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I develop a highly tractable general equilibrium model in which heterogeneous producers face collateral constraints, and study the effect of financial frictions on capital misallocation and aggregate productivity. My economy is isomorphic to a Solow model but with time-varying TFP. I argue that the persistence of idiosyncratic productivity shocks determines both the size of steady-state productivity losses and the speed of transitions: if shocks are persistent, steady-state losses are small but transitions are slow. Even if financial frictions are unimportant in the long run, they tend to matter in the short run and analyzing steady states only can be misleading.

We revisit the transmission mechanism from monetary policy to household consumption in a Heterogeneous Agent New Keynesian (HANK) model. The model yields empirically realistic distributions of wealth and marginal propensities to consume because of two features: uninsurable income shocks and multiple assets with different degrees of liquidity and different returns. In this environment, the indirect effects of an unexpected cut in interest rates, which operate through a general equilibrium increase in labor demand, far outweigh direct effects such as intertemporal substitution. This finding is in stark contrast to small- and medium-scale Representative Agent New Keynesian (RANK) economies, where the substitution channel drives virtually all of the transmission from interest rates to consumption. Failure of Ricardian equivalence implies that, in HANK models, the fiscal reaction to the monetary expansion is a key determinant of the overall size of the macroeconomic response.

We analyze a model economy with many agents, each with a different productivity level. Agents divide their time between two activities: producing goods with the production-related knowledge they already have and interacting with others in search of new, productivity-increasing ideas. These choices jointly determine the economy’s current production level and its rate of learning and real growth. We construct the balanced growth path for this economy. We also study the allocation chosen by an idealized planner who takes into account and internalizes the external benefits of search. Finally, we provide three examples of alternative learning technologies and show that the properties of equilibrium allocations are quite sensitive to two of these variations.

We recast the Aiyagari–Bewley–Huggett model of income and wealth distribution in continuous time. This workhorse model—as well as heterogeneous agent models more generally—then boils down to a system of partial differential equations, a fact we take advantage of to make two types of contributions. First, a number of new theoretical results: (1) an analytic characterization of the consumption and saving behaviour of the poor, particularly their marginal propensities to consume; (2) a closed-form solution for the wealth distribution in a special case with two income types; (3) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one. Second, we develop a simple, efficient and portable algorithm for numerically solving for equilibria in a wide class of heterogeneous agent models, including—but not limited to—the Aiyagari–Bewley–Huggett model.

We develop an efficient and easy to use computational method for solving a wide class of general equilibrium heterogeneous agent models with aggregate shocks together with an open source suite of codes that implement our algorithms in an easy to use toolbox. Our method extends standard linearization techniques and is designed to work in cases when inequality matters for the dynamics of macroeconomic aggregates. We present two applications that analyze a two asset incomplete markets model parameterized to match the distribution of income, wealth, and marginal propensities to consume. First, we show that our model is consistent with two key features of aggregate consumption dynamics that are difficult to match with representative agent models: (1) the sensitivity of aggregate consumption to predictable changes in aggregate income, and (2) the relative smoothness of aggregate consumption. Second, we extend the model to feature capital-skill complementarity and show how factor-specific productivity shocks shape dynamics of income and consumption inequality.

The purpose of this article is to get mathematicians interested in studying a number of partial differential equations (PDEs) that naturally arise in macroeconomics. These PDEs come from models designed to study some of the most important questions in economics. At the same time, they are highly interesting for mathematicians because their structure is often quite difficult. We present a number of examples of such PDEs, discuss what is known about their properties, and list some open questions for future research.

We take an off-the-shelf model with financial frictions and heterogeneity, and study the mapping from a credit crunch, modeled as a shock to collateral constraints, to simple aggregate wedges. We study three variants of this model that only differ in the form of underlying heterogeneity. We find that in all three model variants a credit crunch shows up as a different wedge: efficiency, investment, and labor wedges. Furthermore, all three model variants have an undistorted Euler equation for the aggregate of firm owners. These results highlight the limitations of using representative agent models to identify sources of business cycle fluctuations.

Is there a role for governments in emerging countries to accelerate economic development by intervening in product and factor markets? To address this question, we study optimal dynamic Ramsey policies in a standard growth model with financial frictions. The optimal policy intervention involves pro-business policies like suppressed wages in early stages of the transition, resulting in higher entrepreneurial profits and faster wealth accumulation. This, in turn, relaxes borrowing constraints in the future, leading to higher labor productivity and wages. In the long run, optimal policy reverses sign and becomes pro-worker. In a multi-sector extension, optimal policy subsidizes sectors with a latent comparative advantage and, under certain circumstances, involves a depreciated real exchange rate. Our results provide an efficiency rationale, but also identify caveats, for many of the development policies actively pursued by dynamic emerging economies.

Recent papers argue that the misallocation of resources can explain large cross-country TFP differences. This argument is underpinned by empirical evidence documenting substantial dispersion in the marginal products of resources, particularly capital, in developing countries. But why does misallocation persists? That is, why don't distortions disappear on their own? This is particularly true for capital misallocation, a point we illustrate in a simple model of capital accumulation with credit constraints. We distinguish between misallocation on the intensive and the extensive margin, and show that the former should disappear asymptotically under general conditions, while the latter may persist. We conclude by discussing possible theories of persistent misallocation.

The benefits of new technologies accrue not only to high-skilled labor but also to owners of capital in the form of higher capital incomes. This increases inequality. To make this argument, we develop a tractable theory that links technology to the distribution of income and wealth—and not just that of wages—and use it to study the distributional effects of automation. We isolate a new theoretical mechanism: automation increases inequality by raising returns to wealth. The flip side of such return movements is that automation can lead to stagnant wages and, therefore, stagnant incomes at the bottom of the distribution. We use a multiasset model extension to confront differing empirical trends in returns to productive and safe assets and show that the relevant return measures have increased over time. Automation can account for part of the observed trends in income and wealth inequality.