Stock market dynamics, leveraged network-based financial accelerator and monetary policy
Introduction
The current crisis is showing how business cycle fluctuations can be enlarged by different self-reinforcing mechanisms. Riccetti, Russo, and Gallegati (2013) consider a twofold financial accelerator, composed of the “leverage” and the “network-based” accelerators. The former explains that a negative shock on firms' output make banks less willing to loan funds, with a consequent credit constraint and an increase of the interest rate; furthermore, firms are less prone to invest because they compare a reduced expected profit with an increased cost of funding; therefore, the reduced investments lead again to a lower output in a vicious circle. The network-based financial accelerator (Delli Gatti, Gallegati, Greenwald, Russo, & Stiglitz, 2010) highlights that the presence of a credit network may produce an avalanche of firms' bankruptcies: the bankruptcy of a firm may bring “bad debt” that affects the net worth of banks, which can also go bankrupt or, if they manage to survive, they will react to the deterioration of the net worth increasing the interest rate to all their borrowers (Stiglitz and Greenwald, 2003, p.145), making them incur additional difficulties in servicing debt and thus increasing the weakness of the whole non-financial sector, in another vicious circle. In addition, Bernanke, B. and Gertler, M., 1989, Bernanke, B. and Gertler, M., 1990, Bernanke, B. and Gertler, M., 1995 and Bernanke, Gertler, and Gilchrist (1999) show the presence of another positive feedback mechanism: a reduction of asset values held by the entrepreneurs generates an increase of the borrowers' leverage and, subsequently, of the risk premium with a consequent reduction of the economic activity; in our speech, there is a strengthening of the “leverage accelerator”. The asset we consider in our analysis is the stock market value of firms' equity; therefore, we call this mechanism the “stock market” financial accelerator.
Indeed, starting from Delli Gatti et al. (2010) and Riccetti et al. (2013), in this paper, we build an agent-based macroeconomic model that also considers the presence of the stock market, although it is added in a stylized way. As in Riccetti et al. (2013), the firms' financial structure relies upon the Dynamic Trade-off theory. For a review on the Dynamic Trade-off theory, see for instance Flannery and Rangan (2006), Frank, M.Z. and Goyal, V.K., 2008, Frank, M.Z. and Goyal, V.K., 2015, and Riccetti et al. (2013). Following this theory, we assume that firms have a “target leverage”, implying that a growing firm decides to increase its debt level, thus creating in good periods the basis for the subsequent crisis. In this setting, we also consider the loss given default rate (LGDR) – see Section 4 – that is important because it is one of the components, with the probability of default (PD) and the exposure at default (EAD), of the credit risk models. Moreover, we set the firms' stock market value by using the earning-per-share (EPS) multiplier, consistent with the dividend discount model. Stock market values influence the distance to default (DD), a measure of credit risk widely used by many banks and developed in the Moody's KMV Portfolio Manager model. We use a proxy of the DD, based on stock market return and return's variance, to evaluate firms' financial soundness and, thus, to set the interest rates charged by banks to them. Moreover, we add a risk aversion parameter able to modulate the impact of stock market volatility on firms' DD evaluation. Therefore, we build a methodology in which the agent-based approach, used for modeling the credit market, interacts with some stylized mechanisms, used to represent some features of the stock market, based on techniques derived from the mainstream literature. In other words, beyond the specific conclusions of our simulations, the paper contribution to the existing literature is twofold:
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theoretically, we describe a triple financial accelerator, adding the “stock market accelerator”;
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methodologically, we insert in an agent-based model some simple mechanisms, well known in mainstream literature, able to describe some empirical features, such as the relationship between profits and stock market values or the relationship between stock market values and monetary policy.
Instead, regarding the output of the simulations, our model allows to analyze:
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how a shock on the real side of the economy can be amplified, through the stock market multiplier, further increasing the financial accelerator mechanism and the overall fragility of the system. In other words, the interplay between forward-looking evaluation of firms' future profits provided by the stock market and the interest rate setting due to bank lending attitudes may lead to a boom-bust cycle;
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whether a shock on the financial market may be dangerous for the real economy; indeed, we investigate the evolution of the economic environment when the stock market multiplier increases – considered as a symptom of a mounting financial market bubble – in order to ascertain if this results in a riskier systemic configuration;
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how banks' risk aversion can influence the economic environment;
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how the central bank can influence the economic cycle modifying the interest rate; indeed, the interplay between the interest rate and the stock market evaluation can modify the effectiveness of monetary policy, compared to the case in which the stock market is absent (or non relevant).
The remainder of the paper is organized as follows: in the next section, we present the characteristics of our model. Then firms' behavior is analyzed in Section 3, while Section 4 considers the banking sector. Simulation results are presented in Section 5. A sensitivity analysis on two important parameters regarding the stock market is developed in Section 6. In Section 7, we propose an extension of the baseline model and a monetary policy experiment. Section 8 concludes.
Section snippets
Environment
Our economy is populated by households (final consumers and labor suppliers), firms, and banks. Firms – indexed by i = 1 , 2 , . . . , I – produce consumption goods. Banks, indexed by z = 1 , 2 , . . . , Z, extend credit to firms.
We consider three markets: consumption goods, stock, and credit markets. We will focus on the last market, making simplifying assumptions for the first and second ones. Moreover, we do not explicitly model the labor market.1
Firms
Firms operates on all the three considered markets.
Interest rate setting
As said above, we assume that the stock market works as a secondary market; thus, firms can finance production only by self-financing and bank credit.
Moreover, every bank sets a different interest rate on loans and these spreads imply that firms sometimes change banks to obtain a lower interest rate, following the mechanism explained in Section 3.3. We assume that bank z adopts the following rule in setting the interest rate on loans to borrower i:
Thus, the
Simulations
We analyze our economy by means of computer simulations. We assume that this economy is composed of 500 firms and 50 banks over a time span of 1000 periods. However, we use the first 200 periods to initialize the simulation, therefore we present the last 800 periods only.
At the beginning of the simulation, we set the net worth of each firm and bank to 10. We assume that when a firm or a bank goes bankrupt it is replaced by a new one with net worth equal to a random number between 0 and 2 for
Sensitivity analysis
In this section, we discuss the effect of parameter changes weight and moltp in terms of the following output variables: the mean aggregate production, the volatility of the aggregate production's growth rate, the average interest rate, the mean firms' leverage, the average aggregate firms' net worth, the mean number of firms' bankruptcies, the average value of bad debt ratio (the sum of all debts of defaulted firms in the period divided by the overall outstanding credit), and the average
Varying stock market multiplier and monetary policy experiment
In this section, we compare the effect of a monetary policy expansion (the opposite holds for a policy rate tightening), that is a reduction of the central bank interest rate from 3% to 1% at time 601, on the baseline model and on a slightly different model – that we call “multiplier” model – in which the stock market multiplier is affected by the interest rate level. In this second model we calculate the EPS multiplier in the following way, that considers 40 periods of future discounted cash
Conclusions
In this paper, we add the presence of the stock market to a framework similar to the agent-based model of Riccetti et al. (2013). The stock market values influence the distance to default, used to evaluate firms' financial soundness and, thus, to set the interest rates charged by banks to them. The presence of the stock market enriches the positive feedback mechanism of the Financial Accelerator, that is now threefold:
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Leverage accelerator. Negative shocks on firms' output make banks less
Acknowledgments
We are grateful for helpful comments and suggestions to participants in the “Wolpertinger Conference 2014”, at Università Cattolica del Sacro Cuore, Milan, September 4–6 2014, and to participants in the “17th Annual Workshop on Economic Heterogeneous Interacting Agents” (WEHIA), at University of Pantheon-Assas, Paris II, June 21–23 2012, where an earlier version of the paper was presented. Authors acknowledge the financial support from the European Community Seventh Framework Programme (FP7)
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