Macroeconomic Theory

The descriptive framework of an economy with a decentralized and disaggregated market structure – as observed in most Western monetary economies – is characterized by dominant private ownership of individual economic agents. They interact in markets together with central organizations of significant size such as governments or central banks which represent the institutional elements of empirical economies with markets. They serve as the explanatory framework for the corresponding abstractions used in the theoretical building blocks of a macroeconomic model of an economy as laid out by general equilibrium theory of private ownership economies in the sense of Arrow and Debreu (see Arrow, 1951; Debreu, 1959; Arrow & Hahn, 1971) and extensions thereof (following Keynes, 1936; Hicks, 1939; Patinkin, 1965, and others).

The description of the intertemporal trading structure of commodities, agents, and markets is the one originally proposed by Hicks (1939) and used later by Patinkin (1965). The mathematical presentation here follows Grandmont (1983) which corresponds to an extension of the general finite-dimensional Arrow-Debreu economy to an infinite repetition (sequence) of trading periods of finite-dimensional economies.

The objective of this chapter is to formulate a basic prototype monetary macroeconomic model built along the microeconomic principles of Chapter 2, which will serve as the benchmark for a consistent macroeconomic analysis of the short-run allocations, i.e. of the determination of output and employment with associated prices and wages in each given period, as well as for the long-run behavior of the economy under alternative dynamic scenarios: i.e. with adaptive or rational expectations, under random perturbations, and under different government policies. The modeling structure will be as simple as possible at the beginning and as detailed as necessary in each subsequent section to capture the main intertemporal ingredients of a monetary economy with production in order to discuss the specific economic questions posed in each section.

The analysis of temporary equilibrium allocations in Chapter 3 showed that the structural and behavioral parameters defining the type of equilibrium induce a well defined result in real and monetary terms for the macro economy in any period. In other words, for such a closed economy containing a public sector made up of a government with an integrated central bank as monetary authority supporting the system with fiat money, any feasible temporary allocation under income consistency at given money balances and expectations has an impact on the government deficit. Since government expenditure and tax revenue are endogenously determined the size and the sign of the government deficit in every period is price dependent. Therefore, changes of total money balances held in the private sector occur if and only if the government budget is not balanced. As a consequence, changes of money balances are determined simultaneously with the temporary equilibrium making them endogenous between periods. This chapter derives the main results for a recursive analysis of the development of prices, price expectations, and of money balances. The emphasis will be on characterizing and investigating the conditions under which recursive forecasting schemes exist which induce equilibrium orbits with perfect foresight and rational expectations. In addition, conditions of uniqueness of balanced paths, their stability and their basins of attraction will be examined. Some discussion will be provided for these issues with general adaptive forecasting rules.

In the previous chapters government activity was given by a pair of parameters (g, τ) defining government consumption and a proportional tax rate on income, which were assumed to be constant over time. An important implication of such a stationary government policy was the observation that in each period the government’s deficit is endogenous and determined in size and sign at each temporary equilibrium. As a consequence, the amount of fiat money held by consumers as well as the deficit in each period is endogenous leading to explicit endogenous dynamics of the quantity of money induced by the equilibrium conditions on the two markets. In such cases, neither the sign or size of the deficit nor the change of the quantity of money is directly controlled by the government. Chapter 4 derived the major consequences of such policies showing that the two fisal parameters have a decisive influence on the existence, stability, and on the long-run real performance of the macroeconomy under rational expectations.

Following a reappraisal by Clower (1965, 1967) and Leijonhufvud (1968) of attempts to analyze unemployment phenomena in the Keynesian spirit in monetary environments Barro & Grossman (1971), Benassy (1975b), Drèze (1975), Younès (1975), Malinvaud (1977), and others presented pioneering work integrating disequilibrium trading principles into the Hicksian monetary intertemporal framework. This induced a reconsideration of the Keynesian criticism of equilibrium theory as being an inadequate tool to describe unemployment situations in aggregative economies. Within two decades a considerable number of publications presented extensions and justifications for this approach attempting to provide microeconomic foundations to Keynesian macroeconomics with unemployment configurations. The surge of publications with the joint perspective of microeconomic foundations to potential macroeconomic applications was designed to describe a modeling framework to characterize stationary disequilibrium configurations with typical permanent price and wage rigidities.

The presentation of the model in Chapter 6 showed that the dimension of the state space of the monetary economy in disequilibrium for which the dynamics needs to be defined increased from two to four adding the vector of prices and wages (p, w) to the pair of money balances and expected prices (M, p^e).

An analysis of the role of random perturbations for the dynamics of business cycles in macroeconomic models still represents one of the most challenging tasks in economic theory. The approach taken in Chapter 4 for equilibrium dynamics introduced some new and useful concepts which allowed a dynamic analysis of stochastic phenomena, i.e. the possibility to provide an investigation of stability and convergence properties of random time series as well as to exhibit their time-invariant statistical properties induced by the stationary orbits. They allow a complete analysis of random data under their transient as well as their stationary or time-invariant behavior within the same mathematical framework. The central issue here will be to apply these methods to the disequilibrium setting in order to characterize and show the main features of the cyclical nature of real and monetary phenomena resulting from the interplay of the time-one map under disequilibrium and random perturbations.