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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.
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The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Apr 13, 2017

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Page 1: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 2: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Previous work: Nominal rigidities + Non-Ricardian agents.

Page 3: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Previous work: Nominal rigidities + Non-Ricardian agents.

Page 4: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Previous work: Nominal rigidities + Non-Ricardian agents.

Page 5: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

What we do

This paper:

Revisit this question, taking into account tax distribution.

I Macro evidence:

o Positive spending multipliers only in periods of higher progressivity

- Tax progressivity in the U.S. [1913-2012]

- Large changes associated with spending shocks

I Model:

o Larger multipliers when spending financed with more progressive taxes

- Heterogeneous households & indivisible labor

- Elasticities decline with income

I Micro evidence

I A quantitative evaluation of the mechanism

Page 6: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

What we do

This paper:

Revisit this question, taking into account tax distribution.

I Macro evidence:

o Positive spending multipliers only in periods of higher progressivity

- Tax progressivity in the U.S. [1913-2012]

- Large changes associated with spending shocks

I Model:

o Larger multipliers when spending financed with more progressive taxes

- Heterogeneous households & indivisible labor

- Elasticities decline with income

I Micro evidence

I A quantitative evaluation of the mechanism

Page 7: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

What we do

This paper:

Revisit this question, taking into account tax distribution.

I Macro evidence:

o Positive spending multipliers only in periods of higher progressivity

- Tax progressivity in the U.S. [1913-2012]

- Large changes associated with spending shocks

I Model:

o Larger multipliers when spending financed with more progressive taxes

- Heterogeneous households & indivisible labor

- Elasticities decline with income

I Micro evidence

I A quantitative evaluation of the mechanism

Page 8: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

What we do

This paper:

Revisit this question, taking into account tax distribution.

I Macro evidence:

o Positive spending multipliers only in periods of higher progressivity

- Tax progressivity in the U.S. [1913-2012]

- Large changes associated with spending shocks

I Model:

o Larger multipliers when spending financed with more progressive taxes

- Heterogeneous households & indivisible labor

- Elasticities decline with income

I Micro evidence

I A quantitative evaluation of the mechanism

Page 9: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

What we do

This paper:

Revisit this question, taking into account tax distribution.

I Macro evidence:

o Positive spending multipliers only in periods of higher progressivity

- Tax progressivity in the U.S. [1913-2012]

- Large changes associated with spending shocks

I Model:

o Larger multipliers when spending financed with more progressive taxes

- Heterogeneous households & indivisible labor

- Elasticities decline with income

I Micro evidence

I A quantitative evaluation of the mechanism

Page 10: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

What we do

This paper:

Revisit this question, taking into account tax distribution.

I Macro evidence:

o Positive spending multipliers only in periods of higher progressivity

- Tax progressivity in the U.S. [1913-2012]

- Large changes associated with spending shocks

I Model:

o Larger multipliers when spending financed with more progressive taxes

- Heterogeneous households & indivisible labor

- Elasticities decline with income

I Micro evidence

I A quantitative evaluation of the mechanism

Page 11: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

What we do

This paper:

Revisit this question, taking into account tax distribution.

I Macro evidence:

o Positive spending multipliers only in periods of higher progressivity

- Tax progressivity in the U.S. [1913-2012]

- Large changes associated with spending shocks

I Model:

o Larger multipliers when spending financed with more progressive taxes

- Heterogeneous households & indivisible labor

- Elasticities decline with income

I Micro evidence

I A quantitative evaluation of the mechanism

Page 12: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Macro evidence

Page 13: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Government spending measures

1920 1930 1940 1950 1960 1970 1980 1990 2000

0

0.002

0.004

0.006

0.008

0.01

Government Spending

Quarter1920 1930 1940 1950 1960 1970 1980 1990 2000

-50

0

50

100

News on Defense Spending

Notes: News variable is normalized by last quarter GDP. Source Ramey & Zubairy (2015). Vertical lines correspondto major military events.

Page 14: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 15: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 16: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 17: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 18: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

A century of U.S. tax progressivity

Notes: Tax progressivity corresponds to one minus tax-rate elasticity with respect to income. Authors’ computations.

Page 19: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 20: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 21: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 22: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 23: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 24: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 25: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Output multiplier: the linear case

Notes: Local projection; data 1913-2006; confidence intervals: 68%.

Page 26: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Output multipliers across states

Notes: Local projection; data 1913-2006; confidence intervals: 68%; window: 12 quarters.

Page 27: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Model

Page 28: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 29: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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(·).

Page 30: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 31: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 32: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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)

Page 33: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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)

Page 34: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 35: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 36: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 37: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 38: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 39: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 40: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 41: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

... 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

Page 42: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 43: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Intratemporal and intertemporal tax allocation

Page 44: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Micro evidence

Page 45: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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)

Page 46: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Heterogenous responses across households

Notes: Local projection; data 1962-2006; confidence intervals: 68%; window: 12 quarters.

Page 47: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Solving the puzzle?(preliminary)

Page 48: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Quantitative investigation of the mechanism

+ Data: Typical path for {Gt} and {γt} after a spending shock

- News shock (Ramey), 1960-2006

Page 49: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Quantitative investigation: enough to change signs

Page 50: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 51: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 52: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Appendix

Page 53: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 54: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 55: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 56: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 57: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 58: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 59: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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.

Page 60: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 61: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 62: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 63: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

8.5 9 9.5 10 10.5 11 11.5 12 12.5 13

8.5

9

9.5

10

10.5

11

11.5

12

12.5

13

Log of Pre−government Income

Log

of D

ispo

sabl

e In

com

e

τUS = 0.161

Pre-government Income ×1050 1 2 3 4 5

Tax

Rate

s

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Marginal Tax RateAverage Tax Rate

Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”

Page 64: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Tax progressivity estimate Return

I Tax function given by τ(y) = 1− λy−γ

I Total tax T (y) = τ(y)y and marginal tax T ′(y).

I Simple algebra

γ =T ′(y)− τ(y)

1− τ(y)

I AMTR =∫T ′(y) from Barro & Redlick (2011) and Mertens (2015)

I ATR =∫τ(y) our computations using IRS data and Piketty & Saez

(2003)’s income measure.

Page 65: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Tax progressivity estimate Return

I Tax function given by τ(y) = 1− λy−γ

I Total tax T (y) = τ(y)y and marginal tax T ′(y).

I Simple algebra

γ =T ′(y)− τ(y)

1− τ(y)

I AMTR =∫T ′(y) from Barro & Redlick (2011) and Mertens (2015)

I ATR =∫τ(y) our computations using IRS data and Piketty & Saez

(2003)’s income measure.

Page 66: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Tax progressivity estimate Return

I Tax function given by τ(y) = 1− λy−γ

I Total tax T (y) = τ(y)y and marginal tax T ′(y).

I Simple algebra

γ =T ′(y)− τ(y)

1− τ(y)

I AMTR =∫T ′(y) from Barro & Redlick (2011) and Mertens (2015)

I ATR =∫τ(y) our computations using IRS data and Piketty & Saez

(2003)’s income measure.

Page 67: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Tax progressivity estimate - Robustness Return

Notes: TAXSIM measure is the elasticity of the tax function for fixed income distribution.

Page 68: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

State dependent multipliers: local projection Return

o Progressive state (st = P) if

1

Na

Na−1∑j=0

γt+j >1

Nb

Nb∑j=1

γt−j , Na = 12, Nb = 8.

o An Instrumental Variable estimation:

h∑j=0

∆yt+j = I (st = P)

αP,h + AP,HZt−1 + mP,h

h∑j=0

∆gt+j

+ I (st = R)

αR,h + AR,HZt−1 + mR,h

h∑j=0

∆gt+j

+ trend + εt+h

where ∆xt+j = (xt+h − xt−1)/Yt−1.

Page 69: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

State dependent multipliers: local projection Return

o Progressive state (st = P) if

1

Na

Na−1∑j=0

γt+j >1

Nb

Nb∑j=1

γt−j , Na = 12, Nb = 8.

o An Instrumental Variable estimation:

h∑j=0

∆yt+j = I (st = P)

αP,h + AP,HZt−1 + mP,h

h∑j=0

∆gt+j

+ I (st = R)

αR,h + AR,HZt−1 + mR,h

h∑j=0

∆gt+j

+ trend + εt+h

where ∆xt+j = (xt+h − xt−1)/Yt−1.

Page 70: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

State dependent multipliers: local projection Return

Notes: Spending shocks (Ramey) interacted with state St = P, R.

Page 71: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Equilibrium: definition Return

A stationary recursive competitive equilibrium is given by

+ Households’ value functions {V } and policies {c, a′, h}. Firm’s policies {L,K}.

+ Government’s policies {G , τ,B}+ A measure µ

such that given prices {r ,w}I Households and the firm solve their respective problems.

I Government runs a balanced budget.

I Markets clear

o Capital market clears: K + B =∫B a′(a, x)dµ(a, x)

o Labor market clears: L =∫B xh(a, x)dµ(a, x)

o Goods market clears: Y =∫B c(a, x)dµ(a, x) + δK + G

I Measure µ is stationary

µ(a′, x ′) =

∫I{a′(a, x) = a′}πx (x ′|x)dµ(a, x)

Page 72: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Calibration Return

+ Taxes:

- Flat capital tax rate: τk = 35% (Chen, et al., 2009)

- Progressive labor tax: γ = 0.1 (Heathcote, et al. 2013)

+ Structural parameters:

α = 0.64 Φ = 2.5 δ = 0.025 h̄ = 1/3 a = −2(ρx , σx) = (0.989, 0.287)

+ We calibrate (β,G ,D,B) s.t., in steady-state:

r = 0.01, G/Y = 0.15, E = 0.6, D/Y = 2.4

Distribution of Wealth and Employment

Page 73: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Calibration Return

+ Taxes:

- Flat capital tax rate: τk = 35% (Chen, et al., 2009)

- Progressive labor tax: γ = 0.1 (Heathcote, et al. 2013)

+ Structural parameters:

α = 0.64 Φ = 2.5 δ = 0.025 h̄ = 1/3 a = −2(ρx , σx) = (0.989, 0.287)

+ We calibrate (β,G ,D,B) s.t., in steady-state:

r = 0.01, G/Y = 0.15, E = 0.6, D/Y = 2.4

Distribution of Wealth and Employment

Page 74: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Househoulds Distribution Return

Quintiles 1st 2nd 3rd 4th 5th

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.

Page 75: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Hours and consumption: households distribution Return

Notes: Income is defined as y(a, x) = wxh(a, x) + (1 + r)a − τ(wxh, ar).

Page 76: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Hours and consumption: households distribution Return

Notes: Income is defined as y(a, x) = wxh(a, x) + (1 + r)a − τ(wxh, ar).

Page 77: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 78: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

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

Page 79: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Use taxes, not spending Return

What is the effect of a temporary increase in progressivity?

Exercise:

+ Same path for {γt} as before.

+ No increase in spending.

+ No debt.

Page 80: The heterogeneous effects of government spending, by Axelle Ferriere (European University Institute)

Use taxes, not spending Return

0 10 20 30 40

%

0

0.2

0.4

0.6

0.8

1Government Spending

Increased Spending

Fixed Spending

0 10 20 30 400.095

0.1

0.105

0.11

0.115Progressivity Measure γ

0 10 20 30 400.14

0.142

0.144

0.146

0.148

0.15Tax Level 1− λ

0 5 10 15 20 25 30 35 40

%

-0.05

0

0.05

0.1

0.15

0.2

0.25Output

0 5 10 15 20 25 30 35 40-0.05

0

0.05

0.1

0.15Consumption