Endogenous growth, the distribution of wealth, and optimal policy under incomplete markets and idiosyncratic risk

This paper combines the standard incomplete markets model of uninsurable idiosyncratic risks and borrowing constraints with the Arrow/Romer approach to endogenous growth to analyze the interaction of risk, growth, and inequality, the latter also endogenously determined in equilibrium. We derive conditions on existence and nonexistence of balanced growth paths. Major results include that growth, inequality, and risk are positively related in our model, but we also identify a hump-shaped relationship between welfare and risk, indicating a tradeoff relationship between risk-pooling and growth in the determination of welfare. We employ the prototypical policy implications of the underlying growth model (i.e. subsidizing capital returns) and find that the tax-transfer scheme positively affects growth while simultaneously reducing wealth inequality in the economy. The benefits and burdens of the underlying policy are unequally distributed, which raises the issue of politico-economic equilibria. We provide results on majority voting, finding that that the median voter prefers less than optimal subsidies on investment. Interestingly, the society might even vote against a policy providing full insurance against idiosyncratic risk, because welfare losses of lower growth more than offset welfare gains from lower risk.