Penn Wharton Budget Model: Dynamics July 5, 2016
Penn Wharton Budget Model: Dynamics
July 5, 2016
Dynamic Model Overview
I Dynamic general equilibrium OLG model with heterogeneity
I Idiosyncratic productivity risk ⇒ distribution of earningshistories
I Detailed Social Security system, progressive taxes,immigration
I Evaluates unbalanced fiscal reform over long time horizons
I Considers open and closed economy frameworks
Policy Evaluation
I 75-year CBO debt-to-GDP and government interest rateprojections as baseline
I Policy alternatives increase or decrease debt
I Debt-to-GDP stabilized at year 75, government expendituresadjust as closure rule
I Open economy: prices fixed ⇒ no debt consequences
I Closed economy: prices affected by debt
Dynamic Scoring
I Process of using dynamic model to measure behavioral andmacroeconomic feedback:
1. Generate a Static Score using dynamic model: hold prices andbehavior (decision rules) constant, apply counter-factual policyvariables
2. Evaluate policy using dynamic model as usual
3. Take ratio of dynamic-to-static
4. Multiply ratio and micro-simulation policy projection togenerate Dynamic Score
Dynamic Model
Households
Labor Productivity (z)
I Deterministic dependence on age j
I Permanent shock drawn at birth
I Transitory and persistent (AR1) shocks
I Initial distribution of non-permanent shocks
Households
Taxes, SS Benefits, and Bequests
I Taxes
I Federal income tax (Gouveia-Strauss) on total income y :
τf (y) = a0(y − (y−a1 + a2)−1a1 ) (1)
I Payroll (Social Security) tax on labor income wzn:
τss min {wzn, ytaxmax} , (2)
where ytaxmax is maximum labor income subject to payroll tax.
I Social Security benefit
I Benefit ss(b) depends on average lifetime labor earnings b.
I Accidental bequests are collected by the government andredistributed lump-sum (beq) among all living households.
Households
Working-age household Bellman’s equation:
Vj(k , z , b) = maxk ′,n
{(cγ(1− n)1−γ)1−σ
1− σ+ sj+1βE{z ′|z}[Vj+1(k ′, z ′, b′)]
}(3)
subject to:
c = rpk + wzn − τf (y)− τss min {wzn, ytaxmax} − k ′ + beq (4)
y = (rp − 1)k + wzn − d (5)
bj+1 =1
j
((j − 1)bj + min{wzn, ytaxmax}
), (6)
where (4) is the budget constraint, (5) is income subject to thefederal income tax, (6) determines average earnings for SS benefitcalculation, sj+1 is survival probability, rp is the return tohousehold portfolios, and d is the federal income tax deduction,which is common to all agents.
Households
Retired household Bellman’s equation:
Vj(k , b) = maxk ′
{(cγ(1)1−γ)1−σ
1− σ+ sj+1βVj+1(k ′, b′)
}(7)
subject to:c = rpk + ss(b)− τf (y)− k ′ + beq (8)
y = (rp − 1)k + (1− φss)ss(b)− d (9)
bj+1 = bj , (10)
where φss is the fraction of SS benefits deductible from federalincome taxation, common among all retirees.
Production: Closed Economy
I Output:Y = (K − D)αL1−α, (11)
where K is aggregate household saving, D is government debt,and L is aggregate efficient labor.
I Firms’ problem:
maxK ,L
{(K − D)αL1−α + (1− δ)K − rfK − wL
}, (12)
where δ is depreciation and rf is the rental rate of capitalfaced by firms.
I Firms’ interest rates and wages are determined according to:
rf = 1 + α(K − D)α−1L1−α − δ (13)
w = (1− α)(K − D)αL−α (14)
Production: Open Economy
I Output:Y = K̃αL1−α, (15)
where L is aggregate domestic efficient labor, and K̃ is theaggregate capital determined in international markets.
I Firms’ problem:
maxK ,L
{KαL1−α + (1− δ)K − r∗f K − w∗L
}, (16)
where r∗f and w∗ are the international rental rate of capitaland wages, respectively.
I Then K̃ and L are determined according to:
r∗f = 1 + αK̃α−1L1−α − δ (17)
w∗ = (1− α)K̃αL−α (18)
I World prices set to initial steady-state value determined inclosed economy.
Household Portfolio
I Weighted average of rental rate of capital and governmentinterest rate (rg ):
rp =rfK + rgD
K + D(19)
I Open economy: portfolio return fixed at initial steady statevalues of capital and debt.
I Closed economy: determined in general equilibriumthroughout transition path.
Government Debt
I Sequence of government interest rates rg is exogenous.
I Government debt evolves according to:
D ′ + R = rgD + G , (20)
where R is government revenue and G is governmentexpenditures.
I R and G have explicit model components. For revenue,federal income taxes (FIT) and payroll taxes (SSREV), andfor expenditures, Social Security expenditures (SSEXP).
I We can expand (20) as follows:
D ′ + FIT + SSREV = rgD + SSEXP + G̃ (21)
where G̃ is the non-interest government budget surplus notaccounted by the explicit model revenue and expenditurecomponents.
Simulating Debt Over the Transition Path
I Process of matching CBO debt projection:
1. Choose G̃ to match CBO non-interest surplus in each year inthe open economy.
2. Use CBO government interest rates to generate debt sequence(generates exactly the CBO debt projection).
3. Use resulting G̃ from open economy (no macroeconomicfeedback from debt) to construct government budget in closedeconomy.
I Key intuition: CBO debt projections correspond to our openeconomy (no feedback effects of debt).
I Baseline closed economy accounts for macroeconomicfeedback from this debt sequence.
Calibration Overview and Key Parameters
I Frisch Labor Supply Elasticity: 0.5.
I Elasticity of Intertemporal Substitution: 0.5
I Discount factor (β): 0.985 (KY = 3)
I Depreciation (δ): 0.085 ( δKY = 25.5%)
I Capital share (α): 0.45
I Population growth rate: 1.2%
Key Examples
I Payroll tax increase in 2017: 14.4%, 15.4%, 16.4%
I Benefit change in 2017: 15% ↑, 15% ↓, 25% ↓
I Open economy
I Behavior driven directly by policy
I Closed economy
I Short-run: Behavior driven directly by policy
I Long-run: Behavior dominated by debt’s effect on prices
Open Economy
Open Economy Baseline Debt
2010 2020 2030 2040 2050 2060 2070 2080 20900.6
0.8
1
1.2
1.4
1.6
1.8D
ebt-
to-O
utpu
t
CBOBaseline Economy
Example: Increasing the payroll tax
Payroll Tax Increase: Solving the Model
Process:
1. Solve the baseline economy (open economy first forgovernment debt sequence, then closed), store decision rules.
2. Apply higher tax rates to baseline decision rules and prices forstatic revenue sequence.
3. Aggregate to generate static score over the transition path.
4. Solve equilibrium given higher tax rates to generate optimalresponses and macroeconomic feedback.
5. Aggregate to generate dynamic sequence.
6. Take ratio of dynamic-to-static revenue sequence.
7. Multiply this ratio and micro-simulation estimate to generatedynamic score.
Effect of Tax Increase on Labor Supply
2010 2020 2030 2040 2050 2060 2070 2080 20900.985
0.99
0.995
1
1.005
1.01
1.015La
bor
Sup
ply
Rel
ativ
e to
Bas
elin
e
Payroll tax = 14.4%Payroll tax = 15.4%Payroll tax = 16.4%One-line
Payroll Tax Revenue Dynamic-to-Static Ratio
2010 2020 2030 2040 2050 2060 2070 2080 20900.985
0.99
0.995
1
1.005
1.01
1.015P
ayro
ll T
ax R
even
ue
Payroll tax = 14.4%Payroll tax = 15.4%Payroll tax = 16.4%
SS Expenditures Dynamic-to-Static Ratio
2010 2020 2030 2040 2050 2060 2070 2080 20900.9965
0.997
0.9975
0.998
0.9985
0.999
0.9995
1
1.0005S
S E
xpen
ditu
res
Payroll tax = 14.4%Payroll tax = 15.4%Payroll tax = 16.4%One-line
Effect of Tax Increase on Household Savings
2010 2020 2030 2040 2050 2060 2070 2080 20900.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01S
avin
g R
elat
ive
to B
asel
ine
Payroll tax = 14.4%Payroll tax = 15.4%Payroll tax = 16.4%One-line
Projected Debt: Payroll Tax Increase
2010 2020 2030 2040 2050 2060 2070 2080 20900
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8D
ebt-
to-O
utpu
t
BaselinePayroll tax = 14.4%Payroll tax = 15.4%Payroll tax = 16.4%
Example: Changing Social Security benefits
Effect of Benefit Change on Labor Supply
2010 2020 2030 2040 2050 2060 2070 2080 20900.985
0.99
0.995
1
1.005
1.01La
bor
Sup
ply
Rel
ativ
e to
Bas
elin
e
Benefit increase = 15%Benefit cut = 15%Benefit cut = 25%One-line
Payroll Tax Revenue Dynamic-to-Static Ratio
2010 2020 2030 2040 2050 2060 2070 2080 20900.988
0.99
0.992
0.994
0.996
0.998
1
1.002
1.004
1.006
1.008P
ayro
ll T
ax R
even
ue
Benefit increase = 15%Benefit cut = 15%Benefit cut = 25%One-line
SS Expenditures Dynamic-to-Static Ratio
2010 2020 2030 2040 2050 2060 2070 2080 20900.992
0.994
0.996
0.998
1
1.002
1.004S
S E
xpen
ditu
res
Benefit increase = 15%Benefit cut = 15%Benefit cut = 25%One-line
Effect of Benefit Change on Household Savings
2010 2020 2030 2040 2050 2060 2070 2080 20900.9
0.95
1
1.05
1.1
1.15
1.2S
avin
g R
elat
ive
to B
asel
ine
Benefit increase = 15%Benefit cut = 15%Benefit cut = 25%One-Line
Projected Debt: Benefit Change
2010 2020 2030 2040 2050 2060 2070 2080 20900
0.5
1
1.5
2
2.5D
ebt-
to-O
utpu
t
BaselineBenefit increase = 15%Benefit cut = 15%Benefit cut = 25%
Effects of Debt
I Open economy: baseline prices and other variables unaffectedby debt
I Closed economy: baseline prices significantly affected bygrowing debt
I Rising debt reduces total capital ⇒ interest rates increase
I Wages driven down ⇒ labor supply declines
I Decline in capital and labor ⇒ decline in output
Closed Economy
Closed Economy Baseline Debt
2010 2020 2030 2040 2050 2060 2070 2080 20900.5
1
1.5
2
2.5
3
3.5
4D
ebt-
to-O
utpu
t
CBOBaseline Economy
Baseline Wage
2010 2020 2030 2040 2050 2060 2070 2080 20900.75
0.8
0.85
0.9
0.95
1B
asel
ine
Wag
es
Baseline Labor Supply
2010 2020 2030 2040 2050 2060 2070 2080 20900.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1B
asel
ine
Labo
r S
uppl
y
Baseline Interest Rates
2010 2020 2030 2040 2050 2060 2070 2080 20900.96
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14B
asel
ine
Inte
rest
Rat
es (
abso
lute
rat
es)
MPKPortfolio RateGrowth-Adjusted Government Rate
Baseline Saving
2010 2020 2030 2040 2050 2060 2070 2080 20900.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
1.18B
asel
ine
Sav
ing
Baseline Total Capital
2010 2020 2030 2040 2050 2060 2070 2080 20900.4
0.5
0.6
0.7
0.8
0.9
1B
asel
ine
Tot
al C
apita
l
Baseline Output
2010 2020 2030 2040 2050 2060 2070 2080 20900.65
0.7
0.75
0.8
0.85
0.9
0.95
1B
asel
ine
Out
put
Example: Increasing the payroll tax
Effect of Tax Increase on Wages
2010 2020 2030 2040 2050 2060 2070 2080 20900.95
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4W
ages
Rel
ativ
e to
Bas
elin
e
Payroll tax = 14.4%Payroll tax = 15.4%Payroll tax = 16.4%One-line
Effect of Tax Increase on Labor Supply
2010 2020 2030 2040 2050 2060 2070 2080 20900.98
1
1.02
1.04
1.06
1.08
1.1
1.12La
bor
Sup
ply
Rel
ativ
e to
Bas
elin
e
Payroll tax = 14.4%Payroll tax = 15.4%Payroll tax = 16.4%One-line
Payroll Tax Revenue Dynamic-to-Static Ratio
2010 2020 2030 2040 2050 2060 2070 2080 20900.9
1
1.1
1.2
1.3
1.4
1.5
1.6P
ayro
ll T
ax R
even
ue
Payroll tax = 14.4%Payroll tax = 15.4%Payroll tax = 16.4%One-line
SS Expenditures Dynamic-to-Static Ratio
2010 2020 2030 2040 2050 2060 2070 2080 20900.99
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09S
S E
xpen
ditu
res
Payroll tax = 14.4%Payroll tax = 15.4%Payroll tax = 16.4%One-line
Effect of Tax Increase on Portfolio Rates
2010 2020 2030 2040 2050 2060 2070 2080 20901.055
1.06
1.065
1.07
1.075
1.08
1.085P
ortfo
lio R
ates
(ab
solu
te r
ates
)
BaselinePayroll tax = 14.4%Payroll tax = 15.4%Payroll tax = 16.4%
Effect of Tax Increase on Household Savings
2010 2020 2030 2040 2050 2060 2070 2080 20900.8
0.85
0.9
0.95
1
1.05S
avin
g R
elat
ive
to B
asel
ine
Payroll tax = 14.4%Payroll tax = 15.4%Payroll tax = 16.4%One-line
Projected Debt: Payroll Tax Increase
2010 2020 2030 2040 2050 2060 2070 2080 20900
0.5
1
1.5
2
2.5
3
3.5
4D
ebt-
to-O
utpu
t
BaselinePayroll tax = 14.4%Payroll tax = 15.4%Payroll tax = 16.4%
Example: Changing Social Security benefits
Effect of Benefit Change on Wages
2010 2020 2030 2040 2050 2060 2070 2080 20900.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5W
ages
Rel
ativ
e to
Bas
elin
e
Benefit increase = 15%Benefit cut = 15%Benefit cut = 25%One-line
Effect of Benefit Change on Labor Supply
2010 2020 2030 2040 2050 2060 2070 2080 20900.85
0.9
0.95
1
1.05
1.1
1.15La
bor
Sup
ply
Rel
ativ
e to
Bas
elin
e
Benefit increase = 15%Benefit cut = 15%Benefit cut = 25%One-line
Payroll Tax Revenue Dynamic-to-Static Ratio
2010 2020 2030 2040 2050 2060 2070 2080 20900.6
0.8
1
1.2
1.4
1.6
1.8P
ayro
ll T
ax R
even
ue
Benefit increase = 15%Benefit cut = 15%Benefit cut = 25%One-line
SS Expenditures Dynamic-to-Static Ratio
2010 2020 2030 2040 2050 2060 2070 2080 20900.9
0.95
1
1.05
1.1
1.15S
S E
xpen
ditu
res
Benefit increase = 15%Benefit cut = 15%Benefit cut = 25%One-line
Effect of Benefit Change on Portfolio Rates
2010 2020 2030 2040 2050 2060 2070 2080 20901.05
1.06
1.07
1.08
1.09
1.1
1.11
1.12
1.13P
ortfo
lio R
ates
(ab
solu
te r
ates
)
BaselineBenefit increase = 15%Benefit cut = 15%Benefit cut = 25%
Policy Effect on Household Savings: Benefit Change
2010 2020 2030 2040 2050 2060 2070 2080 20900.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12S
avin
g R
elat
ive
to B
asel
ine
Benefit increase = 15%Benefit cut = 15%Benefit cut = 25%One-Line
Projected Debt: Benefit Change
2010 2020 2030 2040 2050 2060 2070 2080 20900
1
2
3
4
5
6
7
8
9D
ebt-
to-O
utpu
t
BaselineBenefit increase = 15%Benefit cut = 15%Benefit cut = 25%
Open or Closed Economy?
I To generate a single dynamic score, we take a convexcombination of open and closed economy dynamic score.
I Weight: 40% open, 60% closed.
I Motivated by foreign accumulation of U.S. Treasury Debt.
U.S. Treasury Debt Holdings
Penn Wharton Budget Model Dynamic Scoring
I Dynamic models can evaluate behavioral responses andmacroeconomic feedback, but they lack richness because ofextreme computational demands.
I Micro-simulation models have detailed demographics andextensive heterogeneity, but they lack rigorous behavioral andfeedback measurements.
I Our approach combines the strengths of both models toevaluate policy.