Deep Habits
Morten Ravn (EUI)
Stephanie Schmitt-Grohé (Duke)
Martı́n Uribe (Duke)
1
Existing Literature on Habit Formation
• Habits are formed at the level of a composite good. (Superficial Habits)
U (ct − θct−1)
"Z
# 1
1 1− 1
1− 1
η
η
cit di
ct =
0
• This paper: Habits are formed at the level
of individual goods. (Deep Habits)
U (xt)
with
xt =
"Z
1
0
(cit − θcit−1
# 1
1
1− 1
1− η
η
)
di
2
Superficial Habits
Demand side effect: Euler equation with external superficial habit
U 0(ct − θct−1) = βEtU 0(ct+1 − θct)Rt+1
No supply side effects: Demand function for
good i as in a model without habits:
cit =
Pit
Pt
!−η
ct
3
Aggregate Implications of Deep Habits
• The economys demand side (particularly
the consumption Euler equation) is identical under deep and superficial external
habits.
• Under deep habit formation, the supply side
of the economy changes in fundamental
ways.
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Demand Function for Good i Under External
Deep Habit Formation
−η
cit = pit (ct − θct−1) + θcit−1
• Deep Habits give rise to a theory of countercyclical markups. the price elasticity of
demand becomes countercyclical: [ Priceelasticity effect of deep habits]
• the pricing problem becomes dynamic: [
Intertemporal effect of deep habits]
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Three Variations
1. Good Specific Subsistence Points
−η
cit = pit xt + θc∗
2. Relative Deep Habits
−η
θ(1−η)
cit = pit xtcit−1
3. Internal Deep Habits

cit = 
∞
X
k=0
−η
θ k rt,t+k pit+k  Xt + θcit−1
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Equilibrium Under Deep Habits
Ux(xt, ht ) = βRtEtUx(xt+1 , ht+1)
xt = ct − θct−1
Uh(xt, ht )
wt = −
Ux(xt, ht )
ct = Atht
µt =
νt =
At
wt
µt − 1
+ θEtrt,t+1νt+1
µt
ct = η(ct − θct−1)νt


µt = 
1 −
1
η 1−
θct−1
ct
−1

+ θEtrt,t+1vt+1

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Deep Habits and Markups Dynamics in a
Fully Fledged RBC Model
• Slow decay in habits:
"Z
#1/(1−1/η)
1−1/η
1
j
j
xt =
cit − θsit−1
di
,
0
sit = ρsit−1 + (1 − ρ)cit.
• Elastic labor supply and Capital accumulation
• Three shocks:
- Productivity Shocks
- Preference Shocks
- Government Spending Shocks
• Government consumption is subject to deep
habit formation
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Estimating Deep Habits
Fully Fledged Deep-Habit Model: GMM
Estimates of Structural Parameters,
U.S. data from 1967-2003 (Quarterly).
Measurement
C
R
tot
C
RF F R
Joint System Based
σ
θ
1.854
0.861
(0.583) (0.039)
Estimates
η
ρ
5.261
0.848
(1.062) (0.027)
J-test
54.22
[0.749]
Notes: Numbers in parentheses are heteroscedasticity
consistent standard errors. Numbers in square brackets
are P-values.
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Impulse Responses to Positive Preference,
Government Spending, and Productivity
Shocks Under Deep Habit, Superficial Habit,
and No Habit
Markup
Output
Wage
0.4
0.8
0.3
0.2
0.6
0.2
0
0.4
0.1
−0.2
0.2
0
−0.4
0
10
Markup
0
20
0.5
0
−0.5
−1
0
10
Markup
20
0.4
0.2
0.2
0
0
−0.2
1.5
−0.2
1
−0.4
0.5
20
Deep Habit
−0.1
0.4
0
10
20
0.6
2
0
10
Output
0.6
0.2
−0.6
0
0
0
10
Output
20
−0.2
Consumption
1
0.5
0
10
Wage
0
20
0
10
20
Consumption
0.02
0
−0.02
0
10
Wage
−0.04
20
0
1.5
10
20
Consumption
0.4
0.3
1
0.2
0.5
0
10
20
0
0.1
0
10
20
Superficial Habit
0
0
10
20
..... No habit
Row 1: Preference Shock. Row 2: Government Spending Shock. Row 3: Technology shock.
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Conclusion
• Deep habit formation implies that producers face demand functions that depend on
past sales.
• Thus, the deep-habit model provides microfoundations to customer market (PhelpsWinter, 1970) and brand-switching-cost (Klemperer, 1995) models.
• Deep habits induce a theory of endogenous
markup determination.
• Under deep habits markups are countercyclical, which is in line with empirical evidence.
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