This paper examines the conditions needed for equilibrium (in)determinacy in growth models characterized by perfect competition and a balanced-budget rule (BBR). Contrary to the literature that assumes zero public debt, we build an endogenous growth model with a generalized BBR authorizing a constant positive debt level. We show that the emergence of aggregate instability dramatically depends on the dynamics of the debt-to- GDP ratio and the strength of social labor externalities. If the labor demand is positively sloped and steeper than the labor supply, two reachable balanced-growth paths appear – a no growth trap, and a positive growth solution – that gives birth to both local and global indeterminacy, hence aggregate instability driven by self-ful lling beliefs (sunspots). In addition, we show that a scal rule such that the tax rate strongly responds to public- debt increases can remove the no-growth trap, and secure positive long-run growth.