Dampening General Equilibrium: From Micro Elasticities to Macro Effects

Transcription

1 Dampening General Equilibrium: From Micro Elasticities to Macro Effects George-Marios Angeletos MT Chen Lian February 15, 2016 Abstract General equilibrium (GE) effects are key to macroeconomics: they turn partial-equilibrium intuitions on their head; they also limit the usefulness of identifying local responses to local shocks as a method of estimating the macroeconomic effects of aggregate shocks. n this paper, we argue that GE effects are weak in the short run. n particular, we establish an equivalence between (i) the Tâtonnement process of a standard macroeconomic model and (ii) the equilibrium dynamics of a variant model that removes common knowledge of aggregate economic conditions. This offers a formalization of the notion that GE adjustments take time; it provides a justification for extrapolating from the aforementioned kind of micro elasticities to macro effects; and it upsets conventional policy recommendations. General equilibrium (GE) effects are key to macroeconomics: they turn partialequilibrium intuitions on their head; they also limit the usefulness of identifying local responses to local shocks as a method for estimating the macroeconomic effects of aggregate shocks. For example, consider Mian and Sufi (2014). That paper offers compelling evidence that a large part of the cross-sectional variation in US employment during the Great Recession is driven by variation in consumer deleveraging. This, however, does not mean that the same mechanism explains a large part of the employment drop at the aggregate level; equilibrium effects that operate at the national level, such as those associated with relative prices, wages, interest rates, and monetary policy, introduce a wedge between the aggregate effects of an aggregate deleveraging shock and the local effects of a local deleveraging shock. By the same token, even if that paper provides a valid estimate of the micro elasticity of local employment to a local deleveraging shock, this need not be useful in assessing the macro elasticity of aggregate employment to an aggregate deleveraging shock. n this paper, we argue that GE effects, and the resulting disconnect between micro and macro elasticities, can be less important in the short run than what assumed in standard macroeconomic models. 1

2 We do so by inspecting the GE effects in a prototypical macroeconomic model and by devising two complementary mechanisms that can dampen these GE effects. These mechanisms are formalized with the help of two variants of the original model. n the first variant, we relax the standard equilibrium concept in favor of a Tâtonnement process; this helps accommodate the notion that equilibrium adjustment takes time. n the second variant, we maintain the standard equilibrium concept but introduce a certain type of incomplete information, which removes common knowledge of aggregate economic conditions while maintaining local knowledge of local conditions. We then establish two key results. The first is an equivalence between the dynamics of the two variant economies. The second is that the macro elasticities of the variant models are closer to the micro elasticities of the original model in the short run, and closer to its macro elasticities in the long run. Combined, these results clarify how the GE effects of the original model hinged on (i) instantaneous equilibrium adjustment and (ii) perfect coordination. By the same token, if one expects coordination frictions and/or equilibrium adjustment to take time, then one must also expect the GE effects to be dampened in the short run and therefore one must also feel more comfortable to extrapolate from the micro elasticities estimated in, e.g., Mian and Sufi (2014) and Nakamura and Steinsson (2014) to the macro effects of interest. n extensions, we provide additional foundations for such GE dampening on the basis rational inattention, as well as of Reflective Equilibrium (Garcia- Schmidt & Woodford, 2015). There is an extensive literature on inertia in response to shocks, including adjustment cost (Caballero and Engel, 1999), inattention (Sims, 2003; Reis, 2006; Alvarez et al., 2012), etc. These are based on decision-theoretic level mechanisms that tend to dampen both micro and GE effects. Our paper, instead, focuses on how GE effects can be dampened taking as given the (estimated) micro elasticities, and thus help merge micro and macro elasticities. We study several applications in the paper. On the one hand, we turn supplyside economics on its head by showing that payroll tax cuts may be ineffective instruments for stimulating economic activity and, instead, fiscal multipliers can be quite large, even if prices are flexible and wealth effects on labor supply are negligible. On the other hand, we discuss how our mechanism can dampen the effectiveness of monetary policy in a New-Keynesian model. We also draw relations to the empirical literature. 2

3 Dampening General Equilibrium: From Micro Elasticities to Macro Effects George-Marios Angeletos Chen Lian February 14, 2016

4 Outline 1 ntroduction 2 Main Mechanism in an Abstract Dixit-Stiglitz Economy 3 Applications 4 Conclusion

5 ntroduction General equilibrium effect key to macroeconomics Difficult to apply PE intution directly to macro question F Household deleveraging causing recessions? nterest rate may decrease! Difficult to apply empirically estimated micro elasticity to study aggregate effect of macro shocks F Mian-Sufi Stength of GE hinges upon strong assumptions nstataneous adjustment of aggregates to equilibrium level Agents perfect knowledge of those movement This paper: How GE effect is dampened in short run if we relax these assumptions Wrong PE intuition is justified in short run Bridging empirically estimated micro elasticity and macro elasticity

6 Micro vs Macro Elasticity i denotes a micro unit: A differentiated good in Dixit-Stiglitz AzipcodeinMian-Sufi q i :microshocks Micro supply curve, s i = S (p i,q i,p) Micro demand curve, d i = D (p i,q i,p) mposing market clearing at a micro level Micro price and quantity in terms of micro shocks and aggregates qi = f q (q i,p) pi = f p (q i,p) For simplicity, log-linearization P = R p i di; Q = R q i di

7 Micro vs Macro Elasticity Micro elasticity: How micro outcomes respond to qi, holding aggregates P fixed e micro i = f q q i Macro elasticity: How aggregates respond to aggregate (macro) shock e macro = Q q = R ei micro + f q P P q di Macro elasticity = Average Micro elasticity (PE) + mpact through aggregates P (GE) Mainstream macro: GE is both qualitatively and quantitatively important Macro elasticity deviates from micro elasticity

8 Our Paper Formalize how GE effect is dampened in short run Equivalence in terms dampening GE A tâtonnement process Remove common knowledge of aggregate shocks Reflective equilibrium, adaptive expectations, etc A new theory about how macroeconomy responds to aggregate shocks in the short run Ajustificationofusingempiricallyestimatedmicroelasticityasmacro elasticity in the short run Mian-Sufi, Nakamura-Steinsson

9 Micro nertia vs Macro nertia Literature about inertia in response to shocks Adjustment cost, inattention, etc. F Decision-theoretic mechanisms dampening micro elasticity This paper: Dampening GE for given micro elasticity

10 Applications and Policy mplications neffectiveness of payroll tax cut during a recession nertia in response to monetary policy Deleveraging driven recession Mian-Sufi Demand-driven fiscal stimulus Nakamura-Steinsson

11 Outline 1 ntroduction 2 Main Mechanism in an Abstract Dixit-Stiglitz Economy 3 Applications 4 Conclusion

12 Set Up Acontinuumofdifferentiatedgoods A representative firm competitively produce each good Arepresentativehouseholdconsumesthemandanumeraire U = x g u (c)+z u (c)= c1 g c = ( R g e d 1 e 1 e 1 i c i di ) e e 1 Aggregate demand for composite(log-linearization) C = x 1 g P, AD (P,x ) Demand for good i c i = x i e (p i P) {z } relative price 1 g {z} P, D (p i,p,x i ) price of composite x aggregate demand shock, x i = x + d i good specific demand shock

13 Supply Arepresentativefirmcompetitivelyusesnumerairetoproducegoodi yi = a i (l i ) 1 1+k 1 1+k ai good specific technology shock Supply curve for good i (after log-linearization) yi = 1 k p i + k+1 k a i, S (p i,a i ) Aggregate supply of composite Y = 1 k P + k+1 k A, AS (P,A)

14 Micro and Macro Elasticity mposing market clearing for each good: i s price and quantity as a function of micro shocks and aggregates q i = f q (a i,x i,p)= e(k+1) ek+1 a i + 1 ek+1 x i + e 1 g ek+1 P p i = f p (a i,x i,p)= k+1 ek+1 a i + k ek+1 x i + e 1 g k ek+1 Micro elasticity (e.g output to technology shock) e micro i = q i a i Macro elasticity = e(k+1) ek+1 e macro = k+1 g+k = R ei micro di (ge 1)(k+1) (ek+1)(g+k) When e < 1 g,thatis,differentiatedgoodsarecomplements e macro > e micro Postive aggregate technology shock -> low aggregate price -> more consumption of composite goods -> more consumption of goods i P

15 Tâtonnement Start from an ad-hoc economy with a tâtonnement process of aggregate price llustrate how GE is dampened especially in short run How macro elasticity is micro elasticity Here: Adjustment of aggregate price off equilibrium Later: Adjustment on equilibrium With lack of common knowledge of aggregate shocks Replicate the dampening GE effect result

16 Tâtonnement Consider aggregate technology shock A Auctioneer starts conjectured aggregate price from steady state: ˆP 0 = 0 Agents submit their supply/demand curves to auctioneer At round of iteration t, supposeauctioneerconjectureis ˆP t Adjustment according to excess aggregate suply F d ˆP : t dt = c t AS ˆPt,A AD ˆPt,0 ct controls the speed of Tâtonnement Agents uses Walrassian auctioneer s ˆP t as aggregate price qi,t = f q a i,x i, ˆP t ; p i,t = f p a i,x i, ˆP t F Micro market always clearing Q t = R q i,t dj; P t = R p i,t dj

17 Tâtonnement nterpretation of t: Round of iteration Calendar time: Auctioneer adjusts aggregate price in real time F Benchmark economy happens repetitively Macro elasticity in Tâtonnement economy 1 e macro t = Q e (k + 1) (k + 1) e g t A = ek + 1 {z } (ek + 1) 1 + k g PE limt!0 et macro = e micro limt!+ et macro = e macro 1 e k g +1 k R t0 c s ds {z } GE Macro elasticity close to micro elasticity in short run But gradually converges to what traditional paradigm predicts in the long run

18 Tâtonnement: Graph P AS AS' AD P 0 Excess Aggregate Supply GE Q Figure: Tâtonnement

19 Tâtonnement: Graph P,P D(,P 0 ) S S' P 0 P 0 PE Q 0 Q Figure: Tâtonnement

20 Tâtonnement: Graph P,P AD D(,P t ) S/AS S'/AS' P t Excess Supply GE P t Q t Q Figure: Tâtonnement

21 Tâtonnement: Graph P,P AD D(,P 0 ) S/AS D(,P ) S'/AS' P 0 Excess Supply P t P /P GE P t P 0 PE Q 0 Q t Q Q Figure: Tâtonnement

22 ncomplete nformation: Set Up Start from a static economy, dynamics later Same payoff-relevant set up Adding islands for a natural info struture Each differentiated good is produced competitively on an island i The representative household sends one sibling to each island Make consumption decision of that island-specific goods Sibling: A self of a person purchasing a particular product The yesterday myself purchasing milk in Whole Foods Agents informed about local conditions, but not aggregates When buy milk, know price and my taste of the milk Not know/consider the price of clothes Not know/consider CP and interest rate

23 ncomplete nformation Similarly, consider an aggregate technology shock A All agents on island i share the same information set Perfect knowledge of local shock a i F f s a o s A,onecannotinferA from a i Prior about aggregate shock: A N 0,kA 1 Private signals about A: s i = A + p e i we F Where e i N (0,1) and w e is the precision of private signal Average expectation of aggregate technology shock: ĒA= w e w e +k A A, la

24 ncomplete nformation Heterogenous information creates coordination friction within household c: error in optimal composite consumption 1 F C = x g P 1 c P g 1 e {z } g {z } optimal composite consumption error sland demand under incomplete information D inc xi, p i,e i P, x 1 i e p i + e + c g E i P sland supply under incomplete information S inc (ã i, p i ), ỹ i = k 1 p i + k+1 k ãi

25 ncomplete nformation Economic outcome is determined by island market clearing: 1 g ; qi = e(k+1) ek+1 ãi + 1 x ek+1 i + e+c pi = k+1 ek+1ãi + k ek+1 x i + ek+1 E i P = f q,inc ã i, x i,e i P e+c Q = R qi di = f q,inc Ã,0, Ē P 1 g k ã i, x i,e i P ek+1 E i P = f p,inc R ; P = pi di = f Ã,0, p,inc Ē P Aggregate expectation of endogenous aggregate price level: Derived by iterating P = f Ã,0, p,inc Ē P! h 1 Ē P = k+1 e+c 1 ek+1 + g k h=1 ek+1 Ē h k+1 Ã = ek(1 l )+1 k c 1 g l lã Strategic uncertainty generates additional intertia in beliefs about P through higher-order beliefs nformation friction dampens macro elasticity more than micro elasticity

26 ncomplete nformation: Outcome Given Ē P, onecanwrite Q and P in terms of à and c Q = f q,inc Ã,0, Ē P ; P = f p,inc Ã,0, Ē P By definition of c, errorinoptimalcompositeconsumption, 1 Q = x g P 1 c P g 1 e {z } g {z } optimal composite consumption error We derive a fixed point condition about c, solveit: e 1 g (1 l ) c = 1 1 +l (e g )g Under complete information, l = 1, c = 0 Perfect coordination within family maximing composite consumption

27 ncomplete nformation: Outcome Macro elasticity in incomeplete information economy e macro (w e )= e(k+1) ek+1 e+ c ek+1 lim we!0 e macro (w e )=e micro limwe!+ e macro (w e )=e macro 1 g k+1 ek(1 l )+1 k c 1 g l l mprecise information of A: macroelasticityclosetomicroelasticity Precise information: traditional macro elasticity

28 Equivalence Result, Static Proposition 1. For any t and {c s } sapplet governing the speed of Tâtonnement, there exists a precision of private signal w e such that 1 Tâtonnement economy s Q t and P t F same as incomplete information economy s Q and P 2 Walrassian auctioneer s conjectured ˆP (t) F same as ĒP in incomplete infomration economy Similar mapping from incomplete information economy to Tâtonnement economy

29 Equivalence Result, Dynamic nstead of receiving one private signal only Receive private signals continually about A: dsit = Adt + p dw it wet Where Wit is a Brownian Motion and w et is the precision of private signal at time t Proposition 2. For any {c t } governing the speed of Tâtonnement, there exists a series of private signal with precision {w et } such that 1 Tâtonnement economy s Q t and P t F same as incomplete information economy s Q t and P t 2 Walrassian auctioneer s conjectured ˆP (t) F same as Ē t P t in incomplete infomration economy Similar mapping from incomplete information economy to Tâtonnement economy

30 Connection to Literature nertia of response to shocks Adjustment cost (Caballero-Engel); nattention (Reis, Sims, Alvarez-Lippi) Decision-theoretic level mechanism dampens micro and macro elasticity in proportion This paper: How information friction F dampens macro elasticities more than micro elasticities

31 An Alternative Reflective Equilibrium (Garcia-Schmidt & Woodford, 2015) Walrassian auctioneer adjusts conjectured aggregate price ˆP t according to the difference between ˆP t and P t Agents act as aggregate price is ˆP t qi,t = f q a i,x i, ˆP t ; p i,t = f p a i,x i, ˆP t Qt = R q i,t dj; P t = R p i,t dj ˆP t Adjustment: d ˆP t dt = c t ˆPt P t ; ˆP0 = 0 Garcia-Schmidt & Woodford interprets ˆP t agents perceived aggregate price Similar equivalence result

32 Outline 1 ntroduction 2 Main Mechanism in an Abstract Dixit-Stiglitz Economy 3 Applications 4 Conclusion

33 Household Delevaraging Shock Preview: Adding non-tradables Directly mapping Mian-Sufi s estimated micro elasticity to aggregate effect of household deleveraging shock A theory of household deleveraging driven recession without nominal rigidity

34 Household Delevaraging Shock Acontinuumofregionsi For each region i, a representative firm competitively produce region-specific non-tradable goods Arepresentativehouseholdin each region i Consume a common traded good and a region-specific non-traded good (GHH) n ui i = b i appleu c 1+k i 1+k + c i,2 ci = (1 a) 1 e (ci t) e e 1 + a 1 e (ci nt ) e e 1 e e 1 b i < 0: household deleveraging shock Equivalent to a tightening in budget constraint GE effect comes from interest rate: R One tradable -> R second period goods

35 Supply and Demand Unit of account: tradable good Supply of region-specific non-tradable i y nt i = a i + k 1 (a i +(1 a)pi nt )=S(a i,pi nt ) Demand of region-specific non-tradable i: D ({a i,b i },pi nt,r) 1 g(µ+1) R e (1 a)+ a g(µ+1) pi nt + ci nt = 1 g(µ+1) b i µ(1+k) (µ+1)k (a i +(1 a)pi nt ) Second term: intertemporal subsitution Third term: substitution between tradables and non-tradables Fourth term: labor-consumption complementarity as a result of GHH Tradebles are endowed

36 Micro and Macro Elasticity Consider household deleveraging shock: b < 0 Micro elasticity: e micro = e S 1 e S e D g(µ+1) > 0 es, e D slope of local supply/demand curves for non-tradables: Local household deleveraging shock generates local recesssions Because interest rate is fixed, demand of region-specific non-tradable moves downwards Macro elasticity nterest rate drops to crowd in consumption: R = b agg Aggregate output of non-tradables are fixed(ghh): Y nt = C nt = 0 Macro elasticity (of non-tradable output responding to deleveraging shock): e macro = 0

37 This Paper Macro elasticity is close to micro elasticity in short run ntuition: Household deleveraging shock does drive recession When buying meals, people realize tightened budget, but not low interest AD curve does move downward Mian-Sufi uses regions heterogenous exposure to household deleveraging shock To estimate average micro elasticity: e micro n the short run, micro elasticity is close to macro elasticity Aggregate impact of household deleveraging shock: e micro b agg

38 Government Spending Shock Similar setting as household deleveraging shocks Government purchase both traded goods and non-traded goods Lump sum taxation in terms of second-period goods Supply of region-specific non-tradable i: y nt i = k+1 k a i + k 1 (1 a)pnt i = S (a i,pi nt ) Demand of region-specific non-tradable i: :D ({a i,g i },pi nt,r) c 1,nt l i = g(µ+1) R l e (1 a)+ a g(µ+1) pi nt + lµ(1+k) (µ+1)k (a i +(1 a)p nt i )+(1 l)g i

39 Result Micro elastity: e micro = 1 l e S le D > 0 Local government spending shock stimulating local economy Macro elasticity: e macro = 0 nterst rate moves up to crowd out consumption This paper Macro elasticity is close to micro elasticity in short run Government spending does stimulate economy Nakamura-Steinsson uses regions heterogenous exposure to military spending To estimate average micro elasticity: e micro Aggregate impact of government spending shock: e micro G

40 Outline 1 ntroduction 2 Main Mechanism in an Abstract Dixit-Stiglitz Economy 3 Applications 4 Conclusion

41 Conclusion Slow adjustment of beliefs of aggregate endogenous outcomes n short run GE response to macro shock is dampened Empirically estimated micro elasticity is macro elasticity A new theory about how macroeconomy responds to aggregate shocks Robust predictions in multiple settings Tâtonnement, incomplete information, reflective equilibrium