Microfoundation of inflation persistence in the new Keynesian Phillips curve

the New Keynesian Phillips Curve

Marcelle Chauvet and Insu Kim

University of California Riverside University of California Riverside

Vale/EPGE 3rd _{Global Conference Business Cycle}

May 2013 May 2013

O tline

•

Background and Motivation

Outline

Background and Motivation • _{This paper: DSGE model with two sources of price}  stickiness • _{Literature Review} • _{The Model} • _The Model • _Results  Estimation  IRFs, correlation, distribution of price changes • _Conclusion 

Background

Background

• _{Standard New Keynesian Phillips curve (NKPC) based on} 

optimizing behavior of price setters in the presence of nominal optimizing behavior of price setters in the presence of nominal  rigidities. Mostly based on:  _{d f T l (1979 1980) C l (1983)}  staggered contracts of Taylor (1979, 1980), 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:

impacts the economy:

when firms face difficulties in changing some prices, they 

d t t h k b h i i t d th i

may respond to monetary shocks by changing instead their  production and employment levels

Background

g

•_{Popular frameworks to derive NKPC}  Calvo (1983)’s staggered price setting: only a fraction of  firms completely adjusts their prices to optimal level at  discrete time intervals in response to changes in various p g costs  Rotemberg (1982): firms set prices to minimize deviations g p from optimal price subject to quadratic frictions of price  adjustment h d d d l k • _{Both designed to model sticky prices:} Calvo pricing related to the frequency of price changes Rotemberg pricing associated with size of price changes

Motivation

Motivation

• _{Although NKPC has some theoretical appeal, growing g pp g g}

literature on its empirical shortcomings 

• _{Criticism on ability to match some stylized facts on inflationCriticism on ability to match some stylized facts on inflation}  dynamics and effects of monetary policy:   F il t t i fl ti i t Alth h i  Failure to generate inflation persistence. Although price  level responds sluggishly to shocks, inflation rate does not  NKPC does not yield the result that monetary policy  shocks first impact output, and subsequently cause a  delayed and gradual effect on inflation

Motivation

Motivation

• _{Fuhrer and Moore (1995) and Nelson (1998), etc.:} 

 In order for a model to fully explain the time series  In order for a model to fully explain the time series 

properties of aggregate inflation and output it requires that 

l h l l b l h fl b k

This Paper

This Paper

• _{DSGE 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  although firms change prices periodically, they face convex  costs that preclude optimal adjustment

• _{In essence model assumes that price stickiness arises from both}

• _{In essence, model assumes that price stickiness arises from both} 

This Paper

This Paper

• _{Monetary policy shocks first impact economic activity, and y p y p y} subsequently inflation but with a long delay, reflecting  inflation inertia • _{The model captures cross‐dynamic correlation between}  inflation and output gap

Literature

Literature

•

_A

lternative NKPC models that can account for some of the  l f fl d l empirical facts on inflation and output. Most popular ones  are extensions of Calvo’s staggered prices or contracts:  Sticky information  Backward rule‐of‐thumbs  Backward rule of thumbs

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1. Inflation persistence

2 Hump shaped responses 2. Hump‐shaped responses 3. Disinflation Boom (Ball, 1994) t t b t t f t

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Literature

Literature

•_{Sticky information (Mankiw and Reis 2002) ‐ information is} 

costly and, therefore, disseminated slowly:y y  Prices adjust continuously but information does not Model is consistent with inflation persistence  E i i l i li ti i h f tl hi h  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: Bil d Kl 2004 A l i t l 2006 Al 2008 e.g. Bils and Klenow 2004, Angeloni et al. 2006, Alvarez 2008,  Nakamura and Steinsson 2008, Klenow and Malin 2010, etc.

Literature

Literature

Backward Rule of Thumb

H b id NKPC G li d G l (1999) F i f fi

•_{Hybrid NKPC  ‐ Gali and Gertler (1999): Fraction of firms}  changes prices based on past prices of other firms with a  correction for recent inflation

• _{Indexation Models ‐ Christiano, Eichenbaum, Evans (2005),} 

Steinsson (2003), and Smets and Wouters (2003, 2007): part of the p

firms adjusts their prices by automatic indexation to past inflation:  Models explain inflation inertia as they incorporate a lagged

 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 y g p g

backward‐looking in the process of setting prices

Literature

Literature

•_{Hybrid NKPC Models  y}

•_{Generally criticized for being ad‐hoc as they lack a theory} 

of firms to motivate their backward looking behavior

(e.g. . Angeloni et al (2006), Rudd and Whelan 2007, Woodford  2007, Cogley and Sbordone 2008, Benati 2008, etc.)

•_{Indexation Models} • _{More structure as a fixed share of random Calvo‐type yp} firms could set their prices optimally each period while the  rest changes according to past aggregate inflation  Lagged inflation term is derived from firms’  decisions.

Literature

Literature

•_{General Indexation models and Sticky Information models:} 

 imply that prices are adjusted continuously

•_{Evidence not supported by microdata evidence of price}

•_{Evidence not supported by microdata evidence of price} 

stickiness  ‐ both infrequent and small price adjustments

• _{Continuously price updating is an implication of many} 

NKPC models including Reis (2006), Christiano et al (2005), 

N C o e s i c u i g eis ( 006), C is ia o e a ( 005),

Smets and Woulters (2003), Rotemberg(1982), Kozicki andTinsley (2002), among many others

This Paper

This Paper

•_{Proposes a microfounded theoretical model that endogenously} 

e e ate i flatio e i te e a a e ult of o ti i i beha io

generates inflation persistence as a result of optimizing behavior  of the firms

•_{Combines staggered price setting (Calvo) and quadratic costs of} 

This Paper

This Paper

•_{Phillips curve derived from DSGE model, and relates current} 

inflation to inflation expectations lagged inflation and real inflation to inflation expectations, lagged inflation, and real  marginal cost or output gap L d i fl i i d l d i • _{Lagged inflation term is endogenously generated in a}  forward‐looking framework:  Agents remain forward looking and follow an  optimizing behavior

This Paper

This Paper

• _{In contrast to the general indexation models and sticky} 

information models in the proposed model: information models,  in the proposed model:  prices are not continuously adjusted and firms that are  bl h i d f ll dj h d 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 or  quadratic cost) quadratic cost)  Model as an alternative to ad‐hoc hybrid NKPC and  ti k i f ti Philli sticky information Phillips curve

This Paper

This Paper

•

_{Price stickiness}

 direct microeconomic evidence

1. _{When to change prices?   the frequency of price changes} Fixed costs of price adjustment:p j

• _{Physical menu costs}

• _{Implicit and Explicit Contracts (ranked the 1Implicit and Explicit Contracts (ranked the 1 in the EU area} st _{in the EU area}

and 2nd _U.S.) 2 H h t h i ?  th i f i h 2. How much to change prices?  the size of price changes Convex, Variable costs price adjustment : a) Managerial costs ( information gathering costs, decision     making, and internal communication costs) b C d b) Customer costs (communication and negotiation costs) c) Other costs – antagonizing customers  Zb ki Rit L D tt B (2004) d Bli d t l (1998)

Zbaracki,  Ritson, Levy, Dutta, Bergen (2004)

•_{Firm investigated changes prices “once a year”}

•_{However, “the firm reacted to major changes in supply} 

and demand conditions slowly and/or partially because  of the convexity of costs [of price adjustment]…”

Th M d l

The Model

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The Model

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Model

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DSGE Model

DSGE Model

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Estimation

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S ll l SGE d l d h

Results

Results

Co o ay i the lite atu e to e aluate the odel u e

Common ways in the literature to evaluate the model success  in capturing inflation dynamics

•_{Examining the estimated parameter associated with lags} 

of inflation in the Phillips curve

•_{Autocorrelation functions for inflation}

•_{Impulse response functions}

Results

Results

Model Parameters

•_{Evidence of intrinsic inflation persistence} •_{Parameter estimates associated with the two types of price}  stickiness are highly significant, supporting the proposed  d l model   Coefficients associated with lags of inflation in the  Phillips curve are positive and highly significant

Results

Results

Frequency of price changes

y

 Calvo parameter θ, degree of nominal rigidity = 0.75.  1/4 firms  reset prices to optimize profit Average length of time between reset prices to optimize profit. Average length of time between  price changes is 4 quarters

E ti t l l t h i d t id i h

•_{Estimates closely match micro‐data evidence ‐ prices change} 

on avg once a year: 

Klenow and Malin (2010) Alvarez (2008) (18 countries 11  months),  Alvarez et al (2006)  Euro area (4 to 5 quarters).  Eichenbaum, Jaimovich and Rebelo (2008) sticky reference Eichenbaum, Jaimovich and Rebelo (2008) sticky reference  prices among shorter‐lived new prices (11.1 months)

Results

Results

Size of price adjustments

j

•_{Magnitude of adjustment costs large and statistically} 

significant: quadratic adjustment cost c = 171 0, 95% confidence significant:  quadratic adjustment cost, c   171.0, 95% confidence  (143.2, 197.4) E i i l fi di i h tl ll th th Empirical findings: price changes are mostly smaller than the  size of aggregate inflation (e.g. Dhyne et al. 2005, Alvarez et al  (2006), Klenow and Kryvstov 2008, etc.)  Klenow and Kryvtsov (2008) ‐ U.S. consumer price  changes  (absolute value):  44% < 5%    25% < 2.5%   12% < 1%   Ve eule et al (2007) Eu o a ea odu e i e

 Vermeulen et al. (2007) ‐ Euro area producer price:

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Coefficients on Inflation Expectations and Lagged

Coefficient on Lagged Inflation of the Phillips Curve Coefficient on Inflation Expectations of the Phillips Curve

Coefficients on Inflation Expectations and Lagged  Inflation 0.8 0.9 1 Coe c e o agged a o o e ps Cu e =0.5 =0.66 =0.75 =0 85 0.8 0.9 1 Coe c e o a o pec a o s o e ps Cu e 0.5 0.6 0.7 =0.85 0.5 0.6 0.7 0.2 0.3 0.4 0.2 0.3 0.4 0 50 100 150 200 0 0.1 parameter c 0 50 100 150 200 0 0.1 parameter c The coefficient on inflation expectations increases with the Calvo parameter  and decreases with the adjustment cost parameter c

1 s 0.8 1 E x pec ta ti on 0.4 0.6 o n I n fl at io n E 200 0 0.2 C o ef fi c ient o 0 4 0.6 0.8 1 50 100 150 200 0.2 0.4 0 50  C

Slope of the Phillips Curve

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Slope of the Phillips Curve

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Slope of the Phillips Curve

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E ti ti R lt 1960-2008 Estimation Results  Output Gap 1960 2008 likelihood c theta

CBO output gap

-922.3 _{(140.0, 195.6)(} 167.3 _{) (0.70, 0.82)(} 0.76 ₎ HP filtered gap (two sided) 879 1 121.7 0.72 (two-sided) -879.1 _{(97.4, 146.3) (0.63, 0.79)} CF filtered gap _{127 0 0 73} CF filtered gap (one-sided) -836.3 _{(102.5, 152.3)}127.0 _{(0.66, 0.81)}0.73

Priors and Posteriors of Key Parametersy 10 12 0.025 0.03 8 0.02 posterior posterior 4 6 0.01 0.015 prior 2 0.005 prior prior prior 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0  -50 0 50 100 150 200 0 c

Restrictions on c: likelihood estimates (1960 2008)

c=0

Restrictions on c: likelihood estimates (1960‐2008)

Output gap

measure _{likelihood c theta likelihood c theta}

CBO output gap -922.3 167.3

( 6) 0.76 ( 8 ) -1119.8 -0.89 ( 8 ) (140.0, 195.6) (0.70, 0.82) (0.87, 0.91) HP filtered gap ( id d) 879 1 1025 8 -8 (two-sided) -879.1 121.7 (97.4, 146.3) 0.72 (0.63, 0.79) -1025.8 _0.85 (0.83, 0.88) CF filtered gap -CF filtered gap (one-sided) -836.3 127.0 (102.5, 152.3) 0.73 (0.66, 0.81) -1008.3 0.88 (0.86, 0.90)

Sub‐sample Estimates

1960-1979 1983-2008

Sub sample Estimates

likelihood c theta likelihood c theta

-399.2 117.5 ( 89 4 149 4 ) 0.73 (0 65 0 82) -407.5 143.5 ( 112 3 173 9 ) 0.72 (0 64 0 81) ( 89.4, 149.4 ) (0.65, 0.82) ( 112.3, 173.9 ) (0.64, 0.81) -384.3 83.8 ( 55.6, 107.0 ) 0.68 (0.58, 0.79) -379.2 110.7 ( 78.6, 138.5 ) 0.69 (0.58, 0.79) -370.4 98.5 ( 70.8, 129.8) 0.69 (0.59, 0.79) -368.8 111.4 ( 80.4, 140.0) 0.69 (0.59, 0.80)

Cost shocks ARMA(4 1): 1960 2008

GDP deflator NFB deflator

Cost shocks ~ ARMA(4,1): 1960‐2008

Output gap measure

Likel. c theta likelihood c theta

CBO output gap

-906.1 117.7 (75.9, 161.1) 0.68 (0.56, 0.80) -954.7 55.7 ( 28.7, 82.8 ) 0.66 (0.54, 0.78) HP filtered gap (two-sided) -867.3 140.1 (105.8, 170.6) 0.72 (0.64, 0.79) -867.4 139.9 ( 107.2, 171.7 ) 0.72 ( 0.65, 0.80) CF filtered gap (one-sided) -824.8 130.4 (95.0, 165.9) 0.73 (0.64, 0.81) -879.9 90.6 ( 61.4, 121.0) 0.73 (0.66, 0.82)

Di t ibutio

of P i e Cha

e

Distributions of Price Changes

0.12 0.1 Rotemberg 0.08 CEE 0.04 0.06 0.02 proposed model Calvo -50 -40 -30 -20 -10 0 10 20 30 40 50 0 Calvo

pre-1980 post-1980 pre 1980 post 1980 Rotemberg 0.1 0.1 Rotemberg CEE 0.05 0.05 proposed model 0 0 Calvo -50 0 50 -50 0 50

Average ‐ absolute values of price changes (%)

Calvo Our model CEE Rotemberg

1960q1-2008q4 15.51 12.42 5.98 3.18 1960q1-1979q4 16.65 14.61 7.58 3.93 1983q1-2008q4 9.90 8.58 4.07 2.40

Data: Absolute size of price changes

•_{Klenow and Kryvtsov (2008):}

Data: Absolute size of price changes

Klenow and Kryvtsov (2008):

US CPI: mean (median) of absolute price changes  posted price changes: 14% (11 5%)

posted price changes: 14% (11.5%)  regular price changes: 11.3% (9.7%) •_{Nakamura and Steinsson (2008):}  U S fi i h d d d i U.S. finished goods producer prices median of price changes: 7.7% Klenow: median data are more meaningful for macro.

0 2 0 4 -40 -20 0 20 40 0 0.1 0.2 Ca lv o -40 -20 0 20 40 0 0.2 0.4 -40 -30 -20 -10 0 10 20 30 40 0 0.5 1 0 0.1 0.2 p rop os e d m o de l 0 0.2 0.4 0 0.5 1 -40 -20 0 20 40 0 -40 -20 0 20 40 0 -40 -30 -20 -10 0 10 20 30 40 0 0 1 0.2 0.3 CE E 0 2 0.4 0.6 0.5 1 -40 -20 0 20 40 0 0.1 -40 -20 0 20 40 0 0.2 -40 -30 -20 -10 0 10 20 30 40 0 0 2 0.3 rg 0 4 0.6 1

U S CPI: 44% of regular price changes < 5% 25% < 2 5% and 12% <1%

-40 -20 0 20 40 0 0.1 0.2 Ro te m b e -40 -20 0 20 40 0 0.2 0.4 -40 -30 -20 -10 0 10 20 30 40 0 0.5 U.S. CPI:  44% of regular price changes < 5%, 25% < 2.5%, and 12% <1%  in absolute value (Klenow and Kryvtsov 08) Calvo : 35.4% < 5% (Histogram for bin range with 10%. Our model : 46.9% < 5%.

IRF Results

IRF Results

•_{Response of inflation to a contractionary monetary policy}  ho k shock: •_{Standard NKPC model, impact of a monetary policy shock}  on inflation is immediate.

• _{Proposed model the response of inflation is gradual,Proposed model the response of inflation is gradual,}  displaying significant inertia

1 1.5 a ti o n cost-push shock c=0 c=25 c=50 c=100 1 1.5 2 preference shock -0 4 -0.2 0

interest rate shock

0 5 10 15 20 25 0 0.5 time In fl a _c=150 c=167.3 0 5 10 15 20 25 0 0.5 1 time 0 5 10 15 20 25 -0.8 -0.6 0.4 time -0.2 -0.1 0 0.1 cost-push shock p ut G a p 0.5 1 preference shock -0.2 0 0.2

intrest rate shock

0 5 10 15 20 25 -0.5 -0.4 -0.3 time Ou tp 0 5 10 15 20 25 -0.5 0 time 0 5 10 15 20 25 -0.6 -0.4 time cost-push shock preference shock interest rate shock 0.4 0.6 0.8 cost-push shock ter es t R a te 0 5 1 1.5 preference shock 0 0.5 1

interest rate shock

0 5 10 15 20 25 0 0.2 time In t 0 5 10 15 20 25 0 0.5 time 0 5 10 15 20 25 -0.5 0 time

Results

Results

Taylo (1999) o ide a a ya d ti k of a u e of o eta y

•_{Taylor (1999) considers as a yardstick of a success of monetary} 

models their ability to generate the “reverse dynamic” cross‐ correlation between output gap and inflation.

Can the output gap version Phillips curve explain the Can the output gap version Phillips curve explain the  dynamic correlation between output gap and inflation? •It is well known the labor income share version hybrid Phillips y p curve is able to explain the observed dynamic correlation •Since labor’s share of income is countercyclical, we need to  investigate whether the output gap version Phillips curve is able to  account for the dynamic correlation   

Results

Results

Model yield “ e e e dy a i ” e ult

•_{Model yields “reverse dynamic” result:}  current output gap tends to be positively related with  future inflation, whereas past inflation tends to be  negatively associated with current output gap •_{Autocorrelation function for the estimated inflation is high}  and decay gradually, also indicating that inflation is highly  persistent persistent • _{The estimated inflation autocorrelation closely tracks the}  observed data.

Dynamic correlation between output gap measures and inflation

1

Correlation( CBO output gap(t), inflation(t+k) )

Dynamic correlation between output gap measures and inflation 0 0.5 d l -10 -8 -6 -4 -2 0 2 4 6 8 10 -1 -0.5 model data upper bound lower bound no quadratic costs k 1

Correlation( HP-filtered output gap(t), inflation(t+k) )

0 0.5 -10 -8 -6 -4 -2 0 2 4 6 8 10 -1 -0.5 k

continued

1

Correlation(output gap(t), inflation(t+k) ) and Shocks model continued 0 0.5 cost shocks demand shocks interest rate shocks

-10 -8 -6 -4 -2 0 2 4 6 8 10 -1 -0.5 k 0.5 1

Correlation(output gap(t), inflation(t+k) ) and Price Adjustment Cost

-0.5 0 c=167.3 c=150 c=100 c=50 25 c=0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -1 k c=25 c=0

Conclusions

Conclusions

• Inflation persistence endogenously generated in the model p g y g without relying on indexation assumption P d ti k i d l i t d b th d t •Proposed sticky price model is supported by the data. 

•Results are robust to sub‐samples, output gap measures, andResults are robust to sub samples, output gap measures,  and  inflation measures.   

Model

Model

t y t t W _{N i} B B C _{{ }(1 )} 1  t t t t y t t t t t t t _{P P} N i _P C         1) 1 1 }( exp{ 

(2)When equation (1) is replaced with equation (2) and production function (without technology)

t

t N

Y 