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This thesis explores inequality and its effects on the macroeconomy. Each chapter is concerned with heterogeneity between households or firms in some dimension: the first simply explores whether a standard model can capture the degree of inequality observed in the data; the second and third tackle the implications of such inequality for some aspect of policy. In all three papers I adopt the approach now common in the literature of viewing inequality as arising from idiosyncratic shocks and incomplete markets. In this lay summary I briefly discuss each chapter. MATCHING THE WEALTH DISTRIBUTION WITH INCOME INEQUALITY & RISK: I show that a standard incomplete markets model with labour income risk alone, when modelled accurately using a new method, can broadly match the distribution of wealth observed in the US and UK, whereas adding capital income risk does little to concentrate wealth further; both findings are in contrast to the prior literature. Moreover, I show that increased labour income inequality and risk can account for around a third of the rise in the concentration of wealth among the top 1% in the US since the 1970s, and about 0.5pp of the decline in real interest rates. SHOULD I STAY (IN SCHOOL) OR SHOULD I GO (TO WORK): How should governments calibrate the desire for redistribution via progressive taxation against the need to incentivise the accumulation of human capital through schooling? I explore this question in a heterogeneous agent model featuring stochastic human capital accumulation, endogeneous labour supply and an education choice modelled as a stopping time problem, where agents choose an optimal number of years to study before starting work. The latter feature addresses a shortcoming of much of the literature that typically models education decisions as a time allocation problem - which overstates the ability of older workers to insure themselves against obsolesence of their human capital and hence understates the welfare benefits of public insurance, for example through progressive taxation - or as a stylised problem with no resource or opportunity costs, which understates the bite of financial frictions, and hence the potential welfare gains from subsidising higher education. The social welfare-maximising policy features generous subsidies for education and highly progressive labour taxes. This result is robust to myriad extensions, including weakening the extent of financial frictions by allowing students to borrow. EM FOREVER BLOWING BUBBLES: GLOBAL IMBALANCES & THE LIMITS OF FISCAL SPACE: What are the limits on how much a government can borrow when the real interest rate on public debt is below the growth rate of the economy? I explore this question in a framework where household entrepreneurs make risky investments under incomplete markets. Such risks induce them to engage in precautionary saving, which lowers equilibrium interest rates and hence expands the fiscal space available to governments. I expand on the prior literature by introducing emerging market (EM) economies - where entrepreneurs face even greater risk and hence engage in more aggressive precautionary saving - as well as limits to the private supply of safe assets. Both elements reduce equilibrium real interest rates in the developed world and further inflate the bubble in public debt, affording developed market (DM) governments even greater fiscal space. I quantify the extent of fiscal space available to governments: how much debt they can issue without having to run surpluses, or how large a deficit they can sustainably run. But I also show that such borrowing carries risks, and governments must design fiscal rules to ensure their debt is both stable in the short run and sustainable in the long run, and that moreover that such policies are in general not Pareto-improving.

Crises in emerging markets during the 1990’s pose a challenge to understand why economies with apparently strong fundamentals did face severe devaluations and severe disruption in their functioning. We study three different aspects of crises: i) Contagion is defined as the possibility of a domestic financial or currency crisis to spread to other countries. We study the 1990’s crises and introduce a new measure for defining financial crises and isolating their impact on currency crises and vice versa; ii) During the 1990’emerging countries in crises suffered severe adjustments in the level of consumption. We build on Lucas’s measure of welfare loss and derive a more comprehensive measure that includes: total loss; loss related to changes in consumption growth rate; to volatility of consumption; and, to changes in the level of consumption; iii) Trying to explain the behaviour of consumption after crises in emerging markets during the 1990’s we found contradicting theoretical approaches and empirical results. We solve the model of intertemporal maximisation of consumption assuming that agents maximise over several periods at a time. We extend the intertemporal framework to include the decision of participating not only in the loanable funds market but in other financial assets and derive the solution for a stock market. The results imply an alternative to the specification of the Euler equation for consumption with more explanatory variables previously omitted.