Fiscal and Monetary Policy in a Basic Endogenous Growth Model

Abstract

We present a monetary endogenous growth model and analyse the effects of fiscal and monetary policy with real money as an argument in the utility function. We show that a balanced government budget gives a higher balanced growth rate and lower inflation than a situation with permanent public deficits. It also leads to higher welfare compared to a situation with permanent deficits when the government does not put a high weight on stabilizing debt. However, when governments run deficits with a high weight on stabilizing debt, comparative welfare effects depend on the initial conditions with respect to public debt. Further, for a given monetary policy a stricter debt policy yields higher growth, lower inflation and higher welfare. A rise in the nominal money supply can compensate the negative growth effects of a loose debt policy up to a certain point but only at the cost of higher inflation and lower welfare.

Appendix

1.1 Stability of the Balanced Budget Scenario

With a balanced government budget that implies $\phi =-\theta z(k/y)$, the Jacobian of the dynamic system (23)–(25) is given by,

$$\begin{aligned} { J} = \left[ \begin{array}{c@{\quad }c@{\quad }c} {\partial \dot{x}}/{\partial x} &{} \theta x &{} -\beta x\\ {\partial \dot{z}}/{\partial x}&{} (\theta +\rho +\theta z) &{} -\beta z\\ 0 &{} 0 &{} -g \\ \end{array} \right] , \end{aligned}$$

where we also used $\dot{v}=-v (\partial \dot{k}/{\partial k})$, $x^{\star }/z^{\star }=\theta +\rho$ and $v^{\star }=0$ on the BGP and the variables $x$ and $z$ are evaluated at the BGP. Since ${\partial \dot{x}}/{\partial x}=xC_2$ and ${\partial \dot{z}}/{\partial x}=zC_2-1$, with $C_2=\partial (\dot{x}/x)/\partial x>0$, we get $({\partial \dot{x}}/{\partial x})(\theta +\rho +\theta z) -\theta x({\partial \dot{z}}/{\partial x}) =xC_2(\theta +\rho )$ $+\theta x>0$ as well as $({\partial \dot{x}}/{\partial x})+(\theta +\rho +\theta z)>0$, so that there exists one negative eigenvalue of $J$ given by $-g$.$\Box$