The Heterogeneous Effects of Government Spending: It’s All About Taxes. Axelle Ferriere 1 Gaston Navarro 2 1 European University Institute 2 Federal Reserve Board March 2017 These views are those of the authors and not necessarily those of the Board of Governors or the Federal Reserve System.
80
Embed
The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
The Heterogeneous Effects of GovernmentSpending: It’s All About Taxes.
Axelle Ferriere1 Gaston Navarro2
1European University Institute
2Federal Reserve Board
March 2017
These views are those of the authors and not necessarily those of the Board of Governors or the Federal Reserve System.
Motivation
Question:
How expansionary is government spending?
I Evidence: output increases, consumption does not decrease.(Barro & Redlick, 2011), (Blanchard & Perotti, 2002), (Ramey, 2016) More
I Puzzle: “Standard” models predict:
o A moderate output expansion, and a consumption decrease.(Hall, 2009)
o A contraction if distortionary taxes are used.(Baxter & King, 1993), (Uhlig, 2010) More
Notes: News variable is normalized by last quarter GDP. Source Ramey & Zubairy (2015). Vertical lines correspondto major military events.
A tax progressivity measure
Assume a non-linear income tax: τ(y) = 1− λy−γ(Heathcote, Storesletten & Violante, 2013), (Feenberg, Ferriere & Navarro, 2016)
More
I Tax progressivity is captured by More
o If = 0: flat tax rate τ(y) = 1− λo If > 0: progressive tax τ ′(y) > 0
o If = 1: full redistribution [1− τ(y)]y = λ ∀y
I Compute γ for 1913-2012 as More
γ =AMTR − ATR
1− ATR
AMTR = average marginal tax rate, ATR = average tax rate
I Robustness using NBER TAXSIM data.
A tax progressivity measure
Assume a non-linear income tax: τ(y) = 1− λy−γ(Heathcote, Storesletten & Violante, 2013), (Feenberg, Ferriere & Navarro, 2016)
More
I Tax progressivity is captured by γ More
o If γ = 0: flat tax rate τ(y) = 1− λo If γ > 0: progressive tax τ ′(y) > 0
o If γ = 1: full redistribution [1− τ(y)]y = λ ∀y
I Compute γ for 1913-2012 as More
γ =AMTR − ATR
1− ATR
AMTR = average marginal tax rate, ATR = average tax rate
I Robustness using NBER TAXSIM data.
A tax progressivity measure
Assume a non-linear income tax: τ(y) = 1− λy−γ(Heathcote, Storesletten & Violante, 2013), (Feenberg, Ferriere & Navarro, 2016)
More
I Tax progressivity is captured by γ More
o If γ = 0: flat tax rate τ(y) = 1− λo If γ > 0: progressive tax τ ′(y) > 0
o If γ = 1: full redistribution [1− τ(y)]y = λ ∀y
I Compute γ for 1913-2012 as More
γ =AMTR − ATR
1− ATR
AMTR = average marginal tax rate, ATR = average tax rate
I Robustness using NBER TAXSIM data.
A tax progressivity measure
Assume a non-linear income tax: τ(y) = 1− λy−γ(Heathcote, Storesletten & Violante, 2013), (Feenberg, Ferriere & Navarro, 2016)
More
I Tax progressivity is captured by γ More
o If γ = 0: flat tax rate τ(y) = 1− λo If γ > 0: progressive tax τ ′(y) > 0
o If γ = 1: full redistribution [1− τ(y)]y = λ ∀y
I Compute γ for 1913-2012 as More
γ =AMTR − ATR
1− ATR
AMTR = average marginal tax rate, ATR = average tax rate
I Robustness using NBER TAXSIM data.
A century of U.S. tax progressivity
Notes: Tax progressivity corresponds to one minus tax-rate elasticity with respect to income. Authors’ computations.
A century of U.S. tax progressivity
Notes: Tax progressivity corresponds to one minus tax-rate elasticity with respect to income. Authors’ computations.Vertical lines correspond to major military events.
State dependent multipliers: local projection
The linear case: Jorda (2005)
o For a vector xt+h =[Yt+h−Yt−1
Yt−1, Gt+h−Gt−1
Yt−1
]xt+h = αh + AhZt−1 + βhg
∗t + trend + εt+h
- Shock g∗t
- Control Zt : lags of GDP, total spending and g∗t
o Cumulative multiplier at horizon h
mh =
h∑j=0
βYj
/
h∑j=0
βGj
State dependent multipliers: local projection
The linear case: Jorda (2005)
o For a vector xt+h =[Yt+h−Yt−1
Yt−1, Gt+h−Gt−1
Yt−1
]xt+h = αh + AhZt−1 + βhg
∗t + trend + εt+h
- Shock g∗t
- Control Zt : lags of GDP, total spending and g∗t
o Cumulative multiplier at horizon h
mh =
h∑j=0
βYj
/
h∑j=0
βGj
State dependent multipliers: local projection
The state-dependent case: Ramey and Zubairy (2016)
o For a vector xt+h =[Yt+h−Yt−1
Yt−1, Gt+h−Gt−1
Yt−1
]xt+h = I (st = P)
{αh,P + Ah,PZt−1 + βh,Pg
∗t
}+ I (st = R)
{αh,R + Ah,RZt−1 + βh,Rg
∗t
}+ trend + εt+h
o Progressive state (st = P) if γ is higher on average for the next 3 years.
More
+ Cumulative multiplier mh,P ,mh,R
o An Instrumental Variable estimation:
More More
+ Ramey and Blanchard Perotti shocks
State dependent multipliers: local projection
The state-dependent case: Ramey and Zubairy (2016)
o For a vector xt+h =[Yt+h−Yt−1
Yt−1, Gt+h−Gt−1
Yt−1
]xt+h = I (st = P)
{αh,P + Ah,PZt−1 + βh,Pg
∗t
}+ I (st = R)
{αh,R + Ah,RZt−1 + βh,Rg
∗t
}+ trend + εt+h
o Progressive state (st = P) if γ is higher on average for the next 3 years.
More+ Cumulative multiplier mh,P ,mh,R
o An Instrumental Variable estimation:
More More+ Ramey and Blanchard Perotti shocks
State dependent multipliers: local projection
The state-dependent case: Ramey and Zubairy (2016)
o For a vector xt+h =[Yt+h−Yt−1
Yt−1, Gt+h−Gt−1
Yt−1
]xt+h = I (st = P)
{αh,P + Ah,PZt−1 + βh,Pg
∗t
}+ I (st = R)
{αh,R + Ah,RZt−1 + βh,Rg
∗t
}+ trend + εt+h
o Progressive state (st = P) if γ is higher on average for the next 3 years.
More+ Cumulative multiplier mh,P ,mh,R
o An Instrumental Variable estimation:
More More+ Ramey and Blanchard Perotti shocks
Output multiplier: the linear case
Notes: Local projection; data 1913-2006; confidence intervals: 68%.
Output multipliers across states
Notes: Local projection; data 1913-2006; confidence intervals: 68%; window: 12 quarters.
Model
A Bewley economy with indivisible labor
Description of the steady-state:
+ A continuum of households:
- Bond economy with borrowing constraint.
- Indivisible labor choice.
- Idiosyncratic labor productivity shock.
More
+ A representative firm
+ Government:
- A constant level of government expenditures G .
- Financed by constant taxes and debt.
Households
The value function of an agent with productivity x and assets a is:
V (a, x) = maxc,a′,h∈{0,h̄}
{log c − D
h1+Φ
1 + Φ+ βEx′ [V (a′, x ′) |x ]
}subject to
c + a′ ≤ wxh + (1 + r)a− τk ra− τ (wxh) , a′ ≥ a
Productivity follows an AR(1) process: log(x it+1) = ρx log(x it ) + σxεit+1.
Tax progressivity will be captured by the shape of τ(·).
Firm and government
Government:
I Constant government expenditures G
I Government’s budget:
G + (1 + r)B = B +
∫{τk ra + τ (wxh)} dµ(a, x)
Firms:
+ Cobb-Douglas production function: Y = LαK 1−α
+ Firm’s static problem:
Π = maxK ,L
{LαK 1−α − wL− (r + δ)K
}Equilibrium definition Calibration Distribution of Wealth and Employment
Firm and government
Government:
I Constant government expenditures G
I Government’s budget:
G + (1 + r)B = B +
∫{τk ra + τ (wxh)} dµ(a, x)
Firms:
+ Cobb-Douglas production function: Y = LαK 1−α
+ Firm’s static problem:
Π = maxK ,L
{LαK 1−α − wL− (r + δ)K
}Equilibrium definition Calibration Distribution of Wealth and Employment
Government spending shocks
Experiment:
+ At t = 0, an unexpected shock:
- G increases by 1% and returns to steady state.
+ Financed with:
- Constant B and τ k
- A path for progressivity {γt}:
γt − γ = η(Gt − G )
- Adjust {λt} to satisfy its budget constraint:
Gt+rtB = τk rtKt+
∫ (1− λt(wtxht(a, x))−γt
)wtxht(a, x)dµt(a, x)
Government spending shocks
Experiment:
+ At t = 0, an unexpected shock:
- G increases by 1% and returns to steady state.
+ Financed with:
- Constant B and τ k
- A path for progressivity {γt}:
γt − γ = η(Gt − G )
- Adjust {λt} to satisfy its budget constraint:
Gt+rtB = τk rtKt+
∫ (1− λt(wtxht(a, x))−γt
)wtxht(a, x)dµt(a, x)
Effects of spending depend on tax progressivity
0 10 20 30 40
%
0
0.2
0.4
0.6
0.8
1
Government Spending
0 10 20 30 40
0.085
0.09
0.095
0.1
0.105
0.11
0.115
Progressivity Measure γ
0 10 20 30 40
0.14
0.145
0.15
0.155
0.16
Tax Level 1− λ
Effects of spending depend on tax progressivity
0 10 20 30 40
%
0
0.2
0.4
0.6
0.8
1
Government Spending
0 10 20 30 40
0.085
0.09
0.095
0.1
0.105
0.11
0.115
Progressivity Measure γ
0 10 20 30 40
0.14
0.145
0.15
0.155
0.16
Tax Level 1− λ
0 5 10 15 20 25 30 35 40
%
-0.2
-0.15
-0.1
-0.05
0
Output
0 5 10 15 20 25 30 35 40
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
Consumption
Effects of spending depend on tax progressivity
0 10 20 30 40
%
0
0.2
0.4
0.6
0.8
1
Government Spending
0 10 20 30 40
0.085
0.09
0.095
0.1
0.105
0.11
0.115
Progressivity Measure γ
0 10 20 30 40
0.14
0.145
0.15
0.155
0.16
Tax Level 1− λ
= Progressivity
⇑ Progressivity
Effects of spending depend on tax progressivity
0 10 20 30 40
%
0
0.2
0.4
0.6
0.8
1
Government Spending
0 10 20 30 40
0.085
0.09
0.095
0.1
0.105
0.11
0.115
Progressivity Measure γ
0 10 20 30 40
0.14
0.145
0.15
0.155
0.16
Tax Level 1− λ
= Progressivity
⇑ Progressivity
0 5 10 15 20 25 30 35 40
%
-0.2
-0.1
0
0.1
0.2
Output
0 5 10 15 20 25 30 35 40
-0.1
-0.05
0
0.05
0.1
Consumption
Effects of spending depend on tax progressivity
0 10 20 30 40
%
0
0.2
0.4
0.6
0.8
1
Government Spending
0 10 20 30 40
0.085
0.09
0.095
0.1
0.105
0.11
0.115
Progressivity Measure γ
0 10 20 30 40
0.14
0.145
0.15
0.155
0.16
Tax Level 1− λ
= Progressivity
⇑ Progressivity
⇓ Progressivity
Effects of spending depend on tax progressivity
0 10 20 30 40
%
0
0.2
0.4
0.6
0.8
1
Government Spending
0 10 20 30 40
0.085
0.09
0.095
0.1
0.105
0.11
0.115
Progressivity Measure γ
0 10 20 30 40
0.14
0.145
0.15
0.155
0.16
Tax Level 1− λ
= Progressivity
⇑ Progressivity
⇓ Progressivity
0 5 10 15 20 25 30 35 40
%
-0.6
-0.4
-0.2
0
0.2
Output
0 5 10 15 20 25 30 35 40
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
Consumption
Heterogeneous changes in tax rates...
0 10 20 30 40
%
15
15.5
16
16.5
Labor Tax - Total Average
0 10 20 30 40
7
7.5
8
8.5
9
1st Quintile
0 10 20 30 40
14.5
15
15.5
16
2nd Quintile
Quarter0 10 20 30 40
%
17
17.5
18
18.5
3rd Quintile
Quarter0 10 20 30 40
19
19.5
20
20.5
4th Quintile
Quarter0 10 20 30 40
22
22.5
23
23.55th Quintile
... result in heterogenous responses More
0 10 20 30 40
0
0.2
0.4
0.6
0.8
1
%
Government Spending
0 10 20 30 40-0.2
0
0.2
0.4
0.6
0.81st Quintile
hours
consumption
0 10 20 30 40-0.2
0
0.2
0.4
0.6
0.82nd Quintile
0 10 20 30 40
Quarters
-0.2
0
0.2
0.4
0.6
0.8
%
3rd Quintile
0 10 20 30 40
Quarters
-0.2
0
0.2
0.4
0.6
0.84th Quintile
0 10 20 30 40
Quarters
-0.2
0
0.2
0.4
0.6
0.85th Quintile
Intratemporal and intertemporal tax allocation More
How important is debt financing?
Exercise:
+ Same path for {Gt} and {γt} as before.
+ A fraction financed with debt, implies a different path for {λt}.
+ Uhlig (2010): Bt+1 − Bss = (1− ϕ)(ωt − ωss),
WVWXXXXWWwhere ωt = Gt + rtBt − τ k rtAt .
I ϕ = 1: no additional debtI ϕ = 0.05: ≈ 95% of additional spending financed with debt
Intratemporal and intertemporal tax allocation
Micro evidence
State dependent multipliers: local projection
State-dependent local projection method:
o For a vector xt+h =[Yt+h−Yt−1
Yt−1, Gt+h−Gt−1
Yt−1
]xt+h = I (st = P)
{αh,P + Ah,PZt−1 + βh,Pg
∗t
}+ I (st = R)
{αh,R + Ah,RZt−1 + βh,Rg
∗t
}+ trend + εt+h
o Cross-sectional data: TAXSIM
- Pre-tax income of all taxpayers
- 1962-2008; Interpolated (Chow-Lin)
Heterogenous responses across households
Notes: Local projection; data 1962-2006; confidence intervals: 68%; window: 12 quarters.
Solving the puzzle?(preliminary)
Quantitative investigation of the mechanism
+ Data: Typical path for {Gt} and {γt} after a spending shock
- News shock (Ramey), 1960-2006
Quantitative investigation: enough to change signs
Conclusion
+ Tax progressivity is crucial to spending multipliers.
I Heterogeneous responses across households
I Generate changes in signs of multipliers
+ Policy implications: use taxes, not spending More
Conclusion
+ Tax progressivity is crucial to spending multipliers.
I Heterogeneous responses across households
I Generate changes in signs of multipliers
+ Policy implications: use taxes, not spending More
Appendix
Evidence: Output and Consumption Multipliers Return
Output ConsumptionBlanchard and Perotti 0.90 0.5
(0.30) (0.21)
Gali, Lopez-Salido and Valles 0.41 0.1(0.16) (0.10)
Barro and Redlick 0.45 0.005(0.07) (0.09)
Mountford and Uhlig 0.65 0.001(0.39) (0.0003)
Ramey 0.30 0.02(0.10) (0.001)
Note: output/consumption multiplier refers to the increase in output/consumption after a unit increase ingovernment spending.
Why a Puzzle? Return Return
I Assume U(C ,H) = C 1−σ
1−σ − H1+ϕ
1+ϕ and competitive labor markets.
I Then (in logs)
log(1− τt↑) +
mpht
↓
= σct
⇓⇓
+ ϕht
↑
+ Indivisible labor of agents heterogeneous in productivity
+ Distribution of taxes
log(1− ↑↓τ it ) + mpht↓ ≶ σc it + ϕhit↑
+ Progressivity shapes the effects of government spending.
Why a Puzzle? Return Return
I Assume U(C ,H) = C 1−σ
1−σ − H1+ϕ
1+ϕ and competitive labor markets.
I Then (in logs)
log(1− τt↑) +
mpht ↓ = σct⇓
⇓
+ ϕht ↑
+ Indivisible labor of agents heterogeneous in productivity
+ Distribution of taxes
log(1− ↑↓τ it ) + mpht↓ ≶ σc it + ϕhit↑
+ Progressivity shapes the effects of government spending.
Why a Puzzle? Return Return
I Assume U(C ,H) = C 1−σ
1−σ − H1+ϕ
1+ϕ and competitive labor markets.
I Then (in logs)
log(1− τt↑) + mpht ↓ = σct⇓⇓+ ϕht ↑
+ Indivisible labor of agents heterogeneous in productivity
+ Distribution of taxes
log(1− ↑↓τ it ) + mpht↓ ≶ σc it + ϕhit↑
+ Progressivity shapes the effects of government spending.
Why a Puzzle? Return Return
I Assume U(C ,H) = C 1−σ
1−σ − H1+ϕ
1+ϕ and competitive labor markets.
I Then (in logs)
log(1− τt↑) + mpht ↓ = σct⇓⇓+ ϕht ↑
+ Indivisible labor of agents heterogeneous in productivity
+ Distribution of taxes
log(1− ↑↓τ it ) +
mpht↓ ≶ σc it + ϕhit↑
+ Progressivity shapes the effects of government spending.
Why a Puzzle? Return Return
I Assume U(C ,H) = C 1−σ
1−σ − H1+ϕ
1+ϕ and competitive labor markets.
I Then (in logs)
log(1− τt↑) + mpht ↓ = σct⇓⇓+ ϕht ↑
+ Indivisible labor of agents heterogeneous in productivity
+ Distribution of taxes
log(1− ↑↓τ it ) + mpht↓ ≶ σc it + ϕhit↑
+ Progressivity shapes the effects of government spending.
Why a Puzzle? Return Return
I Assume U(C ,H) = C 1−σ
1−σ − H1+ϕ
1+ϕ and competitive labor markets.
I Then (in logs)
log(1− τt↑) + mpht ↓ = σct⇓⇓+ ϕht ↑
+ Indivisible labor of agents heterogeneous in productivity
+ Distribution of taxes
log(1− ↑↓τ it ) + mpht↓ ≶ σc it + ϕhit↑
+ Progressivity shapes the effects of government spending.
A Progressive Taxation Scheme Return
A non-linear labor income tax τ(y) ≡ 1− λy−γ
0 5 10 15 20 25 30−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Income
Tax
rat
e
1−λ = 0.12, γ = 0.1
A Progressive Taxation Scheme Return
A non-linear labor income tax τ(y) ≡ 1− λy−γ
0 5 10 15 20 25 30−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Income
Tax
rat
e
1−λ = 0.12, γ = 0.11−λ = 0.12, γ = 0.2
A Progressive Taxation Scheme Return
A non-linear labor income tax τ(y) ≡ 1− λy−γ
0 5 10 15 20 25 30−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Income
Tax
rat
e
1−λ = 0.12, γ = 0.11−λ = 0.3, γ = 0.1
Heathcote Storesletten Violante (2016) Return
Measurement of τUS
• PSID 2000-06, age of head of hh 25-60, N = 12, 943
• Pre gov. income: income minus deductions (medical expenses,state taxes, mortgage interest and charitable contributions)
• Post-gov income: ... minus taxes (TAXSIM) plus transfers
Share of Wealth- PSID Data −0.00 0.02 0.07 0.15 0.77- Model −0.01 0.04 0.12 0.25 0.61
Participation Rate- PSID Data 0.65 0.75 0.69 0.60 0.57- Model 0.83 0.63 0.57 0.52 0.45
The PSID statistics reflect the family wealth and earnings in the 1984 survey. Thestatistics of ”primary households’ are those for household heads whose education was12 years and whose age is between 35 and 55.
Hours and consumption: households distribution Return
Notes: Income is defined as y(a, x) = wxh(a, x) + (1 + r)a − τ(wxh, ar).
Hours and consumption: households distribution Return
Notes: Income is defined as y(a, x) = wxh(a, x) + (1 + r)a − τ(wxh, ar).
Timing of the change in progressivity Return
How important is the timing of the increase in tax progressivity?
Exercise:
+ Same path for {Gt}.+ {γt} does not react on impact, increases slowly until quarter 5.
+ Debt: Φ = .05
Timing of the change in progressivity Return
0 10 20 30 400
0.2
0.4
0.6
0.8
1
%
Government Spending
0 10 20 30 400.1
0.102
0.104
0.106
0.108
0.11Progressivity Measure γ
0 10 20 30 400.142
0.143
0.144
0.145
0.146
0.147
0.148
0.149Tax Level 1− λ
0 10 20 30 40-0.05
0
0.05
0.1
0.15
0.2
0.25
%
Output
0 10 20 30 40-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
Consumption
0 10 20 30 40-0.05
0
0.05
0.1
0.15
0.2
0.25Government Debt
Use taxes, not spending Return
What is the effect of a temporary increase in progressivity?