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The Intertemporal Keynesian Cross
Adrien Auclert, Matt Rognlie and Ludwig StraubSeptember 2018
1
This paper
Q: How does the macroeconomy propagate shocks?
• what micro moments are important?
• Recent literature: MPCs are crucial for PE e�ects
• Fiscal policy [Kaplan-Violante], monetary policy [Auclert],house prices [Berger et al], inequality [Auclert-Rognlie], . . .
• Here: “intertemporal MPCs” (iMPCs) are crucial for GE
2
Application: When is the �scal multiplier large?
• Lots of theory + empirical work. Two workhorse models:
1. Representative agent (RA) models• response of monetary policy is key• large when at ZLB
[Eggertsson 2004; Christiano-Eichenbaum-Rebelo 2011]
2. Two agent (TA) models• aggregate MPC is key• large when de�cit �nanced, e�ects not persistent
[Galí-López-Salido-Vallés 2007; Coenen et al 2012; Farhi-Werning 2017]
New: Heterogeneous-agents (HA)models→ iMPCs are key, can be used for calibration→ large and persistent Y e�ect when de�cit �nanced
3
Application: When is the �scal multiplier large?
• Lots of theory + empirical work. Two workhorse models:
1. Representative agent (RA) models• response of monetary policy is key• large when at ZLB
[Eggertsson 2004; Christiano-Eichenbaum-Rebelo 2011]
2. Two agent (TA) models• aggregate MPC is key• large when de�cit �nanced, e�ects not persistent
[Galí-López-Salido-Vallés 2007; Coenen et al 2012; Farhi-Werning 2017]
New: Heterogeneous-agents (HA)models→ iMPCs are key, can be used for calibration→ large and persistent Y e�ect when de�cit �nanced
3
Our contribution: Interaction of iMPCs and de�cit-�nancing
1. Benchmark model, allows for RA, TA, HA
• without capital & neutral monetary policy• multiplier = function of iMPCs and de�cits only
= 1 if zero de�cits or �at iMPCs (RA)
> 1 if de�cit-�nanced and realistic iMPCs (HA, TA?)
2. Quantitative model with capital & Taylor rule
• large & persistent Y e�ects, despite these extra elements
• iMPCs still crucial for Y response
3. Role of iMPCs for the GE e�ects of other shocks
4
Our contribution: Interaction of iMPCs and de�cit-�nancing
1. Benchmark model, allows for RA, TA, HA
• without capital & neutral monetary policy• multiplier = function of iMPCs and de�cits only
= 1 if zero de�cits or �at iMPCs (RA)
> 1 if de�cit-�nanced and realistic iMPCs (HA, TA?)
2. Quantitative model with capital & Taylor rule
• large & persistent Y e�ects, despite these extra elements
• iMPCs still crucial for Y response
3. Role of iMPCs for the GE e�ects of other shocks
4
Our contribution: Interaction of iMPCs and de�cit-�nancing
1. Benchmark model, allows for RA, TA, HA
• without capital & neutral monetary policy• multiplier = function of iMPCs and de�cits only
= 1 if zero de�cits or �at iMPCs (RA)
> 1 if de�cit-�nanced and realistic iMPCs (HA, TA?)
2. Quantitative model with capital & Taylor rule
• large & persistent Y e�ects, despite these extra elements
• iMPCs still crucial for Y response
3. Role of iMPCs for the GE e�ects of other shocks
4
Related literature
• Fiscal multipliers• Theory: IS-LM [Gelting 1941, Haavelmo 1945, Blinder-Solow 1973, ...]Rep agent (RA) [Aiyagari-Christiano-Eichenbaum 1992, Baxter-King 1993,Christiano-Eichenbaum-Rebelo 2011, ...]Two agents (TA) [Galí, López-Salido, Vallés 2007, Coenen et al. 2012,Farhi-Werning 2017, Drautzburg-Uhlig 2015, ...]Heterogeneous agent (HA) [Oh-Reis 2010, McKay-Reis 2016,Ferrière-Navarro 2017, Hagedorn-Manovski-Mitman 2017, ...]
• Empirics: Aggregate evidence [Ramey-Shapiro 1998, Blanchard-Perotti2002, Mountford-Uhlig 2009, Ramey 2011, Barro-Redlick 2011,Auerbach-Gorodnichenko 2012, Ramey-Zubairy 2018, ...]Cross-sectional multipliers [Shoag 2010, Chodorow-Reich et al. 2012,Nakamura-Steinsson 2014, Chodorow-Reich 2018, ...]
• Partial to general equilibrium [Farhi Werning 2017, Auclert-Rognlie 2018,Guren-McKay-Nakamura-Steinsson 2018, ...]
5
Outline
1 The intertemporal Keynesian Cross
2 iMPCs in models vs. data
3 Fiscal policy in the benchmark model
4 Fiscal policy in the quantitative model
5 Takeaways
6
The intertemporal Keynesian Cross
Common assumptions Unions
• GE, discrete time t = 0 . . .∞, no aggregate risk
• Mass 1 of households:• idiosyncratic shocks to skills eit, various market structures• real pre-tax income yit ≡ Wt/Pteitnit
nit = Nt
• after tax income zit ≡ yit − Tt(yit) ≡ τty1−λit [Bénabou, HSV]
• Government sets:• tax revenues Tt =
∫(yit − zit)di
rationing
• government spending Gt• “neutral” monetary policy: �xed real rate = r
• Supply side:
relax later
• linear production function Yt = Nt• �exible prices ⇒ Pt = Wt• sticky w⇒ πwt = κw
∫Nt(v′ (nit)− ε−1
ε∂zit∂nit
u′ (cit)di) + βπwt+1
7
Common assumptions Unions
• GE, discrete time t = 0 . . .∞, no aggregate risk
• Mass 1 of households:• idiosyncratic shocks to skills eit, various market structures• real pre-tax income yit ≡ Wt/Pteitnit
nit = Nt
• after tax income zit ≡ yit − Tt(yit) ≡ τty1−λit [Bénabou, HSV]
• Government sets:• tax revenues Tt =
∫(yit − zit)di
rationing
• government spending Gt• “neutral” monetary policy: �xed real rate = r
• Supply side:
relax later
• linear production function Yt = Nt• �exible prices ⇒ Pt = Wt• sticky w⇒ πwt = κw
∫Nt(v′ (nit)− ε−1
ε∂zit∂nit
u′ (cit)di) + βπwt+1
7
Common assumptions Unions
• GE, discrete time t = 0 . . .∞, no aggregate risk
• Mass 1 of households:• idiosyncratic shocks to skills eit, various market structures• real pre-tax income yit ≡ Wt/Pteitnit
nit = Nt
• after tax income zit ≡ yit − Tt(yit) ≡ τty1−λit [Bénabou, HSV]
• Government sets:• tax revenues Tt =
∫(yit − zit)di
rationing
• government spending Gt• “neutral” monetary policy: �xed real rate = r
• Supply side:
relax later
• linear production function Yt = Nt• �exible prices ⇒ Pt = Wt• sticky w⇒ πwt = κw
∫Nt(v′ (nit)− ε−1
ε∂zit∂nit
u′ (cit)di) + βπwt+1 7
Common assumptions Unions
• GE, discrete time t = 0 . . .∞, no aggregate risk
• Mass 1 of households:• idiosyncratic shocks to skills eit, various market structures• real pre-tax income yit ≡ Wt/Pteitnit nit = Nt• after tax income zit ≡ yit − Tt(yit) ≡ τty1−λit [Bénabou, HSV]
• Government sets:• tax revenues Tt =
∫(yit − zit)di rationing
• government spending Gt• “neutral” monetary policy: �xed real rate = r
• Supply side:
relax later
• linear production function Yt = Nt• �exible prices ⇒ Pt = Wt• sticky w⇒ πwt = κw
∫Nt(v′ (nit)− ε−1
ε∂zit∂nit
u′ (cit)di) + βπwt+1 7
Common assumptions Unions
• GE, discrete time t = 0 . . .∞, no aggregate risk
• Mass 1 of households:• idiosyncratic shocks to skills eit, various market structures• real pre-tax income yit ≡ Wt/Pteitnit nit = Nt• after tax income zit ≡ yit − Tt(yit) ≡ τty1−λit [Bénabou, HSV]
• Government sets:• tax revenues Tt =
∫(yit − zit)di rationing
• government spending Gt• “neutral” monetary policy: �xed real rate = r
• Supply side: relax later• linear production function Yt = Nt• �exible prices ⇒ Pt = Wt• sticky w⇒ πwt = κw
∫Nt(v′ (nit)− ε−1
ε∂zit∂nit
u′ (cit)di) + βπwt+1 7
Asset market assumptions
Household i solves
max E[∑
βt {u (cit)− v (nit)}]
• RA: no risk in e (or complete markets)• TA: share µ of agents with cit = zit• HA-std: one asset model
cit + ait = (1+ r)ait−1 + zitait ≥ 0
• HA-iMPC: simpli�ed two asset model• illiquid account ailliq = �xed no. of bonds ( + capital)• liquid account ait = all remaining bonds + railliq
8
The aggregate consumption function Eq de�nition
• Equilibrium de�ned as usual
• Given {ai0} and r, aggregate consumption function is
Ct =∫citdi = Ct ({Zs})
[Farhi Werning 2017, Auclert Rognlie 2016]
with Zt ≡aggregate after-tax labor income
Zt ≡∫zitdi = Yt − Tt
• C summarizes the heterogeneity and market structure
9
Intertemporal MPCs
• Goods market clearing↔
Yt = Gt + Ct ({Ys − Ts})
• Impulse response to shock {dGt,dTt}
dYt = dGt +∞∑s=0
∂Ct∂Zs︸︷︷︸≡Mt,s
· (dYs − dTs) (1)
→ Response {dYt} entirely characterized by {Mt,s}!
• partial equilibrium derivatives, “intertemporal MPCs”
• how much of income change at date s is spent at date t
•∑∞
t=0(1+ r)s−tMt,s = 1
10
The intertemporal Keynesian cross
• Stack objects: M = {Mt,s} ={∂Ct∂Zs
}, dY = {dYt}, etc
• Rewrite equation (1) as
dY = dG−MdT+MdY
• This is an intertemporal Keynesian cross• entire complexity of model is in M
• with M from data, could get dY without model!
• When unique, solution is
dY =M · (dG−MdT)
whereM is (essentially) (I−M)−1
11
The intertemporal Keynesian cross
• Stack objects: M = {Mt,s} ={∂Ct∂Zs
}, dY = {dYt}, etc
• Rewrite equation (1) as
dY = dG−MdT+MdY
• This is an intertemporal Keynesian cross• entire complexity of model is in M
• with M from data, could get dY without model!
• When unique, solution is
dY =M · (dG−MdT)
whereM is (essentially) (I−M)−1
11
Benchmark model takeaway
• Government chooses dG and dT such that∑∞
t=0Gt−Tt(1+r)t = 0
• dY is solution to intertemporal Keynesian cross
dY = dG−MdT+MdY
• iMPCs M = {Mt,s} capture model response of aggregateconsumption to changes in after-tax income
• RA, TA, HA di�er in their M matrices
• Next:
• look at M’s in data and compare with RA, TA, HA
• implications for dY
12
Benchmark model takeaway
• Government chooses dG and dT such that∑∞
t=0Gt−Tt(1+r)t = 0
• dY is solution to intertemporal Keynesian cross
dY = dG−MdT+MdY
• iMPCs M = {Mt,s} capture model response of aggregateconsumption to changes in after-tax income
• RA, TA, HA di�er in their M matrices
• Next:
• look at M’s in data and compare with RA, TA, HA
• implications for dY
12
Benchmark model takeaway
• Government chooses dG and dT such that∑∞
t=0Gt−Tt(1+r)t = 0
• dY is solution to intertemporal Keynesian cross
dY = dG−MdT+MdY
• iMPCs M = {Mt,s} capture model response of aggregateconsumption to changes in after-tax income
• RA, TA, HA di�er in their M matrices
• Next:
• look at M’s in data and compare with RA, TA, HA
• implications for dY
12
iMPCs in models vs. data
Measuring aggregate iMPCs using individual iMPCs
• Object of interest: (aggregate) iMPCs
Mt,s =∂Ct∂Zs
where Ct =∫citdi and Zs =
∫zisdi
• Direct evidence on Mt,s is hard to come by for general s
• More work on column s = 0 (unanticipated income shock)
• Can write
Mt,0 =
∫ zi0Z0︸︷︷︸
income weight
· ∂cit∂zi0︸︷︷︸
individual iMPC
di
→ aggregate iMPCs are weighted individual iMPCs
13
Obtain date-0 iMPCs from cross-sectional microdata
• Two sources of evidence on ∂cit∂zi0
:
1. Fagereng Holm Natvik (2018) measure in Norwegian data
cit = αi + τt +5∑
k=0γklotteryi,t−k + θxit + εit
• Weighting by income in year of lottery receipt⇒ Mt,0
2. Italian survey data (SHIW 2016) on ∂ci0∂zi0
• Construct lower bound for impulse using distribution ofMPCs + stationarity assumption
14
iMPCs in the data
0 1 2 3 4 5
0
0.1
0.2
0.3
0.4
0.5
0.6
Year (t)
Data from Fagereng et al (2018)Lower bound from SHIW 2016
• Annual M0,0 consistent with evidence from other sources15
Compare iMPCs across models Calibration
• RA
• TA: share of hand-to-mouth calibrated to match M0,0
• HA-std: one-asset HA, standard calibration
• HA-iMPC: two-asset HA calibrated to match iMPCs
• . . . and for fun:• BU: bonds-in-utility model, calibrated to match M0,0[Michaillat Saez 2018; Hagedorn 2018; Kaplan Violante 2018]
16
iMPCs across models
0 1 2 3 4 50
0.2
0.4
0.6
Year (t)
iMPC
Mt,0
(a) Data and model �t
DataHA-illiq
0 1 2 3 4 50
0.2
0.4
0.6
Year (t)
(b) Alternative models
DataRATA
HA-stdBU
17
iMPCs across models including TABU
0 1 2 3 4 50
0.2
0.4
0.6
Year (t)
iMPC
Mt,0
(a) Data and model �t
DataHA-illiqTABU
0 1 2 3 4 50
0.2
0.4
0.6
Year (t)
(b) Alternative models
DataRATA
HA-stdBU
18
What about non-date-0 iMPCs?
• Existing evidence useful for response to date-0 incomeshocks, {Mt,0}
• What about respones to future shocks?
→ use calibrated HA-iMPCmodel to �ll in the blanks!
19
Response of HA-iMPC to other income shocks
0 5 10 15 20 25 300
0.2
0.4
0.6
Year t
iMPC
Mt,s
s = 0s = 5s = 10s = 15s = 20
20
Not entirely arbitrary→ TABU is very similar! Durables
0 5 10 15 20 25 300
0.2
0.4
0.6
Year t
iMPC
Mt,s
s = 0s = 5s = 10s = 15s = 20TABU
21
Fiscal policy in the benchmark model
Fiscal policy in the benchmark model
• Recall intertemporal Keynesian cross:
dY = dG−M · dT+M · dY
• dY entirely determined by iMPCs M and �scal policy(dG,dT)
• Next: Characterize role of iMPCs for
1. balanced budget policies, dG = dT
2. de�cit-�nanced policies
22
The balanced-budget unit multiplier
• With balanced budget, dG = dT⇒ multiplier of 1:
dY = dG
• Similar reasoning already in Haavelmo (1945)
• Generalizes Woodford’s RA results
• heterogeneity irrelevant for balanced budget �scal policy
• similar to Werning (2015)’s result for monetary policy
• Proof: dY = dG is unique solution to
dY = (I−M) · dG+M · dY
23
De�cit-�nanced �scal policy
• With de�cit �nancing dG 6= dT we have
dY = dG+M ·M · (dG− dT)︸ ︷︷ ︸dC
Consumption dC depends on primary de�cits dG− dT
• Example: TA model with de�cit �nancing
dY = dG+µ
1− µ (dG− dT)
• consumption dC depends only on current de�cits
• initial multiplier can be large ∈[1, 1
1−µ
]. . .
• but cumulative multiplier is = 1 !∑(1+ r)−tdYt∑(1+ r)−tdGt
= 1
24
De�cit-�nanced �scal policy
• With de�cit �nancing dG 6= dT we have
dY = dG+M ·M · (dG− dT)︸ ︷︷ ︸dC
Consumption dC depends on primary de�cits dG− dT
• Example: TA model with de�cit �nancing
dY = dG+µ
1− µ (dG− dT)
• consumption dC depends only on current de�cits
• initial multiplier can be large ∈[1, 1
1−µ
]. . .
• but cumulative multiplier is = 1 !∑(1+ r)−tdYt∑(1+ r)−tdGt
= 124
Simulate model responses for more general shocks Impulse
• Parametrize: dGt = ρGdGt−1 and dBt = ρB (dBt−1 + dGt)• vary degree of de�cit-�nancing ρB
0 0.2 0.4 0.6 0.8
1
1.5
2
2.5
3
Persistence of debt ρB
dY0/dG
0
Impact multiplier
HA-illiqHA-stdRATATABU
0 0.2 0.4 0.6 0.8
1
1.5
2
2.5
3
Persistence of debt ρB
∑ (1+r)
−t dY t
∑ (1+r)
−t dG t
Cumulative multiplier
Calibration: ρG = 0.7
25
Simulate model responses for more general shocks Impulse
• Parametrize: dGt = ρGdGt−1 and dBt = ρB (dBt−1 + dGt)• vary degree of de�cit-�nancing ρB
0 0.2 0.4 0.6 0.8
1
1.5
2
2.5
3
Persistence of debt ρB
dY0/dG
0
Impact multiplier
HA-illiqHA-stdRATATABU
0 0.2 0.4 0.6 0.8
1
1.5
2
2.5
3
Persistence of debt ρB
∑ (1+r)
−t dY t
∑ (1+r)
−t dG t
Cumulative multiplier
Calibration: ρG = 0.7 25
Fiscal policy in the quantitativemodel
Adding new elements to the HA-iMPC model . . . Calibration
• Government:
• gov spending shock, dGt = ρGdGt−1
• �scal rule, dBt = ρB (dBt−1 + dGt)
• Taylor rule, it = rss + φπt, φ > 1
• Supply side:
• Cobb-Douglas production, Yt = Kαt N1−αt
• Kt subject to quadratic capital adjustment costs
• sticky prices à la Calvo, πt = κpmct + 11+rtπt+1
• Two reasons for lower multipliers:
• monetary policy & crowding-out of investment
26
Sizeable output response to de�cit-�nanced G Other
0 2 4 6 8 100
0.5
1
1.5
Percentofs.s.output
OutputρB = 0.3ρB = 0.5ρB = 0.7ρB = 0.8
0 2 4 6 8 10
0
0.5
1
Consumption
0 2 4 6 8 10
−0.4
−0.2
0Investment
0 2 4 6 8 100
0.20.40.60.81
Government spending
0 2 4 6 8 100
1
2
Years
Hours (% of s.s.)
0 2 4 6 8 10020406080100
Years
In�ation (bps)
0 2 4 6 8 100
20
40
60
Years
Real interest rate (bps)
0 2 4 6 8 100
0.5
1
Years
Government bonds (% of Yss)
Calibration: ρG = 0.7, κw = κp = 0.1, φ = 1.5; vary ρB in dBt = ρB (dBt−1 + dGt)
27
Equilibrium e�ect from Y important for both C and I
0 2 4 6 8 10−0.2
0
0.2
0.4
0.6
0.8
1
Years
Percentofs.s.output
Consumption
r e�ectY e�ect
0 2 4 6 8 10
−0.5
0
0.5
Years
Investment
Calibration: ρG = 0.7, ρB = 0.7, κw = κp = 0.1, φ = 1.5
28
iMPCs still a crucial determinant of response! Impulse
0 0.2 0.4 0.6 0.80
0.5
1
1.5
2
Persistence of debt ρB
dY0/dG
0
Impact multiplier
HA-illiqHA-stdRATA
0 0.2 0.4 0.6 0.80
0.5
1
1.5
2
Persistence of debt ρB∑ (1
+r)
−t dY t
∑ (1+r)
−t dG t
Cumulative multiplier
Calibration: ρG = 0.7, κw = κp = 0.1, ρB = 0.5, φ = 1.5
29
Summary: HA-iMPC & TA have large on-impact multipliers
On-impact multipliers dY0dG0
Fiscal rule Model RA HA-std TA HA-illiq
bal. budgetbenchmark 1.0 1.0 1.0 1.0quantitative 0.6 0.7 0.6 0.7
de�cit-�nancedbenchmark 1.0 1.0 1.8 2.5quantitative 0.6 0.6 1.3 1.6
Calibration: ρG = 0.7, κw = κp = 0.1, ρB = 0.5, φ = 1.5
30
. . . but only HA-iMPC has large cumulative multipliers
Cumulative multipliers∑
t(1+r)−tdYt∑t(1+r)−tdGt
Fiscal rule Model RA HA-std TA HA-illiq
bal. budgetbenchmark 1.0 1.0 1.0 1.0quantitative 0.5 0.5 0.5 0.6
de�cit-�nancedbenchmark 1.0 1.1 1.0 2.6quantitative 0.2 0.4 0.8 1.4
31
Takeaways
What can we learn for other shocks? – back to benchmark
• Aggregate consumption may depend on other shocks θ,
Ct = Ct ({Zs}, θ)
[e.g. deleveraging, inequality, preferences, mon. policy]
• Can de�ne partial equilibrium e�ect as
∂Y ≡ dG−MdT+ Cθdθ
• Same intertemporal Keynesian cross applies:
dY = ∂Y+MdY
→ iMPCs also determine propagation of other shocks
32
Conclusion
M matters for Macro !
→ crucial for GE propagation→ new insights for �scal policy
New avenues:
more evidence on Mimplications for other shocks
33
Extra slides
Unions back
• Mass 1 of unions. Each union k• employs every individual, ni ≡
∫nikdk
• produces task Nk =∫einikdi from member hours
• pays common wage wk per e�cient unit of work e• requires that all individuals work nik = Nk
• Final good �rms aggregate N ≡(∫ 1
0 Nε−1ε
k dk) εε−1
• Union k sets wkt each period to maximize
maxwkt
∑τ≥0
βτ{∫{u (cit+τ )− v (nit+τ )}di−
ψ
2
(wkt+τwkt+τ−1
)2}• ⇒ nonlinear wage Phillips curve
(1+ πwt )πwt =
ε
ψ
∫Nt(v′ (nit)−
ε− 1ε
∂zit∂nit
u′ (cit))di
+ βπwt+1(1+ πwt+1
)34
Equilibrium de�nition back
• Given {Gt, Tt}, a general equilibrium is a set of prices,household decision rules and quantities s.t. at all t:1. �rms optimize2. households optimize3. �scal and monetary policy rules are satis�ed4. the goods market clears
35
iMPCs for model with durables back
0 5 10 15 20 25 300
0.2
0.4
0.6
Year t
iMPC
Mt,s
s = 0s = 5s = 10s = 15s = 20Durab.
Calibration: homothetic durables model with dit = 0.1 · cit and δD = 20%
36
Calibration for benchmark model back
• Preferences: u (c) = c1−1ν
1− 1ν, v (n) = bn
1+ 1φ
1+ 1φ
• Income process: log et = ρe log et−1 + σεt
Parameter Parameter HA-illiq HA-std
ν EIS 0.5φ Frisch 1ρe Log e persistence 0.91σ Log e st dev 0.92λ Tax progressivity 0.181G/Y Spending-to-GDP 0.2A/Z Wealth-to-aftertax income 8.2B/Z Liquid assets to aftertax income 0.15 8.2β Discount factor 0.80 0.92r Real interest rate 0.05κw Wage �exibility 0.1 37
Calibration for quantitative model back
• As in benchmark model, plus:
Parameter Parameter
α Capital share 0.33B/Y Debt-to-GDP 0.7K/Y Capital-to-GDP 2.5µ SS markup 1.015δ Depreciation rate 0.08εI Invest elasticity to q 4κp Price �exibility 0.1κw Wage �exibility 0.1φ Taylor rule coe�cient 1.5
38
Impulse responses in benchmark model back
0 2 4 6 8 100
1
2
Percentofs.s.output
Output
HA-illiqHA-stdRATATABU
0 2 4 6 8 10
0
0.5
1
1.5
Consumption
0 2 4 6 8 100
0.20.40.60.81
Government spending
0 2 4 6 8 10
0
50
100
Years
In�ation (bps)
0 2 4 6 8 10−100
−50
0
50
100
Years
Real interest rate (bps)
0 2 4 6 8 100.2
0.4
0.6
0.8
1
Years
Government bonds (% of Yss)
Calibration: ρG = ρB = 0.7
39
Impulse responses in quantitative model back
0 2 4 6 8 100
0.5
1
1.5
Percentofs.s.output
Output
HA-illiqHA-stdRATA
0 2 4 6 8 10
0
0.5
1Consumption
0 2 4 6 8 10
−0.2
−0.1
0
Investment
0 2 4 6 8 100
0.20.40.60.81
Government spending
0 2 4 6 8 100
0.51
1.52
2.5
Years
Hours (% of s.s.)
0 2 4 6 8 100
20
40
60
Years
In�ation (bps)
0 2 4 6 8 100
10
20
30
40
Years
Real interest rate (bps)
0 2 4 6 8 100.2
0.4
0.6
0.8
1
Years
Government bonds (% of Yss)
Calibration: ρG = ρB = 0.7, κw = κp = 0.1, φ = 1.5
40
True unless very responsive Taylor rule back
0 2 4 6 8 10
0
0.5
1
1.5
2
Years
Percentofs.s.output
Output
φ = 1φ = 1.5φ = 2
0 2 4 6 8 10
−1
−0.5
0
0.5
Years
Investment
Calibration: ρG = 0.7, κw = κp = 0.1, ρB = 0.5, and vary φ in Taylor rule
41
True even with more �exible prices (unless very �exible) back
0 2 4 6 8 10
0
0.5
1
1.5
2
2.5
Years
Percentofs.s.output
Output
κp = 0κp = 0.1κp = 0.25
0 2 4 6 8 10−1.5
−1
−0.5
0
0.5
Years
Investment
Calibration: ρG = 0.7, κw = 0.1, ρB = 0.5, φ = 1.5, and vary κp in price Phillips curve
42
True even with more �exible wages (unless very �exible) back
0 2 4 6 8 10
0
1
2
3
Years
Percentofs.s.output
Output
κw = 0κw = 0.1κw = 0.25
0 2 4 6 8 10−0.4
−0.2
0
0.2
0.4
Years
Investment
Calibration: ρG = 0.7, κp = 0.1, ρB = 0.5, φ = 1.5, and vary κw in wage Phillips curve
43