Since the global financial crisis of 20072008, 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 timevarying 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.
The interaction of macroeconomy and financial sector variables has long been an object of interest to economists. Keynes [
In particular, since the global financial crisis of 20072008, 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 writedowns of $1306 billion by April 2010, while world GDP contracted by 1.6 percent between mid2008 and mid2009 (see [
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 [
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 [
By the end of 2008, the G20 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 [
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 [
Copulabased 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 [
In this paper, we apply timevarying 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
We use a timevarying 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 ARMAGARCH 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 (
To model the margin of return series, we combine an ARMA
The introduction of copulas can be traced back to the statistician Sklar [
A twodimensional copula is a function
for every
Let
Patton [
The conditional copula of
Let
Rank correlation concentrates on modeling the rankings of given observed data rather than on the actual values of the data themselves. There are two wellestablished measures of rank correlation, which are Spearman’s rho and Kendall’s tau.
Let
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 [
We will specify and estimate two alternative copulas, the “symmetrized JoeClayton” (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 twodimensional Gaussian copula is
For the static Gaussian copula, the parameter
The distribution of the SJC copula is derived from the JoeClayton copula by Patton [
Tail dependence captures the behavior of the random variables during extreme events. The normal copula has
For the timevarying form of SJC copula, Patton [
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 twostage 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 twostage maximum likelihood method.
This section contains the empirical part of the paper. First, the data source is described. Afterwards, the ARMAGARCH filtering of the data is sketched, which will ensure that the goodnessoffit tests get i.i.d. data as input. Finally, we estimate the parameters of two timevarying copulas and generate the timevarying correlation coefficient of the loan growth and economy growth. We use the software of Eviews8.0 and Matlab2012 to finish the computation.
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 highpositive 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
Summary statistics.
Loan growth rate  Growth rate of industrial added value  

Mean  18.9048  14.0346 
Std. Dev.  5.1818  4,3156 
Skewness  0.7920  0.7027 
Kurtosis  3.6216  3.7667 
JarqueBera stat  28.4406 
29.0476 
LjungBox stat  1525.3 
876.77 
ARCH LM stat  3.5049 
2.3368 
Linear correlation  0.2556 
This table presents some summary statistics of the data used in this paper. The LjungBox test and ARCH LM test are conducted using 10 lags. An asterisk (*) indicates a rejection of the null hypothesis at the 0.05 level.
The copula model needs i.i.d. data as input. However, both series exhibit positive skewness. The JarqueBera test of each growth rate strongly rejects unconditional normality. Plots of the autocorrelation function and the partial autocorrelation function of the series and the squared series show that the time series exhibit autocorrelation and timevarying conditional volatility. These visual results are also confirmed by formal statistical tests, such as the LjungBox test, which rejects the null hypothesis of no autocorrelation, and Engle’s Lagrange multiplier test, which indicates that there are indeed ARCH effects. To remove autocorrelation and conditional heteroscedasticity in the univariate time series of the growth rates, an ARMA model with GARCH errors is fitted to the raw series, respectively. We use the AIC, SIC, and HannanQuinn criteria to determine the optimal lag length for the conditional mean (ARMA) process. According to these criteria, we select
Results for the marginal distributions.
Loan growth rate  Growth rate of industrial added value  

Coefficient  Std error  Coefficient  Std error  
Mean equation  C 




AR(1) 



 
AR(2) 



 
MA(1) 



 
MA(2)  —  — 

 


Variance equation  C 




ARCH 



 
GARCH 



 


GED parameter 




Applying the LjungBox test and Engle’s LM test to the filtered series, both up to lag 10, the null hypothesis of no autocorrelation and no ARCH effects, respectively, cannot be rejected any more. Then, we transform the standardized error series to uniform distribution series
Stock returns have been found to take on joint negative extremes more often than joint positive extremes, leading to the observation that “stocks tend to crash together but not boom together.” No similar empirical evidence is yet available for the dependence relation of loan growth rate and economy growth rate. We will specify and estimate two alternative copulas, the symmetrized JoeClayton copula and the Gaussian copula. The symmetrized JoeClayton specification allows asymmetric dependence on the lower tail and upper tail. We now present the main results of this paper: the estimation results for the normal and symmetrized JoeClayton (SJC) copula models. For the purpose of comparison, we also present the results for these two copulas without time variation in the copula parameters. The estimated outcome of copula models is presented in Table
Results for the copula models.
Coefficient  Std error  AIC  BIC  LLF  

Static Gaussian 








Static SJC 








 


Timevarying Gaussian 








 


Timevarying SJC  Constant 







 


 
Constant 

 


 



For the static Gaussian copula, the correlation parameter is positive (0.2677) and is statistically significant. For the timevarying Gaussian copula, the parameters
The time path of the conditional correlations implied by the timevarying copula was obtained from simulations based on two marginal models and the estimated timevarying copula models (see [
Figure
Conditional correlation in the timevarying Gaussian copula and Chinese GDP growth rate, with 95% confidence interval for the timevarying correlation.
Implied conditional correlation in the timevarying SJC copula and Chinese GDP growth rate, with 95% confidence interval for the timevarying correlation.
Figure
The conditional upper and lower tail dependence in timevarying symmetrized JoeClayton copula, with 95% confidence interval for the constant correlation case.
All the above indicate that the procyclicality of Chinese loan growth is asymmetrical. The dependence of loan and economy growth is stronger in the decline stage than in the rise stage of the economy. There are three probable reasons which induce this asymmetry.
First, the asymmetry of ratings’ procyclicality during upward and downward period of business cycle may contribute to the asymmetric procyclicality of banking loan growth. As discussed by Amato and Furfine [
Second, asymmetric monetary policy effects can contribute to the asymmetric behavior of loan growth. Bliss and Kaufman [
Third, the possible asymmetry of bank managers’ herd behavior may also induce the asymmetry of banking procyclicality. Rajan [
Coming back to the issue of the decision of taking countercyclical buffer, our research results combined with the previous results of other researchers may partly explain the disfunction of credittoGDP gap for the decision of releasing buffer. First, as illustrated by Repullo and Saurina [
The lag of signalling for releasing countercyclical buffer is crucial in that the supply of credit may be constrained by regulatory capital requirements in downturns, which can contribute to the further recess of macroeconomy and the subsequent banking instability. Actually, the Basel Committee was aware of the shortcomings of the credittoGDP gap, in particular in downturns, and proposed to use supervisory judgment to release the buffer. The committee also suggested that promptly releasing the buffer in times of stress can help to reduce the risk of the supply of credit being constrained by regulatory capital requirements. But how to realize promptly releasing the buffer still is a question waiting for answer. We give two rough answers. First, the authority can use high frequent index as the releasing indicator for timely capturing the turn point. For example, the monthly macroeconomic index such as industrial added value can be used for signalling the start point of releasing. Of course, the selection for proper high frequent index still needs serious study in the future. Second, during the downturn of economy, the authority should accelerate the pace of releasing the buffer compared with building it up in the rise stage of economy. The authority can introduce a releasing adjustment factor, which is larger than one and the value is determined by the asymmetric degree of procyclicality, to accelerate the releasing pace.
This paper applies copula modeling methods in order to study the characteristic of Chinese banking procyclicality. We mainly analyze the existence of asymmetric procyclicality of loan growth by utilizing timevarying copula to Chinese data from January 1992 to December 2013. Standard ARMAGARCH models with GED innovations are employed for the marginal distributions of the growth rate of loan and industrial added value to filter the data. Then the bivariate Gaussian copula and the symmetrized JoeClayton copula, which allows for general asymmetric dependence, were estimated. The timevarying dependence structure is captured by allowing the parameters of the two copulas to comply with an evolution equation.
The empirical research demonstrates that the procyclicality of loan growth is asymmetric. The dependence between loan and economy growth is more correlated in the decline stage than in the rise stage of economy. The asymmetric credit ratings change may induce loan growth’s asymmetric procyclical behavior by the credit supply channel. And also, the asymmetric monetary policy effect and the asymmetric herd behavior of bank managers may contribute to the asymmetric procyclicality.
We conclude that the asymmetric procyclicality and the lag of credit can explain the disfunction of credittoGDP gap for the decision of releasing phase in taking countercyclical buffer of Basel III. The lag of signalling for releasing countercyclical buffer is crucial in that the supply of credit may be constrained by regulatory capital requirements in downturns, which can contribute to the further recess of macroeconomy and the subsequent banking instability. We suggest two rough thoughts for promptly releasing the buffer. First, the authority can use high frequent index as the releasing indicator for timely signalling the release start point. Second, during the downturn of economy, the authority should accelerate the pace of releasing countercyclical buffer compared with building it up in the rise stage of economy.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors thank Andrew Patton who kindly provided the MATLAB code of Patton_copula_toolbox on his home page