Consumption: Micro Vs Macro References Sticky Expectations and Consumption Dynamics Christopher D. Carroll 1 Edmund Crawley 2 Jiri Slacalek 3 Kiichi Tokuoka 4 Matthew N. White 5 1 Johns Hopkins and NBER, ccarroll@jhu.edu 2 Johns Hopkins, ecrawle2@jhu.edu 3 European Central Bank, jiri.slacalek@ecb.int 4 MoF Japan, kiichi.tokuoka@mof.go.jp 5 University of Delaware, mnwecon@udel.edu February 2018 Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Consumption Dynamics: Macro vs Micro Macro: Representative Agent Models Theory (With Separable Utility): C responds instantly, completely to shock Consequences of uncertainty are trivial Evidence: Consumption is too smooth (Campbell & Deaton, 1989) Solution: “Habits” parameter χ Macro ≈ 0 . 6 ∼ 0 . 8 ∆ log C t +1 = ς + χ ∆ log C t + ǫ Micro: Heterogeneous Agent Models Uninsurable risk is essential, changes everything Var of micro income shocks much larger than of macro shocks: var(∆ log p ) ≈ 100 × var(∆ log P ) Evidence: “Habits” parameter χ Micro ≈ 0 . 0 ∼ 0 . 1 Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Persistence of Consumption Growth: Macro vs Micro New paper in EER, Havranek, Rusnak, and Sokolova (2017) Meta analysis of 597 estimates of χ ∆ log C t +1 = ς + χ ∆ log C t + ǫ { χ Macro , χ Micro } = { 0 . 6 , 0 . 1 } Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Claim: It’s Not Habits, It’s Inattention! (Macro not Micro) Our Setup Income Has Idiosyncratic and Aggregate Components Idiosyncratic Component Is Perfectly Observed Aggregate Component Is Stochastically Observed Updating ` a la Calvo (1983) Not ad hoc Identical: Mankiw and Reis (2002), Carroll (2003) Similar: Reis (2006), Sims (2003), . . . Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Why Macro Inattention Is Plausible Idiosyncratic Variability Is ∼ 100 × Bigger If Same Specification Estimated on Micro vs Macro Data Pervasive Lesson of All Micro Data Utility Cost of Inattention Small Micro: Critical (and Easy) To Notice You’re Unemployed Macro: Not Critical To Instantly Notice If U ↑ Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Literature on C Dynamics and Info Frictions C Smoothness: Campbell and Deaton (1989); Pischke (1995); Rotemberg and Woodford (1997) Inattention: Mankiw and Reis (2002); Reis (2006); Sims (2003); Ma´ ckowiak and Wiederholt (2015); Gabaix (2014); . . . Adjustment Costs: Alvarez, Guiso, and Lippi (2012); Chetty and Szeidl (2016) Empirical Evidence on Info Frictions: Coibion and Gorodnichenko (2015); Fuhrer (2017); . . . Macro Habits: Abel (1990); Constantinides (1990); all papers since Christiano, Eichenbaum, and Evans (2005) Micro Habits: Dynan (2000); many recent papers Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Quadratic Utility Frictionless Benchmark Hall (1978) Random Walk Total Wealth (Human + Nonhuman): o t +1 = ( o t − c t )R + ζ t +1 C Euler Equation: u ′ ( c t ) = R β E t [ u ′ ( c t +1 )] ⇒ Random Walk (for R β = 1): ∆ c t +1 = ǫ t +1 Expected Wealth: o t = E t [ o t +1 ] = E t [ o t +2 ] = . . . Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Sticky Expectations—Individual c Consumer who happens to update at t and t + n c t = (r / R) o t c t +1 = (r / R) � o t +1 = (r / R) o t = c t . . . . . . c t + n − 1 = c t Implies that ∆ n o t + n ≡ o t + n − o t is white noise So individual c is RW across updating periods: c t + n − c t = (r / R) ( o t + n − o t ) � �� � ∆ n o t + n Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Sticky Expectations—Aggregate C � 1 Pop normed to one, uniformly dist on [0 , 1]: C t = 0 c t , i d i Calvo (1983)-Type Updating of Expectations: Probability Π = 0 . 25 (per quarter) Economy composed of many sticky- E consumers: (1 − Π) C ✁ π + Π C π C t +1 = t +1 t +1 ���� = C t ∆ C t +1 ≈ (1 − Π) ∆ C t + ǫ t +1 � �� � ≡ χ =0 . 75 Substantial persistence ( χ = 0 . 75 ) in aggregate C growth Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References One More Ingredient: Idiosyncratic Uncertainty . . . Differences: Idiosyncratic vs Aggregate shocks Idiosyncratic shocks: Frictionless observation I notice if I am fired, promoted, somebody steals my wallet True RW with respect to these Aggregate shocks: Sticky observation May not instantly notice changes in aggregate productivity Result: Idiosyncratic ∆ c : dominated by frictionless RW part Aggregate ∆ C : highly serially correlated Law of large numbers ⇒ idiosyncratic part vanishes Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Serious Models Partial Equilibrium/Small Open Economy CRRA Utility Idiosyncratic Shocks Calibrated From Micro Data Aggregate Shocks Calibrated From Macro Data Markov Process (Discrete RW) for Aggr Income Growth Handles changing growth ‘eras’ Liquidity Constraint Mildly Impatient Consumers DSGE Heterogeneous Agents (HA) Model Same! Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Income Process Individual’s labor productivity is θ ≡ p p p t , i ≡ θ θ t , i � �� � � �� � ℓ ℓ t , i = ℓ θ t , i Θ t p t , i P t Idiosyncratic and aggregate p evolve according to p t +1 , i = p t , i ψ t +1 , i = Φ t +1 P t Ψ t +1 P t +1 Φ is Markov ‘underlying’ aggregate pty growth Discrete (bounded) random walk Calibrated to match postwar US pty growth variation Generates predictability in income growth (for IV regressions) Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Blanchard (1985) Mortality and Insurance Household survives from t to t + 1 with probability (1 − D): � 1 for newborns p t +1 , i = p t , i ψ t +1 , i for survivors Blanchardian scheme: � 0 if HH i dies, is replaced by newborn k t +1 , i = � a t , i (1 − D) if household i survives Implies for aggregate: � 1 − d t +1 , i � � 1 K t +1 = a t , i d i = A t 1 − D 0 � K t +1 = A t (Ψ t +1 Φ t +1 ) Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Resources Market resources: ℓ m t , i = W t ℓ ℓ t , i + R t k t , i ���� � �� � � + r t ≡ y t End-of-Period ‘Assets’—Unspent resources: a t , i = m t , i − c t , i Capital transition depends on prob of survival 1 − D: � k t +1 , i = a t , i (1 − D) Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Frictionless Solution For exposition: Assume constant W and R Normalize everything by p p t , i ≡ p t , i P t , e.g. p � m t , i = m t , i ( p t , i P t ) c ( m , Φ) is the function that solves: � � ψ t +1 , i ) 1 − ρ v ( m t +1 , i , Φ t +1 ) u ( c )+(1 − D) β E t ψ v ( m t , i , Φ t ) = max (Φ t +1 ψ c Level of consumption: c t , i = c ( m t , i , Φ t ) × p t , i P t Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Sticky Expectations about Aggregate Income Calvo Updating of Perceptions of Aggregate Shocks True Permanent income: P t +1 = Φ t +1 P t Ψ t +1 Tilde ( � P ) denotes perceived variables Perception for consumer who has not updated for n periods: � � � � � Ω t − n = Φ n P t , i = E t − n P t t − n P t − n because Φ is random walk Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
Consumption: Micro Vs Macro Habits? No! It’s Inattention References Sticky Expectations about Aggregate Income Sequence Within Period 1 Income shocks are realized and every individual sees her true y and m , i.e. y t , i = � y t , i and m t , i = � m t , i for all t and i 2 Updating shocks realized: i observes true P t , Φ t w/ prob Π; forms perceptions of her normalized market resources � m t , i m t , i , � 3 Consumes based on her perception, using c ( � Φ t , i ) Key Assumption: People act as if their perceptions about aggregate state { � P t , i , � Φ t , i } are the true aggregate state { P t , Φ t } Carroll, Crawley, Slacalek, Tokuoka, White Sticky Expectations and Consumption Dynamics
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