What Fiscal Policy is Effective at Zero Interest Rates? Gauti B. - - PowerPoint PPT Presentation

What Fiscal Policy is Effective at Zero Interest Rates?

Gauti B. Eggertsson, NY Fed Talk at Atlanta Fed, Jan 2010 Talk at Atlanta Fed, Jan 2010

Motivation: Fiscal Expansion Today Motivation: Fiscal Expansion Today

• The current fiscal expansion the greatest in

The current fiscal expansion the greatest in peace time since 1933.

• Estimated deficits of gigantic proportions
• Estimated deficits of gigantic proportions
• Basic question: What’s the effect of cutting

d i i di i d d taxes and increasing spending in a standard New Keynesian model at zero interest rates.

Starting point: Some discussion l b d l

• n labor and capital tax cuts
• Labor tax cuts:

( ) – Bils and Klenow (2008):

• Payroll tax cuts stimulates employment directly by reducing tax

penalties

• “Works directly on demand”

Works directly on demand

• “Works under all business cycle models”

– Hall & Woodward, Becker, and Mankiw raise similar arguments. – Edward Prescott, Council of Foreign Relations: , g “Don’t subsidize inefficiency. Cut tax rates to get people to work

• more. This financial stuff is much ado about nothing.“
• Capital tax cuts

( ) – Barro (2009) “On the tax side, we should avoid programs that throw money at people and emphasize instead reductions in marginal income‐tax rates ‐‐ especially where these rates are already high and fall on capital p y y g p income.” ‐‐ Feldstein (2009)

This paper

• Standard “New Keynesian” model
• Fiscal policy under the “current circumstance”.

– Intertemporal shocks so that the nominal interest rate is zero (origin: Intertemporal shocks so that the nominal interest rate is zero (origin: financial sector)

• Consider temporary variations in taxes and spending in response to

this shock.

• Findings:

– Cutting labor taxes and/or capital taxes contractionary. – Cutting sales taxes, investment tax credit or increasing government spending expansionary spending expansionary.

• Special to zero interest rates:

– Cutting labor taxes “normally” expansionary – Cutting capital taxes “normally” has little effect Cutting capital taxes normally has little effect – Increasing government spending (cutting sales taxes) usually less than

• ne. Multiplier more than 6 times larger at zero (goes from 0.32 to

2.27). li i ’ i i l k i i i h – Implication: Can’t use empirical work at positive interest rate. Theory better benchmark.

Basic point Basic point

• At zero interest rates “insufficient demand” is the problem
• Policy (either tax cuts or spending increases) should aim at:

– INCREASING DEMAND – get more spending going. – Increasing supply is counterproductive

• Don’t want to produce more when the problem is that

p p there are not enough buyers!

• Paradox of thrift (old): Giving people the incentive to save

more (cutting capital taxes) reduces spending. [in more (cutting capital taxes) reduces spending. [in equilibrium this reduces aggregate savings ]

• Paradox of toil (new): Giving people the incentive to work

more counterproductive. More supply of labor ‐> lower more counterproductive. More supply of labor lower wages ‐> deflationary pressures higher real rates. [in equilibrium this reduces aggregate work ]

• Sidepoint: What did the “Obamaplan” do? Increase output

Sidepoint: What did the Obamaplan do? Increase output by 3.6 percent.

Plan Plan

1. Basic model, key results –

• i. contractionary labor income tax cuts
• ii. contractionary capital tax cuts

2 Other demand and supply policies

• 2. Other demand and supply policies
• i. a. expansionary government spending
• b. irrelevant government spending
• ii. sales tax cuts
• iii. Cutting taxes on profits and investment tax credit
• iv. monetary policy
• iv. monetary policy
• 3. Quantitative evaluations
• 4. Conclusions

The Model

Households

Utility

shock

T t T T N T S T T t T t

dj j L v G g G C u E ξ β

∑ ∫

∞ = −

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + +

1

)) ( ( ) ( ) ( max

s.t. budget constraint

T P t t t A t t

di i B i B Π − + + − =

∫

) ( ) 1 ( ) 1 )( 1 (

1 1 1 1

τ τ

Fiscal policy instruments

t t t s t T T w t T t t t t t

T C P dj j L j w − + − − +

∫ ∫

− − −

) 1 ( ) ( ) ( ) 1 ( ) ( ) ( ) )( (

1 1 1 1

τ τ

Consumption and price indices

θ θ θ θ θ θ − − − −

⎥ ⎤ ⎢ ⎡ ≡ ⎥ ⎤ ⎢ ⎡ ≡

∫ ∫

1 1 1 1 1 1 1

) ( ) ( di i p P di i c C

θ

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ≡ ⎥ ⎦ ⎢ ⎣ ≡

∫ ∫

) ( , ) ( di i p P di i c C

t t t t

The Model

Sticky Prices

Monapolistically competetive firms and linear production function

θ −

= ) ) ( ( ) (

t t t t

P i p Y i y

) ( ) ( i L i y

t t

=

Calvo prices. Fraction (1‐α) of firms set new prices in each period (exclusive of sales tax).

} ] ) )( ( ) ( )[ 1 ( ) ( { max

* * *

= − −

∑

∞ − − − t t P t T

Y p j w Y p p Q E

θ θ

τ αβ

t

Resource constraint

} ] ) )( ( ) ( )[ 1 ( ) ( { max

,

*

=

∑

=t T T T T T T t T T t t p

Y P j w Y P p Q E

t

τ αβ

N S

G G C Y + +

t t t t

G G C Y + + =

) 1 ( ) 1 ( ) 1 )( 1 (

1 1 , , s s t t t A t t t c t t t c

P P i u E u

+ +

+ + + − = τ τ ξ β ξ

t l t w t

v j W

,

) ( 1 = −τ

) 1 (

1 1 , , s t t

P

+ +

+τ

} ] ) ( [ ) )( 1 ( ) ( {

* 1 *

= − −

∑

∞ − − − T t T t P T T t t T

j W p Y p Q θ τ αβ

θ t c t s t

u P

,

1−τ } ] 1 [ ) )( ( ) ( {

,

−

∑

=t T T T T T T T t

P P P Q θ β

θ θ θ

α α

− − − +

=

1 1 1 1 *

] ) )( 1 [( P p P

≥

t

i

N t S t t t

G G C Y + + =

θ

α α

−

+ − =

1 1 ]

) )( 1 [(

t t t

P p P

t

} { } , , , , , , { } , , , {

* t N t S t p t s t A t w t t t t t t

G G i P p C Y ξ τ τ τ τ − −

Summarizing the model Summarizing the model

shock A s s N N t e t t t t t t

E G G E r E i Y E Y τ σ τ τ σ ξ π σ ˆ ) ˆ ˆ ( ) ˆ ˆ ( )) ( ( ˆ ˆ

1 1

+ + − − − =

+ +

AD

t t t t t t t

E G G E τ σ τ τ σ ) ( ) (

1 1

+ − − − +

+ +

AS

N t w t s t t t t t

G E Y ˆ ] ˆ ˆ [ ˆ

1 1 − +

− + + + = κψσ τ τ κψ π β κ π ≥

t

i

ZB

1 1

ˆ ˆ log

+ −

− + ≡

t t t e t

E r ξ ξ β

Baseline policy Baseline policy

) ˆ max(

e

Y r i φ π φ + + = ) , max(

t y t t t

Y r i φ π φπ + + = ˆ ˆ ˆ ˆ ˆ

A p w s

ˆ ˆ ˆ ˆ and = = = = =

A t p t w t s t t

G τ τ τ τ

Emphasis here: Policy on the margin i e “multipliers” Policy on the margin, i.e. multipliers Well defined “benchmark” and study perturbations from this benchmark Will not talk about optimal policy e.g. Ramsey or Markov Perfect allocations

.

Effect of labor income tax cuts: Standard when no shocks

Experiment: Consider a temporary tax cuts that are Experiment: Consider a temporary tax cuts that are reversed with probability 1‐μ

? ˆ = =

H H

Y π ? ˆ ? = =

L L

Y π

ˆ =

w H

τ

ˆ <

w L

τ

μ − 1 = t

e

T t =

AD

) ( ˆ ) 1 ( ˆ

L L L L

i Y Y π σ μ − − − =

L y L

Y π σφ ρ ρ φ σ

π

+ − − − = 1 ˆ

AS AD

L w L L L

Y βπ μ τ κψ κ π ) 1 ( ˆ ˆ − + + =

AS

y

φ ρ

π L π

L

Y ˆ

Under regular circumstances Under regular circumstances

• “Standard” intuition applies
• Undergraduate textbooks work just as well as

graduate ones

• Will now talk about the peculiar circumstances

that arise when interest rate zero (paradox of (p toil and thrift)

The source of the contraction (G t D i i i f 2008) (Great Depression, crisis of 2008)

Structural Shocks (need this to explain a simultaneous fall in interest rates prices and

• utput in this framework).

e H

r μ − 1 3%

H

ξ

t

e

T t

e L

r ‐4%

L

ξ

= t

e

T t = 1

1 −

= =

−

β r r e

H

– Preference shocks: Reduced form for anything that means that interest rate needs to decline to clear the market (e.g. banking problems, Curdia and Eggertsson (2009))

ˆ < + =

L e L

r r ξ μ

Curdia and Eggertsson (2009)) – Everybody want to spend less today relative to tomorrow.

Solution: Solution:

Boils down to only two equations!

) ( ˆ ˆ

e

r E i Y E Y = π σ

In two unknowns! e

r Y Y σ σμπ μ + + = ˆ ˆ

w t t t t t

E Y τ κϕ π β κ π ˆ ˆ

1 +

+ =

+

) (

1 1 t t t t t t t

r E i Y E Y − − − =

+ +

π σ

L L L L

r Y Y σ σμπ μ + + =

L L L

Y μβπ κ π + = ˆ

e

T t <

Purely forward looking

ˆ For t ≥

e

Y T

ˆ ) 1 ( ˆ For t + <

e

Y Y E T

= =

H H

Y π

) 1 ( ) 1 (

1 1

⋅ + ⋅ − = ⋅ + ⋅ − =

+ + L t t L t t

E Y Y E π μ μ π μ μ and =

t

i

e L L L L

r Y Y σ σμπ μ + + = ˆ ˆ

L L L

Y μβπ κ π + = ˆ

AD AS

A L L L

μβ

AS

= μ

bound a without collapse prices and

• utput

then increases As μ AS

L

π

= μ

> μ

solves where 1 bound a without collapse prices and < μ μ μ A

B

AD

μ > μ

) 1 )( 1 ( = − − − σκ μ μ β μ μ

AD

μ

L

Y ˆ

(a) Interest rate

Output

quarters 10 dur. exp. so 9 . = μ

e H

r

Output collapse

‐0.01 q p μ

(b) Inflation (d) Output

Τe Τe

L

π

‐10%

Τe ‐30%

h ll ?

) ( ˆ ˆ

e

E i Y E Y

Why output collapse?

) (

1 1 e t t t t t t t

r E i Y E Y − − − =

+ +

π σ

Expectations of future deflation EY(t+1) very deflation EY(t+1) very negative vicious cycle Output collapse Real interest rates were in double digits in 29‐33 due to deflation

Contractionary Taxes Contractionary Taxes

for ˆ < < < =

e e w

T t r φ τ for t for ≥ < < < =

e L L

T T t r φ τ

τ

ˆ ˆ = = =

t t w L

Y π τ

t t L

Basic policy analyzed: Basic policy analyzed: “Stimulus package”

e H

r 3%

e t H H t

r i = = 0 ˆ τ ˆ = <

L L t

i τ

H

r μ − 1 3% = t τ = t

e L

r ‐2%

Solution: Solution:

Again boils down to only two equations!

e L L L L

r Y Y σ σμπ μ + + = ˆ ˆ ˆ

τ < t

w L L L L

Y τ κϕ μβπ κ π ˆ ˆ + + =

• For a given taxes, two equations in two unknowns

e L L L L

r Y Y σ σμπ μ + + = ˆ ˆ

ˆ

AD

L L L L

Y τ κϕ μβπ κ π ˆ ˆ + + =

AS AS

L

π

Note: under alternative pricing assumption, Lucas Phillips curve, sticky wages, menu cost models, still

L

Y

upward sloping FE curve.

Note: More flexible prices, steeper FE curve result even stronger

Labor tax cuts are contractionary Labor tax cuts are contractionary

71 < − = = Δ μκψ

L

Y

Intuition

71 . ) 1 )( 1 ( < = − − − = Δ − μσκ β μ τ L

) ( ˆ ˆ

1 1 e t t t t t t t

r E i Y E Y − − − =

+ +

π σ

t t t t t

E Y τ κϕ π β κ π ˆ ˆ

1 +

+ =

+

Payroll tax cut multiplier Gov spending multiplier P iti i t t t 0 096 0 32 Positive interest rate 0.096 0.32 Zero interest rate ‐0.81 2.27

L y L L L

Y i Y ˆ ˆ σφ π σφ σ

π

− − = − =

L y L

Y π σφ σφπ + − = 1 ˆ

e L L L L

r Y Y σ σμπ μ + + = ˆ ˆ

y

φ

AD when i>0 AD when i=0

L

π

) ( ˆ ˆ

1 1 e t t t t t t t

r E i Y E Y − − − =

+ +

π σ

As inflation increases you increase the

As inflation increases you DO NOT increase the

y interest rate more than one to one with inflation

As inflation increases you DO NOT increase the interest rate Real interest rate DECREASE

L

Y ˆ

Real interest rate increase

Discussion: Paradox of Toil Discussion: Paradox of Toil

Paradox of toil : Giving people the incentive to work more

• counterproductive. More supply of labor ‐> lower wages ‐>
• counterproductive. More supply of labor

lower wages deflationary pressures higher real rates. [in equilibrium this reduces aggregate work ] . Classic paradox of composition. ‐‐ Tax story: No spending effect. Is that realistic? Perhaps not under regular circumstances, but not clear if people will spend tax cuts. ‐‐ Extension: “Rule of thumb consumers” a Gali et al. A fraction of consumers spend all their income. ‐‐ Horse race: Who wins? The contractionary effect. “Direct spending effect” weakens the effect (lowers the interest rate elasticity of output) but does not overturn it under plausible elasticity of output) but does not overturn it under plausible calibration (need crazy values). ‐‐ Another issue: Cochrane (2008) suggests that current tax cuts in fact increase effective marginal taxes This would be ideal! in fact increase effective marginal taxes. This would be ideal!

Basic policy analyzed: “Stimulus package II” Cut taxes on capital Cut taxes on capital

e H

r 3%

e t H A L

r i = = 0 ˆ τ ˆ = <

L A L

i τ

H

r μ − 1 3% = t τ = t

e L

r ‐2%

A t e L L L L

r Y Y στ σ σμπ μ + + + = ˆ ˆ

ˆ

AD

L L L

Y μβπ κ π + = ˆ

AS AD AS

L

π

L

Y

Cutting taxes on capital Cutting taxes on capital

• Contractionary because it gives people and incentive to save when the

model cries out for spending but NOT saving.

• Note, no endogneous investment, so no savings in aggregate apart from

government debt.

• What happens with capital (will see later) (savings = investment)
• Turns out that increasing people incentive to save
• Turns out that increasing people incentive to save

reduces aggregate demand reduces peoples ability to save Aggregate savings (investment) collapses because everyone tries to save! Paradox of thrift (Keynes (1936), Christiano (2004))

• Observe, this is a tax on savings, not on “returns”. In practice, capital taxes

are taxes on nominal returns, which are zero for a risk‐free bond.

Labor tax cut multiplier Capital tax cut multiplier Positive interest rate 0 096 ‐0 0033 Positive interest rate 0.096 ‐0.0033 Zero interest rate ‐0.81 ‐0.4048

Plan Plan

• 1. Basic model, key result – contractionary labor and

, y y capital tax cuts

• 2. Other demand and supply policies
• i. a. expansionary government spending
• b. irrelevant government spending

ii l t t

• ii. sales tax cuts
• iii. Cutting taxes on profits and investment tax credit

iv monetary policy

• iv. monetary policy
• 3. Quantitative evaluations

4 Conclusions

• 4. Conclusions

2(i.a) Expansionary Government Spending

T t T T N T S T T t T t

dj j L v G g G C u E ξ β

∑ ∫

∞ = −

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + +

1

)) ( ( ) ( ) ( max

for ˆ < < > =

e e L G N L

T t r G φ for t ≥

e L G L

T φ ˆ ˆ = = =

t t N t

Y G π

L L y L L L L

G Y G i Y ˆ ˆ ˆ ˆ + + = + = σφ π σφ σ

π

CE AD FE CE

L L L L

G Y ˆ ˆ ˆ

1 −

− + = κψσ τ κψ κ π

FE AS A B

π 0 π

ˆ Y

L e L L L L

G r Y Y ˆ ) 1 ( ˆ ˆ μ σ σμπ μ − + + + =

CE

L L L L

G Y ˆ ˆ

1 −

− + = κψσ μβπ κ π

CE FE

L

π

L

Y

Spending is Expansionary Spending is Expansionary

1 27 2 ) 1 )( 1 ( > = − − − = Δ μκψ βμ μ

L

Y

• Intuition

1 27 . 2 ) 1 )( 1 ( > − − − Δ μσκ β μ

N L

G

) ˆ ˆ ( ) ( ˆ ˆ

1 1 1 N t N t t e t t t t t t t

G G E r E i Y E Y

+ + +

− + − − − = π σ

Payroll tax multiplier Gov spending multiplier Positive interest rate 0.0963 0.32 Zero interest rate ‐0.8153 2.28

Implications

• Can show that spending increases welfare, even if it contributes

nothing to utility

• Digging ditches and filling them up.

gg g g p

• Regular cost benefits analysis does not apply to public spending.
• Even better if government spending actually adds to utility.

N t i l if d l E t ti d i t f th k [ l t

• Not crucial if delay: Expectation doing most of the work [relevant

for “Obama stimulus”. ]

• Needs to be explicitly “temporary” and last as long as “the

” emergency”.

• Government spending that simultaneously increases “aggregate

spending”, and reduces “aggregate supply” has biggest effect. W ? N t ll (d t l t f tl ith ) War? Not really (does not correlate perfectly with emergency)

• Why different from some recent studies? Counterfactual.

2(i.b) Irrelevant government spending

“In the end, despite the existence of idle resources, bailouts and stimulus plans do not add to current resources in use. They just move resources from

• ne use to another.” Eugene Fama. Also see also Cochrane (2008) and Barro

(2009) (2009).

T t T T N T S T T t T t

dj j L v G g G C u E ξ β

∑ ∫

∞ = −

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + +

1

)) ( ( ) ( ) ( max

Proposition: Increasing has no effect on aggregate output or inflation.

S T

G People reduce private spending one to one with public spending Both AS and AD equation unchanged q g Spending just “remove resources from one use to another”. Health care an example of irrelevant spending (although could increase demand by increasing expectation of future productivity) Payroll tax multiplier Gov spending multiplier 1 Gov spend multiplier 2 Positive interest rate 0.096 0.32 Zero interest rate ‐0.81 2.27

• 2. (ii) Sales tax cut
• 2. (ii) Sales tax cut
• Sales taxes shows up as:

) ˆ ˆ ( ) ( ˆ ˆ

1 1 1 s t s t t e t t t t t t t

E r E i Y E Y

+ + +

− + − − + = τ τ σ π σ

Note shows up as Government Spending but multiplied with sigma! Same effect

) ( ) (

1 1 1 t t t t t t t t t t + + +

) ˆ ˆ ( ˆ

1 s t w t t t t t

E Y τ τ κψ π β κ π + + + =

+

p p g p g Consider this policy:

∑

∞ =

− = − =

t T e T t w t s t

r r E ] [ ˆ ˆ τ τ

• Revenue neutral policy: Increase payroll taxes and cut sales taxes. Can eliminate the recession in the
• model. Problem: Tax rates cannot be reduced enough, would require consumption subsidy.
• Note VAT does now show up in this fashion! Eggertsson and Woodford (2004)

Payroll tax multiplier Gov spending multiplier 1 Gov spend Multiplier 2 Sales tax Multiplier i>0 0.096 0.32 0.37 i=0 ‐0.8153 2.28 2.64

• 2. (iii) Capital taxes and investment tax

d d f h f credit, paradox of thrift

• Consider a model with capital and an adjustment cost function so that to increase

capital stock from K(t) to K(t+1) one must pay

) ( ) ) ( (

1

i K i K I

t

ξ φ

+

=

• Assume capital income taxes, and also an investment tax credit.

) ( ) , ) ( ( i K i K I

t t t t

ξ φ

t t t t t t t precaptax t

I P i l i w P i y i p i − − = Π ) ( ) ( ) ( ) ( ) (

• Capital tax bill

)] ( ) 1 ( ) ( ) ( ) ( ) ( [ i I P i l i w P i y i p

I p

τ τ + − − )] ( ) 1 ( ) ( ) ( ) ( ) ( [ i I P i l i w P i y i p

t t t t t t t t t

τ τ +

• 2. (iii) Capital taxes and investment tax

d

We get a second Euler Equation

credit.

g q

] ˆ ) 1 ( ˆ [ ] ˆ ) 1 ( ˆ [ ] ˆ ) 1 ( ˆ [ ˆ ) ˆ ( ˆ ˆ

1 1 1 1 1 1 S t S t t P t P t t I t I t t P t t A t e t t t t I N t t N t

E E E E r E i I E I

+ + +

− − − − − + − − + + − − − − = τ λ β τ τ λ β τ τ λ β τ τ ρ χ τ π σ β ] ) 1 ( [ ] ) 1 ( [ ] ) 1 ( [ 1

1 1 1 t t t t t t t t t P

E E E

+ + +

+ − + τ λ β τ τ λ β τ τ λ β τ τ

p t w t s t t t t t

K C L τ τ τ σ ν ρ ˆ ˆ ˆ ˆ ˆ ˆ ) 1 ( ˆ

1

− + + − + + =

−

Basic results: Previous results unaffected by endogenous capital accumulation (quantitatively and qualitatively) (quantitatively and qualitatively). Temporary capital tax cuts are contractionary (tau_p and tau_a, ‐0.44, ‐0.467). Investment credit is expansionary. Investment tax credit multiplier: 0.33 p Paradox of thrift: 1% cut in capital taxes (higher incentive to save) lowers investment by 0.44%

Why does cutting taxes on profits d reduce output?

• Cutting taxes on profits today (so that they are expected to

g p y ( y p increase in the future) gives firms the incentive to delay investment, because they want to pay out as much profits as the can today Reduces investment the can today. Reduces investment

• This is also true at positive interest rates (similar results found

by Auerbach and Summers in the 1980’s).

• Observe, here the assumption of temporary tax cuts

important. N h B (2009) h i i d

• Not what Barro (2009) has in mind.
• Also note: No feedback between stock prices and ability to

borrow (channel emphasized by Feldstein (2008)). borrow (channel emphasized by Feldstein (2008)).

• 2. (iv): Monetary Expansion
• 2. (iv): Monetary Expansion
• Commitment to inflate.

C id it t t i fl t th

• Consider a commitment to inflate the

economy.

) ˆ *) ( * , max(

t y t e t t

Y r i φ π π φ π

π

+ − + + =

• Has a large expansionary effect.
• Equivalent to committing to higher future

Equivalent to committing to higher future money supply.

However, However,

• show in paper that expansionary monetary

policy does not overturn the main results policy does not overturn the main results qualitatively (but changes the quantitatively the value of the multipliers). p )

• Problem with monetary policy:
• Dynamically inconsistent

Dynamically inconsistent.

• Have an incentive to promise inflation and
• utput expansion and renege [Eggertsson
• utput expansion and renege [Eggertsson,

JMCB, 2006].

• AER article mostly about how FDR made a

AER article mostly about how FDR made a policy of reflation “credible”.

• 3. Quantitative evaluation
• Constrained by computational issues, non‐linearity of
• 3. Quantitative evaluation

y p , y zero bound prohibits estimation of the model (in any case too simple as stands). N t l if f l ti ti f th d l

• Not even clear if a formal estimation of the model

would be helpful. These scenarios are “rare” and only

• ne example in the sample (Great Depression)

p p ( p )

• Want model to match a “hypothetical scenario”.
• Formulate “what if” question: Shocks “such that”
• utput is ‐30 percent, deflation of order ‐10 percent.
• Calibrate parameters using priors.

Si l l d f l ti Simple closed for solutions

) 1 )( 1 ( 1 ˆ < − − − =

e L L

r Y κσ μσκ βμ μ 1 ) 1 )( 1 ( < − =

e L L

r σ βμ π μσκ βμ μ ) 1 )( 1 ( < − − −

L L

r σ μσκ βμ μ π

1 27 . 2 ) 1 )( 1 ( ) 1 )( 1 ( > = − − − − − − = Δ Δ μσκ β μ μκψ βμ μ

N L L

G Y

Calibration approach Calibration approach

• Christiano Eichenbaum and Rebelo do a

Christiano, Eichenbaum and Rebelo, do a classic calibration. Pick all the values from literature (problem picking a shock no clear literature (problem picking a shock, no clear guidance)

• Find extreeme sensitivity
• Find extreeme sensitivity

Large multipliers apply only as we approach what Krugman calls “deflationary blackholes” deflationary blackholes

My approach My approach

• Formulate “what if” question: Shocks

Formulate what if question: Shocks “such that” output is ‐30 percent, deflation of order ‐10 percent deflation of order 10 percent.

• Calibrate parameters using priors.

• Only reported “mode”. Of what?

y p

t t t

Y Y + =

data model

ˆ ˆ ε

Measurement

t t t t t

v + =

data t model

π π

Measurement error

• Form priors of parameters based on other data. Update

priors to match calibrated target’s . Minimize priors to match calibrated target s . Minimize

∑

Ω + − + − = ) ( 2 ) ( 2 ) ˆ ˆ (

2 2 target L model 2 2 target model

f Y Y L

L L L

π π

∑

) ( 2 2

2 2

f

v

σ σ ε

Priors

% 10 % 30 ˆ

data t data

− = − = π

t

Y

Choose

t t

Characterize L by using Metrapolis algorithm measurement error,

6 ^ 10 − = =

v

σ σ ε

Priors and posteriors

Multipliers Multipliers

What is the effect of the Obama stimulus plan on output ?

Sensitivity Sensitivity

Taylor et al Taylor et al

• Find tiny government sending multiplier

Find tiny government sending multiplier. Why?

• Because assume a permanent increase in
• Because assume a permanent increase in

spending.

Key: Need to affect spending today, relative to the future.

shock A s s N N e t t t t t t t

E G G E r E i Y E Y τ σ τ τ σ π σ ˆ ) ˆ ˆ ( ) ˆ ˆ ( ) ( ˆ ˆ

1 1

+ + − − − =

+ +

AD

t t t t t t t

E G G E τ σ τ τ σ ) ( ) (

1 1

+ − − − +

+ +

AS

N t w t s t t t t t

G E Y ˆ ] ˆ ˆ [ ˆ

1 1 − +

− + + + = κψσ τ τ κψ π β κ π ≥

t

i

ZB

Conjecture: Permanent increase in G Conjecture: Permanent increase in G contractionary.

Was the New Deal Contractionary? Was the New Deal Contractionary?

E Y ω κϕ π β κ π ˆ ˆ + + =

• In the model, the National Industrial Recovery Act, shows up

t t t t t

E Y ω κϕ π β κ π

1 +

+ =

+

exactly like marginal tax increases

• Increase in monopoly power of firms and workers.
• Expansionary because it increases prices.

Expansionary because it increases prices.

• A reduction/increase in oil prices has the same effect as

variations in taxes. A red ction in oil prices is contractionar !

• A reduction in oil prices is contractionary!
• Our current recession coincides with a collapse in oil prices
• VAR evidence from Japan (in progress)

Industrial Production

Index Index

(1929=100)

110 120 110 120

The Mistake of 1937

90 100 90 100 80 90 80 90

The Reversal of 1938

60 70 60 70

FDR takes power and announces a

40 50 40 50

policy of inflating the price level to 1926 level. Implements NIRA

1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 Source: Federal Reserve Board

Implements NIRA

Was the New Deal Contractionary?

Comparison to Cole and Ohanian (2004)

Cole and Ohanian

Both stories “explain” actual output Difference:

Cole and Ohanian benchmark

Both stories explain actual output. Difference: Counterfactual

Eggertsson New Deal Cole and Ohanian New Deal gg Eggertsson benchmark Predictions: This paper: Suggests that real interest rate should have declined 1933‐37 to negative levels (key reason for recovery) 1933 37 to negative levels (key reason for recovery). Cole and Ohanian story: Real interest rates should have been high during the recovery.

Conclusions Conclusions

• An economic stimulus plan has fundamental

An economic stimulus plan has fundamental different properties at zero interest.

• Theory suggests some tax cuts better than

Theory suggests some tax cuts better than

• thers.
• Should focus on those tax cuts and which

Should focus on those tax cuts and which increase demand – rather than those that increase supply.

• Should focus on government spending that is

not substituting private spending.

Conclusions Conclusions

• An economic stimulus plan has fundamental

An economic stimulus plan has fundamental different properties at zero interest.

• Theory suggests some tax cuts better than

Theory suggests some tax cuts better than

• thers.
• Should focus on those tax cuts and which

Should focus on those tax cuts and which increase demand – rather than those that increase supply.

• Should focus on government spending that is

not substituting private spending.