It has been shown that under perfect competition and constant returns-to-scale, a one-sector growth model may exhibit local indeterminacy when income tax rates are endogenously determined by a balanced-budget rule while government expendi- tures are fixed. This paper shows that the associated aggregate instability does not ensue from the local indeterminacy of a specific stationary equilibrium but from the multiplicity of the stationary equilibria and persists under local determinacy of all of them. We provide a global analysis of the Schmitt-Grohe and Uribe model [1997] and study specific cases that were not investigated in the original paper, when aggregate instability is inherited from the coexistence of two saddle-path equilibria on one hand and from the connection of the two steady states on the other hand.