Heterogeneity in Macroeconomics

In order to study aggregate issues, macroeconomists typically use representative agent models, in which aggregates are the choice of a fictitious average agent in the economy. By construction, these models ignore the tremendous heterogeneity across individual agents documented in microeconomic data. My dissertation addresses this gap by developing tools to incorporate micro heterogeneity into macro models, and using these tools to study an important aggregate issue. In the first chapter, I develop a new method to efficiently solve models with micro heterogeneity. The main challenge is that individual agents base their decisions on the entire distribution of agents, an infinite-dimensional object. I approximate this distribution using a finite-dimensional parametric family. I show how to easily implement the method using Dynare, a publicly available software package commonly used to solve representative agent models. In the second chapter, I use this method to incorporate realistic firm-level investment behavior into a model of aggregate investment. I find that including the extensive margin of whether a firm invests or not has important implications for business cycles and countercyclical stimulus policy. First, aggregate investment is less responsive to productivity shocks in recessions than in expansions, because in recessions fewer firms are likely to make an extensive margin investment. Second, the policy multiplier also falls in recessions. Third, a simple size-dependent policy, which targets extensive margin investment, is five times more cost effective than existing size-independent policies. In the third chapter, I develop a new method to solve heterogeneous agent models in continuous time. Continuous time models are promising in the heterogeneous agent context because they easily handle nonconvexities, like borrowing constraints or fixed costs, which are important for describing micro data. Following Achdou et al. (2015), I use a finite difference method, which approximates individual decisions and the distribution over a finite grid. I solve for the dynamics of these functions using local perturbation methods. I find that the method is very efficient at solving a continuous time version of Krusell & Smith (1998), suggesting that it is able to solve more complicated models which are intractable in discrete time

The uppermost mantle seismic velocity and viscosity structure of central West Antarctica

Accurately monitoring and predicting the evolution of the West Antarctic Ice Sheet via secular changes in the Earth’s gravity field requires knowledge of the underlying upper mantle viscosity structure. Published seismic models show the West Antarctic lithosphere to be ∼70–100 km thick and underlain by a low velocity zone extending to at least ∼200 km. Mantle viscosity is dependent on factors including temperature, grain size, the hydrogen content of olivine, the presence of partial melt and applied stress. As seismic wave propagation is particularly sensitive to thermal variations, seismic velocity provides a means of gauging mantle temperature. In 2012, a magnitude 5.6 intraplate earthquake in Marie Byrd Land was recorded on an array of POLENET-ANET seismometers deployed across West Antarctica. We modelled the waveforms recorded by six of the seismic stations in order to determine realistic estimates of temperature and lithology for the lithospheric mantle beneath Marie Byrd Land and the central West Antarctic Rift System. Published mantle xenolith and magnetotelluric data provided constraints on grain size and hydrogen content, respectively, for viscosity modelling. Considering tectonically-plausible stresses, we estimate that the viscosity of the lithospheric mantle beneath Marie Byrd Land and the central West Antarctic Rift System ranges from ∼ 10 20 – 10 22 Pa s. To extend our analysis to the sublithospheric seismic low velocity zone, we used a published shear wave model. We calculated that the velocity reduction observed between the base of the lithosphere (∼4.4–4.7 km/s) and the centre of the low velocity zone (∼4.2–4.3 km/s) beneath West Antarctica could be caused by a 0.1–0.3% melt fraction or a one order of magnitude reduction in grain size. However, the grain size reduction is inconsistent with our viscosity modelling constraints, suggesting that partial melt more feasibly explains the origin of the low velocity zone. Considering plausible asthenospheric stresses, we estimate the viscosity of the seismic low velocity zone beneath West Antarctica to be ∼ 10 18 – 10 19 Pa s. It has been shown elsewhere that the inclusion of a low viscosity layer of order 1019 Pa s in Fennoscandian models of glacial isostatic adjustment reduces disparities between predicted surface uplift rates and corresponding field observations. The incorporation of a low viscosity layer reflecting the seismic low velocity zone in Antarctic glacial isostatic adjustment models might similarly lessen the misfit with observed uplift rates