First motivation: spending 07-09
The Role of Automatic Stabilizers in
the U.S. Business Cycle
Alisdair McKay and Ricardo Reis
�
In the 1930s, purchases were 78% of spending. In the
2000s, they were 25%-52%.
�
2007-09 saw the largest increase in government spending /
GDP since the Korean war. But 75% was an increase in
transfers, and only 25% were purchases. (Oh, Reis, 2011)
�
Of the $494bn spent 2007-09 in the ARRA, only $37bn
were spent in purchases (CBO, 2012)
�
The United States is not special in both of these facts.
(Oh, Reis, 2011)
�
The times of Keynes are long gone: the money is in
∆Y = (∂Y /∂T ) ∆T now, not in ∆Y = (∂Y /∂G) ∆G
anymore.
Boston University and Columbia University
June 18th
Sciences Po
Second motivation: automatic stabilizers
�
Big: CBO (2011) estimates that automatic stabilizers in
2012 will account for $343bn, or 35% of the federal deficit.
�
Less controversial: Auerbach (2009), Feldstein (2009):
disagree on countercyclical fiscal policy, agree that
automatic stabilizers are valuable.
�
Policy: IMF (2009) recommendation for every country.
�
Virtue of rule: Solow (2004): “The advantage of automatic
stabilization is precisely that it is automatic. It is not
vulnerable to the perversities that arise when a
discretionary “stimulus package” (or “cooling-off package”)
is up for grabs in a democratic government.”
�
Ignorance: Blanchard (2006): “...very little work has been
done on automatic stabilization in the last 20 years.”
What this paper does
�
The question: By how much do the automatic stabilizers in
the U.S. tax-and-transfer system lower the volatility of
aggregate activity?
�
The approach: Quantitative business-cycle model, with a
role for aggregate demand, incentives, and redistribution.
�
Existing literature:
1. Single stabilizer, single mechanism (Christiano, 1984, Gali, 1994,
Andres Domnech, 2006, Dromel, Pintus, 2007);
2. Discretionary policy changes (Oh Reis, 2011, Huntley
Michelangeli, 2011, Kaplan Violante, 2012);
3. Public finance perspective (Auerbach Feenberg, 2000, Auerbach,
2009, Dolls, Fuest Peichl, 2011);
4. Steady state effect (Floden, 2001, Alonso-Ortiz Rogerson, 2010,
Horvath Nolan, 2011).
Outline for today
1. Introduction
2. What are the automatic stabilizers and what is their role?
3. A model
2. The automatic stabilizers: what they are
and what is their role
6$(106-215%!10!$;1.$%2?!-0!23$!0$%0121;127!5=!2->$0!25!1%:54$!./'1%(!23$!<$'15.!*++@AB!C-0!65C$'!
#$$%&$'(!)*+++,!-%.!/01%(!23$!0-4$!4$235.565(78*!!93$!:/4/6-21;$!14<-:2!5=!:3-%($0!1%!2->!
4. First result: neutrality
23-%!-2!-%7!214$!01%:$!23$!DEF+08!!G0214-2$0!=5'!*++H!-%.!23$'$-=2$'!.5!035C!-%!1%:'$-0$.!
5. Second result: complete markets
'$0<5%01;$%$00?!&/2!23$0$!$0214-2$0!'$=6$:2!2->!6-C!-0!1%!$==$:2!41.C-7!23'5/(3!*++H!-%.!
23$'$=5'$!-!02'5%($'!&12$!='54!23$!I62$'%-21;$!J1%14/4!9->!)IJ9,?!23$!$%:'5-:34$%2!5=!C31:3!
6. Third result: redistribution
7. Conclusion
3-0!&$$%!:5%21%/-667!.$6-7$.!&7!-%%/-6!6$(106-215%!1%!'$:$%2!7$-'0?!-%.!$;$%2/-6!'$<$-6!5=!
$00$%21-667!-66!5=!23$!K/03!2->!:/20!$%-:2$.!1%!*++D!-%.!*++@8!!L%$!41(32!231%M!23-2!23$!('5C1%(!
14<5'2-%:$!5=!02-2$!-%.!65:-6!2->$0!5;$'!2310!<$'15.!C5/6.!3-;$!<-'21-667!5==0$2!23$!.$:61%$!1%!
=$.$'-6!4-'(1%-6!2->!'-2$0?!&/2!C123!$00$%21-667!-66!02-2$0!=-:1%(!054$!=5'4!5=!&-6-%:$.A&/.($2!
'$N/1'$4$%20?!23$!%$:$00-'7!2->!1%:'$-0$0!-%.!0<$%.1%(!:/20!C5/6.!3-;$!/%.5%$!2310!<52$%21-6!
What are the stabilizers?
�
�
:/0315%1%(!$==$:28!
Auerbach et al, ∆Taxes / ∆Income
!"#$%&'()'*$+,-.+"/'0&12,31"4&3&11',5'!&6&%.7'8.9&1'+,':3/,-&
Definition: Rules in tax and transfer systems that lead to
automatic adjustments in revenues and outlays in response
to business cycle fluctuations.
+8O+
How can they affect fluctuations?
+8@"
2. By changing relative benefits and costs.
3. Deficit-financing and crowd out or in of capital.
4. Redistribution and consumption (Oh-Reis Keynesian
channel).
5. Redistribution and labor supply (Oh-Reis neoclassical
channel).
�
Examples: personal income tax, safety net transfers,
corporate income tax, unemployment benefits...
.9Q.P
1. By lowering the volatility of cash on hand, X̂ = (1 − τ )X.
+8@+
+8*"
+8*+
DEF+
DEF"
DEB+
DEB"
DEH+
DEH"
DEE+
DEE"
*+++
*++"
*+D+
P$-'
!
��
StDev(Y (·, τ ) ≈ �
�
i=1
A new measure of stabilization
�
�
���
N ��
��
∂T
∂Y
∂X
∂Y
∂P
�
�
i
i
i
i
StDev(Y (·, τ ) ≈ �
1−
+
� StDev(Z).
�
∂Xi ∂ X̂i ∂Z
∂P ∂Z �
i=1
In a simple model
� with one good, N consumers, aggregate
output is: Y = N
i=1 Yi (P, X̂i , τ ), net income is:
X̂i (Xi , τ ) = Xi − Ti (Xi , τ ), gross income is Xi (Z, τ ) and prices
in equilibrium are: P (Z, τ ) then:
V ar(Y (·, τ )) ≈
N �
�
i=1
∂Yi ∂Xi ∂Yi ∂P �
+
� StDev(Z).
∂P ∂Z �
∂ X̂i ∂Z
!""#$%&%'()#*(+,,(-.-"/0(
V ar(Y (·, 0))
− 1.
V ar(Y (·, 1))
�
∂Ti
∂Xi
Accounting for all the effects
The fraction by which the volatility of aggregate activity Y (·, τ )
would increase if we removed automatic stabilizers (τ = 1 to
τ = 0):
S=
1−
∂Ti
1−
∂Xi
�
∂Yi ∂Xi ∂Yi ∂P
+
∂P ∂Z
∂ X̂i ∂Z
�2
1-/2'*#00(-.-"/(
Preferences:
E0
∞
�
t=0
V ar(Z).
βt
� 3.-"/(#%(+"&#%0(
�1−σ
ψ
c3.-"/(#%(4%"-%&5-0(/#(-+*%(
t (1 − nt )
!"#$%$"&'%
(#()*%+*&,-'%
$.%$")%$#+/)%
(1 − σ)
3.-"/(#%(4%"-%&5-0(/#("#%0$6-(
3.-"/(/7*#$'7('-%-*+,(-8$4,49*4$6((
Wealth evolution:
p̂t ct + bt+1 − bt = pt [xt − τ̄ x (xt )]
Preliminaries
Income
�
Time is discrete, agents live forever, aggregate shocks to
xt = (it /pt )bt +productivity
wt s̄nt + dand
t . monetary policy.
3. A quantitative business-cycle model
�
First automatic
�
x
τ̄ (x) =
Population: measure 1 of capital-owners, measure ν of
other households,
measure 1income
of intermediate-good
firms,
stabilizer
is the personal
tax :
representative final-goods firm, representative capital firms.
x
x �
�
τ (x )dx .
0
�
Government collects taxes τ̄ at rates τ , gives transfers T
and spends resources g.
where τ x is weakly increasing.
�
Capture as many possible stabilizers as can, with three
omissions: closed economy, no health care, no retirement.
2
Capital owners
Insure within, preferences of representative agent:
�
�
∞
2
�
n1+ψ
t
t
E0
β ln(ct ) − ψ1
1 + ψ2
t=0
Wealth evolution:
p̂t ct + bt+1 − bt = pt [xt − τ̄ x (xt )] + Tte
Income:
xt = (it /pt )bt + wt s̄nt + dt .
First stabilizer: personal income tax with τ x weakly increasing:
� x
x
τ̄ (x) =
τ x (x� )dx� .
Other households
Same preferences, but can be more impatient β̂ ≤ β.
Income subject to idiosyncratic shocks:
xt (i) = (it /pt )bt (i)+I(et (i) = 2)st (i)wt nt (i)+T u (et (i), st (i)).
The st (i) are skill shocks, which generate a wage distribution.
Progressive taxation then implies redistribution.
Law of motion for wealth:
p̂t ct (i) + bt+1 (i) − bt (i) = pt [xt (i) − τ̄ x (xt (i))] + pt T n (et (i))
0
Safety-net payments
�
et ∈ {0, 1, 2} is employment status, Markov process.
Probabilities depend on exogenous shock, so have a
business cycle in aggregate unemployment.
�
If et (i) = 2 then employed, earn wage st (i)wt nt (i) as part
of taxable income, and no social benefits: T u = T n = 0.
�
If et (i) = 1 then unemployed collecting benefits, which are
taxable. Unemployment benefits �
�
receive T u (et (i), st (i)) = min T̄ u st (i), T̄ u s̄u if
et (i) = 0. Zero otherwise.
Final goods’ firms
Technology:
��
yt =
1
yt (j)1/µ dj
0
�µ
.
By cost minimization and zero profits:
�
If et (i) = 0 then out of the labor force collecting food
stamps, which are not taxable. SNAP / food stamps
receive T¯n (et (i)) if et (i) = 0. Zero otherwise.
pt =
��
1
pt (j)
0
1/(1−µ)
dj
�1−µ
.
Sales tax
After-tax prices p̂t = (1 + τ c )pt so consume 1/(1 + τ c )
fraction of spending.
Intermediate goods’ firms
Capital goods’ firms
Continuum of monopolists with production function:
yt (j) = at kt (j)α �t (j)1−α .
Maximize after-tax nominal profits dit (j):
�
�
1 − τ k [pt (j)yt (j)/pt − wt �t (j) − (rt + δ)kt (j) − ξ] .
Representative firm, maximize after-tax profits dkt :
(1 − τ k )rt kt − ∆kt+1 − Υ(∆kt+1 )kt .
Value of the firm is
vt = dkt − τ p vt + β Et [λt,t+1 Vt+1 ]
Nominal rigidities a la Calvo (1983) with parameter θ.
Corporate income tax
Flat rate τ k attenuates fluctuations in dividends and in
after-tax interest rate.
Property income tax
Rate τ p on vt = qt kt and qt = 1 + Υ� (.) is procyclical.
The last stabilizer: budget constraint
The government budget constraint is:
�ν
�ν
τ c 0 (ct (i)dh + ct )di + τ p qt kt + 0 τ̄ x (xt (i))dh + τ̄ x (xt ) +
�
�
τ k ω dˆi (j)di + rt kt − γ∆kt+1 =
�ν
�ν
Tte + 0 (1 − eht )Ttuh dh + 0 Tt (xt (i), st (i), et (i))di +
gt + (it /pt )Bt − (Bt+1 − Bt ) /pt
Need a fiscal rule to cover deficits. Tax on entrepreneurs is
closest to being separated from other effects:
� �φ
Bt
e
Tt = log
B̄
But also consider alternative with purchases:
�
�
gt
yt Bt /pt φ
=
g
ȳ
B̄
Market clearing
�
Government bonds are the only asset in positive net supply:
� ν
Bt =
bt (i)di + bt .
0
�
Capital goods:
� 1
kt =
kt (j)dj.
0
�
Labor market:
� 1
�
lt =
�t (j)dj =
0
�
ν
et (i)st (i)nt (i)dh + s̄nt .
0
Taylor rule for monetary policy:
it = ī + φp ∆ log(pt ) + φy log(yt /y) + εt
Equilibrium
�
Aggregate shocks to log(at ) and εt are independent AR(1).
Individual shocks to et (i) and st (i) are Markov processes.
�
Employment varies exogenously with aggregate shocks:
probabilities depend on composite shock log(at ), εt .
�
Our measure of real activity is log output and its variance
is evaluated at the ergodic distribution of this economy.
�
Crucial is that we have four groups of stabilizers:
4. First result: neutrality
1. Proportional taxes τ c , τ k , τ p ;
2. Progressive personal tax system τ x (x� );
3. Safety-net transfers T u (et (i), st (i)), T n (et (i), st (i));
4. Deficits, via adjustment rate φ.
Neutrality proposition
Assumption 1: The following set of conditions holds:
Implications
�
Intuition for the result with separable preferences (σ = 1)
1. With flexible prices, there is an aggregate production
function: yt = at ktα lt1−α .
2. k is fixed so proposition holds if labor supply is fixed.
3. Because g/y is fixed, resource constraint says c/y is fixed.
Because production function is Cobb-Douglas, wages are
proportional to y/l. Therefore, c/w is proportional to l.
4. Because of complete markets, consumption same for all.
5. Labor supply condition for employed household:
1. Households trade a complete set of Arrow securities.
2. The personal income tax is proportional.
3. Probability of employment is fixed over time.
4. Capital is fixed (infinite adjustment costs).
5. Prices are flexible (Calvo frequency is infinity).
6. Government purchases are a fixed fraction of GDP.
Proposition Under the conditions of assumption 1, the
variance of the log of output is equal to the variance of the log
of productivity. Therefore, S = 0 for any combination of taxes
and transfers.
nt (i) = 1 −
�
p̂t
ψct (i)
.
pt (1 − τ )wt st (i)
Implications:
�
�
�
Public finance measures would have led you astray.
Net income affects volatility of the level but not log income.
Proportional taxes are weak stabilizers.
Aggregation result
5. Second result: complete markets
Proposition If all households can trade a complete set of Arrow
securities, there is a representative agent. Her preferences are:
�
�
∞
2
�
n1+ψ
t
t
max E0
β log(ct ) − (1 + Et ) ψ1
1 + ψ2
t=0
and her constraints are:
p̂t ct + bt+1 − bt = pt [xt − τ̄ (xt )] + Ttn
it
xt = bt + wt st (1 + Et )nt + dt + Ttu
pt
�
� 1
� ν
1+1/ψ2
1
Et
1+1/ψ2
1+1/ψ2
st =
s̄t
+
si,t
di
,
1 + Et
1 + Et 0
where 1 + Et is total employment, including capital-owners and
households.
More aggregation results
The United States welfare state
Table 1. The government's use and source of funds, average 1997-2007
Lemma The solution to the capital firm’s problem is
represented by a standard Euler equation, taking into account
the adjustment costs.
Lemma The solution to the final- and intermediate-goods
problems is represented by a standard NK Phillips curve.
Revenues
Outlays
Automatic stabilizers
Automatic stabilizers
Personal Income Taxes
Corporate Income Taxes
Sales and excise taxes
Property Taxes
Others
Public deficit
So, overall, very standard macro model augmented to have
many taxes along many margins.
11.22%
2.59%
3.80%
2.75%
Sum
0.29%
0.91%
0.20%
0.17%
0.35%
0.19%
Others
-1.12%
Out of the model
Customs taxes
Licenses, fines, fees
Payroll taxes
Unemployment benefits
Safety net programs
Supplemental nutrition assistance
Family assistance under PRWORA
Security income to the disabled
Others
Government purchases
Net interest income
15.14%
2.25%
Out of the model
0.21%
1.79%
6.26%
27.49%
Notes
28.61%
Retirement-related transfers
Others (esp. rest of the world)
Health benefits (non-retirement)
Sum
7.27%
1.92%
1.74%
27.49%
Calibration of stabilizers
Simulate TaxSim, 88-07, federal plus state, weight states by
population, years equally. Fit a truncated cubic to it, plus an
intercept to match table 1. Get:
Table 1: Parameter Values
Explanation
Value
Panel A. Tax bases and rates
τc
Tax rate on consumption
0.054
β
Discount factor of stock owners
0.989
τp
Tax rate on property
0.003
α
Coefficient on labor in production
0.296
τk
Tax rate on corporate income
0.282
ξ
Fixed costs of production
1.32
µ
Desired gross markup
1.1
Panel B. Government outlays and debt
Tu
Unemployment benefits
0.185
To
Safety-net transfers
0.169
G/Y
Steady-state purchases / output
0.130
φ
Fiscal adjustment speed
1.33
B/Y
Steady-state debt / output
1.66
Panel C. Labor-force status
πeu
Steady-state transition probability E-U 0.026
πue
Steady-state transition probability U-E 0.571
Table
1: Parameter
πup
Steady-state transition
probability
U-P Values
0.297
πpu
Steady-state transition probability P-E 0.087
y
πeu
Cyclical transition probability E-U
-1.20
y
Parameter
Explanation
Value
πue
Cyclical transition probability U-E
3.477
y
πupA. TaxCyclical
transition
1.55
Panel
bases and
rates probability U-P
Panel
distribution
τc D. Income
Tax rateand
on wealth
consumption
0.054
ν
Non-participants
/
stock
owners
4
β h
Discount factor of stock owners
0.989
Discount
of non-participants
0.983
τpβ
Tax
rate onfactor
property
0.003
s̄
Skill level of stock owners
4.66
α
Coefficient on labor in production
0.296
E(s)
Mean of non-participants skill
1.08
τk
Tax rate on corporate income
0.282
Panel E. Business-cycle parameters
ξ
Fixed costs of production
1.32
γ
Coefficient of relative risk aversion
1
µ
Desired gross markup
1.1
θ
Calvo parameter for price stickiness
0.286
Panel B. Government outlays and debt
ψ
Labor supply
21.6
Tu 1
Unemployment benefits
0.185
ψ
Labor supply
2
To 2
Safety-net transfers
0.169
δ
Depreciation rate
0.114
G/Y
Steady-state purchases / output
0.130
φ
Adjustment costs for investment
17.2
φ
Fiscal adjustment speed
1.33
ρz
Autocorrelation of productivity shock
0.923
B/Y
Steady-state debt / output
1.66
σz
St. dev. of productivity shock
0.003
Panel C. Labor-force status
ρm
Autocorrelation of monetary shock
0.500
πeu
Steady-state transition probability E-U 0.026
σm
St. dev. of monetary shock
0.005
πue
Steady-state transition probability U-E 0.571
φp
Interest-rate rule coefficient on inflation 1.50
πupφ
Steady-state
probability
U-P 0.297
Interest-ratetransition
rule coefficient
on output
0.010
y
πpu
Steady-state transition probability P-E 0.087
y
πeu
Cyclical transition probability E-U
-1.20
y
πue
Cyclical transition probability U-E
3.477
2
y
πup
Cyclical transition probability U-P
1.55
Panel D. Income and wealth distribution
ν
Non-participants / stock owners
4
βh
Discount factor of non-participants
0.983
s̄
Skill level of stock owners
4.66
E(s)
Mean of non-participants skill
1.08
Panel E. Business-cycle parameters
γ
Coefficient of relative risk aversion
1
θ
Calvo parameter for price stickiness
0.286
ψ1
Labor supply
21.6
ψ2
Labor supply
2
δ
Depreciation rate
0.114
φ
Adjustment costs for investment
17.2
ρz
Autocorrelation of productivity shock
0.923
σz
St. dev. of productivity shock
0.003
ρm
Autocorrelation of monetary shock
0.500
σm
St. dev. of monetary shock
0.005
φp
Interest-rate rule coefficient on inflation 1.50
φy
Interest-rate rule coefficient on output
0.010
0.4
Target (Source)
Avg. revenue from sales taxes (Table 1)
Consumption-income ratio = 0.689 (NIPA)
Avg. revenue from property taxes (Table 1)
Capital income share = 0.36 (NIPA)
Avg. revenue from corporate income tax (Table 1)
Corporate profits / GDP = 9.13% (NIPA)
Avg. U.S. markup (Basu, Fernald, 1997)
Avg. outlays on unemp. benefits (Table 1)
Avg. outlays on safety-net benefits (Table 1)
Avg. outlays on purchases (Table 1)
Autocorrelation of net government savings / GDP = 0.966 (NIPA)
Avg. interest expenses (Table 1)
Avg. insured unemp. rate = 0.023 (BLS)
Avg. UE flow quarterly = 0.813 (Shimer, 2007)
Avg. SNAP ratio = 0.077 (USDA)
SNAP exit hazard = 0.03 monthly (Mabli et al., 2011)
St. dev. of unemp. rate = 0.009 (BLS)
Target
(Source)
St. dev.
of UE flows = 0.053 (Shimer)
St. dev. of SNAP ratio = 0.020 (USDA)
Avg. revenue from sales taxes (Table 1)
Consumption-income ratio = 0.689 (NIPA)
Wealth
of topfrom
20% property
by wealthtaxes (Table 1)
Avg.
revenue
Income of top 20% by wealth (SCF)
Capital income share = 0.36 (NIPA)
Avg. income in economy normalized to 1
Avg. revenue from corporate income tax (Table 1)
Corporate profits / GDP = 9.13% (NIPA)
Avg. U.S. markup (Basu, Fernald, 1997)
Avg. price spell duration = 3.5 (Klenow, Malin, 2011)
Avg. hours worked = 0.31 (Cooley, Prescott, 1995)
Avg. outlays on unemp. benefits (Table 1)
Frisch elasticity = 1/2
Avg. outlays on safety-net benefits (Table 1)
Annual depreciation expenses / GDP = 0.046 (NIPA)
Avg. outlays on purchases (Table 1)
Corr. of Y and C = 0.88 (NIPA)
Autocorrelation of net government savings / GDP = 0.966 (NIPA)
Autocorrelation of log GDP = 0.864 (NIPA)
Avg. interest expenses (Table 1)
St. dev. of log GDP = 1.539 (NIPA)
Largest autoregressive root of inflation = 0.85 (Pivetta, Reis, 2006)
Avg. insured unemp. rate = 0.023 (BLS)
Share of output variance due to m shock = 0.8
Avg. UE flow quarterly = 0.813 (Shimer, 2007)
St. dev. of inflation = 0.638 (NIPA)
Avg.
SNAP of
ratio
= 0.077
(USDA)
Correlation
inflation
with
log GDP = 0.198 (NIPA)
SNAP exit hazard = 0.03 monthly (Mabli et al., 2011)
St. dev. of unemp. rate = 0.009 (BLS)
St. dev. of UE flows = 0.053 (Shimer)
St. dev. of SNAP ratio = 0.020 (USDA)
Calibration of inequality
Wealth of top 20% by wealth
Income of top 20% by wealth (SCF)
Avg. income in economy normalized to 1
Avg. price spell duration = 3.5 (Klenow, Malin, 2011)
Avg. hours worked = 0.31 (Cooley, Prescott, 1995)
Frisch elasticity = 1/2
Annual depreciation expenses / GDP = 0.046 (NIPA)
Corr. of Y and C = 0.88 (NIPA)
Autocorrelation of log GDP = 0.864 (NIPA)
St. dev. of log GDP = 1.539 (NIPA)
Largest autoregressive root of inflation = 0.85 (Pivetta, Reis, 2006)
Share of output variance due to m shock = 0.8
St. dev. of inflation = 0.638 (NIPA)
Correlation of inflation with log GDP = 0.198 (NIPA)
0.35
0.3
Table 1: Parameter Values
0.25
Parameter
marginal tax rate
Parameter
Calibration of personal income tax
Explanation
0.2
Value
Target (Source)
Panel A. Tax bases and rates
0.15on consumption
τc
Tax rate
0.054 Avg. revenue from sales taxes (Table 1)
β
Discount factor of stock owners
0.989 Consumption-income ratio = 0.689 (NIPA)
0.1on property
τp
Tax rate
0.003 Avg. revenue from property taxes (Table 1)
α
Coefficient on labor in production
0.296 Capital income share = 0.36 (NIPA)
τk
Tax rate
0.282 Avg. revenue from corporate income tax (Table 1)
0.05on corporate income
ξ
Fixed costs of production
1.32 Corporate profits / GDP = 9.13% (NIPA)
µ
Desired gross
markup
1.1
Avg. U.S. markup (Basu, Fernald, 1997)
0
Panel B. Government outlays and debt
u
T
Unemployment
benefits
0.185 Avg. outlays on unemp. benefits (Table 1)
−0.05
To
Safety-net transfers
0.169 Avg. outlays on safety-net benefits (Table 1)
G/Y
Steady-state
purchases / output
0.130 Avg. outlays on purchases (Table 1)
−0.1
φ
Fiscal adjustment
speed
savings / GDP = 0.966 (NIPA)
0
1
2
31.33 Autocorrelation
4
5 of net government
6
7
income
B/Y
Steady-state debt / output multiples of average
1.66 household
Avg. interest
expenses (Table 1)
Panel C. Labor-force status
πeu
Steady-state transition probability E-U 0.026 Avg. insured unemp. rate = 0.023 (BLS)
πue
Steady-state transition probability U-E 0.571 Avg. UE flow quarterly = 0.813 (Shimer, 2007)
πup
Steady-state transition probability U-P 0.297 Avg. SNAP ratio = 0.077 (USDA)
πpu
Steady-state transition probability P-E 0.087 SNAP exit hazard = 0.03 monthly (Mabli et al., 2011)
y
πeu
Cyclical transition probability E-U
-1.20 St. dev. of unemp. rate = 0.009 (BLS)
y
πue
Cyclical transition probability U-E
3.477 St. dev. of UE flows = 0.053 (Shimer)
y
πup
Cyclical transition probability U-P
1.55 St. dev. of SNAP ratio = 0.020 (USDA)
Panel D. Income and wealth distribution
ν
Non-participants / stock owners
4
βh
Discount factor of non-participants
0.983 Wealth of top 20% by wealth
s̄
Skill level of stock owners
4.66 Income of top 20% by wealth (SCF)
E(s)
Mean of non-participants skill
1.08 Avg. income in economy normalized to 1
Panel E. Business-cycle parameters
γ
Coefficient of relative risk aversion
1
θ
Calvo parameter for price stickiness
0.286 Avg. price spell duration = 3.5 (Klenow, Malin, 2011)
ψ1
Labor supply
21.6 Avg. hours worked = 0.31 (Cooley, Prescott, 1995)
ψ2
Labor supply
2
Frisch elasticity = 1/2
δ
Depreciation rate
0.114 Annual depreciation expenses / GDP = 0.046 (NIPA)
φ
Adjustment costs for investment
17.2 Corr. of Y and C = 0.88 (NIPA)
ρz
Autocorrelation of productivity shock
0.923 Autocorrelation of log GDP = 0.864 (NIPA)
σz
St. dev. of productivity shock
0.003 St. dev. of log GDP = 1.539 (NIPA)
ρm
Autocorrelation of monetary shock
0.500 Largest autoregressive root of inflation = 0.85 (Pivetta, Reis, 2006)
σm
St. dev. of monetary shock
0.005 Share of output variance due to m shock = 0.8
φp
Interest-rate rule coefficient on inflation 1.50 St. dev. of inflation = 0.638 (NIPA)
φy
Interest-rate rule coefficient on output
0.010 Correlation of inflation with log GDP = 0.198 (NIPA)
Calibration of other parameters
2
resulting government budget surplus is rebated lump-sum to capital owners.
investment more volatile.
The policy changes would generally raise the steady state level of output because they reduce
4. small government: no government spending, transfers are reduced to 20% of their baseline
distortions. The high marginal tax rates associated with progressive taxation have quite large
C
K
P
level, income taxes are eliminated, τ , τ , and τ are reduced by 10%. Steady state goveffects on steady state levels. The elimination of government spending in the small government
ernment debt remains at itsThe
baseline
level. A lump-sum tax on capital owners balances the
experiments
Results
for S
experiment has a large, if mechanical,
effect on consumption.
budget period by period.
3
1. lower proportional taxes: tax rates τ C , τ P and τ K are
10%. Lost revenue of 0.6% of GDP is replaced
Resultsreduced
for thebyrepresentative
agent economy
by increased lump-sum tax on the capital owners.
In the representative agent economy, the effects of these policies for fluctuations are modest. In
2. without
progressive
taxes:
the slightly
progressive
incomebut
tax
particular, lowering
transfers
would make the
economy
more stable,
in essence has no
effect on volatilities.
Progressive
has veryincome
little effect
output
or the
labor input, but does
is replaced
by ataxation
proportional
tax on
that
raises
contribute to the
stability
of consumption.
My understanding of this result is that it is driven
same
revenue
in steady state.
by intertemporal substitution in the timing of dividends: in a recession, marginal tax rates are
lower and it 3.
is an
attractive
time to
pay out dividends.
Thistomakes
more stable and
low
transfers:
transfers
are reduced
lowerconsumption
spending by
investment more0.8/5
volatile.
of GDP. In steady state, the resulting government
The policy changes would generally raise the steady state level of output because they reduce
budget
surplus is rebated lump-sum to capital owners.
distortions. The high marginal tax rates associated with progressive taxation have quite large
effects on steady state levels. The elimination of government spending in the small government
4. small
no on
government
spending, income
experiment has
a large, government:
if mechanical, effect
consumption.
taxes are eliminated, all other taxes and transfers fall by
amounts
equal to above experiments. Steady state
Table 1: S statistic for representative agent economy
government debt remains at its baseline level. A lump-sum
tax
capital
owners
balances the
budget
every period.
low on
propor.
taxes
w/o progressive
taxes
low transfers
small gov.
Y
N
C
(1)
(2)
(3)
(4)
0.0047
0.0078
-0.0254
-0.0119
0.0019
0.0746
-0.0059
-0.0056
-0.0168
-0.0147
-0.0080
0.0721
Effect on steady state
Table 1: S statistic for representative agent economy
Y
N
C
low propor. taxes
(1)
w/o progressive taxes
(2)
low transfers
(3)
small gov.
(4)
0.0047
0.0078
-0.0254
-0.0119
0.0019
0.0746
-0.0059
-0.0056
-0.0168
-0.0147
-0.0080
0.0721
Progressive income tax only stabilizes C because of timing of
Table 2: Effects on steady state levels for representative agent economy
dividends by capital-goods firm. Transfers not exactly zero
because
taxable, but very close to Ricardian equivalence.
low propor. taxes w/o progressive taxes low transfers small gov.
Y
N
C
(1)
(2)
(3)
(4)
0.0159
0.0007
0.0147
0.0369
0.0369
0.0487
0.0002
0.0002
0.0002
0.0321
0.0167
0.2655
2
Table 2: Effects on steady state levels for representative agent economy
Y
N
C
low propor. taxes
(1)
w/o progressive taxes
(2)
low transfers
(3)
small gov.
(4)
0.0159
0.0007
0.0147
0.0369
0.0369
0.0487
0.0002
0.0002
0.0002
0.0321
0.0167
0.2655
Progressive taxation comes with much lower output though
2
because of its high marginal tax rates.
6. Third result: heterogeneity
Solving the full model
�
�
4
Need to solve a model with:
�
Heterogeneity: must keep track of distributions, as in
Krusell and Smith (1997).
�
Nominal rigidities: as in Oh and Reis (2011) and Guerrieri
and Lorenzoni (2011).
�
Solve for aggregate dynamics: as in Reiter (2009)
We have just finished refining our grids (so no draft yet but
very soon).
How the model works: household savings
employed
1.5
the model works:
capital
Results forHow
the heterogeneous
agent economy
i
The steady state effects are similar to the representative agent economy, but the impact on volatilities are now more substantial.
Transfers in particular have a substantially larger effect here and the
h −1
variance of log output is 13% higher when transfers are reduced. However, aggregate consumption
is more stable when transfers are reduced. This result is driven by the additional accumulation of
precautionary savings in the stationary economy. Lowering /01"#20*.%
transfers increases the precautionary
3'4)-5"%
savings motive of households, which means that they have more
savings with which to smooth
aggregate as well
as
idiosyncratic
shocks.
To
confirm
this
intuition,
we conducted an additional
−1
e
experiment in which we lower the households’ discount factor at the same time that we eliminate
transfers. This experiment is just meant to illustrate the role678,%9'()$'*%"$09:%
of precautionary savings in the model
and is not intended as a true policy experiment because it is not clear how one might achieve this
reduction in discount factor. We choose the new discount factor so that the aggregate assets of
678,% economy despite the fact that transfers are lower. In
the households is the same as in the baseline
201"#20*.%
this alternative economy with low transfers
and a low discount &'()$'*%+#,'-.%
factor, the volatility of consumption
is higher than in the baseline economy"'4)-5"%
by 22% (i.e. S = 0.22). This makes sense as in this case
the households have little private insurance in the form of precautionary savings and little public
insurance in the form of transfers. Therefore, the reduction in employment in a recession has a
strong impact on consumption.
The impact of progressive taxation on the volatility of output is now substantially larger than in
!""#$"%
the representative agent economy. However, while progressive taxation stabilized
consumption in
the representative agent economy, it now destabilizes log consumption. This result also arises out
of the impact of the policy on the steady state. The change to proportional taxes makes the level
of consumption more volatile and larger in steady state. These two effects have opposite effects
on the variance of log consumption. The impact on steady state consumption is stronger in the
Results
S increase in the volatility of the level
heterogeneous agent economy and this
is enough tofor
offset the
of consumption.
�
β
�
(β )
1
Table 3: S statistic for heterogeneous agent economy
0.5
0
0
0.2
0.4
0.6
0.8
1
unemployed
1
Y
N
C
0.5
0
0
0.2
0.4
0.6
0.8
low propor. taxes
(1)
w/o progressive taxes
(2)
low transfers
(3)
small gov.
(4)
0.0036
0.0125
0.0424
0.1454
0.1348
-0.0663
0.1317
0.0640
-0.2270
0.1278
0.1364
-0.0716
1
out of the labor force
5
1
baseline
low transfers
Proportional taxes still mostly irrelevant. Our first extreme
Alternative
Financing
Mechanisms
result is still
a good approximation.
1. Baseline: lump-sum tax adjusts gradually to government debt outstanding.
0.5
2. No deficits: lump-sum tax immediately to clear government budget.
0
0
0.2
0.4
0.6
assets (1 = avg income)
0.8
1
3. Spending: G adjusts gradually to debt outstanding.
3
of the impact of the policy on the steady state. The change to proportional taxes makes the level
of consumption more volatile and larger in steady state. These two effects have opposite effects
on the variance of log consumption. The impact on steady state consumption is stronger in the
heterogeneous agent economy and this is enough to offset the increase in the volatility of the level
Results for S
of consumption.
of consumption more volatile and larger in steady state. These two effects have opposite effects
on the variance of log consumption. The impact on steady state consumption is stronger in the
heterogeneous agent economy and this is enough to offset the increase in the volatility of the level
of consumption.
Results for S
Table 3: S statistic for heterogeneous agent economy
Table 3: S statistic for heterogeneous agent economy
Y
N
C
low propor. taxes
(1)
w/o progressive taxes
(2)
low transfers
(3)
small gov.
(4)
0.0036
0.0125
0.0424
0.1454
0.1348
-0.0663
0.1317
0.0640
-0.2270
0.1278
0.1364
-0.0716
Progressive taxes much more effective at stabilizing output and
5 Alternative
Financing
Mechanisms
employment,
but now destabilize
consumption. Actually C is
more
stable
in
levels,
but
steady-state
level much
so log
1. Baseline: lump-sum tax adjusts gradually to government
debtlower,
outstanding.
C is more volatile.
2. No deficits: lump-sum tax immediately to clear government budget.
Y
N
C
5
low propor. taxes
(1)
w/o progressive taxes
(2)
low transfers
(3)
small gov.
(4)
0.0036
0.0125
0.0424
0.1454
0.1348
-0.0663
0.1317
0.0640
-0.2270
0.1278
0.1364
-0.0716
Transfers are hugely effective on Y, N but destabilize C. With
Alternative
Financing
Mechanisms
low transfers,
precautionary
savings rise allowing for better
smoothing
of shocks.
1. Baseline:
lump-sum
tax adjusts gradually to government debt outstanding.
2. No deficits:
lump-sum
taxhousehold
immediatelydiscount
to clear government
budget.
Experiment:
lower
factor. Now
S for
consumption
+22%. to debt outstanding.
3. Spending:
G adjustsisgradually
3. Spending: G adjusts gradually to debt outstanding.
3
3
Wealth distribution
Results for steady state
employed
0.015
0.01
Table 4: Effects on steady state levels for heterogeneous agent economy
0.005
0
0
2
−4
4
4
6
8
10
unemployed
x 10
Y
N
C
3
2
1
0
0
2
4
6
8
w/o progressive taxes
(2)
low transfers
(3)
small gov.
(4)
0.0164
0.0012
0.0153
0.0413
0.0413
0.0543
0.0017
0.0017
0.0024
0.0347
0.0192
0.2696
10
out of the labor force
0.015
baseline
low transfers
0.01
0.005
0
low propor. taxes
(1)
0
2
4
6
assets (1 = avg income)
8
10
Keynesian effect on bottom group, stabilizes Y,N.
Precautionary effect on other households, C destabilized.
The timing
of the lump-sum
tax hasimpacts
very littleoninfluence
the dynamics
Transfers
have minimal
steady on
state,
unlike of the economy, which
reflects a near
Ricardian
equivalence.
The
reason
that
Ricardian
equivalence
does not hold exactly
progressive taxes.
is that the interest payments on government debt alters taxable income. A fiscal adjustment rule
that has government spending adjust to stabilize government debt leads output and hours to be
more volatile, but consumption to be less volatile. The reason that hours are more volatile is
because of a wealth effect: in a boom, government revenues rise as the tax base increases and
government outlays fall as transfers fall. These forces lead to a reduction in government debt,
which is offset by increased government spending, which generates a wealth effect that increases
labor supply thus reinforcing the boom. This wealth effect also leads consumption to respond less
in a boom making it more stable. The same pattern arises in the representative agent economy.
because of a wealth effect: in a boom, government revenues rise as the tax base increases and
government outlays fall as transfers fall. These forces lead to a reduction in government debt,
which is offset by increased government spending, which generates a wealth effect that increases
labor supply thus reinforcing the boom. This wealth effect also leads consumption to respond less
in a boom making Alternative
it more stable. The same
pattern arises mechanisms
in the representative agent economy.
financing
Keynes or Precautionary?
Table 6: S statistic for hand-to-mouth economy
Table 5: Variance of logs for heterogeneous agent economy
Y
N
C
6
baseline
no deficits
spending
0.0166
0.0135
0.0190
0.0166
0.0135
0.0188
0.0185
0.0156
0.0122
Running deficits is almost irrelevant. Ricardian equivalence not
Results
for hand-to-mouth economy
such a bad approximation.
In this version of the model we assume that the households do not save and consume their after-tax
Government
leads
to calibration
large wealth
effects.
incomes immediately.
I didpurchases
not changeadjusting
any features
of the
except
that I increased the
because
in booms,
surplus, This
leadschange
to rises
coefficients inIncreases
the Taylorvolatility
rule to resolve
an issue
of non-existence.
mayinalter the overall
dynamics in G,
response
a shock,
I hope it will not effect the impact of the experiments too
whichtoare
furtherbut
expansionary.
much.
It is still the case that lowering proportional taxes has close to no effect on volatility. Progressive
taxes also have very limited impact, which is more similar to the representative agent economy
than the heterogeneous agent economy. Reducing transfers now makes consumption more volatile,
which is not surprising as a large part of consumption tracks income mechanically. In this economy,
transfers stabilize labor supply more than in the heterogeneous agent economy. The behavior of
labor supply in the transfer experiment depends in part on the way the transfers are financed.
If we conduct the same experiment under the assumption that government spending adjusts to
4
Y
N
C
low propor. taxes
(1)
w/o progressive taxes
(2)
low transfers
(3)
small gov.
(4)
-0.0002
0.0091
-0.0074
-0.0052
0.0217
0.0210
0.0280
0.0950
0.1518
0.0481
0.1362
0.1043
maintain long-run
budget
balance, then the
volatility
hourshouseholds
is nearly unchanged
by the change
Mankiw’s
savers-spenders,
just
assumeof that
live
in transfers.hand-to-mouth.
One effect of transfers under lump-sum financing is that a positive shock leads to a
positive wealth effect for the capital-owners since they will pay fewer taxes for the transfers. This
is stabilizing since the positive wealth effect leads them to work less. When government spending
Transfers now mechanically stabilize consumption, and because
is used to balance the budget, the positive shock leads to an increase in government spending to
in recession, lump-sum tax on entrepreneurs rises, they work
absorb the budget surplus so there is not the same wealth effect.
more, which is also stabilizing.
Conclusion
�
Follow the money: transfers, tax changes. Focus on
automatic stabilizers.
Contributions / results
7. Conclusion
�
Propose a new measure of stabilization. New method to
solve incomplete-market models with nominal rigidities.
�
Redistribution is the crucial stabilizing force.
�
Progressive taxation and safety-net transfers stabilize
output and hours, but not consumption.
�
Transfers cause small reductions in steady-state wealth.