Public spending, monetary policy and macroeconomic instability

We analyze sunspot‐driven fluctuations in a standard neoclassical growth model with money holdings and public spending. In our economy, money is needed for transaction purpose, while public spending is financed through a flat income tax. Public spending includes an incompressible component and a variable part, and the latter exerts positive externalities on private utility or production. Our theoretical results show that the composition of public spending and externalities have important effects on local stability properties. First, in the absence of externalities, there is a unique steady state, and local indeterminacy depends on the interplay between the share of the cash‐in‐advance constraint and the intertemporal elasticity of substitution of consumption. Second, in the presence of externalities, multiple equilibria might emerge under weak enough production externality, while uniqueness of the steady state prevails under strong production or under consumption externality. We further show that weak production/consumption externality or strong consumption externality could generate local (in)determinacy of the steady state depending on the share of the cash‐in‐advance constraint while strong production externality generates local determinacy of the steady state. Finally, based on numerical examples, we show that an increase in the variable public spending and the income tax rate exert a local stabilizing effect while externalities promote locally the likelihood of local indeterminacy.