I embark to measure the systemic risk of regional banks in Japan through shadow banking (microlevel and macrolevel linkages) using partial least squares structural equation modeling (PLS-SEM). Non-parametric PLS-SEM is used for the first time in the context of Japanese banks. I collect indicator-based data from Orbis Bank Focus but do not find all the indicators suggested by theory. Results indicate systemic risk is explained by 12.5% of shadow banking. I use generalized structured component analysis (GSCA) for robustness test because it belongs to the same family of methods as PLS-SEM; PLS-SEM results are confirmed by GSCA. Regulators need to collect more data regarding shadow banking activities in relation to regional banks in Japan. The missing indicators are critical for explaining systemic risk in regional banks through shadow banking. Once more data are available, researchers can explore whether shadow banking has a substantial effect on the systemic risk of regional banks in Japan.
Japan’s financial crisis started in late 1990s and caused harm for capital and liquidity in its banking system. As a result, the economy fell into a deflationary state. Bank of Japan (BoJ) introduced zero interest rate policy in 1999 and then quantitative easing in March 2001 [
However, the financial system was in trouble with negative yields and flat curves, raising fears about profitability. In September 2016, BoJ implemented yield curve control, monitoring short-term rates and long-term Japanese government bonds. In summary, more than a decade-long low level and volatility of government bonds’ yields produced interest rate risk and inadequate capital among financial institutions; this could lead to systemic risk. International Monetary Fund (IMF) recently highlighted the systemic risk in Japan’s banking system [
It is difficult to quantify systemic risk in integrated markets and it changes dynamically [
For the first time in Japanese banking system, I use partial least squares structural equation modeling (PLS-SEM). PLS-SEM is iterative OLS regression, also known as PLS path modeling [
In the rest of the article, Section 2 covers the conceptual framework, Section 3 describes the data and method, Section 4 reports the results, Section 5 applies the robustness test, and Section 6 concludes.
I focus on regional banks―the second largest group of banks in Japan (N = 64). Furthermore, the International Monetary Fund highlighted some vulnerabilities with regional banks [
I explain the consequences of systemic risk in the regulated banking sector (RBS) by microlevel and macrolevel linkages that can be traced to shadow banking (SB), e.g. market based financing through non-bank channels such as real estate investment trusts, leasing companies, credit guarantee outlets, money market funds, etc.
According to the regulatory arbitrage view, banks use special or structured investment vehicles (SIVs) [
77 Bank Akita Bank Aomori Bank Ashikaga Bank Awa Bank Bank of Fukuoka Bank of Iwate Bank of Kyoto Bank of Okinawa Bank of Saga Bank of The Ryukyus Bank of Toyama Bank of Yokohama Chiba Bank Chiba Kogyo Bank Chikuho Bank Chugoku Bank Daishi Bank Eighteenth Bank Fukui Bank Gunma Bank Hachijuni Bank Higo Bank Hiroshima Bank Hokkaido Bank Hokkoku Bank Hokuetsu Bank Hokuriku Bank Hokuto Bank Hyakugo Bank Hyakujushi Bank Iyo Bank | Joyo Bank Juroku Bank Kagoshima Bank Kinki Osaka Bank Kitakyushu Bank Kiyo Bank Michinoku Bank Mie Bank Miyazaki Bank Musashino Bank Nanto Bank Nishi-Nippon City Bank Ogaki Kyoritsu Bank Oita Bank San-in Godo Bank Senshu Ikeda Bank Shiga Bank Shikoku Bank Shimizu Bank Shinwa Bank Shizuoka Bank Shonai Bank Suruga Bank Tajima Bank Toho Bank Tohoku Bank Tokyo Tomin Bank Tottori Bank Tsukuba Bank Yamagata Bank Yamaguchi Bank Yamanashi Chuo Bank |
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increase as bank regulation becomes more strict (according to Basel III measures). As systemic risk increases, banks under distress lend less to clients (thus, clients invest less) and unemployment rises. This paper uses indicator-based approach that is favored by the Basel Committee and includes microprudential and macroprudential perspectives.
I work with end-of-financial year (i.e. 31 March 2017) data and I collect data from Orbis Bank Focus. Bank Focus is a database of banks worldwide; the information is sourced by Bureau van Dijk from a combination of annual reports, information providers and regulatory sources. Regarding data, not all the indicators in
The distinction between formative and reflective indicators needs further explanation. Formative indicators are considered complementary. That is, a change in a given formative indicator can lead to a change in the associated latent construct. In multiple regression, the formative indicators are independent
Sources of systemic risk in shadow banking and the formative indicators in PLS-SEM | Consequences of systemic risk in regulated banking sector are reflective indicators in PLS-SEM |
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1) Complex derivatives such as collateralized debt obligations (CDOs) ($) {MICRO} Reference [ | 1) Total regulatory capital ratio {MICRO} Reference [ |
2) Complex derivatives such as collateralized loan obligations (CLOs) ($) {MICRO} Reference [ | 2) Non-interest income scaled by interest income {MICRO} Reference [ |
3) Repurchase agreements ($) {MICRO} Reference [ | 3) Non-performing loans scaled by total loans {MICRO} Reference [ |
4) Number of SB facilities incorporated in offshore financial centers associated with a bank adjusted for firm size {MACRO} Reference [ | 4) Financial beta defined as volatility of bank share price relative to the overall stock market {MACRO} Reference [ |
5) Number of associations with structured credit vehicles for a given bank adjusted for firm size {MACRO} Reference [ | 5) Modified Basel Committee on Banking Supervision score approximating domestic systemic importance of banks {MACRO} Reference [ |
6) The ratio of a bank’s stock price to the banking sector stock index {MACRO} Reference [ |
aMACRO―macroprudential perspective; MICRO―microprudential perspective; SB―shadow banking.
variables. On the other hand, reflective indicators are treated as interchangeable because of the overlap among them. Thus, the endogenous latent construct depicted in
PLS-SEM models consist of three main components, namely, the structural or inner model, the measurement or outer models (see
The traditional covariance-based-SEM (CB-SEM) is able to model measurement error structures via a factor analytic approach but at the cost of covariances among the observed variables conforming to overlapping proportionality constraints, i.e. measurement errors are assumed to be uncorrelated [
I identify PLS-SEM method under three models:
Each reflective indicator is related to the endogenous construct or latent variable by a simple regression:
x h = 1 , ... , p = π h _ 0 + π h ξ + ε h (1)
where x h = 1 , ... , p is the hth regression where a reflective indicator is the dependent variable and p equals the number of reflective indicators, π h _ 0 is the intercept, π h is the regression parameter to be estimated and ξ is the latent variable with a mean m and standard deviation of 1. The residual variable ε h has a mean of zero and it is uncorrelated with the latent variable (known as the predictor specification condition, [
1) Internal consistency: According to references [
ρ c = ( ∑ λ i ) 2 var F ( ∑ λ i ) 2 var F + ∑ Θ i (2)
where λ i , F, and Θ i are the factor loading, factor variance, and unique/error variance, respectively where i represents the indicator variable for a specific construct. Composite reliability is only relevant for the reflective measurement model.
2) Indicator reliability: Outer loadings greater than 0.7 are desirable [
3) Convergent validity: Average variance extracted (AVE) greater than 0.5 is preferred; this ratio implies that greater than 50% of the variance of the indicators have been accounted. AVE is only relevant for the reflective measurement model. When examining reflective indicator loadings, it is desirable to see higher loadings in a narrow range, indicating all items are explaining the underlying latent construct, i.e. convergent validity [
AVE = ( ∑ λ i ) 2 var F ( ∑ λ i ) 2 var F + ∑ Θ i (3)
4) Discriminant validity: Fornell-Larcker criterion needs to be satisfied. That is, the square root of AVE must be greater than the correlation of the construct with all other constructs; this criterion is not applicable to formative measurement models and single-item constructs.
Under the formative measurement model, it is assumed that the exogenous construct (latent variable, ξ ) is defined by the formative indicators that could be multidimensional and a residual term found in a linear function.
ξ = ∑ h ϖ h x h + δ (4)
where ϖ h is the weight, the residual vector δ has a mean of zero and it is uncorrelated with the formative indicators x h where h captures the range of formative indicators [
1) Convergent validity: Higher path coefficients linking the exogenous and endogenous constructs are preferred, implying adequate coverage by the formative indicators [
2) Multi-collinearity among indicators: When multi-collinearity exists, standard errors and thus variances are inflated. A variance inflation factor (VIF) is calculated for each of the explanatory variables in OLS regression, and VIF must be less than 5 [
VIF i = 1 ( 1 − R i 2 ) (5)
where R i 2 is the proportion of variance of formative indicator i associated with other indicators in the same block [
3) Significance and relevance of outer weights: “Weight” is an indicator’s relative contribution; “loading” is an indicator’s absolute contribution. One can start with bootstrapping using 5000 sub-samples [
I emphasize that if the outer models, that is, measurement models are not reliable, little confidence can be held in the inner (structural) model. Analysis of the structural model is an attempt to find evidence supporting the theoretical model, i.e. the theorized relationships between exogenous constructs and the endogenous construct.
ξ j = β j o + ∑ i β j i ξ i + v j (6)
where ξ j is the endogenous construct (in this study there is one endogenous construct, therefore j equals 1) and ξ j represents the exogenous constructs (i equals 2); the predictor specification condition applies [
1) Predictive accuracy, coefficient of determination (R2): This statistic indicates to what extent the exogenous construct(s) are explaining the endogenous construct. According to references [
2) Predictive relevance (Q2): This statistic is obtained by the sample re-use technique called ‘Blindfolding’ where omission distance is set between 5 - 10, where the number of observations divided by the omission distance is not an integer [
Q 2 = 1 − ∑ D E D ∑ D O D (7)
where D is the omission distance in blindfolding, E is the sum of squares of prediction error, and O is the sum of squares errors using the mean for prediction.
3) Significance of path coefficients: Bootstrapping is needed, following which p-values for the path coefficients are checked.
In this section, I report the results under three models using PLS-SEM. I use Smart PLS software [
1) Internal consistency: Composite reliability is lower than 0.6 at 0.420, casting some doubt on internal consistency of the reflective measurement model.
2) Indicator reliability: The highest outer loadings belongs to beta (0.930), followed by non-performing loans (0.330), capital ratio (0.257) and non-interest income (−0.055) (see
3) Convergent validity: AVE equals 0.261, below the preferred minimum of 0.5, suggesting less than 50% of the variance of the reflective indicators have been accounted by the latent endogenous construct.
4) Discriminant validity: The square root of AVE (0.511) must be greater than the correlation of the construct with all other constructs. Fornell-Larcker criterion is satisfied.
1) Convergent validity: The path coefficient is −0.429 from the shadow banking to the regulated banking (see
2) Multi-collinearity among indicators: Outer VIF values range between 1.039 - 1.227 and are substantially under 5, indicating absence of multi-collinearity and inflated variance.
3) Significance and relevance of outer weights: Eliminating formative indicators should be approached with caution because formative measurement theory expects the indicators to cover the domain of a construct, i.e. formative indicators are complementary. Since I have three formative indicators, I do not delete any.
1) Predictive accuracy, coefficient of determination (R2): The adjusted R2 is 16.5% and is weak according to the general guidelines.
2) Predictive relevance (Q2): Q2 is smaller than zero at −0.045, suggesting problems with the reflective indicators.
3) Significance of path coefficients: P-value for path coefficient is 0.387 between the shadow banking and regulated banking, indicating insignificance.
I proceed to the second run. The reflective indicators non-interest income and capital ratio should be deleted because outer loadings are low. I proceed without these indicators and report new results (see
References [
GSCA maximizes the average or the sum of explained variances of linear composites, where latent variables are determined as weighted components or composites of observed variables. GSCA follows a global least squares optimization criterion and it is minimized to generate the model parameter estimates. GSCA is not scale-invariant and it standardizes data. GSCA retains the advantages of PLS-SEM, such as fewer restrictions on distributional assumptions, unique component score estimates, and avoidance of improper solutions with small samples [
I use the web-based GSCA software GeSCA (http://www.sem-gesca.org/) for robustness testing of the reduced model. In
PLS-SEM | GSCA | |
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Measurement model | ||
AVE | 0.540 | 0.562 |
Outer loadings of reflective indicators | ||
Non-performing loans | 0.381 | 0.629 |
Beta | 0.967 | 0.853 |
Coefficient of determination (R2) | 12.5 | 12.6 |
confirmed by GSCA; all the figures are similar with the exception of non-performing loans.
I measure the systemic risk of regional banks in Japan using partial least squares structural equation modeling. First run has problems. After I delete the reflective indicators, non-interest income and capital ratio, composite reliability and AVE improves; following bootstrapping, p-value improves. Blindfolding leads to healthy Q2.
As I delete two reflective indicators, the statistics in PLS-SEM improve substantially. Unfortunately, the few available formative indicators with regional banks of Japan do not result in high R2. The shadow banking explains the systemic risk in regulated banking (regional banks) to the tune of 12.5% (adjusted R2). Regulators need to collect more data based on
Regarding the indicators listed in
The authors declare no conflicts of interest regarding the publication of this paper.
Avkiran, N.K. (2018) Measuring the Systemic Risk of Regional Banks in Japan with PLS-SEM. Theoretical Economics Letters, 8, 2024-2037. https://doi.org/10.4236/tel.2018.811132