《Business fluctuations in a creditnetwork economy.pdf》由会员分享，可在线阅读，更多相关《Business fluctuations in a creditnetwork economy.pdf（8页珍藏版）》请在三一文库上搜索。
1、 Business fluctuations in a credit-network economy Domenico Delli Gatti,a* Mauro Gallegati, b Bruce Greenwald, c Alberto Russo,b Joseph E. Stiglitz, c a Catholic University, Milan, Italy b Politechnic University of Marche, Ancona, Italy c Columbia University, New York, USA Abstract We model a networ
2、k economy with three sectors: downstream firms, upstream firms, and banks. Agents are linked by productive and credit relationships so that the behavior of one agent influences the behavior of the others through network connections. Credit interlinkages among agents are a source of bankruptcy diffus
3、ion: in fact, failure of fulfilling debt commitments would lead to bankruptcy chains. All in all, the bankruptcy in one sector can diffuse to other sectors through linkages creating a vicious cycle and bankruptcy avalanches in the network economy. Our analysis show how the choices of credit supply b
4、y both banks and firms are interrelated. While the initial impact of monetary policy is on bank behaviour, we show the interactive play between the choices made by banks, the choices made by firms in their role as providers of credit, and the choices made by firms in their role as producers. * Corre
5、sponding author: domenico.delligattiunicatt.it (D. Delli Gatti). 2 1. Introduction We model a network economy with an inside credit (commercial credit) between firms of different productive sectors, and an outside credit (bank credit), which lends credit to industrial sectors (Stiglitz, Greenwald, 2
6、003). Failure of fulfilling debt commitments could lead to bankruptcy chains. If debt commitments are not fulfilled, bad debt increases and the rate of interest may increase as well. The interest rate increase leads to more bankruptcies: “the high rate of bankruptcy is a consequence of the high inte
7、rest rate as much as a consequence of it” (Stiglitz, Greenwald, 2003: 145). If future is uncertain, what probability is there that the contract will be fulfilled? Are there major consequences of a small shock? This paper will show in what way a business cycle is linked to firm bankruptcies and how a
8、 domino effect (a crescendo in terms of bankruptcy) can arise (and as such be avoided). At the same time, the main facts of firm demography (like power law distribution of size and Laplace growth rates of firms) emerge endogenously (and are more resistant to external shocks.) As opposed to previous
9、models of business cycles, in our model, avalanches are due to the interdependence of the output of a firm on supply and payments from other firms. Similarly to the self-organized criticality inventory cycle proposed by Bak et al. (1993), in our model, small shocks fail to cancel at the aggregate le
10、vel so that large economic fluctuations can occur even without aggregate shocks. According to Bak et al. (1993), we model productive relationships among agents as local interactions (with a different network topology). In addition, we consider firm-bank and firm-firm credit relationships that can am
11、plify the effects of small idiosyncratic shocks on the aggregate. Heterogeneous agent interaction has a second major implication. We will see that the structure of aggregate behaviour (macro) actually emerges from the interaction among the agents (micro). In other words, statistical regularities eme
12、rge as a self-organised process at the aggregate level. Complex patterns of interacting individual behaviour may generate certain regularity at the aggregate level (Delli Gatti et al., 2005). The idea of representing a society by one exemplar (a representative agent) denies the fact that the organiz
13、ational features of the economy play a crucial role in explaining what happens at the aggregate level (Kirman, 1992). The model is presented in section 2. The model simulation and the discussion of results are shown in section 3. Section 4 concludes. 2. The model Consider a sequential economy (t=1,2
14、,T) populated by a multitude of heterogeneous agents belonging to three different sectors: a downstream sector with a number I of firms (labeled by the index i=1,2,I), an upstream sector with J firms (j = 1,2,J) and a banking sector with Z banks (z=1,2,Z). Downstream firms produce and sell final goo
15、ds (at a stochastic price). The production of the final goods requires two productive inputs: labor and intermediate goods. The intermediate goods are produced “on demand” by upstream firms with a technology that requires only labor as input. Upstream firms sell intermediate goods to downstream firm
16、s by means of a commercial credit contract. Firms obtain credit from banks to finance the wage bill. Finally, banks are linked in the interbanking market in order to solve liquidity crises. The network structure of the economy is the following (see figure 1): each downstream firm i is linked to upst
17、ream firms j and j+1; the downstream firm i+1 is linked to upstream firms j+1 3 and j+2, and so on.1 Each firm is linked to a bank: the downstream firm i and the upstream firm j are linked to the bank z, and so on. Finally, each bank is linked to two neighboring banks: bank z is linked to banks z-1
18、and z+1. All in all, downstream firms, upstream firms and banks are linked by productive and credit relationships so that the behavior of one agent influences the behavior of the others through network connections. The production function of downstream firms is given by the equation: Yit=Ait-1, wher
19、e 1, 00 and 0. Final goods are sold at a stochastic price uit.2 Upstream firms produce intermediate goods required by the downstream sector by means of a technology employing only labor as input: Qjt= uNjt, where u0 and, for assumption, Qjt=Qi-1t/2+Qit/2. The output of the upstream sector is sold to
20、 downstream firms at a fixed price p. Figure 1. The network structure of the economy: Downstream firms (), upstream firms (), and banks (). Downstream firms sign a commercial credit contract with upstream firms so that they obtain the ordered quantity of the intermediate goods from upstream firms an
21、d pay back for it in the next period. Upstream firms charge an interest rate ru, constant along time and uniform across firms, on commercial loans. The wage bill is financed by bank loans with an interest rate ritbx (x=d for downstream, x=u for upstream firms).3 We assume that there is an infinite s
22、upply of labor at wage w. Downstream firms profit is equal to: it=uitYit (1+rbdit)wNit (1+ru)pQjt, where rbdit is the interest rate on the bank loan. Upstream firms profit is equal to: jt=p(1+ru)Qjt (1+rbujt)wNjt, where rbujt is the interest rate on the bank loan. At the end of the period, firms net
23、 worth is equal to Axt=Axt-1+xt, and a firm goes bankrupt if Axt0 (x=i for downstream; x=j for upstream). We assume a very simplified mechanism of agents entry-exit: bankrupted 1 Accordingly, the downstream firm I is linked to upstream firms J and 1. 2 That is a random variable that, for the sake of
24、 simplicity, is uniformly distributed in the interval (0,2). 3 See below for the interest rate setting. 4 firms are replaced with new entrants on the basis of a one-to-one replacement. The same holds for banks.4 The commercial credit relationship between downstream and upstream firms is a source of
25、bankruptcy diffusion across the network. In fact, if a downstream firm goes bankrupt then it cannot refund the debt to the upstream ones increasing their probability of bankruptcy (due to the decrease of their net worth). The deterioration of the financial conditions of upstream firms jointly with t
26、he failure of downstream firms can cause bankruptcies even in the banking sector, given that bankrupted firms cannot refund loans to banks. All in all, bankruptcy in one sector can spread to other sectors through connections creating a vicious cycle and bankruptcy avalanches in the network economy,
27、as we will illustrate in section 3. Banks lend funds to downstream and upstream firms in order to finance their production process, that is their wage bills. The total amount of credit each bank can supply to firms is equal to Lszt=Ezt/, where Ezt is the level of bank zs net worth at time t and 1 is
28、 a prudential target set by a regulatory authority that banks have to respect. In other words, the level of credit supply is more than proportional to banks net worth and limited to a maximum depending on the coefficient . In each period banks collect the demand for credit from firms, Ldzt. Given th
29、at the supply of credit is limited to Lszt, firms can be rationed for an amount proportional to Lszt/Ldzt and revise their productive plans on the basis of the effective credit obtained from banks. For the sake of simplicity, we assume that deposits Dzt are a residual variable, given the balance she
30、et of banks. The interest rate paid by banks on deposits is rd, constant along time and uniform across banks. The interest rate on bank loans is: rbxyt=k/(Ayt/xt)k, where 0k1, and xt is the median of the firms net worth distribution at period t, computed separately for upstream and downstream firms
31、(x=d and y=i for downstream firms, x=u and y=j for upstream firms). Accordingly, the higher the financial fragility of firms the higher the interest rate charged on bank loans. Banks profit is equal to: bzt=rbditwNit + rbujtwNjt rdDzt. The level of the banks net worth evolves according to the follow
32、ing equation: Ezt=Ezt-1 + bzt BDzt + IBzt, where BDzt is “bad debt” for bank z, due to the insolvencies produced by upstream and/or upstream firms failures, and IBzt is the result of liquidity adjustments on the interbank market. Banks can lend or borrow funds on the interbank market in order to sol
33、ve liquidity crises or to invest resources in excess with respect to firms demand for credit. We assume that the rate of interest on the interbank market, rbb, is constant along time and uniform across banks. As said above, bank z interacts only with neighbors z-1 and z+1. Accordingly, in period t,
34、each bank can be a fund lender or borrower with respect to the neighbor banks: () () () () + + + + = )(1 )(1 )(1 )(1 1 1 1 1 ivIBIBr iiiIBIBr iiIBIBr iIBIBr IB l zt b zt bb b zt b zt bb l zt l zt bb b zt l zt bb zt 4 Accordingly, the total number of agents in the economy is constant along time. New
35、agents are endowed with an initial amount of net worth equal to that choose for initial conditions (that is, the value of agents variables at time t=1). 5 where l and b indexes mean lending and borrowing, respectively. Let us explain the above four scenarios: (i) bank z lent funds in t1 (and receive
36、s reimbursement with interest in t) and borrows funds in t; (ii) bank z lent funds in t1 and lends funds in t; (iii) bank z borrowed funds in t1 (and refunds the loan with interest in t) and borrows funds in t; (iv) bank z borrowed funds in t1 and lends funds in t. Even though banks operate in the i
37、nterbank market to manage their liquidity and, in particular, to avoid defaults due to firms bad debts, the interbanking activity can be an additional source of spread of bankruptcies (Iori et al., 2004). In fact, a borrowing bank may go bankrupt in a given period generating insolvency for the lendi
38、ng bank. The financial conditions of this last bank can degenerate, resulting in another failure. So, as in the case of firm-firm and firm-bank credit relationships, interbank connections can generate avalanches of defaults, reinforcing the vicious circle of spreading of bankruptcies across the netw
39、ork economy. 3. Simulations We simulate the network economy described above with I=J=Z=250 agents in each sector and analyze the model simulation from period t=1 to T=1000. At the beginning of the simulation, agents (firms and banks) start with an amount of net worth equal to 100. The wage is fixed
40、at level w = 1. The same holds for the intermediate goods price, p = 1; the interest rate on commercial credit, ru = 0.05; the interest rate on deposits, rd=0.01; the interest rate on interbank loans, rbb = 0.01.5 Figure 2 describes the fluctuating behavior of the average production of downstream fi
41、rms. Nevertheless, agents start with the same initial condition. Simulations show that a significant heterogeneity emerges in agent variables. For example, the final distribution (at period T=1000) of the net worth of downstream firms is highly asymmetric and skewed to the right (Axtell, 2001). The
42、same result holds for upstream firms and banks. In addition, figure 3 shows the difference between the firm size distribution that emerges from simulations and a normal one.6 The model also generates a tent-shaped (Laplace) distribution of firm growth rates (Stanley et al., 1996; Bottazzi, Secchi, 2
43、003), as shown in Figure 4. 5 The parameter setting of the simulation is the following: =2.5, =0.9 (production function parameters: downstream firms); =0.5 (intermediate goods requirement function coefficient: downstream firms); d=0.5 (labor requirement function coefficient: downstream firms); u=1 (
44、labor requirement function coefficient: upstream firms); k=0.1 (firm-bank interest rate function parameter); =0.85 (prudential target for credit supply: banks) 6 The Bera-Jarque test refuses the null hypothesis of normality of the agent size distribution at 1% significance level. 6 Figure 2. Downstr
45、eam sector average production Figure 3. Downstream firm size distribution (net worth) Figure 4. The Laplace (double exponential) distribution of firm growth rates.7 7 Pooled data from the last 100 simulation periods. 7 Figure 5. Cross correlation of bankruptcies in different sectors Figure 6. Avalan
46、ches size distribution A central feature of the network economy described in our model is related to the spread of bankruptcies through the productive and credit linkages among agents. If a downstream firm goes bankrupt it cannot refund the debt to the upstream firms it is linked to, decreasing thei
47、r net worth, and increasing their probability of bankruptcy. The weakening of the financial conditions of upstream firms jointly with the failure of downstream firms can cause bankruptcies even in the banking sector, given that bankrupted firms cannot refund loans to banks. All in all, bankruptcy in
48、 one sector can spread to other sectors through network connections creating a vicious cycle and bankruptcy avalanches in the economy. Figure 5 8 shows that the number of bankruptcies per period in a sector is correlated to the number of bankruptcies in other sectors. In addition, figure 6 shows tha
49、t the distribution of the total number of bankruptcies per period has a fatter tail with respect to a normal distribution,8 so that “rare events” are more probable in this setting than in an economy characterized by normal distributions. 4. Conclusive remarks The idea of a snowball phenomenon in which the bankruptcy of one firm somehow affects the financial conditions