How should governments calibrate the desire for redistribution via progressive taxation against the need to incentivise the accumulation of human capital? I explore this question in a heterogeneous agent model featuring stochastic human capital accumulation where agents choose an optimal number of years to study before starting work. The social welfare-maximising policy features generous subsidies for education and highly progressive labour taxes.

When r<g, simple policy rules like constant money growth rates, Taylor rules or constant surpluses can no longer pin down the price level. To restore determinacy, one needs “hyperactive” rules that are even more destabilising to public debt or money off-equilibrium, e.g. raising surpluses when debt is below target. With enough tools at their disposal, either the fiscal or monetary authority can implement the rules required to determine the price level. r<g can explain why inflation was muted following fiscal stimulus over 2008-12, but rose sharply after the 2020-21 stimulus.

Should governments always provide adequate funding for publicly-provided goods like higher education and accept the distortions from higher taxes, or should they limit funding and allow places to be rationed? I develop a model where higher education is funded by the government and rationing of places is possible. Optimal policy should provide just enough funding to avoid rationing. General labour taxes should be highly progressive, while graduate taxes should be near zero.

What are the limits on how much can a government borrow when the real interest rate on public debt is below the growth rate of the economy? I explore this question using a standard model of risky investment under incomplete markets, extended to feature emerging market (EM) economies with even greater risk, and limits to the private supply of safe assets. These two elements further inflate the bubble in public debt, affording developed market (DM) governments even greater fiscal space.

I propose a new way to model income fluctuations using standard survey data. The method accurately captures the degree of earnings inequality and risk, and when embedded in a standard incomplete markets model can broadly match the distribution of wealth observed in the data, even coming close to capturing the extreme concentration at the top in the UK. The method also suggests that changes in earnings inequality and risk since the 1970s in the US can explain around half of the increase in the concentration of wealth at the top since then.

I examine the role that housing plays as collateral in investment by credit-constrained entrepreneurs, who face uninsurable idiosyncratic and aggregate investment risk from their capital.

I explore the implications for the deposit channel of monetary policy when banks face the risk of deposit outflows.