A Dynamic Non-Tatonnement Macroeconomic Model with Stochastic Rationing

Abstract

The paper considers a dynamic macroeconomic model with stochastic quantity rationing. The economy is composed of overlapping-generations consumers, producers and a government who interact in a labor and a consumption goods market. Agents behave optimizing and trade in each period, even when prices are not at their Walrasian level. This is rendered possible by means of feasible allocations using the concept of temporary equilibrium with quantity rationing. We give a complete characterization of the typology of these equilibria (Keynesian, Inflationary, Classical, of Underemployment, as well as Walrasian). Moving to the dynamics of the model, prices and wages are adjusted following, alternatively, linear or non-linear adjustment rules. The size of price adjustment is based on the intensity of rationing, a reliable measure of which is obtained through stochastic rationing. This methodology allows us to encompass a wide variety of interesting economic circumstances, in particular the impact of various degrees of price and wage flexibility on the structural dynamic behavior of the model. Parameters such as the adjustment speed of prices and those referring to government policy are in fact decisive for the type of dynamics that emerges. The model, by providing an endogenous explanation of possible transitions between different (dis)equilibrium regimes, results to be a suitable framework for the analysis of alternative economic policies.Numerical simulations have shown that, contrary to what is commonly expected regarding the stabilizing effect of price flexibility, the economy can be subject to complex dynamics. By deviating from the Walrasian parameter set in some of the relevant parameters (initial conditions, technological coefficients, government policy instruments), the simulations establish the existence of complex and strange geometric objects. In particular it is possible to obtain dynamic phenomena like bifurcations and (strange) attractors. One of the attractors in the plane of wage inflation rate and unemployment rate displays a Phillips curve, which emerges by very construction as a true long-run phenomenon. Moreover, to the best of our knowledge, this is the first example of a Phillips curve generated as an attractor of a dynamical economic system. Also it emerges quite clearly that cycles of different order co-exist for the same parameter set, but for different initial conditions. Therefore, a minor variation in the initial state can drive the system to a completely different cycle or, in other words, there is sensitive dependence of the order of a cycle on initial conditions.Of particular interest in the context of our macroeconomic model is the impact of variations in the values of the government policy instruments. Here we make use of a new technical tool, called cartogram, which provides a concise visualization technique and permits to establish a relationship between the values of the relevant parameters and the structure of the resulting dynamics (although it is not able to distinguish between regular quasi-periodic behavior and ''true'' chaotic motion). As an economic result, the use of this tool suggests quite clearly that the stabilization of the economy by means of fiscal policies is a most delicate matter, even though there is a tendency for nominal wage stickiness to favor this goal.Finally, we show the existence of quasi-stationary states involving underemployment and underutilization of production capacities, proving that the flexibility of prices and wages per se is not sufficient to overcome situations of market imbalances. This is due to the spillover effects between the labor and the consumption goods market, and could not have been obtained in partial equilibrium models. For example, in a state of Keynesian underemployment, there is excess supply on both markets. Therefore both the goods price and the wage diminish. However, if both decrease in the same measure, their ratio (the real wage) remains constant. If, in addition, there is a government balance surplus, the money stock decreases. If this decrease is proportional to the one in price and wage, the real stock of money held by consumers does not change. Thus it is possible that, in addition to the real wage, also the real wealth of households remains constant. In these circumstances, no agent has any incentive to modify her decisions relative to the ones taken in the previous period. Therefore, the state of the economy is stationary with respect to its real variables, although the nominal ones do change.