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When people receive money from the government—a stimulus check, new tax rebate, or any benefit that frees up room in the household budget—the data are clear: Many will spend at least some of it. But two facts of household behavior have made such fiscal transfers a tricky subject for macroeconomists trying to assess the total effect on the economy.
First, people and households differ in how much they will spend from any dollar they receive—their marginal propensity to consume (MPC). All else equal, a more financially constrained person will spend a higher portion of any transfer. Second, each household’s MPC will change as the household becomes less financially stretched from the transfer. Once you’ve been given a hundred dollars, you are a hundred dollars richer and won’t treat the next hundred the same way.
The first complication—households differ—has been greatly helped by the rise of “heterogeneous agent” economic models and the computing power to simulate an economy with millions of varying households. To deal with the second complication—each household’s MPC falls as money rolls in—modelers have relied on a widely used shortcut to cope with the onerous prospect of computing something so complex. This “local linear” approach has been applied by economists in recent years as an approximation of the effect of stimulus in heterogeneous agent models.
In new research, however, Minneapolis Fed Monetary Advisor Javier Bianchi and University of Chicago economist Greg Kaplan demonstrate that this shortcut fails for any but the smallest transfers to households (Minneapolis Fed Working Paper 815, “How Small Is Small? Non-linearities in Heterogeneous Agent Models”). The larger the transfer, the more the linear approximation overstates the overall economic impact, compared with the computationally heavy simulation run by the authors.
In their baseline general equilibrium model, Bianchi and Kaplan consider a stimulus of 2 percent of GDP, or about $3,320 per household in 2019—close to what a low-income household of four would have received from the first round of COVID-19 stimulus checks. They find the linear solution exaggerates the aggregate effect on U.S. GDP by 34 percent. For a transfer of 5 percent of GDP, the error grows to 50 percent. Even for smaller transfers, and across various model calibrations, the pattern persists: For most meaningfully sized transfers, a first-order, linear approximation is too far off to be useful in understanding the aggregate effect.
The reason these methods fail is primarily related to the odd-shaped MPC functions of low-income, low-wealth households, whose responses are fundamental to the overall macroeconomic effect. The economists’ model—calibrated with detailed U.S. panel survey data—reveals that low-income households’ MPC curves are not simply declining with each dollar of wealth. They are kinked (Figure 1).
In this example, the low-income household immediately consumes 100 percent of any transfer (that is, they have an MPC of 1) until they reach around $10,000 in wealth. At this threshold, this household is no longer in subsistence mode. The MPC drops steeply and the household begins to save more than half of each subsequent dollar it receives.
At the aggregate level, the distribution of households smooths out these household-level kinks. But linear estimates do not account for these sudden drops. The larger the transfer, the more families will exhibit this nonlinear shift—and the more linear estimates will overstate the impact on total consumption.
For small-enough amounts, the difference would be negligible. But how small is small enough? Bianchi and Kaplan find that even transfers of less than half a percent of annual GDP lead many households who were initially hand-to-mouth to cross their threshold and exhibit a much lower MPC than prior to the transfer (Figure 2).
The existence of kinked MPCs will tend to foil any methods—not just linear ones—that extrapolate from the impact of the first dollar of a transfer. Even higher-order local methods that account for curvature in the MPC curve will need to approximate the shape of this kinked function to provide accurate estimates for large transfers.
The economists vary their model calibrations to allow flexible wages, different monetary policy rules, and the timing of government payback of debt. The effects of household stimulus on GDP are similar across these variations, reinforcing that even under different transmission channels, the aggregate pass-through of a transfer depends primarily on the underlying failure of “Ricardian equivalence” among households: That is, households do not save the full transfer because they expect to pay more in future taxes. Fiscal shocks that depend on the failure of Ricardian equivalence tend to hinge on low-income, low-wealth households, whose MPCs (1) are high and (2) demonstrate starkly nonlinear behavior.
Bianchi and Kaplan find one version of the model where the linear approximation is more accurate. In this scenario, the government funds the stimulus with debt that it never intends to pay off. Instead, the nominal value of the debt is eroded through higher inflation (the scenario of “the fiscal theory of the price level”). Expecting higher prices in the future and the devaluation of their savings, higher-wealth households also spend more of the transfer, shifting their consumption into the present. When all households are spending more of the stimulus, the kinked MPC functions of low-income households have a smaller overall effect in distorting the linear estimate.
In critiquing common local-linear methods, Bianchi and Kaplan do not propose or presume an alternate method of approximation. The impact of a fiscal transfer across households is extraordinarily complex, and there might be no shortcuts to the complex calculations the authors execute here at small scale. Economists and policy analysts seeking to measure the effects of large government stimulus might have to embrace complexity and make the most of models and computing capability that continue to evolve.
Read the Minneapolis Fed working paper: “How Small Is Small? Non-linearities in Heterogeneous Agent Models”
Jeff Horwich is the senior economics writer for the Minneapolis Fed. He has been an economic journalist with public radio, commissioned examiner for the Consumer Financial Protection Bureau, and director of policy and communications for the Minneapolis Public Housing Authority. He received his master’s degree in applied economics from the University of Minnesota.
