Post on 10-Sep-2019
Aggregation and the PPP Puzzle in a StickyPrice Model�
Carlos CarvalhoFederal Reserve Bank of New York
Fernanda NechioPrinceton University
May 2009
�The views expressed in this presentation are those of the authors and do not necessarily re�ect theposition of the Federal Reserve Bank of New York or the Federal Reserve System.
Real exchange rates and PPP
� Real exchange rate (RER): ratio of prices of basket of goods denominated incommon currency
� Q = EP�P
� Purchasing power parity (PPP) hypothesis: �Q is constant�
� Q = 1: �absolute PPP�
� Q = constant 6= 1: �relative PPP�
US Dollars / "French Franc-Euro"
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FX (left axis) RER (left axis) Price Ratio (right axis)
The puzzle: data + model failure
� �PPP Puzzle� - Rogo¤ (1996)
� High persistence and volatility of real exchange rates (deviations from PPP)
� Hard to reconcile with economic models
� In particular, when deviations arise from nominal shocks in the presence ofprice rigidity
� Quantitative framing of the puzzle:
� Most estimates of half-life of deviations from PPP fall between 3 - 5 years
� Standard sticky-price models with monetary shocks: half-life around 1 year
� �Too much�price rigidity needed to match persistence of the data
Our paper
� Build on ample evidence of heterogeneity in frequency of price adjustment (Bilsand Klenow 2004 and others)
� Average degree of price rigidity not the relevant statistic for aggregatedynamics (Carvalho 2006)
� Potential source of heterogeneity in dynamics of sectoral real exchange rates
� Multi-sector, two-country, sticky-price model:
� Heterogeneity in frequency of price changes
� Price discrimination and local currency pricing
) Heterogeneous sectoral real exchange rates
Summary of the model - K sectors
Consumers Consumers*
Home Foreign
FinalGoods
FinalGoods*
IntermediateGoods
IntermediateGoods*
Sector 1 ... Sector KSector k ...YH,k,j
Y*H,k,j
Sector 1 ... Sector KSector k ...YF,k,j
Y*F,k,j
C
L
C*
L*
Y Y*
YH,k,j Y*H,k,j YF,k,j Y*
F,k,j
Summary of the model - 1 sector
Consumers Consumers*
Home Foreign
FinalGoods
FinalGoods*
IntermediateGoods
IntermediateGoods*
C
L
C*
L*
Y Y*
YH,j Y*H,j YF,j Y*
F,j
Summary of core quantitative results
� Quantitative model
� Discipline our argument: distribution of price stickiness chosen to matchmicro data
� Average frequency of price changes implies average spells of 4.4 months
� Half-life of deviations from PPP in heterogeneous economy: 3.8 years
� Half-life of deviations from PPP in homogeneous economy: 1.2 years
Core results: intuition I
� Sectors with more stickiness are disproportionally important for aggregate dy-namics
� Extreme case: 1 �exible- and 1 sticky-price sector, no pricing complementarities
� Aggregate RER dynamics driven only by sticky-price sector
� Mathematically: measures of persistence (and volatility) are convex in thefrequency of price changes
Core results: intuition II
� E¤ects even stronger in the presence of pricing complementarities!
� Not-so-extreme version of �responders vs non-responders�of Haltiwanger andWaldman (1991)
� Bottom line in terms of persistence:
� heterogeneous economy � homogeneous economy with more price sticki-ness than what�s implied by average frequency of price changes
The model
� Two countries, Home and Foreign, with identical, in�nitely lived consumers
� Commodities are labor, a consumption good and a continuum of intermediategoods
� Consumer supplies labor, invests in complete set of state-contingent assets, andconsumes non-traded �nal good
� Competitive �nal good producers bundle intermediate goods; �exible prices
� Monopolistically competitive intermediate goods producers:
� Price discriminate, setting prices in local currency
� Sticky prices; adjustment frequency varies across sectors
The model - �nal good I
max PtYt �
0@ KXk=1
fk
Z 10PH;k;j;tYH;k;j;tdj +
KXk=1
fk
Z 10PF;k;j;tYF;k;j;tdj
1As:t:
Yt =
XK
k=1f1�k Y
��1�
k;t
! ���1
Yk;t =
!1�Y
��1�
H;k;t + (1� !)1� Y
��1�
F;k;t
! ���1
YH;k;t =
f��1�
k
Z 10Y��1�
H;k;j;tdj
! ���1
YF;k;t =
f��1�
k
Z 10Y��1�
F;k;j;tdj
! ���1
The model - �nal good II
� Demands
YH;k;j;t = !
PH;k;j;t
PH;k;t
!�� PH;k;tPk;t
!�� Pk;tPt
!��Yt
YF;k;j;t = (1� !) PF;k;j;t
PF;k;t
!�� PF;k;tPk;t
!�� Pk;tPt
!��Yt
� Price Indices:
Pt =�XK
k=1fkP
1��k;t
� 11��
Pk;t =�!P
1��H;k;t + (1� !)P
1��F;k;t
� 11��
PH;k;t =
Z 10P 1��H;k;j;tdj
! 11��
PF;k;t =
Z 10P 1��F;k;j;tdj
! 11��
The model - intermediate �rms I
� Intermediate �rms:
� divided into sectors that di¤er in the frequency of price changes
� Calvo (1983) pricing: �k = frequency of price changes in sector k
� indexed by country, sector (k 2 K), and by j 2 [0; 1]
� sectoral weights fk
� produce di¤erentiated varieties using labor
The model - intermediate �rms II
� Choose prices XH;k;j;t; X�H;k;j;t, set in local currencies:
max Et
1Xs=t
�t;s (1� �k)s�t"XH;k;j;tYH;k;j;s + EsX�H;k;j;tY
�H;k;j;s
�WsNk;j;s
#
s:t: YH;k;j;t + Y�H;k;j;t = N
�k;j;t
and demands
� Analogous for Foreign
Closing the model
� Speci�cations for monetary policy that ensure existence and uniqueness of REequilibrium
� Equilibrium: optimality and market clearing conditions
� Solution: loglinearization around zero in�ation steady-state
Counterfactual homogeneous economy
� Counterfactual homogeneous (one-sector) economy:
� Everything the same, except:
� One sector with frequency of price changes � =PKk=1 fk�k
Parametrization
� 36-sector model:
� �k = 1=k, k = 1; :::; 36
� Micro evidence from Nakamura-Steinsson (2008):
� CPI data - no sales/substitutions
� fk = sum of expenditure weights for underlying categories
� 36th sector: f36 = 4:2%
� �� = 0:226 ) Prices changes, on average, every 4:4 months
Quantitative results
Persistence measures: P (q) P�q1 sec
�CIR 79:9 20:2SAC 0:98 0:95LAR 0:94 0:86HL 45 14�1 :98 :96
Volatility measure: V (q)1=2 V�q1 sec
�1=20:10 0:04
Using our structural model - extras
� We provide structural interpretation to the (reduced-form) empirical literatureon heterogeneity, aggregation and PPP
� �PPP Strikes Back/Aggregation Bias�debate between Imbs et al. (2005),and Chen and Engel (2005) / Crucini and Shintani (2008)
� Study persistence in the cross-section of sectoral exchange rates ; touch basewith Kehoe and Midrigan (2008) (this is work in progress)
Decomposition of e¤ect of heterogeneity
P (qt)� P�q1 sect
�| {z }total heterogeneity e¤ect
��P (qt)�
XK
k=1fkP (qk)
�| {z }
aggregation e¤ect
+�XK
k=1fkP (qk)� P
�q1 sect
��| {z }
counterfactuality e¤ect
Applying decomposition
"Eurostatdata
#Data Panel, agg. Panel, sect. Panel, sect.
Estim. method Fixed E¤ects OLS MGP (q) 1
K
PP (qk) P�q1 sec
�Persist. meas.:
CIR 64:39 59:48 33:19SAC 0:98 0:97 0:97LAR 0:97 0:94 0:95HL 46 43:16 26
"Simulateddata
#Economy Heterog. Heterog. One-sectorData Single, agg. Panel, sect Single, agg.
Estim. method OLS OLS OLSP (q) 1
K
PP (qk) P�q1 sec
�Persist. meas.:
CIR 73:4 60:8 36:9SAC 0:98 0:97 0:97LAR 0:96 0:89 0:87HL 43:1 31:6 21:8
Conclusion - I
� Multi-sector, two-country, sticky-price model can produce RER that is as per-sistent as in the data
� One-sector version of same economy with average frequency of price changesfails to do so
� We use our model to explain the apparently con�icting �ndings in reduced-formempirical literature
� Di¤erent papers measured di¤erent objects
� As Chen and Engel (2005) and Crucini and Shintani (2008), we �nd aggre-gation e¤ect to be small (in the parametrized model and in the data)
� As Imbs et al. (2005), we �nd total heterogeneity e¤ect to be large (in theparametrized model and in the data). This is due to the counterfactualitye¤ect
Conclusion - II
� What matters for understanding the gap between data and standard one-sectormodels is total heterogeneity e¤ect
� Heterogeneity in price stickiness goes a long way towards solving the PPPpuzzle
� Such type of heterogeneity known to matter for policy:
� In �closed economies�: Aoki (2001), Benigno (2004), Eusepi, Hobjn andTambalotti (2008), Berriel and Sinigaglia (2008)
� In open economies: ?