in the range of 30 to 50 percent. Guner et al. (2008) analyze the impact that
size-dependent policies, such as the restrictions on retailing in Japan favoring small stores,
can have in an economy. Here, the presence of informational frictions causes the expected
marginal product of capital,

1 r1

2 r2 ,

to deviate from its user cost, re. The distortion is

modelled endogenously. De…ne the induced distortion in investment by d =

1 r1

2 r2

re.

For a country such as Uganda these deviations are fairly large. Figure 8 plots the distribution
of the distortion across plants for Luxembourg and Uganda. As can be seen, both mean level
of the distortion and its dispersion are much larger in Uganda than they are in Luxembourg.
29

Turkey
Uganda
Brazil
Nigeria
Guatemala
Honduras
Kenya
Nicaragua
Peru
El Salvador
Uruguay
Mexico
Colombia
Philippines
Bolivia
Costa Rica
Morocco
South Africa
Sri Lanka
Ethiopia
Pakistan
India
Denmark
United States
Spain
Italy
Mauritius
Iceland
France
Thailand
Israel
Sweden
United Kingdom
Portugal
Austria
Norway
Belgium
Netherlands
Japan
Switzerland
New Zealand
Finland
Australia
Ireland
Luxembourg

140
120
100
80
60
40
20
0

100

30
25
20
15
10
5
0
GDP per worker, % change

reduction in the gap to the frontier, %

TFP, % change

Figure 7: Cross-country results: The impact of a move to …nancial best practice on GDP,
the output gap and TFP

15
10
5

Density

Luxembourg

Uganda

1.2

Distortion

Figure 8: The distribution of distortions across establishments for the Luxembourg and
Uganda–the model

The (capital-weighted) mean level of this distortion is 49.8 percent (4.6 percent) for Uganda
(Luxembourg). It varies across plants a lot, as indicated by a coe¢ cient of variation of 32.7
percent (1.94 percent). If Uganda adopted Luxembourgian …nancial practices the average
size of this distortion would drop to 1.4 percent. Its standard deviation across plants collapses
from 9 percent to just 0.3 percent. The elimination of this distortion results in capital
deepening among the active plants. Average TFP would rise by 26 percent in the model, as
ine¢ cient plants are culled. For the world at large, the average size of the distortion is 23.4
percent, with an average coe¢ cient of variation of 14.6 percent. The mean distortion drops
to 2.6 percent with a world-wide movement to best …nancial practice. The average standard
deviation across plants falls from 14.6 percent to a mere 1.1 percent.
Finally, the model predicts that larger …rms should be found in countries with more
31

developed …nancial systems. It is hard to come up with a comparable dataset for many
countries. Beck et al. (2006) argue that the best available alternative is to use the size of
the largest 100 companies. They …nd that there exists a positive relationship between the
development of a country’s …nancial system and …rm size, after controlling for the size of the
economy, income per capita and several …rm and industry characteristics. As an example,
their estimation implies that if Turkey had the same level of development in the …nancial
sector as Korea (a country with a more developed …nancial system), the average size of the
largest …rms in Turkey would more than double.
On this, imagine running a regression of the following form for both the data and the
model:
ln(size) = constant +

spread +

controls:

Firm size in the data is measured by average annual sales per …rm (in $U.S.) for the top
100 …rms, as taken from Beck et al. (2006). For the analogue in the model, simply use
a country’s GDP divided by the measure of active set A to obtain output per …rm. Once
again the data for interest-rate spreads are obtained from Beck et al. (2000, 2001). Controls
are added for a country’s GDP and population in the regression for the data, while for the
model they are just added for GDP.12 The same list of countries is used for both the data
and model.
The upshot of the analysis is shown in Table 6. A negative relationship is found in the
cross-country data between the interest-rate spread and average …rm size. The model also
produces a negative relationship between these variables. The similarity between the size
of interest-rate spread coe¢ cient, , for the data and model is reassuring. Additionally,
the data estimate of

0:16 implies that if a country with an interest-rate spread of

10 percentage points (which is among the worst 5 percent of nations in terms of …nancial
12

The idea here is that larger countries, as measured by income or population, would tend to have larger
…rms. In a frictionless world …rms could locate anywhere, so there would be no need for such a connection
to hold. Nontraded goods, productivity di¤erences across countries, restrictions on trade, transportations
costs, etc., would all lead to a positive association between average …rm size on the one hand and income or
population on the other.

development) could reduce its spread to just 1 percentage point (which would place it in the
upper 5 percent of countries), then the average size of its top 100 …rms would increase by
144 percent. This is roughly in accord with the Beck et al. (2006) …nding discussed above,
given that Turkey had one of the worst …nancial systems while Korea had one of the best.
Table 6: Cross-Country Firm-Size Regressions

9
9.1

Data

Model

Interest-rate spread coe¢ cient,

-0.16

-0.19

Standard error for

0.07

0.03

Number of country observations

0.51

0.93

Robustness Analysis
Intangible Investments and Capital’s Share of Income

Suppose part of investment spending is undertaken in the form of intangible capital. As
a result, measured investment may lie below true investment. This will lead to measured
income, GDP, falling short of true output, o. This injects an upward (a downward) bias
in the measurement of labor’s (capital’s) share of income. Speci…cally, in context of the
standard neoclassical model, with a Cobb-Douglas production function, measured labor’s
share of income, LSI, will appear as
LSI =

o
GDP

) > (1

Corrado et al. (2007) estimate the amount of intangible investment that was excluded from
measured GDP from 1950 to 2003. They show that when output is adjusted to include these
unrecognized intangibles, true output, o, is 12 percent higher than measured output, GDP,
for the period 2000-2003. As a consequence, it is easy to calculate that
=1

GDP
o

LSI = 1

1
(1
1:12

0:33) = 0:41:

How does this larger estimate for capital’s share of income a¤ect the analysis?
33

The calibration procedure described by P(3) is redone for the case where

= 0:41. The

results are in accord with those obtained earlier. The model again …ts the U.S. data well.
In particular, it matches the …rm-size distributions for 1974 and 2004 extremely well. With
no …nancial innovation, U.S. GDP would have risen by about 1.77 percent a year, compared
with its actual rise of 2.0 percent. Hence, …nancial development accounts for about 40
percent of the growth in GDP. For Taiwan about 60 percent of growth is due to …nancial
development.
Financial intermediation is now more important for economic development. World output
would increase by 88 percent, as opposed to the 65 percent found earlier, if all countries
moved to the best …nancial practice. There is also a bigger impact on TFP. As a result,
suboptimal …nancial practices now make up a larger fraction of the output gap. A more
detailed breakdown of the results is displayed in the Appendix, Figure 9.

Table 7: World-Wide move to best financial practice, z
= 0:41 (intangible capital)
Increase in world output (per worker)

88.2%

Reduction in gap between actual and potential world output 43.5%
Increase in world TFP

33.1%

Fall in dispersion of ln(output) across countries

34.4% ( ' 111.4% - 77.0%)

9.2

Varying the Degree of Substitutability between Capital and
Labor

Let output be produced according to a CES production function of the form
o = [ k + (1

)(x l) ] ; with

This production function will have implications for how labor’s share of income, LSI, will vary
across countries. To see this, think about the one-sector growth model. Here labor’s share
of income can be written as LSI= (w=l)=(w=l + rk) = 1=[1 + (r=w)(k=l)]: Therefore, labor’s
34

share will rise whenever (r=w)(k=l) falls. With the above production function,

= 1=(1

)

represents the elasticity of substitution between capital and labor. Hence, in response to a
shock in some exogenous variable, z, it will happen that d ln(r=w)=dz =

(1= )d ln(k=l)=dz.

If the shock induces capital deepening [d ln(k=l)=dz > 0] then labor’s share will rise or fall
depending on whether the elasticity of substitution is smaller or bigger than one.13 In the
cross-country data, labor’s share either rises slightly or remains constant with per-capita
income. This suggests that for the quantitative analysis,
1=(1

) < 1, which implies

should be restricted so that

< 0; i.e., capital and labor are less substitutable than

Cobb-Douglas.
Let

0:38, roughly in line with Pessoa et al. (2005). The calibration procedure

described above is redone for this value for . The CES framework does not …t the U.S.
…rm-size distributions for 1974 and 2004 nearly as well as the Cobb-Douglas case. In fact,
if one allowed for

0 to be freely chosen in the calibration procedure, then a value

close to zero (Cobb-Douglas) would be picked. For the U.S. economy, the CES speci…cation
predicts a rise in labor’s share from 69.5 to 70.2 percent as the economy grows. The model
with a CES production function has a di¢ cult time matching the observed large variation
in cross-country interest-rate spreads. Speci…cally, it cannot match the very high interestrate spreads observed for some countries.14 All in all, both the U.S. and cross-country data
prefer the Cobb-Douglas speci…cation. With a CES production structure world output would
increase by 32 percent, if all countries move to best …nancial practice. This is lower than
the Cobb-Douglas case for two reasons. First, the model cannot match the high interestrate spreads for some nations. This limited the gain that these countries could realize by a
move to best …nancial practice. Second, the potential for capital deepening is more limited
the higher the degree of complementarity between capital, which is reproducible, and labor,
which is …xed, in production.
13

That is, r=w will decrease by more (less) than k=l rises when the elasticity of substitution is smaller
(greater) than one.
14

See footnote 10.

Conclusions

So, how important is …nancial development for economic development? To address this
question, a costly state veri…cation model is taken to both U.S. and cross-country data. The
model has two unique features. First, …nancial intermediaries choose how much resources to
devote to monitoring their loan activity. The odds of detecting malfeasance are a function
of this. They also depend upon the technology used in …nancial sector. Second, each …rm
faces a distribution of returns. Furthermore, there is an economy-wide distribution across
…rms over these …rm-speci…c distributions. These two features lead to a …nancial theory of
…rm size. The framework is calibrated to …t the U.S. …rm-size distributions for 1974 and
2004, as well as the observed intermediation spreads on loans.
The analysis suggests that …nancial intermediation is important for economic development. In particular, about 30 percent of U.S. growth can be attributed to technological
improvement in …nancial intermediation. Since there was little change in the U.S. interestrate spread, it appears that technological progress in the …nancial sector was in balance with
technological advance in the rest of the economy. Roughly 50 percent of Taiwanese growth
could be attributed to …nancial innovation. Given the dramatic decline in the Taiwanese
interest-rate spread, technological progress in the …nancial sector may have outpaced that
elsewhere.
The model’s predictions for the e¢ ciency of …nancial intermediation in a cross-section of
45 countries matches up well with independent measures. It does a reasonable job mimicking
cross-country capital-output ratios. The average measured distortion in the world between
the expected marginal product of capital and its user cost falls somewhere between 17 and
21 percentage points. The average coe¢ cient of variation in the distortion within a country
is 28 to 29 percent. World output could increase somwhere between 65 and 88 percent if
all countries adopted the best …nancial practice in the world. Adopting this practice leads
to funds being redirected away from ine¢ cient …rms toward more productive ones. This
reallocation e¤ect is re‡ected by a rise in world TFP by 17 to 33 percent. Still, this only
accounts for 36 to 45 percent of the gap between actual and potential world output. This
36

happens because the bulk of the di¤erences in cross-country GDP are explained by the huge
di¤erences in the productivity of the non-…nancial sector.

Data Appendix
Figure 1: For the United States, the spread is computed along the lines of Mehra et
al. (2009). Speci…cally, the spread is de…ned to be “Intermediation Services associated
with household borrowing and lending”divided by “Total Amount Intermediated”(see
de…nitions of these below). The “Intermediation Services associated with household
borrowing and lending”is computed as “Interest Paid”minus “Interest Received”minus “Services Furnished by …nancial intermediaries without payment Interest Paid.”
These numbers are taken from the National Income and Product Accounts [NIPA,
Tables 7.11 (lines 4 and 28) and 2.4.5 (lines 89 and 108)]. The “Total Amount Intermediated” is taken from the Flow of Funds account (2000, Table B.100b.e.) This
number is Assets (line 1) minus Tangible Assets (line 2). For Taiwan, the spread
is obtained from Lu (2008). The initial capital-to-output ratio in each country was
normalized to one (to control for di¤erent de…nitions of the capital stock).
Figure 2, Figure 3 and Section 8: The cross-country data for the interest-rate spreads
are taken from the Financial Structure Dataset, assembled by Beck et al. (2000,
2001) and revised in January 2009. It is de…ned as the accounting value of banks’net
interest as a share of their interest-bearing (total earning) assets averaged over 1997
to 2003. The numbers for the …nancial development measure are obtained from the
same dataset. They represent demand, time and saving deposits in deposit money
banks as a share of GDP, and are also averaged over 1997 to 2003. The other numbers
derive from the Penn World Tables (PWT), Version 6.2— see Heston et al. (2002). The
capital stock for a country, k, is computed for the period 1955-2003 sample period. The
starting value is computed using the formula k = i=(g + ), where i is gross investment
(rgdpl*pop*ki in the PWT’s notation), g is the growth rate in investment, and

rate of depreciation. The depreciation is taken to be 0.06. For the starting value, i
and g are the average over the …rst …ve years available for each country (in general
1950 to 1954). From there on, a time series is constructed for each country using
kt = kt 1 (1

) + it : Again, the numbers used correspond to the average over 1997

to 2003. A country’s total factor productivity, T F P , was computed using the formula
T F P = (y=l)=(k=l) , where y is GDP, l is aggregate labor, and

is capital’s share of

income. A value of 0.35 was picked for .
Figure 5 (Firm size): The data are for establishments. They come from County
Business Patterns (CBP), which is released by the U.S. Census Bureau annually. Due
to a signi…cant shift in the methodology employment by the Census from 1974 on, data
are only used for this time period. The horizontal axis orders establishments (from the
smallest to highest) by the percentile that they lie in for employment. The vertical
axis shows the cumulative contribution of this size of establishment to the employment
in the U.S. economy. Some data are shown below.

Table 8: U.S. Establishment-Size Distribution Data, 1974 & 2004
Establishments with number of workers between:
Series

1-4

5-9

10-19

20-49

50-99

100-249

250-499

500-999

1000 +

Establishments (# in 1,000’s)

2,411

739

463

309

103

55.9

17.5

7.61

4.39

Employees (# in 1,000’s)

4,591

5,222

6,582

9,714

7,223

8,615

6,112

5,286

10,153

Establishments

59%

18%

11%

7.5%

2.5%

1.4%

0.5%

0.2%

0.1%

Employees

7.2%

8.2%

10%

15%

11%

14%

9.6%

8.3%

16%

Establishments (# in 1,000’s)

4,019

1,406

933

637

218

122

31.3

11.5

6.83

Employees (# in 1,000’s)

6,791

9,311

12,598

19,251

15,037

18,314

10,662

7,815

15,295

Establishments

54%

19%

13%

8.6%

3.0%

1.7%

0.4%

0.2%

0.1%

Employees

5.9%

8.1%

11%

17%

13%

16%

9.3%

6.8%

13%

Year 1974

Year 2004

Source: County Business Patterns (CBP).

Figure 6 (relationship between ln z and some other variables): Data for the “rule of law”
are taken from the World Bank’s “Aggregate Governance Indicators, 1996-2008”— see
Kaufmann et al. (2009). Data on personal computers are obtained from the World
Bank publication Information and Communications for Development 2009: Extending
Reach and Increasing Impact. The numbers for the …nancial development measure and
the ratio of overhead costs to assets are available in the revised version of the Beck et
al (2000) dataset mentioned above. Last, average years of education is based on Barro
and Lee (2001).

Table 9: Cross-Country numbers, data and model
Country

Data

Model
Benchmark

K/Y

Spread

GDPpc

Uganda

0.28

0.101

Ethiopia

0.37

Nigeria

Counterfactual

ln(z)

K/Y

GDPpc

Spread

1043

0.03

-2.62

0.59

4228

0.003

1.40

0.34

0.30

0.48

0.031

705

0.01

-1.05

1.42

1478

0.002

0.74

0.17

0.16

0.15

0.61

0.096

1086

0.03

-2.50

0.62

4256

0.003

1.37

0.34

0.30

0.46

Guatemala

0.75

0.091

3786

0.07

-1.17

0.65

13264

0.005

1.25

0.45

0.27

0.42

El Sal.

0.90

0.064

4706

0.07

-0.38

0.86

13140

0.005

1.03

0.40

0.23

0.29

Costa Rica

0.95

0.060

8093

0.09

0.26

0.90

20859

0.006

0.95

0.47

0.21

0.27

S. Africa

1.00

0.049

8207

0.09

0.60

1.04

18997

0.006

0.84

0.42

0.19

0.21

India

1.01

0.032

2630

0.04

0.25

1.42

5235

0.003

0.69

0.22

0.15

0.14

Mauritius

1.09

0.028

14986

0.11

2.19

1.52

24821

0.007

0.50

0.36

0.11

Bolivia

1.16

0.052

2929

0.05

-0.53

1.00

7579

0.004

0.95

0.31

0.21

0.24

Kenya

1.18

0.076

1258

0.03

-1.99

0.75

4251

0.003

1.22

0.31

0.27

0.36

Pakistan

1.18

0.033

2479

0.03

0.09

1.37

5089

0.003

0.72

0.22

0.16

0.15

Sri Lanka

1.22

0.043

3967

0.05

0.13

1.16

8980

0.004

0.82

0.30

0.18

0.19

Morocco

1.28

0.049

3835

0.05

-0.16

1.05

9421

0.004

0.90

0.32

0.20

0.22

Nicaragua

1.34

0.075

3337

0.06

-0.99

0.76

10514

0.004

1.15

0.39

0.25

0.35

Colombia

1.35

0.062

6092

0.08

-0.09

0.88

16455

0.006

0.99

0.43

0.22

0.28

Philipp.

1.52

0.056

3565

0.05

-0.45

0.95

9475

0.004

0.98

0.34

0.22

0.26

Honduras

1.65

0.082

2273

0.05

-1.52

0.70

7780

0.004

1.23

0.37

0.27

0.39

Turkey

1.65

0.127

5559

0.10

-1.30

0.49

23021

0.007

1.42

0.59

0.31

0.59

Ireland

1.85

0.012

24344

0.11

4.28

2.33

27968

0.007

0.14

0.15

0.03

0.02

Uruguay

1.86

0.069

10269

0.11

0.27

0.81

27904

0.007

1.00

0.56

0.22

0.30

Mexico

1.97

0.065

7776

0.09

0.85

21049

0.006

1.00

0.48

0.22

0.29

Brazil

2.03

0.123

7067

0.11

-1.02

0.50

28070

0.007

1.38

0.64

0.30

0.57

GDP

Gap

TFP

(Table 9, continued)
Country

Data

Model
Benchmark

K/Y

Spread

GDPpc

U.K.

2.09

0.026

Peru

2.12

U.S.

Counterfactual

ln(z)

K/Y

GDPpc

Spread

24400

0.14

2.82

1.59

37075

0.008

0.42

0.46

0.09

0.075

4220

0.07

-0.75

0.76

13052

0.005

1.13

0.42

0.25

0.34

2.23

0.042

33524

0.20

2.28

1.17

61061

0.011

0.60

1.00

0.13

0.16

Luxem.

2.36

0.009

45830

0.16

5.40

2.56

45830

0.009

0.00

Portugal

2.40

0.022

16936

0.11

2.76

1.74

24977

0.007

0.39

0.30

0.09

0.08

N. Zealand

2.49

0.017

20605

0.11

3.43

1.99

27036

0.007

0.27

0.25

0.06

0.05

Israel

2.50

0.028

21106

0.13

2.57

1.54

33398

0.008

0.46

0.43

0.10

Iceland

2.57

0.030

25071

0.15

2.57

1.45

40607

0.009

0.48

0.54

0.11

Spain

2.58

0.035

19215

0.13

2.05

1.32

34266

0.008

0.58

0.50

0.13

Sweden

2.60

0.028

24582

0.14

2.72

1.54

38230

0.009

0.44

0.49

0.10

Nether.

2.62

0.020

25600

0.13

3.34

1.83

34881

0.008

0.31

0.36

0.07

0.06

Australia

2.63

0.015

25993

0.13

3.95

2.13

31620

0.008

0.20

0.23

0.04

Denmark

2.64

0.043

27246

0.18

2.03

1.15

51658

0.010

0.64

0.79

0.14

0.17

Belgium

2.69

0.022

24228

0.13

3.16

1.77

34089

0.008

0.34

0.37

0.08

0.07

France

2.71

0.029

24537

0.15

2.61

1.48

39189

0.009

0.47

0.51

0.10

Norway

2.73

0.024

32896

0.17

3.29

1.67

46414

0.009

0.34

0.56

0.08

0.07

Italy

2.74

0.033

22234

0.14

2.29

1.37

38087

0.008

0.54

0.53

0.12

Austria

2.84

0.025

26433

0.15

3.01

1.65

38748

0.009

0.38

0.46

0.08

Thailand

3.09

0.022

6659

0.06

1.86

1.76

10562

0.004

0.46

0.21

0.10

0.09

Finland

3.11

0.016

22207

0.12

3.59

2.04

28434

0.007

0.25

0.24

0.05

Switzer.

3.67

0.019

28363

0.14

3.54

1.88

37403

0.008

0.28

0.36

0.06

0.05

Japan

3.74

0.018

23818

0.12

3.45

1.92

31533

0.008

0.28

0.30

0.06

0.05

GDP

Gap

TFP

100

0
65
60
55
50
45
40
35
30
25
20
15
10
5
0

Uganda
Turkey
Nigeria
Brazil
Guatemala
Honduras
Kenya
Nicaragua
Peru
El Salvador
Colombia
Mexico
Uruguay
Philippines
Bolivia
Costa Rica
Morocco
South Africa
Sri Lanka
Ethiopia
Pakistan
India
Denmark
United States
Spain
Italy
Mauritius
Iceland
France
Thailand
Israel
Sweden
United Kingdom
Portugal
Austria
Norway
Belgium
Netherlands
Japan
Switzerland
New Zealand
Finland
Australia
Ireland
Luxembourg

180
160
140
120
100
80
60
40
20
0
GDP per worker, % change

reduction in the gap to the frontier, %

TFP, % change

Figure 9: Cross-country results with intangible capital,

= 0:41

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