In existing two‐sector, human capital‐based endogenous growth models with social constant returns, local equilibrium indeterminacy emerges based upon either differential factor tax rates or sector‐specific externalities. Two primary results are established in this paper. First, once there are productive public goods, the two existing mechanisms are not robust in establishing local indeterminacy. Second, with the congestion effect in the use of public services, local indeterminacy is regained.