Firm Uncertainty Cycles and the Propagation of Nominal Shocks. eabcn Meeting Banque de France May 5th, 2017

Transcription

1 Firm Uncertainty Cycles and the Propagation of Nominal Shocks Isaac Baley UPF and Barcelona GSE Julio Andrés Blanco U Michigan eabcn Meeting Banque de France May 5th, 2017

2 Motivation Firms operate in constantly changing environments New technologies and products become available Unfamiliar markets and competitors appear Workers and suppliers get replaced 1 / 20

3 Motivation Firms operate in constantly changing environments New technologies and products become available Unfamiliar markets and competitors appear Workers and suppliers get replaced Characteristics of these idiosyncratic changes Evidence Large, infrequent and persistent (fat-tailed risk) Lack of perfect knowledge about their impact = Uncertainty 1 / 20

4 Motivation Firms operate in constantly changing environments New technologies and products become available Unfamiliar markets and competitors appear Workers and suppliers get replaced Characteristics of these idiosyncratic changes Evidence Large, infrequent and persistent (fat-tailed risk) Lack of perfect knowledge about their impact = Uncertainty Questions... How does uncertainty affect firms decisions? Does firm-level uncertainty matter in the aggregate? 1 / 20

5 Our contributions We answer these questions in a general framework Imperfect information about persistent idiosyncratic characteristics Fixed adjustment costs 2 / 20

6 Our contributions We answer these questions in a general framework Imperfect information about persistent idiosyncratic characteristics Fixed adjustment costs In the context of price-setting... Positive relationship between uncertainty and price flexibility Uncertainty and price flexibility move in cycles Identify uncertainty s moments from micro-price data 2 / 20

7 Our contributions We answer these questions in a general framework Imperfect information about persistent idiosyncratic characteristics Fixed adjustment costs In the context of price-setting... Positive relationship between uncertainty and price flexibility Uncertainty and price flexibility move in cycles Identify uncertainty s moments from micro-price data Aggregate effects are quantitatively important Heterogeneous uncertainty amplifies real effects of nominal shocks Real effects up to 9 Golosov and Lucas (2007) Average uncertainty dampens real effects of nominal shocks Monetary policy less effective in more uncertain times 2 / 20

8 Roadmap 1 Price-setting with uncertainty cycles (one firm) 2 Aggregate effects of heterogeneous uncertainty 3 / 20

9 Price-setting with uncertainty cycles

10 Environment Firm chooses prices to maximize profits Pricing friction: menu cost θ 4 / 20

11 Environment Firm chooses prices to maximize profits Pricing friction: menu cost θ Period profits: Π(µ t ) = Bµ 2 t, B > 0 µ t log ω t log ω is log markup gap ω t: markup at t (price t/marginal cost t) ω : static optimal markup 4 / 20

12 Environment Firm chooses prices to maximize profits Pricing friction: menu cost θ Period profits: Π(µ t ) = Bµ 2 t, B > 0 µ t log ω t log ω is log markup gap ω t: markup at t (price t/marginal cost t) ω : static optimal markup Trade-off: losses from µ t 0 vs. paying menu cost θ 4 / 20

13 Environment Firm chooses prices to maximize profits Pricing friction: menu cost θ Period profits: Π(µ t ) = Bµ 2 t, B > 0 µ t log ω t log ω is log markup gap ω t: markup at t (price t/marginal cost t) ω : static optimal markup Trade-off: losses from µ t 0 vs. paying menu cost θ Stochastic process for marginal costs = stochastic process for markup-gaps 4 / 20

14 Markup-gap and Information Unobserved markup-gap: dµ t = σ f dw t + σ u u t dq t W t Weiner; Q t Poisson counter (λ); u t N (0, 1) 5 / 20

15 Markup-gap and Information Unobserved markup-gap: dµ t = σ f dw t + σ u u t dq t W t Weiner; Q t Poisson counter (λ); u t N (0, 1) Noisy signal: ds t = µ t dt + γdz t Noise Z t Wiener, γ measures information frictions (Continuous limit) permanent and transitory shocks 5 / 20

16 Markup-gap and Information Unobserved markup-gap: dµ t = σ f dw t + σ u u t dq t W t Weiner; Q t Poisson counter (λ); u t N (0, 1) Noisy signal: ds t = µ t dt + γdz t Noise Z t Wiener, γ measures information frictions (Continuous limit) permanent and transitory shocks Timing signal: dq t Arrival of Poisson shock is known...but not realization of u t Focus on case E[u t] = 0, extensions 5 / 20

17 Markup-gap and Information Unobserved markup-gap: dµ t = σ f dw t + σ u u t dq t W t Weiner; Q t Poisson counter (λ); u t N (0, 1) Noisy signal: ds t = µ t dt + γdz t Noise Z t Wiener, γ measures information frictions (Continuous limit) permanent and transitory shocks Timing signal: dq t Arrival of Poisson shock is known...but not realization of u t Focus on case E[u t] = 0, extensions Learning technology Filter µ t I t, with I t = σ{(s r, Q r ) r t } Bayesian firms solve filtering problem 5 / 20

18 Filtering with Jumps Uncertainty Cycles Filtering equations Markup-gap s posterior distribution is Normal µ t I t N (ˆµ t, γω t) (estimate) dˆµ t = Ω t dẑt (uncertainty) dω t = σ2 f Ω t 2 γ dt + σ2 u γ dqt 6 / 20

19 Filtering with Jumps Uncertainty Cycles Filtering equations Markup-gap s posterior distribution is Normal µ t I t N (ˆµ t, γω t) (estimate) dˆµ t = Ω t dẑt (uncertainty) dω t = σ2 f Ω t 2 γ dt + σ2 u γ dqt Higher uncertainty Ω t = More volatile estimates ( ) ( ) γ γ st s t ˆµ t+ = ˆµ t + 1 Ω t + γ Ω }{{} t + γ }{{} weight on prior weight on signal 6 / 20

20 Filtering with Jumps Uncertainty Cycles Filtering equations Markup-gap s posterior distribution is Normal µ t I t N (ˆµ t, γω t) (estimate) dˆµ t = Ω t dẑt (uncertainty) dω t = σ2 f Ω t 2 γ dt + σ2 u γ dqt Higher uncertainty Ω t = More volatile estimates ( ) ( ) γ γ st s t ˆµ t+ = ˆµ t + 1 Ω t + γ Ω }{{} t + γ }{{} weight on prior weight on signal Uncertainty cycles If λ = 0 (no jumps), then Ω t converges to σ f If λ > 0 (jumps), then Ω t features cycles Long-run uncertainty Ω = σ 2 f + λσ2 u (E[dΩ t] = 0) 6 / 20

21 Pricing policy Stopping Time Problem [ τ V (ˆµ 0, Ω 0) = max E e ( ) ) ] rt ˆµ 2 t dt + e ( θ rτ + max V (x, Ω τ ) τ x 0 }{{}}{{} payoff from action payoff from inaction s.t. dˆµ t = Ω tdẑ t dω t = σ2 f Ω t 2 γ dt + σ2 u γ dqt θ θ B τ : stopping time x : reset markup-gap estimate r : discount factor 7 / 20

22 Pricing policy Stopping Time Problem [ τ V (ˆµ 0, Ω 0) = max E e ( ) ) ] rt ˆµ 2 t dt + e ( θ rτ + max V (x, Ω τ ) τ x 0 }{{}}{{} payoff from action payoff from inaction s.t. dˆµ t = Ω tdẑ t dω t = σ2 f Ω t 2 γ dt + σ2 u γ dqt θ θ B τ : stopping time x : reset markup-gap estimate r : discount factor Policy: Inaction region that depends on uncertainty change price if (ˆµ t, Ω t) / [ µ(ω t), µ(ω t)] and reset markup-gap estimate to x = 0 7 / 20

23 Pricing effects of uncertainty 1. Uncertainty increases estimate volatility dˆµ t = Ω tdẑt 8 / 20

24 Pricing effects of uncertainty 1. Uncertainty increases estimate volatility dˆµ t = Ω tdẑt 2. Uncertainty widens inaction region ( ) 6 θω 2 1/4 ( ) µ(ω) = with L µ ΩΩ (Ω) 1 + L µ (Ω) 1 Key: Elasticity of inaction region E(Ω) < 1/2 < 1. 8 / 20

25 Pricing effects of uncertainty 1. Uncertainty increases estimate volatility dˆµ t = Ω tdẑt 2. Uncertainty widens inaction region ( ) 6 θω 2 1/4 ( ) µ(ω) = with L µ ΩΩ (Ω) 1 + L µ (Ω) 1 Key: Elasticity of inaction region E(Ω) < 1/2 < Uncertainty decreases expected time to adjustment ( ) 2 E[τ µ(ω) ( ) 0, Ω] = (1 + L τ (Ω)) with L τ ΩΩ (Ω) Ω 1 (1 E(Ω )) Key: Expected time is decreasing and convex in uncertainty. 8 / 20

26 Uncertainty Cycles Adjustment Cycles A. Uncertainty time Ω t Ω B. Policy and Markup 0.4 ˆµ t 0.3 µ(ω t ) time C. Price Changes time 9 / 20

27 Uncertainty Cycles Adjustment Cycles A. Uncertainty time Ω t Ω B. Policy and Markup 0.4 ˆµ t 0.3 µ(ω t ) time C. Price Changes time Low uncertainty: small price changes, unlikely to be changed High uncertainty: large price changes, likely to be changed Suggestive evidence: Bachmann, et.al. ( 13), Vavra ( 14) IFO Firm Survey: corr(freq i, std(forecast errors i)) > 0 9 / 20

28 More suggestive evidence At product level, recurrent episodes of very frequent price changes. (Campbell & Eden, 14) 10 / 20

29 More suggestive evidence At product level, recurrent episodes of very frequent price changes. (Campbell & Eden, 14) Low uncertainty = few price changes High uncertainty = many price changes 10 / 20

30 Clustering = Non-mononotic hazard rate A. Hazard s shape (depends on Ω) Low uncertainty High uncertainty Time since last adjustment τ B. Hazard s slope (depends on γ) Small signal noise Large signal noise Time since last adjustment τ 11 / 20

31 Clustering = Non-mononotic hazard rate A. Hazard s shape (depends on Ω) Low uncertainty High uncertainty Time since last adjustment τ B. Hazard s slope (depends on γ) Small signal noise Large signal noise Time since last adjustment τ Hazard rate: h(τ Ω) = P rob(adjust τ no adjustment until τ) Shape: driven by uncertainty Ω Low uncertainty: increasing hazard (standard menu cost model) High uncertainty: non-monotonic hazard (learning) Slope: driven by information friction γ 11 / 20

32 How do we construct aggregate price statistics? Consider a continuum of firms with independent shocks. 12 / 20

33 How do we construct aggregate price statistics? Consider a continuum of firms with independent shocks. Uncertainty s distribution: Marginal: h(ω) = f(ˆµ, Ω) dˆµ Distribution in whole cross-section Renewal: r(ω) Distribution within adjusters, used for aggregation 12 / 20

34 How do we construct aggregate price statistics? Consider a continuum of firms with independent shocks. Uncertainty s distribution: Marginal: h(ω) = f(ˆµ, Ω) dˆµ Distribution in whole cross-section Renewal: r(ω) Distribution within adjusters, used for aggregation Ratio of renewal to steady-state uncertainty r(ω) h(ω) 1 E[τ (0,Ω)] and is increasing in uncertainty (around Ω ). 12 / 20

35 How do we construct aggregate price statistics? Consider a continuum of firms with independent shocks. Uncertainty s distribution: Marginal: h(ω) = f(ˆµ, Ω) dˆµ Distribution in whole cross-section Renewal: r(ω) Distribution within adjusters, used for aggregation Ratio of renewal to steady-state uncertainty r(ω) h(ω) 1 E[τ (0,Ω)] and is increasing in uncertainty (around Ω ). Price statistics reflect behavior of high uncertainty firms i.e. aggregate decreasing hazard rate Evidence 12 / 20

36 Aggregate effects of heterogenous uncertainty

37 General Equilibrium Model 1 Representative household Consumes, supplies labor, and holds money Access to complete financial markets 13 / 20

38 General Equilibrium Model 1 Representative household Consumes, supplies labor, and holds money Access to complete financial markets 2 Continuum of monopolistic firms Ex-ante identical. Constant demand elasticity Same price-setting problem as before Independent shocks to markup-gaps and signals across firms 13 / 20

39 General Equilibrium Model 1 Representative household Consumes, supplies labor, and holds money Access to complete financial markets 2 Continuum of monopolistic firms Ex-ante identical. Constant demand elasticity Same price-setting problem as before Independent shocks to markup-gaps and signals across firms 3 Equilibrium with constant money supply Nominal wage = Money supply Steady state distribution of markup gaps and uncertainty 13 / 20

40 Calibration to match micro-price data A. Hazard Rate CPI Data Heterog. uncertainty Months B. Markup Gap Distribution High Ω Low Ω ˆµ C. Uncertainty Distribution All firms Adjusters E[Ω] = 0.01 E[Ω adjust] = Ω US Data No heterogeneity Heterogeneous (baseline) uncertainty Moments E[τ] in months std[ p ] hazard rate slope Details 14 / 20

41 Propagation of nominal shocks Unanticipated increase in money supply δ = 1% True markup-gaps fall in 1% Output effects = inaction errors + forecast errors Deviation from steady state (IRF): Ỹ t = 1 Total effect (area under IRF): Three exercises: 0 1 µ t(z)dz = ˆµ t(z)dz + ϕ t(z)dz 0 0 }{{}}{{} M(δ) = 0 inaction error Ỹ t dt = I + F A) Disclosed money shock (fully observed) B) Undisclosed money shock (partially observed) C) Aggregate uncertainty shock 1 forecast error 15 / 20

42 A) Effects of disclosed monetary shock Fully observed shock Only inaction errors Only first price change matters Persistence driven by low uncertainty firms Steady State Deviation % 3.9% Output response No heterogeneity Heterogenous uncertainty Months 16 / 20

43 A) Effects of disclosed monetary shock Fully observed shock Only inaction errors Only first price change matters Persistence driven by low uncertainty firms ( ) E[τ] M(δ) δ 6 }{{} no heterog = 1.6 Steady State Deviation % 3.9% Output response No heterogeneity Heterogenous uncertainty Months 16 / 20

44 A) Effects of disclosed monetary shock Fully observed shock Only inaction errors Only first price change matters Persistence driven by low uncertainty firms ( ) E[τ] M(δ) δ 6 }{{} no heterog = 1.6 Steady State Deviation % 3.9% Output response No heterogeneity Heterogenous uncertainty Low uncertainty High uncertainty Months 17 / 20

45 B) Effects of undisclosed monetary shock Fraction α is observed Forecast errors arise Incomplete pass-through Disclosed (α = 1) Undisclosed (α = 0) % A. Output All firms Low uncertainty firms High uncertainty firms % Months B. Inaction errors Months C. Forecast Errors Months 18 / 20

46 B) Effects of undisclosed monetary shock Fraction α is observed Forecast errors arise Incomplete pass-through ( M(δ, α) δ α E[τ] ) γ2 E[τ] + (1 α) 6 V[ p] }{{} no heterog = 1.6α + 10(1 α) Disclosed (α = 1) Undisclosed (α = 0) % A. Output All firms Low uncertainty firms High uncertainty firms % Months B. Inaction errors Months C. Forecast Errors Months 18 / 20

47 C) Effect of aggregate uncertainty shock Uncertainty shock κe[ω] Forecast errors fall with κ Faster learning A. Output No Ω Shock Small Ω Shock Large Ω Shock B. Inaction Error C. Forecast Error % 9.5% 5.3% Months Months Months 19 / 20

48 C) Effect of aggregate uncertainty shock Uncertainty shock κe[ω] Forecast errors fall with κ Faster learning F(κ) γ2 E[τ] V[ p] ξ(κ), ξ (κ) < 0 }{{} no heterog = 10ξ(κ) A. Output No Ω Shock Small Ω Shock Large Ω Shock B. Inaction Error C. Forecast Error % 9.5% 5.3% Months Months Months 19 / 20

49 C) Effect of aggregate uncertainty shock Uncertainty shock κe[ω] Forecast errors fall with κ Faster learning F(κ) γ2 E[τ] V[ p] ξ(κ), ξ (κ) < 0 }{{} no heterog = 10ξ(κ) A. Output No Ω Shock Small Ω Shock Large Ω Shock B. Inaction Error C. Forecast Error % 9.5% 5.3% Months Months Months Monetary policy is less effective in uncertain times Castelnuovo, et al (2015), Aastveit, et al (2013) Forecast errors are smaller in uncertain times Gorodnichenko et al (2016) 19 / 20

50 Conclusions Pricing theory with menu costs and idiosyncratic uncertainty cycles Macro implications: Uncertainty heterogeneity amplifies effects of money shocks Average uncertainty dampens effects of money shocks Information friction identified with hazard rate General framework, potential applications... Portfolio choice s.t. adjustment fees and uncertain returns Occupational choice s.t. mobility costs and uncertain skills. 20 / 20

51 APPENDIX 21 / 20

52 Characteristics of idiosyncratic shocks Return Evidence of fat-tailed (leptokurtic) risk Price change distribution For US CPI: Klenow and Malin (2011) For French CPI: Alvarez, Le Bihan and Lippi (2016) Employment growth distribution For US Census data: Davis and Haltinwanger (1992) Profit rate, employment, sales and capital growth Own computations using COMPUSTAT annual Evidence of idiosyncratic uncertainty Heterogeneity and time-variation in firm-level uncertainty German firms: Bachmann, Elstner and Hristov (2016) w/ifo Survey US firms: Senga (2016) using I/B/E/S 22 / 20

53 Evidence of Leptokurtic Shocks Return COMPUSTAT annual data, growth rates A. Profit Rate B. Employment C. Sales D. Capital % % % % Moment Profits Employment Sales Capital Mean Median Standard Deviation Skewness Kurtosis / 20

54 Markup gap and signal Return Figure: Illustration of the Markup Gap and the Signal Processes µ A. State: µ t = σ f W t + σ u Q t k=0 u k s B. Signal: s t = t 0 µ s ds + γz t σ u u Qt t t t t 24 / 20

55 Sufficient Conditions for Optimal ST Return Proposition Let φ : R R + R be a function and let φ x. Assume φ satisfies the following conditions: 1. Hamilton-Jacobi-Bellman (HJB) equation: ( ) σ 2 rφ(ˆµ, Ω) = ˆµ 2 f Ω 2 + φ Ω (ˆµ, Ω) + Ω2 φˆµ 2(ˆµ, Ω)+ (1) γ 2 [ ( ) ] + λ φ ˆµ, Ω + σ2 u φ(ˆµ, Ω) (2) γ 2. value matching condition 3. Two smooth pasting conditions φ(0, Ω) θ = φ( µ(ω), Ω) (3) φˆµ ( µ(ω), Ω) = 0, φ Ω ( µ(ω), Ω) = φ Ω (0, Ω) (4) Then φ is the value function φ = V and τ = inf {t > 0 : φ(0, Ω t) θ > φ(ˆµ t, Ω t)} is the optimal stopping time. 25 / 20

56 Markup process in discrete time Stochastic process with permanent and transitory shocks: (T otal) µ t = µ t 1 + µ P t + µ T t (P ermanent) µ P t = µ P t 1 + σ F ε F t + σ U ε U t J t (T ransitory) µ T t = γε T t { J t = ɛ F t, ɛ U t, ɛ T t N (0, 1) 1 w.p. 1 e λ 0 w.p. e λ Firm observes total markup µ t, but not its components separately. Firm knows realization of binomial J t, but not the size of the shock. Timing assumption: Choose price before observing productivity. Return 26 / 20

57 Young prices: more flexible and dispersed Price age is current date minus the last stopping time: a = t τ t 1 Age thresholds: - Young price if a < 7, (20% age percentile) - Old price if a > 66, (80% age percentile) Frequency and dispersion for young and old prices Statistic Data* Model All Young Old Ratio All Young Old Ratio Frequency % std(price gap) Uncertainty* *Campbell and Eden (2014), average all products without discounts, with thresholds a < 3 and a > 4 weeks. Frequency ratio informs about underlying uncertainty. 27 / 20

58 Hazard Rate of Price Adjustment Return Include controls for observed and unobserved heterogeneity 28 / 20

59 Representative Household max E {C t,c t (z),l t,m t } [ 0 ( ) ] e rt log C t l t + log Mt dt P t [ ( 1 ) ] M 0 E Q t p t(z)c t(z)dz + R tm t E tl t Π t dt C t = 0 ( (A t(z)c t(z)) η 1 η dz ) η η 1 Q t : time zero nominal Arrow-Debreu price C t : aggregate consumption with price P t l t : labor with price E t R t M t : opportunity cost of money (R t nominal i-rate) Π t : firms profits s.t A t (z) : quality shocks Return 29 / 20

60 Environment: Firms Continuum of monopolistic firms, indexed with z [0, 1]. Firms choose price to maximize expected profits, discounted at Q t. Period profits are Π (p t(z), A t(z)) = c t(p t(z), A t(z)) (p t(z) A t(z)w t) where quality a t(z) = log A t(z) is iid across firms: da t(z) = σ f dw t(z) + σ uu t(z)dq t(z) Firms observe noisy signals about quality: ds t(z) = a t(z)dt + γdz t(z) Pay menu cost θ. Assumption: firms cannot invert the demand function Return 30 / 20

61 Equilibrium Definition An equilibrium with constant money growth is a set of stochastic processes for i) consumption strategies c t(z), labor supply l t and money holdings M t for the representative consumer ii) labor demand l t(z) and pricing policy p t(z) for firms iii) prices W t, R t, Q t iv) measure of firms that reprice N t such that: Given prices, c t(z), l t and M t solve the consumer s problem with initial M 0 = M. Given the prices and demands, firms policies l t(z) and p t(z) solve her problem. Markets clear at each date. Return 31 / 20

62 Steady State with Constant Money Supply Steady state equilibrium with zero money growth Constant money supply M Constant wage W = M Constant nominal interest rate R = r and discount Q t = e rt Fixed distribution f(ˆµ, Ω) 32 / 20

63 Related literature Price-setting with menu costs Barro ( 72), Caplin & Spulber ( 87), Caplin & Leahy ( 91), Danziger ( 99), Dotsey, King & Wolman ( 99), Golosov & Lucas ( 07), Gertler & Leahy ( 08), Nakamura & Steinsson ( 10), Midrigan ( 11), Alvarez & Lippi ( 14). Price-setting with idiosyncratic information frictions Bachmann & Moscarini ( 12), Alvarez, Lippi & Paciello ( 11, 13), Bonomo, Carvalho, Garcia & Malta ( 14), Argente and Yeh (2016). Uncertainty and real option effects Bernanke ( 82), Dixit ( 91), Bloom ( 09), Vavra ( 14), Senga ( 15). Price micro-data Bils & Klenow ( 04, 10), Nakamura & Steinsson ( 08, 13), Campbell and Eden ( 14), Baley, Kochen, Sámano (2016). 33 / 20

64 Disclosed Money Shock: 3 calibrations Deviation from Steady State Perfect Info (Benchmark) Perfect Info + Regime Changes Imperfect Info + Regime changes Months 34 / 20

65 Calibration details Return US No uncertainty Heterogenous Data (Baseline) Uncertainty Parameters σ f σ u λ γ Moments E[τ] in months std[ p ] hazard rate slope kurtosis[ p] Average menu costs θ such that = 0.5% revenue B such that Average markup = 20% r = 4% year 35 / 20