Andreas Schaab | Macro Paper Warehouse

Micro and Macro Uncertainty

Uncertainty rises sharply during downturns at both the micro level (unemployment risk, firm sales/productivity volatility) and the macro level (stock-market and GDP-growth volatility), but modeling their joint determination has been methodologically elusive, since micro uncertainty requires cross-sectional heterogeneity while macro uncertainty presupposes aggregate risk. This job-market paper makes two contributions. First, it shows – starting from an illustrative two-period model and then a full quantitative Heterogeneous Agent New Keynesian (HANK) model with counter-cyclical unemployment risk and a zero lower bound (ZLB) constraint on monetary policy – that accounting for the interaction between micro and macro uncertainty is essential to understanding the role uncertainty plays in business cycles. Because job separation and finding rates in the model are estimated to move with economic activity, a mean-zero increase in macro uncertainty also raises the dispersion of individual employment outcomes directly, and, in general equilibrium, the resulting fall in aggregate demand raises job separation and lowers job finding further, raising both expected-earnings losses and their variance for employed households; both effects scale with the gap between marginal utility employed and unemployed, meaning households respond to macro uncertainty largely because it translates into micro-level “disaster risk.” Quantitatively, the peak output response to a macro uncertainty shock is 5 to 8 times larger than in a representative-agent (RANK) benchmark, and this amplification is markedly stronger near the ZLB, where the peak output decline from a given uncertainty increase is 50% larger than in normal times. Second, the paper’s methodological contribution is a new global solution method for heterogeneous-agent models with aggregate risk, representing the cross-sectional distribution with a finite-dimensional set of coefficients whose law of motion the paper derives analytically (building on Winberry 2020 and Ahn et al. 2017), avoiding the need to numerically re-fit a law of motion at each iteration and enabling the paper to solve models with over 20 distributional dimensions using an adaptive sparse-grid library. The global solution reveals that macro uncertainty itself rises endogenously during downturns – roughly four times more responsively when micro-macro interaction is present than when unemployment risk is held fixed – through two channels: proximity to the ZLB, which amplifies the effect of demand shocks, and counter-cyclicality in the economy-wide average marginal propensity to consume as more households become hand-to-mouth. This produces a self-reinforcing “Uncertainty Multiplier”: contractions raise uncertainty, which further depresses demand, letting the model match the strong counter-cyclicality, persistence, and large positive skewness and kurtosis of empirical macro-uncertainty proxies without any exogenous second-moment shocks. The paper’s welfare calculation finds that the consumption households would give up to instead live in a representative-agent economy is 3.9% – about two orders of magnitude larger than Lucas’s (1987, 2003) classic estimates of the cost of business cycles.

Optimal Monetary Policy with Heterogeneous Agents: Discretion, Commitment, and Timeless Policy

This paper characterizes optimal monetary policy in a canonical one-asset heterogeneous-agent New Keynesian (HANK) model with wage rigidity – a minimal departure from the representative-agent (RANK) New Keynesian benchmark – and systematically revisits the canonical consensus on optimal monetary policy design under discretion, under commitment, and for short-run stabilization. Under discretion, a utilitarian planner has an incentive to overheat the economy beyond the standard markup-correcting level because lowering interest rates redistributes income toward indebted, high-marginal-utility households; since the public rationally anticipates this, the attempt at stimulus is self-defeating and instead produces inflationary bias in the sense of Barro and Gordon (1983), with the paper’s calibration finding this redistribution channel contributes over four times as much to that bias as the conventional markup distortion. Full commitment restores zero inflation in the long-run stationary equilibrium – because inflation and the nominal rate affect household financial income symmetrically, while only inflation is costly – but the standard Ramsey problem still suffers a “time-0” problem that generates short-run inflationary bias, driven both by the usual forward-looking Phillips curve and, newly in HANK, by each household’s forward-looking value function entering as a planning constraint. To resolve this, the authors extend Marcet and Marimon’s (2019) recursive-multiplier approach to continuous-time heterogeneous-agent economies, defining a “timeless” Ramsey problem augmented with an inflation penalty (now shaped by distributional considerations even in HANK) and a novel distributional penalty that specifically counteracts the planner’s incentive to redistribute toward indebted households; this timeless plan eliminates inflationary bias in both the short and long run and can be implemented either by a discretionary planner confronted with the right penalties or by an appropriately designed inflation target. Finally, characterizing optimal stabilization policy under the timeless Ramsey problem, the paper shows that the classic Divine Coincidence result of RANK models – that inflation and output gaps can always be closed simultaneously absent cost-push shocks – generically fails in HANK even with the correct employment subsidy, because the planner now trades off aggregate stabilization against distributional considerations; a quantitative decomposition traces this departure, in response to demand shocks, specifically to the redistribution wedge. The analysis is conducted in a stylized model with a single financial asset and one particular (interest-rate) redistribution channel, and the authors are explicit that while their qualitative logic should generalize, the exact quantitative conclusions – including the sign of the discretionary inflationary bias – depend on the specific pecuniary channels through which policy redistributes in a given model.

Structural Reinforcement Learning for Heterogeneous Agent Macroeconomics

Standard recursive formulations of heterogeneous-agent models with aggregate risk force the entire cross-sectional distribution of agents into the Bellman equation characterizing individual decisions – the “Master equation” – purely because low-dimensional equilibrium prices, unlike the distribution itself, do not follow a Markov process, so rational agents forecasting prices end up needing to forecast the whole distribution. This extreme curse of dimensionality remains the central computational bottleneck for global solutions of heterogeneous-agent models, so severe that even a Huggett (1993) model with aggregate risk – despite looking simple – proved impossible for any team to solve in an influential benchmarking exercise and was dropped from the project altogether. This paper sidesteps the Master equation entirely using ideas from reinforcement learning (RL): agents learn equilibrium price dynamics directly from simulated paths, as standard RL would, but the paper’s “structural reinforcement learning” (SRL) approach departs from standard RL by assuming agents have structural knowledge of their own individual-state dynamics (their budget constraint and idiosyncratic income process), letting the authors compute exact policy gradients by differentiating through these known dynamics rather than relying on the noisy, approximate policy gradients standard RL methods estimate; only the equilibrium price process itself is treated as unknown and learned from simulation. By further restricting agents to condition their policies only on current (or briefly lagged) prices rather than the full price history or the distribution, the paper solves for a low-dimensional “restricted perceptions equilibrium” in the sense of Sargent (1991) rather than the full rational-expectations equilibrium – expectations are restricted in functional form but remain statistically consistent with actual outcomes. Because policy functions depend only on prices, they double as individual supply/demand schedules that can be integrated across the distribution and market-cleared period-by-period along a simulation, treating market clearing as part of the “environment” (in RL parlance) rather than something solved inside an optimization loop – which is what lets the method efficiently handle nontrivial market-clearing conditions that have historically been very hard. Implemented in JAX on a single GPU, the resulting structural policy gradient (SPG) algorithm solves the Krusell and Smith (1998) model in about 55 seconds, the previously-unsolved Huggett (1993) model with aggregate risk in around one minute, and a one-asset HANK model with a forward-looking New Keynesian Phillips curve in around three minutes – with the Krusell-Smith solution closely matching alternative global solutions of the rational-expectations equilibrium, and allowing agents a longer history of lagged prices barely moving the solution, indicating most of the information relevant for forecasting prices is already contained in current prices. The paper is explicit that its algorithm, as presented, is not itself intended as an empirically realistic theory of how real economic agents form expectations, though it suggests the “sampling”-based logic behind SRL could in principle be developed into one.