ï»¿ WPS6358
Policy Research Working Paper 6358
Background Paper to the 2014 World Development Report
Equilibrium Credit
The Reference Point for Macroprudential Supervisors
Daniel Buncic
Martin Melecky
The World Bank
Development Economics
Office of the Senior Vice President and Chief Economist
&
Europe and Central Asia Region
Financial and Private Sector Department
February 2013
Policy Research Working Paper 6358
Abstract
Equilibrium credit is an important concept because approach ignores heterogeneity in the parameters that
it helps identify excessive credit provision. This paper determine equilibrium credit across countries due to
proposes a two-stage approach to determine equilibrium different stages of economic development. The main
credit. It uses two stages to study changes in the demand drivers of this heterogeneity are financial depth, access to
for credit due to varying levels of economic, financial and financial services, use of capital markets, efficiency and
institutional development of a country. Using a panel funding of domestic banks, central bank independence,
of high and middle-income countries over the period the degree of supervisory integration, and experience
1980â€“2010, this paper provides empirical evidence that of a financial crisis. Countries in Europe and Central
the credit-to-GDP ratio is inappropriate to measure Asia show a slower adjustment of credit to its long-run
equilibrium credit. The reason for this is that such an equilibrium compared with other regions of the world.
This paperâ€”prepared as a background paper to the World Bankâ€™s World Development Report 2014: Managing Risk for
Developmentâ€”is a product of the Development Economics Vice Presidency; and Financial and Private Sector Department,
Europe and Central Asia Region. The views expressed in this paper are those of the authors and do not reflect the views of
the World Bank or its affiliated organizations. Policy Research Working Papers are also posted on the Web at http://econ.
worldbank.org. The author may be contacted at mmelecky@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
E QUILIBRIUM C REDIT: T HE R EFERENCE P OINT
FOR M ACROPRUDENTIAL S UPERVISORS
D ANIEL B UNCIC M ARTIN M ELECKY#
Keywords: Equilibrium Credit, Macroprudential Supervision, Demand for Credit,
Time-Series Panel Data, High- and Middle Income Countries.
JEL Classiï¬?cation: G28, G21, E58.
Sectoral Board: Financial Sector (FSE).
We thank Miguel Dijkman, Joaquin Gutierrez and MarÂ´ Ä±a Soledad MartÂ´ Ä±a for comments on an
Ä±nez PerÂ´
earlier draft of this paper. The views and opinions expressed in the paper are those of the authors and do
not reï¬‚ect those of the World Bank or its Executive Directors.
Corresponding Author: Institute of Mathematics & Statistics, University of St. Gallen, Bodanstrasse 6,
9000 St. Gallen, Switzerland. Tel: +41 (71) 224 2604. Email: daniel.buncic@unisg.ch. Web: http://www.
danielbuncic.com.
# Development Economics and Chief Economist Group , World Bank Group, Mail stop G-5-141. Tel.: +1 202
473 1924. Email: mmelecky@worldbank.org. Web: http://mmelecky.ic.cz.
1
Table of Contents
1 Introduction 3
2 Economic motivation and outline of the proposed framework 6
3 Econometric methodology and data 9
3.1 Notion of equilibrium and econometric approach . . . . . . . . . . . . . . . . 10
3.1.1 Equilibrium as the long-run level . . . . . . . . . . . . . . . . . . . . . 10
3.1.2 First-stage ARDL panel regression . . . . . . . . . . . . . . . . . . . . 12
3.1.3 Second-stage cross-country regression . . . . . . . . . . . . . . . . . . 14
3.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4 Empirical results 18
4.1 Visual overview of the cross-country long-run coefï¬?cients . . . . . . . . . . . 18
4.2 Mean Group (MG) and Pooled Mean Group (PMG) estimation results . . . . 20
4.2.1 Mean Group estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2.2 Pooled Mean Group Estimates . . . . . . . . . . . . . . . . . . . . . . 21
4.2.3 Summary of MG and PMG results . . . . . . . . . . . . . . . . . . . . 23
4.3 Linking the cross country variation to country-speciï¬?c characteristics . . . . 24
4.3.1 Selecting the subset regressors . . . . . . . . . . . . . . . . . . . . . . 25
4.3.2 Shrinking the subset regressors . . . . . . . . . . . . . . . . . . . . . . 26
4.3.3 Results of the cross-country regression models . . . . . . . . . . . . . 27
4.4 Discussion of the cross-country regression results . . . . . . . . . . . . . . . . 29
4.4.1 GDP regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.4.2 GDP Deï¬‚ator regression . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.4.3 Speed of adjustment regression . . . . . . . . . . . . . . . . . . . . . . 31
4.4.4 Correlation between Î² gdp and Î²de f estimates . . . . . . . . . . . . . . 32
5 Conclusion 32
References 34
Figures and Tables 38
Appendix: Additional Estimation Results 47
2
1. Introduction
Excessive credit provision by the ï¬?nancial system was one of the main sources of the
2007 âˆ’ 2008 global ï¬?nancial crisis.1 When credit provision becomes excessive is judged
against an unobserved benchmark known as equilibrium credit. One of the most chal-
lenging aspects of determining excessive credit provision is the estimation of equilibrium
credit.
The Basel III regulatory framework proposed by the Basel Committee on Banking Su-
pervision instructs macroprudential supervisors to estimate equilibrium credit by using
the Hodrick-Prescott (HP) ï¬?lter applied to the ratio of nominal credit to nominal GDP
(henceforth, credit-to-GDP ratio).2 Any â€?signiï¬?cantâ€? deviation of the credit-to-GDP ra-
tio from its HP ï¬?ltered trend then triggers accumulation of the counter-cyclical capital
buffer.3 Although such an approach could be seen as simple and transparent, its purely
statistical nature disregards fundamental changes in equilibrium credit due to economic
and ï¬?nancial development. Greater ï¬?nancial deepening and more credit provision can
improve access to ï¬?nance and economic growth (see, among others, Dellâ€™Ariccia et al.,
2012, page 5). Excessively restrictive credit, on the other hand, especially in developing
economies with increasing credit needs, is likely to result in underinvestment and slow
economic growth. Therefore, a structural approach based on economic fundamentals,
which accounts for the level of ï¬?nancial development of the economy, seems to be a more
appropriate approach to estimate equilibrium credit.
The existing literature has studied equilibrium credit provision by estimating long-
run credit demand functions that also allow for short-run dynamics. Typically, the focus
has been on modelling credit demand with two different dependent variables. For exam-
ple, Cottarelli et al. (2005), Boissay et al. (2005), Kiss and Vadas (2007) and Coudert and
Pouvelle (2010) use the credit-to-GDP ratio, while the ratio of nominal credit to the GDP
Deï¬‚ator (henceforth, real credit) is used in, Calza et al. (2001), Hofmann (2004), Calza et al.
(2003), Brzoza-Brzezina (2005), Durkin et al. (2009), Coudert and Pouvelle (2010) and Eller
et al. (2010).
Deï¬?ning the dependent variable in a credit demand model to be either the credit-to-
GDP ratio or real credit imposes strong a priori restrictions on the statistical model that
is used, which may not be supported by the empirical data and observed economic be-
havior. Namely, such restrictions implicitly assume a unit elastic relationship between
credit demand and GDP and the GDP deï¬‚ator. That is, a one-percent increase in GDP
1 See, for example, Loayza and Ranciere (2006).
2 See page 13 of BCBS (2010).
3 See Step 3 on pages 13 âˆ’ 14 in BCBS (2010) on how exactly deviations from equilibrium are tied to in-
creases in the capital buffer, risk weighted assets and what the term â€?signiï¬?cantâ€? means in relation to per-
centage points away from the HP ï¬?ltered trend. How macroeconomic factors can be incorporated in the risk
weighting of assets over different phases of the business cycle is described in Buncic and Melecky (2013).
3
(or the GDP Deï¬‚ator) â€” the number of transactions in the economy (the average price
of transactions) â€” results in a one-percent increase in the demand for credit. Although
this assumption might be reasonable for some economies, for many others, particulary
developing countries, it will be violated because of the varying levels of credit usage in
economic transactions.4
Â´
The studies by Cottarelli et al. (2005) and Egert et al. (2006) also consider the effects
of changes in development and structural indicators on equilibrium credit demand. They
do so by inserting low frequency development and structural indicators into the credit de-
mand equation (the conditional mean equation of credit), together with higher frequency
variables that determine credit demand over the business cycle. This approach, how-
ever, does not allow for the possibility that the sensitivity of credit to GDP in more credit
intensive economies is likely to be higher than in less credit intensive ones. Moreover,
especially in time-series panels that include a limited number of countries as in Cottarelli
et al. (2005), the development and structural indicators, which change only at a very low
frequency, fail to identify any material effects of the indicators on equilibrium credit. Fur-
ther, mixing higher frequency variables such as GDP, prices and interest rates measured
on a quarterly basis with low frequency indicators like ï¬?nancial liberalization or public
governance, which change typically over a period longer than a business cycle, is likely
to result in statistical collinearity between the long-term and short-term indicators when
both are measured at quarterly frequency. This collinearity will make it difï¬?cult to identify
the true effects of the long-term indicators on equilibrium credit and derive any reliable
policy recommendation.
The objective of this study is to propose a structural framework to estimate equilib-
rium credit, which is anchored in the long-run transaction demand for credit by the real
economy, and accounts for the effects of economic and ï¬?nancial development on equilib-
rium credit. The proposed framework consists of two stages. First, we estimate country
speciï¬?c credit demand functions and conduct cross-country poolability tests on the in-
come and price elasticities of credit. This step is implemented using the Mean Group
(MG) and Pooled Mean Group (PMG) estimation methods of Pesaran and Smith (1995)
and Pesaran et al. (1999) and quarterly panel data for high- and middle-income countries
over the period 1980 âˆ’ 2010.
Second, we model the cross-country variation in the income and price elasticities of
credit, as well as the speed of adjustment of credit to its long-run equilibrium, by re-
gressing the country speciï¬?c coefï¬?cients on a set of relevant development indicators. To
4 As an example, consider the countries of the US and Croatia. Taking the credit-to-GDP ratio as the
dependent variable to model credit demand would imply that the use of credit in economic transactions in
these economies is the same. This seems hard to rationalise. One would clearly expect that US consumers
and businesses use credit much more frequently in their transactions than consumers and businesses in
Croatia.
4
ï¬?nd the set of relevant development indicators, we employ a variable-selection procedure
which reduces the number of possible indicators from 42 to about 10. The set of possi-
ble development indicators is combined from the FinStats database of Al-Hussainy et al.
(2010), the Financial Structure database of Beck et al. (2000) and various supervisory struc-
ture and public governance indicators constructed in Kaufmann et al. (2010) and Melecky
and Podpiera (2012). By explicitly modelling the variation of the parameters that deter-
mine equilibrium credit with our selected set of indicators, we account for the country-
speciï¬?c level of economic, ï¬?nancial and institutional development and are thus able to
more precisely detect excessive credit provision.
We provide empirical evidence to suggest that the credit-to-GDP ratio, which restricts
the response of credit to GDP and the GDP deï¬‚ator to unity, is an inappropriate indicator
to determine equilibrium credit. Empirical evidence of this is twofold. We ï¬?rst estimate
the aggregate cross-country averages of the income and price elasticities of credit within
the MG framework and test the unit elasticity hypothesis. This hypothesis is strongly re-
jected for the income elasticity of credit, and rejected at the 5% level for the price elasticity
of credit. The MG estimate of the price elasticity of credit shows substantial variation and
is, in fact, not signiï¬?cantly different from zero. We then inspect the cross-country distri-
bution of the income elasticity of credit and ï¬?nd strong evidence of bi-modality. We use
the PMG estimation framework to test for cross-country homogeneity of the income and
price elasticities and ï¬?nd that this hypothesis is also strongly rejected by the data.
We show further that the cross-country variation in the elasticities is signiï¬?cantly re-
lated to the level of development of the countries in our sample. The main development
indicators that explain the variation in equilibrium credit elasticities are: ï¬?nancial depth,
access to ï¬?nancial services, use of capital markets, efï¬?ciency and funding of domestic
banks, central bank independence, the degree of supervisory integration, and the experi-
ence of a ï¬?nancial crisis. In addition, countries located in Europe and Central Asia show a
slower adjustment speed of actual credit to its long-run equilibrium than other countries
in our sample.
Based on our ï¬?ndings, we recommend that a structural approach be used to determine
equilibrium credit provision to the real economy to avoid any potential negative effects on
economic growth in developing countries, due to the implementation of overly restrictive
macroprudential policy. The overall objective of our structural estimation of equilibrium
credit is to strike a better balance between managing macro-ï¬?nancial risks and facilitating
ï¬?nancial development in support of sustained and stable economic growth.
The remainder of the paper is organized as follows. Section 2 discusses the economic
motivation behind the proposed empirical approach. Section 3 describes the econometric
methodology employed in the paper and the data used in the construction of the different
variables of interest. Section 4 presents the empirical results and provides a discussion
5
of the economic signiï¬?cance of the cross-country regression results. Section 5 concludes
with a summary of results, policy implications and some directions for future research.
2. Economic motivation and outline of the proposed framework
In economies with developed ï¬?nancial markets credit can ï¬?nance real as well as ï¬?nan-
cial transactions in the same way that cash currency does in less developed economies.
The study by Humphrey et al. (2004) provides empirical evidence that the use of credit
in ï¬?nancing transactions has increased considerably since the mid 1990s. In the context
of traditional money demand models such as, for example, the cash-in-advance model of
Lucas and Stokey (1987), this ï¬?nding implies that the share of credit goods in the econ-
omy increases with ï¬?nancial development. There also exist some earlier theories such as
Mitchell-Innesâ€™s (1914) credit theory of money which postulates that all transactions in an
economy can in fact be viewed as credit-based transactions, stressing the important role
of credit in a ï¬?nancially developed economy.
A convenient way to think about the concept of equilibrium credit is to form a parallel
to the notion of equilibrium money demand. For this purpose, consider the well known
Quantity Theory of Money (QTM) relation of Friedman (1956):
MÃ—V = TÃ—P (1)
where M is the quantity of money, V is the velocity of money, T is the volume of real
transactions in the economy that requires monetary payments, and P is the average unit
price of a transaction. Given the increasing importance of credit based transactions in an
economy, the relation in (1) can equivalently be re-stated with credit (CR) replacing money
( M), giving
CR Ã— V = T Ã— P (2)
where CR stands for total bank credit to the private sector, or simply credit henceforth.
In empirical studies, it is common to approximate the volume of transactions T in
the economy by real GDP. The average unit price of a transaction denoted by P in (2)
above can be approximated by the GDP Deï¬‚ator.5 For estimation purposes, it is further
standard to log-linearize the relation in (2) and explicitly allow the real income and price
level elasticities to differ from unity by re-writing the relation in (2) in a general form as:
crt âˆ’ ( Î² gdp gdpt + Î²de f de f t ) = vt . (3)
5 Itis also possible to use other available price measures such as the CPI or PPI. Nonetheless, since the
GDP Deï¬‚ator is consistent with the calculation of real GDP, we prefer to write the representation in terms of
the GDP Deï¬‚ator. From this point onwards, we will also use the GDP Deï¬‚ator in the notation of the paper.
6
The terms crt , gdpt , de f t and vt in (3) are (natural) logarithms of credit, real GDP, the GDP
Deï¬‚ator and credit velocity.6 The parameters Î² gdp and Î²de f capture, respectively, the sen-
sitivity (or elasticity) of credit to GDP and credit to the price level. These elasticities are
implicitly restricted to unity when the credit-to-GDP ratio is used to determine equilib-
rium credit in an economy. The credit velocity term vt in (3) can be driven by a number of
different determinants. The most commonly used ones are â€?ownâ€? and â€?alternativeâ€? returns
to investment (see Tobin, 1969).7
The considered determinants of velocity in this study are: (i ) own returns on the cost
of credit (the lending rate), (ii ) alternative returns on deposits (the deposit rate), and (iii )
alternative returns from purchasing goods or services (the inï¬‚ation rate), all denominated
in local currency. In empirical money demand studies, Arango and Nadiri (1981) and Bris-
simis and Leventakis (1985), among others, ï¬?nd that the alternative cost of borrowing in
foreign currency is an important determinant of money demand in open economies. Since
the majority of countries in our sample are open economies, we also include the cost of
borrowing in foreign currency, that is, the foreign interest rate adjusted for changes in the
nominal exchange rate, as an alternative return measure to proxy international borrowing
costs.
One practical issue that we encountered when using both domestic lending as well as
deposit rates in the speciï¬?cation of credit velocity in (3) was that for a large number of
countries these rates are highly co-linear. Because of this, we specify the empirical credit
velocity equation in terms of spreads, using the local currency lending rate as the basis. In
our study, the process driving credit velocity thus takes the form:
vt = Î²rr rrt + Î²sprd sprdt + Î² acb acbt (4)
with the main determinants of credit velocity in (4) being the real domestic interest rate
(rrt ), the lending-deposit rate spread (sprdt ), and the alternative cost of borrowing in
foreign currency ( acbt ).8 A priori, we expect that increases in rrt , sprdt and acbt in the
relation in (4) should lead to, respectively, a decline in the demand for credit, an increase
in savings deposits, and a decline in the demand for credit in foreign currency.
Since the global ï¬?nancial crisis, the credit-to-GDP ratio has become the focal point for
macroprudential supervisors when disequilibrium provisions of credit to the real econ-
6 Note that it should be âˆ’vt on the right-hand side of (3). However, since the sign can be absorbed in the
coefï¬?cients of the terms in the velocity equation, this has no signiï¬?cance. We therefore do not explicitly
write down the negative sign.
7 We will focus only on the main drivers of credit velocity v , as there potentially exist several explanatory
t
variables that could be used. The main reason for this is practicality and data availability. Our objective is
thus to condition on a relatively parsimonious set of velocity determinants that will be available for a large
number of countries and over a long enough period in our panel data set.
8 Details regarding the exact construction of these variables are provided in the Data Section.
7
omy are discussed (see, for example, Basel III, 2011 and the technical documentation in
BCBS, 2010). To see how the credit-to-GDP ratio is related to our credit demand speciï¬?ca-
tion, we can combine (3) and (4) to relate the disequilibrium provision of credit to the real
economy to credit velocity as:
crt âˆ’ ( Î² gdp gdpt + Î²de f de f t ) = Î²rr rrt + Î²sprd sprdt + Î² acb acbt . (5)
credit-to-GDP ratio if Î² gdp , Î²de f =1 credit velocity equation
The left-hand side of (5) can be viewed as an â€?unrestrictedâ€? version of the credit-to-GDP
ratio, explicitly allowing the elasticities of credit to GDP and the price level, as measured
by the GDP Deï¬‚ator, to differ from unity. The right-hand side of (5) is a time-varying
measure of disequilibrium credit provision to the real economy which captures the excess
or the lack of credit supplied to the real economy that is not utilised to satisfy transaction
demand. Equation (5) thus postulates that credit in excess of the transaction demand for
credit, as shown on the left-hand side of (5), is provided to satisfy the speculative (or
portfolio) demand for credit. It is this quantity that affects asset prices by stimulating the
formation of asset price bubbles and hence persistent deviations of credit velocity from its
long-run steady-state value. Prudential supervisors should therefore focus on managing
large departures of credit from its transaction demand component, that is, the left hand
side of (5).
The relation in (5) describes a theoretical long-run equilibrium relationship. In order
to compute the right-hand side of equation (5), which captures the time-varying disequi-
librium credit provision to the real economy, one only needs estimates of Î² gdp and Î²de f of
the left-hand side relation of (5). Nevertheless, as for any statistical estimation problem,
one needs to condition on all relevant explanatory variables that inï¬‚uence the dependent
variable to obtain consistent estimates of Î² gdp and Î²de f . In our context, this means that
we need to condition on the velocity determinants that appear on the right-hand side of
equation (5) as well as on the GDP and price level measures, ie., the gdpt and de f t vari-
ables that appear on the left-hand side. Moreover, it is important to leave Î² gdp and Î²de f on
the left-hand side of (5) unrestricted, since estimates of all other parameters in the velocity
equation will be biased if the imposed restrictions are not supported by the data.
Leaving the Î² gdp and Î²de f parameters in (5) unrestricted is an important generalisation
of the credit-to-GDP ratio as it allows us to view any restrictions that are imposed as a
testable implication of the model on the data. In the above context, this means that the
unity restriction, which is imposed on Î² gdp and Î²de f when the credit-to-GDP ratio is used
to estimate equilibrium credit, can be tested statistically for validity. Given that there ex-
ists ample evidence in the empirical literature on money demand that the typical range
of parameter estimates of the income elasticity (of money demand) across countries is be-
tween 0.25 âˆ’ 3.5 (Sriram, 2001, page 360), we also anticipate considerable heterogeneity in
8
the Î² gdp and Î²de f estimates across countries in our sample. This heterogeneity will reï¬‚ect
the different levels of access to credit and intensity of use in transactions in the economy
and therefore is related to the overall level of economic, ï¬?nancial and institutional devel-
opment of the country.
Once estimates of the unrestricted Î² gdp and Î²de f parameters are obtained, we will be
able to address the following three questions of interest to us. First, assuming that the
countries are homogenous with regards to the elasticities of credit to GDP and the price
level, can the average Î² Ë† gdp and Î² Ë† de f coefï¬?cients computed as cross-country sample means
of the long-run coefï¬?cients be validly restricted to unity as the use of the credit-to-GDP
ratio assumes for all countries? Second, if this hypothesis is rejected so that the average
coefï¬?cients cannot be constrained to unity at the aggregate level, can we restrict the coef-
ï¬?cients to be homogenous across countries?9 If this restriction is also rejected by the data,
the third question that we are interested in answering is how the cross-country hetero-
geneity or variation in the Î² Ë† gdp and Î² Ë† de f coefï¬?cients (as well as the speed of adjustment
coefï¬?cient Î±Ë† ) relates to indicators of economic, ï¬?nancial and institutional development.
This last question is addressed by regressing the Î² Ë† de f and Î±
Ë† gdp , Î² Ë† coefï¬?cients on a â€?rele-
vantâ€? set of development indicators. These three questions can be summarized as follows:
(i ) test the unity restriction on the cross-country average of the long-run parameters
(ii ) test the cross-country homogeneity of the long-run parameters
(iii ) determine whether the cross-country heterogeneity can be explained by differences
in economic, ï¬?nancial and institutional development.
The last point above is of particular interest to macroprudential supervisors and poli-
cymakers, as it enables them to tailor the estimation of equilibrium credit to their country
speciï¬?c circumstances. Such a country speciï¬?c estimate of equilibrium credit is a condi-
tional measure, which takes into account the level of development of the economy and is
contrary to current unconditional measures where the smoothed historical trend from the
credit-to-GDP ratio is extracted.
3. Econometric methodology and data
Several methodological approaches to determine equilibrium credit exist in the literature.
We initially describe the conceptual framework that we follow and then outline the statis-
tical approach that we implement to estimate the long-run equilibrium parameters Î² gdp ,
Î²de f and the speed of adjustment parameter Î±. Lastly, we describe how these estimates
relate to a subset of cross-country development indicators.
9 This is a weaker restriction than the previous one, as we only require the coefï¬?cients to be homogenous
across countries but not necessarily equal to unity.
9
3.1. Notion of equilibrium and econometric approach
3.1.1. Equilibrium as the long-run level
The notion of equilibrium credit adopted in this study is in line with the notion of â€?long-
run equilibriumâ€? followed in the economics literature in general as discussed, among oth-
ers, in Pesaran (1997). That is, we perceive equilibrium credit to be linked conceptually to
the economic notion of the â€?long runâ€?. Note that the notion of the long-run in the recent
econometric literature is frequently associated with the literature on co-integration of in-
dividually integrated economic time-series. Although the econometric approach that we
follow allows for the existence of a co-integrating relationship between individually inte-
grated variables, integration of the individual series is not a prerequisite. It is thus still
possible to formulate an equilibrium relationship between a set of stationary variables.
Therefore, there is no need to test for the order of integration of the individual series,
which is typically a requirement when wanting to test for the existence of a long-run equi-
librium using co-integration techniques.10
Given our notion of equilibrium, we specify the econometric model as an Autoregres-
sive Distributed Lag (ARDL) model. To outline brieï¬‚y how the ARDL model is used to
investigate equilibrium relationships, consider the following ï¬?rst order ARDL(1, 1) model.
For simplicity of exposition, we use a general yt and xt notation to denote the dependent
â€?left hand sideâ€? variable and the regressor â€?right hand sideâ€? variables:
y t = k + Ï? y t âˆ’1 + Î³ 0 x t + Î³ 1 x t âˆ’1 + Îµ t (6)
where Îµt is an unobserved noise process and k is an intercept term. In equilibrium, we
have that yt = ytâˆ’1 = y and also that Îµt = 0 so that the ARDL(1, 1) model in (6) gives the
equilibrium relation
y (1 âˆ’ Ï? ) = k + ( Î³0 + Î³1 ) x
y = (1 âˆ’ Ï? ) âˆ’1 k + (1 âˆ’ Ï? ) âˆ’1 ( Î³ 0 + Î³ 1 ) x
y = c + Î²x (7)
where c = (1 âˆ’ Ï?)âˆ’1 k and Î² = (1 âˆ’ Ï?)âˆ’1 (Î³0 + Î³1 ). The term labelled Î² in (7) captures the
long-run equilibrium relationship between yt and xt .
The short-run dynamics, together with the deviations from the long-run equilibrium
value and the adjustment back towards it, can be modeled within the ARDL(1, 1) frame-
work by re-writing the relation in (6) in its so called equilibrium correction model (ECM)
form. Subtracting ytâˆ’1 from both sides of (6) and adding and subtracting Î³0 xtâˆ’1 on the
10 Typical
cointegration tests that require at least two of the series to be integrated of order 1 are the Engle
and Granger (1987) two step estimator or the systems estimator of Johansen (1988, 1991) are used.
10
right hand side of (6) one obtains:
y t âˆ’ y t âˆ’1 = k âˆ’ (1 âˆ’ Ï? ) y t âˆ’1 + Î³ 0 ( x t âˆ’ x t âˆ’1 ) + ( Î³ 0 + Î³ 1 ) x t âˆ’1 + Îµ t
âˆ† y t = k + Î± y t âˆ’1 + Î³ 0 âˆ† x t + Î´ x t âˆ’1 + Îµ t (8)
with Î± = âˆ’(1 âˆ’ Ï?) and Î´ = (Î³0 + Î³1 ). In equilibrium, we have again that yt = ytâˆ’1 = y
and hence âˆ†yt = 0 and âˆ† xt = 0 so that (8) yields
0 = k + Î±y + Î´ x
y = c + Î²x (9)
where Î² = âˆ’Î´/Î± and c = âˆ’k /Î±, which is equivalent to the result found in (7).
Given these results, the equation in (8) can be re-expressed as
âˆ† y t = k + Î± ( y t âˆ’1 âˆ’ Î² x t âˆ’1 ) + Î³ 0 âˆ† x t + Îµ t (10)
where (ytâˆ’1 âˆ’ Î² xtâˆ’1 ) is the equilibrium error or the error correction term at time period
(t âˆ’ 1). The speed of adjustment parameter that captures the rapidness of adjustment to-
wards the long-run equilibrium level is Î±. The Î± parameter is required to be less than zero
for a stable long-run equilibrium relationship between yt and xt to exist (see assumption 2
in Pesaran et al., 1999, page 624 within a panel data setting). In the context of our relation
in (6), this means that the term Ï? has to be less than unity in absolute value, so that yt
cannot contain a unit-root once we have conditioned upon xt and its lagged values.11
Other approaches of determining deviations of credit from its long-run equilibrium
have been used in the literature. One particular approach uses the Hodrick and Prescott
(1997) ï¬?lter (HP ï¬?lter) to extract the â€?smoothâ€? component from the credit-to-GDP ratio.12
This method is implemented, among others, in Gourinchas et al. (2001), Cottarelli et al.
(2005) and is also advocated in the Basel III (2011) regulatory framework. The smooth
component is then given the interpretation of the equilibrium level of credit relative to
GDP and any deviations from this HP ï¬?ltered trend are taken as indications of credit
being above or below the ï¬?nancing needs of the economy.
11 Notice that the relation in (10) has a linear adjustment term. One could also model the adjustment within
a non-linear set-up so that larger deviations are adjusted to at a faster rate, as is done in the empirical
literature on real exchange rates (see, for instance, Taylor et al., 2001). Nonetheless, Buncic (2012) has recently
shown that non-linearity is often very mild and that little is gained from adopting such a framework. For
this reason, we do not consider non-linear adjustments to equilibrium credit.
12 We will use the terminology of a ï¬?lter and smoother interchangeable here. Although the HP ï¬?lter is
referred to as a ï¬?lter, it is in fact a smoother and is a particular type of a smoothing spline that imposes a
penalty for roughness which is proportional to the second difference of the time-series. In that respect, the
HP ï¬?lter is akin to a moving average ï¬?lter, where the trend component is the weighted average of a lags
and leads of the series of interest.
11
The HP ï¬?lter is a widely used tool in the empirical macroeconomics literature partly
because of its computational simplicity and ability to extract the â€?smoothâ€? component of
a time-series. Despite these positive features, the use of the HP ï¬?lter to extract the trend
component of a series has several drawbacks. Some of these are well known. For example,
because the HP ï¬?lter is a two-sided weighted moving average ï¬?lter, the extracted trend
can signiï¬?cantly depend not only on the speciï¬?ed smoothing parameter (often denoted
by Î»), but also on the overall length of the time-series data that are available for compu-
tation. Data sets with a much smaller number of time-series observations will produce
quite different estimates of the trend given relatively small changes in the smoothing pa-
rameter. Also, due to the two-sided nature of the HP ï¬?lter (and in fact any two-sided
ï¬?lter/smoother), the well known â€?end-point biasâ€? constructs highly unreliable trend esti-
mates for the last two data points in the sample.13 This is a rather unfortunate fact from
the viewpoint of a practitioner or a policy maker, as the last few available data points are
the most common ones used to make timely policy decisions.
In the context of the economic notion of long-run equilibrium that was discussed
above, the most important deï¬?ciency that the use of the HP ï¬?lter based equilibrium credit
deï¬?nition entails is that it is based on a univariate representation. It provides no informa-
tion about how credit provision should change in relation to the economic, ï¬?nancial and
institutional development of the economy. We see this as a substantial weakness of the
HP ï¬?ltered credit-to-GDP ratio when used to determine equilibrium credit.14
3.1.2. First-stage ARDL panel regression
We work with the ARDL speciï¬?cation of the long-run equilibrium in our analysis. Since
our main objective is a cross-country comparison of the Î² and Î± parameter estimates in the
ECM speciï¬?cation, we apply the ARDL model to a cross-country panel of data, using the
Mean Group and Pooled Mean Group estimators proposed by Pesaran and Smith (1995)
and Pesaran et al. (1999).
The Mean Group (MG) estimator considers individual country regressions and con-
structs an estimator for the entire group by averaging over the coefï¬?cients of the individ-
ual countries. The Pooled Mean Group (PMG) estimator takes advantage of the possi-
bility that the long-run equilibrium relations across the groups (countries) could be ho-
13 The standard HP ï¬?lter uses two leads and lags to extract the trend component from a series, so one would
need two future time-series observations to get reliable estimates of the trend in the last time period. Due to
this, the technical documentation that accompanies the Basel III (2011) framework actually suggests to use
a one-sided lag version of the HP ï¬?lter (see the middle of page 13 in BCBS, 2010). The standard HP ï¬?lter
imposes initial and terminal conditions to get â€?trendâ€? estimates for the ï¬?rst two and last two observations.
For example, for the last observations this means that the trend at time T is computed only from current and
two lagged values of the series of interest, with the respective weights suitably adjusted.
14 There are various other issues when using the HP ï¬?lter in economic analysis in general, some of which
are discussed in more detail in Harvey and Jaeger (1993).
12
mogenous and restricts all or some of the long-run equilibrium parameters to be the same
across the groups. The aggregate short-run dynamics are again arrived at by averaging
across the country speciï¬?c estimates (see also Pesaran et al., 1999, for a general motivation
of the Pooled Mean Group estimator).
The empirical ECM form of the ARDL model that we work with is as follows:
P Q
âˆ†crit = k i + Î±i (critâˆ’1 âˆ’ Î²i xitâˆ’1 ) + Ï€ pi âˆ†critâˆ’ p + Î³qi âˆ†xitâˆ’q + it (11)
p =1 q =0
where k i and Î±i are the country speciï¬?c intercept and speed of adjustment parameters, Î²i
is a (k Ã— 1) parameter vector capturing the country speciï¬?c long-run equilibrium, ie.,
gdp de f sprd
Î²i = Î²i Î²i Î²rr
i Î²i Î²iacb (12)
and the (k Ã— 1) vector xit contains the variables of interest for country i at time period t,
where xit is deï¬?ned as:
xit = gdpit de f it rrit sprdit acbit . (13)
The parameters Ï€ pi and Î³qi allow for extra dynamics in the dependent variable âˆ†crit up
to lag order P and up to Q extra lags in the vector of explanatory variables, respectively.15
Speciï¬?cations similar to the one given in (11) have been used in previous studies, see,
Â´
for example, Cottarelli et al. (2005) and Egert et al. (2006). However, what distinguishes
our study from earlier ones is that we do not a priori restrict the parameters attached to
GDP and the GDP Deï¬‚ator to unity. Our view is that using the credit-to-GDP ratio as the
dependent variable is overly restrictive and that it is a testable implication of the model
on the data that needs to be veriï¬?ed empirically. In empirical money demand studies,
for example, the typical range of parameter estimates of the income elasticity (of money
demand) across countries is 0.25 âˆ’ 3.5 (see, for instance, Sriram, 2001, page 360). Given
the use of credit in economic transactions, we also expect the income elasticity of credit to
vary considerably across countries.
The approach that we propose leaves the effect of GDP and the GDP Deï¬‚ator on credit
gdp de f
unrestricted by including these variables explicitly in xitâˆ’1 in (11). The Î²i and Î²i pa-
rameters are therefore freely estimated. This enables us to determine how appropriate the
unity restrictions are at the aggregate level. More importantly, it further allows us to look
at the cross-country variation in the Î² Ë† de f coefï¬?cients to see if there are any fun-
Ë† gdp and Î²
i i
15 We use standard i and t subscripts to denote the cross section and the time-series dimensions of a vari-
able or a parameter. In the estimation of (11) we also allow for a non-zero intercept term in the short-run
dynamics to ensure that it has a zero mean.
13
damental differences in their magnitudes. We can then use statistical tests to determine
gdp de f
whether the homogeneity assumption and the unity restrictions on the Î²i and Î²i pa-
rameters across countries, which are imposed when the credit-to-GDP ratio is used on the
left hand side of (11), are supported by the data. It is well known that imposing restric-
tions on a subset of parameters that are not supported by the data leads to substantial
distortions in the estimates of the remaining unrestricted parameters.
3.1.3. Second-stage cross-country regression
We are particularly interested in the cross-country variation of the long-run coefï¬?cients
on real GDP and the GDP Deï¬‚ator in (11); that is, the variation in the Î² Ë† gdp and Î² Ë† de f coefï¬?-
i i
cients and also the speed of adjustment coefï¬?cient Î± Ë† i which measures how fast deviations
from the long-run equilibrium are eliminated. Once estimates have been computed, we
proceed by relating the cross-country variation in Î²Ë† gdp , Î²
Ë† de f and Î±
Ë† i to a set of development
i i
indicators. These are obtained from various sources, such as the FinStats database of Al-
Hussainy et al. (2010) and the Financial Structure data set of Beck et al. (2000). We also
add economic development indicators to this set. No well developed economic theory
exists to guide us in the selection of possible drivers of the variation in Î² Ë† de f and Î±
Ë† gdp , Î² Ë† i.
i i
We therefore also consider traditional scale variables, such as the level of economic devel-
opment (i.e., GDP per capita) a measure of overall GDP and population to control for an
economyâ€™s size, and the degree of openness. We further include data on ï¬?nancial sector
supervisory structures from Melecky and Podpiera (2012). These contain measures of the
degree of integration in prudential supervision, the pursuit and integration of business
conduct supervision, and central bank independence. The Kaufmann et al. (2010) gov-
ernance indicators are also included.16 This yields a total of 42 economic, ï¬?nancial and
institutional development indicators.
Ë† de f and Î±
Ë† gdp , Î²
Our goal here is to relate the cross-country variation in Î² Ë† i to the level of
i i
development of the economy of interest. Once the variation in these coefï¬?cients is linked
to a set of relevant indicators, we will be able to determine equilibrium credit provision
for a speciï¬?c country based on its development stage, its ï¬?nancing needs, and the capacity
of its ï¬?nancial sector to meet these needs. Our proposed framework will therefore enable
macroprudential supervisors to gauge current credit provision in the economy against
what is needed to maintain a ï¬?nancially stable economic growth path over the medium
to long run.
The relationship between the coefï¬?cients and the considered development indicators
16 A description of the explanatory variables that we use is provided in the Data Section.
14
is estimated using a second stage regression model taking the form:
L
m
Î¾i = Ï†0 + Ï† m z i + Îµi , (14)
=1
gdp
Ë† ,Î² Ë† ,Î±de f
where Î¾ i = { Î² i i Ë† } are the coefï¬?cients on real GDP, the GDP Deï¬‚ator and the speed
of adjustment term in (11), {Ï†m L
j } j=0 with m = { gdp, de f , Î± } are the corresponding second
stage regression parameters that capture the cross-country variation in Î¾ i and Îµi is a dis-
turbance term with zero mean and constant variance. The regressors {z i } L=1 are the eco-
nomic and ï¬?nancial development indicators listed above. Notice from the relation in (14)
that once estimates of Ï† are available, it is possible to construct predicted or ï¬?tted values
of the income and price elasticities of credit, conditional on the economic and ï¬?nancial
development of the economy. The advantage here is that the coefï¬?cients can be used to
give a more tailored determination of equilibrium credit provision based on the historical
cross-country evidence of economic and ï¬?nancial development of the countries included
in our sample. This will give policy makers a more appropriate measure to gauge if credit
provision is in excess of the development needs of the economy, rather than using devi-
ations of credit provision from its HP ï¬?ltered trend which has no link to credit demand
based on real economic transactions.
It is evident from the set of potential regressors that are listed above that this set is
rather large compared to the number of cross-country observations that are available.
That is, we identify a total of 42 viable explanatory variables, but have only 49 cross-
country observations to estimate the regression parameters in (14). Since no economic
theory exists to aid in the selection of important regressors and it is not sensible to esti-
mate 42 parameters from 49 observations, we use a statistical approach to determine the
best set of explanatory variables in the relation in (14). We implement this in two steps.
Firstly, we use a Bayesian model averaging (BMA) procedure to narrow down the number
of viable candidate regressors to a subset of around 15 âˆ’ 20 variables. We use the poste-
rior inclusion probability (PIP) of a variable as the criterion to guide in the selection of
the most likely regressors.17 Secondly, we use the Lasso penalized regression estimator
of Tibshirani (1996) as a variable selection tool to shrink the coefï¬?cients of irrelevant or
insigniï¬?cant regressors of the BMA selected subset to zero.18
Our main goal here is to ï¬?nd the smallest possible set of relevant ï¬?nancial and eco-
nomic development indicators. To achieve this goal, we make use of the Lassoâ€™s ability
17 See, for example, Raftery (1995) and Hoeting et al. (1999) for an overview on the use of Bayesian model
averaging and selection methods in social sciences and Chapter 11 in Koop (2003) for a textbook style treat-
ment.
18 See also Zou (2006) and Zhao and Yu (2006) on how the Lasso can be used as a consistent variable selector
and also Section 3.4 in Chapter 3 of Hastie et al. (2009) for a general textbook type treatment of the Lasso
estimator.
15
to shrink small or weakly signiï¬?cant regressors to zero. Because of the shrinkage that the
Lasso imposes in the penalized least squares estimation, parameter estimates are inten-
tionally biased. For this reason, once the relevant set of ï¬?nal regressors has been deter-
mined with the Lasso procedure, we use the Ordinary Least Squares (OLS) estimator to
obtain unbiased estimates of the regression parameters that are not shrunk to 0.
3.2. Data
The source of our data set is the IMFâ€™s International Financial Statistics (IFS) database. All
data is on a quarterly basis. The maximum possible sample size in the time dimension
is from 1980:Q1 to 2010:Q3. The cross sectional dimension of the panel data set, i.e., the
number of countries that are included, is 49.19 The credit variable that we use is deï¬?ned
as total bank credit to the private sector, expressed in local (national) currency units. Since
the scale of private sector credit can be very different across the countries, we create a
credit index, with the base of the index (where the value of the index is equal to 100) being
2001:Q1. The index version of the credit variable is then log transformed before used in
the analysis.
The real GDP data (GDP for short henceforth) and GDP Deï¬‚ator data are taken from
volume measures, and are hence also index measures with different base years. Both,
GDP and the GDP Deï¬‚ator are also log transformed. The lending to deposit rate spread
is computed as the lending rate minus the deposit rate. We use Consumer Price Inï¬‚ation
(CPI) data to construct an ex-post measure of the real interest rate. This is done by com-
puting CPI inï¬‚ation as 100 times the year-on-year inï¬‚ation rate, ie., as 100 Ã— (ln(CPIit ) âˆ’
ln(CPIitâˆ’4 )).20 The real interest rate is then calculated as the lending rate minus year-
on-year inï¬‚ation. The alternative cost of borrowing variable, which captures the cost of
borrowing in foreign currency, is calculated as the country speciï¬?c lending rate minus the
world interest rate minus the year-on-year change in the exchange rate. The exchange
rate is deï¬?ned as the number of local currency units per one US dollar, so that a declin-
ing value indicates an appreciation of the respective countryâ€™s currency against the US
dollar. To avoid unnecessary volatility in the exchange rate series, we use quarterly av-
erages rather than end-of-quarter values. For the US, we use (the inverse) of the Trade
Weighted Exchange Index of major currencies to get a measure of the exchange rate im-
pact on credit.21 The world lending rate is approximated by the US dollar lending rate.
19 We do not provide a separate table that lists the countries included in the panel data set to conserve space,
nonetheless, the x âˆ’axis labels of Figure 2 show explicitly which countries are included in the panel.
20 We use year-on-year values, rather than annualised quarter-on-quarter values, to reduce the volatility of
the inï¬‚ation series.
21 This series was obtained from the FRED2 database of the Federal Reserve Bank of St. Louise. The series
code is DTWEXM. The series was also aggregated to the quarterly average. We use the inverse to be consis-
tent with the deï¬?nition of a decreasing value implying an appreciation of the domestic currency for non-US
countries in the cross-section.
16
A few additional comments on the data set that we use and the data transformations
that we apply are in order. The set of countries consists of a reasonable mix of developed
and emerging market economies with a satisfactory north/south and continental repre-
sentation. The initial cross-sectional dimension consisted of 65 countries, but due to the
lack of largely GDP and GDP Deï¬‚ator data, it was necessary to exclude countries that did
not have GDP related data available for a long enough period.
There were further occasional data gaps that were interpolated with a linear interpola-
tion method to keep the size of the sample as large as possible. These were occasional gaps
in the lending and deposit rates of some countries, and very rarely also in the credit series.
For EU countries, we have converted the relevant variables and the exchange rate to euro-
denominated values prior to the 1st of January 1999, where the ofï¬?cial EU conversion rates
were used.22 Although the real GDP data were marked as seasonally adjusted, it became
evident from visual inspections of the series that for a handful of countries that were in-
cluded in the ï¬?nal data set, this was in fact not the case. It was, therefore, necessary to use
a seasonal ï¬?lter to remove the seasonality in those GDP series. The X12-ARIMA seasonal
ï¬?lter of the US Census Bureau was used.23
The number of time-series observations of each of the 49 countries that are included
in the cross-section ranges from 25 observations for Bulgaria up to 118 observations for
France. Evidently, having less than 40 observations for the time-series dimension is far
from optimal, nonetheless, we chose to leave as many cross-sections in the ï¬?nal data set
as possible. A brief summary of the number of time-series observations of the individual
countries is as follows: there are only 5 countries with less than 40 observations, there are
21 countries with 100 observations or more and the remaining countries have between 40
and 92 time-series observations.
The regressor variables intended to capture the cross sectional variation in the GDP,
GDP Deï¬‚ator and speed of adjustment coefï¬?cients were taken from the FinStats and Fi-
nancial Sector Development Indicators of Al-Hussainy et al. (2010) and Beck et al. (2000).
The economic development indicators are GDP per capita as a measure of economic de-
velopment, the foreign trade to GDP ratio as a measure of an economyâ€™s openness (both
were obtained from the World Bank Central Database), the Kaufmann et al. (2010) over-
all public governance quality indicator, the degree of integration in prudential, business
conduct and overall ï¬?nancial sector supervision of Melecky and Podpiera (2012), a cen-
tral bank political and economic independence indicator, and an indicator for previous
ï¬?nancial crisis experience (also from Melecky and Podpiera, 2012). A list of the ï¬?nal set of
economic, ï¬?nancial and institutional development indicators that we used is provided in
Table 3.
22 See http://ec.europa.eu/economy ï¬?nance/euro/adoption/conversion/index en.htm.
23 Details regarding the computation of the ï¬?lter are available from the Census Bureauâ€™s website available
at: http://www.census.gov/srd/www/x12a/.
17
4. Empirical results
We will initially discuss the estimation results of the ECM parameterisation of the ARDL
model in (11). Note that, as discussed in the Data Section, the time-series dimension for
some of the countries that we included in the ï¬?nal data set is small. For that reason, we
focus on estimating parsimonious models for each country and use the Bayesian Informa-
tion Criterion (BIC) to determine the appropriate lag order of the ECM in (11). Nonethe-
less, we ensure that the chosen lag order of the dynamic speciï¬?cation in (11) does not
result in any signiï¬?cant serial correlation in the residuals of the ï¬?tted models. We initially
start with an upper bound of up to three lags in both Q and P in (11) and then reduce the
lag order until the BIC was minimized. The chosen lag order for the ECM speciï¬?cation of
the ARDL in (11) is Q = P = 1.24
4.1. Visual overview of the cross-country long-run coefï¬?cients
Recall that we are primarily interested in testing whether it is appropriate to restrict the
Î² gdp and Î²de f parameters which determine the long-run equilibrium relation of credit to
unity. This is the assumption that is implicitly made when the credit-to-GDP ratio is used
as the dependent variable. We therefore initially inspect the distribution of the estimates
of the long-run equilibrium parameters, focusing particularly on the Î² Ë† de f coef-
Ë† gdp and Î²
ï¬?cients. To gain some intuition, and before formal statistical tests on the poolability of
the long-run parameters are implemented, we show histograms and density estimates of
Ë† de f in Panels (a) and (c) of Figure 1. In Panel (e) of Figure 1, we also plot the
Ë† gdp and Î²
Î²
empirical distribution of the speed of adjustment parameter Î± Ë† of equation (11). We used
a Gaussian Kernel with an optimal bandwidth selected according to the approach of Shi-
mazaki and Shinomoto (2010) for the density estimates. 95% conï¬?dence intervals, shown
by the dashed line, are based on asymptotic standard errors. The number of bins in the
histograms was chosen optimally according to the method described in Shimazaki and
Shinomoto (2007).
I NSERT F IGURE 1 HERE
Ë† gdp coefï¬?cients plotted in Figure 1 Panel (a) shows visual signs
The distribution of the Î²
of bi-modality, where the peak of the ï¬?rst mode is at a value of around 2 and that of the
second mode at a value of around 4. The density is centered at around 3. This prelim-
inary visual analysis suggests that ï¬?rst, at an aggregate or cross-country average level,
24 We initially allow the lag order to differ across the individual countries, but found that the BIC would,
at times, select a too low lag order for some countries, leading to mild autocorrelation in the residuals.
To remove the residual autocorrelation, we decided to ï¬?x the lag length to 1 for both Q and P across all
countries that were included.
18
the income elasticity of credit seems to be considerably larger than unity. Second, the bi-
modality of the density indicates that substantial heterogeneity in the magnitudes of the
income elasticity of credit across countries exist. The restriction that is imposed when the
credit-to-GDP ratio is used as the dependent variable when modelling equilibrium credit,
thus appears to be rejected by the data.
The distribution of the Î² Ë† de f coefï¬?cients plotted in Panel (c) does not show any visual
evidence of bi-modality, having a single peak centered at 0. Although this distribution
seems to be more inline with the unit elasticity assumption on the GDP Deï¬‚ator param-
eter, it is evident that there exists considerable variation and a mild left skew in the dis-
tribution. This appears to indicate that the cross-sectional mean may not be statistically
different from zero. We will return to this discussion later when formally testing the sig-
niï¬?cance as well as the unity hypothesis on these coefï¬?cients.
The estimates of the speed of adjustment parameter Î± Ë† displayed in Panel (e) of Figure 1
show less evidence of bi-modality, but a decisive left skew. Skewness in a distribution can
come from a variety of sources. If one interprets the left skew as arising from a mixture of
three distributions, then one may argue that three modes are visible at values in the âˆ’0.05
and âˆ’0.10 interval (the main mode), as well as at âˆ’0.20 and âˆ’0.30. This seems to indicate
that some heterogeneity exists in how fast deviations from long-run equilibrium credit are
eliminated. A handful of countries have large (in absolute value) estimates of the speed
of adjustment parameter, with some being around â€” or in excess of â€” 0.4.
The distributions of the Î² Ë† sprd and Î²
Ë† rr , Î² Ë† acb coefï¬?cients that are part of the credit velocity
equation in (5) are displayed in Panels (b), (d) and (f) of Figure 1. Recall that we are not per
se interested in the distributions of these coefï¬?cients and show them only for completeness
and to contrast them with the bi-modality seen in Î² Ë† gdp . Overall, these three distributions
look uni-modal, with the peaks of the densities centered at values marginally below zero.
This suggests that, on average, credit responds negatively to increasing values in the lend-
ing to deposit rate spread, the real interest rate, as well as the alternative cost of borrowing
in foreign currency, when measured at the mode.
The three distributions plotted in the right Panels of Figure 1 show also sizable vari-
ability in the Î² Ë† sprd and Î²
Ë† rr , Î² Ë† acb coefï¬?cients around the zero line, which is an indication
that the population parameters corresponding to the aggregate coefï¬?cients are most likely
not signiï¬?cantly different from zero. Notice here also that although the distributions do
not look Bell-shaped, they are reasonably symmetric. The Î² Ë† rr coefï¬?cients show signs of
fat tails with a high peak at around zero. The Î² Ë† sprd coefï¬?cients, on the other hand, are
somewhat positively skewed. Finally, the Î² Ë† acb coefï¬?cients portray a higher than expected
frequency of values within the âˆ’0.02 to âˆ’0.03 interval, indicated by the bump in the left
tail of Panel (c).
19
4.2. Mean Group (MG) and Pooled Mean Group (PMG) estimation results
We now discuss the results of the Mean Group (MG) and Pooled Mean Group (PMG) es-
timation as well as statistical tests of hypotheses (i ) and (ii ) raised at the end of Section 2.
Since we are primarily interested in the long-run equilibrium relationship between credit
and its macroeconomic determinants, we only report the MG and the PMG estimates of
the long-run equilibrium parameters Î², as well as the intercept and the speed of adjust-
ment terms c and Î±, and do not report results related to the short-run dynamics.25 We
use standard asterisk (âˆ— ) symbols in Table 1 and Table 2 to denote signiï¬?cant values at the
10% (âˆ— ), 5% (âˆ—âˆ— ) or 1% (âˆ—âˆ—âˆ— ) level.
4.2.1. Mean Group estimates
Consider ï¬?rst the results reported in Table 1. The upper part of Table 1 provides the Mean
Group estimates of the long-run equilibrium parameters that are computed from the cross-
Ë† âˆ’1 N Ë†
sectional average of each individual countryâ€™s ARDL regression as Î² MG = N i =1 Î² i .
Note that the long-run coefï¬?cient on GDP is highly signiï¬?cant, centered at a value of
gdp
2.96. Testing the null hypothesis H0 : Î² MG = 1 against the one-sided alternative H1 :
gdp
Î² MG > 1 yields a tâˆ’statistic of (2.96 âˆ’ 1)/0.33 â‰ˆ 6. This result, therefore, provides strong
statistical evidence against a unity restriction at the aggregate cross-country level that the
commonly used credit-to-GDP ratio imposes when employed as the dependent variable
in the estimation of equilibrium credit.
I NSERT TABLE 1 HERE
The MG estimate of the GDP Deï¬‚ator coefï¬?cient is 0.27 with a pâˆ’value of 0.19, indicat-
de f
ing that it is not statistically different from zero. Testing the null hypothesis H0 : Î² MG = 1
against a one-sided alternative results in a tâˆ’statistic of (0.27 âˆ’ 1)/0.32 â‰ˆ âˆ’2.28, which
has a corresponding one-sided pâˆ’value of 0.01. The statistical evidence against the unit
restriction on the GDP Deï¬‚ator parameter is thus somewhat weaker than for the GDP
parameter itself. From a visual inspection of the Î² Ë† de f distribution plotted in Panel (b) of
Figure 1 it may seem surprising that the null of unity is rejected at, for instance, a signiï¬?-
cance level of 5%, given the relatively large dispersion of Î² Ë† de f over the âˆ’6 and 5 interval.
It should be stressed here again that we are testing the Mean Group estimator, which is
25 We used a modiï¬?ed version of the specialised GAUSS code of Pesaran et al. (1999) for MG and PMG
estimation available from http://www.econ.cam.ac.uk/faculty/pesaran/jasa.exe. The complete regression
output from the individual country regressions is large and of no particular interest to us, apart from model
checking purposes. We thus do not report the full results here, but these are available from the authors upon
request.
20
deï¬?ned as:
N
Ë† de f = N âˆ’1
Î² Ë† de f
Î² (15)
MG i
i =1
with corresponding variance
N
2
Ë† de f ) = [ N ( N âˆ’ 1)]âˆ’1
Var( Î² Ë† de f
Ë† de f âˆ’ Î²
Î² . (16)
MG i MG
i =1
The expression in (16) is simply the variance of the sample mean. With the sample stan-
dard deviation of Î²Ë† de f being 2.2129, we can thus see that the MG estimator has a standard
âˆš i
error of 2.2129/ 49 = 0.3161, where N = 49 is the number of observations (countries)
in the cross-section. This leaves a rather tight interval around the point estimate of 0.27,
making the unity restriction statistically unlikely.
The Mean Group estimate of the parameter on the error correction term, shown in the
bottom part of Table 1 suggests that, on average, deviations of credit from its long-run
equilibrium are eliminated with a fast adjustment speed of around 16% per quarter. This
point estimate is signiï¬?cantly different from zero, with a tâˆ’statistic of âˆ’6.94. From the
visual inspection of the coefï¬?cientâ€™s distribution in Panel (e) of Figure 1 we can see that
this result appears to be largely driven by the pronounced left skew in the Î± Ë† density. As
indicated by the mode of the density, the speed of adjustment estimate is in the âˆ’0.10 to
âˆ’0.05 interval for the majority of countries in our sample, suggesting a more reasonable
5% to 10% quarterly adjustment towards the long-run equilibrium level. The MG estimate
of the intercept term is also signiï¬?cantly different from zero, with a point estimate of âˆ’1.86
and a tâˆ’ statistic of âˆ’6.46.
The Mean Group estimates of the parameters on the real interest rate, the lending to
deposit rate spread and the alternative cost of borrowing, which make up the velocity
equation in (4), all have the expected negative point estimates, indicating that a decrease
in either of the three borrowing costs leads to a decrease in credit demand. Nonetheless,
the results reported in Table 1 show that only the coefï¬?cient on the alternative cost of
borrowing in foreign currency is signiï¬?cantly different from zero at the 5% level. In con-
trast, the Î² Ë† sprd coefï¬?cients have tâˆ’statistics well below 1 in absolute value, and
Ë† rr and Î²
are statistically insigniï¬?cant.
4.2.2. Pooled Mean Group Estimates
We now turn more formally to the question whether it is valid to assume that the long-
run parameters that determine equilibrium credit are homogenous across the countries in
21
our sample.26 We investigate this question by estimating the long-run parameters in (11)
using the Pooled Mean Group estimator of Pesaran et al. (1999), which restricts some (or
all) of the long-run parameters in (11) to be the same across all countries. The validity
of these restrictions can then be tested with a standard likelihood ratio ( LR) test. As our
primary interest is in equilibrium credit determined by the Î² gdp and Î²de f parameters, we
only impose the homogeneity restriction on these two parameters, leaving the effect of the
real interest rate, the lending to deposit rate spread and the alternative cost of borrowing
in foreign currency which make up the velocity equation unrestricted.27 These estimates
are reported in Table 2.
I NSERT TABLE 2 HERE
The Pooled Mean Group estimates of the restricted Î² gdp and Î²de f parameters that are
reported in Table 2 are, overall, comparable in size to those of the MG estimator. The PMG
parameters are, nonetheless, estimated with much greater precision. The standard errors
of the MG estimates are about 2.5 and 5 times larger than those of the PMG estimates.
Testing the unity restrictions on the PMG estimates of Î² gdp and Î²de f , with the smaller
standard errors, yields tâˆ’statistics of (3.27 âˆ’ 1)/0.12 = 18.92 and (0.2049 âˆ’ 1)/0.0679 =
âˆ’11.71, indicating that the PMG estimates are also statistically different from 1.
Looking over the remaining unrestricted coefï¬?cients in Table 2, it is noticeable that the
PMG estimates of the three long-run parameters Î²rr , Î²sprd and Î² acb are substantially dif-
ferent from those obtained using the MG estimator. The sign of the coefï¬?cient on the real
Ë† rr ) is now positive and statistically different from zero. The inï¬‚uence of the
interest rate ( Î²
lending to deposit rate spread ( Î² Ë† sprd ) has increased 50 times and is also statistically sig-
niï¬?cant. The effect of the alternative cost of borrowing in foreign currency has increased
about ï¬?ve fold and remains statistically signiï¬?cant at the 5% level. The estimate of the
speed of adjustment parameter Î± under the restricted PMG estimator is now only âˆ’0.02,
which is about 8 times smaller in absolute magnitude than the MG estimate reported in
Table 1. Additionally, there were four instances where the cross-country restrictions im-
posed on the Î² gdp and Î²de f parameters by the PMG estimator lead to positive estimates
of the speed of adjustment parameter, thus violating assumption 2 of Pesaran et al. (1999).
The above reported differences in the PMG and MG estimates of the unrestricted long-run
26 Note that this is a different hypothesis than testing whether the MG estimates are equal to unity. We are
interested in determining whether restricting the long-run coefï¬?cients to be the same across the countries is
sensible and supported by the data.
27 We have also restricted all the long-run equilibrium parameters, which evidently is a stronger re-
strictions. The PMG estimates under this scenarios are 4.4825, âˆ’0.4160, âˆ’0.0098, âˆ’0.0034, âˆ’0.0142 for
Î² gdp , Î²de f , Î²sprd , Î² acb and Î²rr , respectively. The LRâˆ’statistic is 1085, with 240 degrees of freedom, so this
restriction is strongly rejected by the data. Full results are available from the authors.
22
parameters and the speed of adjustment parameter are an indication that the homogene-
ity restrictions of Î² gdp and Î²de f being the same across our sample of countries appears to
be incompatible with the data.
Since the PMG estimator is inconsistent when the restrictions that are imposed on the
long-run parameters are not valid, we perform a poolability test to formally assess the
validity of the restrictions. This is implemented by means of an LR test. Note that the
PMG estimator imposes ( N âˆ’ 1) Ã— R Ëœ restrictions on the ARDL model, where in our case
N = 49 and the number of homogeneity restrictions R Ëœ is equal to 2. The restricted and
unrestricted log-likelihood functions of the PMG estimator are 8089.54 and 8359.71, re-
spectively, resulting in an LR test statistic of over 540. One can see that this corresponds
to a pâˆ’value of effectively 0 for a Chi-squared random variable with 96 degrees of free-
dom.28 We can conclude, therefore, that the two cross-country homogeneity restrictions
on the long-run parameters Î² gdp and Î²de f are strongly rejected by the data.29
4.2.3. Summary of MG and PMG results
With regards to the ï¬?rst two questions or hypotheses that were raised at the end of Sec-
tion 2, the statistical ï¬?ndings of this section can be summarized as follows. First, we ï¬?nd
strong statistical evidence against the hypothesis that the Mean Group estimates of the
Î² gdp and Î²de f parameters are equal to unity. Second, we ï¬?nd considerable heterogeneity
in the cross-country distribution of the Î² gdp estimates. This heterogeneity was initially il-
Ë† gdp coefï¬?cients, which
lustrated by means of a visual inspection of the distribution of the Î²
showed signs of bimodality. We then formally tested for poolability of the Î²de f and Î²de f
parameters using a likelihood ratio test within the PMG estimation framework. This test
resulted in a strong rejection of the poolability hypothesis.
Given these ï¬?ndings, we can conclude that no statistical evidence exists to suggest
28 The LR test statistic is distributed asymptotically as a Chi-squared random variable under the null hy-
pothesis of the restrictions being valid.
29 We should highlight here that the LR test, as remarked by Pesaran et al. (1999), is a fairly stringent test
in the sense that we restrict all the parameters across the different countries to be the same. This is the
restriction that the credit-to-GDP ratio implicitly imposes and the one that we are objecting to. Pesaran et
al. (1999) therefore also implement and suggest to use a Hausman (1978) type test to determine whether
the difference between the aggregate MG and PMG estimates are statistically signiï¬?cant. However, in the
current context, such a test is not overly informative, as the bi-modal distribution is centered around 3
which is in the proximity of the PMG estimates. Given the size of the standard errors of the MG estimates
and the reasonable proximity of the two GDP Deï¬‚ator estimates, a Hausman (1978) type test implemented
Ë†+ âˆ’ Î²
as ( Î² Ë† + ) [Var( Î² Ë† + )âˆ’Var( Î² Ë†+ âˆ’ Î²
Ë† + )]âˆ’1 ( Î² Ë† + ) where Î² Ë† + = (Î² Ë† de f ) , (ie., the vector Î² but
Ë† gdp Î²
MG PMG MG PMG MG PMG
Â¯
including Â¯ the GDPÂ¯and the GDP
only Â¯ Deï¬‚atorÂ¯terms) Â¯ Â¯
yields a test statistic of 2.0675, which with 2 degrees
of freedom returns a pâˆ’value of around 35%. This suggests that the (aggregate) PMG and MG estimates
are not statistically different from one another. But this is not the question that we seek to answer. It would
seem more natural to see if all the parameter estimates are unaffected by the restrictions imposed by the
PMG estimator. This could be done by testing the MG-PMG differences of the full Î² Ë† vectors. Unfortunately,
rr sprd acb
the standard errors of the PMG estimates are in fact larger for Î² , Î² and Î² than the MG ones, resulting
in a non-positive deï¬?nite covariance matrix. This prevents us from implementing a test on the full Î² Ë† vector.
23
that the restrictions that are implied by the use of the credit-to-GDP ratio are supported
by our cross-country panel data. Our view thus is that the use of the credit-to-GDP ratio to
determine equilibrium credit, and therefore also to determine excessive credit provision,
appears to be inappropriate.
4.3. Linking the cross country variation to country-speciï¬?c characteristics
As outlined in Section 3.1.3, we use the BMA framework to reduce the large set of 42
potential development indicators to a smaller subset of around 15 âˆ’ 20 variables. The
criterion for inclusion of a given variable in the subset is its posterior inclusion probability
(PIP). We use a PIP threshold value of 25% for a variable to be included in the subset. This
value may seem low, nonetheless, the purpose here is to perform a ï¬?rst round of â€?pruningâ€?
rather than ï¬?nding the ï¬?nal model.30 Our objective is to reduce the set of all potential
regressors to a smaller set of highly relevant determinants of the cross-country variation
in Î² gdp and Î²de f . The Lasso is thus used as a variable selection tool.31
Note that we follow the same variable selection or reduction procedure to model the
cross-country variation in the Î² Ë† gdp as well as in the Î²Ë† de f and Î±
Ë† coefï¬?cients. To avoid un-
necessary repetition and to keep the section as short and informative as possible, we only
present the BMA and Lasso regression results for the Î² Ë† gdp coefï¬?cient in this section and
provide equivalent results for the Î² Ë† de f and Î±
Ë† coefï¬?cients in the Appendix. Also, we will
initially refer to the regressors in the preliminary discussions of the BMA and Lasso esti-
mations in Section 4.3.1 and Section 4.3.2 by their short names listed in the ï¬?rst column
of Table 3 and Table 4. Although the short names are not very informative, these are only
preliminary discussions to highlight some initial variable exclusion results.32 We discuss
the economic meaning of the regressors and their signiï¬?cance in the context of the ï¬?nal
selected models in detail in Section 4.3.3.
30 Eicher et al. (2011) have recently used a PIP value of 50% as the variable inclusion threshold in a growth
regression context to determine the â€?Number of Effective Regressorsâ€? (see Figure 1 on page 38). One could
thus naturally adopt that value here as well or even set the cut-off mark higher. Nonetheless, we do not
follow such an approach here and use the Lasso penalized regression estimator instead in a second step to
further â€?shrinkâ€? small or irrelevant coefï¬?cients to zero.
31 It should be clear that the posterior mean of the BMA procedure under the given priors that we use is
analogous to a Ridge regression estimator, which is also a penalised regression estimator like the Lasso,
with the penalty function being the sum of squared coefï¬?cients rather than the sum of absolute coefï¬?cients
(see (17) for the objective function of the Lasso). One important difference between the Lasso and the Ridge
regression estimator is that the Ridge estimator cannot shrink coefï¬?cients to zero, but only to small values
to reduce the importance of these variables. This means that all variables are included in the regression,
which we want to avoid, given the large number of potential regressors. The advantage of the Lasso is that
it shrinks unimportant variables to zero, thereby acting as a variable selector. We should also point out here
that the reason why we use the BMA in the ï¬?rst step rather than using the Lasso on the full set of 42 potential
regressors is that we ran into numerical problems when implementing the penalised regression procedure
using the Matlab lasso function. We therefore found it sensible to reduce the number of potential regressors
to a smaller subset ï¬?rst and then proceed with the Lasso.
32 A more detailed description of these variables is provided in the second column of these tables.
24
4.3.1. Selecting the subset regressors
We follow the empirical BMA literature and stay within the natural conjugate prior frame-
work for computational simplicity, thereby avoiding the need to use simulation meth-
ods to compute marginal likelihoods. We use a Normal (Gaussian) prior for the regres-
sion coefï¬?cients with a prior mean of 0 and Zellnerâ€™s gâˆ’prior for the variance, so that
closed form marginal likelihoods can be computed. That is, for a given model (ie., set
of included regressors), we have the prior on the regression parameters being Ï† gdp |Ïƒ2 Îµ âˆ¼
2 âˆ’ 1
N (0, ÏƒÎµ g ( Z Z ) ), where Z is the ( N Ã— L) design matrix representation of the regressors
z i in (14) and g is a prior hyperparameter.33
A well known advantage of using the gâˆ’prior setup is that only the hyperparameter g
needs to be speciï¬?ed by the user. We follow Fernandez et al. (2001) and set g = max( N , L2 )
which in our set-up yields g = L2 . We further use uniform priors on the model probabil-
ities. This choice results in an expected model size of L/2 = 21 variables. It is evident
that having an expected number of 21 regressors in a cross-sectional regression with 49
observations is still rather unsatisfactory. Nevertheless, the uniform prior was used with
the intention to reduce the number of relevant variables to a subset, and not to the ï¬?nal set
of relevant development indicators. Our choice of the model prior is thus a conservative
one, in the sense that we prefer a medium sized expected model size to one that shrinks
the number of variables more aggressively.
As there are 242 > 4.3 Ã— 1012 possible (linear) regression models that can be created
with 42 potential regressors, we use the Model Composition MCMC (MC3 ) algorithm of
Madigan and York (1995) to generate draws from model space.34 We run a chain of 75
million MCMC iterations, where the ï¬?rst 25 million are discarded as burn-in draws. We
check the convergence of the (model space) Markov chain by computing the correlation
between the model iteration counts and analytic posterior model probabilities for the best
5 000 models. This correlation is well over 99%, indicating that the Markov chain on the
model space has converged. The PIPs of the included variables in the BMA procedure,
together with a brief description of the 42 variables included, are reported in Table 3. The
results are sorted by largest to smallest PIP value, with the dashed horizontal line marking
the 25% PIP cut-off value.
I NSERT TABLE 3 HERE
The posterior inclusion probabilities reported in Table 3 show that the prudential1
and cba economic variables have the highest inclusion probabilities with values close to
100%, indicating that these two variables are included in almost every regression model
33 See Koop, 2003 pages 269 âˆ’ 273 for more details regarding this set up and a general overview of BMA.
34 See also Koop, 2003 pages 269 âˆ’ 273 for more details regarding this algorithm.
25
that is ï¬?tted. Two other important variables in terms of high PIPs are the crisis and the
cba political variables with PIPs of 90% and 87%, respectively. Below the cba political
variable, a noticeable drop in the PIP size of around 20% occurs, with the next three im-
portant variables being s02cgp0, s13ifs0, and s01ifs0 with PIP values of 68%, 63% and
60%, respectively. The eca indicator variable has a PIP of only around 54%. Another two
noticeable drops in the PIPs follow the eca variable, of around 10% each, where the PIPs
drop from 54% to 45% and then further to 34% for the s01ess0 variable. When using a
25% cut-off mark in the PIPs, the governance1 variable is the last variable to be included
in the resulting subset of 20 variables. In this subset of 20 variables, there are 12 variables
that have PIPs of less than 50% and 8 variables have PIPs of less than 30%.
4.3.2. Shrinking the subset regressors
We employ the Lasso penalized regression estimator of Tibshirani (1996) as a variable
selection tool to further reduce the subset of economic, ï¬?nancial and institutional devel-
opment indicators selected with the 25% PIP cut-off criterion of the BMA procedure. In
the context of our cross-sectional regression of Î² Ë† gdp on the BMA reduced subset indicators
i
z i , for example, the criterion function for the Lasso is deï¬?ned as:
ï£± ï£¶2 ï£¼
Ls Ls
ï£«
ï£´
ï£² N ï£´
ï£½
Ë† gdp = arg min
Ï† Ë† gdp âˆ’ Ï† gdp âˆ’
ï£Î² Ï†
gdp
z iï£¸ + Î» Ï†
gdp
, (17)
Lasso i 0
s
{Ï†m } L=0
ï£´
ï£³ i =1 ï£´
=1 =1 ï£¾
where Ls denotes the number of subset variables selected with the BMA procedure in
Section 4.3.1, which is equal to 20 here.
The Î» parameter in (17) is a â€?tuningâ€? or â€?complexityâ€? parameter that controls the amount
s gdp
of shrinkage or penalty coming from the L=1 |Ï† | term. When Î» = 0, the penalty term
drops out and the Lasso estimator is equivalent to the OLS estimator. For any non-zero
values of Î», shrinkage will be applied to the regression problem, and some coefï¬?cients
will be shrunk to zero. The larger the value of Î» the more aggressive the shrinkage is. We
use â€?k âˆ’foldâ€? cross-validation to select the value of Î» that minimizes the mean squared
error (MSE). Since our sample size consists of 49 cross-sectional observations, we use a
â€?kâ€? value of 5 in the cross-validation procedure, which corresponds to around 10% of the
sample size.35 The results of the Lasso penalized regression estimator are reported in Ta-
ble 4. Since we are primarily interested in determining which coefï¬?cients are relevant, ie.,
not shrunk to zero, we only report the Lasso point estimates, where we use the notation
â‡’ 0 in Table 4 to denote that a coefï¬?cient was shrunk to 0.
35 Note that k is frequently set to values of either 5 or 10 (see Section 7.10 in Hastie et al., 2009 on this and
also for more details regarding cross-validation in general).
26
I NSERT TABLE 4 HERE
Table 4 shows that 13 of the total of 20 subset development indicators are shrunk to
0. The variables that are selected by the Lasso are the top ï¬?ve variables in terms of
the PIPs obtained from the BMA procedure of Section 4.3.1, namely, the prudential1,
cba economic, crisis, cba political, and s02cgp0 variables, as well as the s01ifso and
eca variables.36 We follow the same procedure to determine the most important develop-
ment indicators for the Î²Ë† de f and Î±
Ë† coefï¬?cients. These results are, without any discussion,
reported in the Appendix.
4.3.3. Results of the cross-country regression models
Since the Lasso estimator yields biased parameter estimates due to the penalty that is im-
posed on the sum of the absolute size of the coefï¬?cients to implement the shrinkage, we
estimate OLS based cross-country regressions of Î² Ë† de f and Î±
Ë† gdp , Î² Ë† on their respective sub-
set of selected development indicators.37 These regression results are reported in Table 5
below. We will initially discuss the overall regression results in terms of ï¬?t for all three
regressions and then proceed to the discussion of the economic signiï¬?cance and interpre-
tation in Section 4.4. Standard asterisk (âˆ— ) notation is again used to denote 10% (âˆ— ), 5%
(âˆ—âˆ— ) and 1% (âˆ—âˆ—âˆ— ) levels of signiï¬?cance.
I NSERT TABLE 5 HERE
Overall, all three regression results reported in Table 5 provide a reasonable cross-
sectional ï¬?t, with about 45%, 53% and 38% of the variation in Î² Ë† de f and Î±
Ë† gdp , Î² Ë† explained
by their respective regression models. Tests of the overall signiï¬?cance of the models yield
F âˆ’statistics of 4.75, 6.22 and 5.31 with corresponding pâˆ’values well below 1% in terms
of signiï¬?cance. We use the Breusch-Pagan LM test to test for heteroskedasticity in the
residuals. The results of this test are reported next to the â€?BP Heteroskedasticityâ€? entry
in Column 2 of Table 5. For all regressions, no statistical evidence of heteroskedasticity
is detected. For this reason, we simply report homoskedastic standard errors in Table 5,
rather than heteroskedasticity consistent ones.
Ë† de f and Î±
Ë† gdp , Î²
To provide some visual indication of how well the models ï¬?t the Î² Ë† series,
36 It is interesting to observe that the s01ifso variable is not shrunk towards 0 by the Lasso estimator
despite of its coefï¬?cient being rather small in magnitude.
37 Recall that we used the Lasso as a variable selection tool to get the smallest possible set of â€?importantâ€?
regressors. Given that we have found the smallest set of important regressors, we use OLS to obtained
unbiased estimates of the parameters.
27
we plot the actual and ï¬?tted series for all three models in the top, middle and bottom
Panels of Figure 2. All three models track the actual series quite well, with a reasonably
good ability to ï¬?t countries that are away from the general centre of the series (see, for
example, the ï¬?ts for Finland, Mexico and Georgia for the Î² Ë† gdp series, the ï¬?ts for Finland
and the Czech Republic for the Î² Ë† de f series and the ï¬?ts for Cyprus and Hong Kong for the Î± Ë†
series). A mildly worse ï¬?t is obtained for some of the countries plotted on the right hand
side of the Panels in Figure 2. For the Î² Ë† de f series, this concerns Poland, Romania, Georgia
and Thailand. For the Î² Ë† gdp series, this concerns Israel, Egypt and South Korea. For the Î± Ë†
series, this concerns the ï¬?ts for Greece, Australia, Israel and Poland. Nevertheless, overall,
we judge the ï¬?ts of the models to be satisfactory.
We also investigate the distributional properties of the Î² Ë† de f and Î±
Ë† gdp , Î² Ë† regression resid-
uals. Similar to the set-up in Section 4.1, we produce histogram and density plots of the
regression residuals. These are shown in Figure 3. Panel (a) of Figure 3 shows the resid-
uals from the Î²Ë† gdp regression. The bi-modality in the distribution of the Î² Ë† gdp coefï¬?cient
disappears and the distribution takes on a more â€?Normalâ€? looking shape once we condi-
tion on the relevant subset cross-country development indicators for Î² Ë† gdp . The skewness
and kurtosis values are 0.1573 and 2.8265, respectively, yielding a Jarque-Bera test statistic
of 0.2582, with a corresponding Monte Carlo simulated pâˆ’value in excess of 0.50.38 The
Jarque-Bera test for Normality thus fails to reject the null hypothesis of the data matching
the skewness and kurtosis of a Normal distribution.39
I NSERT F IGURE 3 HERE
The plot in Panel (b) of Figure 3 shows the empirical distribution of the residuals from
the cross-country regression of Î² Ë† de f on its relevant indicators. Recall that the distribu-
tion of Î²Ë† de f plotted in Panel (c) of Figure 1 showed signs of substantial kurtosis and mild
skewness. By conditioning the Î² Ë† de f coefï¬?cient on its relevant development indicators,
the kurtosis and also the skewness in the distribution are noticeably diminished. Skew-
ness and kurtosis values are âˆ’0.5204 and 3.6797, respectively, yielding a Jarque-Bera test
statistic of 3.0904, with a corresponding Monte Carlo simulated pâˆ’value of 0.1032. The
statistical evidence in favour of the Î² Ë† de f regression residuals being Normally distributed
is thus somewhat weaker than for the Î² Ë† gdp regression residuals.
Ë† regression on its relevant indicators is
The distribution of the residuals from the Î±
38 We use the Matlab function jbtest which relies on Monte Carlo simulation to compute the pâˆ’values of
the Jarque-Bera test due to the well known oversensitivity of the asymptotic Chi-squared approximation in
small samples.
39 This is evidently a weak test of Normality as it only tests the 3rd and 4th moments of a series. Nonetheless,
the intention here is solely to provide some indication that the distribution of the residuals is much better
behaved in terms of shape than the original distribution of the Î² Ë† gdp series.
28
shown in Panel (c) of Figure 3. Comparing this distribution to that of the Î± Ë† one plotted in
Panel (e) of Figure 1, we see that conditioning on the relevant subset development indi-
cators reduces some of the obvious left skew in the Î± Ë† distribution. Nevertheless, the con-
ditioning has a considerably weaker effect on the Î± Ë† residuals than it had on the Î² Ë† gdp and
Ë† de f residuals, as the distribution still shows some evidence of left skewness and excess
Î²
kurtosis. This is also reï¬‚ected in the skewness and kurtosis statistics, which are âˆ’1.2086
and 4.7730, respectively, yielding a Jarque-Bera test statistic of 18.3479, with a correspond-
ing Monte Carlo simulated pâˆ’value of 0.0043. The null hypothesis of Normality of the Î± Ë†
regression residuals is hence rejected.
4.4. Discussion of the cross-country regression results
Having evaluated the overall statistical ï¬?t of the Î² Ë† de f and Î±
Ë† gdp , Î² Ë† regressions on their
relevant development indicators, we now discuss in detail the economic relevance of the
variables that determine the cross-country variation in the Î² Ë† de f and Î±
Ë† gdp , Î² Ë† coefï¬?cients. To
facilitate this discussion, consider again the regression results that are reported in Table 5.
4.4.1. GDP regression
The Private Credit to GDP ratio (s01ifs0), which is a measure of an economyâ€™s ï¬?nancial
Ë† gdp ).40 This suggests
depth, has a positive impact on the income elasticity of credit ( Î²
that, as a countryâ€™s ï¬?nancial system develops, it becomes more responsive (sensitive) to
Ë† gdp increases).
changing credit needs in the economy ( Î²
The effect of the Number of Branches per 100, 000 Adults (s02cgp0) on the income
elasticity of credit is âˆ’4. This is an interesting result. In an economy where customers
rely on face-to-face interactions with bank staff, the Number of Branches variable mea-
sures the access to ï¬?nance, where a higher number suggests that easier access to ï¬?nance
is available. Nonetheless, with the advent of internet based banking and credit availabil-
ity, a decrease in the income elasticity of credit with an increasing number of branches
may in fact capture the effect of ï¬?nancial development of the economy. Many advanced
economies experienced a reduction in the number of bank branches over the last 10 âˆ’ 15
years due to the goal of ï¬?nancial institutions to reduce stafï¬?ng costs. Furthermore, the
popularity of and demand for internet banking has increased substantially. Alternatively,
the negative effect of the Number of Branches on the income elasticity of credit can be
explained by portfolio diversiï¬?cation where agents replace credit with other ï¬?nancial ser-
vices to increase diversity in their ï¬?nancial portfolios. Such a strategy is often pursued
in an effort to manage risks more effectively by using market insurance and investment
diversiï¬?cation instead of credit to reduce the risk of potential portfolio losses (see also
40 Note here that Private Credit to GDP is measured in %, thus at a base value of 100. This means that an
Ë† gdp from 3.21 to 4.815.
increase of 50% in the ratio, ie., from 100 to 150, results in an increase in Î²
29
Ehrlich and Becker, 1972 for additional details).
Greater Integration of Prudential Supervision (prudential1) increases the ï¬‚exibility of
the ï¬?nancial system to respond promptly to changes in credit demand in the economy.
This is due to the effect that Greater Integration of Prudential Supervision has on increas-
ing competition by creating a more harmonised and transparent regulatory framework
across different ï¬?nancial sub-sectors. Both, Central Bank Economic and Political Indepen-
dence (cba political and cba economic) have a positive impact on the income elasticity
of credit. This result follows from the general tendency of many independent central
banks to respond either directly or indirectly to developments in GDP as well as credit.
GDP (or its deviation from potential) and credit are now commonly part of the reaction
Â´
function of a central bank (see Curdia and Woodford, 2010 and Christiano et al., 2007).41
The Financial Crisis Experience dummy (crisis) affects the income elasticity of credit
negatively. Countries that have experienced a ï¬?nancial crisis in the past have a roughly
50% lower income elasticity of credit than the Mean Group estimate across all countries,
which is around 3. This indicates that economies with crises experience are more con-
servative in increasing credit demand and supply when economic activity is expanding.
Also, it is likely that some of our sample countries that have experienced a ï¬?nancial crisis
in the past may have undergone periods where credit was failing much faster than GDP,
irrespective of the credit requirements of the economy.
The estimated positive coefï¬?cient on the Europe and Central Asia (ECA) region dummy
(eca) suggests a higher income elasticity of credit for ECA countries. We explain this ï¬?nd-
ing by the large capital inï¬‚ows into ECA countries preceding the 2007 âˆ’ 2008 global ï¬?nan-
cial crisis and subsequent larger outï¬‚ows once the crisis hit. However, the ECA dummy
coefï¬?cient is estimated rather imprecisely, indicating that considerable variation exists
across the ECA countries in terms of a higher average Î² Ë† gdp relative to non-ECA countries.
4.4.2. GDP Deï¬‚ator regression
Ë† de f ) is positively related to the Number of Branches per
The price elasticity of credit ( Î²
100, 000 Adults (s02cgp0). This suggests that easier access to credit enables the private
sector to adjust credit demand to changes in the average price of a transaction more eas-
ily. Outstanding Domestic Private Debt Securities (s01bis0), on the other hand, decrease
the price elasticity of credit. This result can arise as private agents in more developed
domestic debt markets may rely less on credit and can easily substitute credit by issuing
debt in the domestic capital market. The Cost to Income Ratio (s05bsk0), which mea-
sures the cost effectiveness of banks, has a positive effect on the price elasticity of credit.
This indicates that a more efï¬?cient ï¬?nancial system has greater ï¬‚exibility in responding to
41 See also Cho and Moreno (2006) and Buncic and Melecky (2008) for examples of monetary policy reac-
tions functions in a small New Keynesian model for the US and a small open economy version for Australia.
30
changing credit demand as the average price level in the economy varies.
Integration of Prudential Supervision (prudential1) as well as Central Bank Politi-
cal and Economic Independence (cba political and cba economic) have negative coef-
ï¬?cients, suggesting that an increase in either one of these three indicators leads to a re-
duction in the price elasticity of credit.42 All three indicators measure how independent
monetary policy and, in many cases, macroprudential policy are from political pressures
and industry lobbies. As outlined earlier, many independent central banks now have
explicit targets for GDP, inï¬‚ation as well as credit growth. Any increasing measure of
central bank independence (together with prudential supervision) can thus be taken as an
indication of conservatism on the sensitivity of aggregate price changes to credit and vice
versa.
From the coefï¬?cient on the Financial Crisis Experience dummy (crisis) it is interesting
to see that the experience of ï¬?nancial crises increases the price elasticity of credit. There
could be two reasons for this result. First, from an empirical perspective, countries may
have experienced periods of deï¬‚ation during crisis times due to a negative wealth effect
on prices. Second, from a moral hazard perspective, if excessive risk taking that leads
to a ï¬?nancial crisis is not adequately punished, then otherwise conservative agents may
pursue an active strategy to take on more risky investments, resulting in inï¬‚ated asset
prices. This is then reï¬‚ected in an overall increase in the price elasticity of credit.
4.4.3. Speed of adjustment regression
The speed of adjustment of credit toward its long-run equilibrium (Î± Ë† ) increases with the
Number of Branches per 100, 000 Adults (s02cgp). This positive relation suggests that
greater access to ï¬?nancial services results in faster adjustment speeds, thus keeping credit
closer to its long-run equilibrium value. This positive relation can arise as agents can
afford to hold less precautionary credit to ï¬?nance unexpected transactions. The Gross
Portfolio Equity Assets to GDP ratio (s12ifs0), which measures the share of portfolio
equity assets (claims on non-residents), has a positive effect on the speed of adjustment to
credit equilibrium. A possible explanation of this effect is that countries and their agents
that have the capacity to make investments abroad are able to better monitor over- or
under-supply of credit and respond to it, instead of lending domestically through banks
or capital markets.
The impact of the Consolidated Foreign Claims to GDP ratio (s05bis0) on the speed
of adjustment of credit to its equilibrium is negative. This could stem from the lower abil-
42 Notice here that the parameter estimates of the two central bank independence measures are âˆ’4.82 and
âˆ’4.85, respectively. It may thus seem that the similarity of the two coefï¬?cients is driven by high collinearity
in these two measures. This is, however, not the case here, as the sample correlation between the series is
only 0.22. These two variable therefore measure different parts of Cental Bank independence and its impact
on Î²Ë† de f .
31
ity of countries with larger capital inï¬‚ows to manage credit provision in their economy.
Central Bank Political Independence (cba political) has a positive effect on the speed of
adjustment. Central banks often have the mandate to foster ï¬?nancial stability in addition
to their primary objective of price stability and full employment. Greater Central Bank in-
dependence can thus lead to a more timely and appropriate response of the Central Bank
to excessive credit growth, using either standard monetary or macroprudential tools. The
estimated negative coefï¬?cient on the Europe and Central Asia (ECA) region dummy (eca)
suggests that ECA countries have been less successful in achieving timely and speedy
adjustments of credit to its equilibrium.
Ë† gdp and Î²
4.4.4. Correlation between Î² Ë† de f
The results reported in Table 5 show that the economic and ï¬?nancial development indica-
tors that affect both Î²Ë† gdp and Î² Ë† de f appear to do so consistently with opposite signs. This
appears to indicate that the Î² Ë† gdp and Î² Ë† de f coefï¬?cients are negatively correlated. This is
indeed the case here. The correlation between Î² Ë† de f is âˆ’0.81, with a highly signif-
Ë† gdp and Î²
icant tâˆ’statistic of âˆ’9.50. This is an interesting result that has not been observed or tested
in previous cross-country panel studies of credit demand. Note that this is a robust result
in the sense that it is not driven by outliers in our sample data. To corroborate this point,
we show a scatter plot of Î² Ë† gdp and Î² Ë† de f in Figure 4, with superimposed linear regression
and non-parametric Kernel regression ï¬?ts.43 The two regression lines are consistent with
a signiï¬?cant correlation coefï¬?cient estimate of âˆ’0.81 and overlap reasonably well for the
49 cross-sectional observations in our sample.
Recall that the Î² Ë† de f are the income and price elasticities estimated from the
Ë† gdp and Î²
empirical ECM form of the ARDL model in (11) within the Mean Group estimation frame-
work of Pesaran and Smith (1995). That is, each of the cross-country coefï¬?cients Î² Ë† gdp and
Ë† de f are obtained from separate ARDL regressions on each individual country. Due to this,
Î²
it should be clear that the obtained negative correlation cannot be the result of a restriction
or a model structure that is imposed on the data. Our conjecture is that frequent or large
supply side shocks could be the cause of the negative correlation between Î² Ë† gdp and Î² Ë† de f .
Both GDP and the price level are affected in opposite directions, which could be due to
the credit stock being a more stable process than GDP and or the GDP Deï¬‚ator.
5. Conclusion
This paper carried out a cross-country estimation of equilibrium credit. It utilized the
framework of long-run transaction demand for credit, in which parameters of the equi-
43 The Nadaraya-Watson Kernel regression estimator was used together with the simple plug-in (rule of
thumb) bandwidth of Silverman (1986) (see, for example, Pagan and Ullah, 1999, Chapter 3 for the compu-
tational details).
32
librium credit relation vary with the level of economic, ï¬?nancial, and institutional devel-
opment. It provided empirical evidence that using the credit-to-GDP ratio to gauge equi-
librium credit is inappropriate. This is because such an approach ignores heterogeneity
(cross-country variation) in the parameters that determine long-run equilibrium credit.
The main development indicators driving the variation in the country-speciï¬?c parame-
ters of equilibrium credit as a country develops are: ï¬?nancial depth, access to ï¬?nancial
services, use of capital markets, efï¬?ciency and funding of domestic banks, central bank
independence, the degree of supervisory integration, and the experience of a ï¬?nancial cri-
sis. In addition, countries from the Europe and Central Asia region show a much slower
adjustment of credit to its equilibrium than other countries in our sample.
Our ï¬?ndings have important policy implications. We acknowledge that simplicity and
country speciï¬?city present a tradeoff in the design of an indicator to assess and moni-
tor sustainable provision of credit to the economy. A simple indicator can be preferred
as long as it is not too simplistic. Our results show that the proposal of Basel III to use
the HP ï¬?ltered credit-to-GDP ratio to gauge equilibrium credit could be too simplistic be-
cause it disregards important country speciï¬?cities, that is, how equilibrium credit changes
with ï¬?nancial, economic and institutional development. We provide empirical evidence
that shows that country speciï¬?cities are important and need to be accounted for when
equilibrium credit is estimated, especially for developing countries.
Developed countries might be more concerned about ï¬?nancial stability rather than
ï¬?nancial development as nearly everyone can access ï¬?nance in normal times. Developing
countries, on the other hand, have much to lose if they focus too intensely on ï¬?nancial
stability and severely restrict credit provision to the real economy. Over restrictive credit
provision can hinder ï¬?nancial development and be in the way of more general economic
development.
Concerns by developing countries might have been voiced too little when interna-
tional policy makers were deliberating appropriate indicators to assess sustainable credit
provision and monitor credit cycles in response to the 2007 âˆ’ 2008 global ï¬?nancial crisis.
This paper provides a structural framework that policymakers in developing countries
can use to argue against the rigid implementation of the HP ï¬?ltered credit-to-GDP ratio as
a measure of equilibrium credit in their country. Moreover, this paperâ€™s framework and
results enable policymakers in developing countries to measure equilibrium credit tai-
lored to their countriesâ€™ level of development and thus strikes a balance between ï¬?nancial
development and stability.
33
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Figures and Tables
Ë† gdp
(a) Distribution of Î² Ë† rr
(b) Distribution of Î²
Ë† de f
(c) Distribution of Î² Ë† sprd
(d) Distribution of Î²
Ë†
(e) Distribution of Î± Ë† acb
(f) Distribution of Î²
Figure 1: Histograms and densities of the coeï¬ƒcients Î² Ë† de f and the speed of adjustment Î±
Ë† gdp , Î² Ë† are in the left
Ë†
column and Î² , Î²rr Ë† sprd Ë† acb
and Î² are in the right column. 95% (asymptotic) conï¬?dence intervals are denoted by
the (blue) dashed line. A normal density, centered and scaled at the sample mean and standard deviation, is
plotted in light gray in the background. Optimal smoothing bandwidth and histogram bin size were selected
using the approaches of Shimazaki and Shinomoto (2010, 2007), respectively.
38
Table 1: Mean Group estimation results
Parameter on Variable: Estimate Std. error tâˆ’statistic pâˆ’value 95% CI
GDP 2.9613âˆ—âˆ—âˆ— 0.3260 9.0833 0.0000 [ 2.3223, 3.6002]
GDP Deï¬‚ator 0.2744 0.3161 0.8681 0.1927 [âˆ’0.3452, 0.8940]
Real interest rate âˆ’0.0005 0.0090 âˆ’0.0528 0.4790 [âˆ’0.0181, 0.0171]
Lending to deposit spread âˆ’0.0072 0.0120 âˆ’0.5998 0.2743 [âˆ’0.0308, 0.0164]
Alternative cost of borrowing âˆ’0.0029âˆ—âˆ— 0.0013 âˆ’2.2184 0.0133 [âˆ’0.0056, âˆ’0.0003]
Error correction term âˆ’0.1631âˆ—âˆ—âˆ— 0.0235 âˆ’6.9381 0.0000 [âˆ’0.2092, âˆ’0.1170]
Intercept term âˆ’1.8644âˆ—âˆ—âˆ— 0.2887 âˆ’6.4573 0.0000 [âˆ’2.4304, âˆ’1.2985]
Notes: This table shows the MG estimates of the long-run equilibrium parameters, and the error correction and the
intercept terms in the top and bottom parts of the table, respectively. Estimates are computed as the arithmetic
averages over the N countries that are included
âˆš in the estimation. Standard errors (Std. error) are computed as
the sample standard deviation divided by N (see Pesaran and Smith, 1995 for more details). The column with the
heading pâˆ’values reports one sided probability values under a standard normal distribution. The asterisks âˆ—âˆ—âˆ— , âˆ—âˆ— , and
âˆ— denote signiï¬?cance at the 1%, 5%, and 10% levels, respectively. The full estimation results for each country are
available upon request.
39
Table 2: Pooled Mean Group estimation results
Parameter on Variable: Estimate Std. error tâˆ’statistic pâˆ’value 95% CI
GDP (R) 3.2672âˆ—âˆ—âˆ— 0.1201 27.2110 0.0000 [ 3.0318, 3.5026]
GDP Deï¬‚ator (R) 0.2049âˆ—âˆ—âˆ— 0.0679 3.0170 0.0013 [ 0.0718, 0.3380]
Real interest rate 0.1488âˆ—âˆ—âˆ— 0.0408 3.6476 0.0001 [ 0.0688, 0.2288]
Lending to deposit spread âˆ’0.3387âˆ—âˆ—âˆ— 0.0913 âˆ’3.7110 0.0001 [âˆ’0.5176, âˆ’0.1598]
Alternative cost of borrowing âˆ’0.0140âˆ—âˆ— 0.0078 âˆ’1.7986 0.0360 [âˆ’0.0293, 0.0013]
Error correction term âˆ’0.0238âˆ—âˆ—âˆ— 0.0056 âˆ’4.2416 0.0000 [âˆ’0.0348, âˆ’0.0128]
Intercept term âˆ’0.2424âˆ—âˆ—âˆ— 0.0554 âˆ’4.3722 0.0000 [âˆ’0.3510, âˆ’0.1338]
Unrestricted log-likelihood: 8359.71 Restricted log-likelihood: 8089.54
Notes: This table shows the PMG estimates of the long-run equilibrium parameters and the error correction and the
intercept terms in the top and bottom parts of the table, respectively. Only the GDP and GDP Deï¬‚ator parameters
are restricted to be the same across the groups (countries). This is denoted by (R) in the table above. All other
parameters are left unrestricted. These estimates were computed using the system Maximum Likelihood Estimator of
Pesaran et al. (1999). The column with the heading pâˆ’values reports one sided probability values under a standard
normal distribution. The asterisks âˆ—âˆ—âˆ— , âˆ—âˆ— , and âˆ— denote signiï¬?cance at the 1%, 5%, and 10% levels, respectively. The
full estimation results for each country are available upon request.
40
Ë† gdp from BMA regressions
Table 3: Posterior Inclusion Probabilities for Î²
Variable name Description PIP
prudential1 Integration of prudential supervision 0.9953
cba economic Central bank economic independence 0.9927
crisis Financial crisis experience (0,1 dummy variable) 0.9025
cba political Central bank political independence 0.8675
s02cgp0 Number of Branches per 100,000 Adults, Commercial Banks(1) 0.6809
s13ifs0 Gross Portfolio Debt Assets/GDP (%) 0.6254
s01ifs0 Private Credit/GDP (%) 0.6007
s14ifs0 Gross Portfolio Equity Liabilities/GDP (%) 0.5603
eca Europe and Central Asia (ECA) region dummy 0.5363
s03bis0 Outstanding International Private Debt Securities/GDP (%) 0.4549
s01ess0 Percent of Firms With Line of Credit, All Firms (%) 0.3351
s12ifs0 Gross Portfolio Equity Assets/GDP (%) 0.3045
s01wfe0 Percent Market Capitalization of Top 10 Largest Companies (%) 0.3026
s01wdi0 Stock Market Turnover Ratio (%) 0.2980
s02fsi0 Bank Capital to Assets (%) 0.2748
gdp ppp GDP per Capita PPP adjusted 0.2712
s01axc0 Insurance Premiums (Life)/GDP (%) 0.2637
s02bis0 Outstanding Domestic Public Debt Securities/GDP (%) 0.2621
s01bis0 Outstanding Domestic Private Debt Securities/GDP (%) 0.2609
governance1 Kaufmann et al. (2010) overall governance indicator 0.2577
s05wdi0 Number of Listed Companies(1) 0.2196
s03ifs0 Credit to Government and SOEs/GDP (%) 0.2191
s04fsi0 Provisions to NPLs (%) 0.2150
s01fsi0 Regulatory Capital to Risk-Weighted Assets (%) 0.1900
s05bis0 Consolidated Foreign Claims of BIS-Reporting Banks/GDP (%) 0.1435
tradepgdp Openness (imports plus exports over GDP) 0.1390
s08bsk0 3 Bank Asset Concentration (%) 0.1318
s01 s03 Private Credit/Number of Listed Companies (%) 0.1299
s06bsk0 Return on Assets (%) 0.1224
s10bsk0 Liquid Assets / Deposits and Short Term Funding (%) 0.1119
s02ess0 Percent of Firms With Line of Credit, Small Firms (%) 0.1112
s01nbf0 Pension Fund Assets/GDP (%) 0.1078
s04bis0 Outstanding International Public Debt Securities/GDP (%) 0.0924
s03bsk0 Non-Interest Income / Total income (%) 0.0885
dist crisis Cumulative number of crises experienced by a country 0.0144
s05bsk0 Cost to Income Ratio (%) 0.0139
s09ifs0 Private Credit to Deposits (%) 0.0132
s15ifs0 Gross Portfolio Debt Liabilities/GDP (%) 0.0130
s02nbf0 Mutual Fund Assets/GDP (%) 0.0122
s07bsk0 Return on Equity (%) 0.0112
s03fsi0 NPLs to Total Gross Loans (%) 0.0111
s02axc0 Insurance Premiums (Non-Life)/GDP (%) 0.0020
Notes: This table shows the Posterior inclusion probabilities (PIPs) of the 42 possible economic, ï¬?nancial and institu-
tional development indicators for Î²Ë† gdp computed from a Bayesian model averaging procedure, where a Zellner gâˆ’prior
was used for the speciï¬?cation of the hyperparameter g in the variance prior of Ï• gdp |Ïƒ . The MC3 algorithm of Madigan
and York (1995) was used to generate draws from the model space. A chain with 75 million MCMC draws was run,
where the ï¬?rst 25 million were discarded as a burn-in sample. The dashed line in the table above marks the cut oï¬€
value at PIP = 25%.
(1) denotes values that have been log transformed.
41
Table 4: Lasso penalised regression estimates of Ï† gdp
Variable name Description Lasso estimate of Ï† gdp
prudential1 Integration of prudential supervision 1.2064
cba economic Central bank economic independence 4.5758
crisis Financial crisis experience (0,1 dummy variable) âˆ’1.4273
cba political Central bank political independence 2.0995
s02cgp0 Number of Branches per 100,000 Adults, Commercial Banks(1) âˆ’1.3186
s13ifs0 Gross Portfolio Debt Assets/GDP (%) â‡’0
s01ifs0 Private Credit/GDP (%) 0.0059
s14ifs0 Gross Portfolio Equity Liabilities/GDP (%) â‡’0
eca Europe and Central Asia (ECA) region dummy 0.7137
s03bis0 Outstanding International Private Debt Securities/GDP (%) â‡’0
s01ess0 Percent of Firms With Line of Credit, All Firms (%) â‡’0
s12ifs0 Gross Portfolio Equity Assets/GDP (%) â‡’0
s01wfe0 Percent Market Capitalization of Top 10 Largest Companies (%) â‡’0
s01wdi0 Stock Market Turnover Ratio (%) â‡’0
s02fsi0 Bank Capital to Assets (%) â‡’0
gdp ppp GDP per Capita PPP adjusted â‡’0
s01axc0 Insurance Premiums (Life)/GDP (%) â‡’0
s02bis0 Outstanding Domestic Public Debt Securities/GDP (%) â‡’0
s01bis0 Outstanding Domestic Private Debt Securities/GDP (%) â‡’0
governance1 Kaufmann et al. (2010) overall governance indicator â‡’0
Notes: This table shows the Lasso penalised regression estimates of Ï† gdp . These were computed with a mean squared
error (MSE) cross-validated complexity parameter Î». Coeï¬ƒcients that are shrunk towards zero by the Lasso estimator
are denoted by â‡’ 0.
(1) denotes values that have been log transformed.
42
Table 5: OLS cross-country regressions
Explanatory Variables Dependent Variable
Variable name Description of Variables Ë† gdp
Î² Ë† de f
Î² Ë†
Î±
s01ifs0 0.0321âˆ—âˆ—âˆ—
(std. error) Private Credit/GDP (%) (0.0116) â€” â€”
[ pâˆ’value] [0.0087]
s02cgp0 âˆ’3.9798âˆ—âˆ—âˆ— 3.8461âˆ—âˆ—âˆ— 0.2672âˆ—âˆ—
(std. error) Number of Branches per 100,000 Adults(1) (1.0599) (0.7451) (0.1028)
[ pâˆ’value] [0.0005] [0.0000] [0.0128]
s05bsk0 0.1981âˆ—âˆ—âˆ—
(std. error) Cost to Income Ratio (%) â€” (0.0627) â€”
[ pâˆ’value] [0.0031]
s01bis0 âˆ’0.0353âˆ—âˆ—âˆ—
(std. error) Outstanding Domestic Private Debt Securities/GDP (%) â€” (0.0110) â€”
[ pâˆ’value] [0.0034]
s12ifs0 0.0047âˆ—âˆ—
(std. error) Gross Portfolio Equity Assets/GDP (%) â€” â€” (0.0018)
[ pâˆ’value] [0.0107]
s05bis0 âˆ’0.0079âˆ—âˆ—âˆ—
(std. error) Consolidated Foreign Claims of BIS-Reporting Banks/GDP (%) â€” â€” (0.0019)
[ pâˆ’value] [0.0003]
prudential1 1.5539âˆ—âˆ—âˆ— âˆ’1.0809âˆ—âˆ—âˆ—
(std. error) Integration of Prudential Supervision (0.4373) (0.3731) â€”
[ pâˆ’value] [0.0010] [0.0060]
cba political 2.1719âˆ— âˆ’4.8218âˆ—âˆ—âˆ— 0.1656âˆ—âˆ—
(std. error) Central Bank Political Independence (1.1178) (1.1342) (0.0756)
[ pâˆ’value] [0.0589] [0.0001] [0.0341]
cba economic 6.6749âˆ—âˆ—âˆ— âˆ’4.8525âˆ—âˆ—
(std. error) Central Bank Economic Independence (2.0999) (1.8145) â€”
[ pâˆ’value] [0.0028] [0.0107]
crisis âˆ’1.6136âˆ—âˆ— 2.6972âˆ—âˆ—âˆ—
(std. error) Financial Crisis Experience (0,1 dummy variable) (0.7781) (0.6634) â€”
[ pâˆ’value] [0.0444] [0.0002]
eca 1.0292 âˆ’0.1496âˆ—âˆ—âˆ—
(std. error) Europe and Central Asia (ECA) region dummy (0.9379) â€” (0.0450)
[ pâˆ’value] [0.2789] [0.0004]
Constant 18.56âˆ—âˆ—âˆ— âˆ’13.21âˆ—âˆ—âˆ— âˆ’0.6877âˆ—âˆ—âˆ—
(std. error) Intercept term (6.1237) (4.3810) (0.2261)
[ pâˆ’value] [0.0042] [0.004] [0.0040]
Log-Likelihood âˆ’94.89 âˆ’90.21 31.17
R-squared 0.4479 0.5150 0.3817
{Adjusted R2 } {0.3536} {0.4322} {0.3099}
F âˆ’ statistic 4.7518âˆ—âˆ—âˆ— 6.2200âˆ—âˆ—âˆ— 5.3104âˆ—âˆ—âˆ—
[ pâˆ’value] [0.0006] [0.0001] [0.0007]
BP Heteroskedasticity 5.8273 9.2212 6.5441
[ pâˆ’value] [0.5600] [0.2376] [0.2568]
Notes: This table shows the OLS regression estimates of the Ï† gdp , Ï†de f and Ï†Î± parameters from the regressions of Î² Ë† gdp ,
Ë† de f
Î² Ë† on their respective relevant subset economic, ï¬?nancial and institutional development indicators selected from
and Î±
the BMA and Lasso procedures. Standard errors (denoted by std. error in parenthesis below estimates) are homoskedastic
standard errors. One sided probability values (denoted by pâˆ’value) are reported in square brackets below the estimates and
the standard errors. Values in the bottom part of the table show standard regression goodness-of-ï¬?t and mis-speciï¬?cation
indicators. The entry next to BP Heteroskedasticity is the Breusch-Pagan test for heteroskedasticity. The asterisks âˆ—âˆ—âˆ— , âˆ—âˆ— ,
and âˆ— denote signiï¬?cance at the 1%, 5%, and 10% levels, respectively.
(1) denotes values that have been log transformed.
43
Î±
â€?8
â€?4
0
4
8
â€?4
0
4
8
12
â€?.6
â€?.4
â€?.2
.0
.2
UnitedÂ States UnitedÂ States UnitedÂ States
UnitedÂ Kingdom UnitedÂ Kingdom UnitedÂ Kingdom
Austria Austria Austria
Belgium Belgium Belgium
Fitted
Fitted
Actual
Fitted
Actual
Actual
France France France
Germany Germany Germany
Italy Italy Italy
Netherlands Netherlands Netherlands
Norway Norway Norway
x âˆ’axis labels of the plots.
Sweden Sweden Sweden
Switzerland Switzerland Switzerland
Canada Canada Canada
Japan Japan Japan
Finland Finland Finland
Greece Greece Greece
Portugal Portugal Portugal
Spain Spain Spain
Australia Australia Australia
NewÂ Zealand NewÂ Zealand NewÂ Zealand
SouthÂ Africa SouthÂ Africa SouthÂ Africa
Argentina Argentina Argentina
Brazil Brazil Brazil
Chile Chile Chile
Colombia Colombia Colombia
44
CostaÂ Rica CostaÂ Rica CostaÂ Rica
Mexico Mexico Mexico
Peru Peru Peru
Cyprus Cyprus Cyprus
Israel Israel Israel
Jordan Jordan Jordan
(a) Actual and ï¬?tted values of Î²
(b) Actual and ï¬?tted values of Î²
Ë†
(c) Actual and ï¬?tted values of Î±
Egypt Egypt Egypt
Ë† de f
Ë† gdp
China,P.R.Â HongÂ Kong China,P.R.Â HongÂ Kong China,P.R.Â HongÂ Kong
Indonesia Indonesia Indonesia
Korea,Â RepublicÂ of Korea,Â RepublicÂ of Korea,Â RepublicÂ of
Malaysia Malaysia Malaysia
Thailand Thailand Thailand
Georgia Georgia Georgia
Bulgaria Bulgaria Bulgaria
RussianÂ Federation RussianÂ Federation RussianÂ Federation
CzechÂ Republic CzechÂ Republic CzechÂ Republic
SlovakÂ Republic SlovakÂ Republic SlovakÂ Republic
Estonia Estonia Estonia
Latvia Latvia Latvia
Figure 2: This ï¬?gure shows the actual (blue solid line) and ï¬?tted (dashed red line) values of Î²
Hungary Hungary Hungary
Lithuania Lithuania Lithuania
Croatia Croatia Croatia
Ë† gdp , Î²
Slovenia Slovenia Slovenia
Poland Poland Poland
Romania Romania Romania
indicators as reported in Table 5. The cross-countries that are included in the regressions are shown on the
Ë† from the regressions on their respective relevant subset economic, ï¬?nancial and institutional development
Ë† de f and
Ë† gdp residuals
(a) Distribution of Î²
Ë† de f residuals
(b) Distribution of Î²
Ë† residuals
(c) Distribution of Î±
Figure 3: Histograms and density estimates of the residuals from the Î² Ë† de f and Î±
Ë† gdp , Î² Ë† regressions on their
respective relevant subset economic, ï¬?nancial and institutional development indicators as reported in Table 5.
95% (asymptotic) conï¬?dence intervals are denoted by the (blue) dashed line. A normal density is plotted in
light gray in the background. Optimal smoothing bandwidth and histogram bin size were selected using the
approaches of Shimazaki and Shinomoto (2010, 2007), respectively.
45
12
LinearÂ Fit
KernelÂ Fit
8
GDP
Ë† gdp
4
Î²
0
â€?4
â€?8 â€?7 â€?6 â€?5 â€?4 â€?3 â€?2 â€?1 0 1 2 3 4 5 6
Ë† de f
GDPÂ Î²
Deflator
Ë† de f coeï¬ƒcients together with a linear regression and a non-parametric
Ë† gdp and Î²
Figure 4: Scatter plot of the Î²
(Kernel) regression ï¬?t. The Nadaraya-Watson Kernel regression estimator was used together with the simple
plug-in (rule of thumb) bandwidth of Silverman (1986) (see, for example, Pagan and Ullah, 1999, Chapter 3
for the computational details).
46
Appendix: Additional BMA and Lasso estimation results
Ë† de f from BMA regressions
Table A.1: Posterior Inclusion Probabilities for Î²
Variable name Description PIP
crisis Financial crisis experience (0,1 dummy variable) 0.9974
cba political Central bank political independence 0.9967
prudential1 Integration of prudential supervision 0.9071
s02cgp0 Number of Branches per 100,000 Adults, Commercial Banks(1) 0.6100
s07bsk0 Return on Equity (%) 0.5881
s01bis0 Outstanding Domestic Private Debt Securities/GDP (%) 0.5684
s14ifs0 Gross Portfolio Equity Liabilities/GDP (%) 0.4715
s03bsk0 Non-Interest Income / Total income (%) 0.4406
cba economic Central bank economic independence 0.4148
eca Europe and Central Asia (ECA) region dummy 0.3301
s13ifs0 Gross Portfolio Debt Assets/GDP (%) 0.3147
s15ifs0 Gross Portfolio Debt Liabilities/GDP (%) 0.3112
s12ifs0 Gross Portfolio Equity Assets/GDP (%) 0.3074
s01ifs0 Private Credit/GDP (%) 0.3046
s03bis0 Outstanding International Private Debt Securities/GDP 0.2811
s03ifs0 Credit to Government and SOEs/GDP (%) 0.2799
s05bsk0 Cost to Income Ratio (%) 0.2767
s09ifs0 Private Credit to Deposits (%) 0.2573
s02bis0 Outstanding Domestic Public Debt Securities/GDP (%) 0.2524
s01axc0 Insurance Premiums (Life)/GDP (%) 0.2494
gdp ppp GDP per Capita PPP adjusted 0.2473
s01ess0 Percent of Firms With Line of Credit, All Firms (%) 0.2397
s05bis0 Consolidated Foreign Claims of BIS-Reporting Banks/GDP(%) 0.2035
s02ess0 Percent of Firms With Line of Credit, Small Firms (%) 0.1813
s01fsi0 Regulatory Capital to Risk-Weighted Assets (%) 0.1261
s01wdi0 Stock Market Turnover Ratio (%) 0.1221
s04bis0 Outstanding International Public Debt Securities/GDP (%) 0.1158
s04fsi0 Provisions to NPLs (%) 0.1042
s05wdi0 Number of Listed Companies(1) 0.1027
s02fsi0 Bank Capital to Assets (%) 0.1016
dist crisis Cumulative number of crises experienced by a country 0.1011
s02axc0 Insurance Premiums (Non-Life)/GDP (%) 0.0987
s03fsi0 NPLs to Total Gross Loans (%) 0.0980
s02nbf0 Mutual Fund Assets/GDP (%) 0.0974
s06bsk0 Return on Assets (%) 0.0963
s08bsk0 3 Bank Asset Concentration (%) 0.0889
s01wfe0 Percent Market Capitalization of Top 10 Largest Companies (%) 0.0887
s01 s03 Private Credit/Number of Listed Companies (%) 0.0812
s10bsk0 Liquid Assets / Deposits and Short Term Funding (%) 0.0757
s01nbf0 Pension Fund Assets/GDP (%) 0.0751
governance1 Kaufmann et al. (2010) overall governance indicator 0.0646
tradepgdp Openness (imports plus exports over GDP) 0.0606
Notes: This table shows the Posterior inclusion probabilities (PIPs) of the 42 possible economic, ï¬?nancial and institu-
Ë† de f computed from a Bayesian Model Averaging procedure, where a Zellner gâˆ’prior
tional development indicators for Î²
was used for the speciï¬?cation of the hyperparameter g in the variance prior of Ï•de f |Ïƒ . The MC3 algorithm of Madigan
and York (1995) was used to generate draws from the model space. A chain with 75 million MCMC draws was run,
where the ï¬?rst 25 million were discarded as a burn-in sample. The dashed line in the table above marks the cut oï¬€
value at PIP = 25%.
(1) denotes values that have been log transformed.
47
Table A.2: Lasso penalised regression estimates of Ï†de f
Variable name Description Lasso estimate of Ï†de f
crisis Financial crisis experience (0,1 dummy variable) 2.1993
cba political Central bank political independence âˆ’3.2696
prudential1 Integration of prudential supervision âˆ’1.0071
s01bis0 Outstanding Domestic Private Debt Securities / GDP (%) âˆ’0.0495
s03bsk0 Non-Interest Income / Total income (%) â‡’0
cba economic Central bank economic independence âˆ’3.6348
s02cgp0 Number of Branches per 100,000 Adults, Commercial Banks(1) 1.9805
s07bsk0 Return on Equity (%) â‡’0
s14ifs0 Gross Portfolio Equity Liabilities / GDP (%) â‡’0
eca Europe and Central Asia (ECA) region dummy â‡’0
s13ifs0 Gross Portfolio Debt Assets / GDP (%) â‡’0
s15ifs0 Gross Portfolio Debt Liabilities / GDP (%) â‡’0
s12ifs0 Gross Portfolio Equity Assets / GDP (%) â‡’0
s01ifs0 Private Credit / GDP (%) â‡’0
s03bis0 Outstanding International Private Debt Securities / GDP (%) â‡’0
s03ifs0 Credit to Government and SOEs / GDP (%) â‡’0
s05bsk0 Cost to Income Ratio (%) 0.0884
s09ifs0 Private Credit to Deposits (%) â‡’0
s02bis0 Outstanding Domestic Public Debt Securities / GDP (%) â‡’0
s01axc0 Insurance Premiums (Life) / GDP (%) â‡’0
gdp ppp GDP per Capita PPP adjusted â‡’0
Notes: This table shows the Lasso penalised regression estimates of Ï†de f . These were computed with a mean squared
error (MSE) cross-validated complexity parameter Î». Coeï¬ƒcients that are shrunk towards zero by the Lasso estimator
are denoted by â‡’ 0.
(1) denotes values that have been log transformed.
48
Ë† from BMA regressions
Table A.3: Posterior Inclusion Probabilities for Î±
Variable name Description PIP
s05bis0 Consolidated Foreign Claims of BIS-Reporting Banks/GDP(%) 0.9601
cba political Central bank political independence 0.8951
eca Europe and Central Asia (ECA) region dummy 0.8805
s01wdi0 Stock Market Turnover Ratio (%) 0.8066
s02cgp0 Number of Branches per 100,000 Adults, Commercial Banks(1) 0.7012
s13ifs0 Gross Portfolio Debt Assets/GDP (%) 0.6953
s09ifs0 Private Credit to Deposits (%) 0.6404
s12ifs0 Gross Portfolio Equity Assets/GDP (%) 0.6088
s06bsk0 Return on Assets (%) 0.4485
s05wdi0 Number of Listed Companies(1) 0.3193
s02nbf0 Mutual Fund Assets/GDP (%) 0.2702
s02fsi0 Bank Capital to Assets (%) 0.2129
governance1 Kaufmann et al. (2010) overall governance indicator 0.1715
s10bsk0 Liquid Assets / Deposits and Short Term Funding (%) 0.1389
crisis Financial crisis experience (0,1 dummy variable) 0.1177
s01wfe0 Percent Market Capitalization of Top 10 Largest Companies (%) 0.1095
s01ifs0 Private Credit/GDP (%) 0.1061
s15ifs0 Gross Portfolio Debt Liabilities/GDP (%) 0.0926
s01nbf0 Pension Fund Assets/GDP (%) 0.0874
s04fsi0 Provisions to NPLs (%) 0.0868
s03bis0 Outstanding International Private Debt Securities/GDP 0.0840
s02axc0 Insurance Premiums (Non-Life)/GDP (%) 0.0755
s01 s03 Private Credit/Number of Listed Companies (%) 0.0747
s04bis0 Outstanding International Public Debt Securities/GDP (%) 0.0699
s14ifs0 Gross Portfolio Equity Liabilities/GDP (%) 0.0672
dist crisis Cumulative number of crises experienced by a country 0.0650
s01ess0 Percent of Firms With Line of Credit, All Firms (%) 0.0646
s03ifs0 Credit to Government and SOEs/GDP (%) 0.0628
s01bis0 Outstanding Domestic Private Debt Securities/GDP (%) 0.0617
s02ess0 Percent of Firms With Line of Credit, Small Firms (%) 0.0605
cba economic Central bank economic independence 0.0600
s03bsk0 Non-Interest Income / Total income (%) 0.0575
s01fsi0 Regulatory Capital to Risk-Weighted Assets (%) 0.0556
s03fsi0 NPLs to Total Gross Loans (%) 0.0519
s05bsk0 Cost to Income Ratio (%) 0.0515
s07bsk0 Return on Equity (%) 0.0490
s08bsk0 3 Bank Asset Concentration (%) 0.0467
s01axc0 Insurance Premiums (Life)/GDP (%) 0.0447
gdp ppp GDP per Capita PPP adjusted 0.0444
s02bis0 Outstanding Domestic Public Debt Securities/GDP (%) 0.0431
prudential1 Integration of prudential supervision 0.0402
tradepgdp Openness (imports plus exports over GDP) 0.0401
Notes: This table shows the Posterior inclusion probabilities (PIPs) of the 42 possible economic, ï¬?nancial and institu-
tional development indicators for Î±Ë† computed from a Bayesian Model Averaging procedure, where a Zellner gâˆ’prior
was used for the speciï¬?cation of the hyperparameter g in the variance prior of Ï•de f |Ïƒ . The MC3 algorithm of Madigan
and York (1995) was used to generate draws from the model space. A chain with 75 million MCMC draws was run,
where the ï¬?rst 25 million were discarded as a burn-in sample. The dashed line in the table above marks the cut oï¬€
value at PIP = 25%.
(1) denotes values that have been log transformed.
49
Table A.4: Lasso penalised regression estimates of Ï†Î±
Variable name Description Lasso estimate of Ï†Î±
s05bis0 Consolidated Foreign Claims of BIS-Reporting Banks/GDP(%) âˆ’0.0121
cba political Central bank political independence 0.2456
eca Europe and Central Asia (ECA) region dummy âˆ’0.2521
s01wdi0 Stock Market Turnover Ratio (%) â‡’0
s02cgp0 Number of Branches per 100,000 Adults, Commercial Banks(1) 0.8110
s13ifs0 Gross Portfolio Debt Assets/GDP (%) â‡’0
s09ifs0 Private Credit to Deposits (%) â‡’0
s12ifs0 Gross Portfolio Equity Assets/GDP (%) 0.0083
s06bsk0 Return on Assets (%) â‡’0
s05wdi0 Number of Listed Companies(1) â‡’0
s02nbf0 Mutual Fund Assets/GDP (%) â‡’0
Notes: This table shows the Lasso penalised regression estimates of Ï†Î± . These were computed with a mean squared
error (MSE) cross-validated complexity parameter Î». Coeï¬ƒcients that are shrunk towards zero by the Lasso estimator
are denoted by â‡’ 0.
(1) denotes values that have been log transformed.
50