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An agent based decentralized matching macroeconomic model

Abstract

In this paper we present a macroeconomic microfounded framework with heterogeneous agents—individuals, firms, banks—which interact through a decentralized matching process presenting common features across four markets—goods, labor, credit and deposit. We study the dynamics of the model by means of computer simulation. Some macroeconomic properties emerge such as endogenous business cycles, nominal GDP growth, unemployment rate fluctuations, the Phillips curve, leverage cycles and credit constraints, bank defaults and financial instability, and the importance of government as an acyclical sector which stabilize the economy. The model highlights that even extended crises can endogenously emerge. In these cases, the system may remain trapped in a large unemployment status, without the possibility to quickly recover unless an exogenous intervention takes place.

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Notes

  1. The boundedly rational rules which guide agent behavior are based on a 5 year period of interviews with large US firms and have been formalized in a book (Eliasson 1976).

  2. Moreover, the model shows (see Eliasson 1985, p.78–83) emergent non-trivial phenomena such as the fact that a fast stabilization of prices is detrimental to macroeconomics stability, that structural diversity makes the economy more stable against shocks and lowers growth losses, and that entry is a central feature in an innovative economy.

  3. Although the word “exposure” is usually used in a credit risk context (for instance the exposure at default—EAD—in Basel II agreement), here it exactly refers to the ratio between corporate credit and equity, which is different to the asset/equity ratio, given that in the balance sheet there are also assets which are supposed to be risk free: government bonds and, in the case of mismatches, residual cash. In addition, according to the Basel II framework, all our corporate credits have EAD equal to 1 (especially under the “foundation approach”) then the overall bank EAD is just the sum of the extended corporate loans. For these reasons, we think that the word “exposure” is more appropriate compared to other words (such as “leverage”, that could be a better choice for the asset/equity ratio).

  4. First of all, our choice of introducing the Dynamic Trade-Off theory in the model is due to empirical reasons, as motivated by the literature on the topic cited above. Moreover, in Delli Gatti et al. (2010) the Pecking Order theory is associated to a different production function and a peculiar sectorial structure of the economy. Besides, that paper is an extension of a previous one (Delli Gatti et al. 2005) which was already based on the Pecking Order theory: Delli Gatti et al. (2010) proposed a way to study the diffusion of bankruptcy in such a framework through adding an upstream sector to Delli Gatti et al. (2005). In presence of a downstream sector characterized by a firm’s financial structure based on the Pecking Order theory, the introduction of an upstream sector (without such a financial structure) allowed the model to exhibit bankruptcy avalanches. Instead, in our case we do not need such an assumption, given that the financial structure of firms based on the Dynamic Trade-Off theory allows us to analyze firm and bank defaults in a more natural way.

  5. It is a mean interest rate calculated as the weighted average of interests paid to the lending banks.

  6. We consider government bonds as risk free assets. Banks that do not manage to lend all the disposable money, decide to invest in government bonds to obtain a small but positive risk free return able to cover the return paid on deposits. In the case \(\bar{k}\) is smaller than \(\hat{k}\) the bank has not enough money to lend, and then it cannot reach the maximum admissible leverage on risky assets. On the contrary, when \(\hat{k}\) is smaller than \(\bar{k}\) the bank has an excess of money with respect to the amount that it can invest in risky assets. As a consequence, the bank buy government securities obtaining the remuneration given by the risk free rate.

  7. In order to obtain a more statistical significant result we extended the simulation period to T\(=\)500.

  8. This short business cycle of around three periods could be enlarged by changing the parameter setting. For instance, assuming a different adjustment parameter of prices and wages can impact the macroeconomic system. We tried a simulation with parameter \(\alpha \) used in Eq. 9 equal to 0.10, that is, prices move more rapidly than wages, in a more realistic setting. The macroeconomic system acts similarly to the baseline setting, but the business cycle is longer and more volatile, and the mean unemployment rate is higher, with a higher probability of large crises. More in general, the mismatch between the two mechanism enlarges the unemployment (and then the output) volatility. However, the analysis of different adjustment speeds deserves a deeper study, and it should be very important to simulate asymmetric behaviours (for instance wages and prices could be represented with a stronger rigidity in reductions than in rises). Moreover, an accurate parameter calibration is needed, but should be founded on a more complete model, that we aim to develop starting from this framework.

  9. We test if the quadratic and cubic coefficients fit the data with a t-test on the two coefficients and a F-test on both coefficients jointly: all the tests strongly reject (at 99 % confidence level) the null hypothesis that the coefficients are equal to zero. Moreover, all the information criteria (Akaike, Schwartz and Hannan–Quinn) select the cubic fit as the best. The information criteria also signal that the cubic fit overperforms the fourth degree polynomial fit and the coefficient of the fourth degree component is not statistically significant. The equation of the cubic fit, where U is the unemployment rate and \(L_{f}\) is the aggregate firm leverage level, is the following:

    $$\begin{aligned} U = - 0.08 + 0.52* L_{f} -0.39* L^{2}_{f} + 0.08*L^{3}_{f} \end{aligned}$$
  10. The equation of the quadratic fit, where U is the unemployment rate and \(L_{b}\) is the aggregate bank exposure level, is the following:

    $$\begin{aligned} U = 0.168 - 0.033* L_{b} + 0.003* L^{2}_{b} \end{aligned}$$

    Both coefficients are statistically significant at 99 % level.

  11. The public deficit decreases from \(g = 22\) % to \(g = 28\) %, given that the public expenditure is more than compensated by economic growth and related tax revenues.

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Acknowledgments

We are very grateful to participants at the following conferences for helpful comments and suggestions: 17th Annual Workshop on Economic Heterogeneous Interacting Agents (WEHIA), University of Pantheon-Assas, Paris II, June 21–23, 2012; 18th International Conference Computing in Economics and Finance (CEF), Prague, June 27–29, 2012; Systemic Risk: Economists meet Neuroscientists, Frankfurt Institute for Advanced Studies (FIAS) and the House of Finance, Frankfurt am Main, September 17–18, 2012; 3rd International Workshop on Managing Financial Instability in Capitalist Economies (MAFIN), Genoa, September 19–21, 2012. We want to thank two anonymous referees for insightful comments and useful suggestions. Authors acknowledge the financial support from the European Community Seventh Framework Programme (FP7/2007–2013) under Socio-economic Sciences and Humanities, grant agreement no. 255987 (FOC-II).

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Riccetti, L., Russo, A. & Gallegati, M. An agent based decentralized matching macroeconomic model. J Econ Interact Coord 10, 305–332 (2015). https://doi.org/10.1007/s11403-014-0130-8

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Keywords

  • Agent-based macroeconomics
  • Business cycle
  • Crisis
  • Unemployment
  • Leverage

JEL Classification

  • E32
  • C63