Optimal Trend In ation

Transcription

1 Optimal Trend In ation Klaus Adam University of Mannheim Henning Weber Deutsche Bundesbank September 2017 Adam & Weber () Trend In ation September / 46

2 Introduction Add rm heterogeneity (productivity) to otherwise standard sticky price economy Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 2 / 46

3 Introduction Add rm heterogeneity (productivity) to otherwise standard sticky price economy Productivity at rm level displays systematic trends: - life cycle: rms start small/unproductive, become productive, exit - product life cycle: new products, higher quality, initially higher price Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 2 / 46

4 Introduction Add rm heterogeneity (productivity) to otherwise standard sticky price economy Productivity at rm level displays systematic trends: - life cycle: rms start small/unproductive, become productive, exit - product life cycle: new products, higher quality, initially higher price Productivity trends at the rm level =) strongly a ect optimal in ation dynamics & rationalizes positive steady state in ation Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 2 / 46

5 Introduction Large part of existing sticky price literature: abstracts from rm level heterogeneity, except for price heterogeneity Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 3 / 46

6 Introduction Large part of existing sticky price literature: abstracts from rm level heterogeneity, except for price heterogeneity Technically motivated: aggregating 2-dim. heterogeneity a challenge Strong economic implications: zero in ation optimal Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 3 / 46

7 Introduction Large part of existing sticky price literature: abstracts from rm level heterogeneity, except for price heterogeneity Technically motivated: aggregating 2-dim. heterogeneity a challenge Strong economic implications: zero in ation optimal Productivity of price adjusting rms equal to productivity of non-adjusting rms Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 3 / 46

8 Introduction Large part of existing sticky price literature: abstracts from rm level heterogeneity, except for price heterogeneity Technically motivated: aggregating 2-dim. heterogeneity a challenge Strong economic implications: zero in ation optimal Productivity of price adjusting rms equal to productivity of non-adjusting rms Adjusting rms price = price of non-adjusting rms =) strong force towards zero in ation Woodford(2003), Kahn, King & Wolman(2003), Schmitt-Grohé & Uribe(2010) Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 3 / 46

9 Introduction Golosov&Lucas (2007), Nakamura&Steinsson (2010) idiosyncratic rm level productivity, without systematic trend Do not look at optimal in ation Results sugests zero in ation optimal: av. prod. of adjusting rm av. prod. of non-adjusting rm Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 4 / 46

10 Introduction Enrich basic homogeneous rm setup by adding: Firm entry & exit Measure δ of randomly selected rms: very negative productivity shock & exit Exiting rms replaced by same measure of newly entering rms Alternative interpretations of setup possible (product substitution, quality improvements) Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 5 / 46

11 Introduction Firm-level productivity trends driven by 3 underlying trends: aggregate trend: productivity gains experienced by all rms experience trend: rms become more productive over time cohort trend: productivity level for new cohort of rms Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 6 / 46

12 Introduction Production function of rm j 2 [0, 1]: Y jt = A t Q t sjt G jt where s jt is time since last δ-shock K 1 jt 1 φ 1 φ Ljt F t, A t = a t A t 1, Q t = q t Q t 1, 1 if s G jt = jt = 0, g t G jt 1 otherwise. (a t, q t, g t ) arbitrary stationary process w mean a, q, g Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 7 / 46

13 Introduction Production function of rm j 2 [0, 1]: Y jt = A t Q t sjt G jt where s jt is time since last δ-shock K 1 jt 1 φ 1 φ Ljt F t, A t = a t A t 1, Q t = q t Q t 1, 1 if s G jt = jt = 0, g t G jt 1 otherwise. (a t, q t, g t ) arbitrary stationary process w mean a, q, g Three productivity trends: a, q and g Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 7 / 46

14 Introduction Production function of rm j 2 [0, 1]: Y jt = A t Q t sjt G jt where s jt is time since last δ-shock K 1 jt 1 φ 1 φ Ljt F t, A t = a t A t 1, Q t = q t Q t 1, 1 if s G jt = jt = 0, g t G jt 1 otherwise. (a t, q t, g t ) arbitrary stationary process w mean a, q, g Three productivity trends: a, q and g Measure δ of rms: productivity drops to zero & exit Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 7 / 46

15 Introduction Production function of rm j 2 [0, 1]: Y jt = A t Q t sjt G jt where s jt is time since last δ-shock K 1 jt 1 φ 1 φ Ljt F t, A t = a t A t 1, Q t = q t Q t 1, 1 if s G jt = jt = 0, g t G jt 1 otherwise. (a t, q t, g t ) arbitrary stationary process w mean a, q, g Three productivity trends: a, q and g Measure δ of rms: productivity drops to zero & exit Special cases w/o rm level trends: δ = 0 or if q t g t Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 7 / 46

16 Introduction Figure: Productivity dynamics in a setting with rm entry and exit Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 8 / 46

17 Introduction Setup naturally generates positive steady state in ation, if young rms initially less productive than non-exiting incumbents Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 9 / 46

18 Introduction Setup naturally generates positive steady state in ation, if young rms initially less productive than non-exiting incumbents In line with young rms being small =) av. prod. adjusting rm < av. prod. non-adjusting rm =) relative price of adj. to non-adj. rm larger than one Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 9 / 46

19 Introduction Setup naturally generates positive steady state in ation, if young rms initially less productive than non-exiting incumbents In line with young rms being small =) av. prod. adjusting rm < av. prod. non-adjusting rm =) relative price of adj. to non-adj. rm larger than one Ine cient that existing rms adjust: price dispersion/adjustment costs =) positive rates of in ation optimal in steady state Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 9 / 46

20 Introduction Setup naturally generates positive steady state in ation, if young rms initially less productive than non-exiting incumbents In line with young rms being small =) av. prod. adjusting rm < av. prod. non-adjusting rm =) relative price of adj. to non-adj. rm larger than one Ine cient that existing rms adjust: price dispersion/adjustment costs =) positive rates of in ation optimal in steady state Strength of e ect independent of turnover rate δ > 0 Discontinous jump of optimal in ation: δ = 0! δ > 0 Adam & Weber (University Trend of In ation Mannheim & CEPR Deutsche Bundesbank September 2017) 9 / 46

21 Introduction Aggregate NL model in closed form & determine opt. in ation 10 / 46

22 Introduction Aggregate NL model in closed form & determine opt. in ation Optimal gross steady state in ation rate Π = g q, independent of TFP trend a. 10 / 46

23 Introduction Aggregate NL model in closed form & determine opt. in ation Optimal gross steady state in ation rate Π = g q, independent of TFP trend a. Optimal in ation - cannot be inferred from aggregate productivity trends - has to know rm level trends & shocks to these trends 10 / 46

24 Introduction Aggregate NL model in closed form & determine opt. in ation Optimal gross steady state in ation rate Π = g q, independent of TFP trend a. Optimal in ation - cannot be inferred from aggregate productivity trends - has to know rm level trends & shocks to these trends Optimal in ation Π = 1 if δ = / 46

25 Introduction What is the optimal in ation rate of the US economy? 11 / 46

26 Introduction What is the optimal in ation rate of the US economy? Extend model to multi-sector economy: sector-speci c price stickiness & sector-speci c trends in TFP (a zt ), experience (q zt ) and cohort (g zt ) 11 / 46

27 Introduction What is the optimal in ation rate of the US economy? Extend model to multi-sector economy: sector-speci c price stickiness & sector-speci c trends in TFP (a zt ), experience (q zt ) and cohort (g zt ) Derive in closed form an analytical expression for the optimal SS in ation rate 11 / 46

28 Introduction What is the optimal in ation rate of the US economy? Extend model to multi-sector economy: sector-speci c price stickiness & sector-speci c trends in TFP (a zt ), experience (q zt ) and cohort (g zt ) Derive in closed form an analytical expression for the optimal SS in ation rate Model-consistent approach for estimating SS in ation rate from rm level trends: 147million rm observations from the LBD database (US Census) 11 / 46

29 Introduction What is the optimal in ation rate of the US economy? Extend model to multi-sector economy: sector-speci c price stickiness & sector-speci c trends in TFP (a zt ), experience (q zt ) and cohort (g zt ) Derive in closed form an analytical expression for the optimal SS in ation rate Model-consistent approach for estimating SS in ation rate from rm level trends: 147million rm observations from the LBD database (US Census) Estimated optimal in. rate steadily declined: 1986: 2% =) 2013: 1% 11 / 46

30 Related Literature Few papers: in ation, productivity dynamics All of them nd negative in ation rates optimal: Wolman (JMCB, 2011): two sector economy with di erent sectorial productivity trends, homogeneous rms in each sector, neg. in ation optimal despite monetary frictions being absent Amano, Murchison & Rennison (JME, 2009): homogeneous rm model with sticky prices and wages & aggregate growth; wages more sticky than prices; to depress wage-markups de ation turns out optimal. 12 / 46

31 Related Literature Zero in ation approx. optimal in models w homogeneous rms Woodford (2003), Kahn, King & Wolman (2003), Schmitt-Grohé and Uribe (2010) Zero lower bound cannot justify positive average rates of in ation: Adam & Billi (2006), Coibion, Gorodnichenko & Wieland (2012) Brunnermeier and Sannikov (2016): idiosyncratic risk -> positive in ation increasingly optimal Downward nominal wage rigidity may justify positive in ation rates Kim & Ruge-Murcia (2009), Benigno & Ricci (2011), Schmitt-Grohe & Uribe (2013), Carlsson & Westermark (2016) Positive in ation possibly optimal in models with endogenous entry: Corsetti & Bergin (2008), Bilbiie, Ghironi & Melitz (2008), Bilbiie, Fujiwara & Ghironi (2014) 13 / 46

32 Outline of Remaining Talk 1 Sticky price model with δ-shocks 2 Aggregation & optimality of ex price equilibrium 3 Optimal in ation: main result 4 Multi-sector extension & empirical strategy 14 / 46

33 Sticky Price Model Consider a Calvo sticky price setup: price stickiness parameter α (main results extend to menu cost setting) Continuum of sticky price rms, Dixit-Stiglitz aggregate Y t Random sample δ receives δ-shocks Firm productivity dynamics as described before Competitive labor and capital markets 15 / 46

34 Sticky Price Model Household problem! max E 0 β t [C t V (L t )] 1 σ 1 ξ t t=0 1 σ s.t. C t + K t+1 + B t P t = (r t + 1 d)k t + W t P t L t + Existence of balanced growth path: Z 1 0 Θ jt P t dj + B t 1 P t (1 + i t 1 ) T t β < (aq) φσ and (1 δ) (g/q) θ 1 < 1 16 / 46

35 Outline of Remaining Talk 1 Sticky price model with δ-shocks 2 Aggregation & optimality of ex price equilibrium 3 Optimal in ation: main result 4 Multi-sector extension & empirical strategy 17 / 46

36 Aggregation Highlight the di erences relative to a model with homogeneous rms Will spare you the derivation behind the results / 46

37 Aggregate Output, Capital & Labor Aggregate output Y t : Y t = A tq t t K 1 t 1 φ 1 φ Lt F t, with K t, L t aggregate capital, labor and F t 0 xed costs t : captures joint distribution of prices & productivities: t = Z 1 0 Qt G jt Q t θ Pjt dj (1) sjt P t 19 / 46

38 Price Level Price level: exp.-weighted average of product prices P t = = Z 1 0 Z 1 Yjt 0 1 (P jt ) 1 θ 1 θ dj Y t P jt dj Price level accounts for product substitution (as statistical agencies do) 20 / 46

39 Price Level Price level: exp.-weighted average of product prices P t = = Z 1 0 Z 1 Yjt 0 1 (P jt ) 1 θ 1 θ dj Y t P jt dj Price level accounts for product substitution (as statistical agencies do) In ation: Π t = P t /P t / 46

40 Aggregate Price Level Dynamics Evolution of the aggregate price under opt. price setting: Pt 1 θ (pt = ( {z} δ + (1 α)(1 δ) n ) θ 1 δ ) P? 1 θ t,t + α(1 δ) {z } 1 {z δ } {z} {z } new rms old adj. rms rel. price factor (pt n ) θ 1 = δ + (1 δ) opt price new rm pt n g t 1 q t θ 1. old rms, w/o adj. P t 1 1 θ 21 / 46

41 Aggregate Price Level Dynamics g t q t =) no rm level trends and (p n t ) θ 1! 1 and Pt 1 θ = (δ + (1 α)(1 δ))(p t,t)? 1 θ + α(1 δ)(p t 1 ) 1 θ If - in addition - δ = 0: P 1 θ t = (1 α)(p? t,t) 1 θ + α(p t 1 ) 1 θ Standard price evolution equation in homogeneous rm models. 22 / 46

42 Conditions Insuring E ciency Attaining e ciency requires - eliminating rm s monopoly power by an output subsidy - choosing t in the production function Y t = A tq t K 1 1 φ t t equal to t = e t = Z 1 0 Qt G jt Q t 1 φ Lt sjt F t, 1 θ dj! 1 1 θ 23 / 46

43 Conditions Insuring E ciency Attaining e ciency requires - eliminating rm s monopoly power by an output subsidy - choosing t in the production function Y t = A tq t K 1 1 φ t t equal to t = e t = Z 1 0 Qt G jt Q t 1 φ Lt sjt F t, 1 θ dj! 1 1 θ t = e t decentralized by prices satisfying P jt P t = 1 e t Q t G jt Q t sjt 23 / 46

44 E ciency of Flex Price Equilibrium Proposition: With exible prices (α = 0) & appropriate output subsidy, the equilibrium allocation is e cient. The optimal in ation rate is indeterminate / 46

45 Outline of Remaining Talk 1 Sticky price model with δ-shocks 2 Aggregation & optimality of ex price equilibrium 3 Optimal in ation: main result 4 Multi-sector extension & empirical strategy 25 / 46

46 E ciency under Sticky Prices Empirically relevant case E [g t ] > E [q t ], new rms small/new products expensive 26 / 46

47 E ciency under Sticky Prices Empirically relevant case E [g t ] > E [q t ], new rms small/new products expensive From (pt n ) θ 1 = δ + (1 δ) we tend to get that (p n t ) θ 1 > 1. pt n g t 1 q t θ / 46

48 E ciency under Sticky Prices Empirically relevant case E [g t ] > E [q t ], new rms small/new products expensive From (pt n ) θ 1 = δ + (1 δ) we tend to get that (p n t ) θ 1 > 1. Price level equation Pt 1 θ = (δ + (1 α)(1 δ) (pn t ) θ 1 δ 1 δ pt n g t 1 q t θ 1. )(P? t,t) 1 θ + α(1 δ)(p t 1 ) 1 θ, =) old rms choose higher (P tj ) 1 θ than new rms =) since 1 θ < 0: old rms to set lower prices than new rms 26 / 46

49 E ciency under Sticky Prices Empirically relevant case E [g t ] > E [q t ], new rms small/new products expensive From (pt n ) θ 1 = δ + (1 δ) we tend to get that (p n t ) θ 1 > 1. Price level equation Pt 1 θ = (δ + (1 α)(1 δ) (pn t ) θ 1 δ 1 δ pt n g t 1 q t θ 1. )(P? t,t) 1 θ + α(1 δ)(p t 1 ) 1 θ, =) old rms choose higher (P tj ) 1 θ than new rms =) since 1 θ < 0: old rms to set lower prices than new rms E ciency: old rms that adjust must choose same price as old rms that do not adjust 26 / 46

50 E ciency under Sticky Prices Empirically relevant case E [g t ] > E [q t ], new rms small/new products expensive From (pt n ) θ 1 = δ + (1 δ) we tend to get that (p n t ) θ 1 > 1. Price level equation Pt 1 θ = (δ + (1 α)(1 δ) (pn t ) θ 1 δ 1 δ pt n g t 1 q t θ 1. )(P? t,t) 1 θ + α(1 δ)(p t 1 ) 1 θ, =) old rms choose higher (P tj ) 1 θ than new rms =) since 1 θ < 0: old rms to set lower prices than new rms E ciency: old rms that adjust must choose same price as old rms that do not adjust Need to allow for in ation to achieve e ciency! 26 / 46

51 E ciency under Sticky Prices Proposition: Suppose (1) there is an appropriate output subsidy and (2) initial prices in t = 1 re ect rms relative productivities, i.e., P j, 1 1/(Q 1 sj, 1 G j, 1 ) for all j 2 [0, 1]. The eq. allocation is e cient under sticky price if Π? t = 1 δ/ ( e t ) 1 θ 1 δ! 1 θ 1 for all t 0, where ( e t ) 1 θ = δ + (1 δ) e t 1 q t /g t 1 θ. (2) 27 / 46

52 E ciency under Sticky Prices Proposition: Suppose (1) there is an appropriate output subsidy and (2) initial prices in t = 1 re ect rms relative productivities, i.e., P j, 1 1/(Q 1 sj, 1 G j, 1 ) for all j 2 [0, 1]. The eq. allocation is e cient under sticky price if Π? t = 1 δ/ ( e t ) 1 θ 1 δ! 1 θ 1 for all t 0, where ( e t ) 1 θ = δ + (1 δ) e t 1 q t /g t 1 θ. Prop holds for arbitrary initial prod. distributions & arbitrary shock processes (consistent with balanced growth) (2) 27 / 46

53 E ciency under Sticky Prices Proposition: Suppose (1) there is an appropriate output subsidy and (2) initial prices in t = 1 re ect rms relative productivities, i.e., P j, 1 1/(Q 1 sj, 1 G j, 1 ) for all j 2 [0, 1]. The eq. allocation is e cient under sticky price if Π? t = 1 δ/ ( e t ) 1 θ 1 δ! 1 θ 1 for all t 0, where ( e t ) 1 θ = δ + (1 δ) e t 1 q t /g t 1 θ. Prop holds for arbitrary initial prod. distributions & arbitrary shock processes (consistent with balanced growth) Proof works as follows: under the in ation rate (2) 1. new rms choose relative price as in the ex price economy 2. existing rms do not want to adjust their price. 3. with initial prices right & output subsidy =) ex price alloc. (2) 27 / 46

54 E ciency under Sticky Prices! Π t? = 1 δ/ ( e t ) 1 θ 1 θ 1 1 δ In the absence δ-shocks/ rm level trends (δ = 0 and/or g t q t ) get familiar result: Π t 1 28 / 46

55 E ciency under Sticky Prices! Π t? = 1 δ/ ( e t ) 1 θ 1 θ 1 1 δ In the absence δ-shocks/ rm level trends (δ = 0 and/or g t q t ) get familiar result: Π t 1 Price stability optimal, independently of realized productivity shocks. 28 / 46

56 E ciency under Sticky Prices! Π t? = 1 δ/ ( e t ) 1 θ 1 θ 1 1 δ (3) where ( e t ) 1 θ = δ + (1 δ) e t 1 q t /g t 1 θ. With rm level trends (δ > 0), steady state in ation is lim Π t = g q 29 / 46

57 E ciency under Sticky Prices! Π t? = 1 δ/ ( e t ) 1 θ 1 θ 1 1 δ (3) where ( e t ) 1 θ = δ + (1 δ) e t 1 q t /g t 1 θ. With rm level trends (δ > 0), steady state in ation is SS in ation positive when g > q lim Π t = g q 29 / 46

58 E ciency under Sticky Prices! Π t? = 1 δ/ ( e t ) 1 θ 1 θ 1 1 δ (3) where ( e t ) 1 θ = δ + (1 δ) e t 1 q t /g t 1 θ. With rm level trends (δ > 0), steady state in ation is lim Π t = g q SS in ation positive when g > q SS independent of δ: - fewer unproductive rms enter! lower in ation - existing rms accumulated more experience! higher in ation 29 / 46

59 E ciency under Sticky Prices! Π t? = 1 δ/ ( e t ) 1 θ 1 θ 1 1 δ (4) where ( e t ) 1 θ = δ + (1 δ) e t 1 q t /g t 1 θ. Linearization: π t? = (1 δ)π t? gt 1 + δ 1 + O(2) q t Positive experience shock (g t ): persistent rise in opt. in ation 30 / 46

60 E ciency under Sticky Prices! Π t? = 1 δ/ ( e t ) 1 θ 1 θ 1 1 δ (4) where ( e t ) 1 θ = δ + (1 δ) e t 1 q t /g t 1 θ. Linearization: π t? = (1 δ)π t? gt 1 + δ 1 + O(2) q t Positive experience shock (g t ): persistent rise in opt. in ation Positive chohort shock (q t ): persistent drop in opt in ation 30 / 46

61 E ciency under Sticky Prices! Π t? = 1 δ/ ( e t ) 1 θ 1 θ 1 1 δ (4) where ( e t ) 1 θ = δ + (1 δ) e t 1 q t /g t 1 θ. Linearization: π t? = (1 δ)π t? gt 1 + δ 1 + O(2) q t Positive experience shock (g t ): persistent rise in opt. in ation Positive chohort shock (q t ): persistent drop in opt in ation lim δ!0 : π? t random walk, but Var(π? t )! / 46

62 The Welfare Costs of Strict Price Stability Suppose MP implements Π = 1 in an economy where Π? 6= 1 Analytical result: strictly positive welfare costs even in the limit δ! 0 Numerical illustration highlighting the source of welfare distortions 31 / 46

63 The Welfare Costs of Strict Price Stability Assumptions for the analytical result: there is an optimal output subsidy and initial prices re ect initial productivities there are no aggregate productivity disturbances and δ > 0 xed costs of production are zero (f = 0) disutility of work is given by V (L) = 1 ψl ν, with ν > 1, ψ > 0. g/q > α(1 δ), so that a well-de ned steady state with strict price stability exists consider the limit β(γ e ) 1 σ! 1 32 / 46

64 The Welfare Costs of Strict Price Stability Proposition: Consider a policy implementing the optimal in ation rate Π? t, which satis es lim t! Π? t = Π? = g/q. Let c(π? ) and L(Π? ) denote the limit outcomes for t! for consumption and hours under this policy. Similarly, let c(1) and L(1) denote the limit outcomes under the alternative policy of implementing strict price stability. Then, and c(1) c(π? ) = 1 α(1 δ)(g/q) θ 1 1 α(1 δ) L(1) = L(Π? ) For g 6= q the previous inequality is strict and φθ θ 1 1 α(1 δ) (g/q) 1 1 α(1 δ)(g/q) θ 1! φ 1. (5). lim δ!0 c(1)/c(π? ) < 1 33 / 46

65 The Welfare Costs of Strict Price Stability 1.2 A. Relative cohort price: cohort mean, different inflation rates 1.2 B. Relative cohort price: mean and 2 std.dev. bands 0% inflation rate % Inflation Rate Optimal Inflation Rate: 2% cohort (time since last shock) cohort (time since last shock) Figure: Relative prices and in ation 34 / 46

66 The Welfare Costs of Strict Price Stability e / Aggregate productivity distortion Steady state inflation rate (annualized, in %) Figure: Aggregate productivity as a function of gross steady state in ation (optimal in ation rate is 1.02) 35 / 46

67 Outline of Remaining Talk 1 Sticky price model with δ-shocks 2 Aggregation & optimality of ex price equilibrium 3 Optimal in ation: main result 4 Multi-sector extension & empirical strategy 36 / 46

68 Multi-Sector Extension / Empirical Strategy Goal: quantify in ation rates arising from rm trends Take into account of sector-speci c productivity trends: manufacturing vs services Present a multi-sector extension of our analytical results & model-consistent empirical strategy 37 / 46

69 Multi-Sector Extension / Empirical Strategy z = 1,..., Z sectors, Dixit-Stiglitz competition, sector output Y zt 38 / 46

70 Multi-Sector Extension / Empirical Strategy z = 1,..., Z sectors, Dixit-Stiglitz competition, sector output Y zt Aggregate output Y t = Z (Y zt ) ψ z with z=1 Z ψ z = 1 z=1 38 / 46

71 Multi-Sector Extension / Empirical Strategy z = 1,..., Z sectors, Dixit-Stiglitz competition, sector output Y zt Aggregate output Y t = Z (Y zt ) ψ z with z=1 Z ψ z = 1 z=1 Sector-speci c TFP, cohort and experience trends a zt = a z ε a zt and q zt = q z ε q zt and g zt = g z ε g zt, 38 / 46

72 Multi-Sector Extension / Empirical Strategy z = 1,..., Z sectors, Dixit-Stiglitz competition, sector output Y zt Aggregate output Y t = Z (Y zt ) ψ z with z=1 Z ψ z = 1 z=1 Sector-speci c TFP, cohort and experience trends a zt = a z ε a zt and q zt = q z ε q zt and g zt = g z ε g zt, Sector-speci c price stickiness α z 2 (0, 1) 38 / 46

73 Multi-Sector Extension / Empirical Strategy z = 1,..., Z sectors, Dixit-Stiglitz competition, sector output Y zt Aggregate output Y t = Z (Y zt ) ψ z with z=1 Z ψ z = 1 z=1 Sector-speci c TFP, cohort and experience trends a zt = a z ε a zt and q zt = q z ε q zt and g zt = g z ε g zt, Sector-speci c price stickiness α z 2 (0, 1) Sector-speci c entry/exit rates δ z 2 (0, 1). 38 / 46

74 Multi-Sector Extension / Empirical Strategy z = 1,..., Z sectors, Dixit-Stiglitz competition, sector output Y zt Aggregate output Y t = Z (Y zt ) ψ z with z=1 Z ψ z = 1 z=1 Sector-speci c TFP, cohort and experience trends a zt = a z ε a zt and q zt = q z ε q zt and g zt = g z ε g zt, Sector-speci c price stickiness α z 2 (0, 1) Sector-speci c entry/exit rates δ z 2 (0, 1). Aggregate price level: P t = Z z=1 Pzt ψ z ψz 38 / 46

75 Multi-Sector Extension / Empirical Strategy Proposition: Suppose initial prices re ect initial productivity, no economic disturbances, and an optimal output subsidy. Consider the limit β(γ e ) 1 σ! 1 and suppose monetary policy implements Π t = Π for all t. The in ation rate Π that maximizes the resulting steady state utility is Π? = Z gz γ e z ω z z=1 q z γ e where γ e z γ e = a z q z Z z=1(a z q z ) ψ z is the growth trend of sector z relative to the growth trend of the aggregate economy in the e cient allocation. The sector weights ω z 0 sum to one and are given by ω z = ψ z θα z (1 δ z )(Πγ e /γ e z )θ (q z /g z ) [1 α z (1 δ z )(Πγ e /γ e z )θ (q z /g z )] [1 α z (1 δ z )(Πγ e /γ e z )θ 1 ]., 39 / 46

76 Multi-Sector Extension / Empirical Strategy The optimal steady state in ation rate Π = Z gz γ e z ψ z z=1 q z γ e + O(2), O(2) : second order approximation error. 40 / 46

77 Multi-Sector Extension / Empirical Strategy The optimal steady state in ation rate Π = Z gz γ e z ψ z z=1 q z γ e + O(2), O(2) : second order approximation error. Since ψ z and γ e z /γe can be inferred from sectoral data, one only has to estimate g z /q z from rm level data. 40 / 46

78 Multi-Sector Extension / Empirical Strategy The optimal steady state in ation rate Π = Z gz γ e z ψ z z=1 q z γ e + O(2), O(2) : second order approximation error. Since ψ z and γ e z /γe can be inferred from sectoral data, one only has to estimate g z /q z from rm level data. How to estimate sector speci c productivity trends g z /q z? - rm level productivity: not observed... - rm level prices: not observed... - rm level employment: productivity->prices->demand/employment 40 / 46

79 Multi-Sector Extension / Empirical Strategy Model implies that g z /q z can be estimated from rm level employment trends: ln(l jzt ) = d zt + η z s jzt + ɛ jzt, (6) d zt :sector dummy, s jzt the age of the rm j, and ɛ jzt a stationary residual term, and η z = (θ 1) ln(g z /q z ). 41 / 46

80 Multi-Sector Extension / Empirical Strategy Estimate the rm level trends: - 65 BEA private industries - use LBD database for US Census Data: 147 million rm employment observations - use repeated cross-sections from to estimate g z /q z 42 / 46

81 Multi-Sector Extension / Empirical Strategy Estimate the rm level trends: - 65 BEA private industries - use LBD database for US Census Data: 147 million rm employment observations - use repeated cross-sections from to estimate g z /q z Report (θ 1) Π = (θ 1) Z z=1 ω gz γ e z z q z γ e 42 / 46

82 Optimal US In ation times (θ 1) 43 / 46

83 Optimal US In ation times (θ 1) 44 / 46

84 Multi-Sector Extension / Empirical Strategy 45 / 46

85 Conclusions Aggregate in closed form a sticky price model with rm level productivity trends 46 / 46

86 Conclusions Aggregate in closed form a sticky price model with rm level productivity trends Trends capture: product substitution, product quality improvements, or rm turnover 46 / 46

87 Conclusions Aggregate in closed form a sticky price model with rm level productivity trends Trends capture: product substitution, product quality improvements, or rm turnover Firm level productivity trends key for optimal in ation rate in sticky price models 46 / 46

88 Conclusions Aggregate in closed form a sticky price model with rm level productivity trends Trends capture: product substitution, product quality improvements, or rm turnover Firm level productivity trends key for optimal in ation rate in sticky price models Steady state in ation Π = g q > 1 46 / 46

89 Conclusions Aggregate in closed form a sticky price model with rm level productivity trends Trends capture: product substitution, product quality improvements, or rm turnover Firm level productivity trends key for optimal in ation rate in sticky price models Steady state in ation Π = g q > 1 Productivity disturbances have persistent e ects on optimal in ation 46 / 46

90 Conclusions Aggregate in closed form a sticky price model with rm level productivity trends Trends capture: product substitution, product quality improvements, or rm turnover Firm level productivity trends key for optimal in ation rate in sticky price models Steady state in ation Π = g q > 1 Productivity disturbances have persistent e ects on optimal in ation Optimal US in ation: dropped from approx 2% in 1986 to 1% in / 46