Macroeconomic Dynamics of Assets, Leverage and Trust

A macroeconomic model based on the economic variables (i) assets, (ii) leverage (defined as debt over asset) and (iii) trust (defined as the maximum sustainable leverage) is proposed to investigate the role of credit in the dynamics of economic growth, and how credit may be associated with both economic performance and confidence. Our first notable finding is the mechanism of reward/penalty associated with patience, as quantified by the return on assets. In regular economies where the EBITA/Assets ratio is larger than the cost of debt, starting with a trust higher than leverage results in the highest long-term return on assets (which can be seen as a proxy for economic growth). Therefore, patient economies that first build trust and then increase leverage are positively rewarded. Our second main finding concerns a recommendation for the reaction of a central bank to an external shock that affects negatively the economic growth. We find that late policy intervention in the model economy results in the highest long-term return on assets. However, this comes at the cost of suffering longer from the crisis until the intervention occurs. The phenomenon that late intervention is most effective to attain a high long-term return on assets can be ascribed to the fact that postponing intervention allows trust to increase first, and it is most effective to intervene when trust is high. These results are derived from two fundamental assumptions underlying our model: (a) trust tends to increase when it is above leverage; (b) economic agents learn optimally to adjust debt for a given level of trust and amount of assets. Using a Markov Switching Model for the EBITA/Assets ratio, we have successfully calibrated our model to the empirical data of the return on equity of the EURO STOXX 50 for the time period 2000–2013. We find that dynamics of leverage and trust can be highly nonmonotonous with curved trajectories, as a result of the nonlinear coupling between the variables. This has an important implication for policy makers, suggesting that simple linear forecasting can be deceiving in some regimes and may lead to inappropriate policy decisions.

The Fine Picture

This chapter restricts the m-tuple (fi) of demand functions defining the exchange model to belong to ε‎c. In addition to the assumptions made in the previous chapters (recall that ε‎c is a subset of ε‎r), the demand function fi satisfies the weak axiom of revealed preferences for every consumer, and the slightly stronger negative definiteness of the Slutsky matrix for the consumer whose demand function satisfies desirability (A). These stronger assumptions are aimed at giving more economic flesh to the exchange model. As a consequence, the natural projection inherits much stronger properties that give a specificity of its own to the exchange model. The most important properties of the exchange model with (fi) ɛ ε‎c are the regularity of the no-trade equilibria, the openness and full measure (a.k.a., the genericity) of the set of regular equilibria as a subset of the equilibrium manifold, the inclusion of the set of equilibrium allocations in one and only one connected component of the set of regular economies, the uniqueness of equilibrium for all economies belonging to that component, and the interpretation of that property in terms of trade intensity.

The Broad Picture

This chapter shows that the m-tuple (fi) of demand functions defining the exchange model belongs to ε‎r, i.e., the demand function fi is bounded from below (B) for every consumer and satisfies desirability (A) for at least one consumer. These additional properties will give to the natural projection the very important property of properness. The combination of smoothness and properness will suffice to yield what is now known as the theory of regular economies.

Regular Infinite Economies

The main contribution of this paper is to place smooth infinite economies in the setting of the equilibrium manifold and the natural projection map à la Balasko. We show that smooth infinite economies have an equilibrium set that has the structure of a Banach manifold and that the natural projection map is smooth. We define regular and critical economies, and regular and critical prices, and we show that the set of regular economies coincides with the set of economies whose excess demand function has only regular prices. Generic determinacy of equilibria follows as a by-product.