Optimal Public Debt with Life Cycle Motives William Peterman Erick - PowerPoint PPT Presentation

Optimal Public Debt with Life Cycle Motives William Peterman Erick Sager Federal Reserve Board Bureau of Labor Statistics QSPS May 20, 2016 **The views herein are the authors’ and not necessarily those of the BLS, US DOL, Board of Governors or their staffs.

Intro Model Calibration Results Conclusion Motivation Q: What level of debt should the Government hold? Government Debt • Welfare Costs: • Crowds out capital ⇒ lower output • Financed by distortionary taxes • Welfare Benefits (financial liquidity): • ⇑ return to savings ⇒ reduces cost of holding precautionary savings Aiyagari & McGrattan (1998) • Incomplete markets, infinitely lived • Optimal debt = 2 3 of output • Ignores life cycle • Agents transition through different phases of life cycle Peterman and Sager Optimal Debt 1 / 66

Intro Model Calibration Results Conclusion This Paper Question: What is optimal level of gov’t debt in life cycle model? Effect of Life Cycle on Optimal Pubic Debt • Large effect on optimal public debt • Life cycle model: savings = 160% of output • Infinitely lived agent model: debt = 87% of output • Welfare of adopting misspecified optimal tax policy: CEV = 3.5% • Different policies due to different phases of life cycle Peterman and Sager Optimal Debt 2 / 66

Intro Model Calibration Results Conclusion Mechanism: Example (I) Accumulation Stationary Phase Decumulation Consumption Savings Hours Age • Life cycle all three phases; Infinitely lived only one phase • Changing prices has different effects Peterman and Sager Optimal Debt 3 / 66

Intro Model Calibration Results Conclusion Mechanism: Example (II) Affect of Gov’t Debt on Factor Prices: • Decreases Government Debt (increases Gov’t. savings) • Crowds in Productive Capital • Interest rate ⇓ • Wage ⇑ Infinitely Lived Agent Model • Only stationary phase • Lower interest rate decreases liquidity Life Cycle Model • Accumulation, Stationary, Decumulation Phases • Higher wage more accommodative during accumulation phase Peterman and Sager Optimal Debt 4 / 66

Intro Model Calibration Results Conclusion Literature Effects of government debt with incomplete markets 1. Steady State • Aiyagari & McGrattan (1998) - optimal debt large • Floden (2001) - if transfers below optimal then ⇑ gov’t debt • Dyrda & Pedroni (2015) - if taxes optimized then less debt optimal • Winter & Roehrs (2015) - skewed wealth leads to gov’t savings being optimal 2. Transition • Dydra & Pedron (2015); Winter and Roehrs (2015); Desbonnet & Weitzenblum (2012): Considerable welfare costs in transition Previous analysis of question done with infinitely lived agent model Peterman and Sager Optimal Debt 5 / 66

Intro Model Calibration Results Conclusion Outline 1. Introduction 2. Life cycle Model with Public Debt 3. Calibration 4. Results 5. Conclusion Peterman and Sager Optimal Debt 6 / 66

Intro Model Calibration Results Conclusion Life cycle Model with Public Debt Peterman and Sager Optimal Debt 7 / 66

Intro Model Calibration Results Conclusion Overview of Model • General Equilibrium incomplete markets model • Overlapping generations of heterogenous agents • Idiosyncratic uninsurable shocks: • Agent’s labor productivity • Unemployment spells • Mortality • Labor is supplied elastically • Agents choose when to retire • Social Security and UI programs modeled similar to U.S. Peterman and Sager Optimal Debt 8 / 66

Intro Model Calibration Results Conclusion Production • Representative Firm: • Large number of firms • Sell consumption good • Perfectly competitive product market • Technology: • Cobb-Douglas: Y = K ζ L 1 − ζ • No aggregate uncertainty • Resource Constraint: C + ( K ′ − (1 − δ ) K ) + G = Y Peterman and Sager Optimal Debt 9 / 66

Intro Model Calibration Results Conclusion Demographics • J overlapping generations • s j probability of living to j + 1 given one is alive in j • Remaining assets are accidental bequests ( Tr t ). • If still alive agents die with certainty at age J • Agents retire at endogenously determined age ( J ret ), irreversible • J ret ∈ [ J ret , J ret ] • Population growth = g n Peterman and Sager Optimal Debt 10 / 66

Intro Model Calibration Results Conclusion Labor Earnings (I) Earnings: y ij = we ij h ij (1 − ¯ h ij ) • Labor productivity, e ij • Choice of hours, h ij ∈ [0 , 1] • Unemployment shocks, ¯ h ij Labor Productivity: log( e ij ) = θ j + α i + ǫ ij + ν ij ¯ J ret • Age-profile: { θ j } j =1 iid ∼ N (0 , σ 2 • Idiosyncratic type: α i α ) iid ∼ N (0 , σ 2 • Transitory shock: ǫ ij ǫ ) • Persistent shock: ν ij +1 = ρν ij + η ij +1 iid ∼ N (0 , σ 2 η ij +1 ν ) v i 1 = 0 Peterman and Sager Optimal Debt 11 / 66

Intro Model Calibration Results Conclusion Labor Earnings (II) Earnings: y ij = we ij h ij (1 − ¯ h ij ) • Labor productivity, e ij • Choice of hours, h ij ∈ [0 , 1] • Unemployment shocks, ¯ h ij Unemployment Shock: h i,j • Fraction of period unemployed • Either 0 or d j • Probability of non zero: p j • Probability and duration are age specific • Receive unemployment benefits • b ui ( we ij ) Peterman and Sager Optimal Debt 12 / 66

Intro Model Calibration Results Conclusion Asset Markets Incomplete Asset Markets: • Incomplete w.r.t. idiosyncratic productivity risk, unemployment risk, mortality risk • Agents save using non-contingent bond, a ≥ 0 • Before tax rate of return, r A = K + B Market Clearing: • Supply = Aggregate Savings • Demand = Productive Capital ( K ) + Gov’t Debt ( B ) Peterman and Sager Optimal Debt 13 / 66

Intro Model Calibration Results Conclusion Government Policy Budget Constraint: G + UI + rB = ( B ′ − B ) + Υ y 1. G: Consumes in an unproductive sector 2. UI: Pays insurance when unemployed 3. B: Borrows or saves at interest r 4. Υ y : Finances with progressive income taxation Self Financing Programs: 5. Runs Social Security Program 6. Distributes accidental bequests Peterman and Sager Optimal Debt 14 / 66

Intro Model Calibration Results Conclusion Social Security Overview: • Finances SS with a flat tax on labor income τ ss • Half payed by employer (up to cap) • Pays benefit b ss based on i • Past income AIME: x i • Age of retirement: J ret Detail Peterman and Sager Optimal Debt 15 / 66

Intro Model Calibration Results Conclusion Competitive Equilibrium 1. Agents optimize utility s.t. budget constraint 2. Prices set by marginal product of capital and labor 3. Social Security budget clears 4. General Government budget clears 5. Capital and labor market clear 6. Stationary distribution of individuals over state space • Accounting for GDP growth: g Dynamic Programming Peterman and Sager Optimal Debt 16 / 66

Intro Model Calibration Results Conclusion Calibration Peterman and Sager Optimal Debt 17 / 66

Intro Model Calibration Results Conclusion Firm Production: Y = K ζ N 1 − ζ Notation Parameter Value Source Capital Share ζ .36 CKK I Depreciation δ .0833 Y = 25 . 5% Growth g 0.02 Peterman and Sager Optimal Debt 18 / 66

Intro Model Calibration Results Conclusion Demographics • Agents enter the model at age 20 • s j - Bell and Miller (2002) • Remaining agents die with certainty age 100( J ) • Population growth: g n = 1 . 1% Peterman and Sager Optimal Debt 19 / 66

Intro Model Calibration Results Conclusion Idiosyncratic Labor Productivity Labor Productivity: log( e ij ) = θ j + α i + ν ij + ǫ ij Notation Parameter Value Source σ 2 Persistence Shock 0.017 Kaplan (2012) ν Persistence ρ 0.958 Kaplan (2012) σ 2 Ability 0.065 Kaplan (2012) α σ 2 Transitory Shock 0.081 Kaplan (2012) ǫ ¯ J ret Age Profile { θ j } Kaplan (2012) j =1 Peterman and Sager Optimal Debt 20 / 66

Intro Model Calibration Results Conclusion Unemployment Unemployment Rates and Duration by Age Weeks Pct (March CPS, 1990-2005) 22 16% 14% Average 20 Unemployment Duration 12% 18 10% 16 8% 6% 14 4% 12 Unemployment Rate (right axis) 2% 10 0% 20 25 30 35 40 45 50 55 60 65 Age Peterman and Sager Optimal Debt 21 / 66

Intro Model Calibration Results Conclusion Unemployment Insurance Weekly UI Benefit Replacement Rate Pct Pct (March CPS: 1990-2005) 2 2 Average 1.8 1.8 log(Weekly Earnings) 1.6 1.6 1.4 1.4 1.2 1.2 Weekly Replacement 1 1 Rate 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 log(Weekly Earnings) • Base Benefit: b ui ( we ) = rr ( we ) we h average h • Replacement rate: rr ( we ) = φ ui, 0 ln( we ) φ ui, 1 • b ui ∈ [ . 13 × avg. earnings × h, 1 . 1 × avg. earnings × h ] Peterman and Sager Optimal Debt 22 / 66

Intro Model Calibration Results Conclusion Preferences ((1 − h ) ξ h ) 1+ 1 Preferences: u ( c ) + v ( h, h ) = c 1 − γ σ 1 − γ − χ 1 − χ 2 1 ( j < J ret ) 1+ 1 σ Notation Parameter Value Source K Conditional Discount β 1.0 Y = 2 . 7 Risk aversion γ 2 . 2 Kaplan (2012) Frisch Elasticity σ 0.41 Kaplan (2012) Utility during unemployment ξ 0 Kaplan (2012) Avg. h j = 1 Disutility to Labor χ 1 70.0 3 Fixed Cost to Working χ 2 1.105 70% retire by J nr Peterman and Sager Optimal Debt 23 / 66