1

Is there a relationship between Islamic banking and economic growth?

Evidence from panel smooth-transition models

Walid Mensia,b,*

, Shawkat Hammoudehc,d

, Aviral Kumar Tiwarid, Khamis Hamed Al-

Yahyaeeb

aDepartment of Finance and Accounting, University of Tunis El Manar, Tunis,

Tunisia

bDepartment of Economics and Finance, College of Economics and Political

Science, Sultan Qaboos University, Muscat, Oman cLebow College of Business, Drexel University, Philadelphia, United States

dEnergy and Sustainable Development (ESD), Montpellier Business School, Montpellier,

France

Abstract This study examines the nonlinear relationship between Islamic banking development, key

macroeconomic variables and economic growth for Islamic countries using panel smooth

transition models. The results show a positive nonlinear relationship between Islamic banking

development and economic growth for those countries. Moreover, the relationship between the

macroeconomic variables and economic growth is asymmetric and regime-dependent. Using

those relatively novel panel models, we find evidence that the Islamic banking variables lead

economic growth across quantiles. Specifically, foreign direct investment, one-year lag

economic growth and the terms of trade have a positive impact on economic growth at

different economic (recessionary, normal and expansionary) conditions, while the effect of the

remaining variables (i.e., inflation, human capital index and oil production) is negative.

JEL classification: C58; F65; G12; G15

Keywords: Islamic bank, economic growth, macroeconomic factors, panel smooth transition model,

dynamic panel quantile model.

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1. Introduction

The global Islamic finance industry, as a business model of ethical investing and an

alternative to conventional finance, has been in an upward growth trajectory and has gathered

more momentum in the wake of the 2008-2009 global financial crisis (GFC).1 As this recent

serious crisis morphed into a series of unparalleled financial meltdowns and disruptions in the

international financial system, Islamic financial institutions were less affected, perhaps due to

their Shari'ah-based fundamental operating principles of risk sharing and avoidance of

leverage and speculative financial products. Islamic banks have also a relatively high

capitalization, which when combined with high liquidity reserves serves as a buffer during

financial crises.

There are views which argue that the Islamic banking sector was largely insulated

from the GFC across the globe (Yılmaz, 2009) by their principled environment, that is, by

providing Shariah-compliant modes of funding and financing. This sector continues to

observe rapid growth and demonstrates resilience despite the highly persistent uncertainty

prevailing in the world’s economy.2 It complies with the Shari'ah principles that prohibit the

payment or acceptance of interest charges (known as Riba or interest) for lending and

accepting money, and forbid conducting business in certain industry activities that provide

goods or services considered contrary to those principles (known as Haram or the forbidden).

The Islamic banking sector is the largest segment of the global Islamic finance industry

because 80% of the Islamic financial assets are held within this banking sector. While this

sector provides an alternative investment to Muslim investors, Islamic banking is not

restricted to Muslims or Muslim countries.

1 The Islamic finance industry is expected to achieve further developments in the future, particularly by

introducing new products and services and tapping new markets to reach a wider range of customers. 2 The firm Ernst and Young reports that although the Islamic banks serve 38 million customers globally, almost

80% of the potential customer base for Islamic finance remains untapped, and the Sharia-compliant assets

constitute about 1% of the global financial assets.

3

According to The Banker (2017), there are over 700 Islamic financial institutions,

recognized globally, serving 38 million customers and operating in over 60 countries, 250 of

which are located in the GCC countries, about 100 in other Arab countries, 41 in Malaysia

and 28 in Iran.3

An Islamic banking jurisdiction is considered systematically important when the local

Islamic banking sector commands a certain percentage in a total domestic banking industry or

a certain proportion in the global banking industry. The sector in a country is considered

systemically important when the Islamic banking assets in that country comprise more than

15% of the assets of its total domestic banking sector or when those assets hold at least 5% of

the global Islamic banking assets. Based on this consideration, Saudi Arabia, Malaysia,

United Arab Emirates (UAE) and Bangladesh can be considered systematically Islamic

jurisdictions. The Saudi Islamic banking sector represents 51.3% of the total domestic

banking assets, and also accounts for 18.6% of the global Islamic banking assets in the first

half of 2014. In Malaysia, the Islamic banking assets as a proportion of the total domestic

banking assets represent 21.9% and also account for 9.6% of the global Islamic banking

assets. The corresponding proportions for UAE and Bangladesh are about 17.4% and 17% of

their domestic banking assets, respectively. The shares of the Islamic banking sector as a

proportion of the domestic total banking sector for other systemically important jurisdictions

are as follows: Brunei (41%), Kuwait (38%), Yemen (27.4%) and Qatar, (25.1%). With these

important shares of the Islamic banking in the financial sectors in Islamic countries, it is

interesting and valuable to examine the relationship between Islamic banking and economic

development in those countries, taking into account the nature of this relationship and nuances

of Islamic financial development.

3 http://www.uabonline.org/en/research/financial/recentglobaldevelopmentsofislamicbanking/7471/0.

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Since financial development is indispensable for economic growth, a large body of the

literature addresses the relationship between conventional banking sector development and

economic growth (see Abu-Bader and Abu-Qarn, 2008; Ang, 2008; Bojanic, 2012; Chaiechi

2012; Hsueh et al., 2013; Jalil et al., 2010; Kar et al., 2011; Menyah et al., 2014; Pradhan, et

al., 2014; Wu et al., 2010, among others). In contrast, little attention has been paid to

examining whether the Islamic banking sector fosters economic growth despite the fact that

Islamic finance is one of the most prominent emerging phenomena in the banking industry in

the Middle East and South-East Asia over the last decade (Gheeraert, 2014).

Islamic banks give a high proportion of their loans to construction and real estate

projects, which in turn contribute to expanding capital stock that is a primary source of

economic growth. They can increase the savings of pious individuals who refrain from

depositing their money in conventional banks, which sequentially raises the pool of domestic

savings and enhances financial intermediation. Islamic banks also contribute to financial

stability which is a catalyst for economic growth. They do not have mismatches between their

assets and liabilities since their short-term deposits finance short-term trading. Moreover, their

longer-term deposits fund their longer-term investments (Mirakhor, 2010). There is also

evidence which shows that the development of Islamic banking influences macroeconomic

efficiency in many countries (Gheeraert and Weill, 2015).

In this framework, the aim of this study is to explore whether Islamic banking leads to

economic growth for Islamic countries in the Middle East and North Africa (MENA) and non-

MENA regions over the period 1994 to 2014. More precisely, we address the following

unanswered questions: What are the impacts of both Islamic banking development and the

influential global macroeconomic factors under consideration on the economic growth for the

Islamic countries? Are the relationships asymmetric and nonlinear? Do the linkages depend

on the regimes of financial development? It is also worth noting that the development of

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Islamic banking can be represented by different measures including the amount of loans

extended by these banks to the private sector over GDP, Islamic banking total assets/GDP,

and deposits in Islamic banks/GDP. The latter measure is a useful indicator because it can

gauge the ability of Islamic banks to mobilize savings.

As a robustness check, we consider within the Islamic financial development-

economic growth nexus various economic and financial key factors including government

consumption, foreign direct investments, human capital, inflation, oil production, trade

openness, rule-of-law and terms of trade. Our analysis is motivated by the fact that the Islamic

banking-economic growth nexus is also of significant interest to policymakers and

institutional organizations due to the reasons indicated earlier. In fact, this topic is of great

importance for the countries concerned with developing their Islamic banking.

The contribution of this study to the related literature is three-fold. First, it examines

the nonlinear relationship between Islamic banking development and global macroeconomic

variables and the impact of this relationship on economic growth under different financial

regimes, which have several implications for policymakers who favor the expansion of their

Islamic banking sector. Second, it considers Islamic countries in both the MENA and non-

MENA regions in which the Islamic banking sector exhibits an impressive growth trend.

Islamic banks’ assets are growing at a faster rate than those of their conventional counterparts

in those countries and have become an important element in their societies’ development

endeavors. Third, as far as the empirical methodological framework is concerned, the paper

applies a non-linear hybrid approach namely the dynamic panel smooth-transition models to

assess the behavioral relationships between Islamic banks and economic growth under several

economic conditions.

More precisely, we attempt to capture whether these linkages vary under different

regimes. Specifically, the panel smooth transition regression (PSTR) model allows one to

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obtain a better understanding of this topic. It is worth noting that the main shortcoming of the

dynamic panel model without smooth transition is related to its inability to capture the

nonlinear behavior relationships between the variables during different economic or financial

conditions. However, PSTR gives room for incorporating regime-switching behavior both

when the exact time of the regime change is not known with certainty and when there is a

short transition period to a new regime. Therefore, the smooth-transition (STR) model

provides additional information on the dynamics of variables that shows their value even

during the transition period. Therefore, the STR model is a good candidate to be added to the

dynamic panel to form the PSTR in order to determine the nonlinearities and the regime

switching present in the data.

The selection of this model is usually justified by the fact that the responses of

economic variables, particularly economic growth, to shocks in the financial variables are

slow and not abrupt during the recession-normality-expansion economic stages of the

business cycles. Thus, the PSTR allows the coefficients of the exogenous variables to vary

between the variables and over time, depending on the changes in the threshold variable(s).

This model also provides a parametric approach of the cross-bank heterogeneity and of the

time instability of the coefficients, since these parameters change smoothly as a function of a

threshold variable. Analyzing this relationship in the recession-normal-expansion nature

contributes to the literature on the Islamic banking development-economic growth nexus.

Our results show evidence of a threshold level for the financial development. In

addition, they highlight that for the Islamic countries there is a nonlinear relationship between

Islamic banking development, macroeconomic variables and economic growth. Islamic bank

loans are statistically significant and positive for the intermediate (i.e., normal financial

development) regime and negative for the high (highly expansionary development) regime.

Moreover, we find that almost all macroeconomic conditions have a significant asymmetric

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impact on economic growth. More precisely, increases in inflation and oil prices affect

significantly and positively economic growth. Education has a negative impact in the low and

intermediate regimes but positive for the high regime. Foreign direct investment contributes to

economic growth (EG) during the high regime. By using the dynamic panel quantile model,

we find a positive relationship between Islamic banking development and economic growth

for different quantiles. For the remaining variables, only foreign direct investment and terms

of trade affect positively economic growth at different quantiles, while the other variables

negatively affect economic growth for almost all quantiles.

The remainder of this paper is organized as follows. Section 2 presents the literature

review. Section 3 discusses the methodology. Section 4 provides the data and the descriptive

statistics. Section 5 reports and analyzes the empirical results. Section 6 concludes the paper

and discusses policy implications.

2. Literature review

Due to the importance of the relationship between financial banking sector

development and economic growth for a country, many studies have been conducted on this

causal relationship since the seminal works of McKinnon (1973), Shaw (1973), King and

Levine (1993), among others. Following the onset of GFC, an emerging body of the literature

has addressed the Islamic banking development-economic growth nexus. For instance, Abduh

and Omar (2012) evaluate the short-run and the long-run relationships between Islamic

banking development and economic growth in the case of Indonesia. Using the bounds testing

approach of cointegration and the error correction model, developed within the autoregressive

distributed lag (ARDL) framework, those authors find evidence of short-run and long-run

relations between Islamic financial development and economic growth. They add that the

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relationship is neither a Schumpeter’s supply-leading nor a Robinson’s demand-following but

it appears to be a bi-directional relationship.

Pradhan et al. (2014) examine the relationship between banking sector development,

stock market development, economic growth, and four other macroeconomic variables for the

ASEAN countries over the period 1961–2012. Using the principal component analysis for the

construction of the development indices and a panel vector auto-regressive model for testing

the Granger causalities, the authors find strong evidence of both unidirectional and

bidirectional causality links between the considered variables. Moreover, Pradhan et al.

(2015) examine the linkages between economic growth, oil prices, stock market depth, real

effective exchange rate, inflation rate and real rate of interest for the G-20 countries. The

results show a robust long-run economic relationship between economic growth, oil prices,

stock market depth, real effective exchange rate, inflation rate and real interest rate. In the

long run, real economic growth is found to respond to any deviations in the long-run

equilibrium relationship that are found to exist between different measures of stock market

depth, oil prices and other macroeconomic variables. In the short run, the authors find a

complex network of causal relationships between the variables. Overall, the authors find clear

evidence that real economic growth responds to various measures of stock market depth,

while allowing for real oil price movements and changes in the real effective exchange rate,

inflation rate and real rate of interest.

Furqani and Mulyany (2009) use the cointegration test and the vector ECM to examine

the dynamic linkage between Islamic banking and economic growth in Malaysia, and show

that in the short-run only fixed investment Granger causes Islamic banking. In the long-run,

the authors provide evidence of a bidirectional relationship between Islamic banking and fixed

investment. They also find evidence supporting the demand-following hypothesis of GDP and

Islamic banking, attesting that increases in GDP cause Islamic banking to develop more, and

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not vice versa as stated by the supply-leading hypothesis. Using panel cointegration approach

models, Farahani and Dastan (2013) document the presence of positive long run evidence

between Islamic banks’ financing and both economic growth and capital accumulation in

Malaysia, Indonesia, Bahrain, UAE, Saudi Arabia, Egypt, Kuwait, Qatar and Yemen.

Applying the Granger causality test, the authors reveal a positive and statistically significant

relationship between economic growth and Islamic banks’ financing in the short run and in the

long run. In addition, they show that the long run relationship is stronger than the short run

one. Tabash and Dhankar (2014) evaluate the linkage between the development of the Islamic

finance system and economic growth and its direction in Qatar over the period 1990-2008.

Using the unit root test, cointegration and Granger causality tests, the results show strong

evidence of a positive long-run relationship between Islamic banks’ financing and economic

growth in Qatar. Furthermore, they also indicate that Islamic banks’ financing has contributed

to a positive increase in investment in the long term in Qatar.

More interestingly, Gheeraert and Weill (2015) assess whether the development of

Islamic banking influences macroeconomic efficiency. Using a stochastic frontier approach to

estimate technical efficiency at the country level for a sample of 70 countries over the period

2000 to 2005, the authors provide evidence that Islamic banking development enhances

macroeconomic efficiency. Moreover, they show a non-linear relationship between efficiency

and Islamic banking development. More recently, Imam and Kpodar (2015) study the

relationship between Islamic banking development and economic growth in a sample of low

and middle-income countries over the period 1990-2010 and find that Islamic banking is

positively associated with economic growth even after controlling for various determinants,

including the level of financial depth. Using a sample of 22 Muslim countries with dual-

banking systems, Abedifar et al. (2015) find a significant positive relationship between the

market share of Islamic banks and the development of financial intermediation, financial

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deepening and economic welfare, particularly in the low income or predominantly Muslim

countries, and countries with comparatively a higher uncertainty avoidance index.

3. Methodology

3.1. PSTR specification

To study the relationship between Islamic banking development and economic growth

for the Islamic countries under consideration, we need to examine the relationships under

different smooth regime switches since this evolutionary relationship for panel data is not

abrupt or sudden, given the slow reactions of economic variables to changes in financial

variables.

Recent empirical studies show that smooth–transition (STR) models can successfully

model economic time series that move smoothly between two or more regimes (e.g.,

recessions to expansions). When considering the joint dynamic properties of real GDP growth

and Islamic banking development, in the presence of other considered variables that impact

real GDP growth, it is natural to have a multivariate dynamic panel extension of the STR

model. Among many others, van Dijk et al. (2002) discuss the STR models. Montgomery et

al. (1998) and Marcellino (2004) report favorable forecasting performance for the STR model

forecasts, while Stock and Watson (1999) show that linear models generally dominate

nonlinear models in terms of forecasting performance.4

A simple PSTR model5 with two extreme regimes and a single transition function can

be defined as:

4 Despite specification difficulties, such as the specification of the appropriate transition variable, the number of

regimes, the type of transition functions, and so on, the STR models still prove useful for state-dependent

multivariate relationships. Recent applications (e.g., Rothman et al., 2001; Psaradakis, et al., 2005; Tsay, 1998;

De Gooijer and Vidiella-i-Anguera, 2004) find that the STR approach successfully models nonlinear economic

time-series data. González, et al. (2005) and Fok et al. (2005) extend the STR models to non-dynamic panels. 5 The panel smooth transition (PSTR) approach caters for the heterogeneity problem in a non-linear framework

in panel data. A PSTR model is a fixed effects model with exogenous regressors. This framework is therefore a

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ititititiit cqgxxy ),;('

1

'

0 (1)

where , , and and denote the cross-section and time-dimension of

the panel, respectively. The dependent variable ity (economic growth) is a scalar,

i

represents the fixed country effects, itx is a k-dimensional vector of time-varying exogenous

variables (all independent variables include lagged GDP, Islamic banking development,

inflation, oil production, government consumption, trade openness, terms of trade, rule of law,

education, human capital index, foreign direct investment and financial development), g(.) is

the transition function, itq is the threshold variable (financial development, FD), c is the

threshold parameter (financial development threshold) and it is the residual term. The slope

parameter denotes the smoothness of the transition from one regime to the other.

As , the transition function approaches an indicator function )( jit cqI that

takes the value of 1 if jit cq . That is, as , the transition function becomes a

homogenous or a linear panel regression model with fixed effects. Ibarra and Trupkin (2011)

point out that if is sufficiently high, then the PSTR model reduces to a threshold model with

two regimes as in Khan and Senhadji (2001). Therefore, in such a case, the effect of Islamic

banking development (IBD) on economic growth (EG) will be given by the estimated

parameter '

0 for those countries with FD (the threshold variable) less than or equal to jc ,

and by '

1

'

0 for those countries where FD exceeds jc .

panel model with coefficients that vary across individuals and over time. It is an extension of the smooth

transition regression (STR) modelling of time series to panel data with heterogeneity across the panel members

and over time (Chang and Chiang, 2011). It allows for heterogeneity in the regression coefficients by assuming

that those coefficients are continuous functions of an observable variable through a bounded function of such

variable, referred to as the transition function that fluctuates between extreme regimes (González et al., 2005).

The fact that the transition variable is cross section-specific and time-varying implies that the regression

coefficients for each of the cross-sections in the panel are changing over time.

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The transition function ),;( cqg it is a continuous function of the observable variable itq

and is normalised to be bounded between 0 and 1. These extreme values are associated with

regression coefficients '

0 and '

1

'

0 . In general, the value of ),;( cqg it , and thus the effects

of IBD on EG are given as:

),;('

1

'

0 cqgx

ye it

it

itit

for country i at period t . (2)

We follow Granger and Terasvirta (1993), Terasvirta (1994), Jansen and Terasvirta

(1996), and Gonzalez et al. (2005) and consider the following logistic transition function:

1

1

)(exp1),;(

m

j

jitit cqcqg (3)

where )',...,( 1 mccc is an m -dimensional vector of location parameters, 0 and

mccc ,...,21 are identification restrictions. The PSTR model can be generalised to allow for

more than two different regimes as follows:

it

r

j jj

j

itjitjitiit cqgxxy 1

''

0 ),;( (4)

where the transition functions ),;( jj

j

itj cqg , rj ,...,1 depend on the slope parameters j

and on the location parameters jc . If 1r for jg , rj ,...,1 , it

j

it qq , and j ,

rj ,...,1 , the transition function becomes an indicator function, with I[A]=1 if event A

occurs, and I[A]=0 otherwise. Then the model in Equation (4) becomes a PTR model with

1r regimes. Therefore, this multi-level PSTR can be viewed as a generalization of the

multiple regime PTR model developed in Hansen (1999).

3.2. Specification testing procedure for the PSTR model

González et al. (2005) outline a procedure for testing linearity against a PSTR model.

This is deemed important since the PSTR model is not identified if the data-generating

process (DGP) is linear. Therefore, a linearity test is viewed to be necessary to avoid the

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estimation of unidentified models. The null hypothesis is: 0: 10 H . However, the test is

non-standard because under this null hypothesis, the PSTR model contains unidentified

nuisance parameters (Hansen, 1996). Therefore, we adopt a possible solution developed by

Luukkonen et al. (1988) and replace the transition function ),;( cqg it by its first-order Taylor

expansion around 0 and test the linearity hypothesis as 0:0 H . After re-

parameterization, this restriction leads to the following auxiliary regression:

it

m

ititmitititiit qxqxxy *... '*'*

1

'*

0 (5)

where the parameter vectors '*'*

1 ,..., m are multiples of and itmitit xR '*

1

* , where mR is

the remainder of the Taylor expansion. Therefore testing 0:0 H in Equation (4) is

equivalent to testing 0...:* '*'*

10 mH in Equation (5). Then standard tests can be

applied.

We follow Colletaz and Hurlin (2006) and use the Wald, Fischer and Likelihood ratio

tests to test whether 0...:* '*'*

10 mH in Equation (5), that is, to test the null hypothesis

of zero equality of the beta coefficients of the threshold variable. The Wald LM test can be

expressed as follows:

0

10 )(

SSR

SSRSSRNTLMW

(6)

where 0SSR is the panel sum of squared residuals under the null H0 (i.e., the linear panel

model with individual effects) and 1SSR is the panel of sum of squared residuals under the

alternative H1 (i.e., the PSTR model with m regimes). The Fischer LM test can be written as:

)(

/)(

0

10

mkNTNSSR

mkSSRSSRNTLM F

(7)

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with an approximate distribution of ),( mkNTNmkF , where k is the number of

explanatory variables, m is maximum number of thresholds, and N and T are defined earlier.

The likelihood ratio test can be expressed as:

)]log()[log(2 01 SSRSSRLR (8)

All these linearity tests are distributed )(2 k under the null hypothesis. According to

Teräsvirta (1994), the linearity tests also serve to determine the appropriate order of m of the

logistic transition function in Equation (1) or equivalently the order of extreme regimes. We

therefore test the null of no remaining non-linearity in the transition function. Consider the

auxiliary regression Equation (5) with 2r or three regimes:

ititititititiit cqgxcqgxxy *),;(),;( 22

2

2

'*

211

1

1

'*

1

'*

0 (9)

The null hypothesis of no remaining heterogeneity in an estimated three-regime PSTR

model can be formulated as 0: 20 H in Equation (9). However, as already indicated, this

test is non-standard because under this null hypothesis the PSTR model contains unidentified

nuisance parameters. Therefore, this identification problem is circumvented by replacing the

transition function, ),;( 22

2

2 cqg it by the Taylor expansion around 02 , resulting in the

following auxiliary regression:

ititititititiit qxcqgxxy *),;( 11

1

1

'*

1

'*

0 (10)

where is a coefficient associated with qit and is time varying repressor.

Using the auxiliary regression Equation (10) with 2r , testing the null hypothesis of

no remaining non-linearity is defined as 0:0 H . Denote 0SSR as the panel sum of the

squared residuals under 0H (i.e., in a PSTR model with one transition function), and

1SSR as

the sum of the squared residuals of the transformed Equation (10). Given a PSTR with *r

transition functions, the procedure is as follows: test *:0 rrH against 1*:1 rrH . If 0H

is not rejected, then the procedure ends. Otherwise, the null hypothesis 1*:1 rrH is

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tested against 2*:1 rrH . The testing procedure continues until the first acceptance of the

null hypothesis of no remaining heterogeneity. It should be kept in mind that at each step of

the sequential procedure, the significance level must be reduced by a constant factor , such as

10 in order to avoid excessively large models. As suggested by González et al. (2005),

we assume that 5.0 .

4. Data and stochastic properties

4.1. Sample data

We use annual data for 19 Islamic countries in the MENA and non-MENA regions

(see Table 1). The sample period spans the period from 1994 to 2014, whose start is dictated

by the availability of data for all the countries under consideration. Further, this period is

marked by several episodes of wide instabilities and crises, and thus covers major regional

and global events such as intervals of sharp fluctuations in crude oil markets (particularly in

summer 2008 and mid-2014), the 2001 U.S. terrorist attack, the 2003 Gulf war, the Lehman

Brothers collapse on September 15, 2008, the 2008–2009 GFC and the 2010–2012 Eurozone

sovereign debt crisis. The global economic factors we use in this study provide further

understanding of economic growth in the Islamic countries.

Table 1: List of selected Islamic countries.

MENA Non-MENA

Bahrain Bangladesh

Kuwait Brunei Darussalam

Qatar Gambia

Saudi Arabia Malaysia

United Arab Emirates Pakistan

Jordan Indonesia

Lebanon

Egypt

Turkey

Tunisia

Iran

Sudan

Mauritania

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The data cover the following variables: (a) economic growth which is the dependent

variable and measured by the GDP growth and/or per capital GDP growth rate. (b) The

explanatory variables related to Islamic banking which are the Islamic bank total assets-to-

GDP ratio, the Islamic bank deposits-to-GDP ratio, the Islamic bank loans-to-GDP ratio and

the Islamic bank net loans-to-GDP ratio. The control variables include measures of financial

development, foreign direct investments, government consumption, education, government

consumption, trade openness, rule-of-law, terms of trade, oil production and consumer price

index as a proxy of inflation. The choice of this set of explanatory variables is motivated by

their strong links with the economic growth literature. All the variables are listed in Table 2.

For the Islamic banks, the data are compiled from the World Bank Islamic Group. For

the rest of variables, they are accessed from different sources including the World Bank, IHS

Global Insight, Penn World Table (PWT) 8.0, and the U.S. Energy Information

Administration (EIA).

4.2. Descriptive statistics

Table 3 presents the descriptive statistics of the variables used in this study. We find

that the mean of all variables (except the rule of law) is positive. The FDI variable presents

the highest volatility as measured by the standard deviations, followed by the four proxy

variables of Islamic bank development. Further, all these considered variables deviate from

the Gaussian distribution since their skewness and kurtosis coefficients are different from zero

and three, respectively. This result is confirmed by the Jarque-Bera test.

The correlation matrix results reported in Table 4 show no significant multicollinearity

problem between the endogenous and exogenous variables as the correlation coefficients are

low or negative. For example, that the economic growth variables (dependent variables) are

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negatively correlated with the Islamic bank variables (total loans, net loans, total assets and

total deposits over GDP). The human capital index, inflation, oil production, the rule of law

and financial development are negatively correlated with economic growth but the

correlations are weak. Furthermore, there are no collinearity between the exogenous variables

themselves as the correlation coefficient values between those variables are very low and

close to zero for almost all cases.

Before the estimation step, we check the stationarity of the variables making up the

panels under consideration. Specifically, we use four popular panel unit root tests namely the

panel Augmented Dickey and Fuller, Phillips and Perron, LLC and IPS tests developed by

Dickey and Fuller (1979), and the Phillips and Perron (1988), Levin, Lin and Chu (2002), and

Im, Pesaran and Shin (2003), respectively.

The results of the estimation of these tests for both series in the level (Panel A) and

series in the logarithm (Panel B) are reported in Table 5. For the level series, we find weak

evidence for stationary (GDP growth, GDP per capita growth, human capital index and

inflation series). When we examine the series in a logarithmic form, we find strong evidence

that the null hypothesis of the panel unit roots can strongly be rejected for all the logarithmic

series under consideration. This indicates that the logarithmic series are stationary at a

conventional level of significance (almost all cases are significant at the 1% level). Thus, the

empirical model can be regressed in this logarithmic form.

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Table 2: Definitions and measures of the variables

Variables Definitions & Measures Sources

Panel A: Dependent variables

Economic Growth (Growth) GDP growth (GRGDP) or per capita GDP growth (GRGDPPC) rates World bank

Panel B: Explanatory variables

Lagged GDP One-year lag GDP growth or one-year lag per capita GDP growth rate World bank

Different measures of financial development of

Islamic banking:

*Islamic banking assets-to-GDP ratio (IBASSET).

*Islamic banking loans-to-GDP ratio (IBLOAN): Amount of loans extended by

these banks to the private sector/GDP (Sharia compliant private credit-to-GDP)

which measures the development of Islamic banking in the overall banking

system.

* Islamic bank net loans-to-GDP ratio (IBNETLOAN).

World bank

Level of development of Islamic banking

(IBDEPOSIT)

*Islamic bank deposits-to-GDP ratio: a useful indicator to gauge the ability of

Islamic banks to mobilize savings.

World bank

Panel C: Control variables

Inflation (INFCPI) Inflation as measured by changes in the consumer price index reflects the

annual percentage change in the cost to the average consumer of acquiring a

basket of goods and services that may be fixed or changed at specified intervals,

such as years.

World bank indicators

Oil production (OILPRODGDP) Number of barrels produced each year by a country. Energy Information

Administration

Government consumption (GOVCON) Government consumption includes all government current expenditures for

purchases of goods and services (including compensation of employees). It also

includes most expenditures on national defense and security, but excludes

government military expenditures which are part of government capital

formation.

World bank indicators

Trade Openness (OPEN) Exports of goods and services represent the value of all goods and other market

services provided to the rest of the world. They include the values of

merchandise, freight, insurance, transport, travel, royalties, license fees, and

other services, such as communication, construction, financial, information,

business, personal, and government services. They exclude compensation of

employees and investment income (formerly called factor services) and transfer

payments.

World bank indicators

Terms of Trade (TOT) The terms of trade effect is equal to capacity to import less exports of goods

and services in constant prices.

Penn Word Tables

19

Rule of Law (RULELAW) Rule of law captures perceptions of the extent to which agents have confidence

in and abide by the rules of society, and in particular the quality of contract

enforcement, property rights, the police, and the courts, as well as the likelihood

of crime and violence.

World bank indicators

Education (EDU) Gross enrollment/GDP ratio, primary, both sexes (%) World bank indicators

Human capital index (HC) The Human Capital Index is a new measure for capturing and tracking the state

of human capital development around the world.

Penn World Tables

Foreign direct investment (FDIGDP) Foreign direct investment refers to direct investment equity flows in the

reporting economy. It is the sum of equity capital, reinvestment of earnings, and

other capital. Direct investment is a category of cross-border investment

associated with a resident in one economy having a control or a significant

degree of influence on the management of an enterprise that is resident in

another economy. Ownership of 10 percent or more of the ordinary shares of

the voting stock is the criterion for determining the existence of a direct

investment relationship.

World bank indicators

Financial development (FD) Ratio of private sector credits by bank and nonbank financial institutions over

GDP. Domestic credit-to-private sector refers to financial resources provided to

the private sector by financial corporations, such as through loans, purchases of

non-equity securities, and trade credits and other accounts.

World bank indicators

Notes: This table summarizes the variables used in this study and their corresponding measures and sources. The definitions of these variables are extracted from the World Bank.

Table 3: Descriptive statistics.

FDIGDP GRGDP GOVCON GRGDPPC HC IBASSET IBDEPOSIT IBLOAN IBNETLOAN INFCPI OILPRODGDP OPEN RULELAW EDU FD TOT

Mean 208.0466 4.637118 0.426230 1.603208 3.834933 30.50391 45.64906 104.3637 119.4349 6.272948 1.931058 2.278461 -8.810689 0.725508 3.304665 1.539277

Median -5.067721 4.655519 -0.512445 2.105129 3.194655 5.764509 7.082682 3.873187 4.727165 -4.224133 -9.114622 0.998640 -1.740285 0.445922 1.972685 1.397686

Maximum 61138.63 35.98001 67.96181 15.65423 26.57903 1634.423 4312.089 9298.422 8944.668 2206.687 1433.530 116.4330 400.1545 325.3383 73.87551 18.31225

Minimum -26141.69 -9.679454 -24.22360 -15.14583 -7.277613 -99.19322 -99.89677 -99.53080 -99.58698 -875.7660 -73.20950 -42.97039 -1024.265 -82.90443 -34.64929 -11.77953

Std. Dev. 3638.392 4.429156 11.03694 3.797873 3.854028 142.2904 259.1277 714.1094 732.1873 187.4142 91.75938 14.97079 97.60753 18.68593 12.90226 5.148476

Skewness 11.84686 1.474204 1.892919 -0.646515 2.457328 8.105202 12.68383 10.20192 9.220226 3.609529 13.44292 2.268807 -5.143899 13.19663 0.828494 0.235872

Kurtosis 217.4127 12.25747 11.56198 5.045183 13.08314 79.57178 198.1846 114.4109 95.21532 57.78721 200.6840 17.84662 51.60574 243.6757 6.026515 2.618969

Jarque-Bera 736791.6 1494.568 1387.635 92.69944 1992.207 96995.23 613392.2 203121.2 140025.5 48351.09 510789.8 3816.025 39082.32 928172.3 188.5023 5.822358

Probability 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.054412

Observations 380 380 380 380 380 380 380 380 380 380 308 380 380 380 380 380

Notes: This table presents the descriptive statistics of economic growth, Islamic bank development and macroeconomic variables for nineteen Islamic countries over the period 1994-2014. GRGDP is the GDP growth, GRGDPPC is the per capita GDP growth rate, IBASSET is the Islamic bank assets-to-GDP ratio, IBDEPOSIT is the Islamic bank deposit-to-GDP ratio. IBLOAN is the Islamic bank loans-to-

GDP, IBNETLOAN is the Islamic bank Net Loan to GDP ratio. EDU is education, FD is financial development, FDIGDP is the foreign direct investments to GDP ratio, GOVCON is government

consumption to GDP ratio, HC is the Human capital index (Source: Penn World Tables). INFCPI is the CPI inflation, OILPROD is the oil production, OPEN is the openness, RULELAW is the rule of law

and TOT is the terms of trade (Source: Penn Word Tables).

20

Table 4. Correlation coefficient matrix of the variables.

FDIGDP GRGDP GOVCON GRGDPPC HC IBASSET IBDEPOSIT IBLOAN IBNETLOAN INFCPI OILPRODGDP OPEN RULELAW EDU FD TOT

FDIGDP 1.000000

GRGDP 0.079605 1.000000

GOVCON -0.105804 -0.310889 1.000000

GRGDPPC 0.095144 0.607172 -0.271098 1.000000

HC -0.038977 0.346756 -0.029529 -0.210348 1.000000

IBASSET -0.048849 -0.020173 -0.013237 -0.008019 -0.027349 1.000000

IBDEPOSIT 0.025746 -0.011947 -0.083293 -0.004371 -0.035204 0.350620 1.000000

IBLOAN -0.008289 -0.017029 -0.024690 -0.004892 -0.027913 0.732686 0.129588 1.000000

IBNETLOAN -0.010247 -0.010732 -0.009650 -0.006895 -0.025208 0.695776 0.102353 0.898468 1.000000

INFCPI 0.003428 -0.048068 -0.156328 -0.072935 0.025026 0.028430 0.024861 -0.024364 -0.016054 1.000000

OILPRODGDP 0.003250 -0.040831 0.098808 -0.030873 -0.027588 0.000213 -0.010482 -0.006288 0.011836 -0.005192 1.000000

OPEN -0.015146 0.106455 -0.107593 0.020490 0.001626 -0.044023 -0.014177 0.002993 0.007843 0.113211 0.245794 1.000000

RULELAW -0.001329 -0.013591 -0.019594 -0.017422 0.042458 0.005488 0.018269 -0.006640 0.003676 -0.051854 0.007056 -0.027056 1.000000

EDU 0.031131 0.000256 -0.014141 0.026021 0.002180 0.008869 0.035606 0.007495 0.007300 -0.013373 0.004886 0.007693 -0.014052 1.000000

FD 0.009068 -0.078302 0.345698 -0.077319 0.129677 0.087790 0.027137 0.144158 0.073698 -0.089683 0.246735 0.062876 0.030161 0.000463 1.000000

TOT 0.061826 0.228685 -0.231985 0.221675 0.109939 -0.071306 -0.062935 -0.081002 -0.033625 0.117388 -0.157880 0.062697 0.036628 -0.029145 -0.034294 1.000000

Note: This table summarizes the correlations between the variables (in the level) used in this study

Table 5. Panel unit root tests.

FDIGDP GRGDP GOVCON GRGDPPC HC IBASSET IBDEPOSIT IBLOAN IBNETLOAN

Panel A: Level series

Levin-Lin-Chu test 0.34573 -4.92003*** -1.10987 -3.76126*** -7.1721*** -0.52681 -4.47549*** -0.61358 -0.67180

Im, Pesaran and Shin

test

-0.20633 -4.22865*** 0.27188 -4.22865*** 0.48535 0.41254 -0.72569 0.17174 0.73926

ADF - Fisher Chi-

square

39.9531 81.5150*** 42.7299 81.5150*** 55.4717** 38.6246 47.8962 42.2800 35.1771

PP - Fisher Chi-square 50.3923* 126.631*** 42.7051 126.631*** 16.0947 41.4265 34.5376 65.2403*** 281.597***

Panel B: Series in logarithm

Levin-Lin-Chu test -5.75085 -6.06891*** -7.75287*** -4.72536*** -3.92703*** -64.8951*** -62.9419*** -39.8605*** -10.2328***

Im, Pesaran and Shin test -6.66545*** -6.08706*** -7.94398*** -5.88767*** -5.29815*** -20.3541*** -25.1663*** -16.7326** -12.4389***

ADF - Fisher Chi- 117.322*** 107.740*** 135.519*** 107.192*** 95.5267*** 385.011*** 665.708*** 431.284*** 425.125***

21

square

PP - Fisher Chi-square 307.297*** 169.278*** 278.949*** 161.121*** 169.691*** 407.867*** 245.161*** 231.071*** 454.438***

Notes: This table presents the empirical statistics of the panel unit roots.***, **, and * indicate the rejection of the null hypothesis of a unit root at the 1%, 5% and 10% significance levels, respectively. The length of lags in the tests is chosen by SIC (Schwarz information criterion). GRGDPPC denotes per capita GDP growth rate, IBDEPOSIT refers to the Islamic bank deposits-to-GDP ratio, IBASSET represents the Islamic bank

total assets-to- GDP ratio, IBLOAN denotes the Islamic bank total loans-to-GDP ratio, OILPROD refers to the oil production-to-GDP ratio, OPEN represents the trade openness, TOT denotes the terms of trade, and

INFCPI refers to the CPI inflation rate.

Table 5. (continued)

INFCPI OILPRODGDP OPEN RULELAW EDU FD TOT

Panel A: Level series

Levin-Lin-Chu test -3.2839*** -0.73654 -1.26499 -0.62211 -0.58316 -1.14392 -3.0846***

Im, Pesaran and Shin

test

-1.86202** 0.72946 -0.50372 0.09809 -0.16303 -0.72479 -0.51546

ADF - Fisher Chi-

square

53.7399** 26.2854 42.9876 47.4639 37.9720 46.0988 33.7706

PP - Fisher Chi-square 63.3780*** 41.6629 31.2596 130.501*** 36.0424 37.6317 11.4434

Panel B: Series in logarithm

Levin-Lin-Chu test -6.31539*** -7.54032*** -8.31640*** -34.5207*** -4.59488*** -6.43934*** -8.36340***

Im, Pesaran and Shin

test -7.04390*** -6.17393*** -8.42757*** -14.4175*** -5.87782*** -7.00545*** -6.44181***

ADF - Fisher Chi-

square 120.115*** 101.634*** 143.347*** 400.684*** 105.503*** 120.803*** 108.571*** PP - Fisher Chi-square 285.039*** 146.991*** 283.695*** 428.025*** 171.678*** 239.956*** 154.601***

Notes: This table presents the empirical statistics of the panel unit roots.***, **, and * indicate the rejection of the null hypothesis of a unit root at the 1%, 5% and 10% significance levels, respectively. The length of lags in the tests is chosen by SIC (Schwarz information criterion). GRGDPPC denotes per capita GDP growth rate, IBDEPOSIT denotes the Islamic bank deposits-to-

GDP ratio, IBASSET denotes the Islamic bank total assets-to-GDP ratio, IBLOAN denotes the Islamic bank total loans-to-GDP ratio, OILPROD denotes the oil production-to-GDP ratio, OPEN

denotes the trade openness, TOT denotes the terms of trade, and INFCPI denotes the CPI inflation rate.

22

5. Empirical results

The estimated results are summarized in three sequences. First, we consider the non-

linearity tests and the determination of the number of location parameters. Second, we

estimate the PSTR models. Finally, we test the robustness of our empirical analysis using an

alternative model, namely the dynamic panel quantile model.

5.1. Linearity and no remaining non-linearity results

To justify the use of nonlinearity models, we use three linearity tests namely the Wald

test (LMW), the pseudo likelihood ratio (LRT) and the Fisher test (LMF). The results are

reported in Table 6. Specifically, we test the null hypothesis of the linear model against the

alternative hypothesis of the panel smooth transition (PSTR) model with at least one

threshold variable. We consider financial development as a threshold variable. The choice of

this variable is not arbitrary but is based on its importance for economic growth. In fact, the

contribution of the financial development to EG may be traced back to Goldsmith (1969),

McKinnon (1973) and Shaw (1973) which find positive evidence of the effect of financial

development on EG. Financial development is an important driver of the development of

stock markets and banking systems (Goldsmith, 1969; Durusu-Ciftci et al., 2016).

As shown in these tables, we reject the null of linearity for all models at the

conventional levels of significance using the three linearity tests, thereby highlighting that the

threshold variable is crucial to assess the nonlinear relationship between economic growth

and both the Islamic bank development and macroeconomic variables. This result also

confirms our intuition and motivation to consider the PSTR model.

Table 6: Estimated results of linearity tests Lagrange multiplies-

Wald tests (LMW)

Lagrange multiplies-

Fisher tests (LMF)

Likelihood ratio tests

(LRT)

Model 1 87.409 2.453 98.694

(0.000) (0.000) (0.000)

Model 2 87.667 2.463 99.025

(0.000) (0.000) (0.000)

23

Model 3 87.035 2.440 98.215

(0.000) (0.000) (0.000)

Model 4 87.829 2.469 99.233

(0.000) (0.000) (0.000)

Model 5 67.385 1.777 73.828

(0.003) (0.004) (0.000)

Model 6 66.198 1.739 72.401

(0.004) (0.005) (0.000)

Model 7 63.430 1.653 69.095

(0.008) (0.011) (0.000)

Model 8 64.778 1.695 70.701

(0.006) (0.008) (0.000) Note: The table reports the Wald (W), F, and pseudo likelihood ratio (LRT) tests of linearity against the PSTR model. P-values are in

parenthesis.

Model 1: DGPPC = F (one-lag DGPPC, IBLOAN, EDU, FD, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, RULELAW, OILPRODGDP).

Model 2: GDPPC = F (one-lag GDPPC, IBNETLOAN, EDU, FD, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, RULELAW,

OILPRODGDP). Model 3: GDPPC = F (one-lag GDPPC, IBDEPOSIT, EDU, FDI, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, RULELAW,

OILPRODGDP).

Model 4: GDPPC = F (one-lag GDPPC, IBASSET, EDU, FDI, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, RULELAW, OILPRODGDP).

Model 5: GRGDP = F (one-lag GRGDP, IBLOAN, EDU, FDI, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, RULELAW,

OILPRODGDP) Model 6: GRGDP = F (one-lag GRGDP, IBNETLOAN, EDU, FDI, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, RULELAW,

OILPRODGDP).

Model 7: GRGDP = F (one-lag GRGDP, IBDEPOSIT, EDU, FDI, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, RULELAW, OILPRODGDP).

Model 8: GRGDP = F (one-lag GRGDP, BASSET, EDU, FDI, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, RULELAW,

OILPRODGDP).

In the next step, we apply the model selection test to determine the polynomial order

in the nonlinearity test equation (m which is maximum number of thresholds). That is, we

apply the model selection test to determine the number of thresholds based on the AIC

criterion. The results are summarized in Table 7, which show evidence of the presence of one

threshold (i.e., m=1 is selected for all cases), indicating the presence of a regime-switching.

Economically, this result means that the relationship between EG and the sets of Islamic

banking development and macroeconomic variables depends on the over/under financial

development of an economy.

Table 7: Model Selection Test F test: H03:B3=0 F test: H02:B2=0|B3=0 F test: H01:B1=0|B2=B3=0

Model 1 0.874 0.776 0.683

(0.688) (0.832) (0.927)

Model 2 0.932 0.734 0.673

(0.591) (0.880) (0.934)

Model 3 0.892 0.742 0.686

(0.658) (0.872) (0.924)

Model 4 0.941 0.727 0.676

24

(0.574) (0.888) (0.932)

Model 5 0.871 0.500 0.349

(0.692) (0.995) (1.0001)

Model 6 0.788 0.497 0.402

(0.816) (0.995) (1.000)

Model 7 0.765 0.499 0.342

(0.845) (0.995) (1.000)

Model 8 0.775 0.370 0.500

(0.833) (0.995) (1.000) Note: Select m =2 if the rejection of H02 is the strongest one, otherwise select m=1. Models 1-8 are defined in the notes of Table 6. The p-

values are in the parentheses.

The estimation of the PSTR model with a regime-switching requires one to test the

remaining non-linearity. In this study, we consider that the number of thresholds ranges

between 1 and 3. The testing procedure works as follows. First, we test the null hypothesis of

the presence of one threshold against the alternative hypothesis of the PSTR model with two

thresholds. If we do not reject the null, we assume the PSTR model with one threshold (or

two regimes). In contrast, the rejection of the null requires testing the null of two thresholds

against the alternative hypothesis of three thresholds. Further, we have reported only the

estimation of no remaining non-linearity of the first model in Table 8.6 As shown in this table,

we reject the null of the presence of one threshold (or two regimes) but if we look at the

results of two thresholds, we do not reject the null of double thresholds. This result implies

that the model has two thresholds or three regimes (low financial development, intermediate

financial development and high financial development regimes). The interpretations of the

remaining tables are similar. In fact, we show that the optimal (LMR criterion) number of

threshold functions is r=2, for all models with the exception of Models 2 and 4, given the

choices of rmax =3 and m=1 (i.e., m is the maximum number of thresholds), respectively. In

fact, we do not reject the null hypothesis of no remaining non-linearity. This result indicates

no misspecification of our models.

Table 8: Testing the number of regimes (tests of no remaining non-linearity)

6 To save space, the no-remaining non-linearity results of the remaining models are not reported here but are

available upon request.

25

H0: PSTR with r = 1 against H1:

PSTR with at least r = 2

H0: PSTR with r = 2 against

H1: PSTR with at least r = 3

Model 1 Model 2

Test Statistics P-value Statistics P-value

Lagrange multiplies-Wald Tests

(LMW)

28.562 0.008 16.134 0.242

Lagrange multiplies-Fisher Tests

(LMF)

2.022 0.019 1.063 0.391

Likelihood ratio-LRT Tests (LRT) 29.639 0.005 16.470 0.225

Note: Model Based on GDPPC. Model 1: DGPPC = F (one-lag DGPPC, IBLOAN, EDU, FD, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT,

TOTCH, RULELAW, OILPRODGDP)

5.2. PSTR model estimation

After checking for no remaining non-linearity, we conduct the estimation for the

PSTR models employing eight models. The transition function plots (see the appendix)

illustrate clearly the non-linearity which exists between economic growth and financial

development following the used threshold variables. Tables 9a to 9h present the estimated

model parameters. The threshold level is found to be 80.555 and 49.50 for Model 1, 81.56 for

Model 2, 80.77 and 50.26 for Model 3 and 82.40 for Model 4 when GDP per capita growth is

considered as the dependent variable. Looking at the last four models (Tables 9e-9h), the

expected threshold is similar for these models when GDP growth is the dependent variable. It

is worth noting that the threshold level for the first four models exceeds those of the last four

models.

On the other hand, we show that the effect of almost all independent variables on EG

is nonlinear. More precisely, the one-year lag economic growth has an asymmetric effect on

EG. That is, the relationship between the past EG and the current EG is regime dependent.

This relationship is statistically significant and negative for an intermediate regime and

positive for both the extreme (low and high) regimes. This result indicates that past economic

growth promotes current economic growth under extreme financial development conditions.

Thus, policymakers can make use of the economy’s historical performance as a forecasting

indicator to implement or alter programs.

Similarly, the relationship between the Islamic bank loans and EG is nonlinear. More

26

precisely, the effect of Islamic banking loans on EG is statistically significant and positive in

the intermediate regime (or normal financial development) where there are no excessive bad

or too little lending and speculations. This result indicates that the loans of Islamic banking

contribute to the development of financial system and EG of the Islamic countries. In fact, the

banking authorities in this regime is confident and give more credit, which in turn increases

investment and consummation, resulting in improving EG. However, this relationship is

negative in the high regime (strong financial development expansion). This result indicates

the presence of an asymmetric relationship between these two variables and confirms the

validity of using the nonlinear method. The negative relationship may economically be

explained by the over private sector credits offered by banks and nonbank financial

institutions. For the low regime (financial development contraction), the relationship is

insignificant. This result may be explained by the credit rationing and the lack of confidence

by the banking authorities in the economic situation.

An asymmetric relationship is found between the threshold variable (i.e., financial

development) and EG. Indeed, it has a negative effect on EG during the low regime which

may be due to a slow financial development of the financial system. It also confirms the

existence of deficiencies in credit allocation in the Islamic countries and suggests a presence

of weak financial regulations and supervision or restrictions on credit. This relationship has a

positive effect in the high regime which entails a high financial development. This result is in

line with that of Levine (2005) which concludes that financial development contributes to

growth by providing information about potential projects, monitoring the implementation of

investments, enhancing risk management and diversification, pooling savings and facilitating

the exchange of goods and services. In fact, we can conclude that financial development

improves EG only in the high financial development regime. In contrast to the Islamic bank

loans, the Islamic bank deposits and the Islamic bank size as measured by the Islamic bank

27

total assets have a positive and statistically significant effect on EG under the normal regime

and a negative effect in the high regime. We can explain this result by the fact that Islamic

agents prefer Islamic bank as a safe place to save their funds. It is also possible that Islamic

funds feed speculations in real estate in this regime. Also, the result can be due to the

important size of some Islamic bank especially in Saudi Arabia (e.g., Al-Rajhi bank is the

largest Islamic bank in the world). In the low regime, the relationship is insignificant in this

low financial development environment.

The financial development has a negative impact on EG in the low regime and a

positive effect in the high regime when we consider Model 1 (dependent variable is GDP per

capital and the explanatory variable of Islamic banks is total loans/GDP). For Model 3

(dependent variable is GDP per capital and the explanatory variable of Islamic bank is total

deposits/GDP), we find a negative relationship with the growth of the GDP per capita for the

normal regime and a positive effect for the high regime. This result highlights that financial

development contributes to improving economic growth during high financial development

only.

Regarding the foreign direct investment, it is negatively related to the growth of GDP

per capita in the high regime (see Models 1&3). When examining the growth of GDP, we

find that FDI leads to growth of the GDP in the high regime (or high financial development)

but decreases it in the intermediate regime. This means FDI needs strong financial

development to contribute positively to economic growth.

We find little evidence of the effect of trade openness on EG. In fact, only for the first

model (Model 1) we find that EG responds positively to trade openness in the normal regime

and negatively for the high regime, which implies that trade openness supports economic

growth in an environment of normal financial but not in the case of accelerated financial

development. For the remaining cases, there is no significant effect. On the other hand,

28

government consumption has a negative and statistically significant effect on EG for the

intermediate regimes for all models (with two thresholds) and a positive effect for the high

regime for some cases. It is possible there is a crowding out from increases in government

spending in the normal regime. The human capital index has a generally insignificant effect

on EG for all models, with the exception of Model 2 for the low regime where we find a

positive and significant linkage between human capital and growth in GDP per capita.

Inflation has a statistically significant and positive effect on EG during the low and

normal financial development regimes for the first four models. In contrast, the result is

insignificant for the high regime as well as for the remaining last four models. For the first

three models (see Tables 9a-9c) oil production has a negative effect on economic growth

during only the normal regime and but is insignificant for the other regimes. This result may

be explained by the fact that almost all the countries (except those of the GCC and Iran which

could be affected by the oil curse or the Dutch disease) in our sample are net oil-importing

countries. These economies are sensitive to the oil production level, indicating a transfer of

resources from the non-oil emerging countries to the oil exporting countries when oil

production increases.

The rule of law contributes to improving the per capita GDP for both the intermediate

and high regimes which supports the old adage that best way for countries to grow is to “get

the policies right”. In contrast, the rule of law-per GDP relationship is negative at the low

regime that is when financial landscape is weak. This result indicates an asymmetric

relationship between these variables. However, the terms of trade affects positively economic

growth in the intermediate or normal regime when GDP growth is the dependent variable.

Table 9a: PSTR model estimation Model 1: Dependent variable (GDPPC), Islamic bank variable (IBLOAN)

Variable B0 B1 B2

one-lag GDPPC -0.0054 [-0.0693] -0.3954 [2.3351] 0.3634 [3.0242]

IBLOAN 0.0000 [0] 4.1558 [2.3922] -2.4589 [-2.6525]

EDU -0.0088 [-0.3706] -0.5173 [-4.7498] 0.0896 [2.3108]

29

FD -0.0036 [-2.3054] -0.1845 [-1.5226] 0.1895 [3.2212]

FDIGDP 0.0438 [1.0956] 0.0507 [0.9004] -0.1487 [-2.8631]

INFCPI 0.1047 [2.3884] 0.6069 [2.4645] -0.0739 [-0.6355]

OPEN -0.0159 [-0.8648] 0.2349 [0.6662] -0.3293 [-3.3269]

GOVCON 0.0325 [0.8411] -0.2896 [4.3290] 0.1431 [2.4402]

HC -0.0131 [2.4402] -0.4115 [-1.1158] -0.0678 [-0.5116]

TOT 0.0283 [1.0016] 1.3323 [1.0016] 0.2196 [1.7981]

RULELAW 0.6766 [0.7563] 8.4306 [2.8797] 0.5886 [0.3645]

OILPRODGDP 214.6758 [0.8295] -10596.6770 [-2.6650] 742.4794 [1.2265] Transition parameters Threshold (c) Location Parameters 80.5584 49.5049

Slope (gamma) 0.9882 0.6923

Standard Errors of Estimated Parameters Corrected of Heteroskedasticity (per column for each transition function)

Note: Model Based on GDPPC. Model 1: GDPPC = F (one-lag GDPPC, IBLOAN, EDU, FD, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, TOTCH, RULELAW,

OILPRODGDP).

Table 9b: PSTR model estimation

Model 2: Dependent variable (GDPPC), Islamic bank variable (IBNETLOAN)

Variable B0 B1 B2

one-lag GDPPC 0.1534 [2.3943] -0.0758 [-0.4265]

IBNETLOAN 0.0000 [0] 1.0354 [0.6624]

EDU 0.0296 [1.4838] -0.3084 [-3.6959]

FD -0.0030 [-1.7904] -0.0501 [-0.4478]

FDIGDP -0.0150 [-0.7154] -0.0390 [-1.2638]

INFCPI 0.0844 [2.0136] 0.6790 [3.5657]

OPEN -0.0158 [-0.8979] -0.2831 [-0.8719]

GOVCON 0.0537 [1.9848] -0.1188 [-1.8984]

HC 0.0223 [0.2510] -0.1882 [-0.5710]

TOT 0.0291 [1.0538] 0.6112 [2.1917]

RULELAW 0.9034 [1.0671] 3.4814[1.5374]

OILPRODGDP 269.2672 [1.0300] -8548.3968 [-2.7781] Transition parameters

Threshold (c) Location Parameters 81.5679

Slope (gamma) 0.2564

Standard Errors of Estimated Parameters Corrected of Heteroskedasticity (per column for each transition function)

Note: Model 2 Based on GDPPC

Model 2: GDPPC = F (one-lag GDPPC, IBNETLOAN, EDU, FD, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, TOTCH, RULELAW, OILPRODGDP)

Table 9c: PSTR model estimation Model 3: Dependent variable (GDPPC), Islamic bank variable (IBDEPOSIT)

Variable B0 B1 B2

one-lag GDPPC 0.0012 [0.0153] -0.4285 [-2.5530] 0.3944 [3.3821]

IBDEPOSIT 0.0000 [0] 4.7088[2.7830] -2.1199 [-2.3580]

EDU -0.0112 [-0.7080] -0.4628 [-5.1518] 0.0456 [1.7350]

FD -0.0027 [-1.7045] -0.2113 [-1.9234] 0.1671 [2.9355]

FDIGDP 0.0510 [1.4775] 0.0030 [0.0537] -0.1108 [-2.1508]

INFCPI 0.1038 [2.3725] 0.6376 [2.8071] -0.0492 [-0.4299]

OPEN -0.0151 [-0.8308] 0.0820 [0.2408] -0.3198 [-3.2678]

GOVCON 0.0274 [0.7487] -0.2473 [-3.8874] 0.1242 [2.3162]

HC -0.0258 [-0.2747] -0.2968 [-0.8661] -0.1232 [-0.9652]

TOT 0.0380 [1.3469] 1.3017 [3.9769] 0.1239 [1.1722]

RULELAW 0.8262 [0.9189] 8.8156 [3.1307] -0.2577 [-0.1718]

OILPRODGDP 278.2875 [1.0666] -14863.5380 [-3.6121] 709.3256 [1.2199] Transition parameters

Threshold (c) Location Parameters 80.7790 50.2606

Slope (gamma) 0.9799 4.6345 Standard Errors of Estimated Parameters Corrected of Heteroskedasticity (per column for each transition function)

Note: Model 3 Based on GDPPC

30

Model 3: GDPPC = F (one-lag GDPPC, IBDEPOSIT, EDU, FDI, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, TOTCH, RULELAW, OILPRODGDP).

Table 9d: PSTR model estimation

Model 4: Dependent variable (GDPPC), Islamic bank variable (IBASSET)

Variable B0 B1 B2

one-lag GDPPC 0.1641 [2.5899] -0.1082 [-0.6104]

IBASSET 0.0000 [0] 1.8492 [1.2052]

EDU 0.0045 [0.5024] -0.2652 [-4.4206]

FD -0.0028 [-1.6614] -0.1079[-1.0310]

FDIGDP -0.0127 [-0.6437] -0.0452 [-1.4544]

INFCPI 0.0852 [2.0111] 0.7199 [3.9147]

OPEN -0.0167 [-0.9480] -0.3630 [-1.0870]

GOVCON 0.0504 [1.8417] -0.0971 [-1.6075]

HC 0.0035 [0.0382] -0.1945[-0.6047]

TOT 0.0331 [1.1960] 0.7059 [2.5850]

RULELAW 0.9236 [1.0899] 4.8799 [2.1058]

OILPRODGDP 278.8150 [1.0466] -12342.0877 [-3.8176] Transition parameters

Threshold (c) Location Parameters 82.4046 Slope (gamma) 0.3066

Standard Errors of Estimated Parameters Corrected of Heteroskedasticity (per column for each transition function)

Note: Model 4 Based on GDPPC

Model 4: GDPPC = F (one-lag GDPPC, IBASSET, EDU, FDI, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, TOTCH, RULELAW,

OILPRODGDP)

Table 9e: PSTR model estimation

Model 5: Dependent variable (GRGDP), Islamic bank variable (BLOAN)

Variable B0 B1 B2

one-lag GRGDP -0.2227[1.6752] -2.0759 [-4.0949] 2.3844 [4.0631]

IBLOAN 0.0000 [0] 9.3238 [3.8362] -7.1128 [-2.9470]

EDU -0.0291 [-0.7077] -0.4100 [-3.4596] 0.3996 [2.8565]

FD 0.0079 [0.8086] -0.0008 [-0.0824] -0.0102 [-0.5577]

FDIGDP 0.0637 [0.4378] -2.1476 [-2.8630] 1.9985 [2.8055]

INFCPI 0.1890 [1.0019] 0.3234 [0.6953] -0.3211 [-0.5002]

OPEN -0.0403 [-1.1760] -0.1021 [-0.9467] 0.1334 [1.3020]

GOVCON 0.1086 [1.3466] -0.4518 [-2.7380] 0.2920 [1.4405]

HC 0.3078 [1.5557] -0.0957 [-0.2605] -0.6606 [-1.3088]

TOT -0.0481 [-0.7296] 0.1413 [0.6872] 0.0154 [0.0710]

RULELAW -4.5027 [-2.2703] -19.6991 [-2.7449] 25.4293 [3.2145]

OILPRODGDP -692.2783 [-0.9392] 2838.5265 [1.8272] -1731.2254[-0.8243] Transition parameters

Threshold (c) Location Parameters 29.4061 27.1620

Slope (gamma) 40.721 0.2332 Standard Errors of Estimated Parameters Corrected of Heteroskedasticity (per column for each transition function)

Note: Model 5 Based on GRGDP Model 5: GRGDP = F (one-lag GRGDP, IBLOAN, EDU, FDI, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, TOTCH, RULELAW,

OILPRODGDP)

Table 9f: PSTR model estimation

Model 6: Dependent variable (GRGDP), Islamic bank variable (IBNETLOAN)

Variable B0 B1 B2

one-lag GRGDP -0.2061 [-1.6031] -2.1274 [-3.9375] 2.4165 [3.9388]

IBNETLOAN 0.0000 [0] 9.4679 [3.8496] -7.0524 [-2.9326]

EDU 0.0478 [0.0479] -0.3303 [-3.1271] 0.2447 [2.1092]

FD 0.0085 [0.7314] 0.0006 [-0.1020] -0.0124 [-0.4969]

FDIGDP 0.0808 [0.4271] -2.2400 [-2.9286 ] 2.0754 [2.8554]

INFCPI 0. [ 1.0898] 0.3327 [0.7755] -0.3222 [-0.6063]

31

OPEN -0.0391 [-1.2867] -0.1114 [-0.9619] 0.1475 [1.3502]

GOVCON 0.1232 [1.5945] -0.4651 [-2.7151] 0.2882 [1.3537]

HC 0.3248 [1.6554] -0.0116 [-0.1612] -0.7661 [-1.4447]

TOT -0.0323 [-0.7779] 0.1947 [1.0003] -0.0606 [-0.2062]

RULELAW -3.6793 [-2.1226] -18.2714 [-2.6197] 22.9557 [3.0569]

OILPRODGDP -811.5285 [-2.1226] 2601.7120 [1.7618 ] -1323.5937 [-0.5762] Transition parameters

Threshold (c) Location Parameters 29.4055 27.3714 Slope (gamma) 41.4405 0.2435

Standard Errors of Estimated Parameters Corrected of Heteroskedasticity (per column for each transition function)

Note: Model 6 Based on GRGDP

Model 6: GRGDP = F (one-lag GRGDP, IBNETLOAN, EDU, FDI, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, TOTCH,

RULELAW, OILPRODGDP).

Table 9g: PSTR model estimation

Model 7: Dependent variable (GRGDP), Islamic bank variable (IBDEPOSIT)

Variable B0 B1 B2

one-lag GRGDP -0.2116 [-1.6031] -2.0913 [-3.9375] 2.3955 [3.9388]

IBDEPOSIT 0.0000 [0] 9.4221 [3.8496] -7.1937 [-2.9326]

EDU 0.0015 [0.0479] -0.2524 [-3.1271] 0.2087 [2.1092]

FD 0.0070 [0.7314] -0.0010 [-0.1020] -0.0092 [-0.4969]

FDIGDP 0.0632 [0.4271] -2.2320 [-2.9286] 2.0840 [2.8554]

INFCPI 0.2056 [1.0898] 0.3828 [0.7755] -0.4063 [-0.6063]

OPEN -0.0443 [-1.2867] -0.1063 [-0.9619] 0.1433 [1.3502]

GOVCON 0.1263 [1.5945] -0.4518 [-2.7151] 0.2717 [1.3537]

HC 0.3223 [1.6554] -0.0588 [-0.1612] -0.7215 [-1.4447]

TOT -0.0516 [-0.7779] 0.2080 [1.0003] -0.0456 [-0.2062]

RULELAW -4.2890 [-2.1226] -18.2229 [-2.6197] 23.8741 [3.0569]

OILPRODGDP -1115.1432 [1.5400] 2669.5393 [1.7618] -1169.8043 [-0.5762] Transition parameters Threshold (c) Location Parameters 29.4017 27.4104

Slope (gamma) 57.2515 0.2309

Standard Errors of Estimated Parameters Corrected of Heteroskedasticity (per column for each transition function)

Note: Model 7 Based on GRGDP Model 7: GRGDP = F (one-lag GRGDP, IBDEPOSIT, EDU, FDI, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, TOTCH,

RULELAW, OILPRODGDP).

Table 9h: PSTR model estimation

Model 1: Dependent variable (GRGDP), Islamic bank variable (IBASSET)

Variable B0 B1 B2

one-lag GRGDP -0.2059[-1.5918] -2.1898[-4.0939] 2.4834 [4.0711]

IBASSET 0.0000 [0] 9.7077 [3.8655] -7.1951 [-2.8727]

EDU 0.0316 [1.1837] -0.1689 [-2.5331] 0.1134 [1.3798]

FD 0.0075 [0.8149] 0.0001 [0.0065] -0.0109 [-0.6058]

FDIGDP 0.1169 [0.7771] -2.3463 [-2.9858] 2.1467 [2.8580]

INFCPI 0.1909 [1.0549] 0.3810 [0.7556] -0.3842 [-0.5720]

OPEN -0.0404 [-1.2345] -0.1146 [-1.0382] 0.1488 [1.4322]

GOVCON 0.1298 [1.6675] -0.4732 [-2.7994] 0.2903 [1.4406]

HC 0.3372 [1.8164] 0.0391 [0.1058] -0.8475 [-1.7019]

TOT -0.0340 [-0.5241] 0.2500 [1.1517] -0.1136 [-0.5005]

RULELAW -3.4572 [-1.7209] -17.4118 [-2.3980] 22.0049 [2.7372]

OILPRODGDP -1072.4804 [-1.5613] 2510.5196 [1.6107] -936.0692 [-0.4602] Transition parameters

Threshold (c) Location Parameters 29.4026 27.5043

Slope (gamma) 51.2027 0.2438 Standard Errors of Estimated Parameters Corrected of Heteroskedasticity (per column for each transition function)

Note: Model 8 Based on GRGDP

Model 8: GRGDP = F (Ione-lag GRGDP, BASSET, EDU, FDI, FDIGDP, INFCPI, OPEN, GOVCON, HC, TOT, TOTCH, RULELAW,

OILPRODGDP).

32

5.3. Results of the dynamic panel quantile model- additional insights

In order to get more insights from the data, based on several economics conditions, we

use the panel quantile regression model. The PSTR model captures the non-linearity of the

data and is able to provide regime-wise information. However, the use of the panel quantile

can definitely add value and provide additional insights, where PSTR fails to do so. This has

motivated to us to use the panel quantile model. It is important to note that since PSTR is

based on the fixed effect model and thus is able to capture the cross-sectional effect, we can

use the advanced panel quantile model developed by Powell (2016) which is robust to cross-

sectional dependence in the panel data and also allows dynamics to hold. Therefore, in this

study, we estimate the dynamic panel quantile model.7

This model is well suited for capturing the nonlinear aspects of the exogenous

variables during changes in the environment under consideration. This top-down model is a

flexible tool that can model the relationships between the covariates and the unobserved

heterogeneity. The results of the dynamic panel quantile model are available upon request.

These results show that all of the variables of interest are statistically significant at the

conventional levels and across the quantiles.8 Taking for example Table A1(a), one can see

that the Islamic banking development, past economic growth, foreign direct investments and

terms of trade affect positively economic growth at different financial development

conditions. More interestingly, these coefficients vary across the quantiles, indicating a

nonlinearity effect of the exogenous variables. As for the financial development, human

capital index, inflation, government consumption, trade openness, rule of law, term of trades

and oil production, these variables have a negative and statistically significant effect on

7 For further details on the dynamic panel quantile model, see Koenker (2004) and Galvao (2011).

8 The lower quantiles (from q=0.05 to q= 0.15) usually reflect economic recessions but in this paper they

represent low Islamic financial development. Similarly, the intermediate quantiles (from q=0.25 to q=0.5)

reflect normal Islamic financial development, while the upper quantiles (q= 0.75 to q=0.95) indicate high

financial development.

33

economic growth across the quantiles (from the lower to upper quantiles). The results of the

dynamic panel quantile models confirm those of the PSTR models.

6. Conclusions and policy implications

The spectacular development of the Islamic banking in many Islamic countries makes

it relevant and timely to have a good understanding of its effects on economic growth in

different financial environments. This study examines the impact of Islamic banking

development on economic growth for nineteen Islamic countries. We also consider the effect

of several key macroeconomic variables (financial development, foreign direct investments,

trade openness, education, inflation, human capital, government consumption, terms of trade,

oil production and the rule-of-law) on economic growth in those countries.

To this end, we apply the panel smooth transition (PSTR) model to discern the

relationship between economic growth and those variables. This model is an extension of the

smooth transition regression (STR) model to panel data embedded with heterogeneity across

the panel individuals and over time.

For additional insights into the results, we also apply the dynamic panel quantile

model in order to assess the considered relationships under different financial development

conditions (i.e., low, medium and high financial development). We first test for the presence

of threshold effects before using the non-linear methods. Using three popular tests, namely

the Wald tests, the Fisher tests and the likelihood ratio tests, we find evidence attesting that

financial development is a threshold variable, thus underpinning the presence of different

financial development regimes. The estimated results for the PSTR models indicate that the

relationships between economic growth and the independent variables are nonlinear during

different financial development conditions. Moreover, past economic growth affects

positively current economic growth.

34

Islamic banking loans impact positively economic growth in the intermediate regime

(normal financial development), while the relationship is negative for the high regime (strong

financial development), indicating that Islamic banking loans reduce economic growth for

Islamic countries, perhaps due to higher risk sharing during economic overheating or to their

disposition to real estate investments which may not be very productive. The Islamic bank net

loans improve GDP growth in the tranquil (normal) financial development regime but they

decrease it in the high regime period. This result confirms our intuition of the presence of an

asymmetric relationship between these two variables under different financial development

conditions.

In contrast to the effect of the Islamic bank loans, Islamic bank deposits and the

Islamic bank size as measured by the Islamic bank total assets have a positive and statistically

significant effect on economic growth in the normal regime but a negative effect in the high

regime. In the low regime, the relationship is insignificant which means Islamic banking

cannot help economic growth during financial development contraction or restrictions. In

sum, financial development has a negative effect on economic growth during the low

financial development regime but has a positive effect in the high regime.

Foreign direct investment is negatively related to the growth in GDP per capita in the

high financial development regime probably because of a high risk bearing or a lack of

incentives. However, when we look at the growth of GDP, we find that FDI leads GDP

growth in the high regime probably due to its prior contribution but decreases it in the

intermediate regime. Furthermore, there is little evidence of an effect of trade openness on

economic growth for these Islamic countries. Moreover, government consumption has a

negative and statistically significant effect on economic growth in the intermediate regimes

for all models (with two thresholds) and a positive effect in the high regime for some cases.

35

This result indicates that during a high level of financial development, increases in

government consumption improve economic growth.

The human capital index has generally an insignificant effect on economic growth in

our setting. This result may be due to under investment in human capital or the presence of

temporary foreign labor that does foster continuity in schooling and returns on education.

Inflation has a statistically significant and positive effect on economic growth during the low

and normal financial development regimes for the first four models. In contrast, this result is

insignificant for the high regime as well as for the remaining last four models.

Oil production has a negative effect on economic growth during only the normal

regime but the effect is insignificant for the other regimes probably due to symptoms of the

Dutch disease in the oil exporting countries and transfer of resources from the oil-importing

countries. The rule of law contributes to improving the per capita GDP for both the

intermediate and high regimes. In contrast, the rule of the law-per capita GDP relationship is

negative for the low regimes. This result may be due to having an environment with a low-

quality governance and an inefficient property rights system. The terms of trade affects

positively the growth in the intermediate regime when GDP growth is the dependent variable.

These results have important policy implications. Domestic financing provided by the

Islamic banking sector has been found to contribute to the growth of the MENA and non-

MENA economies. This positive relationship means that the more developed the Islamic

financial system is, the better the growth of the associated economy is. The GCC countries,

which have a strong financial system, should continue to promote Islamic banking, while

other countries with a slow economic growth can develop their Islamic banking by adopting

and developing legislation and regulations to foster financial development. The Islamic

financial system can thus support and sustain the leading economic sectors in the process of

growth.

36

Policymakers should adopt economic and financial reforms to encourage foreign

direct investments and relax the constraints that hinder the entry of foreign investors. This is

the aim of the future visions adopted recently by the GCC countries (e.g., Vision 2030 of

Saudi Arabia and Qatar, among others). Further, banks should be cautious of allowing an

acceleration of credits to the private sector. Finally, authorities should support more

investments in human capital to allow the economy to grow fast and that increasing trade

openness may be favorable to economic growth when institutional quality improves.

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Appendix: Transition function Plots

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

Model 7 Model 8

0 20 40 60 80 100 120 140 160 1800

0.5

1

Function V

alu

e

Region 1

Transition Function Plot

0 20 40 60 80 100 120 140 160 1800

0.5

1

Function V

alu

e

Region 20 20 40 60 80 100 120 140 160 180

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Function V

alu

e

Region 1

Transition Function Plot

0 20 40 60 80 100 120 140 160 1800

0.5

1

Function V

alu

e

Region 1

Transition Function Plot

0 20 40 60 80 100 120 140 160 1800

0.5

1

Function V

alu

e

Region 20 20 40 60 80 100 120 140 160 180

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Function V

alu

e

Region 1

Transition Function Plot

0 20 40 60 80 100 120 140 160 1800

0.5

1

Function V

alu

e

Region 1

Transition Function Plot

0 20 40 60 80 100 120 140 160 1800

0.5

1

Function V

alu

e

Region 2

0 20 40 60 80 100 120 140 160 1800

0.5

1

Function V

alu

e

Region 1

Transition Function Plot

0 20 40 60 80 100 120 140 160 1800

0.5

1

Function V

alu

e

Region 2

41

Figure A1. Transition Function Plots.

0 20 40 60 80 100 120 140 160 1800

0.5

1

Function V

alu

e

Region 1

Transition Function Plot

0 20 40 60 80 100 120 140 160 1800

0.5

1

Function V

alu

e

Region 2

0 20 40 60 80 100 120 140 160 1800

0.5

1

Function V

alu

e

Region 1

Transition Function Plot

0 20 40 60 80 100 120 140 160 1800

0.5

1

Function V

alu

e

Region 2