Christian Bayer

Large fiscal transfers shift households between regions with high and low marginal propensities to consume (MPCs), resulting in nonlinear aggregate responses. We develop a Nonlinear DEGM Update (NDU) method that shifts the wealth distribution nonlinearly over a short time window while solving the aggregate economy using a fast, first-order state-space approximation. A 10 percent transfer of annual GDP increases output by 4.5 percent in the nonlinear and NDU solutions, but by 12.0 percent in the linear solution. The empirical liquid-wealth distribution around zero disciplines this nonlinearity and exhibits a strong asymmetry. A stochastic debt-entry cost closely reproduces this empirical pattern.

Modeling continuous choices in heterogeneous agent models as ``lotteries’’ over a discretized state space is standard practice (Young, 2010), but renders the distributional dynamics linear in optimal policies. We present a novel, simple method that captures nonlinearities and solves the distributional dynamics with interpolation instead of integration using the idea of an endogenous grid. Our approach solves for a stationary equilibrium as quickly as the lottery method for a given precision, outperforms it for linear dynamics, and accommodates nonlinear dynamics and aggregate risk. We demonstrate its efficacy by studying a model with aggregate investment risk with a third-order perturbation solution.

We show how a heterogeneous-agent New-Keynesian (HANK) model with incomplete markets and portfolio choice can be estimated in state space using a Bayesian approach. To render estimation feasible, the structure of the economy can be exploited and the dimensionality of the model automatically reduced based on the Bayesian priors. We apply this approach to analyze how much inequality matters for the business cycle and vice versa. Even when the model is estimated on aggregate data alone and with a set of shocks and frictions designed to match aggregate data, it broadly reproduces observed US inequality dynamics.

We provide evidence that expansionary fiscal policy lowers return differences between public debt and less liquid assets—the liquidity premium. We rationalize this finding in an estimated heterogeneous-agent New-Keynesian model with incomplete markets and portfolio choice, in which public debt affects private liquidity. This liquidity channel stabilizes fixed-capital investment. We then quantify the long-run effects of higher public debt and find little crowding out of capital, but a sizable decline of the liquidity premium, which increases the fiscal burden of debt. We show that the revenue-maximizing level of public debt is positive and has increased to 60 percent of US GDP post-2010.

In response to the COVID-19 pandemic, large parts of the economy were locked down and, as a result, households’ income risk rose sharply. At the same time, policy makers put forward the largest stimulus package in history. In the U.S., it amounted to $2 trillion, a quarter of which represented transfer payments to households. To the extent that such transfers were i) announced in advance and ii) conditional on recipients being unemployed, they mitigated income risk associated with the lockdown - in contrast to unconditional transfers. We develop a baseline scenario for a COVID-19 recession in a medium-scale HANK model and use counterfactuals to quantify the impact of transfers. For the short run, we find large differences in the transfer multiplier: it is negligible for unconditional transfers and about unity for conditional transfers. Overall, we find that the transfers reduced the output loss due to the pandemic by some 2 percentage points at its trough.

This paper describes a method for solving heterogeneous agent models with aggregate risk and many idiosyncratic states formulated in discrete time. It extends the method proposed by Reiter (2009) and complements recent work by Ahn et al. (2017) on how to solve such models in continuous time. We suggest first solving for the stationary equilibrium of the model without aggregate risk. We then write the functionals that describe the recursive equilibrium as sparse expansions around their stationary equilibrium counterparts. Finally we use the perturbation method of Schmitt-Grohé and Uribe (2004) to approximate the aggregate dynamics of the model.

Households face large income uncertainty that varies substantially over the business cycle. We examine the macroeconomic consequences of these variations in a model with incomplete markets, liquid and illiquid assets, and a nominal rigidity. Heightened uncertainty depresses aggregate demand as households respond by hoarding liquid “paper” assets for precautionary motives, thereby reducing both illiquid physical investment and consumption demand. We document the empirical response of portfolio liquidity and aggregate activity to surprise changes in idiosyncratic income uncertainty and find both to be quantitatively in line with our model. The welfare consequences of uncertainty shocks and of the policy response thereto depend crucially on a household’s asset position.