Microfoundation of Inflation Persistence of a New Keynesian Phillips Curve

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1 Microfoundation of Inflation Persistence of a New Keynesian Phillips Curve Marcelle Chauvet and Insu Kim

2 1 Background and Motivation 2 This Paper 3 Literature Review 4 Firms Problems 5 Model 6 Empirical Results

3 Outline Background and Motivation This paper: Infrequent and Incomplete Price Adjustment Literature Review The Model Empirical Results Estimation IRFs, dynamic correlation between inflation and output gap, distribution of price changes Size and Frequency of Price Adjustment Conclusion

4 Background Standard New Keynesian Phillips curve (NKPC) based on optimizing behavior of price setters in the presence of nominal rigidities. Mostly based on: staggered contracts of Taylor (1979, 198), Calvo (1983), and quadratic adjustment cost model of Rotemberg (1982) Framework used in analysis of monetary policy: price rigidity main transmission mechanism through which it impacts the economy: when firms face difficulties in changing some prices, they may respond to monetary shocks by changing instead their production and employment levels

5 Background Popular frameworks to derive the NKPC Calvo (1983) s staggered price setting: only a fraction of firms completely adjusts their prices to optimal level at discrete time intervals Rotemberg (1982): firms set prices to minimize deviations from optimal price subject to quadratic frictions of price adjustment Both designed to model sticky prices: Rotemberg : Calvo : P t = c 2 (P t P t 1 ) 2 Y t P t = f q (P t 1,... ) [ ] (1 θ) P 1/(1 λ f ) t + θp 1/(1 λ f ) 1 λf t 1 P t = f c (P t 1,... ) Rotemberg: ˆπ t = βe t ˆπ t+1 + a 1 c mc ˆ t Calvo: ˆπ t = βe t ˆπ t+1 + λmc ˆ t Calvo pricing related to the frequency of price changes Rotemberg pricing associated with size of price changes

6 Motivation: Phillips Curve Econometric Phillips curve: π t = βπ t 1 + λy t NKPC: π t = βe t π t+1 + λy t Taylor (198 JPE), Rotemberg (1982 JPE), and Calvo (1983 JME) 1. Inflation persistence 2. Delayed response of inflation to a monetary shock 3. Delayed response of inflation to changes in output gap 4. Costly disinflation - Disinflation Boom (Ball, 1994 AER) HNKPC: π t = α f E t π t+1 + α b π t 1 + λy t CEE (25 JPE): automatic indexation to past inflation Lack of Microfounation: Rudd and Whelan (27 JMCB), Woodford (27, JMCB), Cogley and Sbordone (28, AER), Benati (28 QJE), etc.

7 Motivation: Welfare Analysis π t = βe t π t+1 + λy t - failure to explain the dyanmics of inflation Loss t = β k E t [π 2 t+k + δy 2 t+k ] π t = α f E t π t+1 + α b π t 1 + λy t - failure to explain individual price changes Loss t = β k E t [(π t+k π t+k 1 ) 2 + δy 2 t+k ] Source: Chari, Kehoe, and McGrattan(29)

8 This Paper: Infrequent and Incomplete Price Adjustment Sticky price model that endogenously generates inflation persistence We consider that firms face two sources of price rigidities, related to both the inability to change prices frequently and to the cost of sizeable adjustments although firms change prices periodically, they face convex costs that preclude optimal adjustment In essence, model assumes that price stickiness arises from both the frequency and size of price adjustments

9 This Paper Monetary policy shocks first impact economic activity, and subsequently inflation but with a long delay, reflecting inflation inertia The model captures the joint dynamic correlation between inflation and output gap The frequency and size of price changes

10 Literature Alternative New Keynesian models that can account for some of the empirical facts on inflation and output. Most popular ones are extensions of Calvo s staggered prices or information: Sticky information Indexation Models

11 Literature Sticky information (Mankiw and Reis 22 QJE) - information is costly and, therefore, disseminats slowly: Prices adjust continuously but information does not Model is consistent with inflation persistence Empirical implication: prices change frequently, which contradicts widespread micro-data studies Evidence found across countries and different data sources is that firms keep prices unchanged for several months: e.g. Bils and Klenow 24, Angeloni et al. 26, Alvarez 28, Nakamura and Steinsson 28, Klenow and Malin 21, etc. Fabiani et al (25): Firms review their prices more often than the frequency of price adjustment.

12 Literature: Sticky Information Sticky Information Phillips Curve (Mankiw and Reis 22 QJE) π t = [ ] αλ 1 λ y t + λ j= (1 λ)j E t 1 j (π t + α y t ) m t = p t + y t and m t =.5 m t 1 + ɛ t Fuhrer (29): m t =.5 m t 1 + ɛ t versus m t =.25 m t 1 + ɛ t In this model, one can see by inspection (and the authors verify) that inflation will inherit the persistence of the output process.

13 Literature Indexation Models - Gali and Gertler (1999), Christiano, Eichenbaum, and Evans (25), and Smets and Wouters (23, 27): a fraction of the firms adjust their prices by automatic indexation to past inflation: Models explain inflation inertia as they incorporate a lagged inflation term into the resulting hybrid NKPC Arbitrary role given to past inflation as at least some agents are backward-looking in the process of setting prices firms do not reoptimize prices each given period

14 Literature Indexation models and Sticky Information models: imply that prices are adjusted continuously imply that the size of price adjustments is small Evidence not supported by microdata evidence of price stickiness both infrequent, small and large price adjustments Continuously price updating is an implication of many NKPC models including Reis (26), Christiano et al (25), Smets and Woulters (23, 27), Rotemberg(1982), Kozicki andtinsley (22), among many others

15 This Paper: Infrequent and Incomplete Price Adjustment Proposes a microfounded theoretical model that endogenously generates inflation persistence as a result of optimizing behavior of the firms Combines staggered price setting (Calvo) and quadratic costs of price adjustment (Rotemberg) in a unified framework

16 This Paper Phillips curve derived from DSGE model, and relates current inflation to inflation expectations, lagged inflation, and real marginal cost or output gap Lagged inflation term is endogenously generated in a forward-looking framework: Agents remain forward-looking and follow an optimizing behavior

17 This Paper In contrast to the general indexation models and sticky information models, in the proposed model: prices are not continuously adjusted and firms that are able to change prices do not fully adjust them due to convex costs of adjustment New Phillips curve based on dual stickiness nests the standard NKPC as a special case (Calvo pricing) Model as an alternative to ad-hoc hybrid NKPC and sticky information Phillips curve

18 This Paper Price stickiness direct microeconomic evidence firms decisions (frequency and size of price changes)

19 Firms Face Two Problems When to change prices? - frequency of price changes Physical menu costs Implicit and explicit contracts (ranked the first and second in the EU area) Coordination failure (ranked the first in the U.S.) How much to change prices? - size of price changes Managerial costs ( information gathering costs, decision making, and internal communication costs) Customer costs (communication and negotiation costs) Other costs antagonizing customers Zbaracki et al. (24): These costs are sizable and greater than physical menu costs.

20 Zbaracki, Ritson, Levy, Dutta, Bergen (24) the firm reacted to major changes in supply and demand conditions slowly and/or partially because of the convexity of costs [of price adjustment]... Quantitatively, they show that managerial costs are 6 times, and customer costs are 2 times greater than the physical menu costs. Firm investigated changes prices once a year We can t change prices biannually, it is not the culture here. -Pricing manager- (Source: Zbaracki et al. 24) Implicit and explicit contracts matter.

21 Model Firms Problems and the Phillips Curve Two types of firms: Representative final goods-producing firm Continuum of intermediate goods-producing firms

22 Firms Problems and the Phillips Curve Final Goods-Producing Firm The final goods-producing firm purchases a continuum of intermediate goods, Y it, at input prices, P it, indexed by i [, 1]. The final good, Y t, is produced by bundling the intermediate goods: [ 1 Y t = ] λf Y 1/λ f it di The final-good-producing firm chooses Y it to maximize its profit in a perfectly competitive market taking both input (P it ) and output prices (P t ) as given, solving the following problem: P t [ 1 λf 1 Y 1/λ f it di] P it Y it di

23 Firms Problems and the Phillips Curve Final Goods-Producing Firm Y it = ( Pit P t ) λf /(λ f 1) Y t where λ f /(λ f 1) measures the constant price elasticity of demand for each intermediate good. The relationship between the prices of the final and intermediate goods can be obtained by integrating the equation: [ 1 P t = ] 1 λf P 1/(1 λ f ) it di The final good price can be interpreted as the aggregate price index.

24 Firms Problems and the Phillips Curve Intermediate Goods-Producing Firm - Calvo pricing P t = [ ] (1 θ) P 1/(1 λ f ) t + θp 1/(1 λ f ) 1 λf t 1 where P t denotes the optimal price set by the intermediate good-producing firms.

25 Firms Problems and the Phillips Curve We assume that each intermediate goods-producing firm faces a quadratic adjustment cost of adjusting its price given by: QAC = c 2 ( P t π t P t 1 ) 2 Yt QAC = c 2 ( P t P ) 2 t 1 Y t P t P t 1 It is costly for current individual price to deviate from past price level, which makes prices sticky.

26 Firms Problems and the Phillips Curve c 2 (P t π t P t 1 ) 2 Y t ˆπ t = E t ˆπ t+1 + a 1 mc ˆ t βc (c/2) (P t πp t 1 ) 2 Y t ˆπ t = βe t ˆπ t+1 + a 1 mc ˆ t c

27 Firms Problems and the Phillips Curve The firm chooses P t to maximize E t k= (θβ) k [ ( P t mc t+k P t+k )Y it+k P t+k subject to the demand function Y it = ] c ( P t P ) 2 t 1 Y t 2 P t P t 1 ( P t P t ) λf /(λ f 1) Yt.

28 Firms Problems and the Phillips Curve Log-linearization of the first order condition gives rise to: E t (θβ) k [ ( ˆp t + ˆX tk ˆmc t+k ) ] = k= c 1 a ( ˆp t ˆp t 1 ) where X tk 1/π t+1 π t+2...π t+k and a λ f /(λ f 1).

29 Firms Problems and the Phillips Curve The first order condition [ and ] Calvo pricing (P t = (1 θ) P 1/(1 λ f ) t + θp 1/(1 λ f ) 1 λf t 1 ) yield π t = Λ f E t π t+1 + Λ l π t 1 + λmc t

30 Firms Problems and the Phillips Curve FOC: E t (θβ) k [ ( ˆp t + ˆX tk ˆmc t+k ) ] = k= c 1 a ( ˆp t ˆp t 1 ) Calvo pricing: [ ] P t = (1 θ) P 1/(1 λ f ) t + θp 1/(1 λ f ) 1 λf t 1 ˆp t = θ 1 θ ˆπ t p t P t /P t : ˆp t denotes the log-deviation of p t from its steady state value. E t (θβ) k [ ( ˆp t + ˆX tk ˆmc t+k ) ] = k= c 1 a θ 1 θ ( ˆπ t ˆπ t 1 )

31 Firms Problems and the Phillips Curve Intuition behind lagged inflation term: ( c P t P ) 2 t 1 Y t P t = f q (P t 1,... ) 2 P t P t 1 P t = [ ] (1 θ) P 1/(1 λ f ) t + θp 1/(1 λ f ) 1 λf t 1 P t = f c (P t 1,... ) P t = f c (f q (P t 1,... ),...) = f (P t 2,... )

32 Phillips Curve π t = Λ f E t π t+1 + Λ l π t 1 + λmc t If c =, the model collapses into the New Keynesian Phillips Curve. π t = βe t π t+1 + κmc t

33 Properties of the Model - Coefficients Coefficient on Inflation Expectations c θ.6.8 1

34 Properties of the Model - Coefficients Slope of the Phillips Curve θ=.5 θ=.66 θ=.75 θ= parameter c

35 Christiano, Eichenbaum, and Evans (JPE, 25) The firm chooses P t to maximize [ ] ( (θβ) k P t mc t+k P t+k )Y it+k E t k= subject to the demand function Y it = ( Pit P t P t+k ) λf /(λ f 1) Y t The first [ order condition and (P t = (1 θ) P 1/(1 λ f ) ] t + θ(π t 1 P t 1 ) 1/(1 λ 1 λ f ) f ) yield π t = α f E t π t+1 + α b π t 1 + λmc t

36 DSGE Model Households maximize the expected present discounted value of utility, ( C 1 1/σ E t β k t+k 1 1/σ N 1+ϕ ) t+k, 1 + ϕ k= subject to the budget constraint, C t+k + B t+k = ( W t+k )(N t+k ) + exp( ξ t+k 1 )(1 + i t+k 1 )( B t+k 1 ) + Π t+k P t+k P t+k P t+k where C t is the composite consumption good, N t is hours worked, Π t is real profits received from firms, and B t is the nominal holdings of one-period bonds that pay a nominal interest rate i t. As in Smets and Wouters (27), we include the risk premium shock, ξ t 1.

37 DSGE Model The IS curve is given by: y t = E t y t+1 σ(i t E t π t+1 ) + ε y t We interpret the disturbance term as the preference shock, ε y t σξ t, which is assumed to follow the AR(1) process, with ν y t N(, σ 2 y ). ε y t = δ π ε y t 1 + νy t,

38 DSGE Model y t = E t y t+1 σ(i t E t π t+1 ) + ε y t π t = α f E t π t+1 + α b π t 1 + λmc t + +ε π t mc t = ( 1 σ + ϕ)y t i t = ρi t + (1 ρ)(α π E t π t+1 + α y y t ) + ε i t

39 Cost-push Shock E t The shock ε π t can be introduced into the model by considering an exogenous cost component (et π ) in the objective function of firms as follows: [ ( (θβ) k P t exp(et π ] )mc t+k P t+k )Y it+k c ( P t P ) 2 t 1 Y t 2 P t P t 1 k= P t+k ε π t can be expressed as a linear function of e π t. The shock ε π t can be also introduced into the model by allowing λ f to vary over time as in the literature.

40 Estimation Table : Estimation Results - Double Sticky Price DSGE model: 196:1~28:4 parameter prior prior prior posterior 95% of dist. mean st. dev. mean confidence interval θ beta [.7,.82] c normal [14., 195.6] σ invg 1.16 [.13,.18] ρ beta [.76,.81] α π normal [1.6, 1.87] α y normal [.35,.65] δ y beta [.93,.98] σ π invg [.63,.76] σ y invg [.13,.19] σ i invg [.89, 1.7]

41 Infrequent and Incomplete Price Adjustment posterior.2 posterior prior.1.5 prior θ c

42 Model Parameters Evidence of intrinsic inflation persistence Parameter estimates associated with the two types of price stickiness are highly significant, supporting the proposed model

43 Frequency of Price Changes Calvo parameter θ, degree of nominal rigidity =.76. 1/4 firms reset prices to optimize profit. Average length of time between price changes is 4 quarters Estimates closely match microeconomic evidence on price changes: Klenow and Malin (21) Alvarez (28) (18 countries 11 months), Alvarez et al (26) Euro area (4 to 5 quarters). Eichenbaum, Jaimovich and Rebelo (28) (11.1 months) These research studies individual prices during the Great Moderation period. Our estimates of θ: 9 months ~ 12.5 months for the Great Moderation period.

44 Size of Price Adjustment Magnitude of adjustment costs is large and statistically significant: quadratic adjustment cost, c = with 95% confidence interval [14., 195.6] Empirical findings: price changes are mostly smaller than the size of aggregate inflation (e.g. Dhyne et al. 25, Alvarez et al (26), Klenow and Kryvstov 28, etc.) Klenow and Kryvtsov (28) - U.S. consumer price changes (absolute value): 44% < 5% 25% < 2.5% 12% < 1% Vermeulen et al. (27) - Euro area producer price: 25% <1% Mean price change only 4%

45 Impulse Response Functions Inflation cost push shock c= c=25 c=5 c=1 c=15 c= preference shock interest rate shock time time time.1 cost push shock 1 preference shock.2 intrest rate shock Output Gap time time time.8 cost push shock 1.5 preference shock 1 interest rate shock Interest Rate time time time

46 Dynamic Correlation Between the Output Gap and Inflation Taylor (1999) considers as a yardstick of a success of monetary models their ability to generate the reverse dynamic crosscorrelation between output gap and inflation.

47 Dynamic Correlation Between the Output Gap and Inflation 1 Correlation( CBO output gap(t), inflation(t+k) ).5 model data.5 upper bound lower bound no quadratic costs k 1 Correlation( HP filtered output gap(t), inflation(t+k) ) k

48 Dynamic Correlation Between the Output Gap and Inflation 1 Correlation(output gap(t), inflation(t+k) ) and Shocks.5.5 interest rate shocks demand shocks model: c=167.3 cost shocks k 1 Correlation(output gap(t), inflation(t+k) ) and Price Adjustment Cost.5.5 c= c=25 c=5 c=1 c=15 c= k

49 Average of the Absolute Values of Price Changes Calvo our model CEE Rotemberg 196:1-28: :1-1979: :1-28: Klenow and Kryvtsov (28) report that the mean (median) value of price changes in regular prices is 11 percent (1 percent) in absolute value. Nakamura and Steinsson (28) report a median size of 7.7 percent for U.S. finished goods producer prices. In the Euro area, Dhyne et al. (25) present that the average value of consumer price decrease (increase) is 1 percent (8 percent). These research studies individual prices during the Great Moderation period.

50 Distribution of Price Changes: Post-198 bin range = 2% bin range = 5% 1 bin range = 1% Calvo proposed model CEE Rotemberg

51 Distribution of Price Changes: Post-198 Distribution of Price Changes P ( p < 5%) P ( p < 2.5%) P ( p < 1%) data 44% 25% 12% model 47% 25% 11% CEE 73% 44% 19% Rotemberg 9% 59% 26% Calvo 38% 2% 8% data: Klenow and Kryvtsov (28) - U.S. consumer price changes (absolute value)

52 Distribution of Price Changes: Subsamples pre 198 post 198 Rotemberg.1.1 CEE.5.5 proposed model Calvo

53 Model Comparison Table : Restriction on c: likelihood and estimates (196:1~28:4) gap no restriction on c restriction on c (c = ) likelihood c θ likelihood θ CBO ( 14., 195.6) (.7, 82) (.87,.91)) HP (97.4, 146.3) (.63,.79) (.83,.88) CF (12.5, 152.3) (.66,.81) (.86,.9)

54 Subsample Estimates: 196:1~28:4 gap CBO HP CF c θ c θ ( 89.4, 149.4) (.65,.82) ( 112.3, 173.9) (.64,.81)) (55.6, 17.) (.58,.79) (78.6, 138.5) (.58,.79) (7.8, 129.8) (.59,.79) (8.4, 14.) (.59,.8)

55 Cost Shocks ~ ARMA(4,1): 196:1~28:4 gap GDP deflator likel. c θ CBO (75.9, 161,1) (.56,.8) HP (15.8, 17.6) (.64,.79) CF (95., 165.9) (.64,.81)

56 Cost Shocks ~ ARMA(4,1): 196:1~28:4 gap NFB deflator likel. c θ CBO (28.7, 82.8) (.54,.78)) HP (17.2, 171.7) (.65,.8) CF (61,4, 121.) (.66,.82)

57 End Thank You.