(1) Permanent Income Hypothesis (2) Precautionary Savings · Permanent Income Hypothesis (PIH)...

Lecture 2

(1) Permanent Income Hypothesis

(2) Precautionary Savings

Erick Sager

September 21, 2015

Econ 605: Adv. Topics in MacroeconomicsJohns Hopkins University, Fall 2015

Last Time (8/31/15)

Finished thinking about aggregation

• Gorman Form

ci(p, wi) = ai(p) + b(p)wi =⇒ C(p, w) = C(p,W )

Erick Sager Lecture 2 (9/21/15) 1 / 36

Last Time (9/14/15)

• Negishi Planner’s Problem:

V (µiNi=1, k0) = maxcitNt=1,kt+1∞t=0

∞∑t=0

βtN∑i=1

µiu(cit)

s.t.(∑N

i=1 µicit

)+ kt+1 = f(kt) + (1− δ)kt

• Constantinides Decomposition:

1. Individual Allocation

U(Ct) = maxcitNi=1

N∑i=1

µiu(cit) s.t.

N∑i=1

πicit ≤ Ct

2. Aggregate Allocation

maxCt,kt+1∞t=0

∞∑t=0

βtU(Ct)

s.t. Ct + kt+1 = f(kt) + (1− δ)ktk0 given


Last Time (9/14/15)



∞∑t=0

βtN∑i=1

µiu(cit)

s.t.(∑N

i=1 µicit

)+ kt+1 = f(kt) + (1− δ)kt



U(Ct) = maxcitNi=1

N∑i=1

µiu(cit) s.t.

N∑i=1

πicit ≤ Ct


maxCt,kt+1∞t=0

∞∑t=0

βtU(Ct)



Last Time (9/14/15)



∞∑t=0

βtN∑i=1

µiu(cit)

s.t.(∑N

i=1 µicit

)+ kt+1 = f(kt) + (1− δ)kt



U(Ct) = maxcitNi=1

N∑i=1

µiu(cit) s.t.

N∑i=1

πicit ≤ Ct


maxCt,kt+1∞t=0

∞∑t=0

βtU(Ct)



Last Time (9/14/15)



∞∑t=0

βtN∑i=1

µiu(cit)

s.t.(∑N

i=1 µicit

)+ kt+1 = f(kt) + (1− δ)kt



U(Ct) = maxcitNi=1

N∑i=1

µiu(cit) s.t.

N∑i=1

πicit ≤ Ct


maxCt,kt+1∞t=0

∞∑t=0

βtU(Ct)



Last Time (9/14/15)

Maliar and Maliar (2003)

• Complete markets

• Idiosyncratic labor productivity shocks

Planner’s Problem

U(Ct, 1− Lt) = maxcit,hiti∈I

∫Iαiu(cit, h

it)dµ

i

s.t.∫I c

itdµ

i ≤ Ct∫I ε

ithitdµ

i ≤ Lt

First Order Conditions:

cit =

(αi) 1σ∫

I

(αi) 1σ dµi

Ct , 1− hit =

(αi) 1γ(εit)− 1

γ∫I

(αi) 1γ (εit)

1− 1γ dµi

(1− Lt)


Last Time (9/14/15)




Planner’s Problem


∫Iαiu(cit, h

it)dµ

i

s.t.∫I c

itdµ

i ≤ Ct∫I ε

ithitdµ

i ≤ Lt


cit =

(αi) 1σ∫

I

(αi) 1σ dµi

Ct , 1− hit =


γ∫I

(αi) 1γ (εit)

1− 1γ dµi

(1− Lt)


Last Time (9/14/15)




Planner’s Problem


∫Iαiu(cit, h

it)dµ

i

s.t.∫I c

itdµ

i ≤ Ct∫I ε

ithitdµ

i ≤ Lt


cit =

(αi) 1σ∫

I

(αi) 1σ dµi

Ct , 1− hit =


γ∫I

(αi) 1γ (εit)

1− 1γ dµi

(1− Lt)


Last Time (9/14/15)

Maliar and Maliar (2003)∫Iαi[

(cit)1−σ

1− σ+ ψ

(1− hit)1−γ

1− γ

]dµi =

(Ct)1−σ

1− σ+ Ψt

(1− Lt)1−γ

1− γ

• “Labor Wedge” endogenously arises:

Ψt ≡ ψ∫I

(αi) 1γ(εit)1− 1

γ(∫I (αi)

1γ (εit)

1− 1γ dµi

)1−γ dµi = ψ

(∫I

(αi) 1γ (εit)

1− 1γ dµi

)γ

• Labor Wedge:

ψ(1− ht)−γ = (1− τt)wtc−σt =⇒ τt = 1− 1

(1− α)Yt/Lt· ψ(1− ht)−γ

c−σt


Last Time (9/14/15)


(cit)1−σ

1− σ+ ψ

(1− hit)1−γ

1− γ

]dµi =

(Ct)1−σ

1− σ+ Ψt

(1− Lt)1−γ

1− γ


Ψt ≡ ψ∫I

(αi) 1γ(εit)1− 1

γ(∫I (αi)

1γ (εit)

1− 1γ dµi

)1−γ dµi = ψ

(∫I

(αi) 1γ (εit)

1− 1γ dµi

)γ

• Labor Wedge:

ψ(1− ht)−γ = (1− τt)wtc−σt =⇒ τt = 1− 1

(1− α)Yt/Lt· ψ(1− ht)−γ

c−σt


Last Time (9/14/15)


(cit)1−σ

1− σ+ ψ

(1− hit)1−γ

1− γ

]dµi =

(Ct)1−σ

1− σ+ Ψt

(1− Lt)1−γ

1− γ


Ψt ≡ ψ∫I

(αi) 1γ(εit)1− 1

γ(∫I (αi)

1γ (εit)

1− 1γ dµi

)1−γ dµi = ψ

(∫I

(αi) 1γ (εit)

1− 1γ dµi

)γ

• Labor Wedge:

ψ(1− ht)−γ = (1− τt)wtc−σt =⇒ τt = 1− 1

(1− α)Yt/Lt· ψ(1− ht)−γ

c−σt


Last Time (9/14/15)

• Permanent Income Hypothesis (PIH)

• Restrict asset space

• Exogenously incomplete asset markets

• Cannot write asset contracts contingent on specific future states

ct +1

1 + rtat+1 ≤ yt + at

• “Strict” Permanent Income Hypothesis

• Utility: u(c) = −(α/2)(ct − c)2

• Time Preference: β(1 + r) = 1

• No Ponzi Condition


Last Time (9/14/15)

• Permanent Income Hypothesis (PIH)

• Restrict asset space

• Exogenously incomplete asset markets

• Cannot write asset contracts contingent on specific future states

ct +1

1 + rtat+1 ≤ yt + at

• “Strict” Permanent Income Hypothesis

• Utility: u(c) = −(α/2)(ct − c)2

• Time Preference: β(1 + r) = 1

• No Ponzi Condition


Last Time (9/14/15)

PIH Characterization

• Consumption is random walk: Et[ct+1] = ct

• Consumption equals permanent income

ct =r

1 + r

at +

∞∑j=0

(1

1 + r

)jEt[yt+j ]

≡ r

1 + r

(at + ht

)• Consumption does not depend on income variance

• Consumption responds to news

∆ct =r

1 + r

∞∑j=0

(1

1 + r

)j (Et[yt+j ]− Et−1[yt+j ]

)• Assets offset expected income fluctuations

1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r

)jEt[∆yt+j ]


Today (9/21/15)

• Finish: Empirical evaluation of theory

• Excess Sensitivity Puzzle (β1 > 0):

∆ct = β0 + β1∆yt−1 + εt

• Excess Smoothness Puzzle• Reconciliation of Puzzles

(Campbell and Deaton (1989))

• Start: Buffer Stock Savings Model

• Borrowing Constraints

• Prudence

• Patience


Today (9/21/15)

• Finish: Empirical evaluation of theory

• Excess Sensitivity Puzzle (β1 > 0):

∆ct = β0 + β1∆yt−1 + εt

• Excess Smoothness Puzzle• Reconciliation of Puzzles

(Campbell and Deaton (1989))

• Start: Buffer Stock Savings Model

• Borrowing Constraints

• Prudence

• Patience


Excess Smoothness

• Suppose income is serially correlated and persistent

• Strict PIH predicts:

σ∆c > σ∆y

• In the data:

σ∆c < σ∆y

• Illustrate this puzzle using the Strict PIH model

• Use three different income processes:

• yt = εt + γεt−1

• yt = yt−1 + εt• ∆yt = γ∆yt−1 + εt


Excess Smoothness



σ∆c > σ∆y

• In the data:

σ∆c < σ∆y




• yt = yt−1 + εt• ∆yt = γ∆yt−1 + εt


Excess Smoothness



σ∆c > σ∆y

• In the data:

σ∆c < σ∆y




• yt = yt−1 + εt• ∆yt = γ∆yt−1 + εt


Excess Smoothness



σ∆c > σ∆y

• In the data:

σ∆c < σ∆y




• yt = yt−1 + εt• ∆yt = γ∆yt−1 + εt


Excess Smoothness



σ∆c > σ∆y

• In the data:

σ∆c < σ∆y




• yt = yt−1 + εt• ∆yt = γ∆yt−1 + εt


Excess Smoothness



σ∆c > σ∆y

• In the data:

σ∆c < σ∆y




• yt = yt−1 + εt• ∆yt = γ∆yt−1 + εt


Excess Smoothness



σ∆c > σ∆y

• In the data:

σ∆c < σ∆y




• yt = yt−1 + εt

• ∆yt = γ∆yt−1 + εt


Excess Smoothness



σ∆c > σ∆y

• In the data:

σ∆c < σ∆y




• yt = yt−1 + εt• ∆yt = γ∆yt−1 + εt


Excess Smoothness

Process 1: yt = εt + γεt−1

• Optimal consumption dynamics

∆ct =r

1 + r

(εt +

(1

1 + r

)γεt

)

• Assume r = 0.04, γ = (1 + r)/2

σ∆c =r

1 + r

(1 +

γ

1 + r

)σε =

0.04

1.04(1 + 0.5)σε ≈ 0.06σε

• Then too smooth: σ∆c/σε nearly zero


Excess Smoothness



∆ct =r

1 + r

(εt +

(1

1 + r

)γεt

)

• Assume r = 0.04, γ = (1 + r)/2

σ∆c =r

1 + r

(1 +

γ

1 + r

)σε =

0.04

1.04(1 + 0.5)σε ≈ 0.06σε



Excess Smoothness



∆ct =r

1 + r

(εt +

(1

1 + r

)γεt

)

• Assume r = 0.04, γ = (1 + r)/2

σ∆c =r

1 + r

(1 +

γ

1 + r

)σε =

0.04

1.04(1 + 0.5)σε ≈ 0.06σε



Excess Smoothness



∆ct =r

1 + r

(εt +

(1

1 + r

)γεt

)

• Assume r = 0.04, γ = (1 + r)/2

σ∆c =r

1 + r

(1 +

γ

1 + r

)σε =

0.04

1.04(1 + 0.5)σε ≈ 0.06σε



Excess Smoothness



∆ct =r

1 + r

(εt +

(1

1 + r

)γεt

)

• Assume r = 0.04, γ = (1 + r)/2

σ∆c =r

1 + r

(1 +

γ

1 + r

)σε =

0.04

1.04(1 + 0.5)σε ≈ 0.06σε



Excess Smoothness

Process 2: ∆yt = εt


∆ct = εt

• Then too volatile: σ∆c = σε


Excess Smoothness



∆ct = εt



Excess Smoothness



∆ct = εt



Excess Smoothness



∆ct = εt



Excess Smoothness

Process 3: ∆yt = γ∆yt−1 + εt


∆ct =1 + r

1 + r − γεt

• Assume r = 0.04, γ = 0.26

σ∆c =1 + r

1 + r − γσε =

1.04

1.04− 0.26σε = 1.33σε

• Then too volatile: σ∆c > σε


Excess Smoothness



∆ct =1 + r

1 + r − γεt

• Assume r = 0.04, γ = 0.26

σ∆c =1 + r

1 + r − γσε =

1.04

1.04− 0.26σε = 1.33σε



Excess Smoothness



∆ct =1 + r

1 + r − γεt

• Assume r = 0.04, γ = 0.26

σ∆c =1 + r

1 + r − γσε =

1.04

1.04− 0.26σε = 1.33σε



Excess Smoothness



∆ct =1 + r

1 + r − γεt

• Assume r = 0.04, γ = 0.26

σ∆c =1 + r

1 + r − γσε =

1.04

1.04− 0.26σε = 1.33σε



Excess Smoothness



∆ct =1 + r

1 + r − γεt

• Assume r = 0.04, γ = 0.26

σ∆c =1 + r

1 + r − γσε =

1.04

1.04− 0.26σε = 1.33σε



Resolution

Campbell and Deaton (1989)

• Suppose individuals have more information than econometrician

• Classic source of bias: estimating income variability with error

• Strategy: Use information on savings as predictor of income growth


Resolution






Resolution






Resolution

• It is individual’s information set

• Ωt ⊂ It is econometrician’s information set

• Econometrician’s prediction error is:

1

1 + r

(∆ait+1 −∆aet+1

)= −

∞∑j=1

(1

1 + r

)j (Et[∆yt+j | Ωt]−Et[∆yt+j | It]

)



Resolution




1

1 + r


)= −

∞∑j=1

(1

1 + r


)



Resolution




1

1 + r


)= −

∞∑j=1

(1

1 + r


)



Resolution




1

1 + r


)= −

∞∑j=1

(1

1 + r


)



Resolution

• Assume: (∆yt

11+r∆at+1

)=

(ζ11 ζ12

ζ21 ζ22

)(∆yt−11

1+r∆at

)+

(u1t

u2t

)

• Rewritten in vector notation:

xt = Axt−1 + ut

• Rewrite using e1 = (1, 0) and e2 = (0, 1):

e1xt = ∆yt

e2xt =1

1 + r∆at+1


Resolution

• Assume: (∆yt

11+r∆at+1

)=

(ζ11 ζ12

ζ21 ζ22

)(∆yt−11

1+r∆at

)+

(u1t

u2t

)


xt = Axt−1 + ut


e1xt = ∆yt

e2xt =1

1 + r∆at+1


Resolution

• Assume: (∆yt

11+r∆at+1

)=

(ζ11 ζ12

ζ21 ζ22

)(∆yt−11

1+r∆at

)+

(u1t

u2t

)


xt = Axt−1 + ut


e1xt = ∆yt

e2xt =1

1 + r∆at+1


Resolution

• j-step ahead forecasts:

Et[xt+j ] = Ajxt

• Rewrite:

Et[∆yt+j ] = e1Ajxt+j

1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r

)je1A

jxt

• Rewrite:

e2xt = −e1

∞∑j=1

(1

1 + r

)jAjxt

• Implies parameter restrictions:

ζ21 = ζ11

ζ22 = ζ12 + (1 + r)


Resolution


Et[xt+j ] = Ajxt

• Rewrite:


1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r

)je1A

jxt

• Rewrite:

e2xt = −e1

∞∑j=1

(1

1 + r

)jAjxt


ζ21 = ζ11

ζ22 = ζ12 + (1 + r)


Resolution


Et[xt+j ] = Ajxt

• Rewrite:


1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r

)je1A

jxt

• Rewrite:

e2xt = −e1

∞∑j=1

(1

1 + r

)jAjxt


ζ21 = ζ11

ζ22 = ζ12 + (1 + r)


Resolution


Et[xt+j ] = Ajxt

• Rewrite:


1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r

)je1A

jxt

• Rewrite:

e2xt = −e1

∞∑j=1

(1

1 + r

)jAjxt


ζ21 = ζ11

ζ22 = ζ12 + (1 + r)


Resolution

• Restrictions imply consumption is a random walk:

∆ct = ∆yt + ∆at −1

1 + r∆at+1 = u1t − u2t

• Campbell and Deaton (1989) estimate the VAR xt = Axt−1 + ut

• Find that ζ11 6= ζ21

• Suppose ζ21 = ζ11 − χ such that:

A =

(ζ11 ζ12

ζ11 − χ ζ12 + 1 + r

)

• Implies excess sensitivity:

∆ct = χ∆yt−1 + (u1t − u2t)


Resolution


∆ct = ∆yt + ∆at −1

1 + r∆at+1 = u1t − u2t




A =

(ζ11 ζ12

ζ11 − χ ζ12 + 1 + r

)


∆ct = χ∆yt−1 + (u1t − u2t)


Resolution


∆ct = ∆yt + ∆at −1

1 + r∆at+1 = u1t − u2t




A =

(ζ11 ζ12

ζ11 − χ ζ12 + 1 + r

)


∆ct = χ∆yt−1 + (u1t − u2t)


Resolution


∆ct = ∆yt + ∆at −1

1 + r∆at+1 = u1t − u2t




A =

(ζ11 ζ12

ζ11 − χ ζ12 + 1 + r

)


∆ct = χ∆yt−1 + (u1t − u2t)


Resolution


∆ct = ∆yt + ∆at −1

1 + r∆at+1 = u1t − u2t




A =

(ζ11 ζ12

ζ11 − χ ζ12 + 1 + r

)


∆ct = χ∆yt−1 + (u1t − u2t)


Resolution

• What does assuming “excess sensitivity” imply for “excess smoothness”?

• Some heroic algebra shows:

∆ct =u1t − u2t

1− χ1+r

• Magnitude of excess sensitivity determines consumption response

• Cases: χ→ 0, χ→ 1 + r

• “There is no contradiction between excess sensitivity and excess

smoothness; they are the same phenomenon.”

• If past savings predicts income, then savings affects permanent income


Resolution



∆ct =u1t − u2t

1− χ1+r


• Cases: χ→ 0, χ→ 1 + r





Resolution



∆ct =u1t − u2t

1− χ1+r


• Cases: χ→ 0, χ→ 1 + r





Resolution



∆ct =u1t − u2t

1− χ1+r


• Cases: χ→ 0, χ→ 1 + r





Resolution



∆ct =u1t − u2t

1− χ1+r


• Cases: χ→ 0, χ→ 1 + r





Resolution



∆ct =u1t − u2t

1− χ1+r


• Cases: χ→ 0, χ→ 1 + r





Next Steps

• Other mechanisms that generate excess sensitivity and smoothness?

• Precautionary Savings

• Borrowing constraints

• Prudence in utility

• Friedman / Buffer Stock model

• Add impatience to precautionary motives

• Marginal Propensity to Consume out of income shocks


Next Steps









Next Steps









Next Steps









Next Steps









Next Steps









Next Steps









Precautionary Savings

Borrowing Constraints

• Empirical Observation (Parker (1999), Souleles (1999), others)

• Consumption is sensitive to anticipated income changes

• Study government transfers (tax rebates, social security changes)

• Consumption response larger for low income/liquid wealth households

• Suggestive of borrowing constraints impeding consumption smoothing




































• Consider “Strict” Permanent Income Hypothesis

• Add No Borrowing Constraint : at+1 ≥ 0

• If borrowing constraint binds:

ct = yt + at −1

1 + rat+1︸︷︷︸

=0• Optimal consumption is:

ct =

Et−1[ct] if at+1 > 0

yt + at if at+1 = 0







ct = yt + at −1

1 + rat+1︸︷︷︸


ct =


yt + at if at+1 = 0







ct = yt + at −1

1 + rat+1︸︷︷︸

=0

• Optimal consumption is:

ct =


yt + at if at+1 = 0







ct = yt + at −1

1 + rat+1︸︷︷︸


ct =


yt + at if at+1 = 0




• Recall optimal savings dynamics:

1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r

)jEt[∆yt+j ]

• Suppose: yt = yt−1 + εt, ε ∼ N (0, σ2ε )

• Then ∆at+1 = 0

• Borrowing constraint always binds:

ct = yt + at ∀ t





1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r

)jEt[∆yt+j ]


• Then ∆at+1 = 0


ct = yt + at ∀ t





1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r

)jEt[∆yt+j ]


• Then ∆at+1 = 0


ct = yt + at ∀ t





1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r

)jEt[∆yt+j ]


• Then ∆at+1 = 0


ct = yt + at ∀ t




• Suppose: yt = εt s.t. ε ∼ N (0, σ2ε )

• Then: ∆yt+j = εt+j − εt−1+j

• Optimal savings dynamics:

1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r

)jEt[∆yt+j ] = εt

• Savings is a random walk

• Borrowing constraint binds with probability one as t→∞







1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r










1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r










1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r










1

1 + r∆at+1 = −

∞∑j=1

(1

1 + r








• Optimal consumption:

ct =

r

1+r (at + yt) if at+1 > 0

yt + at if at+1 = 0

= min

yt + at,

r

1 + r(at + yt)

• Agent is constrained when:

r

1 + r(at + yt) > yt + at ⇒ yt < −at

• Future borrowing constraints affect current consumption:

ct = Et[minyt+1 + at+1,Et+1[ct+2]]

• What happens if σε increases?

→ Increase Precautionary Savings






ct =

r

1+r (at + yt) if at+1 > 0

yt + at if at+1 = 0

= min

yt + at,

r

1 + r(at + yt)


r

1 + r(at + yt) > yt + at ⇒ yt < −at










ct =

r

1+r (at + yt) if at+1 > 0

yt + at if at+1 = 0

= min

yt + at,

r

1 + r(at + yt)


r

1 + r(at + yt) > yt + at ⇒ yt < −at










ct =

r

1+r (at + yt) if at+1 > 0

yt + at if at+1 = 0

= min

yt + at,

r

1 + r(at + yt)


r

1 + r(at + yt) > yt + at ⇒ yt < −at










ct =

r

1+r (at + yt) if at+1 > 0

yt + at if at+1 = 0

= min

yt + at,

r

1 + r(at + yt)


r

1 + r(at + yt) > yt + at ⇒ yt < −at










ct =

r

1+r (at + yt) if at+1 > 0

yt + at if at+1 = 0

= min

yt + at,

r

1 + r(at + yt)


r

1 + r(at + yt) > yt + at ⇒ yt < −at










ct =

r

1+r (at + yt) if at+1 > 0

yt + at if at+1 = 0

= min

yt + at,

r

1 + r(at + yt)


r

1 + r(at + yt) > yt + at ⇒ yt < −at



• What happens if σε increases? → Increase Precautionary Savings



Prudence

• Another mechanism: Prudence (Kimball, 1990)

• Preferences for smooth consumption profile

⇒Self-insurance against low income realizations

⇒Income variability increases Precautionary Motive

• Keep in mind: CRRA but NOT Quadratic or CARA

u(c) =c1−σ

1− σ



Prudence






u(c) =c1−σ

1− σ



Prudence






u(c) =c1−σ

1− σ



Prudence

• Consider: u : R+ → R, u′(c) > 0, u′′(c) < 0

• Arrow-Pratt measure of of absolute risk aversion:

A(c) ≡ −u′′(c)

u′(c)

• Decreasing absolute risk aversion (DARA) implies:

A′(c) = −u′′′(c)

u′(c)+

(u′′(c)

u′(c)

)2

< 0

• Condition on the third derivative of the utility function:

u′′′(c) >u′′(c)2

u′(c)> 0

• Prudence: Convexity of the marginal utility function, e.g. u′′′(c) > 0



Prudence



A(c) ≡ −u′′(c)

u′(c)


A′(c) = −u′′′(c)

u′(c)+

(u′′(c)

u′(c)

)2

< 0


u′′′(c) >u′′(c)2

u′(c)> 0




Prudence



A(c) ≡ −u′′(c)

u′(c)


A′(c) = −u′′′(c)

u′(c)+

(u′′(c)

u′(c)

)2

< 0


u′′′(c) >u′′(c)2

u′(c)> 0




Prudence



A(c) ≡ −u′′(c)

u′(c)


A′(c) = −u′′′(c)

u′(c)+

(u′′(c)

u′(c)

)2

< 0


u′′′(c) >u′′(c)2

u′(c)> 0




Prudence



A(c) ≡ −u′′(c)

u′(c)


A′(c) = −u′′′(c)

u′(c)+

(u′′(c)

u′(c)

)2

< 0


u′′′(c) >u′′(c)2

u′(c)> 0




Prudence

• Prudence implies:

• Uncertainty increases

• Consumption today decreases

• Savings for tomorrow increases

• Consider two period example (Leland, 1968)

• Board work



Prudence

• Prudence implies:

• Uncertainty increases

• Consumption today decreases

• Savings for tomorrow increases

• Consider two period example (Leland, 1968)

• Board work


Permanent Income Hypothesis

Next Time

• Continue discussion of Prudence

• Patience: β versus (1 + r)

• Characterization of Buffer Stock model

• Marginal Propensity to Consume


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