An agent based decentralized matching macroeconomic model

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).

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.

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.

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

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.

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

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.

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:

The equation of the quadratic fit, where U is the unemployment rate and \(L_{b}\) is the aggregate bank exposure level, is the following:Both coefficients are statistically significant at 99 % level.

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.