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The Shadow Price of Bad Loans: A study of Chinese Commercial Banks Mingquan Zhou, Maryam Hasannasab and Dimitris Margaritis
Department of Accounting & Finance University of Auckland Business School
Abstract
This paper estimates the shadow price (opportunity cost) of non-performing loans of Chinese commercial banks by applying a directional distance function and duality theory. This method is based on the information of input and output quantities without the need to observe the market price of bad loans. This is important recognising the true quality of bank assets in China is generally unknown. Using an unbalanced panel of 741 observations from 2011 to 2017, we find that the average shadow price of non-performing loans grows. Our results also show that government-controlled banks face the lowest shadow price to reduce bad loans.
Key Words
Shadow price, Non-performing loans, Directional distance function, Chinese commercial banks
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1. Introduction
Against the backdrop of the recent slowdown in the Chinese economy, uncertainty in the Chinese banking industry has increased. Decreasing values of collateral and insolvencies caused by the economic slowdown are adding upward pressure to the growth in non- performing loans (NPLs). Figure 1 shows that, between 2011 and 2018, the amount of NPLs grew almost five-fold, from 428 billion to 2.03 trillion yuan, while the provision coverage ratio decreased from 278% to 186%(China Banking Regulatory Commission, 2018). Furthermore, a report from the Bank of China (2018) shows that the ratio of special mention loans to NPLs of Chinese listed banks was 194% in 2017 while the corresponding figure for systematically important banks globally was 100%.
Fig. 1 NPLs and Provision Coverage Ratio of Chinese commercial banks: 2011 to 2018
An increase in the number and size of NPLs threatens not only banks profitability but also the stability of the financial system. At the individual bank level, growing NPLs decrease interest income and increase the administrative cost of managing loans. High levels of NPLs also affect bank profitability because the bank needs to write down the value of the loan to allow for credit losses (Fredriksson & Frykström, 2019). These effects may prove particularly detrimental for highly leveraged banks with low profitability. Bank failures often occur after a period of a high level of NPLs (Barr, Seiford, & Siems, 1994; Demirgüç-Kunt, 1989). Moreover,
0%
50%
100%
150%
200%
250%
300%
350%
2011 2012 2013 2014 2015 2016 2017 2018 ¥0
¥500
¥1,000
¥1,500
¥2,000
¥2,500
NPLs Provision Coverage Ratio
Unit: Billion CNY
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the failure of a large bank or a series of failures of small banks can spread to other banks threatening the stability of the banking system (Zhang, Cai, Dickinson, & Kutan, 2016).
Banks need to exert additional managerial efforts and incur expenses to deal with NPLs (Karim, Chan, & Hassan, 2010). The strategies for reducing NPLs are primarily based on the cost incurred. A bank can either tighten the standards of credit evaluation to reduce default risk or wait for an economic recovery. When NPLs emerge, banks can take over and sell the collateral to get some of the money back or seize the bad loans and sell them to external investors. However, NPLs are infrequently traded in China. Therefore, the market price of NPLs is volatile and the price data do not appear to provide an accurate assessment of the riskiness of loan portfolios (Macdonald & Zhang, 2019). This is important recognising China’s banking system is now the largest in the world (Cerutti & Zhou, 2018) and the true quality of its assets is unknown (Kauko, 2020). To measure the cost of NPLs, we apply a shadow pricing method that estimates the marginal abatement cost of undesirable outputs in a production process without the need to obtain their market prices(Hasannasab, Margaritis, & Staikouras, 2019).
Several studies estimate the shadow cost of reducing NPLs in developed financial markets from the perspective of the opportunity cost (e.g. Fukuyama & Weber, 2008; Hasannasab et al., 2019). Following Fukuyama and Weber (2008) and Hasannasab et al. (2019), we apply a directional distance function approach that jointly models the production of desirable (good) and undesirable (bad) outputs to estimate the shadow cost of NPLs for Chinese commercial banks. To the best of our knowledge, this study marks the first attempt to investigate NPLs in the Chinese banking industry from the perspective of shadow pricing.
We provide new insights into the risk-taking behaviour of Chinse commercial banks. We model the joint production of performing and non-performing loans by Chinese banks explicitly incorporating the amount of leverage they carry in their capital structure reflecting the riskiness of their production decisions. We compare the shadow price of NPLs across different types of ownership such as government-controlled banks, stated-owned- enterprises controlled banks, privately controlled banks and find that government-controlled banks have lower shadow prices on average. This finding is in contrast with the results of Dong, Meng, Firth, and Hou (2014) who show that government-controlled banks are more likely to
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take excessive risk. We also find that large banks have lower opportunity costs for NPLs measured in terms of the net interest income foregone in managing NPLs.
We recognise most evidence suggests that government ownership for banks leads to poor economic outcomes and greater financial instability (La Porta, Lopez‐de‐Silanes, &
Shleifer, 2002). Mian (2003) reports that government-owned banks in many emerging economies have higher NPLs and are less profitable than private banks. Similarly, Cornett, Guo, Khaksari, and Tehranian (2010) show that state-owned banks in Asian countries were less profitable as well as exposed to greater credit risk prior to the Asian crisis although the gap appears to have been closing since then. Lin and Zhang (2009) find that the ‘Big Four’
state-owned banks are less profitable, less efficient and have lower asset quality than other types of banks in China. However, Chinese banks have gradually expanded non-interest generating business since the interest rate liberalisation in 2013, which reduces credit risk of banks. This liberalisation, to some extent, increases the competitiveness in interest-earning business and lessens borrower adverse selection and moral hazard risk. In addition, more recent evidence suggests that state-owned banks report lower NPLs during economic downturns than their private domestic or foreign owned counterparts. This may reflect either that the relative asset quality of state-owned banks improves during the economic downswing or they report NPLs more evenly over the business cycle (Bertay, Demirgüç-Kunt,
& Huizinga, 2012).
The rest of this paper is organised as follows. Section 2 describes the methodology.
Section 3 presents the empirical results. Section 4 concludes the article.
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2. Methodology
We apply a distance function approach, exploiting the duality between the directional distance function and the profit function, to estimate the shadow price of NPLs. A distance function is a generalisation of the more familiar production function to model multi-output multi-input technologies (see Koutsomanoli-Filippaki, Margaritis, & Staikouras, 2009, 2012).
We follow the two-step method used by Fukuyama and Weber (2008) and Hasannasab et al.
(2019) to price NPLs. The first step is to construct a directional distance function parametrically, and in the second step, we use the Lagrangian form of a constrained profit maximisation problem to obtain the pricing rule.
The bank’s production process is described as follows: bank 𝑘𝑘 (𝑘𝑘= 1,2, … ,𝐾𝐾) uses 𝑁𝑁 inputs (𝑥𝑥𝑛𝑛, 𝑛𝑛 = 1,2, … ,𝑁𝑁) to produce 𝑀𝑀 desirable outputs (𝑦𝑦𝑚𝑚, 𝑚𝑚= 1,2, … ,𝑀𝑀) and 𝐿𝐿 undesirable outputs (𝑏𝑏𝑙𝑙, 𝑙𝑙= 1,2, … ,𝐿𝐿) simultaneously. This production technology is expressed by the technology set
𝑇𝑇= {(𝑥𝑥,𝑦𝑦,𝑏𝑏):𝑥𝑥 ∈ 𝑅𝑅+𝑁𝑁 𝑐𝑐𝑐𝑐𝑛𝑛 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝 (𝑦𝑦,𝑏𝑏) ∈ 𝑅𝑅+𝑀𝑀×𝑅𝑅+𝐿𝐿}.
The corresponding directional technology distance function is defined as:
𝐷𝐷��⃗𝑇𝑇 �𝑥𝑥,𝑦𝑦,𝑏𝑏;−𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,−𝑔𝑔𝑏𝑏�= max �𝛽𝛽: (𝑥𝑥 − 𝛽𝛽𝑔𝑔𝑥𝑥, 𝑦𝑦+𝛽𝛽𝑔𝑔𝑦𝑦,𝑏𝑏 − 𝛽𝛽𝑔𝑔𝑏𝑏 ∈ 𝑇𝑇�.
The directional distance function (DDF) expands good outputs such as loans and securities and contracts inputs such as deposits and bad outputs such as NPLs simultaneously so that technical efficiency is achieved.
We construct the unobservable technology parametrically using a quadratic functional form for the DDF as follows:1
𝐷𝐷��⃗𝑇𝑇�𝑥𝑥𝑘𝑘,𝑦𝑦𝑘𝑘,𝑏𝑏𝑘𝑘;𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏�= 𝛼𝛼0+� 𝛼𝛼𝑛𝑛𝑥𝑥𝑛𝑛𝑘𝑘
𝑁𝑁 𝑛𝑛=1
+ � 𝛽𝛽𝑚𝑚𝑦𝑦𝑚𝑚𝑘𝑘
𝑀𝑀 𝑚𝑚=1
+� 𝛾𝛾𝑙𝑙𝑏𝑏𝑙𝑙𝑘𝑘
𝐿𝐿
𝑙𝑙=1
+1
2� � 𝛼𝛼𝑛𝑛𝑛𝑛́𝑥𝑥𝑛𝑛𝑘𝑘𝑥𝑥𝑛𝑛𝑘𝑘́ 𝑁𝑁
𝑛𝑛´=1 𝑁𝑁 𝑛𝑛=1
+1
2� � 𝛽𝛽𝑚𝑚𝑚𝑚´𝑦𝑦𝑚𝑚𝑘𝑘𝑦𝑦𝑚𝑚´𝑘𝑘
𝑀𝑀 𝑚𝑚´=1 𝑀𝑀 𝑚𝑚=1
+1
2� � 𝛾𝛾𝑙𝑙𝑙𝑙´𝑏𝑏𝑙𝑙𝑘𝑘𝑏𝑏𝑙𝑙´𝑘𝑘
𝐿𝐿 𝑙𝑙´=1 𝐿𝐿 𝑙𝑙=1
1As shown by Färe and Sung (1986) the quadratic is the preferable choice of a parametric functional form for the directional distance function since it provides a second order approximation to the true but unknown production technology, with parameters restrictions to satisfy the translation property.
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+∑ ∑𝑀𝑀 𝛿𝛿𝑛𝑛𝑚𝑚𝑥𝑥𝑛𝑛𝑘𝑘𝑦𝑦𝑚𝑚𝑘𝑘 𝑁𝑁 𝑚𝑚=1
𝑛𝑛=1 +∑ ∑𝐿𝐿 𝜈𝜈𝑛𝑛𝑙𝑙𝑥𝑥𝑛𝑛𝑘𝑘𝑏𝑏𝑙𝑙𝑘𝑘
𝑁𝑁 𝑙𝑙=1
𝑛𝑛=1 +∑ ∑𝐿𝐿 𝜇𝜇𝑚𝑚𝑙𝑙𝑦𝑦𝑚𝑚𝑘𝑘𝑏𝑏𝑙𝑙𝑘𝑘
𝑀𝑀 𝑙𝑙=1
𝑚𝑚=1 .
Where (𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏) is the directional vector indicating the direction by which inputs and outputs are scaled towards the technological frontier. A bank is less efficient when it has a higher value of 𝐷𝐷��⃗𝑇𝑇, whereas the value of zero of 𝐷𝐷��⃗𝑇𝑇 indicates full technical efficiency. We set the directional vector (𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏) equal to (−1, 1,−1) so that the directional model objective is to yield a unit contraction of inputs and bad outputs and a unit expansion of good outputs.
We estimate the parameters ( 𝛼𝛼,𝛽𝛽,𝛾𝛾,𝛿𝛿,𝜈𝜈 𝑐𝑐𝑛𝑛𝑝𝑝 𝜇𝜇) of 𝐷𝐷��⃗𝑇𝑇�𝑥𝑥𝑘𝑘,𝑦𝑦𝑘𝑘,𝑏𝑏𝑘𝑘;𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏� by minimising the sum of deviations of the distance function value from the frontier of production technology subject to the constraints imposed by the technology using the method proposed by Aigner and Chu (1968). The constraints include the feasibility, monotonicity and translation property of the distance function as shown below. As per standard practice, we also impose symmetry. While technological restrictions are recognised in the empirical parametric literature, they are often assumed to hold locally at a particular data point rather than globally as in our approach. We further assume the technology set must be convex. This guarantees the duality between the directional distance function and the profit function, which as we explain below, is used to obtain shadow prices.
The constrained estimation problem is formulated as follows:
min� 𝐷𝐷��⃗𝑇𝑇�𝑥𝑥𝑘𝑘,𝑦𝑦𝑘𝑘,𝑏𝑏𝑘𝑘;𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏�
𝐾𝐾
𝑘𝑘=1
𝑠𝑠.𝑡𝑡.
(1) 𝐷𝐷��⃗𝑇𝑇�𝑥𝑥𝑘𝑘,𝑦𝑦𝑘𝑘,𝑏𝑏𝑘𝑘;𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏� ≥0, 𝑘𝑘 = 1, … ,𝐾𝐾
(2) 𝜕𝜕𝑦𝑦𝑚𝑚𝐷𝐷��⃗𝑇𝑇�𝑥𝑥𝑘𝑘,𝑦𝑦𝑘𝑘,𝑏𝑏𝑘𝑘;𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏� ≤0, 𝑘𝑘 = 1, … ,𝐾𝐾, 𝑚𝑚= 1, … ,𝑀𝑀 (3) 𝜕𝜕𝑥𝑥𝑛𝑛𝐷𝐷��⃗𝑇𝑇�𝑥𝑥𝑘𝑘,𝑦𝑦𝑘𝑘,𝑏𝑏𝑘𝑘;𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏� ≥0, 𝑘𝑘= 1, … ,𝐾𝐾, 𝑛𝑛= 1, … ,𝑁𝑁 (4) 𝜕𝜕𝑏𝑏𝑙𝑙𝐷𝐷��⃗𝑇𝑇�𝑥𝑥𝑘𝑘,𝑦𝑦𝑘𝑘,𝑏𝑏𝑘𝑘;𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏� ≥0, 𝑘𝑘= 1, … ,𝐾𝐾, 𝑙𝑙= 1, … ,𝐿𝐿 (5) − � 𝛼𝛼𝑛𝑛𝑔𝑔𝑥𝑥+
𝑁𝑁 𝑛𝑛=1
� 𝛽𝛽𝑚𝑚𝑔𝑔𝑦𝑦−
𝑀𝑀 𝑚𝑚=1
� 𝛾𝛾𝑙𝑙𝑔𝑔𝑏𝑏
𝐿𝐿 𝑙𝑙=1
=−1,
− � 𝛿𝛿𝑛𝑛𝑚𝑚𝑔𝑔𝑥𝑥
𝑁𝑁 𝑛𝑛=1
+ � 𝛽𝛽𝑚𝑚𝑚𝑚´𝑔𝑔𝑦𝑦
𝑀𝑀 ḿ=1
− � 𝜇𝜇𝑚𝑚𝑙𝑙𝑔𝑔𝑏𝑏
𝐿𝐿 𝑙𝑙=1
= 0,
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− � 𝜈𝜈𝑛𝑛𝑙𝑙𝑔𝑔𝑥𝑥
𝑁𝑁 𝑛𝑛=1
+ � 𝜇𝜇𝑚𝑚𝑙𝑙𝑔𝑔𝑦𝑦
𝑀𝑀 𝑚𝑚=1
− � 𝛾𝛾𝑙𝑙𝑙𝑙′𝑔𝑔𝑏𝑏
𝐿𝐿 𝑙𝑙=1
= 0,
− � 𝛼𝛼𝑛𝑛𝑛𝑛́𝑔𝑔𝑥𝑥
𝑁𝑁 𝑛𝑛´=1
+ � 𝛿𝛿𝑛𝑛𝑚𝑚𝑔𝑔𝑦𝑦
𝑀𝑀 m=1
− � 𝜈𝜈𝑛𝑛𝑙𝑙𝑔𝑔𝑏𝑏
𝐿𝐿 𝑙𝑙=1
= 0,
(6) 𝛼𝛼𝑛𝑛𝑛𝑛´= 𝛼𝛼𝑛𝑛´𝑛𝑛,𝑛𝑛 ≠ 𝑛𝑛́; 𝛽𝛽𝑚𝑚𝑚𝑚´=𝛽𝛽𝑚𝑚´𝑚𝑚,𝑚𝑚 ≠ 𝑚𝑚´; 𝛾𝛾𝑙𝑙𝑙𝑙´= 𝛾𝛾𝑙𝑙´𝑙𝑙,𝑙𝑙 ≠ 𝑙𝑙´.
The next step is to calculate shadow prices. Specifically, we are interested in estimating the shadow price of a bad output (NPLs). We do this by exploiting the duality between the profit function and the directional distance function. The Lagrangian form of the profit maximisation subject to the DDF constrain is given by:
L =𝑝𝑝𝑦𝑦 − 𝑤𝑤𝑥𝑥 − 𝑝𝑝𝑏𝑏 − 𝜆𝜆 𝐷𝐷��⃗𝑇𝑇�𝑥𝑥,𝑦𝑦,𝑏𝑏;𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏�
where 𝑝𝑝, 𝑤𝑤 and 𝑝𝑝 represent the prices of desirable outputs, inputs and undesirable outputs, respectively. λ is the Lagrangian multiplier which is equal to the value of the directional vector (see Fare, Grosskopf, & Margaritis, 2019).
The first order conditions of the Lagrangian profit maximisation problem are given by:
(7) 𝑝𝑝 − 𝜆𝜆𝛻𝛻𝑦𝑦𝐷𝐷��⃗𝑇𝑇�𝑥𝑥,𝑦𝑦,𝑏𝑏;𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏�= 0 (8) − 𝑤𝑤 − 𝜆𝜆𝛻𝛻𝑥𝑥𝐷𝐷��⃗𝑇𝑇�𝑥𝑥,𝑦𝑦,𝑏𝑏;𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏�= 0 (9) − 𝑝𝑝 − 𝜆𝜆𝛻𝛻𝑏𝑏𝐷𝐷��⃗𝑇𝑇�𝑥𝑥,𝑦𝑦,𝑏𝑏;𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏�= 0
Assuming any one of the input prices or desirable output prices is known, say the price of loans (𝑝𝑝1
),
we can use the information to shadow price NPLs as:(10) 𝑝𝑝=−𝑝𝑝1𝜕𝜕𝑏𝑏1𝐷𝐷��⃗𝑇𝑇�𝑥𝑥,𝑦𝑦,𝑏𝑏;𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏�
𝜕𝜕𝑦𝑦1𝐷𝐷��⃗𝑇𝑇�𝑥𝑥,𝑦𝑦,𝑏𝑏;𝑔𝑔𝑥𝑥,𝑔𝑔𝑦𝑦,𝑔𝑔𝑏𝑏�.
Where the right-hand side of the pricing equation comprises entirely of observed information.
In this case, we have defined the price of NPLs in terms of the price of loans. Hence, the estimated shadow price in (10) can be interpreted as the opportunity cost of reducing NPLs by an additional unit expressed in terms of lowering the production of loans.
In conclusion, we have shown this shadow pricing method is primarily based on the quantities of inputs and outputs. It only uses the observed price of one input or output as the
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“known” price. If price data is not available, the pricing rule can be modified to utilise information on observed profits instead of prices (see Fare et al., 2019). In addition, this shadow price has an intuitive economic interpretation in our context: it indicates the difficulty of reducing NPLs — a higher price represents an increase in the cost of managing NPLs in a riskier environment.
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3. Data and Empirical Analysis 3.1 Data
The data is sourced from the annual reports of Chinese commercial banks from 2011 to 2017. As some banks do not publish their reports consistently, our sample is an unbalanced panel of 741 annual observations. It includes 4 major state-owned banks, 12 national joint- stock banks and at least 76 city and rural commercial banks.
We follow the intermediation approach to select inputs and outputs (Fukuyama &
Weber, 2008; Hasannasab et al., 2019). We choose four inputs, two good outputs and one bad output. Inputs include fixed assets, deposits and other borrowings, the number of employees and total equity. The good outputs are total loans and non-interest income, and the bad output is NPLs. We set the price of loans to be the “known” price. It is calculated as interest income from loans over total loans.
Table 1 reports descriptive statistics of bank inputs and outputs as well as loan prices. It is evident that there is significant variation in the size and operations of Chinese banks. Loan interest income is on average 7 times higher than non-interest income, indicating that the banks depend more heavily on the traditional loan-lending business to generate revenue. This is important in our context recognising that NPLs can have a substantial adverse effect on bank interest income.
Table 1 Descriptive statistics of bank inputs and outputs: 2011 to 2017
2011-2017 Mean Min Max SD
Inputs
Emp 828,733 7,215 18,533,179 2,523,687
FA 8,916 31 213,533 30,386
Depo 22,832 381 503,082 77,042
Equity 82,027 1,149 2,063,864 250,084
Good Outputs
Loans 574,684 3,644 13,392,081 1,760,430
NII 8,434 -522 197,463 26,263
Bad Outputs
NPLs 8,035 0 223,388 26,957
Price
PoL 11.14% 4.20% 28.70% 3.33%
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Notes: Emp is the number of employees, FA is fixed assets, Depo is deposits and other borrowings, Equity is total equity, Loans is total loans, NII is non-interest income, NPLs is non-performing loans, PoL proxies the price of loans. All inputs and outputs are in millions of CNY except Emp.
China’s predominantly state-controlled banking system presents some structural and institutional problems that require special attention. Public officials tend to use bank lending as a policy tool channelling credit to firms which are not necessarily the best performing or more creditworthy thereby exacerbating risks on bank lending portfolios (Avgouleas & Xu, 2017; Bailey, Huang, & Yang, 2011). Against this backdrop, it is not surprising that loan quality problems are pervasive in Chinese banks (Kauko, 2020). Dong et al. (2014) report that banks’
risk-taking behaviour depends on their controlling shareholders. To examine whether the shadow cost of reducing NPLs is associated with the ownership structure, we divide our sampled banks into three categories: government-controlled (GCBs), state-owned enterprises controlled (SOECBs) and privately controlled (PCBs).
Table 2 reports the mean values of bank inputs and outputs and the price of loans across different ownership types. It shows that GCBs are the largest banks, whereas SOECBs and PCBs are about the same size on average. GCBs also have a larger volume of NPLs compared with SOECBs and PCBs albeit in relative terms all NPL ratios hover around 1.4%. The prices of loans of GCBs, SOECBs and PCBs are very similar at 11% on average.
Table 2 Inputs and outputs by bank type
GCBs SOECBs PCBs
Inputs
Emp 87,559 8,028 7,173
FA 34,712 2,791 2,923
Depo 2,915,650 340,194 336,222
Equity 285,646 32,950 35,531
Good Outputs
Loans 2,023,156 235,358 238,662
NII 28,892 3,506 3,760
Bad Outputs
NPLs 28,805 3,188 3,115
Loan Price
PoL 11.00% 11.20% 11.10%
Notes: Emp is the number of employees, FA is fixed assets, Depo is deposits and other borrowings, Equity is total equity, Loans is total loans, NII is non-interest income, NPLs is non-performing loans, PoL proxies the price of loans. All inputs and outputs are in millions of CNY except Emp. CGBs are government controlled banks, SOECBs are state-owned enterprises controlled banks, and PCBs are privately controlled banks.
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3.2 Empirical Results
Table 3 presents the estimated technical efficiency by bank type. These efficiency scores are calculated as 1/(1+DDF). As we pointed out in Section 2, high efficiency scores indicate technically efficient performance. As shown in Table 3, the average efficiency of Chinese commercial banks remains stable, ranging from 0.9733 to 0.9804. Table 3 also indicates that GCBs are the least technically efficient while PCBs are the most efficient among the three types. Our results are consistent with Lin and Zhang (2009), suggesting that government ownership negatively affects banks’ efficiency. Political intervention may limit the operations of GCBs because GCBs generally perform as a policy-lending channel for the government.
Dong et al. (2014) argue that the administrative officers of GCBs are generally appointed by the government, and their promotions and rewards largely depend on the performance of the implementation of governments’ instructions instead of the creation of bank value. Hence, the incentive of GCBs to improve their performance is reduced.
Table 3 The average technical efficiency by year and bank type
Year All GCBs SOECBs PCBs
2011 0.9786 0.9619 0.9803 0.9854
2012 0.9783 0.9672 0.9780 0.9842
2013 0.9733 0.9631 0.9752 0.9766
2014 0.9804 0.9743 0.9816 0.9820
2015 0.9762 0.9604 0.9794 0.9808
2016 0.9748 0.9533 0.9769 0.9827
2017 0.9736 0.9507 0.9760 0.9814
Table 4 reports shadow price averages of NPLs from 2011 to 2017. These prices are estimated using the pricing rule given by (10) above. Our results show an increasing trend in the average shadow price of NPLs wherein the average shadow prices of NPLs in the first two years are significantly lower than in other years. This strong growth in the shadow price of NPLs is associated with a change in the macroeconomic environment. In response to the global financial crisis (GFC), the Chinese government launched a stimulus package in 2008,
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gradually injecting 4 trillion yuan into infrastructure, social welfare and other industries in the following 4 years. As a result, a large proportion of credit flew into state-owned enterprises, local infrastructure projects and property development through the banking system. This package alleviated the impact of the GFC on the Chinese economy. Combining with the low amount of NPLs in 2011 and 2012, this package may explain the low level of shadow prices of NPLs in these two years as shown in Table 4.
However, the economic stimulus package raised private sector debt, which subsequently increases banks’ credit risk exposure. Banks competed for market shares relaxing their lending standards during this period. Many companies and local governments had difficulties in repaying their loans since economic growth started to fade in 2013. Against the backdrop of a credit boom, the economic slowdown increased the cost of managing NPLs for banks. The default probability of existing borrowers increased. The amount of NPLs surged after 2013, indicating banks were under growing pressure to manage portfolio losses. This change in the macroeconomic environment is likely to have contributed to the growing trend in the shadow price of NPLs shown in Table 4.
Table 4 Descriptive statistics of the shadow price of NPLs: 2011 to 2017 (Unit: %)
Table 5 shows that the shadow prices of NPLs vary by bank ownership type. GCBs have the lowest average shadow price of NPLs among the three ownership types. To shed more light, we introduce the NPLs cost ratio to measure the proportion of net interest income devoted to managing NPLs. Table 5 shows the NPLs cost ratio of GCBs is also the lowest during this period. These findings suggest that GCBs can manage NPLs at a relatively lower cost
Year Mean Min Max SD
2011 0.196 0 0.500 0.092
2012 0.336 0 0.788 0.143
2013 4.004 0 8.039 1.481
2014 2.293 0 4.282 0.784
2015 3.324 0 6.445 1.165
2016 2.676 0 6.737 0.962
2017 3.955 0 11.231 1.412
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compared with PCBs and SOECBs. Hence our results appear to contrast evidence with the view that GCBs are more likely to take excessive risk (see Bai, Ba, Huang, & Hu, 2019; Dong et al., 2014). One important difference is that our measure of the riskiness of the bank lending portfolio is based on the implicit economic cost (potential reduction in the value of loans) arising from a unit increase in NPLs rather than more conventional accounting measures of risk-taking used in previous studies based on the distance to default such as the Z-score or capital adequacy ratio.
Higher risk tends to be positively associated with higher returns, and banks under increasing competitive pressure may engage in riskier lending activities to retain profitability.
This becomes more evident as lending surges in response to a policy stimulus designed to support the slowing economy. In turn, this is adding extra pressures to the banks’ capital needs further exacerbated by tighter capital requirements and new rules to curb off-balance lending. Our results also show that both the shadow price of NPLs and NPL cost ratio rise in 2017. The increase in the opportunity cost of NPLs may be related to a new rule introduced in 2017 requiring asset management companies (AMCs) to adopt a more stringent capital adequacy ratio. This rule makes it more difficult for banks to reduce NPLs fast as AMCs cannot buy more NPLs until they sell their existing NPLs or raise fresh capital.
Table 5 The average shadow price of NPLs and NPLs cost ratio by bank type (Unit: %)
Year SP_NPLs NPLs cost ratio
GCBs SOECBs PCBs GCBs SOECBs PCBs
2011 0.169 0.211 0.193 0.020 0.043 0.030
2012 0.318 0.347 0.331 0.035 0.058 0.055
2013 3.434 4.157 4.126 0.422 0.776 0.727
2014 2.076 2.307 2.381 0.353 0.475 0.520
2015 2.875 3.288 3.360 0.798 0.916 0.981
2016 2.422 2.673 2.799 0.882 0.972 1.214
2017 3.904 3.921 4.015 2.279 1.665 3.596
Notes: 1. SP_NPLs represents the shadow price of NPLs. 2. NPLs cost ratio is the ratio of the total cost of reducing NPLs divided by interest income.
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Table 6 shows the average shadow price of NPLs and the NPLs cost ratio by bank size.
We observe an inverted U relationship for the shadow price of NPLs in relation to bank size.
Compared with banks in quartiles 2 and 3, banks in quartiles 1 and 4 have lower shadow prices of NPLs. Table 6 also shows that banks in quartile 4 have lower NPLs cost ratios. Either a lower shadow price of NPLs or a smaller NPLs cost ratio indicates that economies of scale may also apply to banks’ risk management. Bhagat, Bolton, and Lu (2015) find that large banks tend to be more risk takers than smaller banks although higher risk-taking may be tied to the unusually high leverage of larger banks. But larger banks can achieve better diversification of their assets, which reduces credit risk, and better diversification of their deposits, which reduces liquidity risk (Hughes & Mester, 2013). Since CGBs are also the larger banks, our results suggest that lower shadow prices for CGBs reflect better diversification potential.2
Table 6 The average shadow price of NPLs and NPLs cost ratio by bank size (Unit: %)
Year SP_NPLs NPL cost ratio
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4
2011 0.190 0.209 0.224 0.162 0.026 0.033 0.0383 0.037
2012 0.349 0.397 0.377 0.220 0.066 0.052 0.0549 0.036
2013 4.372 4.226 4.380 3.061 0.812 0.742 0.673 0.529
2014 2.104 2.424 2.412 2.238 0.481 0.504 0.462 0.434
2015 2.870 3.588 3.632 2.860 1.149 0.964 0.876 0.670
2016 2.364 3.046 2.892 2.410 1.567 0.983 0.848 0.785
2017 3.341 4.474 4.269 3.768 2.687 4.552 1.587 1.375
Notes: 1. SP_NPLs represents the shadow price of NPLs. 2. NPL cost ratio is the ratio of the total cost of reducing NPLs divided by interest income. 3. Bank size is measured by the log value of total assets. 4.Q1-Q4 are the quartiles of bank size.
Table 7 presents the results of the panel regression of the shadow price of NPLs on macroeconomic variables and bank-specific characteristics. GDP growth rate is negatively and statistically significantly related to the shadow price of NPLs, indicating an improved economic environment benefits the quality of banks’ assets. Table 7 also shows that bank capitalisation is positively associated with the shadow price of NPLs. This relationship indicates that a bank
2 Particularly banks which diversify their operations to fee-based non-traditional activities such as securities brokerage and insurance sales that generate more stable revenue rather than riskier asset-based non-traditional activities such as venture capital, investment banking and asset securitisation (Berger, Molyneux, & Wilson, 2015).
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perceived higher price of credit risk may build more economic capital to cover its high level of credit risk.
Table 7 Shadow price of NPLs panel regression: 2011-2017
(1) (2) (3) (4)
SP_NPLs SP_NPLs SP_NPLs SP_NPLs
Constant -0.192*** -0.246*** -0.24*** -0.262***
GDP growth rate -1.056*** -0.909*** -0.945*** -0.933***
SHIBOR 0.978*** 0.917*** 0.927*** 0.923***
Size 0.047*** 0.054*** 0.054*** 0.055***
Equity ratio 0.086*** 0.084*** 0.086***
NPL ratio -0.091* -0.079
Eff 0.018
No. of Obs 741 741 741 741
R-Sq 0.833 0.836 0.837 0.838
Notes: SP_NPLs represents the dependent variable: shadow price of NPLs. GDP growth rate and SHIBOR (Shanghai Interbank Offered Rate) are two macroeconomic variables. Size is bank size, Equity ratio is the ratio of equity to total assets, Eff is the technical efficiency scores.
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4. Conclusion
This paper uses a sample of Chinese commercial banks from 2011 to 2017 to estimate the shadow price of NPLs by applying the directional distance function in conjunction with duality theory. We first find that there is an increase in the shadow price of NPLs when the Chinese economy starts to slow down. In addition, we find that both the shadow price of NPLs and the NPLs cost ratio of GCBs are lower compared with those of SOECBs and PCBs.
Furthermore, our results show that, compared with smaller banks, larger banks spend a smaller proportion of their interest income managing NPLs. These findings support the view that larger banks may better in managing credit and liquidity risk as they are better diversified than smaller banks. In addition, smaller joint-stock or private banks may be under pressure to take excessive risks to retain profitability as competition for market share intensifies.
Our approach focussing on the implicit economic cost rather than more conventional distance to default accounting measures of risk-taking offers a fresh look at the Chinese NPLs issue. This is important recognising the true quality of Chinese bank assets is generally unknown. For example, Fredriksson and Frykström (2019) point out that it is difficult for investors to estimate the actual value of NPLs due to the low transparency of the NPLs market.
Existing studies conclude that lower performance incentives and soft budget constraints explain the excessive risk-taking of Chinese banks, particularly GCBs. Our findings clearly point in a different direction in the debate on economies of scale versus too-big-to-fail in banking with obvious policy implications.
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