penn wharton budget model: dynamics€¦ · dynamic scoring i process of using dynamic model to...

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


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


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


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



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


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


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



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



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


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

)


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


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


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


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



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



2010 2020 2030 2040 2050 2060 2070 2080 20900.9

0.95

1

1.05

1.1

1.15S

S E

xpen

ditu

res


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

)


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


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.

penn wharton budget model: dynamics€¦ · dynamic scoring i process of using dynamic model to...

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