Credit Resource Misallocation and Macroeconomic Fluctuations in China: From the Perspective of Heterogeneous Financial Frictions

2.1 Data

While much macroeconomic data indicates a negative relationship between productivity and financial frictions, it is difficult to eliminate confounding factors, and we explore the empirical evidence of these stylized facts using microdata. We use firm-level data from the Chinese Industrial Enterprises Database, which contains basic information and financial data of firms covering the period from 1998 to 2015 (2010 data are excluded due to severe missing data). More than 90 % of the industrial enterprises in this database are manufacturing enterprises, including all SOEs and non-SOEs above the designated size.^[2] We further screened the sample according to the following criteria: (1) removing samples with missing variables, e.g. removing samples with missing industrial output value, fixed assets, number of employees, etc.; (2) defining SOEs as “state-controlled” and “collectively-controlled” enterprises, and deleting the sample of foreign- or Hong Kong-, Macao-, and Taiwan-held enterprises; (3) winsorizing the data at 1st and 99th percentile. Meanwhile, we use the annual new loan data by province to measure the change in total credit supply faced by firms, obtained from the CEIC database.

2.2 Measurement of Productivity

We measured the firm’s productivity using three methods: the OP method (Olley and Pakes 1996), the LP method (Levinsohn and Petrin 2003), and the capital efficiency method (Chen and Song 2013). The first two methods assume that the firm’s production function is of the Cobb–Douglas form

where y _t denotes the logarithm of the firm’s output, l _t , k _t and m _t denote the labor, capital and intermediate goods inputs required for production, respectively, ω _t denotes the TFP observable when the firm decides on the amount of inputs, but ω _t is not observed by econometricians, and η _t denotes a random factor unrelated to the firm’s decision. On the one hand, for the econometricians, the error term contains both ω _t and η _t , and direct use of OLS regressions will yield biased and inconsistent estimates, i.e. a simultaneity bias is generated. On the other hand, firms will choose to continue their business or exit the market based on their current capital stock or productivity, and what is observed in the data is only those firms that choose to continue their business, thus generating a sample selection bias.

Olley and Pakes (1996) solved the simultaneity bias by controlling for the correlation between the level of factor inputs and the productivity of the firm, using investment as a proxy variable for the TFP ω _t , and solved the sample selection bias by estimating the survival probability of the firm. It is assumed that the firm’s objective is to maximize the discounted value of future profits so that the firm forms an understanding of the future market structure based on the currently available information, and then makes entry and exit decisions and investment size decisions. Assuming that ω _t obeys the first-order Markov process and defining x _t as the variable measuring whether a firm exits the market and i _t as the firm’s investment size, the optimization problem is as follows:

and

Assuming that the size of a firm’s investment is strictly increasing with respect to productivity, productivity can be expressed as a function of investment and capital

Therefore, the simultaneity bias can be corrected by controlling the investment size. Substituting (2) into (1), it is thus possible to use the OLS method to estimate

where ϕ i t , k t = a 0 + a k k t + h i t , k t is a second-order polynomial in investment i _t and capital k _t , and denote ϕ ̂ t as its estimate. The expectation for both sides of equation (3) yields

Combining equations (3) and (4) yields

The estimation of equation (5) yields the consistent estimates a l ̂ and a m ̂ for a _l and a _m . Therefore,

where h i t , k t = ϕ i t , k t − a 0 − a k k t can be expressed as a function of ϕ and k, i.e. h i t , k t = g ϕ t − 1 − a 0 − a k k t − 1 + ξ t . Then equation (6) can be rewritten as

The parameters a _k can be identified using nonlinear least squares (NLS) estimation for equation (7). To avoid the sample selection bias, we need to estimate the firm’s survival probability P _t , and denote P ̂ t as the fitted value obtained by building a Probit model of x _t with respect to investment i _t and capital k _t . Then we can use NLS to estimate the following equation

where g ⋅ can be approximated by a second-order polynomial with respect to ϕ ̂ t − 1 − a k k t and P ̂ t . Thus, the OP method estimation of TFP results in

However, due to the intermittent investment by many firms, a large amount of data with an investment size of 0 is excluded from the estimation. The LP method addresses this problem by using intermediate goods inputs as a proxy variable for the TFP ω _t . Given a firm’s capital size, it is assumed that the marginal output of intermediate goods will increase as the firm’s productivity increases, and thus the firm will increase its input of intermediate goods, further increasing output. The demand function for intermediate goods is

Under the monotonicity assumption, productivity can be written as a function of intermediate goods m _t and capital k _t

Levinsohn and Petrin (2003) argue that the sample selection bias is negligible, and a large number of firms have zero investment. Therefore, consistent estimates of TFP can be obtained using intermediate goods inputs as a proxy variable.

To further verify the robustness of the findings, we also use the capital productivity (KP) from Chen and Song (2013) to measure firms’ productivity, which is defined as

2.3 Heterogeneity in Financial Frictions and Productivity

3.1 Households

The model is populated by a continuum of identical households. Households maximize their expected utility by choosing the quantity of final goods consumed C _h,t , labor hours H _t , and saving D _t . The representative household’s utility function is given by

where E ₀ denotes the expectation operator, the parameter β ∈ (0, 1) denotes the subjective discount factor, Ψ > 0 reflects negative utility from labor, and η is the inverse Frisch elasticity of labor supply. The term z _t represents a shock to the households’ patience factor that follows the AR(1) process

where ρ _z ∈ (0, 1) is the persistence parameter, σ _z is the standard deviation of the innovation, and u _z,t is an independent and identically distributed (i.i.d.) standard normal process.

Denoting the real wage by W _t , the gross real loan rate by R _t , the earnings received from capital good firms based on the household’s ownership share by Div _t , the flow of funds constraint for the household is given by

The household chooses C _h,t , H _t , and D _t to maximize (10) subject to (11) and (12).

3.2 Final Good Firms

The final good for consumption and investment Y _t is a composite of intermediate goods given by

where Y _s,t and Y _p,t denote the intermediate products produced by SOEs and POEs, respectively. Denote by P _s,t and P _p,t the relative price of SOEs’ products and POEs’ products, respectively. The cost-minimization problem of final good firms is

which implies

The zero-profit condition for the final good sector means

3.3 Capital Good Firms

Capital good firms produce capital and sell it to the intermediate entrepreneurs. Capital good firms maximize their discounted sum of profits

where λ _t is the lagrangian multiplier of households’ budget constraint, Q _t is the capital price in consumption units, Ω > 0 is the adjustment cost parameter. Following Christiano, Motto, and Rostagno (2014), we interpret ζ _t as the investment-specific shock in producing capital. The investment-specific shock ζ _t follows the stochastic process

The parameter ρ _ζ ∈ (0, 1) is the persistence parameter, σ _ζ is the standard deviation of the innovation, and u _ζ,t is an i.i.d. standard normal process.

3.4 The Intermediate Entrepreneurs

Intermediate goods are produced by two types of intermediate entrepreneurs: SOEs (type s) and POEs (type p). The intermediate entrepreneurs have the utility function

where C _j,t denotes the type j intermediate entrepreneurs’ consumption and β′ < β is the subjective discount factor.

The intermediate entrepreneurs produce intermediate goods using labor and capital as inputs, with the production function

where A _j,t denotes the total factor productivity of type j entrepreneurs, K _j,t−1 and H _j,t denote the inputs of capital and labor, respectively, and the parameter α ∈ (0, 1) measures the output elasticity of labor. We assume the total factor productivity A _j,t is composed of a permanent component A _j and a transitory component v _t such that A _j,t = A _j v _t , where the transitory component follows the stochastic process

The parameter ρ _v ∈ (0, 1) is the persistence parameter, σ _v is the standard deviation of the innovation, and u _v,t is an i.i.d. standard normal process.

The type j entrepreneurs are endowed with K _j,−1 units of initial capital stock. Capital accumulation follows the law of motion

where I _j,t denotes the investment of type j entrepreneurs. The net worth shock ω _t follows the stochastic process

The parameter ρ _ω ∈ (0, 1) is the persistence parameter, σ _ω is the standard deviation of the innovation, and u _ω,t is an i.i.d. standard normal process.

The type j entrepreneurs face the flow of funds constraint

where B _j,t−1 denotes the amount of matured debt and B _j,t denotes the amount of new debt.

The entrepreneurs face the credit constraint

Heterogeneity in financial frictions is that POEs face tighter credit constraint, i.e. m _p < m _s . Under heterogeneous financial frictions, the amount that POEs can borrow is less than that of SOEs with the same amount of capital. We interpret this heterogeneity due to different contract enforcement costs: if both types entrepreneurs fail to pay the debt, the creditor can recoup up a larger fraction of the capital value from SOEs. The entrepreneurs choose C _jt , H _j,t , I _j,t , K _j,t , and B _j,t to maximize (14) subject to (15) through (20).

3.5 Market Clearing and Equilibrium

In a competitive equilibrium, the markets for goods, labor, and bonds all clear. The goods market clearing condition implies

where I _t = I _s,t + I _p,t denotes aggregate investment. The labor market clearing condition implies that labor demand equals labor supply

The bond market clearing condition implies that

A competitive equilibrium consists of sequence of prices and allocations such that (i) taking the prices as given, the allocations solve the optimizing problems for the households, entrepreneurs, and firms, and (ii) all markets clear.

3.6 TFP Loss, First-best Economy, and Misallocation

We need to define TFP loss due to heterogeneous financial frictions to prepare for analysis. In our baseline model, aggregate TFP is defined as

The no financial frictions heterogeneity scenario is an economy such that the debt to output ratio D t Y t is equal to that of the baseline model and m _s = m _p . Denote by A y , t EFF the TFP of the no financial frictions heterogeneity scenario, TFP loss due to heterogeneous financial frictions is

We also need to define the first-best allocation to calculate the misallocation. The first-best allocation is the allocation that marginal products of inputs of all intermediate entrepreneurs would be equalized and satisfy

which equates the return of households’ savings to the marginal products of capital and the resale value of the un-depreciated capital. Denote by D* the savings of households at the first-best allocation, K s * K p * the capital stock ratio of SOEs and POEs at the first-best allocation. The credit resources misallocation between households and entrepreneurs Mis _b,t is defined as

The credit resources misallocation within entrepreneurs Mis _w,t is defined as

Finally, the leverage ratio of the economy is defined as

4.1 Calibration

In the model, a period corresponds to one quarter. The calibrated parameters fall into three categories. The first category includes the parameters related to the household’s optimal decision. The subjective discount factor β is set to 0.9943 for households, implying a risk-free rate of 2.3 %. The negative utility coefficient of labor Ψ is calibrated to normalize the labor supply to 0.4 for households. We set the parameter η = 2, which implies the Fisher labor elasticity is 0.5.

The second category includes the parameters related to the firms’ or the entrepreneurs’ production decisions. The parameter ϕ is calibrated to 0.45, implying the steady-state share of SOEs’ output is 0.24. The elasticity of substitution between POEs’ and SOEs’ intermediate goods σ is calibrated to 3, in line with Chang et al. (2015). The subjective discount factor β′ is set to 0.955 for entrepreneurs, which implies the return on capital is 18.9 %. The labor income share parameter α is set to 0.5, which is estimated by Brandt, Hsieh, and Zhu (2008) based on household data. Consistent with the stylized facts, we normalize SOEs’ TFP to 1 and calibrate POEs’ TFP to 1.42. The capital depreciation rate is set to 0.035. Following Liu, Wang, and Zha (2013), we set the capital adjustment cost parameter Ω to 0.175. The heterogeneous financial frictions parameters m _s and m _p are set to 0.7 and 0.4, respectively, which implies the total debt-to-asset ratio is 0.49, as in the Chinese data.

The third category of calibrated parameters is those related to stochastic processes. The persistence parameters are calibrated to 0.6 and the standard deviation of the innovation parameters are calibrated to 0.01, which are calibrated following the standard real business cycle literature. These calibrated parameters of our baseline model are summarized in Table 3.

4.2 Heterogeneous Financial Frictions and Macroeconomic Volatility

To assess the relationship between heterogeneous financial frictions and macroeconomic volatility, we first describe the comparable models of our baseline model. When SOEs and POEs are considered as a whole, total financial frictions can be measured by the leverage ratio of the economy lev _t . Given lev _t equals that of our baseline model, there is a one-to-one correspondence between the loan-to-value ratio parameter of SOEs m _s and the loan-to-value ratio parameter of POEs m _p , as shown in Figure 1. In China’s economy, SOEs receive preferential credit treatment, as we show in Section 2. Therefore, the models with the leverage ratio equal to that of our baseline model and m _s > m _p are the comparable models. For the comparable models, an increase in m _s is associated with a decrease in m _p , implying that heterogeneity in financial frictions within entrepreneurs is increasing.

Figure 1:

The one-to-one correspondence between the Loan-to-value ratio parameter of SOEs m _s and the Loan-to-value ratio parameter of POEs m _p , with the leverage ratio equals that of our baseline model. In the baseline model, we calibrate m _s = 0.7 and m _p = 0.4; In the model that all entrepreneurs with equal financial frictions (EFF), we have m _s = m _p = 0.483.

The equal financial frictions (EFF) model is defined as the model in which the leverage ratio equal to that of our baseline model and m _s = m _p . To analyze the degree of economic fluctuations caused by a shock, we define the output volatility ratio O V R m s as follows

where Y t m s and Y s s m s denote the response and the steady-state of output in the model given m _s , respectively; Y t EFF and Y s s EFF denote the response and the steady-state of output in the EFF model, respectively; the parameter T denotes the total number of response periods in our experiment. An O V R m s less than 1 indicates that heterogeneity in financial frictions can reduce economic volatility.

Figure 2 visualizes the output volatility ratio of four shocks: the preference shock, the net worth shock, the investment efficiency shock, and the TFP shock. We make two observations. First, as m _s increases, heterogeneity in financial frictions becomes larger, and the output volatility ratio becomes smaller. Therefore, heterogeneity in financial frictions plays a stabilizing role in the economy. Second, the effect of stabilizing the economy is related to the type of shock. For the TFP shock and net worth shock, heterogeneity in financial frictions reduces output fluctuations by no more than 2 %. However, for the preference shock, it can reduce output fluctuations by more than 20 %. In addition, Figure 2 also shows that heterogeneity in financial frictions has a nonlinear effect on output volatility. The increase in heterogeneity in financial frictions will lead to an increasing decrease in output volatility.

Figure 2:

The output volatility ratio O V R m s under different shocks. This graph plots the relationship between the heterogeneity of financial frictions and the output volatility. The total number of response periods T is set to 30.

4.3 The Mechanism

To illustrate the transmission mechanism, we examine the impulse response of several macroeconomic variables following a positive preference shock, displayed in Figure 3.

Figure 3:

Impulse responses to a positive preference shock. The baseline model: solid lines; the model with equal financial frictions: dashed lines. The horizontal axes show the quarters after the impact period of the shock. The units on the vertical axes are percent deviations from the steady state levels.

In the baseline model, a positive preference shock raises SOEs’ output, POEs’ output, and the total output. The total output response is larger in the EFF model. This result is due to the procyclicality of the credit resources misallocation within entrepreneurs Mis _w,t and the TFP loss TFP loss _t .

In the EFF model, the marginal productivity of capital for SOEs and POEs is equal because of m _s = m _p . Therefore, the response of the misallocation within entrepreneurs Mis _w,t is always zero in the EFF model. However, in the baseline model, a positive preference shock leads to a procyclical increase of Mis _w,t and, therefore, a procyclical increase of TFP loss _t .

The credit resource misallocation between households and entrepreneurs Mis _b,t may also have an impact on explaining the response difference. However, as shown in Figure 3, the responses of Mis _b,t in the baseline model and in the EFF model are slightly different. Meanwhile, the variation of Mis _b,t is much smaller than that of Mis _w,t .

4.4 How This Mechanism Related to Shocks?

As shown in Figure 2, the stabilization role of heterogeneous financial frictions has a significant difference under different shocks. In this section, we show how the stabilization role is related to the type of shocks. To achieve this goal, we first define the relative credit resources misallocation under a shock

For a given m _s and output volatility, a larger R M R m s implies that the shock causes greater procyclicality of credit resource misallocation within entrepreneurs, which in turn affects the aggregate TFP to a greater extent. The variation in the value of R M R m s with the parameter m _s for different shocks is shown in Figure 4. Figure 4 illustrates that the preference shock has a much greater impact on misallocation within entrepreneurs than on output, which is consistent with Figure 2 that heterogeneity in financial frictions can reduce the economic volatility caused by preference shocks to a greater extent than that caused by other shocks. Meanwhile, the ordering of the R M R m s values of different shocks given the parameter m _s is opposite to the ordering of the O V R m s values of different shocks given the parameter m _s in Figure 2. Thus, the extent to which heterogeneous financial frictions can mitigate economic volatility depends on the relative magnitude of the impacts of the shock on the credit resources misallocation within entrepreneurs and on the output.

Figure 4:

The relative credit resources misallocation R M R m s under different shocks. This graph plots the relationship between the heterogeneity of financial frictions and the relative misallocation ratio. The total number of response periods T is set to 30.

4.5 The Cost of Stabilization

Heterogeneous financial frictions can reduce economic volatility by inducing procyclicality in credit resource misallocation within entrepreneurs. However, it cannot be ignored that this stabilizing effect has a cost, i.e. heterogeneity in financial frictions leads to the existence of credit resource misallocation within entrepreneurs at the steady state, which reduces the economy’s aggregate TFP and output at the steady state. Figure 5 illustrates the decline in output and aggregate TFP due to heterogeneous financial frictions.

Figure 5:

The decline in output and aggregate TFP due to the heterogeneity of financial frictions.

First, Figure 5 shows that the benchmark model reduces the steady-state output by about 0.5 percent and the steady-state aggregate TFP by about 0.3 percent compared to the EFF model. Second, consistent with Figures 2 and 4, the effect of the degree of heterogeneity in financial frictions on steady-state output and steady-state aggregate TFP is also characterized by significant nonlinearities.

However, the impact of heterogeneity in financial frictions on social welfare has a trade-off: on the one hand, heterogeneity in financial frictions reduces economic volatility, allowing households to smooth consumption to a greater extent and increasing social welfare; on the other hand, heterogeneity in financial frictions leads to lower steady-state output and household consumption, thereby reducing social welfare. Thus, the impact of heterogeneity in financial frictions on social welfare depends on the economy’s sensitivity to the level and volatility of consumption.

5.1 Sensitivity to Parameters

How would the stabilization effect of heterogeneous financial frictions react to different parameters? To analyze this issue, we compare the result of our baseline model with results of models calibrated to several different parameters: (1) the share parameter for SOEs output in intermediate good, ϕ, (2) the elasticity of substitution between SOEs’ and POEs’ products, σ, (3) the labor income share, α, (4) the TFP for SOEs and POEs, A _s and A _p , respectively. Results are shown in Table 4.

Panel A of Table 4 shows the correlation coefficient between the degree of credit resource misallocation within entrepreneurs and output. For the baseline model, the degree of credit resource misallocation within entrepreneurs shows a procyclical characteristic under different shocks. Similarly, when we adjust the parameter values that may affect the conclusion within a reasonable range, the procyclicality still exists, and the degree of procyclicality does not change much.

Panel B of Table 4 shows how the output volatility ratio O V R m s corresponds to different parameters. The output volatility ratio of the EFF model is O V R m s = 0.483 . For the benchmark model, the volatility ratio under different shocks is less than 1, indicating that heterogeneity in financial frictions can reduce economic volatility. Similarly, when we adjust the parameter values that may affect the conclusion within a reasonable range, the conclusion still holds.

5.2 Extensions

We test the robustness of three important characteristics related to credit resource allocation or enterprises’ heterogeneity in China’s economy: household heterogeneity, supply chain structure, and earning-based borrowing constraints.