Discrete Dynamics in Nature and Society

Volume 2015, Article ID 318732, 9 pages

http://dx.doi.org/10.1155/2015/318732

## Asymmetric Procyclicality of Chinese Banking and the Countercyclical Buffer of Basel III

^{1}School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China^{2}Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou 510275, China

Received 22 October 2014; Revised 15 December 2014; Accepted 17 December 2014

Academic Editor: Carlo Piccardi

Copyright © 2015 Yufeng Li and Zhongfei Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Since the global financial crisis of 2007-2008, the importance of the procyclicality in the banking sector has been highlighted. One of the Basel III objectives is to promote countercyclical buffers and reduce procyclicality. We apply time-varying copula combined with GARCH model to test the existence of asymmetric procyclicality of Chinese banking. The results show that the procyclicality of Chinese banking is asymmetric, where the dependence between loan and economy growth is more correlated during the decline stage than the rise stage of economy. Based on this asymmetry, we suggest that the authority can use high frequent index for signalling the start point of releasing countercyclical buffer and accelerate the releasing pace to avoid the supply of credit being constrained by regulatory capital requirements in downturns.

#### 1. Introduction

The interaction of macroeconomy and financial sector variables has long been an object of interest to economists. Keynes [1] argued that informational asymmetry was an inherent problem in the functioning of the financial markets and this uncertainty fluctuates with the real economy. Bernanke and Blinder [2] and Kiyotaki and Moore [3] argued that even relatively small shocks to the economy could be amplified by endogenous changes in the credit market conditions, and this phenomenon leads to the propagation of the business cycle by introducing the financial accelerator model.

In particular, since the global financial crisis of 2007-2008, the importance of the procyclicality in the banking sector has been highlighted. Ideally, the banking system should provide a safety net to enterprises and households to mitigate economic volatility. However, the financial crisis and the decline of output can be observed at the same time and they even intensify each other. During this crisis, the major global banking institutions reported cumulative losses and write-downs of $1306 billion by April 2010, while world GDP contracted by 1.6 percent between mid-2008 and mid-2009 (see [4]).

There is a considerable literature, both theoretical and empirical, which indicates that bank loan growth is cyclical to the changing macroeconomy activity. Loan supply is determined by bank capital and credit standards, which are dependent on the economic activity cycle. Jokipii and Milne [5] argued for the presence of a negative relationship between European banks’ capital buffers and the GDP over the economic cycle. Puri et al. [6] reported that Changes in a bank’s capital might induce changes in its loan supply. Berger et al. [7] argued that US banks changed their bank credit standards depending on the current phase of the economic cycle. ECB [8] argued that the high GDP growth was accompanied by softer bank credit standards, increased loan amounts, and maturities. Bank of Greece [9] indicated that the decline in GDP during the last quarter of 2009 was accompanied by more stringent bank credit standards and higher rejection rates for small and medium enterprises.

Due to this procyclicality of loan growth behavior, banks usually provide loans to those risky projects with marginally positive or even a negative net present value in the upturns, while they do the opposite in the downturns. Thus, the banking system, rather than compensating for swings in the economic activity over the cycle, makes them even more intense. The procyclicality of loan growth has transformed banks from mitigation mechanisms to amplifiers of changes in economic activity, potentially affecting financial stability and economic growth [10].

By the end of 2008, the G-20 agreed that it was important “to address the issue of procyclicality in financial markets regulations and supervisory systems.” They called upon the IMF, the Financial Stability Board, and the Basel Committee to identify ways to alleviate it. Now several suggestions have been forwarded to attenuate procyclicality, in the form of rules and discretion. Some of the suggestions have been adopted under the Basel III framework, which explicitly addresses the issue of procyclicality.

Basel III reforms are meant to strengthen the banking sector and raise the resilience of individual banking institution to the period of stress. One of the Basel III objectives is to promote countercyclical buffers and reduce procyclicality. The objective of the countercyclical buffer is to ensure the ability of the whole banking sector to provide loans to the economy during recessions and to protect banks from taking significant risks during periods of excessive credit growth. Banks will be subject to a countercyclical buffer that varies between 0% and 2.5% to total risk weighted assets [11]. It will be built up when excess aggregate credit growth is judged to be associated with a buildup of system-wide risk to ensure that the banking system has a buffer of capital to protect it against future potential losses. Also, the buffer will be released in times of stress to reduce the risk of the supply of credit being constrained by regulatory capital requirements. The commission suggested that the credit/GDP guide was a useful common reference point in taking buffer decisions. According to the guide, the size of the buffer (in percent of risk-weighted assets) is 0 when credit/GDP gap is below the lower threshold 2%, while it reaches its maximum level 2.5% when the gap exceeds the upper threshold 10%. When the credit-to-GDP gap is between 2% and 10%, the buffer add-on will vary linearly between 0% and 2.5% [12]. A lot of research has demonstrated that credit-to-GDP gap performed well for taking buffer decision in the build-up phase. Drehmann et al. [13] indicated that the credit-to-GDP ratio tended to rise smoothly well above trend before the most serious episodes. Unfortunately, related research indicated that the variable credit-to-GDP gap was not an ideal indicator variable for signalling the release phase.

Naturally, we suspect that the asymmetry dependence on loan growth and economy activity may be the reason of the above disfunction of taking buffer decisions in release phase. Actually, the asymmetric procyclicality of credit risk has been verified, which indicated that the effect of the business cycle on credit risk is more pronounced during downturns by Marcucci and Quagliariello [14]. However, the asymmetric procyclicality of loan growth has been paid little attention.

Copula-based models provide a great deal of flexibility in modeling multivariate distributions, allowing the researcher to specify the models for the marginal distributions separately from the dependence structure (copula) that links them to form a joint distribution [15]. It has become a popular concept for measuring the stochastic dependence between random variables. Copulas can deal with complex multivariate correlation structure such as nonlinearity and asymmetry in that they provide a way of isolating the description of the dependence structure from the marginal distribution function. Mendes [16] investigated the asymmetric extreme interdependence of emerging equity markets applying copula approach and indicated that the dependence was typically stronger during bear markets. Durante and Jaworski [17] investigated the spatial contagion between financial markets based on a threshold copula approach. Recently, copula theory has been extended to the conditional case, allowing the use of copulas to model dynamic structures. Patton [18] extended the theory of (unconditional) copulas to the conditional case, which allow us to use copula theory in the analysis of time-varying conditional dependence, and examined the dependence structure of daily Deutsche mark-US dollar (DM-USD) and Japanese yen-US dollar (Yen-USD) exchange rates.

In this paper, we apply time-varying copula combined with GARCH model to analyze the dependence of banking loan and macroeconomy growth in China. We mainly test the existence of asymmetric procyclicality of Chinese banking, which can provide beneficial suggestion for the implementation of the countercyclical buffer policy. The remainder of the paper is structured as follows. In Section 2, the copulas employed in this paper are described. Section 3 contains the data description, the data processing, and the empirical results. In Section 4, we analyze the reason of asymmetric procyclicality and its implications for financial controlling and regulatory. Finally, the main conclusions are summarized in Section 5.

#### 2. Methodology

We use a time-varying copula approach to examine the dependence structure between banking loan and economy growth over time. We begin with modeling the margin of each time series by fitting appropriate ARMA-GARCH specifications to the data and extracting the standardized residuals. We then apply the empirical cumulative distribution function (ECDF) to obtain approximate i.i.d. (independently and identically distributed) Unif () series that are suitable for further statistical analysis in copulas. At last, we estimate the static and time-varying parameters of copulas.

##### 2.1. Models for Marginal Distributions

To model the margin of return series, we combine an ARMA process with a standard GARCH model. This combination can successfully characterize some important stylized facts of time series such as volatility clustering and time-varying volatility. Given a time series , an ARMA -GARCH model can be written as (see [19]) where , , , is a constant term of the conditional mean equation, is a sequence of i.i.d. random variables with zero mean and unit variance, and denotes the conditional variance of return series at time , which depends on both past return innovations and past conditional variances . Usually, random variable is assumed to be a standard normal distribution, standardized Student’s distribution, or standardized GED (generalized error distribution).

##### 2.2. Definitions and Properties of Copula Functions

The introduction of copulas can be traced back to the statistician Sklar [20]. He proposed the famous Sklar theorem, which shows that any -dimensional joint distribution function may be decomposed into its marginal distributions and a copula, which completely describes the dependence between the variables. Sklar [20] also gave the definition of “copula” as follows.

*Definition 1. *A two-dimensional copula is a function that has the following properties:(i) is increasing in and ;(ii); ; ;(iii)for every such that and , we have .

Theorem 2 (Sklar’s theorem (see [20])). *Let be a -dimensional distribution function with marginals with . Then, there exists a copula such that, for random variables , one has
**
If are continuous for all , then is unique. Conversely if is a copula and are distribution functions, then the function defined above is a joint distribution with margins .*

Patton [18] extended the theory of (unconditional) copulas to the conditional case, which allows us to use copula theory in the analysis of time-varying conditional dependence. He gave the definition of conditional copula as follows.

*Definition 3. *The conditional copula of is the conditional joint distribution function of and given , where and .

Theorem 4. *Let be the joint conditional distribution of . Assume that and are continuous in and for all . Then there exists a unique conditional copula such that
*

*2.3. Dependence Relation*

*Rank correlation concentrates on modeling the rankings of given observed data rather than on the actual values of the data themselves. There are two well-established measures of rank correlation, which are Spearman’s rho and Kendall’s tau.*

*Let and be continuous random variables whose copula is . Spearman’s rho for and is given by
Kendall’s tau for and is given by
*

*Tail dependence is applied to measure the dependence between the extreme values of random variables for copula models. Informally, it measures the probability that we will observe an extremely large positive (negative) realization of one variable, given that the other variable also took on an extremely large positive (negative) value. The definition of tail dependence is given by Nelsen [21]. Let and be continuous random variables with distribution functions and , respectively. The upper tail dependence coefficient between and is defined as
if this limit exists. The same concept is applied to define the lower tail dependence coefficient as
if this limit exists. These parameters are nonparametric and depend only on the copula of and . The following formulas give the relationship between tail dependence parameters with copula functions:
The measure quantifies the amount of extremal dependence within the class of asymptotically dependent distributions. It provides a natural way for ordering copulas. If , then and are said to be asymptotically dependent in the upper tail. If , then and are said to be asymptotically independent in the upper tail. It is similar for the lower tail dependence parameter.*

*2.4. Two Copulas*

*We will specify and estimate two alternative copulas, the “symmetrized Joe-Clayton” (SJC) copula and the Gaussian copula, both with and without time variation. We will assume that the functional form of the copula remains fixed over the sample whereas the parameters vary according to some evolution equation.*

*The two-dimensional Gaussian copula is
*

*For the static Gaussian copula, the parameter is assumed to be constant over time. For the time-varying Gaussian copula, the correlation parameter is assumed to be evolving through time. In this paper, we assume that the time-varying correlation matrix
complies with a DCC () process (see [22]):
where is the sample covariance of and is a square matrix with zeros as off-diagonal elements and diagonal elements as the square root of those of . The parameter constraints for the DCC are the same for the univariate GARCH () models: , .*

*The distribution of the SJC copula is derived from the Joe-Clayton copula by Patton [18]:
where is the upper tail dependence coefficient and is the lower tail dependence coefficient. The Joe-Clayton copula is defined as follows:
where and .*

*Tail dependence captures the behavior of the random variables during extreme events. The normal copula has when correlation parameter is less than one, meaning that in the extreme tails of the distribution the variables are independent. The Joe-Clayton copula allows both upper and lower tail dependence to range from zero to one freely of each other. One major drawback of the Joe-Clayton copula is that even when the two tail dependence measures are equal, there is still some (slight) asymmetry. The symmetrized Joe-Clayton (SJC) copula has overcome this drawback by a slight modification of the original Joe-Clayton copula, which ensures that the tail dependence is symmetric when .*

*For the time-varying form of SJC copula, Patton [18] suggested that the tail dependence coefficients follow something akin to a restricted ARMA (1,10) process:
where denotes the logistic transformation so as to keep the parameters of SJC copula in and and come from the probability integral transform series and by using the marginal cumulative distribution function of the original series. The tail dependence evolution equation contains an autoregressive term and a forcing variable, which is the mean absolute difference between and over the previous 10 observations.*

*2.5. Estimation*

*This paper’s main interest is to estimate the dependence parameters in copula functions. Maximum likelihood is the natural estimation procedure to use in this context that specifies models for the two marginal distributions and the copula. There are two approaches to estimate the parameters in a copula function using maximum likelihood estimation (MLE). The first and most direct estimation method is to estimate the copula and the marginal distributions simultaneously. But in this approach, the large number of parameters can make numerical maximization of the likelihood function difficult. The second approach is a two-stage maximum likelihood estimation method that the marginal distribution functions are estimated with the assumption of independence between the two random variables firstly and then the dependence parameter of copula function is estimated by substituting the marginal distribution into the copula function. In this paper, we apply the two-stage maximum likelihood method.*

*3. Empirical Analysis*

*This section contains the empirical part of the paper. First, the data source is described. Afterwards, the ARMA-GARCH filtering of the data is sketched, which will ensure that the goodness-of-fit tests get i.i.d. data as input. Finally, we estimate the parameters of two time-varying copulas and generate the time-varying correlation coefficient of the loan growth and economy growth. We use the software of Eviews8.0 and Matlab2012 to finish the computation.*

*3.1. Data*

*In our empirical analysis, it includes two indices which are economy growth index and loan growth index. GDP is the most ideal variable of economy growth. But it is well known that GDP is a quarterly statistical index. To increase the sample point, we choose the growth rate of Chinese industrial added value, which is a monthly economic index, as the proxy of economy growth. In fact, the growth rate of GDP and industrial added value has high-positive correlation. The growth rate of industrial added value is gathered from the WIND database and the website of National Bureau of Statistics of China. The loan growth rate is gathered from the website of People’s Bank of China and China Financial Statistics (1949–2005). The monthly data covers the period of January, 1992 to December, 2013. According to Chinese industrial statistics rules, the industrial added value of January has not been submitted from the year of 2007. We apply the average interpolation approach to complete the data series. Table 1 presents some summary statistics of the data.*