Measuring the Instability of China’s Financial System: Indices Construction and an Early Warning System

: In this paper, employing several econometric techniques, we construct a financial stress index (CNFSI) and a financial conditions index (CNFCI) to measure the instability of China’s financial system . The indices are based on the monthly data collected from China’s inter-bank markets, stock markets, foreign exchange markets and debt markets. Using two indices, we identify the episodes of systemic financial stress, and then evaluate the indices. The empirical results suggest that the CNFSI performs better than the CNFCI. Furthermore, we propose four leading indicators for monitoring China’s financial instability, and provide a primary early warning system for China’s macroprudential regulations.


Introduction
The global financial crisis of 2008 has renewed the post-crisis research interests in the instability of financial sector. Although full-blown financial crises did not take place in China during past decades, China did experience several periods of financial instability since 1978. Specifically, the high non-performing loans ratio in China's banking sector, hurt the soundness of financial system and thereby depressing China's sustainable rapid economic development during mid-1990s. Empirical studies have suggested that the stability of financial system is not only the precondition, but the foundation for sustainable economic developments. Therefore, exploring the methods to measure and monitor the instability of China's financial system, and thereby providing early warning signals and preventing possible financial distress has important implications for ensuring the stability and sustainability of China's economic growth.
In this paper, first, we construct a financial stress index (FSI) and a financial conditions index (FCI) to measures the systemic risks in China's financial system.
Several techniques, including GARCH modelling, VAR approach and econometric benchmarking are employed in developing two indices. China's FSI (CNFSI) comprises several sub-indices, which gauge the instabilities of different financial markets including interbank markets, stock markets, foreign exchange markets and debt markets. China's FCI (CNFCI) is built up by extracting the financial information from the numerous variables and covering the same above markets.
Second, by using two indices, we identify the episodes of financial stress for China, and then conduct predictive tests and total errors analysis to evaluate them.
The predictive tests show that both CNFSI and CNFCI perform better, but the empirical results from total errors analysis suggest that the CNFSI is more suitable for measuring and assessing China's financial instability than the CNFCI.
Third, we seek to find some variables, which help predict the systemic financial stress identified by the indices. Based on the empirical results, We propose four types of leading indicators for monitoring China's financial instability: the growth rates of deposits and loans (Credit Indicator), real estate prosperity index or housing price index (Investment or Property Indicator), CPI inflation (Price Indicator) and the growth rates of M2 (Monetary Indicator). Combining the leading indicators and the CNFSI constructed, finally, we provide a primary early warning system for China's macroprudential regulations.
The rest of the paper is structured as follows. Section 2 gives a literature review.
Section 3 describes the Data. Section 4 constructs the indices, identifies the episodes of financial stress, and compares the two indices. Section 5 examines the leading indicators for China's financial instability and proposes an early warning system for China's macro-prudential regulations. Section 6 concludes.

Literature Review
Financial instability has many sources. Our study, likely in the recent research heart of macro-finance linkages, focuses on the instability of a financial system as a whole, viz the financial instability caused by systemic risks. Systemic risk, according to the definition by Bandt and Hartmann (2000), is "a systemic event that affects a considerable number of financial institutions or markets in a strong sense, thereby impairing the general well-functioning of the financial system". ECB (2010)  Many measures of systemic risk have been developed, one direction in which is attempting to construct a continuous financial index, which contains a whole set of information, describes conditions of the entire financial system, either loose or stress by predetermined standards. These financial indices, including FSIs and FCIs, which can "provide a timely snapshot of the contemporaneous severity in a financial system", and can be "updated in a more timely fashion with forwarding-looking features" according to Illing and Liu (2003), are very useful in measuring and assessing the soundness or instability of a financial system. The indices eliminate some drawbacks derived from binary measures and logit models for systemic risk. Moreover, a well-constructed index "should not be meaningful as a monitoring tool, but also useful within a large EWS (Early Warning System)" 3 .
An FCI, is used to reflect and assess the "stress exerted on economic agents by uncertainty and changing expectations of loss in financial markets and institutions" (Illing and Liu (2003)). It "is a continuous variable with a spectrum of values, where extreme values are called financial crises." FSIs can be employed for identifying the financial distress severity and dating the systemic conditions, and thereby warning and predicting the possible breakthrough of a crisis in the financial system. One of the advantages in using FSIs is that an FSI is continuous of high frequency (daily, weekly, monthly etc.), covering numerous systemically important financial markets. There are two key elements in constructing an FSI: variables choice and weighting method.
The variables adopted should cover the main components (markets) of the regarding financial system. Literature gives alternative weighting schemes: (1) Hatzius et al. (2010) argued that "an FCI should measure financial shocks-exogenous shifts in financial conditions, eliminating variability in the financial variables that can be explained by current and past real activity" so that it reflects exogenous information associated with the financial sector rather than feedback from macroeconomic conditions, which are incorporated into most "old" FCIs. Against this background, our CNFCI follows most old ones. Some researchers, for example, Hatzius et al. (2010), take FSIs as a special form of FCIs, hence, FCIs should reflect the information contained in FSIs and beyond. But Oet et al. (2011) argued that a financial stress index approach is more fitting than a financial conditions approach.
Using leading indicators and early warning system to monitor financial instability has a long history. Regarding literature dates back to the 1970s. KLR (1998) provided a review of the literature for indicators of crises in the Appendix of their paper.
Methodologically, EWS is divided into two groups: parametric (regression based) and non-parametric (signal extraction). Using parametric methods, Frankel and Saravelos (2012) investigated the crisis incidence of the global financial crisis in 2008-09. They find that foreign exchange reserves, real exchange rate, credit growth, real GDP growth and the current account balance as a percentage of GDP are the most reliable indicators to explain crisis incidence. A typical non-parametric EWS, the so called

China's Financial and Financial Regulation System
China's financial system (Figure 1), consisting of banking sector, financial markets, and nonstandard financial sector, is dominated by the banking sector. The banking sector is still controlled by the big-four state-owned commercial banks even with the entrance and growth of many domestic and foreign banks and financial institutions in recent years. The total assets and liabilities of the banking sectors, according to CBRC, China's regulator of the banking system, are 13.36 trillion yuan (RMB)  China's money market consists of three submarkets; the inter-bank borrowing market, the inter-bank bonds repurchase market and the commercial paper market.

Foreign Exchange
severe constraints: the non-performing loans ratios are annually, housing price index is not available after 2012, and most bond yield data dated from Jan. 2012. A detailed description of variables and data sources see Table A in the Appendix.
China's financial system mainly comprise the banking sector (Interbank markets), equity (stock) markets, debt markets, foreign exchange markets, and derivative security markets. Given that the derivative markets are tiny, underdeveloped and very shallow at the moment, we focus on the former four markets in this paper. The variables employed in constructing an FSI and an FCI for China's economy include various spreads, non-performing-loans ratio, deposits-to-loans ratio, exchange rates and foreign reserves, stock index, see Table A in Appendix and Section 4.
In addition, some macroeconomic variables are also included in the sample set

A National Financial Stress Index for China's Financial System (CNFSI)
Our FSI designed to gauge the severity of financial instability in China comprises eight variables covering four markets: banks risk spread, banks non-performing loan ratio, and banks loan-to-deposit ratio for banking industry; shanghai stock market index for stock markets; exchange rate and foreign reserves for foreign exchange markets; and risk spread and sovereign spread for debt markets. As mentioned in section 3, the variables are summarized in the Table A of the Appendix.

Banking Sector
Three measures with four variables are adopted to reflect the stress in the banking sector: risk spread, non-performing loans ratio, and overall loans-to-deposits ratio. We calculate the FSI for the banking sector (BankFSI) by variance-equal weighting.

Risk spread
Risk spread in banking sector is the spread between risky and risk-free rates to reflect the interbank liquidity constraints and the expectations of default risk. The calculation is where 3 mons L t denotes the three-month borrowing rates in China's interbank market; 3 mons TBR t is the three-month government bond rates.

Non-Performing loan ratio
The overall non-performing loan ratio for the state-owned commercial banks is chosen to assess the stress of banking sector in China. This is because the capital owned by the state commercial banks dominated the capital structure of China's banking industry 4 . The data sources from the website of China Banking Regulatory Commission, the official regulator of China's banking system, and Shi and Peng (2003).

Loans-to-Deposits ratio
This variable measures the constraint and default risks faced by China's banking sector. The calculation is straightforward.

FSI for the banking sector (BankFSI)
Using equal-variance weighting method, we build a sub-FSI for China's banking industry since 1997, shown in Figure 7. If we exclude the bank risk spread because the data is not available until 1997, an alternative BankFSI for China's banking sector covering the period from January 4 The share of the capitals owned by the state banks has been above 70%, according to the CBRC.  1994-1995 and 1998-1999. Comparing Figure 8 with Figure 7, we see that the second BankFSI is more smoothing than the first one, and two BankFSIs demonstrate similar trends after 1997.

Stock Markets
The systemic stress and risks in stock markets are measured by the volatility of the stock index. We estimated the volatility using a GARCH (1, 1) model.
Following Bollerslev (1986), a simple GARCH (1, 1) model is defined as 0 , (0,1) where t V denotes the month-to-month change in shanghai stock market index in our study, the standard deviation t  predicts the risk in the stock market.
The FSI for China's stock markets (SMFSI) constructed by GARCH (1, 1) is presented in Figure 9. Figure 9 indicates that China's stock markets are very volatile over the examined period.

Foreign Exchange Market
The stress in China's foreign markets is also measured by the volatility. Following

Bond yield spread
The spread between long-term bond yield and the short-term bond yield is used to be a possible predictor for the economic recession, and to proxy the uncertain in the

Bond yield spread t =C 10 TB t -C 1TB t (5)
where C10TB represents the 10-year government bond yields, C1TB denotes 1-year government bond yield. That we don't use 3-month Treasury bill yields is because, on one hand, the 3-months bond in China's short-term bond market is less issued and its volume of issuance is tiny, on the other hand, the 1-year government bond is most populous and has very long issuing history in China.

Sovereign debt spread
This term is defined by China's 10-year government bond yields minus the US 10-year government bond yields: Sovereign debt spread t = C 10 TB t -US 10 TB t Combining the bond yield spread and the sovereign debt spread, we obtain an FSI for China's debt markets by equal-variance weighting in figure 11.

Figure 11 FSI for China's Debt Markets
In figure 11, we find that the financial stress increased in China's debt market after 2009 due to the contagion effects of the international financial crisis.

Overall FSI for China's Financial System (CNFSI)
We employ both equal-variance weighting to construct an overall FSI (CNFSI) for China's financial system, and then take the better one as the CNFSI.
Given that the sample period for the debt market is too short (from 2002 onwards), and the trade volume in debt market is very tiny in China, we construct the CNFSI excluding DMFSI by equal-variance weighting from 1994 to 2012, Figure 12 plots the CNFSI. When the CNFSI is two times of standard deviation more than the long-term average level, it suggests a financial systemic stress.
Hence, the identification standard of a system financial stress is defined as where CNFSIE denotes the identification standard,  To provide useful and convenient tools for the supervisors and the public, we develop a non-parametric alarming grade system in terms of the degree of deviations constructing the FCI, we replace the loans-to-deposits ratio by deposits-to-loans ratio, which provide positive contributions to financial conditions. The set of chosen variables includes: deposits-to-loans ratio of banking industry, non-performing-loans ratios of banking industry, risk spread of banks, 3 months interbank borrowing rates, these four variables for banking system; growth rates of M2 for money supply, CPI inflation for the change of price level; national housing price index for asset price and the real estate prosperity index for the demand for investment, stock market index for equity market, exchange rate and the change of foreign reserves for foreign exchange markets.
Following Swiston (2008), Osorio et al. (2011), we estimate the CNFCI using the weighted average approach, in which the weights are extracted from a VAR model by: where t y is a (m We use the cumulative responses of growth of industrial production to a one unit shock in financial variables within 12 periods (months) to calculate the weights for each financial indicator. The VAR models satisfy the requirements of mathematical stability, no heterogeneity, no AR and normal distributions in residuals. Figure 14 presents the CNFCI without debt market since 1997 constructed by weights-sum approach.
Figure 14 CNFCI without debt market constructed by weight-sum approach.
In Figure 14, we find that the financial conditions had a deep fall in 1998, which could be caused by the spill overs of Asian financial crisis, and then raise gradually, but declined dramatically after 2008, which could be explained by the global financial crisis; eventually recovered after 2009 with fluctuations.

Episodes of Financial Vulnerability by CNFCI
We

Evaluation by Predictive Analysis
We examine and compare the two indices by testing their ability to predict the output gap secondly. As our data is monthly, we use the growth rates of industrial production to proxy the growth rates of GDP.

In-Sample Predictions:
Firstly, we carry out formal predictive tests by using an in-sample estimation equation: where IPgrowthgap denotes the gap of the growth rates of industrial production, proxy for the gap of output growth. Index denotes the CNFSI or the CNFCI, respectively. C is the constant, t  is the error term. IPgrowthgapis calculated by H-P filter. To be simple, we use the OLS to investigate the indices' ability to predict the output growth gap. The results are reported in Table 3.

Pseudo-Out-Of-Sample Predictions:
Following Hatzious et al. (2010) and Osiorio et al. (2011), we conduct a "pseudo-out-of-sample" prediction tests by estimating the same equation (10) recursively and calculating the root mean squared error (RMSE). The results are also shown in Table 3.
The in-sample and post-sample prediction tests in Table 2 show that both CNFSI and CNFCI are effective in predicting the fluctuations of GDP, and the CNFCI performs a little better than the CNFSI.  *denotes the coefficient is significant in 5% level. ** denotes significant in 10% level.

Evaluation by Total Errors and Noise/Signal Analysis
In this section, we employ the ratios of noises to true signals, Type I errors, Type II errors and Total errors to evaluate the two indices. The noise/signal ratio is defined as a ratio of wrongly alarming to rightly warning signals. Type I errors measure the ratio of failing to signal a "true" high-stress event, calculated by the number of no-signal-issuing for "true" stress divided by the total number of "true" stress. Type II errors are ratios that falsely signals, calculated by the number of wrong signals divided by the number of total signals. The "true" high-stress events are judged and justified by the reality of China's financial situations from 1994 to 2012 and literature 6 .
Following Comelli (2013), we assume that the policymakers are more cautious, they dislike more missing a stress episode than issuing a false signal. This implies that the policymakers think that missing the alarm of a stress episode can potentially be much costlier than issuing a false signal in terms of foregone output. Therefore, we calculate the total errors according to the following equation: Total Errors= (2/3)*Type I Errors+ (1/3)*Type II Errors.
The performance of the index can be assessed by comparing the total errors and noise/signal ratio. The better index should be the one that can minimize the total errors and the noise/signal ratio.  for China's financial instability. We choose eight variables including the growth rates of total loans and total deposits and most variables in dataset for constructing the two indices. These indicators are commonly employed in the macroprudential literature to predict financial instability (Borio andLowe, 2002 and2004). They capture the building up of financial vulnerability and imbalance in macroeconomic conditions. Table 4 summarizes the indicators.
Methodologically, following the "signals approach" by Kaminsky and Reinhart (1996) and KLR (1998) Figure 15 depicts the volatilities of these indicators, their thresholds for issuing alarming signals (precautious lines) and the identified episodes of financial stress with the early warning window (12 months prior to the start of the systemic financial stress). Table 4 reports the performance of these early warning indicators. On the basis of total errors and noise/signal ratio, it is shown that the volatilities of banking deposits-to-loans ratios, growth rates of M2, three months inter-bank borrowing rates, CPI inflation, housing price index, real estate prosperity index, growth rates of total deposits and total loans are fitting to be the leading indicators (early warning indicators) of China's financial vulnerabilities.
The results suggest that the deposits-to-loans ratio, the growth rates of deposits  (2002), when the deviations of any two of the four indicators from their long run trends exceed their regarding thresholds (4% for deposits-to-loans ratio, 6% for growth rates of aggregate loans, 4% for CPI inflation, 5% for housing price index or 4% for real estate property index, and 4% for growth rates of M2), the policymakers and regulators should pay attention to a possible financial stress within 12 months, if the CNFCI also meet the identification standard of a systemic risk, the regarding alarm signal should be issued and the macro-prudential policy would be implemented to avoid the possible financial distress.

Concluding Remarks
In this paper, we construct a financial stress index (CNFSI) and a financial conditions index (CNFCI) to measure and assess the instability of China's financial system. The The evaluation of the two indices is carried out by predictive tests and total errors analysis. The empirical results from both comparisons suggest that the CNFSI and the CNFCI constructed in our paper are both useful for measuring the stability of China's financial system. The total error analysis supports that the CNFSI is more fitful for monitoring the financial instability in China than the CNFCI.
Using the identified episodes of financial stress, we find four leading indicators for China's financial instability: deposits-to-loans ratio, or growth rates of total loans and deposits (credit indicator), CPI inflation (Price indicator), housing price index or real estate prosperity index (asset or investment indicator), growth rates of M2 (monetary indicator). Combining these leading indicators with the CNFSI, and their thresholds, we form an early warning system for China's macroprudential regulations.
Further research is necessary for seeking more effective methods to examine the thresholds of financial disruptions, and exploring the nexus of monetary instability and financial instability.