Micro and Macro Uncertainty

“A framework that allows for the joint determination of micro and macro uncertainty has thus far remained elusive, in part because it poses considerable methodological challenges. Modeling uncertainty at the micro level requires cross-sectional heterogeneity, while uncertainty at the macro level presupposes aggregate risk” (Introduction, p. 2). The paper’s two contributions directly target this gap: an economic argument for why the interaction between the two levels of uncertainty is central to business-cycle transmission, and a new global solution method capable of solving the resulting heterogeneous-agent model with aggregate risk.

“The direct effects of uncertainty are those that arise from a change in households’ beliefs about future shock realizations holding prices constant. Indirect effects arise in general equilibrium as prices respond to the change in household behavior induced by direct effects” (Introduction, p. 2). Without interaction with micro uncertainty, the only direct effect of macro uncertainty to second order is the standard Kimball (1990) precautionary-savings motive, proportional to u’’’(·); but once unemployment risk interacts with macro uncertainty, new direct and indirect “interaction effects” emerge, both of which “are proportional to the jump scaling factor u’(c_E) - u’(c_U) that is characteristic of uncertainty at the micro level” – meaning macro uncertainty matters to households largely because it is disaster risk at the micro level, not because of a marginal-utility-smoothing motive (pp. 3-4).

“I show that the peak response of output to an increase in macro uncertainty is 5 to 8 times larger than in the associated RANK benchmark. The interaction between micro and macro uncertainty is the main source of this amplification” (Introduction, pp. 4-5). In the RANK model the direct precautionary-savings response is small at a conservative risk-aversion coefficient of γ=2, so the overall effect of uncertainty is modest; in the heterogeneous-agent model, by contrast, the direct precautionary channel is “relatively muted” while the interaction with micro (unemployment) uncertainty becomes “the dominant driver of transmission,” alongside other indirect channels operating through portfolio returns and disposable income.

“I show that the peak decline in output in response to a given increase in macro uncertainty is 50% larger when the economy is already at the cusp of the ZLB than during normal times” because, close to the ZLB, “the relationship between economic activity and aggregate risk exhibits a degree of negative skewness,” so a mean-zero spread in aggregate risk contracts activity in expectation (Introduction, p. 5). The paper states that “identifying the importance of the ZLB crisis region for the behavior of uncertainty in my model is only possible because I use a global solution method” – a local, first-order approximation would miss this asymmetric, state-dependent amplification.

“In general equilibrium… a strong feedback loop emerges between uncertainty and economic activity: When activity contracts, uncertainty about the future rises, which itself depresses aggregate demand further. This feedback loop can be instructively characterized as an ‘Uncertainty Multiplier’” (Introduction, p. 6). The paper identifies two channels generating this endogenous responsiveness: first, the zero lower bound, which prevents monetary policy from accommodating negative demand shocks and is itself made more binding by prior expansionary policy moving the economy closer to it; second, counter-cyclical average marginal propensity to consume, as contracting activity pushes more households into unemployment and toward their borrowing constraints, raising the economy’s overall sensitivity to further demand shocks (pp. 5-6).

“I show that endogenous macro uncertainty is 4 times more responsive to a negative, first-moment discount rate shock when I account for the interaction with micro uncertainty. Indeed, when I hold unemployment risk constant, macro uncertainty hardly responds at all to discount rate shocks during normal times” (Introduction, p. 5). This lets the model reproduce the observed counter-cyclicality, persistence, and positive skewness/kurtosis of empirical macro-uncertainty measures without positing any exogenous shocks to volatility itself.

The paper approximates the cross-sectional distribution g_t(x) with a finite-dimensional representation F(α_t)(x), and shows that “for a large class of models, the coefficients α_t follow a diffusion process with drift and volatility [for which] I derive analytical formulas… that can be easily computed. In this sense, and in sharp contrast to the Krusell and Smith (1998) algorithm, finding the [consistent] law of motion incurs almost no increase in numerical complexity” (“Methodological Contribution,” pp. 6-7). Building on Winberry (2020) and generalizing Ahn et al. (2017), the paper also develops a non-parametric algorithm for choosing F(·) and, with an adaptive sparse-grid library (Schaab and Zhang 2020), solves the benchmark Krusell-Smith model with over 20 distributional dimensions – far beyond what standard global methods can handle.

“An interplay between uncertainty at the micro and macro level provides a new perspective on the welfare cost of business cycles. I show that the implied share of consumption households are willing to forego to instead ’live’ in a representative-agent economy is 3.9%, or about two orders of magnitude larger than the original estimates in Lucas (1987) and Lucas (2003)” (Introduction, p. 6). This large gap reflects that, unlike Lucas’s representative-agent framework, the model embeds incomplete markets, borrowing constraints, and counter-cyclical unemployment risk directly exposing low-wealth households to business-cycle fluctuations.

The paper builds directly on Winberry (2020) and Ahn et al. (2017)’s finite-dimensional distribution representations, extending them from the local-perturbation context to a genuinely global solution method (“Methodological Contribution” and Literature Review, pp. 6-8). It positions itself against the “variants of the original Krusell and Smith (1998) algorithm” that “largely remain the method of choice,” with “notable exceptions” including Fernández-Villaverde et al. (2019) and Pröhl (2019) – an earlier generation of global methods that DeepHAM (Han, Yang and E, 2021) and the structural-reinforcement-learning approach of Yang, Wang, Schaab and Moll (2025) would later cite Schaab (2020) alongside as one of the few pre-existing solution methods able to handle a nonlinear HANK model with an occasionally-binding macro constraint (the ZLB) at all.