Financial Shocks, Deleveraging and Macroeconomic Fluctuations in China

3.1 Representative Households

Representative households get access to labor-based wage income, which they use on consumption and bank savings. Household income for term t includes term-t risk-free securities A_t with a risk-free rate of return Rtd, labor income W_tN_t of labor N_t provided to the goods sector in the form of wage W_t , and common profit Π_t of the capital goods sector, goods sector and banks. Term t-end household expenditure consists of consumption C_t and the next-term risk-free securities A_t+1. Term-t budget constraint equation of households is Ct+At+1=RtdAt+WtNt+Πt. Households’ maximized anticipatory utility for selecting consumption C_t , labor N_t , and risk-free securities A_t+1 is E0∑t=0∞βtlnCt−ξNt1+χ1+χ where β means discount factor, ξ means disutility weight _Σof labor, and χ means reciprocal of labor supply elasticity. First-order conditions for optimization in the household sector are 1Ct=λt,ξNtx=λtWtandλt=βRt+1dEtλt+1, where λ_t represents Lagrange multiplier of the budget constraint equation.

3.2 Goods Sector

Goods sector uses capital K_t and labor N_t for production, and the output Y_t is eventually used for household consumption and capital formation. Assume the production function of the goods sector has constant returns to scale and the production function equation is Yt=Nt1−αKtα, where α means share of capital. Goods sector selects labor N_t and capital K_t for term t and realizes maximization of the current income Πtg=Yt−WtNt−rtKt. To seek the solution for income maximization leads to first-order conditions for the goods sector, namely the wage determination equation Wt=(1−α)YtNt and the determination equation for capital interest rate rt=αYtKt.

3.3 Banks

At the end of term t, banks of perfect competition sell risk-free securities A_t+1 to the household sector and promise them risk-free rate of return Rt+1d, and meanwhile provide loan portfolio B_t+1 for entrepreneurs i,i∈[0,1] . We use B _t +1 ( i ) to represent inter-temporal loans granted by banks to a single entrepreneur i and get Bt+1=∫01Bt+1(i)di. For the sake of simplicity, the paper refers to Bernanke et al. (1999) and supposes the risk-free securities sold to households are the sole source of capital of banks’ loan portfolio:

In the perfect competition market, in order to ensure that banks can pay households principal and interest of risk-free securities each term, the expected total return of bank loan portfolio should be equal to the opportunity cost of the risk-free securities that banks sell to households in any possible state. But in this paper, bank loans to each entrepreneur face overall risk and heterogeneity risk. In order to fulfill the previous condition, this paper refers to Bernanke et al. (1999), assuming that entrepreneurs are risk-neutral and each one is willing to undertake overall risk of loans and pay back “state-contingent” loans. Now, bank loans only suffer entrepreneur-related heterogeneity risk, and banks can eliminate such risk with large enough loan portfolios. This paper uses Ψ_t+1 to mean the expected total return of bank loan portfolios for term t+1, and bank budget constraint equation is:

3.4 Entrepreneurs

The economic activities of entrepreneur i include entrepreneur i buying capital K _{t +1} ( i ) for the new term from the capital goods sector at a price q_t at the end of term t, its leasing capital to the goods sector at an interest rate of r_t+1 at the beginning of term t+1, and its selling capital after depreciation back to the capital goods sector at the price q_t+1 at the end of term t+1. The fund for entrepreneur i to purchase capital K _{t +1} ( i ) at the end of term t is sourced from its own term t-end net worth X _{t +1} ( i ) and loans B _{t +1} ( i ) from loan contracts signed with banks, and therefore term t-end credit determination equation of entrepreneur i can be shown as q _t K _t+1 ( i ) = X _t+1 ( i ) + B _t+1 ( i ) . Its term t-end leverage ratio is defined as the ratio between assets and net worth, i.e. Lt(i)=qtKt+1(i)Xt+1(i). Assume the return on capital of entrepreneur i faces heterogeneity risk and overall risk, and its return on capital for term t+1 can be set as Rt+1k(i)=ωt+1(i)Rt+1k.ωt+1(i) means the heterogeneity part in the return on capital, and Rt+1k means the ex-post average return on capital only subject to influence of overall risk:

δ is capital depreciation. In reference to Bernanke et al. (1999), we assume ω can only be observed by entrepreneurs and is subject to the logarithmic normal distribution with a mean value of 1 and a standard deviation of σ_ω, and the distribution function is recorded as F(ω).

To avoid the scenario where entrepreneurs of sufficient net worth of their own have no need of external financing, the paper refers to Bernanke et al. (1999) and includes the possibility of entrepreneur bankruptcy in the model to ensure entrepreneurs have to resort to banks for external financing. Define the survival rate of entrepreneurs as γ, which means at a term end, a 1-γ ratio of entrepreneurs exits from economy and meanwhile a 1-γ ratio of new ones enters the economy. The γ ratio of surviving entrepreneurs and the 1-γ ratio of newcomers both get access to transfer payment W ^e.

3.5 Banks and Standard Loan Contracts

In the model, banks provide entrepreneurs with loans by signing loan contracts. For specific arrangement, at the term t end, banks offer entrepreneur i a new term of loans for a mount of B _{t +1}( i ) , and specify the “state-contingent” loan interest rate Rt+1l(i) to be paid by the entrepreneur for loan repayment for the term t+1. In the term t+1, banks recover loans from the entrepreneur, depending on the realization status of heterogeneity shock ω_t+1 (i) , the issued loans face two possibilities: default and non-default. When the heterogeneity shock is heavy enough, the entrepreneur can pay Rt+1l(i) for the loans; when the heterogeneity shock is low, the entrepreneur cannot repay the loan principal and interest agreed in the contract and faces bankruptcy, in which case banks shoulder a certain ratio of default cost to get access to entire income of the entrepreneur (supposing the proportion of term t+1 default cost in the entrepreneur’s total income ωt+1(i)Rt+1kqtKt+1(i)isθt+1 and θ_t+1 can be observed by all the economic entities). For banks, there exists a heterogeneity shock lower-limit ϖ_t+1 (i) meeting entrepreneur loan repayment conditions (named default threshold in the paper), which enables the entrepreneur to pay back the loans. In another word, the default threshold ϖ_t+1 (i) fulfills the condition ϖt+1(i)Rt+1kqtKt+1(i)=Rt+1l(i)Bt+1(i). Define Γϖt+1(i)=1−Fϖt+1(i)ϖt+1(i)+∫0σt+1(i)ωdF(ω)andGϖt+1(i)=∫0σt+1(i)ωdF(ω). Based on the features of loan contracts and the expression of ω_t+1 (i) , the expected return Ψ_t+1 (i) of banks for providing the entrepreneur i with loans for term t+1 can be expressed as Ψt+1(i)=Γϖt+1(i)−θt+1Gϖt+1(i)Rt+1kqtKt+1(i).

When economy reaches the system equilibrium, we have ∫01Kt+1(i)di=Kt+1, ∫01Xt+1(i)di=Xt+1,∫01Ψt+1(i)di=Ψt+1,and∫01Lt(i)di=Lt, and meanwhile all the entrepreneurs face the same default threshold ϖ_t+1 , i.e. ϖ _t+1 (i) = ϖ _t+1 ，∀i . According to the definition of ϖt+1(i),Rt+1l(i)=Rt+1l,∀i. The credit determination equation during equilibrium can be expressed as:

According to equation (1) and equation (2), we come to:

Given the definition of leverage ratio and equation (5), bank zero-profit equation is expressed as:

3.6 Contracts of Entrepreneurs

Entrepreneurs are risk-neutral and pursue the optimal goal of maximized expected net income. The expected net income function of entrepreneur i is Vt+1(i)=∫σt+1(i)∞ωRt+1kqtKt+1(i)−Rt+1l(i)Bt+1(i)dF(ω). In this paper, the net income function is divided by the opportunity cost Rt+1dXt+1(i) of the entrepreneur’s own net worth to get standardized net income function, i.e. Ωt+1(i)=1−Γϖt+1(i)Rt+1kRt+1dLt(i). When economy reaches the system equilibrium, we have ∫01Vt+1(i)di=Vt+1 and ∫01Ωi+1(i)di=Ωi+1. So, the contract issue of all the entrepreneurs at the term t end can be stated as selecting default threshold ϖ_t+1 and leverage L_t to realize the maximization of expected net income under the premise of meeting the bank zero-profit equation (6). By straightening out the first-order conditions of entrepreneur optimization, we get:

3.7 Capital Goods Sector

The capital goods sector of perfect competition uses the capital after depreciation (1−δ )K_t purchased from entrepreneurs and the investment I_t originated from the goods sector at the term t end to produce the new term of capital K_{t +1} . We refer to Fernández-Villaverde (2010) and express the capital accumulation equation as:

SItIt−1 means the adjustment cost of investment and satisfies S(1)=S′(1)=0 and S" (1) > 0 . The function is φ2ItIt−1−12, where φ refers to the intensity of investment adjustment cost. The capital goods sector realizes the maximization of expected income by choosing investment I_t in the term t, i.e. ItmaxEt∑t=0∞βtλtλ0qt1−SItIt−1It−It. The first-order condition of the capital goods sector is qt1−SItIt−1−S′ItIt−1ItIt−1+βEtλt+1λtqt+1S′It+1ItIt+1It2=1.

3.8 Exogenous Shocks

The paper presumes that default costs follow the exogenous shock process:

θ‾ is the steady-state value of default costs, and ρ is the persistence parameter of financial shocks and ρ < 1 . In this paper, we use financial shock ϑ_t in reflection of default cost changes to describe the changes with deleveraging policies. When regulation is relaxed in China, banks use shadow banking to break investment limitations and steer capital into industries with low default costs, which is expressed in the model as the decrease of the average default cost θ_t in economy; in the case of tight regulation, shadow banking shrinks and capital is kept from effectively flowing into investment-limited industries, which is shown in the model as the increase of the average default cost θ_t.

Furthermore, the paper hopes to discuss response of economic individuals to the news of future default costs. By referring to Gunn and Johri (2013) and Gunn (2018), it divides exogenous shocks into unanticipated current shock and anticipatable shock, i.e. ϑt=εt−pp+εt×εt−pp is anticipated shock and means in the term t − p , the agent already gets news that can only be obtained in the term t, but actual influence on default cost θ_t can be produced only in the term t. ε_t means unanticipated exogenous shocks that newly occur in the term t. Besides, suppose Etεtp=0 and standard deviation is σεp,Etεt=0 and standard deviation is σ _ε , and σεp and σ _ε are uncorrelated.

3.9 Other Equations

Output of the goods sector is mainly used in consumption, investment and entrepreneurs’ loan default loss. The resource constraint equation is:

The equation for entrepreneurs’ net worth during equilibrium is:

To support the analysis, this paper defines term-t external finance premium as the ratio between entrepreneurs’ expected return on capital and risk-free interest rate, i.e. st=EtRt+1kRt+1d, and defines term-t credit spread as the ratio between contracted loan interest rate and risk-free interest rate, i.e. spreadt=RtlRtd⋅1. ^[1]

6.1 Unanticipated Shocks

We now analyze the changes with macroeconomic variables as a result of negative unanticipated financial shocks (default costs dropping). Figure 6 indicates that lower default costs increase the credit supply, push up the entrepreneur leverage, lower the credit spread, and also cause the output and investment to rise. ^[1] As the entrepreneur leverage L and risk-free interest rate R^d in the model are determined by the previous term, according to the bank zero-profit equation (6), the drop of default costs θ means the default threshold ϖ and return on capital R^k will first change in the current term of shocks. As anticipated bank return consists of the non-default loan value and the default loan value, decreased default costs mean that banks’ current non-default loan value falls and default threshold drops accordingly. The drop of default threshold is associated with the decrease of current credit spread spread ^[2] and the increase of entrepreneur net worth X (result of the equation (11)). Higher X indicates that entrepreneur demand for capital K rises correspondingly (entrepreneurs are the buyer of capital). According to equation (8), the capital goods sector will increase investment I, and the goods sector will raise output Y to satisfy the incremental investment (result of the equation (10)). The investment changes cause the capital price q to climb and further drive up the return on capital R^k (result of the equation (3)). According to equation (6), higher R^k will lead to lower default threshold and trigger the decrease of credit spread spread and the increase of entrepreneur net worth X. In the current term of shocks, therefore, changes with the default threshold ϖ, credit spread spread, and entrepreneur net worth X are subject to the joint influence of default costs and return on capital.

Figure 6

Impulse Response of Negative Financial Shocks (Default Costs Dropping)

Similarly, rise of the current entrepreneur net worth X will further drive up entrepreneur demand for capital K of the next term (the 2nd term), which will cause the capital goods sector to correspondingly increase the new-term investment I, the goods sector to correspondingly raise the new-term output Y, and the capital price q to keep climbing positively. This will drive return on capital R^k to grow continuously and further trigger lower default threshold ϖ for the new term, lower credit spread spread and higher entrepreneur net worth X. According to the entrepreneur credit determination equation (4), increase of the entrepreneur net worth X for the new term is sufficient to raise its loan demand, to which end banks need raise more funds, causing the risk-free interest rate R^d for the new term to rise. Households provide banks with more risk-free securities A, and according to equation (1), new-term loan B keeps expanding positively. In addition, according to the implicit expression of leverage equation (12), since the drop of default costs θ affects entrepreneur leverage L both directly and indirectly, under the dual effects, new-term entrepreneur leverage responds negatively, which sustains for only the first few terms, and afterwards the leverage keeps rising positively. This means the direct effects of default costs on entrepreneur leverage take a predominant position and lower default costs generally push up the entrepreneur leverage. In this paper, we understand the default cost changes caused by financial shocks as the actual default cost changes as a result of changing financial regulation policies in recent years. When regulation is relaxed, average default costs of economy in the model decline, leading to rise of entrepreneur leverage, expansion of loans and drop of credit spread; when regulation is tight, the average default costs rise, bringing about lower entrepreneur leverage, contracted loans and higher credit spread. The synchronous changes with leverage, credit spread, credit and other macroeconomic variables caused by the actual default cost changes can be verified by the economic changes of China in recent years (the second part in the paper).

6.2 Anticipated Shocks

Furthermore, we hope to analyze the response of the model to anticipated changes with default costs and pay close attention to the influence of decrease of the anticipated costs (presuming banks get the news of default cost decrease for the 10th term in the first term).

First, we look at the changes with various macroeconomic variables in the case of expectation realization (i.e. the news of default cost decrease proves to be correct), and closely follow the response of the economic variables before actual shocks occur. Figure 7 reflects that after the expectation is realized, investment and output continue to grow, loans keeps expanding positively, credit spread drops, and entrepreneur leverage positively rises. In the first to tenth term before actual shocks occur, lower anticipated default costs cause investment output and loans to expand positively and credit spread to drop negatively. Under the dual effects of default costs, entrepreneur leverage is briefly negative for the first few terms and then turns to climb positively under the predominant direct effect. In general, default costs show no alteration after the 10th term, but the solely expectation-driven model economy fluctuates in expansion.

Figure 7

Impulse Response under Expectation Realization

Next, we turn to the response of the economic variables during expectation reversal (i.e. the news of default cost decrease is not realized in the 10th term). According to Figure 8, compared with the 10th term, starting with the 11th, investment and output plunge after hitting the peak, credit spread surges, and entrepreneur leverage and loans gradually drop back. Regarding credit spread, since the news of actual default cost drop fails to materialize, compared with the 10th term, credit spread declines to the bottom and rapidly climbs to the highest point in the 11th. As to entrepreneur leverage, it keeps rising in the current term of actual news occurrence and both before and after that, and its changes relatively lag behind credit spread with the advent of the news. As the news fails to realize, starting with the 11th term, entrepreneurs will select new leverage ratio and default threshold, and Figure 8 indicates the positive response of leverage reaches the peak in the 11th term before gradually dropping back. In the case of expectation reversal, anticipated changes alone can drive the economy to fluctuate in “expansion–contraction”.

Figure 8

Impulse Response under Expectation Reversal

Based on the above-mentioned impulse response result, this paper believes that the changes with expectation dimensions of default costs can be used to explain China’s macroeconomic reality before and after the deleveraging policies were adopted. Prior to 2016, banks placed hope on the prosperity of the real estate market and the implicit guarantee from local government for city investment platforms and industries of high energy consumption, heavy pollution and overcapacity, and their favorable expectations for growing real estate market and implicit guarantee prompted banks’ expectation for declining default costs. Banks used shadow banking to introduce massive funds into the investment-limited industries, causing credit and leverage to rise and credit spread to drop, even though the real estate market didn’t change in any material way. Since the second half of 2016, however, central government put into effect a series of documents for fending off major risks and enhancing financial regulation. In the first quarter of 2017, CBRC issued seven documents intensively; CSRC, CIRC and industrial associations continued to launch various regulatory regulations and systems for financial rectification; the central bank included off-balance sheet wealth management into MPA assessment. Driven by the deleveraging policies, central government could reverse banks’ expectation for default costs by releasing signals of regulating real estate, breaking rigid repayment of implicit debts and changing the confidence level of local implicit guarantee, so as to attain the purpose of narrowing down economic credit and reducing leverage.