Price Expectations and Stability in a Short-Run Multi-Asset Macro Model
Traditionally, macroeconomic models are void of asset price dynamics. One explanation of this neglect involves the notion of short-run If one defines a equilibrium to be a situation in which relative asset prices are constant, the problem of asset price dynamics is assumed away at the outset. But this abstraction from the dynamics of relative asset prices in general is unjustified. The typical macroeconomic equilibrium is characterized by two features: 1) The stocks of assets (money, bonds, and capital goods) are fixed (instantaneously). 2) Asset markets are in equilibrium in the sense that we observe points lying on the asset demand functions. In general neither 1) nor 2) requires that relative asset prices be constant in equilibrium. But as we shall note below, one case in which this will be so is if the actual prevailing values of the real rates of return and coupon rates on the assets are expected to continue unchanged throughout all future periods. Under this extremely restrictive assumption of static expectations the existing asset prices will be expected to continue throughout the future, and the price dynamics degenerates. More generally we define dynamic equilibrium to be a situation in which 1) and 2) are satisfied and in addition relative asset prices are constant. The uniqueness and stability of such a shortrun dynamic equilibrium becomes the crucial question that we will discuss below. If we discover that an economy always converges rapidly to a unique dynamic equilibrium, that fact would provide a justification for models which do not contain price dynamics. On the other hand, rapid convergence cannot be presumed a priori, and in fact we shall discover that some rather strong regularity conditions are required to ensure stability. When these regularity conditions are not satisfied, the possibility arises of dynamic instability, a result that would destroy the validity of macroeconomic models formulated on the assumption that a dynamic equililibrium prevails at every instant. Thus we will carefully examine the underlying mechanism generating price dynamics. Since we do not postulate dynamic equilibrium, our formulation may be viewed as a disequilibrium approach to macroeconomics. Our model contains three main ingredients: (i) A new adaptive-type mechanism for generating price expectations simultaneously with a portfolio rate of return condition. (ii) A savings function, postulated to depend upon (expected) disposable income and wealth, with disposable income defined to ensure the consistency of planned savings and planned (expected) wealth accumulation. (iii) Asset demand functions that determine the value of the stocks of various assets as functions of expected rates of return, income, and wealth. Capital gains play a crucial role because they enter via the definition of the expected rates of return