The basic stochastic macroeconomic model and the short-term interest rate dynamics

In this chapter, we will develop a stochastic analogue to the dynamic macroeconomic model already discussed in the last chapter. This is accomplished by modeling the economy’s technology not as a fixed parameter, but as a certain continuous-time stochastic process. As a consequence, holding capital involves the bearing of risk. The intertemporal consumption/asset allocation problem of the private households becomes risky. This risky decision-making reflects the reality of how financial markets form their behavioral rules much better than the deterministic model in the previous chapter. Hence, we can expect our model to ‘produce’ prices for assets traded on the financial market that will generally not be constant but change dynamically as it happens in reality. Specifically, interest rates will no longer be equal to the net return on capital but rather react on changes in the economy, especially on fiscal policy changes. The link between fiscal policy and the term structure of interest rates is a new aspect of this model. In equilibrium, the model in this chapter will produce nonlinear, stochastic dynamics describing the evolution of output, capital, private wealth and public debt. For this reason, this chapter lays the basis for the analysis of all interesting economic aspects to be discussed in subsequent chapters: the relationship between fiscal policy and the term structure of interest rates, the question how economic growth is affected by the financial market, and the dynamics of public debt in the light of stochastically varying interest rates.