Asset bubbles, banking stability and economic growth

Accepted Manuscript Asset bubbles, banking stability and economic growth Shengquan Wang, Langnan Chen, Xiong Xiong PII:

S0264-9993(18)30504-2

DOI:

10.1016/j.econmod.2018.08.014

Reference:

ECMODE 4722

To appear in:

Economic Modelling

Received Date: 8 April 2018 Revised Date:

5 June 2018

Accepted Date: 19 August 2018

Please cite this article as: Wang, S., Chen, L., Xiong, X., Asset bubbles, banking stability and economic growth, Economic Modelling (2018), doi: https://doi.org/10.1016/j.econmod.2018.08.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Asset bubbles, banking stability and economic growth

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Shengquan Wang Lingnan(University) College, Sun Yat-sen University, Guangzhou, China; Email: [email protected]

Langnan Chen

Corresponding author. Lingnan(University) College, Sun Yat-sen University, Guangzhou 510275, China; Email: [email protected]; Tel: +86 13570115839

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Xiongxiong

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College of Management and Economics, Tianjin University, Tianjin, China; Email: [email protected]

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Asset bubbles, banking stability and economic growth

Abstract: This paper examines the relationships between the asset bubble and the banking stability

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from both theoretical and empirical perspectives. The theoretical analysis demonstrates that the moral hazard caused by the deposit insurance and limited liability might facilitate the banks to hold bubble assets for the purpose of risk premium. Meanwhile the supervisory intensity, leverage ratio and credit spread provide the conditions for banks to hold bubble assets through their effects on risk

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premium. Once the banks hold the bubble assets, their stability will deteriorate because of four types of effects, namely internal leverage, cash withdrawal, credit friction and network effects. This paper

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also utilizes the BMA-PVAR model to test the theoretical findings by employing the data from 26 representative economies for a period between 2000 and 2014. The empirical evidences are consistent with the theoretical findings that the equity bubbles will lower the banking stability. The empirical evidences also suggest that the banking instability will be detrimental to the economic growth.

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Keywords： ：Asset bubble; Banking stability; BMA-PVAR; Partial equilibrium model JEL Classification: E44; G01; G21; O40

Introduction

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1.

There are at least two outcomes of asset bubbles. First, the bubble assets will crowd out the real

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economy once they burst. Second, the asset bubble is an important source of financial risk. Aoki and Nikolov (2015) suggests that the risk effect of asset bubbles deserves more attentions than the extrusion effect. The asset bubbles could be amplified through transmission in the financial system and exert a profound impact on the real economy. In 1990s, the collapsed property bubbles lead to the banking crisis and a ‘Lost Decade’ in Japan. One recent example is that the recent subprime mortgage crisis in the United States triggered by the burst of housing bubbles has finally evolved into a global financial crisis. The historical evidences have uncovered the significant explanation of asset bubbles on the determination of financial stability. However, most studies, e.g. Claessens et al.

1

ACCEPTED MANUSCRIPT (2001), Vives (2002), Gertler and Kiyotaki (2015) and Collard et al. (2017), ignore the impacts of asset bubbles on the financial stability. We examine the relationships between the asset bubbles and the banking stability from both theoretical and empirical perspectives. First of all, we develop a partial equilibrium model based on

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Aoki and Nikolov (2015) by assuming that the asset bubbles could influence the banking stability only if the banks hold the bubble assets directly or indirectly. Through the derivation of the proposed model, we find that the moral hazard induced by the deposit insurance and limited liability facilitates the banks to hold bubble assets for the purpose of risk premium while the supervisory intensity,

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leverage ratio and credit spread provide the conditions for the banks to hold bubble assets through their effects on the risk premium. Once the banks hold bubble assets, their stability will deteriorate

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because of four types effects, namely the internal leverage, cash withdrawal, credit friction and network effects.

Further, we test the results derived from the theoretical model by utilizing the Bayesian model averaging panel VAR model (or BMA-PVAR, Koop and Korobilis, 2016) and the data from 26 representative economies from 2000 to 2014. We find that the supervisory intensity, leverage ratio

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and credit spreads have the effects on the banking stability significantly, which is consistent with the theoretical results. We also find that both domestic and foreign equity bubble shocks are the important driven-forces of banking stability. Finally, we find that the banking instability is

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detrimental to the economic growth.

This paper contributes to the literature as follows. First, we fill the gap in the literature on the determinants and channels of banking stability from the perspective of asset bubble by developing a

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theoretical model to quantify the bank's behavior of risk-taking. Second, we employ the BMA-PVAR, a newly developed method, to test the theoretical findings. In addition to the advantages of investigating the spillover effects of financial shocks, the proposed empirical model produce more robust results as it overcomes the problems of overparameterization and subjective constraints in the traditional PVAR model. Third, we extend the literature on banking stability to its effect on the economic growth through empirical study. The remainder of the paper proceeds as follows. Section 2 presents the literature review on the asset bubbles and banking stability. Section 3 develops the partial equilibrium model and presents the 2

ACCEPTED MANUSCRIPT theoretical results. Section 4 tests the theoretical results from Section 3 by utilizing the BMA-PVAR model. Section 5 concludes. 2.

Literature review

The existing literature on the effects of asset bubbles include both growth effect and welfare effect.

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Samuelson (1958) argues that the bubbles complete the market in an overlapping generation model, and thus enhance the welfare. Tirole (1985) suggests that the bubbles crowd out the over-investment and raise the welfare in a dynamically inefficient economy. On the contrary, Grossman and

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Yanagawa (1993), King and Ferguson (1993), and Saint-Paul (1992) reveal that the accumulation of capital is insufficient and the bubbles may exacerbate the economic growth and welfare by crowding

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out the investment in an economy with externality. Azariadis and Reichlin (1996) finds that the bubbles raise the welfare in an economy with variant marginal production of capital and weak externality. Olivier (2000) argues that the equity bubbles raise the market value of firms, which in turn encourages them to invest in innovation, and thus promotes the growth. Since 2008 when the financial crisis occurred, the literature have incorporated the financial

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friction into the bubble theories. Caballero and Krishnamurthy (2006) and Farhi and Tirole (2012) find that the bubbles provide the firms with liquidity by relaxing the financial friction in an economy, thus stimulate the investment and economic growth. Kocherlakota (2009) and Miao and Wang (2011) suggest that the bubbles inflate the collateral value of firms, which in turn facilitates the loan

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accessibility and the economic growth. Ventura (2012) reveals that the financial friction obstacles the capital flow among countries and the capital stock will drop when the bubbles exist. Miao and Wang

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(2014) incorporates the bubbles into a two-sector economy model with the credit friction and finds that the bubbles produce both the credit easing effect and capital reallocation effect. The former will increase the efficiency while the latter might misallocate the capital, depending on the interaction between the sectors. Therefore, the growth effect of bubbles depends on the directions and extents of these two effects. The existing literature on the determination of banking stability have diverse views. Claessens et al. (2001) finds that the entry of foreign banks will stabilize the banking sector of host countries. Gale and Vives (2002) suggests that dollarization could improve the banking stability by ex-ante control on the moral hazard. Following this paper, the deposit insurance and limited liability have 3

ACCEPTED MANUSCRIPT been widely discussed in the determinants of banking stability. Kim and Santomero (1988) reveals that the banks tend to hold the risky portfolio because of inefficient deposit insurance while the capital requirement lower the banks' risk-taking. Gertler and Kiyotaki (2015) finds that the deposit insurance alleviates the pro-cyclical effect caused by the bankruptcy. Meanwhile the moral hazard

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will increase the likelihood of bankruptcy. Collard et al. (2017) suggests that the over risk-taking caused by the limited liability and deposit insurance is an important source of banking stability. However, the existing literature above pay little attention to the banking stability effect of asset bubbles. This paper intends to examine the impact of asset bubbles on the banking stability and the

Theoretical model

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3.

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impact of banking stability on the economic growth from both theoretical and empirical perspectives.

This section develops a partial equilibrium model to investigate the relationship between the asset bubbles and the banking stability. 3.1. A partial equilibrium model

It is assumed that there is an economy where all lending practices are mediated by the banks and the bankers are risk-neutral. A bank issues a loan (
 ) to a firm by using its net worth ( ) and

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borrowings from the depositors ( ), and buy the bubble assets (  ) at price  and the consumption goods ( ). Thus, a bank is subject to the following balance sheet constraint:

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 +
 +   =  + 

(1)

As the bubble assets have no intrinsic value, they cannot be served as the productive inputs or

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consumption goods. Following Blanchard and Watson (1982) and Weil (1987), we incorporate the bubbles in the model. The bubbles will burst at time t with probability 1 − . The price of bubble assets follows the process of.

̂  = 

 , 0,

where ̂  is the price of bubble assets at time t + 1.

1−

(2)

It is assumed that there is no cost of intermediary business for a bank with limited liability. Thus, the dynamics of a bank's net worth is subject to. 4

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 =  (
 + ̂   −   , 0)

(3)

Eq. (3) implies that a bank's net worth is no less than zero, and a bank will declare bankruptcy when its asset is lower than its liability. Aoki and Nikolov (2015) argues that the implicit government guarantees provided by the

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deposit insurance lead to two types of moral hazard, and the corresponding constraints of moral hazards play a key role in shaping the behavior of holding bubble assets. Type I of moral hazard is that the depositors have no incentive to monitor the banks because of the implicit government guarantees. A bank may make a trade-off between transferring (1-λ) deposit and going concern.

(4)

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(1 − ) ≤ ( )

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Based on Gertler and Karadi (2011), a bank is subject to the following constraint.

The left side of Eq. (4) is the value that a bank receives if it transfers the deposit, and the right side is the value if a bank goes concern. This constraint must be met to ensure that a bank operates normally.

Type II of moral hazard originates from the bank's over-investment in bubble assets. When the

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bubbles burst, Repullo and Suarez (2004) suggests that the banks might tend to receive recovery value as little as possible as the banks could maximize their compensation from the deposit insurance institutions when going bankrupt. This compensation is called deposit insurance premium. One

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method to prevent the banks from over-holding bubble assets is to tighten Eq. (4) (Martinez-Miera and Suarez, 2014). However, this will limit the amount of banks' productive loan. Another method is

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to impose incomplete banking supervision while the total amount of productive loan remains unchanged. The total amount of bubble assets held by a bank cannot be greater than a ratio, total asset. In other words, the proportion of assets lower than

where

  ≤ (
 +   )

is the supervisory intensity, and the smaller the

of

cannot be regulated or supervised. (5)

, the more intensive the supervision. Eq.

(5) is a regulatory constraint. Through the above analysis, a bank will adjust its investment strategies between a loan bank and a bubble bank each time. Loan bank: the optimal decision of a loan bank can be summarized as a value function: 5

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  ( ) = max{%& ,'} { + )* [( )]}, subject to constraint (2) and (3). Because of the risk &

neutrality of bankers, we assume that the value function is a linear form of net worth,   ( ) =

-  .If - > 1. A bank will invest all of its assets in loan and consume only when it gets repaid. Because the transfer between a loan bank and a bubble bank is cost-less, we can estimate the value of bank's

going

concern

as

  ( ) = max[  ( ),   ( )] = max/- , - 0  =

* 1-

̂  2 < * (- ) 

(6)

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met.

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- . In equilibrium, a bank will not hold the bubble assets as long as the following condition is

Eq. (6) is consistent with the economic intuition. When the interest rate of loan is greater than

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the rate of return on the bubble assets, a bank will not hold the bubble assets. If  >  , the borrowing constraint is bounded, the deposit is  =

calculate

the

return

 - = )* [- 7 ].

of

one

unit

of

4&'

56

wealth

 . Combining Eq. (1) with Eq. (2), we can

as,

&  7 =  + ( −  ) 56 ,

4'

where

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Bubble bank: similar to the above, we assume that the value function of a bubble bank is

&   ( ) = -  . When the borrowing constraint is bounded, the deposit is  = 56  . Because of

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the limited liability, a bank will choose bankruptcy when bubbles burst for fear of suffering loss while a bank gains the welfare when bubbles persist. Therefore, a bank will hold the bubble assets 9&

>  . The return of one unit of wealth for a bubble bank is.

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9&:;

 ?(1 − )  +  + {(1 − )  +  −   } - ,    =   1− =  - > max [(1 − ) + {(1 − ) −  } , 0], = 1− <

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only if

 7

1−

 The above equation shows that 7 ≥ 0. Therefore, a bank will hold bubble assets as much as

 possible, and - = )* [- 7 ].

Equilibrium strategy: the equilibrium requires that the value function of a loan bank equals to   − 7 0B = 0, - = that of a bubble bank, i.e. - = - = - , or * A- /7

6

CD& [4&:; E&' ] '

H

F GF 5CD& [4&:; & & ] ;GI

.

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to define the deposit insurance premium. If the bubbles burst at time J + 1, a bubble bank can

receive the premium from the deposit insurance, K = max (  − 
 , 0). The premium of one L =

K 1 -  = max [  −  (1 − ), 0]  1 −  + -   , , - , and

Based on Eq. (7), we can derive M4&

P(E&' 5E&H )

> 0, thus

MO

MN&

M(E&' 5E&H )

≥ 0,

MN& M6

≥ 0,

MN&

M4&

(7)

≥ 0. With other

≥ 0, implying that a bank can obtain

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variables being constant, we have:

MN&

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unit of bubble asset is.

risk premium from the deposit insurance. The higher the leverage, the more insufficient the

bank prefers to hold the bubble assets. 3.2. Bank bubbles and banking stability

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supervision, the wider the credit spread, and the higher premium a bank can receive. Therefore, a

The above analysis demonstrates that the banks will hold the bubble assets and have an incentive to hold additional bubble assets because of the risk compensation effect caused by the deposit insurance

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under certain conditions. As suggested in Eq. (2), the asset bubbles may burst at any time. The literature infers that the procyclicality and networking effects of financial institutions generate the internal instability when they face great fluctuations of asset prices (Brunnermeier, 2009).

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The procyclicality of financial institution stems from the internal leverage, credit friction and investors' withdrawal. Adrian and Shin (2010) suggests that the financial leverage will be lifted when

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the asset prices decline. However, the banks may deleverage by dumping the assets to meet the Basel requirements, which triggers a further decline of asset prices. As a consequence, the banking stability deteriorates. Gertler and Karadi (2011) introduces the credit rationing into the financial institutions, namely amount of financing in total net asset. If the prices of assets decline, the financial institutions' ability of receiving deposits will be weakened, and the liquidity risk is aggravated. Brunnermeier and Sannikov (2014) argues that the credit friction will cause the economy off the steady with a speed-up and touch off crisis when the financial institutions face large amount of asset loss. The investors' withdrawal effect is intuitive. The investors' panics triggered by the decline of asset prices will result in withdrawal phenomenon, and thus the insolvency risk. 7

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and Gale, 2000). In an open economy, the financial institution's stability effect of asset prices will be transferred to foreign financial institutions due to their transnational network (Demirer et al., 2017). 4.

Empirical test

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This section utilizes a newly-developed econometric approach to investigate the impacts of asset bubbles on the banking stability and the impact of banking stability on the economic growth.

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4.1. The BMA-PVAR model

The panel vector autoregression (PVAR) model is widely employed to examine the spillover effect of financial shocks (Canova and Ciccarelli, 2009). Demirer et al. (2017) find a strong tie among 150 largest global banks. Traditional PVAR suffers from the problems of overparameterization and subjective constraints. A combination of Bayesian model averaging and PVAR (Koop and Korobilis, 2016) can overcome those problems and provide the robust results.

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QR is a matrix composed of S variables, T(T = 1 … V) and J(J = 1 … W) are country and

Y Y Y time respectively, X = (Q … QZ ) . The VAR model for country T can be presented as.

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QR = [R X5 + ⋯ + []R X5] + ^R

(8)

where for each lag order _ = 1, … , ` , []R is a matrix with S × VS dimensions. ^R is the

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uncorrelated time subject to V(0, bRR ), and bRR is the co-variance matrix with S × S dimensions. cd/^R , ^e 0 = */^R , ^e 0 = bRe is the co-variance matrix of disturbance errors between country T

and country f. Eq. (8) is an unrestricted PVAR model, which might face the overparameterization problem caused by high dimensions. Thus, it is common to add the restricted conditions during applications. Canova and Ciccarelli (2013) distinguishs three types of restricted conditions: the dynamic inter-dependency (DI), the static inter-dependency (SI) and the cross-section heterogeneity (CSH). DI represents that the relationships among countries is from the coefficients of PVAR model 8

ACCEPTED MANUSCRIPT where the endogenous variables for each country depend on the lag term of endogenous variables for all other countries. Taking country f and country g as an example, in order to depict whether the

variables' lag term of country g exist in the VAR model of country f, we define a matrix [hei with S × S dimensions. If country f is not dynamic dependence on country g, [ei = [jei = ⋯ =

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[]ei = 0, f, g = 1, … , V, f ≠ g. By alternating f and g, there are V(V − 1) constraints in total.

SI is a picture about the co-variance of disturbance errors. If there is no static inter-dependency

between country f and country g, bei = 0. By alternating f and g, there are

Z(Z5) j

constraints

in sum. CSH means the difference in coefficients of VAR models among countries1. If there is Z(Z5) j

constraints in total.

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g, there are

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cross-sectional homogeneity between country f and country g, []ee = []ii . By alternating f and

Koop and Korobilis (2016) develops an algorithm of stochastic search specification selection

(K l ) based on the SSVS algorithm (George et al., 2008) for the restricted VAR model. Monte Carlo simulation shows that this algorithm can adequately select the right constraints when the number of observations is relatively smaller than that of parameters2. We rewrite the PVAR model in a more compact way.

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X = m n + ^

(9)

where ^ ~V(0, b), n is a vector with p = `(VS)j VAR coefficients, m is a matrix with

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r VS × p dimensions, ` is the lag order, m = q ⋮ 0

⋯ ⋱ ⋯

0 Y Y Y ⋮ u, and r = (X5 , X5j , … , X5] ). ne r

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represents the f v element of n, and is subject to a hierarchal prior of the mixture of two normal distributions3.

ne |xe ~/1 − xe 0V(0,  × yej ) + xe V(0, yej )

1

(10)

We can also set the homogeneity constraint to the co-variance matrix of disturbance error. However, this specification is

unreasonable in the empirical application of macroeconomics or finance, and thus we leave this type specification negligible. 2

The empirical application in this paper meets this requirement.

3

Hierarchal prior means that the object prior depends on other parameters, and then these parameters are also subject to an unknown

prior. 9

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where xe | e ~z{|c7}}T( e ), e ~z{J(1, ~), and yej ~S(1, )4. x ‚ is a vector with V(V − 1) dimensions, x ƒ‚ with

Z(Z5) j

Z(Z5) j

dimensions, and x „ƒ… with

dimensions. Their elements are both binary. They are used to control DI, SI, and CSH

constraints respectively, and x = (x ‚ , x ƒ‚ , x „ƒ… ). DI and SI can be sampled based on Eq. (10) in the

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MCMC. CSH is different from DI and SI. For simplicity, we take V = 3 and S = 1. Under CSH constraint, we can write Eq. (10) as

ne |xe„ƒ… ~/1 − xRe„ƒ… 0V(ni ,  × yej ) + xRe„ƒ… V(0, yej ) „ƒ… xŠ 0 0‰，‡Š = ˆ 0 0 1

„ƒ… 1 − xj 1 0

0 1 0

„ƒ… 1 0 1−xŠ „ƒ… 0 ‰，‡jŠ = ˆ0 xjŠ 0 0 1

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„ƒ… xj ‡j = ˆ 0 0

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To describe all combination of CSH, we define constraint selection matrix ‡ei as

0 „ƒ… ‰ 1 − xjŠ 1

„ƒ… „ƒ… „ƒ… where xj , xŠ and xjŠ are the restricted vectors of country pairs 1 and 2, 1 and 3, 2 and 3

respectively. If there is a homogeneity between country 1 and 2,

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‡Š × ‡jŠ covers all possible combinations of CSH.

„ƒ… xj = 0. Matrix ‡ = ‡j ×

In summary, after the PVAR model is transferred as shown above, it is convenient to sample the constraint coefficients from the posterior distributions, and then average the samples by using the

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MCMC algorithm, which is called the BMA process. 4.2. Data and variables

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Based on Demirer et al. (2017), we select 26 representative countries for a period from 2000 to 20145,. The data is downloaded from the Global Financial Development Database (GFDD) released by the World Bank. This database includes financial institutions and market indices of 203 countries starting from 1960. All variables in this paper can be found in this database, and the missing data is complemented by using the FRED database. 4.2.1. Variables 4 5

We select parameter , ~,  by reference to Koop and Korobilis (2016). The country list: United States, Japan, Canada, Italy, Australia, China, Great Britain, Spanish, Sweden, France, Korea, Swiss,

Belgium, Germany, Ireland, Malaysia, Portugal, Singapore, Austria, Finland, Greece, Netherlands, Norway, Russia, South Africa. 10

ACCEPTED MANUSCRIPT First, we list the driven-factors of bank's holding of bubble assets. The theoretical analysis above demonstrates that, except for the institutional factors, the willingness of bank's holding of bubble assets is related to the supervisory intensity, leverage ratio and credit spreads. The theoretical results suggest that the former is negatively correlated with the bank's holding of bubble assets while the =

‹_TJ} Œ{| K7_{|dT Tg Ž{TℎJ{ [{J ‹_TJ} = [{J

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two latter variables are positively connected. The three variables can be calculated as follows.

(12) (13)

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  −   = ‘c J{ − ’{_cTJ J{

(11)

Second, the asset bubble is a key variable in this paper. We use the volatility of main stock

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market indices as a proxy of equity bubbles. The more volatile the asset price, the more likely the equity bubbles will occur (Narayan et al., 2013). In this paper, the stock volatility (d) is calculated by averaging the daily stock indices in one year.

Third, the banking stability is another key variable. By following Ana et al. (2016), we employ Z-score as a measure of banking stability. Z-score is a mirror of bank's exposure at default. The

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greater the Z-score, the stabilizer the banking sector. Besides, we incorporate the growth of real GDP per capita (|_) into the model to explore the growth effect of banking stability. We develop a PVAR model with six variables. Based on the above theoretical analysis, and the

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order of each variable is (|_, m − c|{, d, , ,   −   )6.

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4.2.2. Descriptive statistics

Table 1 summarizes the descriptive statistics of the variables considered in this study. The mean of the growth of real GDP per capita is 1.783, which is close to 1.394 of global growth7, suggesting that the sample is a good representative. The standard deviation of Z-score in full sample is 6.560, with minimum value of -4.107 and maximum value of 40.750, implying that there are non-negligible differences among countries. Further, the stock volatility and the bank Z-score have the two greatest standard deviations, namely the asset bubbles might unstabilise the banking sector, which is consistent with the theoretical results. 6

In robustness checks, we will change the order of the latter three variables.

7

We calculate the global growth in our sample period by using the data from the World Bank Database. 11

ACCEPTED MANUSCRIPT Table 1 Descriptive statistics. Standard deviation

Minimum

Maximum

Observations

1.783

3.116

-8.998

13.600

N=390

between

1.880

-0.259

9.100

n=26

within

2.511

-10.730

11.570

T=15

6.560

-4.107

40.750

N=390

between

5.523

3.725

24.850

n=26

within

3.692

-2.220

36.500

T=15

9.180

7.563

67.980

N=390

overall

d

overall

12.060

overall



22.450

between

4.782

13.880

within

7.889

6.684

2.305

2.700

14.600

N=390

between

2.076

4.073

12.310

n=26

within

1.076

2.860

13.330

T=15

overall

6.673

overall

13.570

between  − 



within overall

4.271

between within

35.520

n=26

54.910

T=15

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m − c|{

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|_

Mean

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Variable

2.807

2.500

22.500

N=390

1.874

9.060

17.140

n=26

2.119

7.005

24.720

T=15

6.456

-0.067

45.110

N=390

6.341

0.124

34.720

n=26

1.707

-10.86

14.840

T=15

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Fig. 1 provides the primary evidence of baseline results by plotting the relationship between the banking Z-score and the stock volatility for each country. The banking Z-score and the stock volatility are calculated by averaging the values across the sample period. As we can see, there is a

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significantly negative co-relationship between the two variables. When the stock volatility is large,

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the banking Z-score is relatively low, meaning worse banking stability.

12

25

ACCEPTED MANUSCRIPT AUT

Bank Z-score

USA

20

Fitted values

SGP

15

CHN

CAN

ZAF DEU ESP

MYS

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ITA

FIN BRA

10

NLD FRA JPN GBRCHE BEL KOR

AUS

RUS

IRL 15

SC

5

NOR PRT SWE

GRC

20

25 Stock Volatility

30

35

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Fig. 1. Scatter plot between the banking stability and the stock volatility. 4.2.3. Unit root test

To avoid spurious regression, we test the stationary of data. Depending on the existence of cross-sectional dependence, the unit root tests for panel data can be divided into two types of tests.

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We employ the CD statistics (Pesaran, 2004) to test the cross-sectional dependence and present the results in Table 2. The growth of real GDP per capita and the stock volatility reject the null hypothesis at 1% significance level, implying the existence of cross-sectional dependence. There is

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cross-sectional dependence for the Banking Z-score at 10% significance level. Because of this, we should test the stationary of panel data by utilizing the second-generation tests with consideration of the cross-sectional dependence. We employ the CIPS statistics (Pesaran, 2007) when n and T are in

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the same magnitude. The results of unit root test are reported in Table 2. As the stock volatility and the credit spreads reject the null hypothesis at 5% significance level, they are stationary. The growth of real GDP per capita, the banking Z-score, the leverage and the banking supervision have the unit roots, but are stationary series after the first order difference. Therefore, in the PVAR model we use the first order difference of variables except for the stock volatility and the credit spreads.

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ACCEPTED MANUSCRIPT Table 2 Cross-sectional dependence test and unit root test. Unit Root Test8

Cross-sectional Test Variable

m − c|{ d 

 − 



P value

t-bar statistics9

P value

44.530

0.000***

-1.878（-2.348）

0.232（0.002***）

1.900

0.057*

-1.699（-2.831）

0.538（0.000***）

46.780

0.000***

-2.195

0.014**

5.480

0.000***

-1.299（-2.042）

28.710

0.000***

-1.710（-2.121）

18.720

0.000***

-2.176

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|_

CD statistics

0.974（0.067*） 0.519（0.032*） 0.017**

***, **, * indicate 1%, 5%, 10% significance levels respectively. Value in brackets is the relevant t-bar statistics and P value for the

SC

variables with one order difference.

4.3. Empirical results and analysis

M AN U

By comparing the AIC and SIC with different lag orders of the PVAR model, we find that the optimal lag order is 1. The BMA-PAVR model is superior to the traditional PVAR model in that the former can simultaneously identify the optimal restricted conditions by using the MCMC algorithm. Tables 3 through 5 report the restricted conditions selected by the BMA approach. As shown in Table 3, the invalid dynamic inter-dependency exists in 175 pairs of countries

TE D

among 650 (=26×25) pairs. First, it is noted that the DI may be unidirectional, namely the lagged variables of one country occur in another country's VAR model, but not vice versa. For example, the lagged variables of China appear in Japanese VAR model while those of Japan do not appear in

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Chinese VAR model. Second, except for Brazil, the bidirectional relation is valid between other 24 countries in our sample and the United States, implying the dominant position and relative openness

AC C

of its economy to the rest of the world. Third, South Africa, Spain, Russia and Sweden only appear in the list of From countries, meaning that the four countries have the impacts on all other countries' dynamics of economic variables. From the view of financial contagion, we can observe that the number of invalid dynamic inter-dependency in Asian countries, like China, Japan and Korea, is lower than that of the developed countries, such as the United States and Spain, suggesting that the developed countries play more important role in the process of financial contagion than other countries.

8

We set the existence of intercept term and time trend term, the lag order is 1.

9

By reference to Pesaran (2007), the critical value for 1%, 5% and 10% significance levels are -2.340, -2.170 and -2.070 respectively. 14

ACCEPTED MANUSCRIPT Table 3

To

From

To

From

To

From

To

From

To

From

To

From

To

AUS

DEU

BEL

DEU

CHN

BRA

FRA

DEU

GRC

AUT

GBR

AUT

MYS

NLD

AUS

JPN

BEL

MYS

CHN

FIN

FRA

IRL

GRC

BRA

GBR

NLD

MYS

ESP

AUS

GBR

BEL

NLD

CHN

FRA

FRA

JPN

GRC

CAN

GBR

NOR

MYS

GBR

AUT

BEL

BEL

NOR

CHN

DEU

FRA

KOR

GRC

CHN

JPN

AUT

NLD

AUT

AUT

CHN

BEL

SWE

CHN

GRC

FRA

NLD

GRC

FIN

JPN

CHN

NLD

BRA

AUT

FIN

BEL

CHE

CHN

ITA

FRA

SGP

GRC

DEU

JPN

FIN

NLD

CAN

AUT

FRA

BRA

FRA

CHN

MYS

DEU

AUT

GRC

IRL

JPN

FRA

NLD

DEU

AUT

DEU

BRA

ESP

CHN

NLD

DEU

BEL

GRC

JPN

JPN

DEU

NLD

ITA

AUT

GRC

BRA

USA

CHN

PRT

DEU

BRA

GRC

KOR

JPN

IRL

NLD

JPN

AUT

IRL

CAN

AUS

CHN

GBR

DEU

CAN

GRC

MYS

JPN

ITA

NLD

KOR

AUT

JPN

CAN

AUT

FIN

AUT

DEU

FIN

GRC

NLD

JPN

NLD

NLD

NOR

AUT

KOR

CAN

CHN

FIN

CAN

DEU

GRC

GRC

RUS

JPN

RUS

NLD

PRT

AUT

MYS

CAN

FIN

FIN

CHN

AUT

NLD

CAN

DEU

FIN

FRA

AUT

NOR

CAN

GRC

FIN

DEU

AUT

PRT

CAN

IRL

FIN

GRC

AUT

ESP

CAN

JPN

FIN

KOR

AUT

CHE

CAN

KOR

FIN

MYS

AUT

GBR

CAN

MYS

FIN

NLD

ITA

GRC

CAN

NLD

FIN

NOR

ITA

NLD

CAN

NOR

ITA

GBR

CAN

PRT

ITA

GRC

CAN

ZAF

ITA

NLD

CAN

GBR

ITA

GBR

CHE

GRC

PRT

GRC

CHE

M AN U IRL

GRC

ESP

JPN

ZAF

NLD

RUS

DEU

JPN

GRC

GBR

JPN

SWE

NLD

ZAF

DEU

KOR

IRL

AUT

JPN

GBR

NLD

GBR

DEU

MYS

IRL

BRA

KOR

AUT

NOR

AUT

DEU

NLD

IRL

CHN

KOR

CAN

NOR

DEU

DEU

NOR

IRL

DEU

KOR

FRA

NOR

NLD

DEU

PRT

IRL

GRC

KOR

DEU

NOR

PRT

DEU

RUS

IRL

JPN

KOR

IRL

NOR

ZAF

NOR

GBR

TE D

DEU

FIN

PRT

DEU

ZAF

IRL

KOR

KOR

MYS

FIN

SGP

DEU

ESP

IRL

NLD

KOR

NLD

FIN

SWE

DEU

SWE

IRL

RUS

KOR

RUS

FIN

CHE

DEU

GBR

IRL

ZAF

KOR

ZAF

FIN

GBR

IRL

ESP

KOR

ESP

IRL

GBR

KOR

GBR

EP NLD

RI PT

From

SC

Country pairs with invalid dynamic inter-dependency.

SGP

DEU

AC C

The probability lower than 0.5 is considered as an invalid dynamic inter-dependency under the MCMC algorithm.

Table 4 and 5 report the valid country pairs of CSH and SI. The total number of pairs is 325

(=

j”×j• j

). What deserve mentioning is that there are only 12 valid pairs of CSH, which are matched

with the United States, suggesting that the heterogeneity across countries in our sample is high. It is noted that the cross-sectional homogeneity only means the same VAR coefficients among countries rather inter-linkages of those countries. Except for Australia, Brazil and Singapore, the countries with valid pairs of CSH are both from Europe. This is perhaps due to the similarity in the economic structure between the United States and Europe. As shown in Table 5, the valid SI exists in 78 country pairs. SI means that the co-variance 15

ACCEPTED MANUSCRIPT matrix between the countries is not zero and mirrors the contemporaneous relationships among countries. It is noted that, although the United States formulates the DI relationship with all other countries, it does not formulate the SI relationship with all other countries. Table 4

Country 1

Country 2

Country 1

AUS

USA

DEU

BRA

USA

GRC

CAN

USA

ITA

USA

PRT

USA

SGP

CHE

USA

Country 2 USA

USA

USA

USA

USA

SC

FIN FRA

RI PT

Country pairs with valid cross-sectional heterogeneity.

GBR

USA

Table 5

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The probability that is greater than 0.5 is considered as a valid cross-sectional heterogeneity under the MCMC algorithm.

Country pairs with valid static inter-dependency. Country 2

Country 1

Country 2

Country 1

Country 2

Country 1

Country 2

AUS

AUT

CAN

CHN

ESP

CHE

BEL

BRA

AUS

BEL

CAN

FRA

ESP

GBR

BEL

CHN

AUS

BRA

CAN

GRC

SWE

GBR

BEL

FIN

AUS

CHN

CAN

IRL

SWE

USA

BEL

DEU

AUS

FIN

CAN

KOR

BRA

CAN

BEL

IRL

AUS

FRA

CAN

MYS

BRA

CHN

BEL

ITA

AUS

GRC

CAN

NLD

BRA

FIN

BEL

NLD

AUS

IRL

CAN

CHE

BRA

DEU

BEL

NOR

AUS

JPN

CHN

JPN

BRA

ITA

BEL

SGP

AUS

NOR

FIN

GRC

BRA

KOR

BEL

SWE

AUS

PRT

FIN

NOR

BRA

NLD

SGP

ZAF

AUS

RUS

FRA

DEU

BRA

NOR

SGP

ESP

ZAF

FRA

GRC

BRA

RUS

SGP

SWE

ESP

FRA

IRL

BRA

SGP

SGP

GBR

GBR

FRA

ITA

BRA

USA

SGP

USA

USA

FRA

JPN

RUS

SGP

ITA

JPN

CHN

FRA

KOR

RUS

CHE

ITA

MYS

ZAF

SWE

FRA

NLD

RUS

GBR

ITA

PRT

PRT

USA

FRA

NOR

RUS

USA

IRL

ITA

GRC

ITA

IRL

MYS

AUS AUS AUS AUT

EP

AC C

AUS

TE D

Country 1

The probability that is greater than 0.5 is considered as a valid static inter-dependency under the MCMC algorithm.

As suggested in the theoretical analysis, the banking supervisory intensity, leverage ratio, and 16

ACCEPTED MANUSCRIPT credit spreads have the impacts on the bank's risk premium, which provides an incentive for banks to hold the bubble assets. Fig. 2 presents the impulse response of banking stability to the supervision, leverage ratio and credit spreads shocks. The sample covers 26 countries. Through the impulse response for each country, we can find that the responses are similar. For brevity and

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representativeness, we only report the results of impulse responses for China and the United States. First, both in China and the United States, a positive shock of banking supervision lowers the risk premium and weakens the willingness of bank's holding of bubble assets. As a consequence, the banking stability improves, which is consistent with the theoretical results and Benjamin et al. (2016).

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Similarly, a positive shock of bank leverage ratio and credit spreads raises the risk premium and strengthens the willingness of bank’s holding of bubble assets. As a result, the banking stability

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worsens, which is consistent with the theoretical results and Avgouleas (2015) and Geremew (2016). Second, there are differences in impulse response in terms of depth and duration between China and the US. Particularly, a positive banking supervision shock raises the Z-score in China by 0.25% at the beginning and reaches the maximum level of 0.45% in due course while the values for Z-score in the United States are 0.15% and 0.3% respectively. The duration of shock in China is nine periods while

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that in United States is five periods, suggesting that the banking supervision shock in China has a more intensive and longer impact on the banking stability than that in the United States. This phenomenon may root in the relative scarcity of financial instruments, and strict supervision in China.

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The banking leverage and credit spreads shocks also have the heterogeneous impacts on the banking

AC C

stability in China and the United States.

17

The shadowy area represents 84% Bayesian credible interval.

SC

RI PT

ACCEPTED MANUSCRIPT

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Fig. 2. Impulse response of banking stability to supervision, leverage ratio and credit spreads shocks. Fig. 3 presents the impulse response of banking stability to the domestic equity bubble shocks. For comparative purpose, we only report the results of the BRICS countries, including China, Russia, Brazil and South Africa, and selected OECD countries, including United States, Japan, Australia and

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Great Britain. First, in both BRICSs and OECDs, the Z-score responds negatively to a positive shock of equity bubble, namely the banking stability worsens. Similar to this result, Albertazzi and Gambacorta (2010) find a negative co-relationship between the stock volatility and the banking profit before tax. Second, the depth of impulse of BRICSs is apparently weaker than that of the selected

EP

OECD countries. The banking Z-score declines initially by 0.2% and then by 0.4% for BRICSs while 0.5% on average for the selected OECD countries. The detrimental impacts on BRICSs will diminish

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earlier than that in OECD countries.

18

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RI PT

ACCEPTED MANUSCRIPT

The shadowy area represents 84% Bayesian credible interval.

Fig. 3. Impulse response of banking stability to the domestic equity bubble shock.

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As the asset bubbles could diffuse among countries, the foreign asset bubbles may generate a negative influence on the domestic banking stability. Fig. 4 illustrates the response of other countries to the equity bubbles from China and United States. First, similar to the domestic equity bubble

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shock, the foreign equity bubble shock will deteriorate the banking stability. Second, the equity bubble shock of United States has more serious impact on the banking stability in other countries

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than that of China has. For example, the Japanese response to United States bubble shock is -0.5%, while that to China is only -0.2%. For duration, we find that China’ impacts of bubble shock disappear more rapidly than United States' impacts. The spillover effects of equity bubbles demonstrate the existence of global banking network, which is consistent with Brunnermeier (2009), Affinito and Pozzolo (2017) and Demirer et al. (2017). Therefore, the fact of imported asset bubbles is verified in this paper.

19

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ACCEPTED MANUSCRIPT

The shadowy area represents 84% Bayesian credible interval.

4.4. Robustness checks

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Fig. 4. Impulse response of banking stability to foreign equity bubble shock.

To ensure the robustness of the above baseline results, we conduct two types of tests. First, we test the robustness by changing the order of banking supervision, leverage and credit spreads in our

EP

model. Second, we employ the alternative measure of banking stability. By following Ana et al. (2016), we replace the banking Z-score with the ratio of non-performing loans (NPL) and the ratio of

AC C

loan-loss reserves to total loan (PROV) respectively, which are both widely used to measure the bank's credit risk. As shown in Fig. 5, the impulse responses are basically consistent with the baseline results, namely there exists a significantly negative effect of equity bubble shock on the banking stability.

20

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The shadowy area represents 84% Bayesian credible interval.

SC

RI PT

ACCEPTED MANUSCRIPT

Fig. 5. Robustness checks. 5.

Banking stability and economic growth

We extend this study by investigating the impacts of banking stability on the economic growth in this section.

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Fig. 6 plots the impulse response of economic growth to the banking stability of the representative economies, the BRICS and OECD countries. Consistent with the prior literature (Rajan and Zingales, 1998; Claessens and Laeven, 2003; Levine, 2005; Lin and Huang, 2012), the

EP

declining shock of banking stability will produce a significantly detrimental effect on the economic growth in the selected countries. At the initial period of shocks, the economic growth lowers by 0.2%,

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and this negative effect will reach the maximum value at the second period before diminishing gradually for the selected countries. Besides, there are also heterogeneities among countries on the duration of this effect. For instance, the effect will disappear by the sixth period in China, the seventh period in the United States and the eighth period in Great Britain. The finding that the banking instability deteriorates the economic growth can be justified by the asymmetric information theory on the financial instability (Mishkin, 1998). Banking instability is one of the key sources of financial instability. Banks, in essence, are engaged in producing information to facilitate the productive investment. The decline of banks' ability to act as intermediaries or lending money directly will lead to a decline in investment and aggregate economic 21

ACCEPTED MANUSCRIPT activity. When the banking system is shocked and the information flow is intervened, the banks cannot normally function as intermediaries that directs capital to the productive investment. As a

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SC

RI PT

consequence, the banking stability worsens and output contracts.

The shadowy area presents 84% Bayesian credible interval.

Fig. 6. Impulse response of economic growth to (negative) banking stability shock. Conclusion

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6.

Considering the dominance of the banking sector in the overall financial system in many countries,

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the banking stability deserves a special attention. We examine the mechanism and conditions of banks' holding of bubble assets by developing a partial equilibrium model. We also employ the BMA-PVAR model and the data of 26 representative countries for a period from 2000 to 2014 to test the theoretical results.

For theoretical analysis, we prove that the moral hazard induced by the deposit insurance and limited liability might facilitate banks to hold the bubble assets for the purpose of risk premium while the supervisory intensity, leverage ratio and credit spread provide the conditions for banks to hold bubble assets through their effects on risk premium. Once the banks hold the bubble asset, their

22

ACCEPTED MANUSCRIPT stability will deteriorate because of four types channels, namely internal leverage, cash withdrawal, credit friction and network effects. For empirical study, the results suggest that the supervisory intensity, leverage ratio and credit spreads have the effects on the banking stability significantly, which is consistent with the theoretical

RI PT

results. Further, both domestic and foreign equity bubble shock are the significantly driving factors of banking stability. Finally, we investigate the growth effect of banking stability, and find that the banking instability is detrimental to the economic growth.

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References

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Samuelson, P. A. An Exact Consumption Loan Model of Interest with or without the Contrivance of Money. Journal of Political Economy, 1958, 66(1): 32-35. Saint-Paul, G. Fiscal Policy in an Endogenous Growth Model. Quarterly Journal of Economics, 1992, 107(4):1243-1259. Tirole, J. Asset Bubbles and Overlapping Generations. Econometrica, 1985, 53:1499-1528. Ventura, J. Bubbles and Capital Flows. Journal of Economic Theory, 2012. 147(2):738-758. Weil, P. Confidence and the Real Value of Money in an Overlapping Generations Economy. Quarterly Journal of Economics, 1987, 102(1):1-22.

25

ACCEPTED MANUSCRIPT •

This paper examines the relationships between asset bubble, banking stability and economic growth.

•

The moral hazard caused and limited liability might facilitate the banks to hold bubble assets. The supervisory intensity, leverage ratio and credit spread provide the conditions for banks to hold bubble assets.

RI PT

•

This paper also utilizes the BMA-PVAR model to test the theoretical findings.

•

This paper employs the data from 26 representative economies between 2000

SC

•

and 2014.

EP

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The empirical evidences are consistent with the theoretical findings.

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•