A Stochastic Blanchard Model with a State-of-Market Dependent Reaction Coefficient

Abstract

We reformulate and extend the Blanchard model of output dynamics, the stock market and interest rates that studies Keynesian IS-LM analysis from the perspective of a richer array of financial assets, namely equities and long-term bonds. Investment demand now depends on Tobin’s average q in the place of the real rate of interest and as a result share price dynamics feed back into the real sector. Our main contribution is to extend the model to allow imperfect asset substitutability, imperfect forecasts of capital gains in the place of Blanchard’s limit case of perfect substitutes and myopic perfect foresight, and the assumption of a state-of-the-market dependent speed of reaction to expected asset return differentials. These elements introduce an underlying nonlinear dynamic feedback mechanism between the real and financial sectors. Furthermore we introduce some stochastic elements into the model and use numerical simulations to study the interaction of the nonlinear and stochastic elements. We focus in particular on the propensity of the model to generate stock market booms and crashes when the underlying deterministic model is locally unstable.