Sticky Expectations and Consumption Dynamics · Sticky Expectations and Consumption Dynamics ......

References

Sticky Expectations and Consumption Dynamics

Christopher D. Carroll1 Jirka Slacalek2

1Johns Hopkins and [email protected]

http://www.econ.jhu.edu/people/ccarroll/

2European Central [email protected]

http://www.slacalek.com/

November 2007

Carroll and Slacalek Sticky Expectations and Consumption Dynamics

References

Consumption Dynamics

Theory: Uninsurable Risk Is Unimportant

Evidence: Consumption Is Too Smooth

Conclusion: Habits ≈ 0.75

Theory: Uninsurable Risk Is Essential

Evidence: Habits =0.75 Rejectable With Confidence = ∞var(∆ log c) ≈ 100 var(∆ log C)

References

Proposal: Macro (Not Micro) Inattention

Income Has Idiosyncratic And Aggregate Components

Idiosyncratic Component Is Perfectly Observed

Aggregate Component Is Stochastically Observed

Not ad hoc

Identical: Mankiw and Reis (2002), Carroll (2003)

Similar: Sims (2003), Woodford (2001), Reis (2003)

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Not ad hoc

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Not ad hoc

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Not ad hoc

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Not ad hoc

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Not ad hoc

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Why This Is Plausible

Idiosyncratic Variability Is ∼ 100× Bigger

If Same Equation Estimated on Micro vs Macro Data

Pervasive Lesson Of All Micro Data

Utility Cost Of Inattention

Micro: Critical (and Easy) To Notice You’re Unemployed

Unlike Pischke (1995)

Macro: Not Critical To Instantly Notice If U ↑

References

Related Literature

Smoothness: Campbell and Deaton (1989), Pischke (1995),Rotemberg and Woodford (1997)

Inattention: Pischke (1995); Mankiw and Reis (2002); Reis(2003); Sims (2003)

Macro Habits: Abel (1990); Constantinides (1990); manyrecent papers

Micro Habits: Dynan (2000);

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Related Literature

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Related Literature

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Related Literature

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Quadratic Utility Benchmark

Total Wealth:

zt+1 = (zt − ct)R + ζt+1, (1)

Euler Equation:

u′(ct) = RβEt [u′(ct+1)], (2)

Random Walk:

∆ct+1 = εt+1. (3)

Expected wealth:

zt = Et [zt+1] = Et [zt+2]... (4)

References

Sticky Expectations

Consumer Who Happens To Update At t and t + n

ct = (r/R)zt

ct+1 = (r/R)zt+1 = (r/R)zt = ct

......

ct+n−1 = ct .

Implies that ∆nzt+n ≡ zt+n − zt is white noise

So individual c is RW across updating periods:

ct+n − ct = (r/R) (zt+n − zt)︸︷︷︸∆nzt+n

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Sticky Expectations

ct = (r/R)zt

ct+1 = (r/R)zt+1 = (r/R)zt = ct

......

ct+n−1 = ct .

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Sticky Expectations

ct = (r/R)zt

ct+1 = (r/R)zt+1 = (r/R)zt = ct

......

ct+n−1 = ct .

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Sticky Expectations

Pop normed to one, uniformly dist on [0, 1]

0ct,i di .

Calvo (1983) Type Updating Of Expectations:

Probability Π = 0.25

Economy Composed Of Many Sticky Conumers:

∆Ct+1 ≈ (1− Π)︸︷︷︸=0.75

∆Ct + εt+1 (6)

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Sticky Expectations

0ct,i di .

∆Ct+1 ≈ (1− Π)︸︷︷︸=0.75

∆Ct + εt+1 (6)

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Sticky Expectations

0ct,i di .

∆Ct+1 ≈ (1− Π)︸︷︷︸=0.75

∆Ct + εt+1 (6)

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Sticky Expectations

0ct,i di .

∆Ct+1 ≈ (1− Π)︸︷︷︸=0.75

∆Ct + εt+1 (6)

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One More Ingredient ...

Distinguish idiosyncratic and aggregate shocks

Frictionless observation of idiosyncratic shocksTrue RW with respect to theseSticky observation of aggregate shocks

Result:

Idiosyncratic ∆c dominated by frictionless RW partAggregate ∆C highly serially correlatedLaw of large numbers: idiosyncratic part vanishes

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Result:

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Result:

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Result:

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Result:

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Result:

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Result:

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Result:

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Muth–Pischke/Lucas/Kalman

Muth (1960)-Pischke (1995)/Lucas (1973) - Kalman filter

All you can see is Y

Lucas: Can’t distinguish agg. from idio.Muth-Pischke: Can’t distinguish tran from perm

Here: Can see own circumstances perfectly

Only the (tiny) aggregate part is hard to see

But can’t permit signal extraction wrt aggregate

Signal extraction wrt agg implies agg random walk

Will return to this below

References

Serious Model

Partial Equilibrium/Small Open Economy

CRRA Utility

Idiosyncratic Shocks Calibrated From Micro Data

Aggregate Shocks Calibrated From Macro Data

No Liquidity Constraints

Mildly Impatient Consumers

DSGE Model

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Serious Model

CRRA Utility

DSGE Model

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Serious Model

CRRA Utility

DSGE Model

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Serious Model

CRRA Utility

DSGE Model

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Serious Model

CRRA Utility

DSGE Model

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Serious Model

CRRA Utility

DSGE Model

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Serious Model

CRRA Utility

DSGE Model

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Serious Model

CRRA Utility

DSGE Model

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Income Process

Individual’s labor productivity is

`t+1 =

≡θθθt+1︷︸︸︷θt+1Θt+1 pt+1Pt+1︸︷︷︸

≡pt+1

Idiosyncratic and aggregate p evolve according to

pt+1 = ptψt+1 (8)

Pt+1 = PtΨt+1 (9)

Et [θt+n] = Et [Θt+n] = Et [ψt+n] = Et [Ψt+n] = 1 ∀ n > 0

References

Income Process

`t+1 =

≡θθθt+1︷︸︸︷θt+1Θt+1 pt+1Pt+1︸︷︷︸

≡pt+1

pt+1 = ptψt+1 (8)

Pt+1 = PtΨt+1 (9)

References

Income Process

`t+1 =

≡θθθt+1︷︸︸︷θt+1Θt+1 pt+1Pt+1︸︷︷︸

≡pt+1

pt+1 = ptψt+1 (8)

Pt+1 = PtΨt+1 (9)

References

Resources

Market resources:

mt+1 = Wt+1`t+1︸︷︷︸≡yt+1

+ Rt+1︸︷︷︸1+rt+1

kt+1 (10)

‘Assets’: Unspent resources

at = mt − ct (11)

Capital transition depends on prob of survival Ω:

kt+1 = at/Ω (12)

References

Resources

Market resources:

mt+1 = Wt+1`t+1︸︷︷︸≡yt+1

+ Rt+1︸︷︷︸1+rt+1

kt+1 (10)

at = mt − ct (11)

kt+1 = at/Ω (12)

References

Resources

Market resources:

mt+1 = Wt+1`t+1︸︷︷︸≡yt+1

+ Rt+1︸︷︷︸1+rt+1

kt+1 (10)

at = mt − ct (11)

kt+1 = at/Ω (12)

References

Frictionless Solution

Assume constant R,WNormalize everything by ptPt e.g. mt = mt/ptPt

c(mt) is the function that solves

v(mt) = maxcu(c) + βEt [ψψψ1−ρ

t+1v(mt+1)]

Level of consumption given by

ct = c(mt)pt .

References

t+1v(mt+1)]

ct = c(mt)pt .

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t+1v(mt+1)]

ct = c(mt)pt .

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t+1v(mt+1)]

ct = c(mt)pt .

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Blanchard (1985) Mortality

Agent survives from t to t + 1 with probability Ω

pt+1,i =

1 for newborns

pt,iψt+1,i for survivors,

Implies steady-state distribution of p with variance:

var(p) =

(1− Ω

1− ΩE [ψ2]− 1

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Blanchard (1985) Mortality

Agent survives from t to t + 1 with probability Ω

pt+1,i =

1 for newborns

pt,iψt+1,i for survivors,

Implies steady-state distribution of p with variance:

var(p) =

(1− Ω

1− ΩE [ψ2]− 1

References

Blanchard (1985) Insurance

kt+1,i =

0 if agent at i dies, is replaced by a newborn

at,ik/Ω if agent at i survives

Implies

Kt+1 =

0ωt+1,ikat,i/Ωdi

Kt+1 = kAt/Ψt+1

References

Sticky Aggregate Expectations

Θt,i =

Θt for updaters

1 for nonupdaters

Pt+1,i = πt+1,iPt+1 + (1− πt+1,i )Pt,i (13)

Sequence within period:

1 Shocks are Realized

2 Each Individual Updates (Or Not)

3 Consume Based on Beliefs

4 Consumer Sees End-Of-Period Bank Balance

References

Θt,i =

Θt for updaters

1 for nonupdaters

Pt+1,i = πt+1,iPt+1 + (1− πt+1,i )Pt,i (13)

References

Θt,i =

Θt for updaters

1 for nonupdaters

Pt+1,i = πt+1,iPt+1 + (1− πt+1,i )Pt,i (13)

References

Θt,i =

Θt for updaters

1 for nonupdaters

Pt+1,i = πt+1,iPt+1 + (1− πt+1,i )Pt,i (13)

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Behavior

Consumers behave according to frictionless consumption function:

ct,i = c(mt,i )

ct,i = ct,i Pt,ipt,i

Correctly perceive level of spending

at,i = mt,i − ct,i (14)

kt+1,i = ωt+1,ik (at,iπt+1,i + at,i (1− πt+1,i )) /Ω + (1− ωt+1,i )0(15)

References

Cost Of Stickiness

Newborns’ value can be approximated by

v(W) ≈ ←−v (W)− (κ/Π)σ2Ψ. (16)

If Newborns Pick Optimal Π, they solve

←−v (W)− (κ/Π)σ2Ψ − ιΠ. (17)

Solution:

Π = (κ/ι)0.5σΨ (18)

References

Muth–Pischke Perception Dynamics

Pt+1 = ΠPt+1 + (1− Π)Pt (19)

Observe Y

Define signal-to-noise ratio ϕ = σ2ψ/σ

Optimal Estimate of P obtained from

Pt+1 = ΠYt+1 + (1− Π)Pt (20)

1 + 2/(ϕ+√ϕ2 + 4ϕ)

), (21)

References

Muth–Pischke Perception Dynamics

Pt+1 = ΠPt+1 + (1− Π)Pt (19)

Observe Y

Define signal-to-noise ratio ϕ = σ2ψ/σ

Optimal Estimate of P obtained from

Pt+1 = ΠYt+1 + (1− Π)Pt (20)

1 + 2/(ϕ+√ϕ2 + 4ϕ)

), (21)

References

Comparison

1 + 2/(ϕ+√ϕ2 + 4ϕ)

), (22)

Pischke (1995): This is why C is too smooth

If we calibrate using observed micro data

⇒ ∆ log Ct+1 ≈ 0.967 ∆ log Ct

Goes too far!

It’s because people can’t tell agg from ind shocks

But calibration where they can see agg Y ⇒ RW

Maybe could fiddle with calibration assumptions . . .

References

Comparison

1 + 2/(ϕ+√ϕ2 + 4ϕ)

), (22)

⇒ ∆ log Ct+1 ≈ 0.967 ∆ log Ct

Goes too far!

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Comparison

1 + 2/(ϕ+√ϕ2 + 4ϕ)

), (22)

⇒ ∆ log Ct+1 ≈ 0.967 ∆ log Ct

Goes too far!

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Comparison

1 + 2/(ϕ+√ϕ2 + 4ϕ)

), (22)

⇒ ∆ log Ct+1 ≈ 0.967 ∆ log Ct

Goes too far!

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Comparison

1 + 2/(ϕ+√ϕ2 + 4ϕ)

), (22)

⇒ ∆ log Ct+1 ≈ 0.967 ∆ log Ct

Goes too far!

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Comparison

1 + 2/(ϕ+√ϕ2 + 4ϕ)

), (22)

⇒ ∆ log Ct+1 ≈ 0.967 ∆ log Ct

Goes too far!

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DSGE Model

Frictionless:

No Idiosyncratic Shocks

Aggregate Shocks Same as PE/SOE

Cobb-Douglas production: Mt = Kt + K εt Θ1−ε

V (Mt) = maxCt

u(ct) + βEt [Ψ1−ρ

t+1V (Mt+1)]

At = Mt − Ct

Kt+1 = Atk/Ψt+1

Mt+1 = Rt+1Kt+1 +Wt+1Θt+1.

References

DSGE Model

Frictionless:

V (Mt) = maxCt

t+1V (Mt+1)]

At = Mt − Ct

Kt+1 = Atk/Ψt+1

Mt+1 = Rt+1Kt+1 +Wt+1Θt+1.

References

DSGE Model

Frictionless:

V (Mt) = maxCt

t+1V (Mt+1)]

At = Mt − Ct

Kt+1 = Atk/Ψt+1

Mt+1 = Rt+1Kt+1 +Wt+1Θt+1.

References

Sticky Expectations DSGE

Perception Dynamics Identical to Sticky PE/SOE

Mt = Kt + K εt Θ1−ε

Solution: Ct = C (Mt)Pt

References

Benchmark: Random Walk

∗ ∆ log Ct+1 ≈ ς + ϑEt [rt+1] + µXt−1 + εt+1, (24)

and random walk means µ = 0.In GE, r depends on A so ∗ is equivalent to:

∆ log Ct+1 ≈ ς + αAt + µXt−1 + εt+1 (25)

In either case, lots of Xt−1 were found for which µ 6= 0.

References

Campbell and Mankiw (1989)

∆ log Ct+1 ≈ ς + αAt + ηE[∆ log Yt+1] + εt+1 (26)

Claims:

η estimates fraction of ‘rule-of-thumb’ C = Y consumers

η ≈ 0.5 robustly for U.S. and other countries

No further predictability in ∆ log Ct+1

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Claims:

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Claims:

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Macro Habits

Campbell and Deaton (1989); Rotemberg and Woodford (1997);Fuhrer (2000); Sommer (2001)Dynan (2000)/Sommer specification:

∆ log Ct+1 ≈ ς + αAt + ηE[∆ log Yt+1] + χE[∆ log Ct ] + εt+1

Claims:

η no longer statistically significant

χ ≈ 0.75 (Habits are huge!)

OID tests succeed

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Macro Habits

Claims:

OID tests succeed

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Macro Habits

Claims:

OID tests succeed

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Micro Evidence

∆ log ct+1 ≈ ς + αat + ηE[∆ log yt+1] + χE[∆ log ct ] + εt+1

Separable Theory:

α < 0

0 < η < 1

χ ≈ 0

Micro Evidence on Habits:

No: Meghir and Weber (1996); Dynan (2000); Flavin andNakagawa (2005)

Maybe a little: Carrasco, Labeaga, and Lopez-Salido (2005)

References

Micro Evidence

Separable Theory:

α < 0

0 < η < 1

χ ≈ 0

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Micro Evidence

Separable Theory:

α < 0

0 < η < 1

χ ≈ 0

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Micro Evidence

Separable Theory:

α < 0

0 < η < 1

χ ≈ 0

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Micro Evidence

Separable Theory:

α < 0

0 < η < 1

χ ≈ 0

References

Micro Vs Macro

∆ log Ct+1 ≈ ς + χ∆ log Ct + ηEt [∆ log Yt+1] + αAt + εt+1

χ η α

Micro (Separable)Theory ≈ 0 0 < η < 1 < 0Data ≈ 0 0 < η < 1 < 0

MacroTheory:Separable ≈ 0 ≈ 0 < 0Theory:CampMan ≈ 0 ≈ 0.5 < 0Theory:Habits ≈ 0.75 ≈ 0 < 0

References

Calibration—DSGE

DSGE Model

Calibrated Parameters

ρ 2. Coefficient of Relative Risk Aversion

k 0.941/4 Quarterly Depreciation FactorK/K ε 12 Perf Foresight SS Capital/Output Ratioσ2

Θ 0.00001 Variance Qtrly Tran Agg Pty Shocksσ2

Ψ 0.00004 Variance Qtrly Perm Agg Pty Shocks

Steady State Solution of Model With σΨ = σΘ = 0

K = 121/(1−ε) ≈ 48.55 Steady State Quarterly K/P RatioM = K + K ε ≈ 52.6 Steady State Quarterly M/P RatioW = (1− ε)K ε ≈ 2.59 Quarterly Wage RateR = 1 + εK ε−1 = 1.03 Quarterly Gross Capital Income Factor

R = Rk ≈ 1.014 Quarterly Between-Period Interest Factorβ = R−1 ≈ 0.986 Quarterly Time Preference Factor

References

Calibration—PE/SOE

Partial Equilibrium/Small Open Economy (PE/SOE) Model Parameters

Calibrated Parameters

σ2~ψ

0.016 Variance Annual Perm Idiosyncratic Shocks (PSID)

σ2~θ

0.03 Variance Annual Tran Idiosyncratic Shocks (PSID)℘ 0.05 Quarterly Probability of Unemployment SpellΠ 0.25 Quarterly Probability of Updating Expectations

(1− Ω) 0.005 Quarterly Probability of Mortality

Calculated Parameters

β = 0.99Ω/E [(ψψψ)−ρ]R 0.965 Satisfies Impatience Condition: β < Ω/E [(Ψψ)−ρ]Rσ2ψ 0.004 Variance Qtrly Perm Idiosyncratic Shocks (=σ~ψ/4)

σ2θ 0.12 Variance Qtrly Tran Idiosyncratic Shocks (=4σ~θ)

References

Equilibrium

PE/SOE Economy DSGE EconomyFrictionless Sticky Frictionless Sticky

MeansA 6.650 6.648 49.382 49.371C 2.684 2.684 3.290 3.289

Standard DeviationsAggregate Time Series (‘Macro’)

log A 0.089 0.091 0.085 0.085∆ log C 0.005 0.002 0.003 0.001∆ log Y 0.008 0.003 0.005 0.002

Individual Cross Sectional (‘Micro’)log a 1.273 1.273log c 1.207 1.207log p 1.221 1.221log y|y > 0 0.846 0.846∆ log c 0.151 0.149

Cost Of Stickiness 0.31× 10−4 0.53× 10−5

References

Micro Theory: Frictionless

∆ log ct+1,i = ς + χ∆ log ct,i + ηEt,i [∆ log yt+1,i ] + αat,i

Model ofExpectations χ η α R2 nobsFrictionless

0.083 0.007 76020(0.077)

0.003 -0.000 76020(0.004)

−0.111 0.000 76020(0.052)

0.083 0.009 −0.059 0.007 76020(0.004) (0.004) (0.024)

References

Micro Theory: Sticky

∆ log ct+1,i = ς + χ∆ log ct,i + ηEt,i [∆ log yt+1,i ] + αat,i

Model ofExpectations χ η α R2 nobsSticky

0.084 0.007 76020(0.077)

0.003 -0.000 76020(0.004)

−0.111 0.000 76020(0.051)

0.083 0.009 −0.059 0.007 76020(0.004) (0.004) (0.024)

References

DSGE Macro: Frictionless

∆ log Ct+1 = ς + χ∆E[log Ct ] + ηE[∆ log Yt+1] + αE[At ]

Expectations:Dep Var OLS 2nd Stage IV F p-val

Independent Variables or IV R2 IV OIDFrictionless: ∆ log Ct+1

∆ log Ct ∆ log Yt+1 At

0.010 OLS -0.001(0.032)

0.184 IV 0.007 0.000(0.050) 0.001

−0.0002 OLS 0.010(0.0001)

−0.019 0.152 −0.0002 IV 0.007(0.027) (0.052) (0.0001)

References

DSGE Macro: Sticky

Independent Variables or IV R2 IV OID

Sticky∆ log Ct ∆ log Yt+1 At

0.823 OLS 0.677(0.018)

∆ log ˜Ct

0.387 OLS 0.141(0.030)0.845 IV 0.422 0.000

(0.042) 0.2100.815 IV 0.395 0.000

(0.025) 0.000−0.0004 OLS 0.115

(0.0000)0.750 0.065 −0.0001 IV 0.423

(0.148) (0.146) (0.0000) 0.126

Memo: For instruments Zt , ∆ log Ct+1 = Ztζ, R2 = 0.425

References

Small Open Economy: Frictionless

Independent Variables or IV R2 IV OIDFrictionless: ∆ log Ct+1

0.022 OLS 0.000(0.010)

0.028 IV 0.000 0.000(0.016) 0.030

−0.0008 OLS 0.000(0.0004)

0.019 0.028 −0.0005 IV 0.000(0.010) (0.016) (0.0004)

References

Small Open Economy: Sticky

Independent Variables or IV R2 IV OID

0.345 OLS 0.121(0.009)0.805 IV 0.363 0.000

(0.014) 0.0001.150 IV 0.352 0.000

(0.015) 0.0000.498 0.496 −0.0007 IV 0.375

(0.028) (0.040) (0.0005) 0.000

Memo: For instruments Zt , ∆ log Ct+1 = Ztζ, R2 = 0.390

References

Empirical Results for U.S.

∆ log Ct+1 = ς + χ∆ log Ct + ηE[∆ log Yt+1] + αAt

Consumption Method IV F p-val

Series χ η α OLS/IV R22 IV OID

Nondurables and Services0.358∗∗∗ OLS 0.123

(0.066)0.577∗∗∗ IV 0.172 0.000

(0.118) 0.7020.0006 OLS 0.002

(0.0006)0.826∗∗∗ IV 0.143 0.000

(0.147) 0.7140.731∗∗∗ 0.071 0.0000 IV 0.135

(0.230) (0.118) (0.0003) 0.482

Memo: For instruments Z,∆ log Ct+1 = Zζ, R2 = 0.168

Instruments: L(2/3).diffcons L(2/3).wyRatio L(2/3).bigTheta L(2/3).dfedfunds L(2/3).ics

Time frame: 1960Q1–2004Q3, σ2Ψ = .0000429, σ2

Θ = .0000107

References

Abel, Andrew B. (1990): “Asset Prices under Habit Formationand Catching Up with the Joneses,” American EconomicReview, 80(2), 38–42.

Blanchard, Olivier J. (1985): “Debt, Deficits, and FiniteHorizons,” Journal of Political Economy, 93(2), 223–247.

Calvo, Guillermo A. (1983): “Staggered Contracts in aUtility-Maximizing Framework,” Journal of MonetaryEconomics, 12, 383–98.

Campbell, John Y., and Angus S. Deaton (1989): “Why IsConsumption So Smooth?,” Review of Economic Studies, 56,357–74.

Campbell, John Y., and N. Gregory Mankiw (1989):“Consumption, Income, and Interest Rates: Reinterpreting theTime-Series Evidence,” in NBER Macroeconomics Annual, 1989,ed. by Olivier J. Blanchard, and Stanley Fischer, pp. 185–216.MIT Press, Cambridge, MA.

Carrasco, Raquel, Jose M. Labeaga, and J. DavidLopez-Salido (2005): “Consumption and Habits: Evidence

References

from Panel Data,” Economic Journal, 115(500), 144–165,available athttp://ideas.repec.org/a/ecj/econjl/v115y2005i500p144-165.html.

Carroll, Christopher D. (2003): “MacroeconomicExpectations of Households and Professional Forecasters,”Quarterly Journal of Economics, 118(1), 269–298, http://econ.jhu.edu/people/ccarroll/epidemiologyQJE.pdf.

Constantinides, George M. (1990): “Habit Formation: AResolution of the Equity Premium Puzzle,” Journal of PoliticalEconomy, 98, 519–43.

Dynan, Karen E. (2000): “Habit Formation in ConsumerPreferences: Evidence from Panel Data,” American EconomicReview, 90(3).

Flavin, Marjorie J., and Shinobu Nakagawa (2005): “AModel of Housing in the Presence of Adjustment Costs: AStructural Interpretation of Habit Persistence,” ManuscriptUCSD.

References

Fuhrer, Jeffrey C. (2000): “An Optimizing Model forMonetary Policy: Can Habit Formation Help?,” AmericanEconomic Review, 90(3).

Lucas, Robert E. (1973): “Some International Evidence onOutput-Inflation Tradeoffs,” American Economic Review, 63,326–334.

Mankiw, N. Gregory, and Ricardo Reis (2002): “StickyInformation Versus Sticky Prices: A Proposal to Replace theNew Keynesian Phillips Curve,” Quarterly Journal of Economics,117(4), 1295–1328.

Meghir, Costas, and Guglilelmo Weber (1996):“Intertemporal Non-Separability or Borrowing Restrictions? ADisaggregate Analysis Using a U.S. Consumption Panel,”Econometrica, 64(5), 1151–82.

Muth, John F. (1960): “Optimal Properties of ExponentiallyWeighted Forecasts,” Journal of the American StatisticalAssociation, 55(290), 299–306.

References

Pischke, Jorn-Steffen (1995): “Individual Income,Incomplete Information, and Aggregate Consumption,”Econometrica, 63(4), 805–40.

Reis, Ricardo (2003): “Inattentive Consumers,” Manuscript,Harvard University.

Rotemberg, Julio J., and Michael Woodford (1997):“An Optimization-Based Econometric Model for the Evaluationof Monetary Policy,” in NBER Macroeconomics Annual, 1997,ed. by Benjamin S. Bernanke, and Julio J. Rotemberg, vol. 12,pp. 297–346. MIT Press, Cambridge, MA.

Sims, Christopher A. (2003): “Implications of RationalInattention,” Journal of Monetary Economics, 50(3), 665–690,available athttp://ideas.repec.org/a/eee/moneco/v50y2003i3p665-690.html.

Sommer, Martin (2001): “Habits, Sentiment and PredictableIncome in the Dynamics of Aggregate Consumption,”

References

Manuscript, The Johns Hopkins University,http://econ.jhu.edu/pdf/papers/wp458.pdf.

Woodford, Michael (2001): “Imperfect Common Knowledgeand the Effects of Monetary Policy,” NBER Working PaperNumber 8673.

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