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Tracing the Pandemic Possibility Frontier for the US

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Tracing the Pandemic Possibility Frontier for the US The Great Lockdown and the Big Stimulus: Tracing the Pandemic Possibility Frontier for the U.S. Greg Kaplan Ben Moll Gianluca Violante Mean Field Games in Economics EIEF September 2020 Slides at http://benjaminmoll.com/PPF_MFG_slides/ Today’s talk: what you can do with MFGs • An epi-macro MFG to analyze COVID-19 crisis, health & economic policy responses to it • background: entire emerging epi-macro field, e.g. Alvarez-Argente-Lippi (=6 MFG) • Hybrid of 1. SIR model from epidemiology – see e.g. https://benjaminmoll.com/SIR_notes/ 2. heterogeneous agent model from macro = MFG of income & wealth dist’n (Aiyagari) – see e.g. https://benjaminmoll.com/HACT/ • Paper: rich, complicated model – see https://benjaminmoll.com/PPF/ • Today: • MFG system of very stripped down version to give you gist of things • But show you results from full model 1 Kaplan, Moll and Violante (2020) Objectives • US policy response to COVID-19: • Lockdown: workplace and social sector • Fiscal stimulus: CARES Act • Goal: quantify trade-offs • Aggregate: Lives versus livelihoods • Distributional: Who bears the economic costs? • Approach: distributional Pandemic Possibility Frontier (PPF) ! PPF • Name in analogy to “Production Possibility Frontier” = key economic concept • Compare policies without taking stand on economic value of life • Seek policies that flatten and shift the frontier 2 Kaplan, Moll and Violante (2020) Distributional Pandemic Possibility Frontier 10 Mean w/o Fiscal Support p10-p90 w/o Fiscal Support Mean w/ Fiscal Support p10-p90 w/ Fiscal Support 17-Month 8 Lockdown 12-Month 6 Lockdown 4 US Lockdown US Policy Laissez-faire 2 Economic Welfare Cost (Multiples of Monthly Income) 0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Deaths (% of Population) ! back to intro 3 Kaplan, Moll and Violante (2020) Simplified Model 4 Kaplan, Moll and Violante (2020) Epidemiological Model: SIR Model • • St : susceptible It : infectious • • Rt : recovered Nt : population = St + It + Rt 2 3 2 3 2 I I 3 S_ S −β t β t 0 t t t Nt t Nt 4 5 T 4 5 4 5 I_t = A It ; A = 0 −γ γ(1 − δ) R_ t Rt 0 0 0 • Deaths (flow) D_ t = δγIt , cumulative deaths Dt . Key feature: βt = β(Ct ): infections depend on aggregate consumption Ct 5 Kaplan, Moll and Violante (2020) Economic Model: Households • ... differ in their wealth a, income y, and health state h 2 fS; I; Rg • household state x = (a; y; h) • value function v(x; t) – households’ problem on next slide • joint distribution g(x; t) • Note non-standard notation relative to MFG literature: (v; g) instead of (u; m) • To simplify notation a bit: • ignore mass points (which do typically arise) & work with density R • write some equations as if h 2 fS; I; Rg were a continuous state, e.g. g(x; t)dx • Accounting: Z Z Nt = g(x; t)dx; St = g(a; y; S; t)dady; Z Z It = g(a; y; I; t)dady; Rt = g(a; y; R; t)dady 6 Kaplan, Moll and Violante (2020) Economic Model: Households solve Z 1 −ρt max E0 e u(ct ; It )dt s.t. fct gt≥0 0 dat = (yt + rat + τt − ct )dt dyt = µ(yt )dt + σ(yt )dWt at ≥ a • c : consumption t p • u: utility function, e.g. u(c; I) = c × e−I . Dependence on infections I = “fear factor” • ρ: discount rate • E0: expectations operator, takes into account death rate δγ > 0 in I state (like higher ρ) • r : fixed interest rate • Wt : Wiener process, independent across households • yt 2 [y; y¯]: income, reflected at boundaries if it ever reaches them • τt : transfers = fiscal stimulus – set τ = 0 on next slides to simplify notation • a > −∞: borrowing limit e.g. if a = 0, can only save More general y-processes also possible, e.g. jumps7 = unemployment Kaplan, Moll and Violante (2020) Comment: source of MFG coupling • Usually, in Aiyagari-type heterogeneous agent models, interest rate rt determined in equilibrium by condition like Z 0 = ag(x; t)dx all t ≥ 0 • Interpretation: for everyone who borrows (a < 0) there is someone who lends (a > 0) • Econ terminology: “bonds are in zero net supply” • and usually = source of MFG coupling (in Galo’s words: “coupling through prices”) • Here instead: • interest rate r = fixed scalar • coupling through epi variables 8 Kaplan, Moll and Violante (2020) MFG System in absence of lockdowns Functions v and g on (a; 1) × (y; y¯) × fS; I; Rg × (0; 1) satisfy σ2(y) ρv = max u(c; It ) + (y + ra − c)@av + µ(y)@y v + @yy v + Av + @t v (HJB) c 2 with state constraint a ≥ a and 0 = @y v(a; y; h; t) = @y v(a; y;¯ h; t) all a; h; t 1 @ g = − @ (sg) − @ (µ(y)g) + @ (σ2(y)g) + ATg (FP) t a y 2 yy −1 s :=y + ra − c; c = (uc ) (@av; I); 2 3 It It Z −β(Ct ) N β(Ct ) N 0 4 t t 5 A = 0 −γ γ(1 − δ) ;Ct = c(x; t)g(x; t)dx (EPI) 0 0 0 Z It = g(a; y; I; t)dady (I) g(x; 0) = g0(x) Note two-way feedback: 1. epi ! econ through (HJB) and (I) 2. econ ! epi through (EPI) 9 Kaplan, Moll and Violante (2020) Lockdowns • Policy that requires c(x; t) ≤ c¯ • Lockdowns reduce virus transmissions because 2 3 It It Z −β(Ct ) N β(Ct ) N 0 4 t t 5 A = 0 −γ γ(1 − δ) ;Ct = c(x; t)g(x; t)dx 0 0 0 • Full model: different consumption goods, lockdowns only restrict “social” goods 10 Kaplan, Moll and Violante (2020) Full Model 11 Kaplan, Moll and Violante (2020) Full Model • Integrated SIR + Heterogeneous Agent model with necessary ingredients • Goods: (i) regular; (ii) social; (iii) home production • Types of labor: (i) workplace; (ii) remote; (iii) home production • Occupation heterogeneity: (i) flexibility; (ii) social intensity; (iii) essentiality • Two-way feedback: between virus and economic activity • Economic exposure to pandemic correlated with financial vulnerability • Calibrate model to U.S. economy and examine counterfactuals • Laissez-faire vs lockdown vs fiscal policy (CARES Act) • Smarter policies: (i) targeted lockdowns; (ii) Pigouvian taxes 12 Kaplan, Moll and Violante (2020) Main Findings in Full Model 1. Economic welfare costs of pandemic: large and heterogeneous, regardless of lockdown • Large welfare costs for rigid, social-intensive occupations • Large welfare costs for middle of earnings distribution: fiscal stimulus 2. Slope of PPF varies with length lockdown • Driven by hospital constraint and eventual arrival of vaccine • Reconcile conflicting views on extent of trade-off 3. U.S. CARES Act: • Reduced economic cost by 20% on average, highly redistributive • Explains rapid recovery in consumption of poor households 4. Taxation-based alternatives to lockdown: favorable mean trade-off but more dispersion 5. Model prediction for fall/winter: with current U.S. policy, 2nd wave & double-dip recession ! dimensions not considering today 13 Kaplan, Moll and Violante (2020) Outline 1. Full model: some more details 2. Parameterization 3. Results 4. Conclusions 5. Linked Slides 13 Kaplan, Moll and Violante (2020) Full Model: Add Different Occupations • Full model features 5 occupation classes • These differ in “flexibility” = remote-work ability, and sector they are employed in High Flexibility Low Flexibility High intensity in C Software engineer, architect Car mechanic, miner High intensity in S Event planner, social scientist Waiter, shop assistant Essential Police, nurse, supermarket clerk 14 Kaplan, Moll and Violante (2020) Outline 1. Full model: some more details 2. Parameterization 3. Results 4. Conclusions 5. Linked Slides 14 Kaplan, Moll and Violante (2020) Key Aspects of Parameterization 1. Epidemiological block • SEIR parameters: epidemiological and clinical studies ! SEIR parameters 2. Occupational parameters • Flexibility measures by occupation: O*NET, ATUS ! occupation flexibility details • Sectoral employment intensities in C and S: OES, CPS ! occupation sectoral details • Earnings and liquid wealth by occupation: SIPP, CPS, SCF ! exposure vs vulneability 3. Two-way feedback: virus $ economic activity • ! ! Economic activity ! virus: drop in R0 after lockdown feedback: activity virus • Virus ! economic activity: VSL literature !! feedback: virus ! activity 15 Kaplan, Moll and Violante (2020) Outline 1. Full model: some more details 2. Parameterization 3. Results 4. Conclusions 5. Linked Slides 15 Kaplan, Moll and Violante (2020) Laissez-faire vs Lockdown Dynamics (a) Monthly Death Rate (%) (c) Labor Income (CF: C-intensive, Flexible) (%) (e) Labor Income (SF: S-intensive, Flexible) (%) 0.12 0 0 Laissez-faire 0.10 Full Lockdown 10 10 0.08 20 20 0.06 30 30 0.04 40 40 0.02 Laissez-faire Laissez-faire Full Lockdown Full Lockdown 0.00 50 50 Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Month (b) Output (%) (d) Labor Income (CR: C-intensive, Rigid) (%) (f) Labor Income (SR: S-intensive, Rigid) (%) 0 0 0 5 10 10 10 20 20 15 30 30 20 40 40 Laissez-faire Laissez-faire Laissez-faire Full Lockdown Full Lockdown Full Lockdown 25 50 50 Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Month • Lockdown ! second wave, but fewer deaths • Lockdown ! longer, deeper contraction and W -shaped recovery • Large drop in income for S-intensive occupations even in laissez faire • Lockdown ! further drop in income for C-intensive occupations 16 Kaplan, Moll and Violante (2020) ! lockdown path ! laissez-faire dynamics ! lockdown dynamics ! lockdown decomposition Pandemic Possibility Frontier (PPF) Mean 10 p25-p75 p10-p90 p5-p95 17-Month 8 Lockdown 12-Month Lockdown 6 4 US Lockdown Laissez-faire 2 Economic Welfare Cost (Multiples of Monthly Income) 0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Deaths (% of Population) • Large average economic costs with very non-linear trade-off: ICU constraint vs vaccine • Heterogeneity in economic costs exacerbated with longer lockdowns ! ppf by occupation 17 Kaplan, Moll and Violante
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