WPS4608
Policy ReseaRch WoRking PaPeR 4608
The Econometrics of Finance and Growth
Thorsten Beck
The World Bank
Development Research Group
Finance and Private Sector Team
April 2008
Policy ReseaRch WoRking PaPeR 4608-
Abstract
This paper reviews different econometric methodologies differences-in-differences techniques that try to overcome
to assess the relationship between financial development the identification problem by assessing the differential
and growth. It illustrates the identification problem, effect of financial sector development across states with
which is at the center of the finance and growth different policies or across industries with different needs
literature, using the example of a simple Ordinary Least for external finance. Finally, it discusses firm-level and
Squares estimation. It discusses cross-sectional and household approaches that allow analysts to dig deeper
panel instrumental variable approaches to overcome into the channels and mechanisms through which
the identification problem. It presents the time-series financial development enhances growth and welfare, but
approach, which focuses on the forecast capacity of pose their own methodological challenges.
financial development for future growth rates, and
This paper--a product of the Finance and Private Sector Team, Development Research Group--is part of a larger effort in
the department to understand the link between financial sector development and economic development. Policy Research
Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at TBeck@
worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
The econometrics of finance and growth
Thorsten Beck1
Keywords: Finance and growth; instrumental variables; time-series econometrics;
differences-in-differences estimation
JEL Classification Codes: C2; C3; G2; O4
1World Bank, tbeck@worldbank.org. I am grateful to George Clarke, Aart Kraay,
Luc Laeven, Ross Levine, Kerry Patterson, and Peter Rousseau for comments and useful
discussions. This paper's findings, interpretations, and conclusions are entirely those of
the author and do not necessarily represent the views of the World Bank, its Executive
Directors, or the countries they represent. This paper was prepared for the Palgrave
Handbook of Econometrics, Vol. 2.
1. Introduction
Economists have discussed over the past 100 years whether or not financial development
has a causal impact on economic development. Theory suggests that effective financial
institutions and markets that help overcome market frictions introduced by information
asymmetries and transaction costs can foster economic growth through several channels.
Specifically, they help (i) ease the exchange of goods and services by providing payment
services, (ii) mobilize and pool savings from a large number of investors, (iii) acquire and
process information about enterprises and possible investment projects, thus allocating
society's savings to its most productive use, (iv) monitor investments and exert corporate
governance, and (v) diversify and reduce liquidity and intertemporal risk. However, other
models show that higher returns from better resource allocation may depress saving rates,
resulting in overall growth rates actually slowing with more effective financial markets
and institutions.2
While the finding of a positive correlation between indicators of financial
development and economic growth cannot settle this debate, advances in computational
capacity and availability of large cross-country data sets with relatively large time
dimensions have enabled researchers to rigorously explore the relationship between
financial development and economic growth. Further, as more disaggregated data sets
have become available, the finance and growth literature has proceeded from using
country-level data, to using industry- and firm-level data, to more recently using
household data. While the cross-country literature has developed more sophisticated
models to address biases introduced by measurement error, reverse causation and omitted
variables, the progress to firm- and household-level data allows not only additional ways
to address these biases, but also tests of the specific channels through which finance
might enhance economic growth.
The econometrics of finance and growth can be summarized in the following
simple regression model:
g(i,t)= y(i,t)- y(i,t -1)= + i f (i,t)+ C(i,t)i + (i)+(i,t) (1)
where y is the log of real GDP per capita or of another measure of welfare, g is the
growth rate of y, f is an indicator of financial development, C is a set of conditioning
2See Levine (1997, 2005) for surveys of the theoretical literature.
information, and are error terms, i is the observational unit, be it a country, an
industry, a firm or a household, and t is the time period. While is a white noise error
with a mean of zero, is a country-specific element of the error term that does not
necessarily have a mean of zero. The explanatory variables are measured either as an
average over the sample period or as an initial value. The sign and significance of the
coefficient i is at the center of the debate. As discussed in the remainder of this paper,
the estimate of i can be biased for a variety of reasons, among them measurement error,
reverse causation and omitted variable bias. While the cross-country literature assumes i
= , with some research supporting this assumption (Loayza and Ranciere, 2006), the
time series literature does not impose this restriction. Further, several industry and firm-
level studies test whether varies across industries or firms with different characteristics,
utilizing interaction terms.
This paper is concerned with an unbiased, consistent and efficient estimator of
i.3 In this context, we abstract from a number of other problems in the finance and
growth literature. First, the paper does not cover problems arising from the lack of
appropriate data, although we are concerned about measurement error in the financial
indicators and the bias this introduces in the estimation. Second, while we are concerned
about the bias introduced by the potential reverse causation from growth to finance, we
are not concerned about this reverse causation per se, i.e. we do not discuss in depth the
literature focusing on the impact of economic on financial development and bi-directional
causality. Finally, the paper does not intend to be a fully fledged survey of the empirical
finance and growth literature, as is Levine (2005), but rather focuses on studies with
methodological contributions.
While this paper is concerned about estimating the relationship between finance
and growth, some remarks about measuring financial development might be useful.
While the theoretical literature links specific functions of the financial system to
economic growth, data limitations have forced researchers to focus on variables capturing
the size, activity or efficiency of specific financial institutions or markets. The first
generation of papers in the finance and growth literature have built on aggregate data on
financial institutions, mainly banks, available for 30 to 40 year periods for a large number
3For a broader survey on the econometrics of growth regressions, see Durlauf, Johnson and Temple (2005).
2
of developed and developing countries. Such indicators include monetization variables,
such as M2 or M3 to GDP, or financial depth indicators, such as private credit
(outstanding claims of financial institutions on the private sector) to GDP. Later papers
have added indicators of the size and liquidity of stock markets, albeit available for fewer
countries and shorter time periods. Indicators for the efficiency and competitiveness of
financial systems, non-bank financial institutions such as institutional investors and, most
importantly, the outreach of financial systems, are available for only a few countries and
often do not have a time dimension.4 Within-country studies allow researchers to utilize
more micro-based data or focus on specific policy interventions or reforms.
The remainder of the paper is structured as follows. Section 2 illustrates the
identification problem, which is at the center of the finance and growth literature, using
the example of a simple Ordinary Least Squares (OLS) estimation of regression (1).
Section 3 discusses instrumental variable (IV) approaches using cross-sectional and panel
data. Section 4 discusses time-series approaches and section 5 differences-in-differences
techniques. Section 6 discusses the use of firm- and household-level data and the
methodological challenges this implies. Section 7 concludes and looks forward to new
research directions.
2. Correlation vs. causality -- the identification problem
Goldsmith (1969) was the first to empirically show the positive correlation between
financial development and GDP per capita, using data on the assets of financial
intermediaries relative to GNP and data on the sum of net issues of bonds and securities
plus changes in loans relative to GNP for 35 countries over the period 1860 to 1963. Such
a correlation, however, does not control for other factors that are associated with
economic growth and might thus be driven by other country characteristics correlated
with both finance and growth. Second, such a correlation does not provide any
information on the direction of causality between finance and growth. The early finance
and growth literature has therefore used standard cross-country OLS regressions that
4See Beck, Demirguc-Kunt and Levine (2000) for an overview of different cross-country indicators of
financial development and Beck et al. (2008) for a discussion of the different dimensions of financial
development, such as depth, efficiency and reach. See World Bank (2007) for a discussion of financial
outreach indicators.
3
build on an augmented Barro growth regression as in (1), with data for each country
averaged over the sample period, assuming i = and i = for all countries, and
including the lagged dependent variable as control variable:
g(i)= y(i,t)- y(i,t -1)= + f (i)+C(i) +y(i,t -1)+(i) (2)
Unlike regression (1), regression (2) has thus only a cross-country, but not a time-
series, dimension. The log of initial income per capita is included to control for
convergence predicted by the Solow-Swan growth models. Including other country
characteristics, such as initial levels of human or physical capital, and policy variables,
such as government consumption or trade openness, in a set of conditioning information
allows testing for an independent partial correlation of finance with growth. The
coefficient is of interest for finance and growth researchers, who interpret a positive
and significant coefficient as evidence for a positive partial correlation between finance
and growth.
Running this cross-country regression for a sample of 77 countries over the period
1960 to 1989, King and Levine (1993) found a positive and significant relationship
between several financial development indicators and GDP per capita growth. Their
study focuses mostly on monetization indicators and indicators measuring the size and
relative importance of banking institutions. Using initial values of financial development
confirms their finding. Levine and Zervos (1998) expanded the analysis to include
measures of stock market development and found a positive partial correlation of both
stock market and bank development with GDP per capita growth over the period 1976 to
1994.5 Interestingly, they found a positive and significant link between liquidity of stock
markets as measured by a turnover indicator or value traded to GDP and economic
growth, but no robust relationship between the size of stock markets and economic
growth. The empirical relationship between finance and growth, however, is not only
statistically, but also economically significant. Levine and Zervos (1998) found that a one
standard deviation in stock market liquidity and banking sector development explains an
5Other early finance and growth studies using cross-sectional OLS regressions include Atje and Jovanovic
(1993) and De Gregorio and Guidotti (1995).
4
annual GDP per capita growth difference of 0.8 and 0.7 percentage, respectively, adding
up to a total difference in GDP per capita of 31% over the 18 year sample period.
OLS estimates, however, are only consistent if the following orthogonality
conditions hold:
E[C(i)'(i)]= 0; E[ (i,t)'(i)]= 0; E[f (i)'(i)]= 0 (3)
A violation of this condition can arise for several reasons. First, the presence of an
unobserved country-specific effect (i) as in regression (1) results in a positive
correlation of the lagged dependent variable with the error term as, unlike the error term
(i), (i) does not have a mean of zero, so that:
E[ (i,t -1)'((i)+(i))] 0 (4)
Omitted variable bias can also arise if other explanatory variables are correlated with the
unobserved country-specific effect or if explanatory variables that should be included in
regression (2) are (i) not included and (ii) correlated with included explanatory variables,
so that:
E[C(i)'((i)+(i))] 0 (5)
Second, reverse causation from GDP per capita growth to financial development
or another explanatory variable could violate the orthogonality condition and thus bias
the estimator of if (i) and (i) are correlated with each other, as would occur if:
f (i) = y(i,t -1)+ (i) (6)
Third, one of the explanatory variables could be mis-measured, so that:
f *(i) = f (i)+ u(i) (7)
where f* is the true level and f is the measured level of financial development. This could
result in attenuation bias, if the measurement error is correlated with f.
5
Several simple approaches to overcome these biases have been suggested. First,
controlling for other country traits and policies can help minimize the omitted variable
bias and allow testing for the robustness of the finance and growth link (Levine and
Renelt, 1992). However, the number of observations, and thus degrees of freedom,
severely limits this approach in a typical cross-country regression. Second, several
studies have used initial values of financial development, rather than values averaged
over the same period as GDP per capita growth. If the true time span over which an
improvement in financial development results in higher growth is shorter than the sample
period used in the regression, then using initial values might reduce biases stemming
from reverse causation. On the other hand, using initial values does not correct for biases
introduced by omitted variables, measurement error or the inclusion of the lagged
dependent variable, and implies a loss of information to be used in the estimation. Third,
using panel regressions with fixed country effects would eliminate any time-invariant
omitted variable bias and time-invariant measurement bias. However, the correlation
between the transformed lagged dependent variable and the transformed error term will
make the fixed effect estimator biased, and this bias is only eliminated as the number of
time periods goes towards infinity, which is certainly not the case for the typical growth
regression with fewer than 40 annual data points. Finally, fixed effect regressions also
have the conceptual shortcoming that they effectively limit the analysis to within-country
variation in growth and financial development by differencing out cross-country variation.
3. Instrumental variable approach
The classical approach in cross-country growth regressions to overcome the biases
related to OLS is to identify an instrument that helps isolate that part of the variation in
the endogenous variable that is not associated with reverse causation, omitted variables
and measurement error. Following the seminal work by La Porta et al. (1997, 1998), who
identified variation in countries' legal origin as an historical exogenous factor explaining
current variation in countries' level of financial development, an extensive literature has
utilized this variable to extract the exogenous component of financial development.
To overcome biases related to the inclusion of the lagged dependent variable and
omitted variable bias, while at the same time controlling for reverse causation and
6
measurement error, researchers have utilized dynamic panel regressions using lagged
values of the explanatory endogenous variables as instruments. Finally, to control for
country heterogeneity in the finance-growth relationship, researchers have utilized Pooled
Mean Group (PMG) estimators. We will discuss each methodology in turn.
3.1. Cross-sectional regressions
Underlying instrumental variable estimation is the following specification:
g(i)= (i,t)- (i,t -1)=1 + 1 f (i)+C(i)1 +1 (i,t -1)+(i) (8)
f (i)=2 + Z(i)2 +C(i)2 +2 (i,t -1)+(i) (9)
f *(i) = f (i)+ u(i) (10)
where C are the included exogenous and Z the excluded exogenous control variables; the
latter are also referred to as instrumental variables which allow us to extract the
exogenous component of f(i) that is not correlated with (i), i.e. E[Z(i)'(i)]= 0 , and
E[Z(i)'u(i)]= 0 .6 Estimating regression (8) with instruments can help alleviate biases
arising from reverse causation, omitted variable and measurement error.
Regression (8) is typically estimated with a Two-Stage-Least Squares Estimator
(TSLS). Unlike the OLS estimator, the TSLS estimator only uses the variation in the
explanatory variables that is correlated with the instrument and therefore uses less
information than the OLS estimator. If OLS is consistent, it is therefore more efficient
than IV, whereas if OLS is inconsistent, the IV estimator is both consistent and efficient.7
The TSLS estimator can also be derived as a General Method of Moments
(GMM) estimator that minimizes a set of orthogonality conditions (Hansen, 1982). In the
case, where there are more excluded exogenous than endogenous variables, a weighting
matrix has to be used. While the TSLS estimator uses a weighting matrix constructed
under the assumption of homoskedasticity, the weighting matrix of the GMM estimator is
constructed as the inverse of the variance-covariance matrix, thus assigning different
6Most of the papers using this approach assume that only financial development is an endogenous variable
and thus treat all control variables as exogenous.
7The literature has developed several tests to resolve the issue of OLS vs. IV, including the Hausman test.
7
weights to the orthogonality condition, according to their variances. While the TSLS
estimator is thus consistent, it is inefficient as it does not use all the available information.
On the other hand, the GMM estimator relies on asymptotic characteristics and therefore
suffers from a finite-sample bias as the optimal weighting matrix is a function of fourth
moments (Hayashi, 2000).8
Using legal origin as an instrument for financial development, Levine (1998,
1999) finds a positive relationship between finance and economic growth. Researchers
have also used other historical and exogenous country characteristics as instruments for
financial development, such as settler mortality and latitude, to proxy for geographic
conditions, ethnic fractionalization, religious composition of the population, and years
since independence (McCraig and Stengos, 2005). Guiso, Sapienza and Zingales (2004)
use sub-national variation in historical bank restriction indicators across 20 Italian
regions and its 103 provinces as instrumental variables to assess the impact of financial
development and competition on economic growth and other real sector outcomes.
IV regressions depend on the quality of the instrumental variables, independent of
whether TSLS or GMM is applied. As discussed above, these instruments are typically
exogenous country characteristics, such as geographic traits, or based on historical
experience, such as legal origin. The challenge is to identify the economic mechanisms
through which the instrumental variables influence the endogenous variable financial
development while at the same time assuring that the instruments are not correlated
with growth directly. An extensive literature has discussed the historic determinants of
financial sector development and the channels through which, for example, legal origin
has helped shape current financial sector development,9 but there are also several formal
econometric conditions to be fulfilled in order for an instrument to be valid. First, the
exogenous variables cannot be correlated with error terms, i.e., E[Z(i)'(i)]= 0
(orthogonality or exogeneity condition). Second, the excluded exogenous instruments
have to explain the variation in the endogenous variables after controlling for the
included exogenous variables, i.e. the F-test for Z(i) in (9) is rejected at conventional
levels (relevance condition).
8The presence of heteroskedasticty can be examined with a test proposed by Pagan and Hall (1983).
9See Beck and Levine (2005) for an overview.
8
The orthogonality condition is typically tested with the Sargan (1958) test of
overidentifying restrictions (OIR) if there are more instruments than explanatory
variables, that is: 'Z(Z'Z)-1Z'/ , where = (') / n and is the vector of
2 2
residuals from estimating regression (8). This test can easily be calculated from a
regression of the IV regression's residuals on included and excluded exogenous variables.
It is distributed as ² with (J - K) degrees of freedom under the null hypothesis that the
residuals are not correlated with the exogenous variables, where J is the number of
instruments and K the number endogenous variables.10 Hansen's (1982) J-test is a
generalization of the Sargan OIR test to the GMM context and is the value of the GMM
objective function evaluated at the efficient GMM estimator: 'Z(Z' Z)-1Z' , where
is the estimated variance-covariance matrix of the residuals from regression (8). As
with the Sargan test, Hansen's test is distributed as ² with (J - K) degrees of freedom.
The test of overidentifying restrictions, however, is relatively weak. First, the test
only assesses the validity of any additional instruments, i.e. it cannot be performed if the
number of excluded exogenous variables is the same as the number of endogenous
variables. Further, the test tends to reject the null hypothesis of valid instruments too
often in small samples (Murray, 2006). Most importantly, the test over-rejects if the
instruments are weak, i.e. if they do not explain the endogenous variables in the first
stage.
The second condition of instrument relevance can be tested in different ways.
First, one can use an F-test of the joint significance of the instruments in (9); the critical
values of this F-test for IV estimation, however, are larger than for OLS estimation; for
the case of a single endogenous variable, Staiger and Stock (1997) show, using Monte
Carlo simulations, that for most specifications and independent of the degrees of freedom
a critical value of 10 is sufficient to reject the null hypothesis, and Stock and Yogo
(2005) derive critical values for this F-test for the case of several endogenous variables,
10An alternative test was developed by Basmann (1960) and does not impose the overidentifying
restrictions.
9
with the critical values increasing with the number of instruments.11 Second, one can use
a partial R2 of the first-stage regression (9) that takes into account the intercorrelation
among the instruments (Shea, 1997). Sepcifically, Godfrey (1999) shows that this
OLS
i 2
statistic for endogenous regressor i is where i is the estimated
IV
i [((1- RIV )
1- ROLS )],
2
asymptotic variance of the coefficient i. This measure thus tests for the relevance of the
individual instruments, unlike the F-test, which tests for the overall relevance.
Weak instruments can bias the IV results towards OLS and turn them inconsistent.
Further, weak instruments can result in an over-rejection of the overidentification test
discussed above. If instruments are both invalid and irrelevant, the bias thus increases in
a multiplicative way.12
Most of the cross-country finance and growth papers utilizing instrumental
variables find that the IV estimator of 1 is higher than the OLS estimator.13
Manipulating regressions (8), (9) and (10), one can show that this implies:
+ ( < 1(1-1 )(
) u)
2 2 (11)
() ()
where is the correlation between and and the other parameters are taken from
regressions (8), (9) and (10). There are several possible explanations for this finding and
thus for inequality (11) to hold (Kraay and Kaufman, 2002). First, there could be
negative reverse causation (2 < 0), which would bias the OLS estimator of the 1
coefficient downwards. Given empirical studies showing the positive relationship
between economic and financial development, this explanation seems rather unlikely
(Harrison, Sussman and Zeira, 1999). A second explanation that makes inequality (11)
hold is that omitted variables are correlated with growth and finance with opposite signs
11In the case of several endogenous variables, the Stock and Yogo test also requires each instrument to
predict primarily just one of the endogenous variables.
12For further discussion on weak instruments and how to deal with them, see Murray (2006) and Baum,
Schaffer and Stillman (2003).
13Most papers in the literature, however, do not formally test whether the difference between the OLS and
the IV estimate is significant, which could be done with a Hausman test.
10
( < 0), an explanation for which, again, little evidence exists. A third - and most
commonly adopted - explanation relies on attenuation bias, where measurement error in
financial development ( (u) ) biases the OLS estimate downwards and makes inequality
(11) hold. Critically, however, if the instrumental variables are positively correlated with
omitted variables and the exclusion condition is thus violated, the IV estimator of 1 is
biased upwards. This is of concern, as a few instrumental variables, such as historical
country traits, have been used for many different institutional variables in the context of
growth regressions (Pande and Udry, 2006). Specifically, legal origin has been shown to
be associated with an array of institutional arrangements, ranging from financial markets
over general regulatory approaches, to labor market institutions. A significant correlation
between institutional variables left out of the regressions and the instrumental variables
can therefore also result in an upwardly biased IV estimator of 1.
3.2. Dynamic panel analysis
While the cross-sectional IV regressions address biases related to omitted variables,
reverse causation and measurement error, they do face several limitations. First, cross-
country studies using cross-sectional IV regressions typically control only for the
endogeneity and measurement error of financial development, but not of other
explanatory variables entering the growth regressions. Second, in the presence of
country-specific omitted variables, the lagged dependent variable is correlated with the
error term if it is not instrumented.
As an alternative to cross-sectional IV regressions, researchers have therefore
used dynamic panel regressions of the following format:
g(i,t)= + f (i,t)+C(1)(i,t)1 +C(2)(i,t) 2 +y(i,t -1)+ (i)+ (t)+(i,t) (12)
where C(1) represents a set of exogenous explanatory variables, C(2) a set of endogenous
explanatory variables, and a vector of time dummies. Note that is still assumed to be
constant across countries, a restriction that we will relax further below.
11
Unlike the cross-sectional regressions, which use external instruments, i.e.
variables that are completely external to the second stage regression, the dynamic panel
regressions use internal instruments, i.e. lagged realizations of the explanatory variables.
While this method does not control for full endogeneity, it does control for weak
exogeneity, which means that current realizations of f or variables in C(2) can be affected
by current and past realizations of the growth rate, but must be uncorrelated with future
realizations of the error term. Thus, under the weak exogeneity assumption, future
innovations of the growth rate do not affect current financial development.
In order to address the different biases in regression (12), Arellano and Bond
(1991) suggest first-differencing the regression equation to eliminate the country-specific
effect, as follows:14
g(i,t)= f (i,t)+1'C(1 (i,t)+2'C(2 (i,t)+y(i,t)+ (t)+ (i,t)
) ) (13)
where x(t) = x(t) - x(t-1). This procedure solves the omitted variable bias, as described
above, but introduces a correlation between the new error term, (i,t), and the lagged
dependent variable, y(i,t-1). To address this correlation and the endogeneity and
measurement problems, Arellano and Bond (1991) suggest using lagged values of the
explanatory variables in levels as instruments for current differences of the endogenous
variables. Under the assumptions that there is no serial correlation in the error term and
that the explanatory variables f and C(2 are weakly exogenous, one can use the following
)
moment conditions to estimate regression (13):
E[f (i,t - s)'(i,t)]= 0, for each t = 3,...T,s 2
E C(2 (i,t - s)'(i,t) = 0 , for eacht = 3,...T,s 2
[ ) ]
E[y(i,t - s)'(i,t)]= 0, for each t = 3,...T,s 2 (14)
Using these moment conditions, Arellano and Bond (1991) propose a two-step
GMM difference estimator. In the first step, the error terms are assumed to be both
independent and homoskedastic across countries and over time, while in the second step,
14Alternatively, one can use the forward orthogonal deviation transformation.
12
the residuals obtained in the first step are used to construct a consistent estimate of the
variance-covariance matrix, thus relaxing the assumptions of independence and
homoskedasticity. Simulations, however, have shown very modest efficiency gains from
using the two-step as opposed to the one-step estimator, while the two-step estimator
tends to underestimate the standard errors of the coefficient given that the two-step
weight matrix depends on estimated parameters from the one-step estimator (Bond and
Windmeijer, 2002).
There are several conceptual and econometric shortcomings with the difference
estimator. First, by first-differencing we lose the pure cross-country dimension of the data.
Second, differencing may decrease the signal-to-noise ratio, thereby exacerbating
measurement error biases (see Griliches and Hausman, 1986). Finally, Alonso-Borrego
and Arellano (1999) and Blundell and Bond (1998) show that, if the lagged dependent
and the explanatory variables are persistent over time, i.e. have very high autocorrelation,
then the lagged levels of these variables are weak instruments for the regressions in
differences.15 Simulation studies show that the difference estimator has a large finite-
sample bias and poor precision.
To address these conceptual and econometric problems, Arellano and Bover
(1995) suggest an alternative estimator that combines the regression in differences with
the regression in levels. Using Monte Carlo experiments, Blundell and Bond (1998) show
that the inclusion of the level regression in the estimation reduces the potential biases in
finite samples and the asymptotic imprecision associated with the difference estimator.
Using the regression in levels, however, does not directly eliminate the country-specific
effect . Lagged differences of the explanatory variables can be used as instruments for
the levels of the endogenous explanatory variables under the assumption that the
correlation between and the levels of the explanatory variables is constant over time,
such that:
E[f (i,t + p)'(i)]= E[f (i,t + q)'(i)], for all p and q
E C(2 (i,t + p)'(i) = E C(2 (i,t + q)'(i) , for all p and q
[ ) ] [ ) ] (15)
15Formal unit root tests as discussed in section 4 are not feasible in this context, as there are too few
observations.
13
Under this assumption, lagged differences are valid instruments for the regression
in levels, and the moment conditions for the regression in levels are as follows:
E[f (i,t - s)'((i,t)+ (i))]= 0 , for each t = 3,...,T, s = 2
E C(2 (i,t - s)'((i,t)+ (i)) = 0, for each t = 3,...,T,s = 2
[ ) ]
E[y(i,t - s)'((i,t)+ (i))]= 0 , for each t = 3,...,T,s = 2 (16)
The system thus consists of the stacked regressions in differences and levels, with
the moment conditions in (14) applied to the first part of the system, the regressions in
differences, and the moment conditions in (16) applied to the second part, the regressions
in levels.16 As with the difference estimator, the model is estimated in a two-step GMM
procedure.
The consistency of the GMM estimator depends both on the validity of the
instruments (exclusion condition) and the assumption that the error term, , does not
exhibit serial correlation. Arellano and Bond (1991) propose two tests to examine these
assumptions. The first is a Sargan test of over-identifying restrictions, which is
constructed in a similar manner to the cross-sectional test discussed above. In the context
of the system estimator, one can also compute a "difference-in-Sargan" test, the C-
statistic (Eichenbaum, Hansen and Singleton, 1988), to test the orthogonality condition of
a subset of instruments, such as the instruments applied to the level regressions. The C-
statistic is computed as the difference of two Sargan/Hansen statistics, the one for the
regression using the full set of instruments and the one using a smaller set of instruments.
The C-statistic is distributed as ² with the degrees of freedom equal to the number of
instruments dropped from the second regression.
The second test examines the assumption of no serial correlation in the error
terms, specifically whether the differenced error term is second-order serially correlated
as, by construction, the error term (i,t) from the difference regression is first-order
16Given that lagged levels are used as instruments in the difference regressions, only the most recent
difference is used as an instrument in the level regressions, as using additional differences would result in
redundant moment conditions (Arellano and Bover, 1995).
14
serially correlated and we cannot use the error terms from the regression in levels since
they include the country-specific effect . This test is based on the standardized average
residual autocovariances and, under the null hypothesis of no second-order serial
correlation, has a standard normal distribution.
Rousseau and Wachtel (2000) use the difference estimator with annual data over
the period 1980 to 1995 across 47 countries and find a positive link between indicators of
bank and stock market development and economic growth.17 Using five-year averages
over the period 1960 to 1995 across 74 countries, Beck, Levine and Loayza (2000) and
Levine, Loayza and Beck (2000) use both the difference and the system estimator and
find a positive and significant relationship between indicators of financial intermediary
development and GDP per capita growth, with the specification tests referred to above
confirming the validity of both instruments and econometric model.18 Beck, Levine and
Loayza (2000) also find that the effect of finance on growth is through productivity
growth, while there is no robust relationship between financial development and capital
accumulation when controlling for biases due to simultaneity, omitted variables and
measurement error.
The dynamic panel estimators have typically been applied to panels with few time
periods and many countries. Further, the instrumental variable matrix Z is typically
constructed with separate columns for instruments in different time periods, resulting in a
quadratic increase in the number of columns of Z as the number of time periods increases
(Roodman, 2007). This results in an overfit of the endogenous variables, biasing the
coefficient estimates towards OLS estimates and biasing the Sargan/Hansen test for joint
validity of the instruments towards over-accepting the null hypothesis (Bowsher, 2002).
In order to avoid overfitting, one can limit the number of lags used in the difference
regression or combine instruments into smaller sets, effectively imposing the constraint
that instruments of each lag distance have the same coefficient when projecting
regressors onto instruments (Beck and Levine, 2004, Roodman, 2007). In this case, the
orthogonality conditions for the difference regressions are:
17Rousseau and Wachtel (2000) was also the first paper to combine dynamic panel techniques with VAR
techniques discussed in the next section.
18Other papers using dynamic panel techniques include Rioja and Valev (2004a,b) and Benhabib and
Spiegel (2000). The latter, however, assume exogeneity of financial development and weak exogeneity
only for capital accumulation, but not the other control variables.
15
E[f (i,t - s)'(i,t)]= 0, for each s 2
E C(2 (i,t - s)'(i,t) = 0 , for each s 2
[ ) ]
E[y(i,t - s)'(i,t)]= 0, for each s 2 (17)
and the orthogonality conditions for the levels regressions are:
E[f (i,t - s)'((i,t)+ (i))]= 0 , for each s = 2
E C(2 (i,t - s)'((i,t)+ (i)) = 0, for each s = 2
[ ) ]
E[y(i,t - s)'((i,t)+ (i))]= 0 , for each s = 2 (18)
Given that data on financial sector indicators for a broad cross-section of
countries are only available for a 25 to 40 year period, most studies split the sample
period into non-overlapping five-year periods, thus controlling for business cycle effects,
while at the same time having a reasonable number of time periods. An alternative to
splitting the sample period into a number of five-year periods is to utilize overlapping
five year periods, as proposed by Bekaert, Harvey and Lundblad (2005), thus allowing
researchers to increase the number of time periods in the panel. In order to control for the
MA(4) character of the data, the weighting matrix of the GMM estimator has to be
adjusted accordingly.
Both the cross-sectional and the dynamic panel regressions discussed up to now
assume a homogenous relationship between finance and growth across countries, i.e. i =
. At the other extreme, the time series approach, discussed in the next section, assumes
complete country heterogeneity, but relies on a sufficiently large time series of data.
When both cross-country and time-series dimension are sufficiently large, Pesaran, Smith
and Im (1995) show that a consistent mean coefficient across countries is the unweighted
average of the coefficients from independent country regressions (mean group, MG,
estimator). The Pooled Mean Group (PMG) Estimator, introduced by Pesaran, Shin and
Smith (1999), is in between these two extremes of cross-country and time-series
approaches, as it imposes the same coefficient across countries on the long-run
coefficients, but allows the short-run coefficients and intercepts to be country-specific.
16
Loayza and Ranciere (2006) use the PMG estimator on a sample of 75 countries and
annual data over the period 1960 - 2000 and find a positive long-run relationship between
financial development and growth, while the mean short-run coefficient on current
financial development enters negatively.19 Using the Hausman test that compares the MG
with the PMG model, they cannot reject the hypothesis that the long-run coefficients on
finance are the same in a cross-country panel growth regression. This is also evidence
that the assumption that i = in the cross-country estimations discussed so far is a valid
one, as long as the focus is on the long-term relationship between financial development
and economic growth.
4. Time-series approach
The use of higher-frequency data, often limited to one or a few countries, and the concept
of causality, are the main differences between the time series approach and the cross-
country approach discussed in the previous section. First, the time-series approach relies
on higher-frequency data, mostly yearly, to gain econometric power, while the cross-
country approach typically utilizes multi-year averages.20 Further, the time-series
approach relaxes the somewhat restrictive assumption of the finance - growth relationship
being the same across countries i.e. I = and allows country heterogeneity of the
finance-growth relationship; most studies therefore focus their analysis on a few
countries with long time-series data. The time-series approach also directly addresses
biases introduced by the persistence and potential unit root behavior of financial
development, as we will see in the following.
Second, and more importantly, different causality concepts underlie the two
approaches. The time-series approach relies on the concept of Granger causality, as first
developed by Granger (1969). A time series X is said to Granger-cause Y if, controlling
for lagged Y values, lagged X values provide statistically significant information about
the current value of Y. Granger causality tests are tests of forecast capacity; i.e. to what
extent does one series contain information about the other series? Unlike the cross-
19This negative short-run coefficient is consistent with the finding of the banking crisis literature. See for
example, Demirguc-Kunt and Detragiache (1999).
20It is important to note, however, that the power of such high-frequency tests depends on the span of the
time series rather than the number of observations.
17
country panel regressions discussed earlier, this concept therefore does not control for
omitted variable bias by directly including other variables or by controlling with
instrumental variables. Rather, by including a rich lag structure, which is lacking in the
cross-sectional approach, the time series approach hopes to capture omitted variables.
The cross-country approach, on the other hand, estimates the empirical relationship
between finance and growth controlling for the different biases discussed in section 2,
including the omitted variable bias, by extracting an exogenous component of finance
that is related to growth only through finance.
In the context of the finance and growth literature, finance is said to Granger-
cause GDP per capita if the inclusion of past values of finance in a regression of GDP per
capita on its lags and the conditioning information set reduces the mean squared error
mse. Formally:
mse[y(t + s)/ y(t), y(t -1),...]> mse[y(t + s)/ y(t), y(t -1),..., f (t), f (t -1),...] (19)
where the null hypothesis of no Granger causality is typically tested using F-tests on
current and lagged values of f. Most studies test for bi-directional Granger causality using
the following vector autoregression (VAR) system:
Y(t)=1Y(t -1)+2Y(t - 2)+...+ Y(t - j)+ (t) (20)
j
where Y is a vector comprising both GDP per capita and finance, as well as possibly other
macroeconomic variables, and is a matrix of error terms. Jung (1986) finds evidence
for Granger causality from finance to GDP per capita for a sample of 56 countries, with
some evidence of reverse Granger causality in the case of developed countries.
Testing for Granger causality between finance and GDP per capita using a levels
VAR has the shortcoming that both finance and GDP per capita are nonstationary
variables in most countries, as shown by standard tests for unit roots, such as the
Augmented Dickey-Fuller (ADF) and Phillips and Perron (PP) tests, but stationary in first
differences. However, only if two (or more) nonstationary series are co-integrated, i.e. if
some linear combination of the series is stationary, can one use a levels VAR to test for
Granger causality (Toda and Phillips, 1993, 1994). Cointegration thus implies a long-run
18
equilibrium relationship between finance and GDP per capita. As in the case of Granger-
causality, cointegration does not directly control for omitted variable or measurement
biases, but rather exploits the long time-series of data to assess whether there is a stable
relationship between these two variables.
If the vector Y is cointegrated, regression (19) can be re-written in the vector error
correction (VEC) form (Engle and Granger, 1987):
Y(t)=1Y(t -1)+2Y(t -2)+...+'Y(t -1)+ (t) (21)
where the vector of error correction coefficients (loading factors) indicates the direction
and speed of adjustment of the respective dependent variable to temporary deviations
from the long-run relationship, while the vector is the cointegrating vector. If there
exists a non-zero cointegrating vector such that `Y(t) is stationary, the variables in Y are
considered cointegrated. Testing for cointegration of the vector Y(t) therefore is
equivalent to a test that `Y(t) is stationary. If we can reject the null hypothesis that
`Y(t) is stationary, we can also reject the null hypothesis that Y(t) is cointegrated. In the
case of two variables, this implies testing the residuals from a regression of y(1,t) on
y(2,t) or y(2,t) on y(1,t) for stationarity (Engle and Granger, 1987). While the standard
ADF test can be applied, the critical values are not the same as the test is performed on
estimated residuals (Engle and Yoo, 1987). If there is no unit root, the two variables are
cointegrated. In the case of more than two variables, inferences on the number and
coefficients of the cointegrating vectors can be based on Johansen's (1991) Full-
Information Maximum Likelihood approach. Johansen (1988) and Johansen and Juselius
(1990) show that the Maximum Likelihood estimator of and can be derived as a
solution of a generalized eigenvalue problem and likelihood ratio tests, based on these
eigenvalues, can be used to test hypotheses on the number of cointegrating vectors.21 The
number of linear independent cointegrating vectors is equal to the rank of the matrix .
Alternatively, one can test the hypothesis of a specific known cointegrating vector
(Horvath and Watson, 1995), as done by Neusser and Kugler (1998).
21Specifically, the "trace" test can be used to test the hypothesis of r against zero cointegrating vectors,
while the "-max" or maximum eigenvalue test can be used to test the hypothesis of r+1 cointegrating
vectors against r cointegrating vectors.
19
Demetriades and Hussein (1996) and Luintel and Khan (1999) use the VEC
specification and test for weak exogeneity of finance to GDP per capita by testing the
null hypothesis that the corresponding loading factor in the GDP per capita regression in
(21) is zero, while they follow Toda and Phillips' (1993) suggestion and use the product
of loading factor and the cointegrating parameter to test for long-run causality. While
Demetriades and Hussein (1996) find evidence for bidirectional causality and reverse
causation from income to finance across a sample of 16 developing countries with at least
27 annual observations, with results varying substantially from country to country,
Luintel and Khan (1999) find consistent evidence for bidirectional causality across a
sample of ten developing countries with at least 36 years of data.
In the case of a cointegrating relationship between finance and GDP per capita,
however, a levels VAR as in (20) can be used to test for short-term Granger causality,
with conventional F-test statistics applying (Toda and Phillips, 1993, 1994; Sims, Stock
and Watson, 1990)22 and the VEC representation in (21) to estimate the adjustment speed
. Rousseau and Wachtel (1998) use both the VAR specification of (20) and the VEC
specification of (21) to determine the direction of causality between economic and
financial development for five industrialized countries for the period 1870 to 1929.
Specifically, using the VEC specification of (21), they find a co-integrating relationship
for all five countries, while Granger causality tests suggest that finance leads GDP per
capita in all five countries.23 In addition, Neusser and Kugler (1998) apply the Granger
and Lin (1995) test to measure the strength of causality from finance to GDP per capita at
frequency zero, i.e. in the long-term, which is a function of the correlation of the errors in
a bivariate VEC model and the adjustment coefficient vector .
In order to gain degrees of freedom, as unit root and cointegration tests have low
power in the case of short time-series, several studies have expanded the time-series
approach to panel data (Neusser and Kugler, 1998; Christopoulos and Tsionas, 2004).
Averaging individual Dickey-Fuller unit root tests yields the Im, Pesaran and Shin (2003)
test, while combining p-values from individual ADF tests yields the Maddala and Wu
22Specifically, Toda and Phillips (1993, 1994) and Sims, Stock and Watson (1990) show that in the case of
cointegrated series the conventional Wald statistic converges to a 2 distribution.
23Following this approach, Rousseau and Sylla (2005) use data for the U.S over the period 1850 to 1997,
Bell and Rousseau (2001) use data for India and Xu (2000) uses data for 43 countries over the period 1960
to 1993; all find robust evidence for a leading role of finance.
20
(1999) test, both of which allow testing for a unit root in panels. To establish
cointegration relationships in a panel, Pedroni (1997) suggests estimating the
cointegrating regression by OLS separately for each country before a unit root test similar
to the Phillips-Perron test is applied to the stacked residuals. Further, the VEC
specification (21) can be extended to a panel with country-specific fixed effects to test for
both long- and short-run relationships between finance and GDP per capita.
Christopoulos and Tsionas (2004) find evidence for cointegration and long-run Granger
causality from finance to GDP per capita for a sample of ten developing countries for the
period 1970 to 2000, both for individual countries and for the panel. Unlike other studies
in the time series tradition, they also confirm their findings by applying dynamic panel
regression techniques using lagged values as instruments in the panel version of (21).
Using Geweke's (1982) measure of linear dependence, Calderon and Liu (2003)
compute the relative strength of the Granger causality from finance to GDP per capita,
from GDP per capita to finance and the instantaneous feedback between finance and
GDP per capita. Specifically, using variance-covariance matrices calculated under
different restrictions on the system (20) allows calculating a measure of the overall
strength of the relationship between two variables and the three different sources. They
find a stronger effect from finance to GDP per capita than for the reverse effect for
developing countries, which increases when they average data over longer time periods.
While they consider the linear decomposition in the context of panel regressions, with
data averaged over five-year periods, they do not assess the finance-GDP per capita
relationship at different frequencies.
5. Differences-in-differences estimations
While the cross-country IV approach focuses on identifying instruments to overcome the
different biases found in an OLS regression, and the time-series approach focuses on the
forecast capacity of finance in a VAR including GDP per capita, the differences-in-
differences technique can be understood as a "smoking-gun" or controlled treatment
approach. Specifically, traditional differences-in-differences estimation consists of
comparing the difference between the treatment and the control groups before and after a
21
treatment, such as a policy change, thus controlling for other confounding influences on
growth.24
The seminal paper in this literature is Jayartne and Strahan (1996), who exploit
the fact that states across the U.S deregulated intra-state branch restrictions at different
times over the period 1970 to 1995 and relate this policy change to subsequent state-level
growth. In this case the treatment and control groups are in flux; at any point in time, the
treatment group consists of states that have deregulated, while the control group consists
of those states that have not deregulated yet. By controlling for state- and year-specific
effects, this approach effectively measures the impact of deregulation on state-level
growth relative to the average state-level growth rate over the sample period and relative
to the average growth rate in the U.S in this specific year. The specification is:
g(i,k)= (i)+ (k)+ (External(k)* f (i))+ yShare(i,k)+ '(Industry(k)*Country(i))+(i,k)
(22)
where (i) is a vector of state dummies, (t) a vector of year dummies, C(i,t) a vector of
time-varying state characteristics and d the treatment variable, which is branch
deregulation in the case of Jayaratne and Strahan (1996), who found a positive and
significant coefficient , thus suggesting that branch deregulation led to higher growth.25
They also find evidence for a large economic effect of branch deregulation, explaining an
annual growth difference of at least 0.5 percentage points, compared to an average annual
growth rate across states of 1.6%. Consistent with cross-country results, they also find
evidence that the finance-growth nexus worked through improved lending efficiency
rather than more lending and investment.
The differences-in-differences estimator reduces, but does not eliminate, the
biases of reverse causation and omitted variables. Specifically, any omitted variable has
to be time-variant in order to bias the results, because otherwise it would be picked up by
the state dummies. Further, by considering sub-national variation, differences-in-
24While we treat such exogenous policy changes in the context of differences-in-differences estimations,
one could also use them as instruments for financial development in the context of regular cross-sectional
regressions (Guiso, Sapienza and Zingales, 2004).
25Following the model of Jayartne and Strahan (1996), Dehejia and Lleras-Muney (2007) show that, over
the period 1900 to 1940 across states of the U.S, regulatory changes that allowed branching accelerated the
mechanization of agriculture and spurred growth in manufacturing, while the introduction of deposit
insurance had negative consequences.
22
differences estimation is less subject to biases introduced by unobserved heterogeneity
across countries and measurement error is reduced as the focus is on one specific policy
measure, implemented in the same way but at different times across sub-national units.26
On the other hand, the events in different states, such as branch deregulation, were not
independent from each other, but rather came in waves, which might bias the estimate of
(Huang, 2008). Further, the concern of reverse causation can only be addressed by
utilizing instrumental variables or by showing that the decision to implement the policy
change across states is not correlated with future growth rates, as was done by Jayaratne
and Strahan (1996).
Apart from the problem of endogeneity, serial correlation of the error terms in
differences-in-differences estimations can lead to underestimation of standard errors, as
shown by Bertrand, Duflo and Mullainathan (2004).27 This problem increases with the
number of time periods and the persistence of the dependent variable and is exacerbated
by the fact that the treatment variable, e.g. branch deregulation, shows little change
across states, at most one change from zero to one. Using Monte-Carlo simulation,
Bertrand, Duflo and Mullainathan (2004) show that collapsing data to before and after-
treatment28 or allowing for correlation within states (clustering) are solutions that resolve
the problem of underestimated standard errors.
Going even more local, Huang (2008) uses county-level data from contiguous
counties only separated by a state border in cases where one state deregulated at least
three years earlier than the other. This helps reduce concerns of omitted variables, as one
can assume a very similar structure of two contiguous counties and also helps reduce
26On the other hand, focusing on one country reduces the policy relevance of its findings, as the
relationship might vary across countries with different economic and institutional settings. Further,
subnational variation might not be independent from each other given the higher mobility of capital and
labor within than across countries.
27Bertrand, Duflo and Mullainathan (2004) find overrejection of the null hypothesis using randomly
assigned placebo treatments in Monte Carlo simulation
28Specifically, this would imply regressing growth on state and year fixed effects and other time-varying
control variables, taking the residuals and averaging them for the period before and after the treatment for
each state. The estimate of the treatment can then be obtained from a regression of this two-period state
panel on the treatment dummy.
23
concerns of reverse causation, as expected higher future growth of a specific county is
unlikely to affect state-level political decisions.29,30
A somewhat related differences-in-differences approach is suggested by Rajan
and Zingales (1998), who conjecture that the effect of financial development should vary
by sector or industry according to the financing need of each sector or industry. They
thus assess the finance and growth link by focusing on a specific channel through which
financial development should foster economic development, i.e. the channeling of
society's savings to industries with the highest demand for external finance. Specifically,
they use variation across industries in their dependence on external finance and variation
across countries in their level of financial development to assess the impact of finance on
industry growth, and apply the following specification:31
g(i,k) = (i)+ (k)+ (External(k)* f (i))+ yShare(i,k)+ (Industry(k)*Country(i)) + (i,k) (23)
where g is growth of value added in industry k in country i; and are vectors of country
and industry dummies; Share is the initial share of industry k's value added in total
manufacturing value added of country i; External is the external dependence of industry
k; f is a measure of financial development in country i; Industry is a vector of other
industry characteristics that do not vary across countries; and Country is a vector of other
country characteristics that do not vary across industries. By including industry and
country specific effects, the coefficient measures the differential growth impact of
financial development on high-dependence industries relative to low-dependence
industries. When redefining this exercise in terms of a controlled experiment, we could
see industries (rather than states) as the treated objects, some of which (high external
29This argument, however, is only valid if there is sufficient variation in growth across different counties
within the state.
30Given the lack of randomness of the sample relative to the population, Huang (2008) constructs critical
values from a distribution of the effects of fictitious placebo treatments on county pairs on non-event
borders, taking into account spatial correlation across counties along the same borders. Only if 95% of all
placebo treatments result in a growth difference below a certain value can this value be considered a
significant growth difference for a real world treatment at the 5% significance level.
31Rajan and Zingales (1998) compute the industry-level dependence on external finance from data of listed
firms in the U.S, i.e. firms that should have the least problems in raising external finance and thus face a
perfectly elastic supply curve, to get measures of industry-level demand for external finance. They
conjecture that demand for external finance measured in this way proxies for the industry-inherent demand
for external finance, rather than country- or firm-specific characteristics, in the U.S.
24
dependence) are subjected to the treatment of financial development. In a sample of 41
countries and 36 manufacturing industries, Rajan and Zingales (1998) find robust
evidence for a significant and positive , which is even stronger when focusing on young
firms in the computation of external dependence. To gauge the economic significance,
Rajan and Zingales (1998) assess the growth difference between the industries at the 75th
and 25th percentile of external dependence in the countries at the 75th and 25th percentiles
of their financial development indicator. Their results suggest that the annual growth
difference between Machinery (75th percentile of external dependence) and Beverages
(25th percentile of external dependence) is 1.3 percentage points higher in Italy (75th
percentile financial development) than in Philippines (25th percentile financial
development). This compares to an average industry growth rate of 3.4%, thus a
relatively large effect.
As in the case of Jayaratne and Strahan (1996), regression (23) does not control
for biases due to omitted variables or reverse causation. Rajan and Zingales (1998)
address concerns of the endogeneity of the treatment, i.e. of financial development, by
focusing on the smallest 50% of industries in terms of initial value added in each country,
as it is less likely that the financial sector develops in response to the smallest industries.
They address the omitted variable bias by including other interaction terms between
industry and country characteristics that can explain cross-country, cross-industry growth
variation and utilizing instrumental variables for financial development.32 Critically, the
differences-in-differences estimator depends on the assumption that there are industry-
inherent characteristics that do not vary across countries and that they are properly
measured by the data in the U.S (von Furstenberg and von Kalckreuth, 2006, 2007).
6. Firm- and household-level approaches
While the three approaches discussed so far - cross-country instrumental variable
regressions, VAR models and differences-in-differences estimation - have tried to
32The differences-in-differences approach of Rajan and Zingales has subsequently been used by many
other researchers interested in the linkage between financial development and growth and specific
mechanisms and channels, including Beck and Levine (2002), Beck (2003), Beck, Demirguc-Kunt, Laeven
and Levine (2005), Braun and Larrain (2005), Claessens and Laeven (2003) Fisman and Love (2003) and
Raddatz (2006).
25
address the different biases resulting from the standard OLS cross-country growth
regression, a fourth approach has used disaggregated firm and, more recently, household
level data to assess the impact of access to financial services on firm growth and
household welfare. The advantage of using micro-level data is that it allows more clearly
the disentangling and testing of the mechanisms and channels through which financial
development enhances economic growth. A disadvantage is that it focuses on the direct
effect of finance on firm growth and household welfare but commonly does not consider
spill-over effects on other firms and households and therefore does not allow for
individual effects to be added up to an aggregate growth effect.33
Further, as in the case of cross-country regressions, biases due to omitted
variables, measurement error and reverse causation have to be addressed. This section
discusses several studies using micro-data that assess whether easier access to finance is
associated with faster firm growth and higher household welfare. Unlike the previous
section, this section does not introduce new methodologies, but rather discusses
methodological challenges stemming from the use of micro, as opposed to country-level,
data.
6.1 Firm-level approaches
The different approaches discussed in this section consist of relating firm-level growth or
investment to country-level financial development measures. As in the case of cross-
country regressions, however, this implies controlling for biases stemming from reverse
causation and omitted variables. A first approach, suggested by Demirguc-Kunt and
Maksimovic (1998), compares firm growth to an exogenously given benchmark.
Specifically, they calculate for each firm in an economy the rate at which it can grow,
using (i) only its internal funds or (ii) using its internal funds and short-term borrowing,
based on the standard "percentage of sales" financial planning model (Higgins 1977).
33Indirect effects of financial development can be very important, as shown by Beck, Levine and Levkov
(2007), who find that the main channel through which branch deregulation across U.S states led to lower
income inequality was through labor market effects rather than through providing increased access to
finance.
26
Given a set of simplifying assumptions, the external financing needs EFN at time t of a
firm growing at rate g(t) is given by: 34
EFN(t) = g(t)* Assets(t)-[1- g(t)]* Earnings(t)*b(t) (24)
where b(t) is the fraction of the firm's earnings that are retained for reinvestment at time t.
Assuming that the firm retains all its earnings, i.e. b(t)=1, the internally financed growth
rate IG(t) is the maximum growth rate that can be financed with internal resources only,
that is:
IG(t) = ROA(t)/[1- ROA(t)] (25)
Demirguc-Kunt and Maksimovic (1998) then regress the percentage of firms in a country
that grow at rates exceeding IG(t) on financial development, other country characteristics
and averaged firm characteristics in a simple OLS set-up and show, for a sample of 8,500
firms across 30 countries, that the proportion of firms growing beyond the rate allowed
by internal resources is higher in countries with better developed banking systems and
more liquid stock markets.35
An alternative approach to assess the impact of access to finance on firm growth
is the use of firm-level survey data, as done by Beck, Demirguc-Kunt and Maksimovic
(2005), who use firm-level survey data for over 4,000 firms in 54 countries to run the
following regression:
g(i,k)= + 1o(i,k)+ 2 f (i)+ 3o(i,k)* f (i)+ C(1)(i,k)1 + C(2)(i) 2 +(i,k) (26)
where g is sales growth of firm k in country i over the period 1996 to 1999, C(1) is a set of
firm-level control variables, C(2 is a set of country-level control variables, o is the
)
financing obstacle as reported by the firm and f is a country-level financial development
indicator. The financing obstacle is the response by the firm to the question of whether
34The three simplifying assumptions are as follows: First, the ratio of assets used in production to sales is
constant. Second, the firm's profits per unit of sales are constant. Finally, the economic deprecation rate
equals the accounting depreciation rate.
35 Subsequently, this technique has been applied by Demirguc-Kunt and Maksimovic (2002) and Guiso,
Sapienza and Zingales (2004), among others.
27
financing is an obstacle to its operation and growth, and responses are coded as no
obstacle (1) minor obstacle (2), moderate obstacle (3) and major obstacle (4). While 1
indicates the relationship between the reported financing obstacle and firm growth, 3
indicates whether this relationship varies across countries with different levels of
financial development. Beck, Demirguc-Kunt and Maksimovic (2005) find a negative
and significant coefficient on 1 and a positive and significant coefficient on 3,
suggesting that firms reporting higher financing obstacles experience slower sales growth,
but that this relationship is less strong in countries with better developed financial
systems. Further, using triple interaction terms, they show that the mitigating effect of
financial development on the relationship between financing obstacles and firm growth is
stronger for small firms than for large firms.
Another methodology consists of assessing the relationship between country-level
financial development and firms' financing constraints derived from a structural
investment model, such as the Euler equation (Love, 2003; Laeven, 2003). Specifically,
the Euler equation derives the optimal investment decision as the point where the
marginal cost of today's investment is equal to the discounted marginal cost of
postponing investment until the next period, which includes the marginal product of
capital, the adjustment cost and the price of investment tomorrow. In the absence of
credit market constraints, firms' investment decisions should thus be independent of
firms' cash flow holdings, while the investment decisions of credit constrained firms
should be a positive function of available cash. Financial sector development, on the
other hand, should reduce the dependence of firms' investment on cash holdings. To test
for the presence of credit market constraints and the impact of financial development on
the relationship between credit market constraints and investment, the following
regression is used:
I(k,t)=(k) + (t) + 1Cash(k,t -1)+ 2Cash(k,t -1)* f (i,t)+C(1)(k,t)1 +C(2)(k,t -1) 2 +(i,k,t)
(27)
where I is investment, (k) is a vector of firm dummies, (t) a vector of time dummies,
Cash is liquid assets relative to total assets, C(1) and C(2) are sets of current and lagged
firm-level control variables, such as investment-to-capital ratios and sales-to-capital
28
ratios, and the subscript i refers to countries. The existence of credit constraints implies
1> 0, while the alleviating role of financial sector development implies 2< 0. As
regression (27) poses similar problems in terms of the different biases identified in
section 2 for cross-country growth regressions, most studies use the dynamic panel
techniques suggested by Arrellano and Bond (1991) and Arrellano and Bover (1995) to
control for these biases. Using data for 5,000 firms across 36 countries, Love (2003)
shows that financial development reduces firms' dependence on cash holdings for
investment, while Laeven (2003) shows, for a sample of 400 firms across 13 countries,
that financial liberalization helped reduce small firms' financing dependence on internal
cash, while it adversely affected large firms' financing possibilities. The effect of
financial development and liberalization is also economically significant. Love (2003)
shows that firms' financing constraints as measured by the cost of capital in countries
with low levels of financial development are twice as high as in countries with average
levels of financial development, while Laeven (2003) shows that financial liberalization
had a significant economic effect on firms' financing constraints, reducing small firms'
constraints by 80%.
6.2. Household-level approaches
While the availability of financial information for listed companies and survey data for
non-listed companies has resulted in a rapid expansion of firm-level studies, the lack of
comparable data for households has impeded similar research for the effect of access to
finance on household welfare until recently. As in the case of aggregate and firm-level
studies, the identification problem prevents inference from cross-sectional household
surveys with data on welfare and access to finance variables. A final and very recent
technique therefore uses controlled experiments with households and/or
microentrepreneurs, whose financing constraints are randomly alleviated and who are
then compared to a control group whose constraints were not alleviated. The challenges
of these studies are less in estimation techniques than in the proper identification of
treatment and control groups and of the experimental treatment itself. In the following,
we will discuss three examples.
29
First, Pitt and Khandker (1998) use household survey data to assess the impact of
microcredit on household welfare across several programs in Bangladesh. However, as
in the case of cross-country regressions, omitted variable bias and reverse causation
would bias the result of a simple OLS estimation, as illustrated by the following system:
(i, j)=C(i, j)1 +f (i, j)+(i)+(i, j) (28)
f (i, j)= C(i, j)2 + Z(i, j) + (i)+(i, j) (29)
where y is a measure of household welfare of household i in village j, f is the amount of
credit obtained by a household, C is a vector of household characteristics, and Z is a set
of household or village characteristics that serve as instruments for the endogenous credit
variable. and are unobservable village characteristics, that are correlated with
household welfare and credit, respectively. Correlations between and and between
and can result in a biased OLS estimate of in (28). These correlation can arise
because microcredit program placement is nonrandom, often related with specific village
characteristics, such as poverty levels. Further, unmeasured household and village
characteristics can influence both the demand for microcredit and household outcomes y.
Pitt and Khandker (1998) therefore use the exogenously imposed restriction that only
farmers with less than a half-acre of land are eligible to borrow from microfinance
institutions in Bangladesh as an exclusion condition to compare eligible and non-eligible
farmers in program and non-program villages. Using survey data for 1,800 households
and treating landownership as exogenous to welfare outcomes, they exploit the
discontinuity in access to credit for households above and below the threshold and find a
positive and significant effect of credit on household consumption expenditures.
Morduch (1998), however, shows that mistargeting, i.e. allowing farmers with
landholdings above the threshold to access microcredit, violates the exclusion condition,
and that different econometric techniques exploiting the landholding restriction lead to
different findings.
Coleman (1999) exploits the fact that future microcredit borrowers are identified
before the roll-out of the program in Northern Thailand and can thus exploit the
30
differences between current and future borrowers and non-borrowers in both treated and
to-be-treated villages.36 His model is:
(i, j)=C(1 (i, j) +p(i, j)+C(2 (j) +M(i, j)+(i, j)
) ) (30)
where y is an array of measures of household welfare, C(1) is a set of observable
household and C(2) a set of observable village characteristics, M is dummy that takes the
value one for current and future borrowers and p is a dummy that takes the value one for
villages that already have access to credit programs. M can be thought of as proxy for
unobservable household characteristics that determine whether a household decides to
access credit or not, whereas measures the impact of the credit program by comparing
current and prospective borrowers. Coleman (1999) does not find any robustly
significant estimate of and therefore rejects the hypothesis that microcredit helps
households in this sample and this institutional setting.
A final example is Karlan and Zinman (2006), who used a sample of marginally
rejected applicants of a South African consumer credit institution. They convinced the
credit institution to provide loans to a randomly chosen subset of these borrowers.
Surveying both treatment and control groups six and twelve months after providing credit
to the treatment group, they find that borrowers were more likely to retain wage
employment and less likely to experience hunger in their household and be impoverished.
(i)=C(i) +p(i)+(i) (31)
where y is an indicator of household welfare, C is a vector of household characteristics
and p is the treatment dummy that takes the value one if the individual surveyed has
received a loan.
While controlled experiments can assess the effect of access to credit (or other
financial services) on the growth of micro-enterprises or household welfare, there are
shortcomings to this methodology. First, they are very costly to conduct. Second, they are
environment-specific and it is not clear whether the results will hold in a different
36This technique is also referred to as pipeline matching (Goldberg and Karlan, 2005).
31
environment with a different sample population. Third, the controlled experiments, as
they have been undertaken up to now, do not consider any spill-over effects of access to
credit by the treated individuals or enterprises to other individuals or enterprises in the
economy.
7. Concluding remarks
The finance and growth literature has come a long way from simple correlation and OLS
regressions to dynamic panel regressions and the use of firm- and household- level data.
While each of the different methodologies and aggregation levels has its shortcomings,
the body of evidence accumulated over the past 15 years provides a strong case for a
relationship between financial development and economic growth that is not driven by
omitted variables, measurement error or reverse causation.
While the profession has made great progress in measuring financial development,
especially by moving towards micro-data, this paper has focused on methodological
advances to overcome the biases illustrated by a simple cross-country OLS regression.
Most importantly, overcoming endogeneity and simultaneity biases with a proper
identification strategy has been the main challenge for researchers. While the cross-
country literature has focused on finding external and internal instruments, the time-series
literature has exploited high-frequency data, a rich lag structure, and the forecast capacity
of finance for GDP per capita. Differences-in-differences approaches address the
identification challenge by assessing natural experiments, exploiting either exogenous
policy reforms or inherent industry characteristics that result in a differential impact of
financial development.
Using firm- and household-level data allows a deeper look into the mechanisms
through which finance enhances firm growth and household welfare and thus provides
additional evidence, but poses its own set of identification challenges. While many of the
methodologies used at the cross-country-level, such as instrumental variables or
differences-in-differences, can also be applied at the firm- and household-level,
randomized controlled experiments with households and microentrepreneurs open new
and exciting research opportunities, as they allow researchers to subject households and
microenterprises to a specific treatment under the control of the researcher.
32
Different methodologies imply different aggregation levels. While assessing the
finance and growth relationship on a more disaggregated level might allow better
controlling for different biases such as measurement error when considering a specific
policy change on the sub-national level or simultaneity bias when using household data in
a controlled randomized experiment this has to be balanced with the limited extent to
which we can draw policy conclusions from such a specification. Further, using firm-
level or household level data does not properly control for spill-over effects, are often
very costly exercises, and do not lend themselves easily to compute the aggregate growth
effect of financial development. While randomized experiments have the advantage that
they are the cleanest exercise possible, as they are controlled by researchers, they might
not properly mimic the real world, and might not allow inferences outside the geographic
and institutional experiment area.
While a wide array of cross-country techniques has been applied to the finance
and growth field, some techniques have not been used yet, such as identification through
heterogeneity in structural shocks (Rigobon, 2003). Further, it is easy to predict that there
will be further advances in GMM techniques that control better for country heterogeneity
and in techniques to assess the finance and growth relationship at different frequencies.
As before, the finance and growth literature will benefit in the years to come from
methodological advances in neighboring fields, especially in growth econometrics.
Merging VAR and cross-country techniques two literatures which have moved mostly
parallel to each other up to now also promises further methodological insights.
More important than these advances at the aggregate level, however, will be
advances at the micro-level, and specifically on two fronts. First, randomized
experiments involving both households and micro- and small enterprises will shed light
on the effect of access to finance on household welfare and firm growth. One of the
challenges to overcome will be to include spill-over effects and thus move beyond partial
equilibrium results to aggregate results. Second, further studies evaluating the effect of
specific policy interventions can give insights into which policy reforms are most
effective in enhancing financial development and positive real sector outcomes.37
37One example assessing the effect of different legal reforms is Haselmann, Pistor and Vig (2005).
33
Advances in both areas, however, will depend on the collection of micro-based data on
access to and use of financial services.
34
References
Alonso-Borrego, C. and M. Arellano (1999) Symmetrically normalised instrumental-
variable estimation using panel data. Journal of Business & Economic Statistics 17(1),
36-49.
Arellano, M. and S. Bond (1991) Some tests of specification for panel data: Monte Carlo
evidence and an application to employment equations. Review of Economic Studies 58(2),
277-97.
Arellano, M. and O. Bover (1995) Another look at the instrumental-variable estimation of
error-components models. Journal of Econometrics 68(1), 29-52.
Atje, R. and B. Jovanovic (1993) Stock markets and development. European Economic
Review 37(2-3), 632-40.
Basmann, R.L. (1960) On finite sample distributions of generalized classical linear
identifiability test statistics. Journal of the American Statistical Association 55(292),
650-59.
Baum, C, M. Schaffer, and S. Stillman (2003) Instrumental variables and GMM:
Estimation and testing. Stata Journal 3(1), 1-31.
Beck, T. (2003) Financial dependence and international trade. Review of International
Economics 11, 296-311.
Beck, T., R. Levine and A. Levkov (2007) Big bad banks? The impact of U.S. branch
deregulation on income distribution. World Bank Policy Research Working Paper 3340.
Beck, T., A. Demirgüç-Kunt, L. Laeven and R. Levine (2004) Finance, firm size, and
growth. World Bank Policy Research Working Paper 3485.
Beck, T., A. Demirgüç-Kunt, R. Levine (2000) A new database on financial development
and structure. World Bank Economic Review 14, 597-605
Beck, T., A. Demirgüç-Kunt and V. Maksimovic (2005) Financial and legal constraints
to firm growth: Does firm size matter? Journal of Finance 60, 137-77.
Beck, T., E. Feijen, A. Ize and F. Moizeszowicz (2008) Measuring financial development.
World Bank mimeo.
Beck, T. and R. Levine (2005) Legal institutions and financial development. In C.
Menard and M. Shirley (eds.), Handbook of New Institutional Economics. The
Netherlands: Kluwer Dordrecht.
35
Beck, T. and R. Levine (2004) Stock markets, banks and growth: Panel evidence. Journal
of Banking and Finance 28, 423-42.
Beck, T. and R. Levine (2002) Industry growth and capital allocation: Does having a
market- or bank-based system matter? Journal of Financial Economics 57, 107-31.
Beck, T., R. Levine and N. Loayza (2000) Finance and the sources of growth. Journal of
Financial Economics 58, 261-300.
Bell, C. and P.L. Rousseau (2001) Post-independence India: A case of finance-led
industrialization? Journal of Development Economics 65, 153-75.
Bekaert, G, C. Harvey and C. Lundblad (2005) Does financial liberalization spur
economic growth? Journal of Financial Economics 77, 3-55.
Benhabib, J and M. Spiegel (2000) The role of financial development in growth and
investment. Journal of Economic Growth 5, 341-60.
Bertrand, M., E. Duflo and S. Mullainathan (2004) How much should we trust differences-
in-differences estimates. Quarterly Journal of Economics 119, 249-275.
Blundell, R. and S. Bond (1998) Initial conditions and moment restrictions in dynamic
panel data models. Journal of Econometrics 87, 115-43.
Bond, S. and E. Windmeijer (2002) Finite sample inference for GMM estimators in linear
panel data models. Cemmap Working Paper 04/02, Centre for Microdata Methods and
Practice, Institute for Fiscal Studies, London.
Bowsher, C. (2002) On testing overidentifying restrictions in dynamic panel data models.
Economics Letters 77, 211-20.
Braun, M. and B. Larrain (2005) Finance and the business cycle: International, inter-
industry evidence. Journal of Finance 60, 1097-1128.
Calderon, C and L. Liu (2003) The direction of causality between financial development
and economic growth. Journal of Development Economics 72, 321-34.
Christopoulos, D. and E. Tsionas (2004) Financial development and economic growth:
Evidence from panel unit root and cointegration tests. Journal of Development Economics
73, 55-74.
Claessens, S. and L. Laeven (2003) Financial development, property rights and growth.
Journal of Finance 58, 2401-36.
Coleman, B. (1999) The impact of group lending in northeast Thailand. Journal of
Development Economics 60,105-42.
36
De Gregorio, J. and P. Guidotti (1995) Financial development and economic growth.
World Development 23, 433-48.
Dehejia, R. and A. Lleras-Muney (2007) Financial development and pathways of growth:
State branching and deposit insurance laws in the United States, 1900-1940. Journal of
Law and Economics 50, 239-72.
Demetriades, P.O. and K.A. Hussein (1996) Does financial development cause economic
growth? Time-series evidence from 16 countries. Journal of Development Economics 51,
387-441.
Demirgüç-Kunt, A. and E. Detragiache (1999) Financial liberalization and financial
fragility. In B. Pleskovic and J. Stiglitz (eds.), Proceedings of the World Bank Annual
Conference on Development Economics. Washington, DC:World Bank.
Demirgüç-Kunt, A. and V. Maksimovic (2002) Funding growth in bank-based and
market-based financial systems: Evidence from firm-level data. Journal of Financial
Economics 65, 337-63.
Demirgüç-Kunt, A. and V. Maksimovic (1998) Law, finance and firm growth. Journal of
Finance 53, 2107-37.
Durlauf, S.N., P.A. Johnson and J.R.W. Temple (2005) Growth econometrics. In P.
Aghion and S. Durlauf (eds.), Handbook of Economic Growth. Elsevier.
Eichenbaum, M.S., L.P. Hansen and K.J. Singleton (1988) A time-series analysis of
representative agent models of consumption and leisure. Quarterly Journal of Economics
103, 51-78.
Engle, R.W. and C.W.J. Granger (1987) Cointegation and error correction: representation,
estimation, and testing. Econometrica 55, 251-76.
Engle, R.W. and S.B. Yoo (1987) Forecasting and testing in cointegrated systems.
Journal of Econometrics 35, 143-59.
Fisman, R.J. and I. Love (2003) Trade credit, financial intermediary development, and
industry growth. Journal of Finance 58, 353-74.
Geweke, J. (1982) Measurement of linear dependence and feedback between multiple
time series. Journal of the American Statistical Association 77, 304-24.
Godfrey, L.G. (1999) Instrument relevance in multivariate linear models. Review of
Economics and Statistics 81, 550-52.
Goldberg, N. and D. Karlan (2005) The impact of microfinance: A review of
methodological issues. Mimeo, Yale University.
37
Goldsmith, R. W. (1969) Financial Structure and Development. New Haven, CT: Yale
University Press.
Guiso, L., P. Sapienza and L. Zingales (2004) Does local financial development matter?
Quarterly Journal of Economics 119(3), 929-69.
Granger, C. (1969) Investigating causal relations by econometric models and cross-
spectral methods. Econometrica 37, 424-38.
Granger, C. and J. Lin (1995) Causality in the long run. Econometric Theory 11, 530-36.
Griliches, Z. and J. Hausman (1986) Errors in variables in panel data. Journal of
Econometrics 31, 93-118.
Hansen, L. P. (1982) Large sample properties of generalized method of moments
estimators. Econometrica 50, 1029-54.
Harrison, P., O. Sussman and J. Zeira (1999) Finance and growth: New evidence.
Finance and Economics Discussion Series, Board of Governors of the Federal Reserve
System.
Haselmann, R., K. Pistor and V. Vig (2005) How law affects lending. Columbia Law and
Economics Working Paper No. 285..
Hayashi, F. (2000) Econometrics, 1st ed. Princeton, NJ: Princeton University Press.
Higgins, R.C. (1977) How much growth can a firm afford? Financial Management 6,
3-16.
Horvath, M. and M. Watson (1995) Testing for cointegration when some of the
cointegrating vectors are prespecified. Econometric Theory 11, 894 1014.
Huang, R. (2008) Did branching deregulation accelerate growth? Forthcoming in
Journal of Financial Economics.
Im, S.K., H.M. Pesaran and Y. Shin (2003) Testing for unit roots in heterogeneous panels.
Journal of Econometrics 11, 53-74.
Jayaratne, J. and P.E. Strahan (1996) The finance-growth nexus: Evidence from bank
branch deregulation. Quarterly Journal of Economics 111, 639-70.
Johansen, S. (1988) Statistical analysis of cointegration vectors. Journal of Economic
Dynamics and Control 12, 231-54.
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in
Gaussian vector autoregressive models. Econometrica 59, 1551-80.
38
Johansen, S. and K. Juselius (1990) Maximum likelihood estimation and inference on
cointegration with applications to the demand for money. Oxford Bulletin of Economics
and Statistics 52, 169-210.
Jung, W. (1986) Financial development and economic growth: International evidence.
Economic Development and Cultural Change 34, 333-46.
Karlan, D. and J. Zinman (2006) Expanding credit access: Using randomized supply
decisions to estimate the impacts. Mimeo, Yale University.
King, R. G. and R. Levine (1993) Finance and growth: Schumpeter might be right.
Quarterly Journal of Economics 108, 717-38.
Kraay, A. and D. Kaufmann (2002) Growth without governance. Economia 3(1, Fall),
169-78.
La Porta, R., F. Lopez-de-Silanes, A. Shleifer and R.W. Vishny (1997) Legal
determinants of external finance. Journal of Finance 52, 1131-50.
La Porta, R., F. Lopez-de-Silanes, A. Shleifer and R.W. Vishny (1998) Law and finance.
Journal of Political Economy 106, 1113-55.
Laeven, L. (2003) Does financial liberalization reduce financing constraints? Financial
Management 32, 5-34.
Levine, R. (2005) Finance and growth: Theory and evidence. In P. Aghion and S. Durlauf
(eds.), Handbook of Economic Growth. The Netherlands: Elsevier Science.
Levine, R. (1997) Financial development and economic growth: Views and agenda.
Journal of Economic Literature 35, 688-726.
Levine, R. (1998) The legal environment, banks, and long-run economic growth. Journal
of Money, Credit, and Banking 30, 596-620.
Levine, R. (1999) Law, finance, and economic growth. Journal of Financial
Intermediation 8, 8-35.
Levine, R., N. Loayza and T. Beck (2000) Financial intermediation and economic
growth: Causes and causality. Journal of Monetary Economics 46, 31-77.
Levine, R. and D. Renelt (1992) Sensitivity analysis of cross-country growth regressions.
American Economic Review 82, 942-63.
Levine, R. and S. Zervos (1998) Stock markets, banks, and economic growth. American
Economic Review 88, 537-58.
39
Loayza, N., and R. Ranciere (2006) Financial development, financial fragility, and
growth. Journal of Money, Credit, and Banking 38, 1051-76.
Love, I. (2003) Financial development and financing constraints: International evidence
from the structural investment model. Review of Financial Studies 16, 765-91.
Luintel, K.B. and M. Khan (1999) A quantitative reassessment of the finance-growth
nexus: Evidence from a multivariate VAR. Journal of Development Economics 60,
381-405.
Maddala, G.S. and S. Wu (1999) A comparative study of unit root tests with panel data
and a new simple test. Oxford Bulletin of Economics and Statistics 61, 631-52.
McCraig, B and T. Stengos (2005) Financial intermediation and growth: Some robustness
tests. Economics Letters 88, 306-12.
Morduch, J. (1998) Does microfinance really help the poor? New evidence from flagship
programs in Bangladesh. Mimeo, Princeton University.
Murray, M. (2006) Avoiding invalid instruments and coping with weak instruments.
Journal of Economic Perspectives 20, 111-32.
Neusser, K. and M. Kugler (1998) Manufacturing growth and financial development:
Evidence from OECD countries. Review of Economics and Statistics 80, 638-46.
Pagan, A.R. and D. Hall (1983) Diagnostic tests as residual analysis. Econometric
Reviews 2, 159-218.
Pande, R. and C. Udry (2006) Institutions and development: A view from below. Mimeo,
Yale University.
Pedroni, P. (1997) Panel cointegration: Asymptotic and finite sample properties of the
pooled time series tests with an application to the PPP hypothesis: New results. Indiana
University.
Pesaran, H., R. Smith and K. Im (1995) Dynamic Linear Models for Heterogeneous
Panels. In L. Matyas and P. Sevestre (eds.), The Econometrics of Panel Data. Dordrecht:
Kluwer Academic Publishers, pp. 145-95.
Pesaran, H., Y. Shin and R. Smith (1999) Pooled mean group estimation of dynamic
heterogeneous panels. Journal of the American Statistical Association 94, 621-34.
Pitt, M.M. and S.R. Khandker (1998) The impact of group-based credit programs on poor
households in Bangladesh: Does the gender of participants matter? Journal of Political
Economy 106, 958-96.
40
Raddatz, C. (2006) Liquidity needs and vulnerability to financial underdevelopment.
Journal of Financial Economics 80(3), 677-722.
Rajan, R., and L. Zingales (1998) Financial dependence and growth. American Economic
Review 88, 559-87.
Rigobon, R. (2003) Identification through heteroskedasticity. Review of Economics and
Statistics 85(4), 777-92.
Rioja, F. and N. Valev (2004a) Does one size fit all? A reexamination of the finance and
growth relationship. Journal of Development Economics 74(2), 429-47.
Rioja, F. and N. Valev (2004b) Finance and the sources of growth at various stages of
economic development. Economic Inquiry 42(1), 127-40.
Roodman, D. (2007) A short note on the theme of too many instruments. CDGEV
Working Paper 125, Center for Global Development, Washington, D.C.
Rousseau, P.L. and R. Sylla (2005) Emerging financial markets and early U.S. growth.
Explorations in Economic History 42, 1-16.
Rousseau, P. L. and P. Wachtel (2000) Equity markets and growth: Cross-country
evidence on timing and outcomes, 1980-95. Journal of Banking and Finance 24, 1933-57.
Rousseau, P. L. and P. Wachtel (1998) Financial intermediation and economic
performance: Historical evidence from five industrial countries. Journal of Money, Credit,
and Banking 30, 657-78.
Sargan, J.D. (1958) The estimation of economic relationships with instrumental variables.
Econometrica 26, 393-415.
Shea, J. (1997) Instrument relevance in multivariate linear models: A simple measure.
Review of Economics and Statistics 79, 348-52.
Sims, C.A., J. Stock and M.W. Watson (1990) Inference in linear time series models with
some unit roots. Econometrica 58, 113-44.
Staiger, D. and J.H. Stock (1997) Instrumental variables regressions with weak
instruments. Econometrica 65, 557-86.
Stock, J.H. and M. Yogo (2005) Testing for weak instruments in IV regressions. In
D.W.K. Andrews and J.H. Stock (eds.), Identification and Inference for Econometric
Models: Essays in Honor of Thomas Rothenberg. New York: Cambridge University Press,
pp. 80-108.
41
Toda, H and P. Phillips (1993) Vector autorregression and causality. Econometrica 61,
1367-93.
Toda, H and P. Phillips (1994) Vector autorgression and causality: A theoretical
overview and simulation study. Econometric Review 13, 259-85.
Von Furstenberg, G.M. and U. Von Kalckreuth (2006) Dependence on external finance:
An inherent industry characteristic? Open Economies Review 17, 541-59.
Von Furstenberg, G.M. and U. Von Kalckreuth (2007) Dependence on external finance:
Examining the measure and its properties. Économie Internationale 111, 55-80.
World Bank (2007) Finance for All? Policies and Pitfalls in Expanding Access.
Washington, D.C.
Xu, Z. (2000) Financial development, investment and economic growth. Economic
Inquiry 38, 331-44.
42