ConsumptionResponse 2020-10-05, time:19:06:00
|Live Dashboard||See effect of modifying main assumptions|
|econ-ark.github.io/Pandemic||HTML version of paper|
|github.com/econ-ark/Pandemic||Full codebase: Modify combos of assumptions|
|zip file: root of repo||contains full replication files (code+text)|
|LaTeX directory in repo||PDF version of paper|
|LaTeX directory in repo||Presentation slides|
|LaTeX directory in repo||Preferred BibTeX citation|
To predict the eﬀects of the 2020 U.S. CARES Act on consumption, we extend a model that matches responses to past consumption stimulus packages. The extension allows us to account for two novel features of the coronavirus crisis. First, during lockdowns, many types of spending are undesirable or impossible. Second, some of the jobs that disappear during the lockdown will not reappear. We estimate that, if the lockdown is short-lived (the median point of view as we are writing in April 2020), the combination of expanded unemployment insurance beneﬁts and stimulus payments should be suﬃcient to allow a swift recovery in consumer spending to pre-crisis levels. If the lockdown lasts longer (or there is a ‘second wave’), an extension of enhanced unemployment beneﬁts will likely be necessary for consumption spending to recover quickly.
1Carroll: Department of Economics, Johns Hopkins University, http://econ.jhu.edu/people/ccarroll/, email@example.com 2Crawley: Federal Reserve Board, firstname.lastname@example.org 3Slacalek: DG Research, European Central Bank, http://www.slacalek.com/, email@example.com 4White: Department of Economics, University of Delaware, firstname.lastname@example.org
The ﬁrst public version of this paper appeared April 15, 2020. A publicly available pre-print appeared in the Centre for Economic Policy
Research pre-print journal Covid Economics on April 27, 2020 (as a pre-print journal, Covid Economics does not obtain copyright claims to
its content, which is why the ﬁnished version of the paper can be published in a peer-reviewed journal which does obtain the copyright).
Thanks to the Consumer Financial Protection Bureau for funding the original creation of the Econ-ARK toolkit, whose latest version we used to produce all the results in this paper; and to the Sloan Foundation for funding Econ-ARK’s extensive further development that brought it to the point where it could be used for this project. The toolkit can be cited with its digital object identiﬁer, 10.5281/zenodo.1001067, as is done in the paper’s own references as Carroll, Kaufman, Kazil, Palmer, and White (2018). We are grateful to Kiichi Tokuoka, who provided valuable feedback and input as this project progressed, Mridul Seth, who created the dashboard and conﬁgurator, and to Luc Laeven, who swiftly handled our submission to IJCB. The views presented in this paper are those of the authors, and should not be attributed to the Federal Reserve Board or the European Central Bank.
“Economic booms are all alike; each recession contracts output in its own way.” — with apologies to Leo Tolstoy
In the decade since the Great Recession, macroeconomics has made great progress by insisting that models be consistent with microeconomic evidence (see Krueger, Mitman, and Perri (2016) in the Handbook of Macroeconomics for a survey). To predict the eﬀects of the 2020 CARES Act (Coronavirus Aid, Relief, and Economic Security) on consumption, we take, from this new generation, one model that is speciﬁcally focused on reconciling apparent conﬂicts between micro and macro evidence about consumption dynamics,1 and adapt it to incorporate two aspects of the coronavirus crisis.
First, because the tidal wave of layoﬀs for employees of shuttered businesses will have a large impact on their income and spending, assumptions must be made about the employment dynamics of laid oﬀ workers. Speciﬁcally, the unemployed in our model consist of two categories: normal unemployed and deeply unemployed. Similar to a normal recession, the normal unemployed will be able to quickly return to their old jobs (or similar ones). However, in addition, some people become deeply unemployed, facing a more persistent unemployment shock. This feature reﬂects the fact that some kinds of jobs will not come back quickly after the lockdown, and that people who worked in these sectors will have more diﬃculty ﬁnding a new job.2
On the second count, we model the restricted spending options by assuming that during the lockdown spending is less enjoyable (there is a negative shock to the ‘marginal utility of consumption.’) Based on a tally of sectors that we judge to be substantially shuttered during the ‘lockdown,’ we calibrate an percent reduction to spending. Thus households will prefer to defer some of their consumption into the future, when it will yield them greater utility. (See Cox, Ganong, Noel, Vavra, Wong, Farrell, and Greig (2020), Carvalho, Garcia, Hansen, Ortiz, Rodrigo, Rodriguez, and Ruiz (2020) and Andersen, Hansen, Johannesen, and Sheridan (2020) showing a strong eﬀect of this kind in US, Spanish and Danish data, respectively).3
Our model captures the two primary features of the CARES Act that aim to bolster consumer spending:
We estimate that the combination of expanded unemployment insurance beneﬁts and stimulus payments should be suﬃcient to expect a swift recovery in consumer spending to its pre-crisis levels under our default description of the pandemic, in which the lockdown ends after two quarters on average. Overall, unemployment beneﬁts account for about 30 percent of the total aggregate consumption response and stimulus payments explain the remainder.
Our analysis partitions households into three groups based on their employment state when the pandemic strikes and the lockdown begins.
First, households in our model who do not lose their jobs initially build up their savings, both because of the lockdown-induced suppression of spending and because most of these households will receive a signiﬁcant stimulus check, much of which the model says will be saved. Even without the lockdown, we estimate that only about 20 percent of the stimulus money would be spent immediately upon receipt, consistent with evidence from prior stimulus packages about spending on nondurable goods and services. Once the lockdown ends, the spending of the households that remained employed at the onset of the pandemic rebounds strongly thanks to their healthy household ﬁnances.
The second category of households are the ‘normal unemployed,’ job losers who perceive that it is likely they will be able to resume their old job (or get a similar new job) when the lockdown is over. Our model predicts that the CARES Act will be particularly eﬀective in stimulating their consumption, given the perception that their income shock will be largely transitory. Our model predicts that by the end of 2021, the spending of this group recovers to the level it would have achieved in the absence of the pandemic (‘baseline’); without the CARES Act, this recovery would take more than a year longer.
Finally, for households in the ‘deeply unemployed’ category, our model says that the marginal propensity to consume (MPC) from the checks will be considerably smaller, because they know they must stretch that money for longer. Even with the stimulus from the CARES Act, we predict that consumption spending for these households will not fully recover until the middle of 2023. Even so, the Act makes a big diﬀerence to their spending, particularly in the ﬁrst six quarters after the crisis. For both groups of unemployed households, the eﬀect of the stimulus checks is dwarfed by the increased unemployment beneﬁts, which arrive earlier and are much larger (per recipient).
Perhaps surprisingly, we ﬁnd the eﬀectiveness of the combined stimulus checks and unemployment beneﬁts package for aggregate consumption is not substantially diﬀerent from a package that distributed the same quantity of money equally among households. The reason for this is twofold: ﬁrst, the extra unemployment beneﬁts in the CARES Act are generous enough that many of the ‘normally unemployed’ remain ﬁnancially sound and can aﬀord to save a good portion of those beneﬁts; second, the deeply unemployed expect their income to remain depressed for some time and therefore save more of the stimulus for the future. In the model, the fact that they do not spend immediately is actually a reﬂection of how desperately they anticipate these funds will be needed to make it through a long period of low income. While unemployment beneﬁts do not strongly stimulate current consumption of the deeply unemployed, they do provide important disaster relief for those who may not be able to return to work for several quarters (see Krugman (2020) for an informal discussion).
In addition to our primary scenario’s relatively short lockdown period, we also consider a more severe scenario in which the lockdown is expected to last for four quarters and the unemployment rate increases to 20 percent. In this case, we ﬁnd that the return of spending toward its no-pandemic path takes roughly three years. Moreover, the spending of deeply unemployed households falls steeply unless the temporary unemployment beneﬁts in the CARES Act are extended for the duration of the lockdown.
Our modeling assumptions — about who will become unemployed, how long it will take them to return to employment, and the direct eﬀect of the lockdown on consumption utility — could prove to be oﬀ, in either direction. Reasonable analysts may diﬀer on all of these points and prefer a diﬀerent calibration. To encourage such exploration, we have made available our modeling and prediction software, with the goal of making it easy for fellow researchers to test alternative assumptions. Instructions for installing and running our code can be found here; alternatively, adjustments to our parametrization can be explored with an interactive dashboard here.
There is a potentially important reason our model may underpredict the bounceback in consumer spending when the lockdown ends: ‘pent up demand.’ This term captures the fact that purchases of ‘durable’ goods can be easily postponed, but that when the reason for postponement abates some portion of the missing demand is made up for.4 For simplicity, our model does not include durable goods, because modeling spending on durables is a formidable challenge. But it is plausible that, when the lockdown ends, people may want to spend more than usual on memorable or durable goods to make up for earlier missing spending.
Many papers have recently appeared on the economic eﬀects of the pandemic and policies to manage it. Several papers combine the classic susceptible–infected–recovered (SIR) epidemiology model with dynamic economic models to study the interactions between health and economic policies (Eichenbaum, Rebelo, and Trabandt (2020) and Alvarez, Argente, and Lippi (2020), among others). Guerrieri, Lorenzoni, Straub, and Werning (2020) shows how an initial supply shock (such as a pandemic) can be ampliﬁed by the reaction of aggregate demand. The ongoing work of Kaplan, Moll, and Violante (2020) allows for realistic household heterogeneity in how household income and consumption are aﬀected by the pandemic. Glover, Heathcote, Krueger, and Ríos-Rull (2020) studies distributional eﬀects of optimal health and economic policies. Closest to our paper is some work analyzing the eﬀects of the ﬁscal response to the pandemic, including Faria-e-Castro (2020b) in a two-agent DSGE model, and Bayer, Born, Luetticke, and Müller (2020) in a HANK model.
All of this work accounts for general equilibrium eﬀects on consumption and employment, which we omit, but none of it is based on a modeling framework explicitly constructed to match micro and macroeconomic eﬀects of past stimulus policies, as ours is.
A separate strand of work focuses on empirical studies of how the economy reacts to pandemics; see, e.g., Baker, Farrokhnia, Meyer, Pagel, and Yannelis (2020), Jorda, Singh, and Taylor (2020), Correia, Luck, and Verner (2020), Chetty, Friedman, Hendren, Stepner, and Team (2020), Garner, Saﬁr, and Schild (2020), Casado, Glennon, Lane, McQuown, Rich, and Weinberg (2020) and Coibion, Gorodnichenko, and Weber (2020).
Our model extends a class of models explicitly designed to capture the rich empirical evidence on heterogeneity in the marginal propensity to consume (MPC) across diﬀerent types of household (employed, unemployed; young, old; rich, poor). This is motivated by the fact that the act distributes money unevenly across households, particularly targeting unemployed households. A model that does not appropriately capture both the degree to which the stimulus money is targeted, and the diﬀerentials in responses across diﬀerently targeted groups, is unlikely to produce believable answers about the spending eﬀects of the stimulus.
Speciﬁcally, we use a lifecycle model calibrated to match the income paths of high school dropouts, high school graduates, and college graduates.5 Households are subject to permanent and transitory income shocks, as well as unemployment spells.6 Within each of these groups, we calibrate the distribution of discount factors to match their distribution of liquid assets. Matching the distributions of liquid assets allows us to achieve a realistic distribution of marginal propensities to consume according to education group, age, and unemployment status, and thus to assess the impact of the act for these diﬀerent groups.7
To model the pandemic, we add two new features to the model.
First, our new category of ‘deeply unemployed’ households was created to capture the likelihood that the pandemic will have long-lasting eﬀects on some kinds of businesses and jobs (e.g., the cruise and airline industries), even if the CARES Act manages to successfully cushion much of the initial ﬁnancial hit to total household income. Moreover, evidence in Yagan (2019) indicates that unemployment shocks from the Great Recession had long-lasting impacts on individuals’ employment.
Each quarter, our ‘deeply unemployed’ households have a two-thirds chance of remaining deeply unemployed, and a one-third chance of becoming ‘normal unemployed.’ The expected time to re-employment for a ‘deeply unemployed’ household is four and a half quarters, much longer than the historical average length of a typical unemployment spell. Reﬂecting recent literature on the ‘scarring eﬀects’ of unemployment spells (e.g., Oreopoulos, von Wachter, and Heisz (2012) and Heathcote, Perri, and Violante (2020)), permanent income of both ‘normal’ and ‘deeply’ households declines by 0.5 percent each year due to ‘skill rot’ (relative to following the default age proﬁle that would have been followed if the consumer had remained employed).
Second, a temporary negative shock to the marginal utility of consumption captures the idea that, during the period of the pandemic, many forms of consumption are undesirable or even impossible.8
The pandemic is modeled as an unexpected (MIT) shock, sending many households into normal or deep unemployment, as well as activating the negative shock to marginal utility. Households understand and respond in a forward-looking way to their new circumstances (according to their beliefs about its duration), but their decisions prior to the pandemic did not account for any probability that it would occur. For simplicity, we assume that each household correctly recognizes whether it is ‘deeply’ or ‘normal’ unemployed and react accordingly.
The calibration choices for the pandemic scenario are very much open for debate. We have tried to capture something like median expectations from early analyses, but there is considerable variation in points of view around those medians. Section B below presents a more adverse scenario with a longer lockdown and a larger increase in unemployment.
Unemployment forecasts for Q2 2020 range widely, from less than 10 percent to over 30 percent, but all point to an unprecedented sudden increase in unemployment.9 We choose a total unemployment rate in Q2 2020 of just over 15 percent, consisting of ﬁve percent ‘deeply unemployed’ and ten percent ‘normal unemployed’ households.
Our model assumes that the unemployment shock from the pandemic is a singular event, with no change in the longer run job separation rate for employed households (calibrated to generate a steady state unemployment rate of 5%). Consequently, agents in our model who remain employed in Q2 2020 have no additional precautionary saving motive against a heightened risk of unemployment, and any change in their consumption behavior arises from the marginal utility shock.
We calibrate the likelihood of becoming unemployed to match empirical facts about the relationship of unemployment to education level, permanent income and age, which is likely to matter because the hardest hit sectors skew young and unskilled.10 Figure 1 shows our assumptions on unemployment along these dimensions. In each education category, the solid or dashed line represents the probability of unemployment type (‘normal’ or ‘deep’) for a household with the median permanent income at each age, while the dotted lines represent the probability of unemployment type for a household at the 5th and 95th percentile of permanent income at each age; Appendix A with Table A2 detail the parametrization and calibration we used.
To calibrate the drop in marginal utility, we estimate that 10.9 percent of the goods that make up the consumer price index become highly undesirable, or simply unavailable, during the pandemic: food away from home, public transportation including airlines, and motor fuel. As we use a coeﬃcient of risk aversion equal to one, we simply multiply utility from consumption during the period of the epidemic by a factor of 0.891.11 This calibration is in line with recent evidence in Cox, Ganong, Noel, Vavra, Wong, Farrell, and Greig (2020) and Chetty, Friedman, Hendren, Stepner, and Team (2020). Furthermore, we choose a one-half probability of exiting the period of lower marginal utility each quarter, accounting for the possibility of a ‘second wave’ if restrictions are lifted too early — see Cyranoski (2020).12
We model the two elements of the CARES Act that directly aﬀect the income of households:
We model the stimulus checks as being announced at the same time as the crisis hits. However, only a quarter of households change their behavior immediately at the time of announcement, as calibrated to past experience. The remainder do not respond until their stimulus check arrives, which we assume happens in the following quarter. The households that pay close attention to the announcement of the policy are assumed to be so forward looking that they act as though the payment will arrive with certainty next period; the model even allows them to borrow against it if desired.14
The extra unemployment beneﬁts are assumed to both be announced and arrive at the beginning of the second quarter of 2020, and we assume that there is no delay in the response of unemployed households’ consumption to these beneﬁts.
Figure 2 shows the path of labor income — exogenous in our model — in the baseline and in the pandemic, both with and without the CARES Act. Income in quarters Q2 and Q3 2020 is substantially boosted (by around 10 percent) by the extra unemployment beneﬁts and the stimulus checks. After two years, aggregate labor income is almost fully recovered. See below for a brief discussion of analyses that attempt to endogenize labor supply and other equilibrium variables.
This section presents our simulation results for the scenario described above. In addition, we then model a more pessimistic scenario with a longer lockdown and higher initial unemployment rate.
Figure 3 shows three scenarios for quarterly aggregate consumption: (i) the baseline with no pandemic; (ii) the pandemic with no ﬁscal response; (iii) the pandemic with both the stimulus checks and extended unemployment beneﬁts in the CARES Act. The pandemic reduces consumption by ten percentage points in Q2 2020 relative to the baseline.
Without the CARES Act, consumption remains depressed through to the second half of 2021, at which point spending returns to the baseline level as a result of the buildup of liquid assets during the pandemic by households that do not lose their income. We capture the limited spending options during the lockdown period by a reduction in the utility of consumption, which makes households save more during the pandemic than they otherwise would have, with the result that they build up liquid assets. When the lockdown ends, the pent up savings of the always-employed become available to ﬁnance a resurgence in their spending, but the depressed spending of the two groups of unemployed people keeps total spending below the baseline until most of them are reemployed, at which point their spending (mostly) recovers while the always-employed are still spending down their extra savings built up during the lockdown.
Figure 4 decomposes the eﬀect of the pandemic on aggregate consumption (with no ﬁscal policy response), separating the drop in marginal utility from the reduction in income due to mass layoﬀs. The ﬁgure illustrates that the constrained consumption choices are quantitatively key in capturing the expected depth in the slump of spending, which is already under way; see Baker, Farrokhnia, Meyer, Pagel, and Yannelis (2020) and Armantier, Kosar, Pomerantz, Skandalis, Smith, Topa, and van der Klaauw (2020) for early evidence. The marginal utility shock hits all households, and directly aﬀects their spending decisions in the early quarters after the pandemic; its eﬀect cannot be mitigated by ﬁscal stimulus. The loss of income from unemployment is large, but aﬀects only a fraction of households, who are disproportionately low income and thus account for a smaller share of aggregate consumption. Moreover, most households hold at least some liquid assets, allowing them to smooth their consumption drop — the 5 percent decrease in labor income in Figure 2 induces only a 1.5 percent decrease in consumption in Figure 4.
Figure 5 shows how the consumption response varies depending on the employment status of households in Q2 2020. For each employment category (employed, unemployed, and deeply unemployed), the ﬁgure shows consumption relative to the same households’ consumption in the baseline scenario with no pandemic (dotted lines).15 The upper panel shows consumption without any policy response, while the lower panel includes the CARES Act. The ﬁgure illustrates an important feature of the unemployment beneﬁts that is lost at the aggregate level: the response provides the most relief to households whose consumption is most aﬀected by the pandemic. For the unemployed — and especially for the deeply unemployed — the consumption drop when the pandemic hits is much shallower and returns faster toward the baseline when the ﬁscal stimulus is in place.
Indeed, this targeted response is again seen in Figure 6, showing the extra consumption relative to the pandemic scenario without the CARES Act. The short-dashed and dotted lines show the eﬀect of the stimulus check in isolation (for employed workers this is the same as the total ﬁscal response). For unemployed households, this is dwarfed by the increased unemployment beneﬁts. These beneﬁts both arrive earlier and are much larger. Speciﬁcally, in Q3 2020, when households receive the stimulus checks, the eﬀect of unemployment beneﬁts on consumption makes up about 70 percent and 85 percent of the total eﬀect for the normally and deeply unemployed, respectively.
Figure 7 aggregates the decomposition of the CARES Act in Figure 6 across all households. In our model economy, the extra unemployment beneﬁts amount to $544 per household, while the stimulus checks amount to $1,054 per household (as means testing reduces or eliminates the stimulus checks for high income households). Aggregated, stimulus checks amount to $267 billion, while the extended unemployment beneﬁts amount to just over half that, $137 billion.16 The ﬁgure shows that during the peak consumption response in Q3 2020, the stimulus checks account for about 70 percent of the total eﬀect on consumption for the average household and the unemployment beneﬁts for about 30 percent. Thus, although the unemployment beneﬁts make a much larger diﬀerence to the spending of the individual recipients than the stimulus checks, a small enough proportion of households becomes unemployed that the total extra spending coming from these people is less than the total extra spending from the more widely distributed stimulus checks.
The previous graphs show the importance of the targeted unemployment beneﬁts at the individual level, but the aggregate eﬀect is less striking. Figure 8 compares the eﬀect of the CARES Act (both unemployment insurance and stimulus checks) to a policy of the same absolute size that distributes checks to everybody. While unemployment beneﬁts arrive sooner, resulting in higher aggregate consumption in Q2 2020, the un-targeted policy leads to higher aggregate consumption in the following quarters.
The interesting conclusion is that, while the net spending response is similar for alternative ways of distributing the funds, the choice to extend unemployment beneﬁts means that much more of the extra spending is coming from the people who will be worst hurt by the crisis. This has obvious implications for the design of any further stimulus packages that might be necessary if the crisis lasts longer than our baseline scenario assumes.
Given the uncertainty about how long and deep the current recession will be, we investigate a more pessimistic scenario in which the lockdown is expected to last for four quarters. In addition, the unemployment rate increases to 20 percent in Q2 2020, consisting of 15 percent of deeply unemployed and 5 percent of normal unemployed. In this scenario we compare how eﬀectively the CARES package stimulates consumption, also considering a more generous plan in which the unemployment beneﬁts continue until the lockdown is over. We model the receipt of unemployment beneﬁts each quarter as an unexpected shock, representing a series of policy renewals.
Figure 9 compares the eﬀects of the two ﬁscal stimulus policies on income. The persistently high unemployment results in a substantial and long drop in aggregate income (long-dashed) as compared to the no pandemic scenario. The CARES stimulus (medium-dashed) provides only a short term support to income for the ﬁrst two quarters. In contrast, the scenario with unemployment beneﬁts extended as long as the lockdown lasts (dotted) keeps aggregate income elevated through the recession.
Figure 10 shows the implications of the two stimulus packages for aggregate consumption. The long lockdown causes a much longer decline in spending than the shorter lockdown in our primary scenario. In the shorter pandemic scenario (Figure 3) consumption returns to the baseline path after roughly one year, while in the long lockdown shown here the recovery takes around three years; the CARES stimulus shortens the consumption drop to about two years. The scenario with extended unemployment beneﬁts ensures that aggregate spending returns to near the baseline path after just over one year, and does so by targeting the funds to the people who are worst hurt by the crisis and to whom the cash will make the most diﬀerence.
Our model suggests that there may be a strong consumption recovery when the social-distancing requirements of the pandemic begin to subside. We invite readers to test the robustness of this conclusion by using the associated software toolkit to choose their own preferred assumptions on the path of the pandemic, and of unemployment, to understand better how consumption will respond.
One important limitation of our analysis is that it does not incorporate Keynesian demand eﬀects or other general equilibrium responses to the consumption ﬂuctuations we predict. In practice, Keynesian eﬀects are likely to cause movements in aggregate income in the same direction as consumption; in that sense, our estimates can be thought of as a “ﬁrst round” analysis of the dynamics of the crisis, which will be ampliﬁed by any Keynesian response. (See Bayer, Born, Luetticke, and Müller (2020) for estimates of the multiplier for transfer payments). These considerations further strengthen the case that the CARES Act will make a substantial diﬀerence to the economic outcome. A particularly important consideration is that forward-looking ﬁrms that expect consumer demand to return forcefully in the third and fourth quarters of 2020 are more likely to maintain relations with their employees so that they can restart production quickly.
The ability to incorporate Keynesian demand eﬀects is one of the most impressive achievements of the generation of heterogeneous agent macroeconomic models that have been constructed in the last few years. But the technical challenges of constructing those models are such that they cannot yet incorporate realistic treatments of features that our model says are quantitatively important, particularly diﬀering risks of (and types of) unemployment, for diﬀerent kinds of people (young, old; rich, poor; high- and low-education). This rich heterogeneity is important both to the overall response to the CARES Act, and to making judgments about the extent to which it has been successfully targeted to provide beneﬁts to those who need them most. A fuller analysis that incorporates such heterogeneity, which is of intrinsic interest to policymakers, as well as a satisfying treatment of general equilibrium will have to wait for another day, but that day is likely not far oﬀ.
Andersen, Asger Lau, Emil Toft Hansen, Niels Johannesen, and Adam Sheridan (2020): “Consumer Responses to the COVID-19 Crisis: Evidence from Bank Account Transaction Data,” Covid Economics, 7, 88–111.
Armantier, Olivier, Gizem Kosar, Rachel Pomerantz, Daphne Skandalis, Kyle Smith, Giorgio Topa, and Wilbert van der Klaauw (2020): “Coronavirus Outbreak Sends Consumer Expectations Plummeting,” URL link retrieved on 04/07/2020 here.
Baker, Scott R., R. A. Farrokhnia, Steffen Meyer, Michaela Pagel, and Constantine Yannelis (2020): “How Does Household Spending Respond to an Epidemic? Consumption During the 2020 COVID-19 Pandemic,” working paper 26949, National Bureau of Economic Research.
Brown, Jeffrey, Jeffrey B. Liebman, and Joshua Pollett (2002): “Estimating Life Tables That Reﬂect Socioeconomic Diﬀerences in Mortality,” in The Distributional Aspects of Social Security and Social Security Reform, ed. by Martin Feldstein, and Jeﬀrey B. Liebman, pp. 447–457. University of Chicago Press.
Carroll, Christopher D., Edmund Crawley, Jiri Slacalek, Kiichi Tokuoka, and Matthew N. White (2020): “Sticky Expectations and Consumption Dynamics,” American Economic Journal: Macroeconomics, 12(3), 40–76.
Carroll, Christopher D., Alexander M. Kaufman, Jacqueline L. Kazil, Nathan M. Palmer, and Matthew N. White (2018): “The Econ-ARK and HARK: Open Source Tools for Computational Economics,” in Proceedings of the 17th Python in Science Conference, ed. by Fatih Akici, David Lippa, Dillon Niederhut, and M Pacer, pp. 25 – 30. doi: 10.5281/zenodo.1001067.
Carroll, Christopher D., Jiri Slacalek, Kiichi Tokuoka, and Matthew N. White (2017): “The Distribution of Wealth and the Marginal Propensity to Consume,” Quantitative Economics, 8, 977–1020, At http://econ.jhu.edu/people/ccarroll/papers/cstwMPC.
Carvalho, V.M, J.R. Garcia, S. Hansen, A. Ortiz, T. Rodrigo, J.V. Mora Rodriguez, and J. Ruiz (2020): “Tracking the COVID-19 Crisis with High-Resolution Transaction Data,” Discussion paper, Cambridge University.
Casado, Miguel Garza, Britta Glennon, Julia Lane, David McQuown, Daniel Rich, and Bruce A Weinberg (2020): “The Eﬀect of Fiscal Stimulus: Evidence from COVID-19,” Working Paper 27576, National Bureau of Economic Research.
Chetty, Raj, John Friedman, Nathaniel Hendren, Michael Stepner, and The Opportunity Insights Team (2020): “How Did COVID-19 and Stabilization Policies Aﬀect Spending and Employment? A New Real-Time Economic Tracker Based on Private Sector Data,” working paper, Harvard University.
Cox, Natalie, Peter Ganong, Pascal Noel, Joseph Vavra, Arlene Wong, Diana Farrell, and Fiona Greig (2020): “Initial Impacts of the Pandemic on Consumer Behavior: Evidence from Linked Income, Spending, and Savings Data,” Brookings Papers on Economic Activity, forthcoming.
Guerrieri, Veronica, Guido Lorenzoni, Ludwig Straub, and Ivan Werning (2020): “Macroeconomic Implications of COVID-19: Can Negative Supply Shocks Cause Demand Shortages?,” working paper 26918, National Bureau of Economic Research.
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Parker, Jonathan A, Nicholas S Souleles, David S Johnson, and Robert McClelland (2013): “Consumer spending and the economic stimulus payments of 2008,” The American Economic Review, 103(6), 2530–2553.
The baseline model is adapted and expanded from Carroll, Slacalek, Tokuoka, and White (2017). The economy consists of a continuum of expected utility maximizing households with a common CRRA utility function over consumption, , where is a marginal utility shifter. Households are ex ante heterogeneous: household has a quarterly time discount factor and an education level (for dropout, high school, and college, respectively). Each quarter, the household receives (after tax) income, chooses how much of their market resources to consume and how much to retain as assets ; they then transition to the next quarter by receiving shocks to mortality, income, their employment state, and their marginal utility of consumption.
For each education group , we assign a uniform distribution of time preference factors between and , chosen to match the distribution of liquid wealth and retirement assets. Speciﬁcally, the calibrated values in Table A1 ﬁt the ratio of liquid wealth to permanent income in aggregate for each education level, as computed from the 2004 Survey of Consumer Finance. The width of the distribution of discount factors was calibrated to minimize the diﬀerence between simulated and empirical Lorenz shares of liquid wealth for the bottom 20%, 40%, 60%, and 80% of households, as in Carroll, Slacalek, Tokuoka, and White (2017).
When transitioning from one period to the next, a household with education that has already lived for periods faces a probability of death. The quarterly mortality probabilities are calculated from the Social Security Administration’s actuarial table (for annual mortality probability) and adjusted for education using Brown, Liebman, and Pollett (2002); a household dies with certainty if it (improbably) reaches the age of 120 years. The assets of a household that dies are completely taxed by the government to fund activities outside the model. Households who survive to period experience a return factor of on their assets, assumed constant.
Household ’s state in period , at the time it makes its consumption–saving decision, is characterized by its age ,17 a level of market resources , a permanent income level , a discrete employment state (indicating whether the individual is employed, normal unemployed, or deeply unemployed), and a discrete state that represents whether its marginal utility of consumption has been temporarily reduced (). Denote the joint discrete state as .
Each household inelastically participates in the labor market when it is younger than 65 years () and retires with certainty at age 65. The transition from working life to retirement is captured in the model by a one time large decrease in permanent income at age .18 Retired households face essentially no income risk: they receive Social Security beneﬁts equal to their permanent income with 99.99% probability and miss their check otherwise; their permanent income very slowly degrades as they age. The discrete employment state is irrelevant for retired households.
Labor income for working age households is subject to three risks: unemployment, permanent income shocks, and transitory income shocks. Employed () households’ permanent income grows by age-education-conditional factor on average, subject to a mean one lognormal permanent income shock with age-conditional underlying standard deviation of . The household’s labor income is also subject to a mean one lognormal transitory shock with age-conditional underlying standard deviation of . The age proﬁles of permanent and transitory income shock standard deviations are approximated from the results of Sabelhaus and Song (2010), and the expected permanent income growth factors are adapted from Cagetti (2003). Normal unemployed and deeply unemployed households receive unemployment beneﬁts equal to a fraction of their permanent income, ; they are not subject to permanent nor transitory income risk, but their permanent income grows at rate less than if employed, representing “skill rot”.19
The income process for a household can be represented mathematically as:
A working-age household’s employment state evolves as a Markov process described by the matrix , where element of is the probability of transitioning from to . During retirement, all households have (or any other trivializing assumption about the “employment” state of the retired). We assume that households treat and as zero: they do not consider the possibility of ever attaining the deep unemployment state from “normal” employment or unemployment, and thus it does not aﬀect their consumption decision in those employment states.
We specify the unemployment rate during normal times as , and the expected duration of an unemployment spell as 1.5 quarters. The probability of transitioning from unemployment back to employment is thus , and the probability of becoming unemployed is determined as the ﬂow rate that oﬀsets this to generate 5% unemployment (about 3.5%). The deeply unemployed expect to be unemployed for much longer: we specify and , so that a deeply unemployed person remains so for three quarters on average before becoming “normal” unemployed (they cannot transition directly back to employment). Thus the unemployment spell for a deeply unemployed worker is 2 quarters at a minimum and 4.5 quarters on average.20
Like the prospect of deep unemployment, the possibility that consumption might become less appealing (via marginal utility scaling factor ) does not aﬀect the decision-making process of a household in the normal state. If a household does ﬁnd itself with , this condition is removed (returning to the normal state) with probability each quarter; the evolution of the marginal utility scaling factor is represented by the Markov matrix . In this way, the consequences of a pandemic are fully unanticipated by households, a so-called “MIT shock”; households act optimally once in these states, but did not account for them in their consumption–saving problem during “normal” times.21
The household’s permanent income level can be normalized out of the problem,
dividing all boldface variables (absolute levels) by the individual’s permanent income
, yielding non-bold normalized variables, e.g., . Thus the only state
variables that aﬀect the choice of optimal consumption are normalized market resources
and the discrete Markov states . After this normalization, the household
consumption functions satisfy:
Starting from the terminal model age of , representing being 120 years old (when the optimal choice is to consume all market resources, as death is certain), we solve the model by backward induction using the endogenous grid method, originally presented in Carroll (2006). Substituting the deﬁnition of next period’s market resources into the maximand, the household’s problem can be rewritten as:
To solve the age- problem numerically, we specify an exogenous grid of end-of-period asset values , compute end-of-period marginal value of assets at each gridpoint (and each discrete Markov state), then calculate the unique (normalized) consumption that is consistent with ending the period with this quantity of assets while acting optimally. The beginning-of-period (normalized) market resources from which this consumption was taken is then simply , the endogenous gridpoint. We then linearly interpolate on this set of market resources–consumption pairs, adding an additional bottom gridpoint at to represent the liquidity-constrained portion of the consumption function .
The standard envelope condition applies in this model, so that the marginal value of market resources equals the marginal utility of consumption when consuming optimally:
The marginal value function for age can then be used to solve the age problem, iterating backward until the initial age problem has been solved.
When the pandemic strikes, we draw a new employment state (employed, unemployed, deeply unemployed) for each working age household using a logistic distribution. For each household at (the beginning of the pandemic and lockdown), we compute logistic weights for the employment states as:
where for dropouts, high school graduates, and college graduates and is the household’s age. The probability that household draws employment state is then calculated as:
Our chosen logistic parameters are presented in Table A2.
Households are modeled as individuals and incomes sized accordingly. We completely abstract from family dynamics. To get our aggregate predictions for income and consumption, we take the mean from our simulation and multiply by 253 million, the number of adults (over 18) in the United States in 2019. To size the unemployment beneﬁts correctly, we multiply the beneﬁts per worker by 0.8 to account for the fact that 20 percent of the working-age population is out of the labor force, so the average working-age household consists of 0.8 workers and 0.2 non-workers. With this adjustment, there are 151 million workers eligible for unemployment beneﬁts in the model. Aggregate consumption in our baseline for 2020 is just over $11 trillion, a little less than total personal consumption expenditure, accounting for the fact that some consumption does not ﬁt in the usual budget constraint.22 Aggregating in this way underweights the young, as our model excludes those under the age of 24.
Our model estimates the aggregate size of the stimulus checks to be $267 billion, matching the the Joint Committee on Taxation’s estimate of disbursements in 2020.23 This is somewhat of a coincidence: we overestimate the number of adults who will actually receive the stimulus, while excluding the $500 payment to children.
The aggregate cost of the extra unemployment beneﬁts depends on the expected level of unemployment. Our estimate is $137 billion, much less than the $260 billion mentioned in several press reports, but in line with the extent of unemployment in our pandemic scenario.24 We do not account for the extension of unemployment beneﬁts to the self-employed and gig workers.
Households enter the model at age with zero liquid assets. A ‘newborn’ household has its initial permanent income drawn lognormally with underlying standard deviation of 0.4 and an education-conditional mean. The initial employment state of households matches the steady state unemployment rate of 5%.25
We assume annual population growth of 1%, so older simulated households are appropriately down-weighted when we aggregate idiosyncratic values. Likewise, each successive cohort is slightly more productive than the last, with aggregate productivity growing at a rate of 1% per year. The proﬁle of average income by age in the population at any moment in time thus has more of an inverted-U shape than implied by the permanent income proﬁles from Cagetti (2003).
We model the ‘lockdown’ as a reduction in the marginal utility of consumption. This can be interpreted as an increase in the quality-adjusted price of goods, where the quality of basic goods such as shelter and housing has not decreased, but more discretionary goods such as vacations and restaurants have decreased in quality.
Figure 11 shows how this works. In normal times, the cost of a consumption unit is equal to one, represented by the blue line. During the lockdown, the cost of a unit of consumption is increasing in the number of units bought. As shown here, the number of consumption units that can be bought follows the lower envelope of the blue and orange lines, where the orange line is equal to . As long as the household is consuming above the kink, their utility is , exactly equivalent to the reduction in marginal utility we apply. Taking this interpretation seriously, the drop in marginal utility should not be applied to households with very low levels of consumption, below the kink. Our implementation abstracts from this, taking the marginal utility factor to be the same for all agents.
An alternative interpretation is that consumption is made up of a Cobb-Douglass aggregation of two goods:
1As articulated long ago by Deaton (1992) and documented recently Havranek, Rusnak, and Sokolova (2017).
2The cruise industry, for example, is likely to take a long time to recover. Demand for airline travel is expected to remain depressed, with the International Air Traﬃc Association projecting that passenger travel will not return to pre-pandemic levels until 2024.
3A shock to marginal utility may not perfectly capture the essence of what depresses consumption spending, but it accomplishes our purposes and is a kind of shock commonly studied in the literature. Any analysis of the welfare consequences of the lockdown would probably need a richer treatment to be credible.
4We put ‘durable’ in quotes because ‘memorable’ goods (Hai, Krueger, and Postlewaite (2013)) have eﬀectively the same characteristics.
5The baseline model is very close to the lifecycle model in Carroll, Slacalek, Tokuoka, and White (2017).
6Households exit unemployment with a ﬁxed probability each quarter — the expected length of an unemployment spell is one and a half quarters.
7For a detailed description of the model and its calibration see Appendix A.
8For the purposes of our paper, with log utility, modeling lockdowns as a shock to marginal utility is essentially equivalent to not allowing consumers to buy a subset of goods (which are combined into composite consumption by a Cobb–Douglas aggregator). However, the two approaches would yield diﬀerent implications for normative evaluations of economic policies.
9As of April 16, about 22 million new unemployment claims have been ﬁled in four weeks, representing a loss of over 14 percent of total jobs. JP Morgan Global Research forecast 8.5 percent unemployment (JPMorgan (2020), from March 27); Treasury Secretary Steven Mnuchin predicted unemployment could rise to 20 percent without a signiﬁcant ﬁscal response (Bloomberg (2020a)); St. Louis Fed president James Bullard said the unemployment rate may hit 30 percent (Bloomberg (2020b) — see Faria-e-Castro (2020a) for the analysis behind this claim). Based on a survey that closely follows the CPS, Bick and Blandin (2020) calculate a 20.2 percent unemployment rate at the beginning of April.
10See Gascon (2020), Leibovici and Santacreu (2020) and Adams-Prassl, Boneva, Golin, and Rauh (2020) for breakdowns of which workers are at most risk of unemployment from the crisis. See additional evidence in Kaplan, Moll, and Violante (2020) and modeling of implications for optimal policies in Glover, Heathcote, Krueger, and Ríos-Rull (2020).
11See the Cobb-Douglass interpretation in Appendix C.
12The CBO expects social distancing to last for three months, and predicts it to have diminished, on average and in line with our calibration, by three-quarters in the second half of the year; see Swagel (2020).
13The act also includes $500 for every child. In the model, an agent is somewhere between a household and an individual. While we do not model the $500 payments to children, we also do not account for the fact that some adults will not receive a check. In aggregate we are close to the Joint Committee on Taxation’s estimate of the total cost of the stimulus checks.
14See Carroll, Crawley, Slacalek, Tokuoka, and White (2020) for a detailed discussion of the motivations behind this way of modeling stimulus payments, and a demonstration that this model matches the empirical evidence of how and when households have responded to stimulus checks in the past — see Parker, Souleles, Johnson, and McClelland (2013), Broda and Parker (2014) and Parker (2017), among others. See also Fagereng, Holm, and Natvik (2017) for a natural experiment measured using national registry data.
15Households that become unemployed during the pandemic might or might not have been unemployed otherwise. We assume that all households that would have been unemployed otherwise are either unemployed or deeply unemployed in the pandemic scenario. However, there are many more households that are unemployed in the pandemic scenario than in the baseline.
16See Appendix B for details on how we aggregate households.
17Households enter the model aged 24 years, so model age corresponds to being 24 years, 0 quarters old.
18The size of the decrease depends on education level, very roughly approximating the progressive structure of Social Security: , , .
19Unemployment is somewhat persistent in our model, so the utility risk from receiving 15% of permanent income for one quarter (as in Carroll, Slacalek, Tokuoka, and White (2017)) is roughly the same as the risk of receiving 30% of permanent income for 1.5 quarters in expectation.
20Our computational model allows for workers’ beliefs about the average duration of deep unemployment to diﬀer from the true probability. However, we do not present results based on this feature and thus will not further clutter the notation by formalizing it here.
21Our computational model also allows households’ beliefs about the duration of the reduced marginal utility state (via social distancing) to deviate from the true probability. The code also permits the possibility that the reduction in marginal utility is lifted as an aggregate or shared outcome, rather than idiosyncratically. We do not present results utilizing these features here, but invite the reader to investigate their predicted consequences using our public repository.
22PCE consumption in Q4 2019, from the NIPA tables, was $14.8 trillion. Market based PCE, a measure that excludes expenditures without an observable price was $12.9 trillion. Health care, much of which is paid by employers and not in the household’s budget constraint, was $2.5 trillion.
23The JCT’s 26 March 2020 publication JCX-11-20 predicts disbursements of $267 billion in 2020, followed by $24 billion in 2021.
24While $260 billion was widely reported in the press, back-of-the-envelope calculations show this to be an extreme number. Furthermore, the origin of this reported number is unclear.
25This is the case even during the pandemic and lockdown, so the death and replacement of simulated agents is a second order contribution to the proﬁle of the unemployment rate.