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 1980–2010, 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 paper—prepared as a background paper to the World Bank’s World Development Report 2014: Managing Risk for Development—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 Mar´ ıa Soledad Mart´ ıa for comments on an ınez Per´ earlier draft of this paper. The views and opinions expressed in the paper are those of the authors and do not reflect 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 Deflator regression . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.4.3 Speed of adjustment regression . . . . . . . . . . . . . . . . . . . . . . 31 4.4.4 Correlation between β gdp and βde 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 − 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, Dell’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 Deflator (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 deflator. 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 − 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 Deflator) — the number of transactions in the economy (the average price of transactions) — 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 ´ 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 − 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 deflator 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-Innes’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): M×V = T×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 × V = T × 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 Deflator.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 − ( β gdp gdpt + βde 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 Deflator is consistent with the calculation of real GDP, we prefer to write the representation in terms of the GDP Deflator. From this point onwards, we will also use the GDP Deflator 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 Deflator and credit velocity.6 The parameters β gdp and βde 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 inflation 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 = βrr rrt + βsprd sprdt + β 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 −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 − ( β gdp gdpt + βde f de f t ) = βrr rrt + βsprd sprdt + β acb acbt . (5) credit-to-GDP ratio if β gdp , βde 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 Deflator, 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 β gdp and βde 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 influence the dependent variable to obtain consistent estimates of β gdp and βde 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 β gdp and βde 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 β gdp and βde 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 β gdp and βde 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 − 3.5 (Sriram, 2001, page 360), we also anticipate considerable heterogeneity in 8 the β gdp and βde f estimates across countries in our sample. This heterogeneity will reflect 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 β gdp and βde 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 β ˆ gdp and β ˆ 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 β ˆ gdp and β ˆ de f coefï¬?cients (as well as the speed of adjustment coefï¬?cient αˆ ) relates to indicators of economic, ï¬?nancial and institutional development. This last question is addressed by regressing the β ˆ de f and α ˆ gdp , β ˆ 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 β gdp , βde f and the speed of adjustment parameter α. 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 briefly 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 −1 + γ 0 x t + γ 1 x t −1 + ε t (6) where εt is an unobserved noise process and k is an intercept term. In equilibrium, we have that yt = yt−1 = y and also that εt = 0 so that the ARDL(1, 1) model in (6) gives the equilibrium relation y (1 − Ï? ) = k + ( γ0 + γ1 ) x y = (1 − Ï? ) −1 k + (1 − Ï? ) −1 ( γ 0 + γ 1 ) x y = c + βx (7) where c = (1 − Ï?)−1 k and β = (1 − Ï?)−1 (γ0 + γ1 ). The term labelled β 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 yt−1 from both sides of (6) and adding and subtracting γ0 xt−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 − y t −1 = k − (1 − Ï? ) y t −1 + γ 0 ( x t − x t −1 ) + ( γ 0 + γ 1 ) x t −1 + ε t ∆ y t = k + α y t −1 + γ 0 ∆ x t + δ x t −1 + ε t (8) with α = −(1 − Ï?) and δ = (γ0 + γ1 ). In equilibrium, we have again that yt = yt−1 = y and hence ∆yt = 0 and ∆ xt = 0 so that (8) yields 0 = k + αy + δ x y = c + βx (9) where β = −δ/α and c = −k /α, which is equivalent to the result found in (7). Given these results, the equation in (8) can be re-expressed as ∆ y t = k + α ( y t −1 − β x t −1 ) + γ 0 ∆ x t + ε t (10) where (yt−1 − β xt−1 ) is the equilibrium error or the error correction term at time period (t − 1). The speed of adjustment parameter that captures the rapidness of adjustment to- wards the long-run equilibrium level is α. The α 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 λ), 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 β and α 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 ∆crit = k i + αi (crit−1 − βi xit−1 ) + Ï€ pi ∆crit− p + γqi ∆xit−q + it (11) p =1 q =0 where k i and αi are the country speciï¬?c intercept and speed of adjustment parameters, βi is a (k × 1) parameter vector capturing the country speciï¬?c long-run equilibrium, ie., gdp de f sprd βi = βi βi βrr i βi βiacb (12) and the (k × 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 γqi allow for extra dynamics in the dependent variable ∆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, ´ 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 Deflator 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 − 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 Deflator on credit gdp de f unrestricted by including these variables explicitly in xit−1 in (11). The βi and βi 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 β ˆ de f coefï¬?cients to see if there are any fun- ˆ gdp and β 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 βi and βi 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 Deflator in (11); that is, the variation in the β ˆ gdp and β ˆ de f coefï¬?- i i cients and also the speed of adjustment coefï¬?cient α ˆ 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 βˆ gdp , β ˆ de f and α ˆ 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 β ˆ de f and α ˆ gdp , β ˆ 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 economy’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. ˆ de f and α ˆ gdp , β Our goal here is to relate the cross-country variation in β ˆ 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 ξi = φ0 + φ m z i + εi , (14) =1 gdp ˆ ,β ˆ ,αde f where ξ i = { β i i ˆ } are the coefï¬?cients on real GDP, the GDP Deflator and the speed of adjustment term in (11), {φm L j } j=0 with m = { gdp, de f , α } are the corresponding second stage regression parameters that capture the cross-country variation in ξ i and εi 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 φ 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 − 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 Lasso’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 IMF’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 Deflator data are taken from volume measures, and are hence also index measures with different base years. Both, GDP and the GDP Deflator are also log transformed. The lending to deposit rate spread is computed as the lending rate minus the deposit rate. We use Consumer Price Inflation (CPI) data to construct an ex-post measure of the real interest rate. This is done by com- puting CPI inflation as 100 times the year-on-year inflation rate, ie., as 100 × (ln(CPIit ) − ln(CPIit−4 )).20 The real interest rate is then calculated as the lending rate minus year- on-year inflation. 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 country’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 −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 inflation 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 Deflator 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 Deflator 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 economy’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 Bureau’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 β gdp and βde 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 β ˆ de f coef- ˆ gdp and β 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 ˆ de f in Panels (a) and (c) of Figure 1. In Panel (e) of Figure 1, we also plot the ˆ gdp and β β empirical distribution of the speed of adjustment parameter α ˆ 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 ˆ gdp coefï¬?cients plotted in Figure 1 Panel (a) shows visual signs The distribution of the β 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 β ˆ 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 Deflator 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 α ˆ 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 −0.05 and −0.10 interval (the main mode), as well as at −0.20 and −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 — or in excess of — 0.4. The distributions of the β ˆ sprd and β ˆ rr , β ˆ 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 β ˆ 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 β ˆ sprd and β ˆ rr , β ˆ 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 β ˆ rr coefï¬?cients show signs of fat tails with a high peak at around zero. The β ˆ sprd coefï¬?cients, on the other hand, are somewhat positively skewed. Finally, the β ˆ acb coefï¬?cients portray a higher than expected frequency of values within the −0.02 to −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 β, as well as the intercept and the speed of adjust- ment terms c and α, and do not report results related to the short-run dynamics.25 We use standard asterisk (∗ ) symbols in Table 1 and Table 2 to denote signiï¬?cant values at the 10% (∗ ), 5% (∗∗ ) or 1% (∗∗∗ ) 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- ˆ −1 N ˆ sectional average of each individual country’s ARDL regression as β MG = N i =1 β 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 : β MG = 1 against the one-sided alternative H1 : gdp β MG > 1 yields a t−statistic of (2.96 − 1)/0.33 ≈ 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 Deflator coefï¬?cient is 0.27 with a p−value of 0.19, indicat- de f ing that it is not statistically different from zero. Testing the null hypothesis H0 : β MG = 1 against a one-sided alternative results in a t−statistic of (0.27 − 1)/0.32 ≈ −2.28, which has a corresponding one-sided p−value of 0.01. The statistical evidence against the unit restriction on the GDP Deflator parameter is thus somewhat weaker than for the GDP parameter itself. From a visual inspection of the β ˆ 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 β ˆ de f over the −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 ˆ de f = N −1 β ˆ de f β (15) MG i i =1 with corresponding variance N 2 ˆ de f ) = [ N ( N − 1)]−1 Var( β ˆ de f ˆ de f − β β . (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 βˆ de f being 2.2129, we can thus see that the MG estimator has a standard √ 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 t−statistic of −6.94. From the visual inspection of the coefï¬?cient’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 α ˆ density. As indicated by the mode of the density, the speed of adjustment estimate is in the −0.10 to −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 −1.86 and a t− statistic of −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 β ˆ sprd coefï¬?cients have t−statistics well below 1 in absolute value, and ˆ rr and β 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 β gdp and βde 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 β gdp and βde 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 β gdp and βde f , with the smaller standard errors, yields t−statistics of (3.27 − 1)/0.12 = 18.92 and (0.2049 − 1)/0.0679 = −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 βrr , βsprd and β acb are substantially dif- ferent from those obtained using the MG estimator. The sign of the coefï¬?cient on the real ˆ rr ) is now positive and statistically different from zero. The influence of the interest rate ( β lending to deposit rate spread ( β ˆ 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 α under the restricted PMG estimator is now only −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 β gdp and βde 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, −0.4160, −0.0098, −0.0034, −0.0142 for β gdp , βde f , βsprd , β acb and βrr , respectively. The LR−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 β gdp and βde 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 − 1) × 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 p−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 β gdp and βde 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 β gdp and βde f parameters are equal to unity. Second, we ï¬?nd considerable heterogeneity in the cross-country distribution of the β gdp estimates. This heterogeneity was initially il- ˆ gdp coefï¬?cients, which lustrated by means of a visual inspection of the distribution of the β showed signs of bimodality. We then formally tested for poolability of the βde f and βde 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 Deflator estimates, a Hausman (1978) type test implemented ˆ+ − β as ( β ˆ + ) [Var( β ˆ + )−Var( β ˆ+ − β ˆ + )]−1 ( β ˆ + ) where β ˆ + = (β ˆ de f ) , (ie., the vector β but ˆ gdp β MG PMG MG PMG MG PMG ¯ including ¯ the GDP¯and the GDP only ¯ Deflator¯terms) ¯ ¯ yields a test statistic of 2.0675, which with 2 degrees of freedom returns a p−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 β ˆ vectors. Unfortunately, rr sprd acb the standard errors of the PMG estimates are in fact larger for β , β and β than the MG ones, resulting in a non-positive deï¬?nite covariance matrix. This prevents us from implementing a test on the full β ˆ 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 − 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 β gdp and βde 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 β ˆ gdp as well as in the βˆ de f and α ˆ 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 β ˆ gdp coefï¬?cient in this section and provide equivalent results for the β ˆ de f and α ˆ 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 Zellner’s g−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 φ gdp |σ2 ε ∼ 2 − 1 N (0, σε g ( Z Z ) ), where Z is the ( N × 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 g−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 × 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 − 273 for more details regarding this set up and a general overview of BMA. 34 See also Koop, 2003 pages 269 − 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 β ˆ gdp on the BMA reduced subset indicators i z i , for example, the criterion function for the Lasso is deï¬?ned as:  2  Ls Ls    N   ˆ gdp = arg min φ ˆ gdp − φ gdp − β φ gdp z i + λ φ gdp , (17) Lasso i 0 s {φm } L=0   i =1  =1 =1  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 λ 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 |φ | term. When λ = 0, the penalty term drops out and the Lasso estimator is equivalent to the OLS estimator. For any non-zero values of λ, shrinkage will be applied to the regression problem, and some coefï¬?cients will be shrunk to zero. The larger the value of λ the more aggressive the shrinkage is. We use â€?k −foldâ€? cross-validation to select the value of λ 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 ⇒ 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 βˆ de f and α ˆ 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 β ˆ de f and α ˆ gdp , β ˆ 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 (∗ ) notation is again used to denote 10% (∗ ), 5% (∗∗ ) and 1% (∗∗∗ ) 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 β ˆ de f and α ˆ gdp , β ˆ explained by their respective regression models. Tests of the overall signiï¬?cance of the models yield F −statistics of 4.75, 6.22 and 5.31 with corresponding p−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. ˆ de f and α ˆ gdp , β To provide some visual indication of how well the models ï¬?t the β ˆ 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 β ˆ gdp series, the ï¬?ts for Finland and the Czech Republic for the β ˆ de f series and the ï¬?ts for Cyprus and Hong Kong for the α ˆ 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 β ˆ de f series, this concerns Poland, Romania, Georgia and Thailand. For the β ˆ gdp series, this concerns Israel, Egypt and South Korea. For the α ˆ 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 β ˆ de f and α ˆ gdp , β ˆ 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 βˆ gdp regression. The bi-modality in the distribution of the β ˆ 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 β ˆ 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 p−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 β ˆ de f on its relevant indicators. Recall that the distribu- tion of βˆ de f plotted in Panel (c) of Figure 1 showed signs of substantial kurtosis and mild skewness. By conditioning the β ˆ 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 −0.5204 and 3.6797, respectively, yielding a Jarque-Bera test statistic of 3.0904, with a corresponding Monte Carlo simulated p−value of 0.1032. The statistical evidence in favour of the β ˆ de f regression residuals being Normally distributed is thus somewhat weaker than for the β ˆ gdp regression residuals. ˆ regression on its relevant indicators is The distribution of the residuals from the α 38 We use the Matlab function jbtest which relies on Monte Carlo simulation to compute the p−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 β ˆ gdp series. 28 shown in Panel (c) of Figure 3. Comparing this distribution to that of the α ˆ 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 α ˆ distribution. Nevertheless, the con- ditioning has a considerably weaker effect on the α ˆ residuals than it had on the β ˆ gdp and ˆ de f residuals, as the distribution still shows some evidence of left skewness and excess β kurtosis. This is also reflected in the skewness and kurtosis statistics, which are −1.2086 and 4.7730, respectively, yielding a Jarque-Bera test statistic of 18.3479, with a correspond- ing Monte Carlo simulated p−value of 0.0043. The null hypothesis of Normality of the α ˆ regression residuals is hence rejected. 4.4. Discussion of the cross-country regression results Having evaluated the overall statistical ï¬?t of the β ˆ de f and α ˆ gdp , β ˆ 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 β ˆ de f and α ˆ gdp , β ˆ 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 economy’s ï¬?nancial ˆ gdp ).40 This suggests depth, has a positive impact on the income elasticity of credit ( β that, as a country’s ï¬?nancial system develops, it becomes more responsive (sensitive) to ˆ gdp increases). changing credit needs in the economy ( β The effect of the Number of Branches per 100, 000 Adults (s02cgp0) on the income elasticity of credit is −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 − 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 ˆ gdp from 3.21 to 4.815. increase of 50% in the ratio, ie., from 100 to 150, results in an increase in β 29 Ehrlich and Becker, 1972 for additional details). Greater Integration of Prudential Supervision (prudential1) increases the flexibility 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 ´ 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 inflows into ECA countries preceding the 2007 − 2008 global ï¬?nan- cial crisis and subsequent larger outflows 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 β ˆ gdp relative to non-ECA countries. 4.4.2. GDP Deflator regression ˆ de f ) is positively related to the Number of Branches per The price elasticity of credit ( β 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 flexibility 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, inflation 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 deflation 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 inflated asset prices. This is then reflected 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 (α ˆ ) 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 −4.82 and −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 βˆ de f . 31 ity of countries with larger capital inflows 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. ˆ gdp and β 4.4.4. Correlation between β ˆ de f The results reported in Table 5 show that the economic and ï¬?nancial development indica- tors that affect both βˆ gdp and β ˆ de f appear to do so consistently with opposite signs. This appears to indicate that the β ˆ gdp and β ˆ de f coefï¬?cients are negatively correlated. This is indeed the case here. The correlation between β ˆ de f is −0.81, with a highly signif- ˆ gdp and β icant t−statistic of −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 β ˆ gdp and β ˆ 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 −0.81 and overlap reasonably well for the 49 cross-sectional observations in our sample. Recall that the β ˆ de f are the income and price elasticities estimated from the ˆ gdp and β 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 β ˆ gdp and ˆ de f are obtained from separate ARDL regressions on each individual country. Due to this, β 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 β ˆ gdp and β ˆ 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 Deflator. 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 − 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 paper’s framework and results enable policymakers in developing countries to measure equilibrium credit tai- lored to their countries’ level of development and thus strikes a balance between ï¬?nancial development and stability. 33 References Al-Hussainy, E., A. Coppola, E. Feyen, A. Ize and H. Ren (2010): “FinStats: A ready-to-use tool to benchmark ï¬?nancial countries and time,â€? Mimeo, World Bank. Arango, Sebastian and M. Ishaq Nadiri (1981): “Demand for money in open economies,â€? 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Journal of the American Statistical Association, 101(476), 1418–1429. 37 Figures and Tables ˆ gdp (a) Distribution of β ˆ rr (b) Distribution of β ˆ de f (c) Distribution of β ˆ sprd (d) Distribution of β ˆ (e) Distribution of α ˆ acb (f) Distribution of β Figure 1: Histograms and densities of the coefficients β ˆ de f and the speed of adjustment α ˆ gdp , β ˆ are in the left ˆ column and β , βrr ˆ sprd ˆ acb and β 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 t−statistic p−value 95% CI GDP 2.9613∗∗∗ 0.3260 9.0833 0.0000 [ 2.3223, 3.6002] GDP Deflator 0.2744 0.3161 0.8681 0.1927 [−0.3452, 0.8940] Real interest rate −0.0005 0.0090 −0.0528 0.4790 [−0.0181, 0.0171] Lending to deposit spread −0.0072 0.0120 −0.5998 0.2743 [−0.0308, 0.0164] Alternative cost of borrowing −0.0029∗∗ 0.0013 −2.2184 0.0133 [−0.0056, −0.0003] Error correction term −0.1631∗∗∗ 0.0235 −6.9381 0.0000 [−0.2092, −0.1170] Intercept term −1.8644∗∗∗ 0.2887 −6.4573 0.0000 [−2.4304, −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 √ 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 p−values reports one sided probability values under a standard normal distribution. The asterisks ∗∗∗ , ∗∗ , and ∗ 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 t−statistic p−value 95% CI GDP (R) 3.2672∗∗∗ 0.1201 27.2110 0.0000 [ 3.0318, 3.5026] GDP Deflator (R) 0.2049∗∗∗ 0.0679 3.0170 0.0013 [ 0.0718, 0.3380] Real interest rate 0.1488∗∗∗ 0.0408 3.6476 0.0001 [ 0.0688, 0.2288] Lending to deposit spread −0.3387∗∗∗ 0.0913 −3.7110 0.0001 [−0.5176, −0.1598] Alternative cost of borrowing −0.0140∗∗ 0.0078 −1.7986 0.0360 [−0.0293, 0.0013] Error correction term −0.0238∗∗∗ 0.0056 −4.2416 0.0000 [−0.0348, −0.0128] Intercept term −0.2424∗∗∗ 0.0554 −4.3722 0.0000 [−0.3510, −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 Deflator 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 p−values reports one sided probability values under a standard normal distribution. The asterisks ∗∗∗ , ∗∗ , and ∗ denote signiï¬?cance at the 1%, 5%, and 10% levels, respectively. The full estimation results for each country are available upon request. 40 ˆ gdp from BMA regressions Table 3: Posterior Inclusion Probabilities for β 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 βˆ gdp computed from a Bayesian model averaging procedure, where a Zellner g−prior was used for the speciï¬?cation of the hyperparameter g in the variance prior of Ï• gdp |σ . 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 off value at PIP = 25%. (1) denotes values that have been log transformed. 41 Table 4: Lasso penalised regression estimates of φ gdp Variable name Description Lasso estimate of φ gdp prudential1 Integration of prudential supervision 1.2064 cba economic Central bank economic independence 4.5758 crisis Financial crisis experience (0,1 dummy variable) −1.4273 cba political Central bank political independence 2.0995 s02cgp0 Number of Branches per 100,000 Adults, Commercial Banks(1) −1.3186 s13ifs0 Gross Portfolio Debt Assets/GDP (%) ⇒0 s01ifs0 Private Credit/GDP (%) 0.0059 s14ifs0 Gross Portfolio Equity Liabilities/GDP (%) ⇒0 eca Europe and Central Asia (ECA) region dummy 0.7137 s03bis0 Outstanding International Private Debt Securities/GDP (%) ⇒0 s01ess0 Percent of Firms With Line of Credit, All Firms (%) ⇒0 s12ifs0 Gross Portfolio Equity Assets/GDP (%) ⇒0 s01wfe0 Percent Market Capitalization of Top 10 Largest Companies (%) ⇒0 s01wdi0 Stock Market Turnover Ratio (%) ⇒0 s02fsi0 Bank Capital to Assets (%) ⇒0 gdp ppp GDP per Capita PPP adjusted ⇒0 s01axc0 Insurance Premiums (Life)/GDP (%) ⇒0 s02bis0 Outstanding Domestic Public Debt Securities/GDP (%) ⇒0 s01bis0 Outstanding Domestic Private Debt Securities/GDP (%) ⇒0 governance1 Kaufmann et al. (2010) overall governance indicator ⇒0 Notes: This table shows the Lasso penalised regression estimates of φ gdp . These were computed with a mean squared error (MSE) cross-validated complexity parameter λ. Coefficients that are shrunk towards zero by the Lasso estimator are denoted by ⇒ 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 ˆ gdp β ˆ de f β ˆ α s01ifs0 0.0321∗∗∗ (std. error) Private Credit/GDP (%) (0.0116) — — [ p−value] [0.0087] s02cgp0 −3.9798∗∗∗ 3.8461∗∗∗ 0.2672∗∗ (std. error) Number of Branches per 100,000 Adults(1) (1.0599) (0.7451) (0.1028) [ p−value] [0.0005] [0.0000] [0.0128] s05bsk0 0.1981∗∗∗ (std. error) Cost to Income Ratio (%) — (0.0627) — [ p−value] [0.0031] s01bis0 −0.0353∗∗∗ (std. error) Outstanding Domestic Private Debt Securities/GDP (%) — (0.0110) — [ p−value] [0.0034] s12ifs0 0.0047∗∗ (std. error) Gross Portfolio Equity Assets/GDP (%) — — (0.0018) [ p−value] [0.0107] s05bis0 −0.0079∗∗∗ (std. error) Consolidated Foreign Claims of BIS-Reporting Banks/GDP (%) — — (0.0019) [ p−value] [0.0003] prudential1 1.5539∗∗∗ −1.0809∗∗∗ (std. error) Integration of Prudential Supervision (0.4373) (0.3731) — [ p−value] [0.0010] [0.0060] cba political 2.1719∗ −4.8218∗∗∗ 0.1656∗∗ (std. error) Central Bank Political Independence (1.1178) (1.1342) (0.0756) [ p−value] [0.0589] [0.0001] [0.0341] cba economic 6.6749∗∗∗ −4.8525∗∗ (std. error) Central Bank Economic Independence (2.0999) (1.8145) — [ p−value] [0.0028] [0.0107] crisis −1.6136∗∗ 2.6972∗∗∗ (std. error) Financial Crisis Experience (0,1 dummy variable) (0.7781) (0.6634) — [ p−value] [0.0444] [0.0002] eca 1.0292 −0.1496∗∗∗ (std. error) Europe and Central Asia (ECA) region dummy (0.9379) — (0.0450) [ p−value] [0.2789] [0.0004] Constant 18.56∗∗∗ −13.21∗∗∗ −0.6877∗∗∗ (std. error) Intercept term (6.1237) (4.3810) (0.2261) [ p−value] [0.0042] [0.004] [0.0040] Log-Likelihood −94.89 −90.21 31.17 R-squared 0.4479 0.5150 0.3817 {Adjusted R2 } {0.3536} {0.4322} {0.3099} F − statistic 4.7518∗∗∗ 6.2200∗∗∗ 5.3104∗∗∗ [ p−value] [0.0006] [0.0001] [0.0007] BP Heteroskedasticity 5.8273 9.2212 6.5441 [ p−value] [0.5600] [0.2376] [0.2568] Notes: This table shows the OLS regression estimates of the φ gdp , φde f and φα parameters from the regressions of β ˆ gdp , ˆ de f β ˆ on their respective relevant subset economic, ï¬?nancial and institutional development indicators selected from and α 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 p−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 ∗∗∗ , ∗∗ , and ∗ denote signiï¬?cance at the 1%, 5%, and 10% levels, respectively. (1) denotes values that have been log transformed. 43 α â€?8 â€?4 0 4 8 â€?4 0 4 8 12 â€?.6 â€?.4 â€?.2 .0 .2 United States United States United States United Kingdom United Kingdom United 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 −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 New Zealand New Zealand New Zealand South Africa South Africa South Africa Argentina Argentina Argentina Brazil Brazil Brazil Chile Chile Chile Colombia Colombia Colombia 44 Costa Rica Costa Rica Costa Rica Mexico Mexico Mexico Peru Peru Peru Cyprus Cyprus Cyprus Israel Israel Israel Jordan Jordan Jordan (a) Actual and ï¬?tted values of β (b) Actual and ï¬?tted values of β ˆ (c) Actual and ï¬?tted values of α Egypt Egypt Egypt ˆ de f ˆ gdp China,P.R. Hong Kong China,P.R. Hong Kong China,P.R. Hong Kong Indonesia Indonesia Indonesia Korea, Republic of Korea, Republic of Korea, Republic of Malaysia Malaysia Malaysia Thailand Thailand Thailand Georgia Georgia Georgia Bulgaria Bulgaria Bulgaria Russian Federation Russian Federation Russian Federation Czech Republic Czech Republic Czech Republic Slovak Republic Slovak Republic Slovak 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 β Hungary Hungary Hungary Lithuania Lithuania Lithuania Croatia Croatia Croatia ˆ gdp , β 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 ˆ from the regressions on their respective relevant subset economic, ï¬?nancial and institutional development ˆ de f and ˆ gdp residuals (a) Distribution of β ˆ de f residuals (b) Distribution of β ˆ residuals (c) Distribution of α Figure 3: Histograms and density estimates of the residuals from the β ˆ de f and α ˆ gdp , β ˆ 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 Linear Fit Kernel Fit 8 GDP ˆ gdp 4 β 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 ˆ de f GDP β Deflator ˆ de f coefficients together with a linear regression and a non-parametric ˆ gdp and β Figure 4: Scatter plot of the β (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 ˆ de f from BMA regressions Table A.1: Posterior Inclusion Probabilities for β 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- ˆ de f computed from a Bayesian Model Averaging procedure, where a Zellner g−prior tional development indicators for β was used for the speciï¬?cation of the hyperparameter g in the variance prior of Ï•de f |σ . 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 off value at PIP = 25%. (1) denotes values that have been log transformed. 47 Table A.2: Lasso penalised regression estimates of φde f Variable name Description Lasso estimate of φde f crisis Financial crisis experience (0,1 dummy variable) 2.1993 cba political Central bank political independence −3.2696 prudential1 Integration of prudential supervision −1.0071 s01bis0 Outstanding Domestic Private Debt Securities / GDP (%) −0.0495 s03bsk0 Non-Interest Income / Total income (%) ⇒0 cba economic Central bank economic independence −3.6348 s02cgp0 Number of Branches per 100,000 Adults, Commercial Banks(1) 1.9805 s07bsk0 Return on Equity (%) ⇒0 s14ifs0 Gross Portfolio Equity Liabilities / GDP (%) ⇒0 eca Europe and Central Asia (ECA) region dummy ⇒0 s13ifs0 Gross Portfolio Debt Assets / GDP (%) ⇒0 s15ifs0 Gross Portfolio Debt Liabilities / GDP (%) ⇒0 s12ifs0 Gross Portfolio Equity Assets / GDP (%) ⇒0 s01ifs0 Private Credit / GDP (%) ⇒0 s03bis0 Outstanding International Private Debt Securities / GDP (%) ⇒0 s03ifs0 Credit to Government and SOEs / GDP (%) ⇒0 s05bsk0 Cost to Income Ratio (%) 0.0884 s09ifs0 Private Credit to Deposits (%) ⇒0 s02bis0 Outstanding Domestic Public Debt Securities / GDP (%) ⇒0 s01axc0 Insurance Premiums (Life) / GDP (%) ⇒0 gdp ppp GDP per Capita PPP adjusted ⇒0 Notes: This table shows the Lasso penalised regression estimates of φde f . These were computed with a mean squared error (MSE) cross-validated complexity parameter λ. Coefficients that are shrunk towards zero by the Lasso estimator are denoted by ⇒ 0. (1) denotes values that have been log transformed. 48 ˆ from BMA regressions Table A.3: Posterior Inclusion Probabilities for α 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 αˆ computed from a Bayesian Model Averaging procedure, where a Zellner g−prior was used for the speciï¬?cation of the hyperparameter g in the variance prior of Ï•de f |σ . 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 off value at PIP = 25%. (1) denotes values that have been log transformed. 49 Table A.4: Lasso penalised regression estimates of φα Variable name Description Lasso estimate of φα s05bis0 Consolidated Foreign Claims of BIS-Reporting Banks/GDP(%) −0.0121 cba political Central bank political independence 0.2456 eca Europe and Central Asia (ECA) region dummy −0.2521 s01wdi0 Stock Market Turnover Ratio (%) ⇒0 s02cgp0 Number of Branches per 100,000 Adults, Commercial Banks(1) 0.8110 s13ifs0 Gross Portfolio Debt Assets/GDP (%) ⇒0 s09ifs0 Private Credit to Deposits (%) ⇒0 s12ifs0 Gross Portfolio Equity Assets/GDP (%) 0.0083 s06bsk0 Return on Assets (%) ⇒0 s05wdi0 Number of Listed Companies(1) ⇒0 s02nbf0 Mutual Fund Assets/GDP (%) ⇒0 Notes: This table shows the Lasso penalised regression estimates of φα . These were computed with a mean squared error (MSE) cross-validated complexity parameter λ. Coefficients that are shrunk towards zero by the Lasso estimator are denoted by ⇒ 0. (1) denotes values that have been log transformed. 50