Essays in Macroeconomics

My dissertation presents essays on topics in macroeconomics. In Chapter 1, I study the interplay between micro and macro uncertainty. I show that its effect on unemployment risk is the dominant transmission channel of macro uncertainty. Accounting for this channel, the overall effect of a macro uncertainty shock on activity is 2-3 times larger. In Chapter 2, which is joint work with Allen Zhang, we develop an adaptive sparse grid method for solving continuous-time dynamic programming problems. While standard finite-difference discretization leads ton inconsistent solutions of differential equations on irregular grids, we show that a generalized sparse finite-difference method restores consistency. Our paper is accompanied by a general-purpose toolbox for solving partial differential equations on adaptive sparse grids. In Chapter 3, which is joint work with Christopher Clayton, we develop a theory of dynamic inflation targets. We study a dynamic mechanism design problem between a government (principal) and a central bank (agent). A “dynamic inflation target” implements the constrained efficient inflation level: the central bank reports its target one period in advance, with a linear incentive scheme for deviations from the target.