Forward Guidance without Common Knowledge November 9, 2017 1/30 - PowerPoint PPT Presentation

Forward Guidance without Common Knowledge November 9, 2017 1/30 George-Marios Angeletos ∗ Chen Lian ∗∗ ∗ MIT and NBER, ∗∗ MIT

• Standard: RE with CK Forward Guidance: Context or Pretext? • How does the economy respond to news about the future? • e.g., news about future interest rates or government spending • Key mechanisms: • forward-looking expectations (e.g., of infmation and income) • This paper: RE without CK 2/30 • general-equilibrium efgects (Keynesian multiplier, π - y feedback)

Forward Guidance: Context or Pretext? • How does the economy respond to news about the future? • e.g., news about future interest rates or government spending • Key mechanisms: • forward-looking expectations (e.g., of infmation and income) • This paper: RE without CK 2/30 • general-equilibrium efgects (Keynesian multiplier, π - y feedback) • Standard: RE with CK

• lessen forward guidance puzzle • ofger rationale for the front-loading of fjscal stimuli Main Insight and Applications • Removing CK reduces • potency of GE efgects (Keynesian multipliers etc) • it is as if agents apply extra discounting on future outcomes • Application to ZLB context • arrest response of AD to news about interest rates • arrest response of infmation to news about marginal costs • ... 3/30 • responsiveness of forward-looking expectations • Efgects increase with horizon

Main Insight and Applications • Removing CK reduces • potency of GE efgects (Keynesian multipliers etc) • it is as if agents apply extra discounting on future outcomes • Application to ZLB context • arrest response of AD to news about interest rates • arrest response of infmation to news about marginal costs • lessen forward guidance puzzle • ... 3/30 • responsiveness of forward-looking expectations • Efgects increase with horizon • ofger rationale for the front-loading of fjscal stimuli

Roadmap 1. Recast IS and NKPC as Dynamic Beauty Contests 2. Show GE Attenuation and Horizon Efgects 3. Application to Forward Guidance and Fiscal Stimuli 4. Comparison to Related Work that Drops RE 4/30

Mapping the IS and the NKPC to Dynamic Beauty Contests

Framework • Starting point: textbook NK model • Main departure: remove CK of innovations in fundamentals/policy • Auxiliary: enough “noise” to prevent revelation through prices • variant with similar results: rational inattention • uncertainty about future infmation and income • not uncertainty about the fundamentals/policy per se 5/30 • Key friction: uncertainty about how others will respond • to understand how it matters → IS and NKPC as beauty contests

The Euler/IS Curve with Common Knowledge • implication robust to borrowing constraints (e.g., McKay et al) • even though the aggregate Euler equation itself is difgerent 6/30 c t = − E t [ r t + 1 ] + E t [ c t + 1 ] • Key implication: c = f ( expected path of r )

The Euler/IS Curve without Common Knowledge • Defjnes a dynamic beauty contest among the consumers 7/30 { + ∞ } { + ∞ } β k − 1 ¯ β k − 1 ¯ ∑ ∑ c t = − E t [ r t + k ] + ( 1 − β ) E t [ c t + k ] k = 1 k = 1 • Key implication: c ̸ = f(expected path of r ). Instead, HOB matter.

The NK Philips Curve with Common Knowledge 8/30 π t = mc t + β E t [ π t + 1 ] • Key implication: π = f ( expected path of mc )

The NK Philips Curve without Common Knowledge E f • Defjnes a dynamic beauty contest among the fjrms E f 9/30 { + ∞ } { + ∞ } ( βθ ) k ¯ ( βθ ) k ¯ ∑ ∑ + 1 − θ π t = mc t + t [ mc t + k ] t [ π t + k ] θ k = 1 k = 1 • Key implication: π ̸ = f(expected path of mc ). Instead, HOB matter

So Far, and What’s Next • So far: represent IS and NKPC as dynamic beauty contests • What’s next: the beauty of dynamic beauty contests! • consider a more abstract setting (nests other applications too) • develop broader insights • apply insights to context of interest • Note: Higher Order Beliefs = a window to Rational Expectations 10/30

Attenuation and Horizon Efgects in Dynamic Beauty Contests

1 E t a t E t a t An Abstract Dynamic Beauty Contest k 1 t a t representative-agent Euler • With CK k k 1 k t • Consider models in which the following Euler-like condition holds: 1 E t k 1 k t a t dynamic beauty contest • Iterate over t and aggregate over i 11/30 a i , t = θ t + γ E it [ a i , t + 1 ] + α E it [ a t + 1 ] • θ t = fundamental, a it = individual outcome, a t = aggregate outcome • γ > 0 parameterizes PE efgects, α > 0 parameterizes GE efgects

E t a t An Abstract Dynamic Beauty Contest • Consider models in which the following Euler-like condition holds: 1 t a t representative-agent Euler • With CK 11/30 a i , t = θ t + γ E it [ a i , t + 1 ] + α E it [ a t + 1 ] • θ t = fundamental, a it = individual outcome, a t = aggregate outcome • γ > 0 parameterizes PE efgects, α > 0 parameterizes GE efgects • Iterate over t and aggregate over i ⇒ dynamic beauty contest { + ∞ } { + ∞ } γ k − 1 ¯ γ k − 1 ¯ ∑ ∑ a t = θ t + γ E t [ θ t + k ] + α E t [ a t + k ] k = 1 k = 1

An Abstract Dynamic Beauty Contest • Consider models in which the following Euler-like condition holds: 11/30 a i , t = θ t + γ E it [ a i , t + 1 ] + α E it [ a t + 1 ] • θ t = fundamental, a it = individual outcome, a t = aggregate outcome • γ > 0 parameterizes PE efgects, α > 0 parameterizes GE efgects • Iterate over t and aggregate over i ⇒ dynamic beauty contest { + ∞ } { + ∞ } γ k − 1 ¯ γ k − 1 ¯ ∑ ∑ a t = θ t + γ E t [ θ t + k ] + α E t [ a t + k ] k = 1 k = 1 • With CK ⇒ representative-agent Euler a t = θ t + ( γ + α ) E t [ a t + 1 ]

Question of Interest • c response to news about interest rates • Formally: 12/30 • How does a t responds to news about θ t + T ? • π infmation response to news about marginal costs • hold θ τ constant (say, at 0) for all τ ̸ = t + T • treat θ t + T as a random variable (Normally distributed with mean 0) • study ϕ T ≡ projection coeffjcient of a t on ¯ E t [ θ t + T ]

• With CK, HOB collapse to FOB, the “usual” scenario applies, and T hinges on The Role of HOB • and so on, up to beliefs of order T 2. how HOB load in a t T t 1. how HOB co-move with E t • Without CK, things are more tricky: T T 13/30 E t E t • By iterating, we can express a t as a linear function of • 1st-order beliefs: ¯ E t [ θ t + T ] • 2nd-order beliefs: ¯ [ ¯ ] ∀ τ : t < τ < t + T E τ [ θ t + T ] ∀ τ, τ ′ : t < τ < τ ′ < t + T • 3rd-order beliefs: ¯ [ ¯ [ ¯ E τ ′ [ θ t + T ] ]] E τ

The Role of HOB E t 2. how HOB load in a t • and so on, up to beliefs of order T 13/30 E t • By iterating, we can express a t as a linear function of • 1st-order beliefs: ¯ E t [ θ t + T ] • 2nd-order beliefs: ¯ [ ¯ ] ∀ τ : t < τ < t + T E τ [ θ t + T ] ∀ τ, τ ′ : t < τ < τ ′ < t + T • 3rd-order beliefs: ¯ [ ¯ [ ¯ E τ ′ [ θ t + T ] ]] E τ • With CK, HOB collapse to FOB, the “usual” scenario applies, and φ ∗ T = ( γ + α ) T • Without CK, things are more tricky: φ T hinges on 1. how HOB co-move with ¯ E t [ θ t + T ]

2. Longer horizons raise the relative importance of HOB Two Basic Insights T • longer horizons therefore raise the load of HOB on outcomes • but this is akin to ascending the hierarchy of beliefs! a t 1 a t 1 T a t 1. HOB vary less than FOB a t T t • the distant future enters through multiple rounds of GE efgects: news, I am likely to think that your beliefs moved less than mine” • “unless I am 100% sure that you heard and paid attention to the 14/30

Two Basic Insights 1. HOB vary less than FOB • “unless I am 100% sure that you heard and paid attention to the news, I am likely to think that your beliefs moved less than mine” • the distant future enters through multiple rounds of GE efgects: • but this is akin to ascending the hierarchy of beliefs! • longer horizons therefore raise the load of HOB on outcomes 14/30 2. Longer horizons raise the relative importance of HOB θ t + T → a t + T → a t + T − 1 → ... → a t + 1 → a t

2. Attenuation efgect increases with the horizon T decreases in T 3. Attenuation efgect grows without limit Results even if noise is tiny* 0 as T T T • T 1. Attenuation at any horizon • • “CK maximizes GE efgect” 15/30 • ϕ T bounded between PE efgect and CK counterpart: γ T < ϕ T < ϕ ∗ T = ( γ + α ) T

Results 1. Attenuation at any horizon • “CK maximizes GE efgect” 2. Attenuation efgect increases with the horizon 3. Attenuation efgect grows without limit • T T 0 as T even if noise is tiny* 15/30 • ϕ T bounded between PE efgect and CK counterpart: γ T < ϕ T < ϕ ∗ T = ( γ + α ) T • ϕ T /ϕ ∗ T decreases in T

Results 1. Attenuation at any horizon • “CK maximizes GE efgect” 2. Attenuation efgect increases with the horizon 15/30 • ϕ T bounded between PE efgect and CK counterpart: γ T < ϕ T < ϕ ∗ T = ( γ + α ) T • ϕ T /ϕ ∗ T decreases in T 3. Attenuation efgect grows without limit • ϕ T /ϕ ∗ T → 0 as T → ∞ even if noise is tiny*