Why is Brazilian Inflation so high? Inflation persistence in Brazil and other emerging markets

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1 Why is Brazilian Inflaion so high? Inflaion persisence in Brazil and oher emerging markes Fernando Siqueira dos Sanos Marcio Holland Absrac: This paper analyzes inflaion persisence in Brazil. Boh aggregae and disaggregaed inflaion persisence are compued. We also compare inflaion persisence in Brazil wih esimaes for oher emerging counries wih a long hisory of high inflaion. The resuls indicae ha inflaion persisence in Brazil is higher han in oher emerging markes. Core inflaion presens more inflaion persisence han headline inflaion, paricularly due o he exclusion of he low persisence food iems. Despie he large persisence in Brazilian inflaion, disaggregaed daa are more sensible o expeced inflaion han lagged inflaion and hus indicaes a major role for forward looking behavior. Resumo: Ese rabalho esima a persisencia da inflação no Brasil ano em ermos agregados quano desagregados. O rabalho ainda compara a persisência da inflação no Brasil com a persisência em ouros países emergenes. Os resulados indicam que a persisência da inflação no Brasil é maior do que em ouros países, mas ese resulado não é obido para odos os meodos de esimação uilizados. A persisência no núcleo da inflação é maior do que na inflação cheia. Apesar da persisência elevada, nossos resulados indicam que a expecaive de inflação é uma variável mais imporane na deerminação da inflação correne do que a inflação passada. JEL Classificaion: C11, C22, E31 Keywords: inflaion persisence, Phillips curve We like o hank Wagner O. Moneiro for his suppor wih several rouines/codes used in his paper. PhD Candidae a he São Paulo School of Economics (EESP-FGV).. Secreary of Economic Policy a he Minisry of Finance, Brazil, Professor a he São Paulo School of Economics (EESP-FGV) and CNPq Associae Researcher. The view expressed in his aricle are ha of he auhor and do no necessarily represen ha of he Brazilian Minisry of Finance. 1

2 1 Inroducion Afer reaching a hyperinflaion environmen for some years, Brazilian inflaion decreased o more normal levels afer he inroducion of he Real Plan in Despie he sharp fall in Brazilian inflaion and he convergence o he level observed in he emerging marke economies, i is sill higher han hose observed in developed counries. The aim of his paper is o compare inflaion persisence in Brazil wih oher emerging markes, paricularly hose wih a long hisory of high inflaion. We consider his a firs sep o beer undersand wha lies beneah he larger inflaion in Brazil. Oher imporan differences may be due o larger marginal coss (posiive oupu gaps), larger pass-hrough of commodiy price shocks, larger inflaion expecaions, among ohers. All hese aspecs may be furher invesigaed in fuure works relaed o Brazilian inflaion. Larger inflaion persisence could help explain why Brazilian inflaion is higher han in oher counries: As he counry evolves from a high inflaion o a low inflaion environmen, large persisence raes could make his process slower in some counries. In his paper we focus on emerging markes inflaion, paricularly on counries wih a hisory of high inflaion in recen years. The quesion we address is why Brazilian inflaion is higher han inflaion raes in oher emerging markes. We do no exacly aim o answer why inflaion is higher in emerging markes. We hink his could be an imporan sep owards undersanding why some counries reach lower and sable inflaion han ohers. We do no deal wih some aspecs of inflaion ha could explain large inflaion in some counries such as he behavior of inflaion expecaions and he effec of indexaion. Indexaion mechanisms are relaed o inflaion persisence bu hey are no he same. The main reason no o deal wih hese quesions is he lack of comparable variables in each counry. Therefore, a few counries have daa on inflaion expecaions and usually he mehodology varies from counry o counry; ha makes comparisons very difficuly. The characerizaion of inflaion expecaions daa in each counry, is evoluion and impacs on curren inflaion is undoubedly a subjec ha should be furher invesigaed. In his paper we use inflaion expecaion daa only for he esimaion of he Phillips curve in Brazil. And, as we already menioned, a deeper analysis of inflaion expecaions in Brazil and oher counries is lef for fuure research. The counries we include in our sample of emerging markes wih a hisory of high inflaion in recen years are: Brazil, Colombia, Peru, Chile and México in Lain America; Souh Africa in Africa; Czech Republic, Poland and Hungary in Europe and Israel in Asia. All hese counries have a hisory of high or hyperinflaion early in he 90 s and hey have all pursued low inflaion hrough an inflaion arge regime during he las en years or more. We do include neiher developed counries nor emerging counries in Asia in our sample due o heir long hisory of low inflaion. 2

3 Table 1: Inflaion in Seleced Emerging Markes ( ) 1980 o o o o o 2010 Brazil 782,1 10,7 19,4 8,7 5,0 Chile 20,1 4,2 6,0 2,8 3,8 Colombia 24,4 9,7 17,9 7,3 4,7 Czech Republic n.a. 4,0 7,5 2,6 2,7 Hungary 14,5 10,0 18,9 7,1 5,1 Israel 81,9 4,0 8,2 1,6 2,4 Mexico 51,5 11,2 24,5 6,0 4,4 Peru 856,6 4,4 8,4 2,4 2,6 Poland 91,0 7,5 16,4 4,4 2,6 Souh Africa 13,9 6,5 7,3 5,5 6,6 Turkey 58,6 40,3 81,0 37,7 8,7 Mean 199,5 10,2 19,6 7,8 4,4 Median 55,0 7,5 16,4 5,5 4,4 Source: IMF Our resuls indicae ha inflaion persisence in Brazil beween 1995 and 2011 is larger han esimaed for oher emerging markes in he same period. This resul is valid boh for headline inflaion and core inflaion measures and is based in simple auoregressive models. Using he Hansen (1999) mehod of median unbiased esimaion he esimaed is close o our sample mean of he emerging markes inflaion persisence. The inflaion persisence in Brazil is also close o persisence esimaed for developed counries by oher auhors. Our resul indicaes ha core inflaion is more persisen han headline inflaion. This resul arises as a consequence of he exclusion of food producs from core inflaion. Regarding he deerminans of inflaion persisence, our resuls are inconclusive as he persisence of mos variables used in our Phillips Curves esimaion is very close o each oher. Despie he relaively large inflaion persisence in Brazil, our proxy for expeced inflaion is more imporan for inflaion deerminaion han lagged inflaion. This resul is more pronounced when we use disaggregaed han aggregaed daa. Our resuls indicae ha disaggregaed inflaion persisence is much lower han aggregaed inflaion persisence. This resul is also repored by oher auhor s esimaion of disaggregaed inflaion persisence for oher counries (mainly developed counries). This can be a resul of common facors presen a aggregaed daa bu no idenifiable in disaggregaed daa as indicaed by Granger (1987). In such cases, inflaion expecaions may capure only his common facor which could explain our resuls. We le his quesion as an issue for fuure research. 2 Phases in Brazilian Inflaion afer he Real Plan In his secion we use an unobserved componens model of inflaion o explain he evoluion of Brazilian inflaion since he Real Plan by using monhly daa since Many auhors have already described he evoluion of Brazilian inflaion using small sample periods such as Minela e al (2008). In general, auhors recognize a leas wo differen periods in Brazilian inflaion afer he Real Plan: a) he firs years afer he inroducion of he Plan when inflaion was sill high bu ending downwards (in he 10-year period before he Real Plan inflaion was higher han 100% per year on average) and b) he following years, when he Real Plan was already consolidaed and inflaion remained low for some ime. There are also some ineresing episodes 3

4 during hese periods, e.g. he inroducion of he Inflaion Targeing Regime in 1999 and he confidence crisis of Figure 1 shows he evoluion of he underlying level of Brazilian inflaion esimaed by using an unobserved componens model. I is clear ha inflaion diminished in he years ha followed he inroducion of he Real Plan in 1994 and increased afer he exchange rae devaluaion in he beginning of Anoher increase in inflaion occurred in he confidence crisis of Afer 2003, inflaion had remained beween 1% and 2% per quarer. The figures indicaes ha Brazilian inflaion presen a clear seasonal paern: inflaion is higher a year end and also a he beginning of each year. The seasonal paern is more pronounced in he second half of our sample. We did no es for srucural breaks in Brazilian inflaion daa. We will include a ime rend for he firs half of our sample (up o 4Q98) in our esimaions of he Phillips curve whenever his is possible. We will also include seasonal dummy variables or AR(4) models as our preferred specificaion due o he seasonaliy of inflaion in Brazil. Figure 1: Inflaion Decomposiion - Srucural Time Series Model ( ) 4

5 Noe: Srucural Time Series (STM) model for Brazilian inflaion. The lef column presens he esimaed componens of headline inflaion while he righ column presens he core inflaion. Inflaion componens are Level (firs row), Seasonal componen (second row) and Irregular componen (hird row). 3 Inflaion Persisence in Brazil: Aggregaed Daa 3.1 Inroducion Inflaion persisence has been widely sudied in developed counries bu no so much in developing counries. Levin and Piger (2004) and O Reilly and Whelan (2005) are good references for he sudy of inflaion persisence in advanced economies. Gerlach (2008) sudies inflaion persisence in Asian counries. In Brazil, here are some sudies of inflaion persisence by using long memory (ARFIMA) models like Figueiredo and Marques (2009) and Rebelo e al (2009) and also by using auoregressive models wihou long memory and srucural models (Phillips curve) like Oliveira and Perassi (2010). A useful way o sudy inflaion persisence is by esimaing a simple auoregressive model and compuing he sum of coefficiens on lagged inflaion: p π = a + λ π + e i i i= 1 (1) Where π is he quarerly inflaion rae. Anoher specificaion ha is useful o analyze inflaion persisence is rewriing he inflaion process as: π = a + ρπ + c π + e 1 i i i= 1 p (2) By his equaion, we can focus on he parameer ρ. The main advanage of his specificaion is ha i is easier o sudy he evoluion of inflaion persisence as i is measured by jus one coefficien insead of p parameers as in he AR(p) model. We also esimaed an AR(1) model wih seasonal dummies. The advanage of his model is ha we preserve he sample size in he esimaion. Wih he use of an AR(p), he firs p observaions is los in he esimaion process as p lagged values for he exogenous variable are necessary o iniiae he esimaion. This will be 5

6 imporan for he esimaion of disaggregaed daa in he nex secion. We esimaed his model also wih aggregaed daa for he sake of comparabiliy in he laer secion of his sudy. The model wih seasonal dummy variables can be wrien as: π = a + λπ + d T + e = 1 q q q 2 4 (3) Where q refers o he quarers and T is he dummy variable: q=2 indicaes he second quarer of he year and so on up o he fourh quarer (q=4). Our measure of persisence in his case is he coefficien b. An issue usually addressed by oher auhors is he possibiliy of srucural breaks in he series or model coefficiens. Since we are using a small sample, he chances ha a srucural break occurred a some poin of he sample is small. Even so, we esimae some of he srucural parameers as random walks (ime varying coefficien) o increase he confidence in he resuls. We also include a dummy variable a he beginning of he sample in some esimaions due o he iniial effecs of he sabilizaion program in The Real Plan was inroduced in he beginning of 3Q94 and inflaion was reduced from more han 10% per monh o less han 2% in he following monhs (his can be clearly seen in figure 1). Our dummy variable goes up o he end of I is no clear however if he low inflaion in 1997 and mainly in 1998 was due o coninued effec of he sabilizaion plan or a consequence of low GDP growh in Brazil and also in he world as a resul of several financial crises ha occurred in 1997 and Global GDP growh was below he average in 1998 and commodiy prices fell ha year, conribuing o he low inflaion in Brazil (exchange rae was fixed a ha momen). Finally, we esimaed his simple model including a measure of oupu gap and also a measure of exernal inflaion and a measure of inflaion expecaion. Hisorically, many empirical works in Brazil used he exchange rae depreciaion as one of he inflaion deerminans. Despie his being a good proxy for he 1999 and 2002 episodes of exchange rae depreciaion, his is a poor proxy in oher periods as his measure of foreign inflaion does no capure he global inflaion facor. We experimen wih wo differen measures of global inflaion: The CRB commodiy price index and he average CPI inflaion in he OECD counries. Ciccarelli and Mojon (2010) show ha he global inflaion is an aracor of local inflaion for several counries. Ciccarelli and Mojon (2010) use a facor model o derive heir global inflaion facor bu call aenion o he fac ha he average inflaion is a good approximaion o he global facor 1. The resuls for he esimaions using he global inflaion variable are no repored: When his measure of global inflaion is used, i leads o a highly significan coefficien and also makes almos all oher coefficiens in he model no significan a usual levels. We inerpre his as one more indicaion ha inflaion is a global phenomenon in some aspecs. Bu his also indicaes ha his measure of global inflaion is no exogenous or an independen variable. Boh he Brazilian inflaion and he global inflaion (OECD median inflaion, as we defined earlier) are deermined by he same facors, which characerize an endogenous regressor. The use of commodiy price index is a beer proxy for he effecs of changes in exernal inflaion during he period as Brazil had a fixed exchange rae regime in he firs par of he sample and changes in foreign prices in domesic currency where dominaed by changes in foreign prices in he exernal currency. In 1999 and also 2002 due o he large depreciaion of he Real, radable prices (and also regulaed prices) presened high raes of inflaion. In oher periods, like in and laer in , he exchange rae appreciaion was no sufficien o avoid an escalaion of radable prices as commodiy prices surged around 1 This seems clear in figure 1 in Ciccarelli and Mojon (2010). 6

7 he world. Some more heoreical papers also refer o he impor price as a measure of exernal inflaion. We consider he commodiy price index as a wider definiion of exernal inflaion and preferred in our esimaions. In our esimaions we use he average of commodiy prices and exchange rae in he las monh of he quarer: $ P = E P and π = ln( E P ) ln( E 1P 1) where exchange rae in R$/US$. $* P is he commodiy price index in dollar and E is he Our measure of oupu gap is derived using he deviaion of GDP from a rend (HP filer). Several auhors have used he variaion in labor share as a measure of marginal cos. Daa on labor coss in Brazil are available only afer 2001 due o a change in he employmen and unemploymen survey. Allowing for he oupu gap as an addiion explanaory variable is imporan due o he fac ha some models aribue he persisence of inflaion o he persisence of he driving variable, namely he oupu gap (or marginal cos). This is called inheried persisence. Some auhors such as Fuhrer (2006) discuss his hypohesis. Finally, we included he welve monhs ahead inflaion expecaions (denoed by PHI_E) provided by he Brazilian Cenral Bank - BCB as a measure of inflaion expecaion. The inflaion expecaion is he main deerminan of inflaion in mos economic models since he appearance of he raional expecaions models in he 60 s. This variable is provided by he BCB on a daily basis and we used he average of he las monh of he quarer as our measure of inflaion expecaion. We also experimened using his variable wih wo lags insead of jus one as is he common pracice. Indeed, we consider his our preferred specificaion. The reason is clear: The oupu gap used in he Phillips curve equaion is y 1, which is known by marke paricipans a ime -1. Therefore, exchange rae and commodiy prices movemens are known a ime -1 (we use π 1 and π 1 in he Phillips curve esimaion). In his case, E E E he resul of using π 1 insead of π 2 is clearly o overesimae he impac of π in he deerminaion of π and underesimae he impac of oher variables. Indeed, in his case, he impac of oher variables is jus he E impac no pondered ino π 1. This could include, for insance, some kind of marke paricipans uncerainy abou he rue Phillips curve or sluggish adjusmen of marke paricipans forecas projecions. E There is anoher obvious explanaion for no using π 1 : I may also capure influences already known o affec inflaion in period. For insance, some already announced price adjusmen (his is paricularly rue for moniored prices) and also any oher kind of price shocks known a ime -1. Therefore, if marke paricipans know inflaion is persisen in a way consisen wih an auoregressive model like he ones we are considering E in his paper, he inclusion of π 1 in he esimaion ogeher wih π 1 will also end o underesimae he impac of π 1 in he Phillips curve equaion. Considering his complee specificaion for he Phillips curve, he equaion we esimae can be wrien as: π = a + ρπ + φπ + βπ + γ y + e (4) E 1 1, Dummy variables for each quarer are also incorporaed ino his equaion o conrol for seasonal effecs. 7

8 3.2 Inflaion persisence using aggregaed daa In able 2 we provided a summary of he main saisics of dependen and independen variables used in our esimaions. The main highligh of his able is he high auocorrelaion of all inflaion daa 2. The auocorrelaion of exernal price index is relaively small. This is an expeced resul as he variable is composed of exchange rae and commodiy prices and boh variables can be considered a financial asse and so heir movemens are close o random walks. The esimaion resuls for inflaion persisence using aggregaed daa are presened in able 2. Overall, he inflaion persisence esimaes are quie similar if we use he AR(1) or he AR(4) model. The inclusion of he dummy variable leads o an increase in he inflaion persisence esimae. This is no differen from resuls repored by oher auhors using differen echniques. Many auhors repor resuls indicaing larger inflaion persisence when he sample period is shorer: In mos of hese sudies, he shorer period accouns for possible breaks in he inflaion process. In his paper, we used a dummy variable insead o conrol for possible breaks or changes in he inflaion process. Table 2 Summary Saisics of Variables: 1Q1995 o 1Q2011 Inflaion persisence is larger for core inflaion han headline inflaion. Core inflaion excludes food prices and also moniored prices, wo groups wih low inflaion persisence. The inflaion persisence of food prices will be discussed in he nex secion. The low persisence of moniored prices seems o arise from he fac ha his group of prices are indexed o wo differen price indexes, he consumer price index (IPCA) and also he general price index (IGP), which is a mixure of producer price index, consumer price index and also consrucion cos index. The indexaion mechanism also changed during he las years due o he inclusion of produciviy gains clauses aimed a reducing he indexaion and due o he change in he composiion of he baskes of price index used by regulaors for deermining he moniored prices adjusmens. In oher words, he low persisence of moniored prices inflaion does no mean ha his group of price does no have srong mechanisms o propagaed inflaion shocks. 2 These inflaion groups are no compleely differen from one anoher. For insance, core inflaion excludes moniored prices and par of he food produc in he CPI (IPCA) baske. So, core inflaion includes mos of he free prices or nonradable prices. Non-radable prices are also free prices and so on. Despie his overlap, he segmenaion is imporan since hese groups are usually referred o in macroeconomic analysis boh by he Cenral Bank and by marke paricipans. 8

9 Table 3 Inflaion persisence esimaes IPCA Core Moniored Prices Free Prices Tradables Non Tradables AR (4) 0,430 0,502 0,529 0,367 0,309 0,312 ρ 0,408 0,538 0,492 0,361 0,317 0,507 Wih dummy for 1996:1 o 1998:4 AR (4) 0,514 0,692 0,418 0,477 0,290 0,692 ρ 0,488 0,681 0,352 0,499 0,277 0,695 Wih oupu gap, dummy for 1996:1 o 1998:4 ρ 0,513 0,699 0,332 0,546 0,303 0,705 γ 0,039 0,026-0,076 0,085 0,063 0,131 Wih oupu gap, exernal prices, dummy for 1996:1 o 1998:4 ρ 0,474 0,704 0,301 0,520 0,285 0,714 γ 0,008 0,015-0,135 0,058 0,047 0,124 γ/(1 ρ) 0,015 0,051-0,193 0,121 0,066 0,434 β 0,028 0,024 0,040 0,030 0,066 0,012 β/(1 ρ) 0,053 0,081 0,057 0,063 0,092 0,041 The inclusion of he oupu gap does no lead o a sensible change in he persisence esimaes. The coefficien of oupu gap has he wrong sign in he moniored prices equaion. This resul is no compleely unexpeced since moniored prices inflaion depends largely on pas inflaion: If oupu gap leads o an overall inflaion rise in year one and hen due o a more rigid moneary policy he oupu gap urns negaive in nex year, he moniored prices inflaion will rise when he oupu gap had already fallen. Despie his wrong sign, he coefficien is no significan. The impac of oupu gap is larger on free prices and paricularly in non-radable prices as expeced. The esimaed impac on core prices is also small. This resul seems a odds wih he large impac of oupu gaps on free prices, which comprehends he majoriy of he core inflaion componens. In he las group of coefficiens esimaes in able 3 we presen he resul from he esimaion of a Phillips curve wih exernal price inflaion. Again, he difference in he persisence coefficien from previous esimaions is minimal. The larges difference beween persisence esimaes arise when we allow for a ime rend in he firs par of our sample. This resul is in line wih several oher papers on he subjec ha consider breaks in he inflaion process. In our model, he ime rend for he pos-sabilizaion period is used o represen his break. In his las group of coefficien esimaes we include he esimaed long-run impac ( γ / (1 ρ) and also β / (1 ρ) ). The oupu gap coefficien, γ, is smaller when we include he exernal inflaion variable bu in some cases his difference is very small (we did no make saisical ess for his difference). The impac of oupu gap is larger for non-radable inflaion (services represen a good porion of his group) and negaive for moniored prices as was he case in he previous se of coefficiens esimaes. The impac of he exernal price inflaion is larger on radable prices and lower for non-radable prices, wo resuls ha are in line wih convenional heory. 9

10 3.3 Time-varying inflaion persisence In his subsecion we assess he evoluion of inflaion persisence during he las years. We do so by using a random coefficien approach for he inflaion persisence coefficien. The random coefficien is esimaed by using he Kalman filer. In order o reduce he number of parameers o be esimaed, we adjused he inflaion series o eliminae he seasonal facors. The seasonal adjusmen was made by using he X-12 procedure bu he resuls are prey much he same if we had used he unobserved componens models previously discussed. Using he seasonally adjused series, he model we esimae is: π = λ π 1+ γ y 1 + e λ = λ + ε 1 (5) Where π = π π is he deviaion of curren inflaion from he average inflaion. We included he dummy variable in all esimaions. The reason o use deviaion from mean is o eliminae he consan coefficien in he equaion o be esimaed. The consan coefficien in he above equaion usually leads o more volaile ime-varying coefficiens and can also lead o non-convergence in some specificaions. The resuls from he ime-varying coefficien display no clear rend in our sample (figures 2a and 2b). For headline inflaion, he coefficien is indeed larger in he second half of our sample. The resuls do no change significanly if we include more variables in he Phillips curve equaion. The resuls for core inflaion show less variabiliy and also no clear rend in he upward or downward in our sample period. I is ineresing o noice ha in boh cases he inflaion persisence parameer increases afer A possible explanaion for his resul is he change in he CPI baske in 3Q06. Figure 2a: ime-varying AR(1) model (random walk coef.) Headline inflaion Core inflaion Time_Varying AR(1) ± 2 RMSE Time-Varying AR(1) ± 2 RMSE 10

11 Figure 2b: recursive esimae of AR(1) model Headline inflaion Core inflaion 3.4 Sources of inflaion persisence in aggregaed daa The previous secion presened evidence ha inflaion persisence in Brazil is high if we use simple auoregressive models bu low if we include some explanaory variables in he inflaion dynamics. This resul can be explained by using he inheried versus inrinsic hypohesis for inflaion persisence. Le us consider a simple raional expecaions model for inflaion (usually called New Keynesian Phillips Curve, NKPC) in which he oupu gap follows an AR(1) process 3 : π = β E π + γ y + e + 1 y = ρ y + u 1 (6) In his case, i is possible o show ha: γρ π = y + κ e + κ u 1 ρβ (7) Where parameers κ 1 and κ 2 are funcions of he oher parameers in he firs equaion. I is clear from he equaion above ha he persisence of he inflaion variable depends on he degree of persisence of he oupu gap. This is called he inheried inflaion persisence. If we assume e 0, i is also possible o express he inflaion equaion as: π = γπ + κu (8) 1 Again, he inflaion persisence will depend on he persisence of he driving forces of he inflaion process. If we use more complex specificaion like equaion (4), i ges very difficul o ge an analyical soluion for he inflaion equaion. Despie ha, i is possible o ge some indicaion abou he forces behind he inflaion 3 This example is based on Fuhrer (2006). 11

12 persisence by looking a he impac of each variable ha enered ino he Phillips curve equaion, is coefficien and is auocorrelaion. Wih he use of he resuls from able 3 and summary saisics of he variables in able 2, i is difficul o infer he causes of inflaion persisence in Brazil. Excep for exernal price inflaion, he explanaory variables are all highly persisen and have almos he same sandard deviaion. The expeced inflaion variable is he mos persisen variable bu his is clearly a resul of using expeced inflaion for he nex welve monhs on a quarerly basis. The resuls indicae ha more informaion is sill needed for us o have a beer undersanding of he high inflaion persisence in Brazil. 4 Inflaion Persisence in Brazil: Disaggregaed Daa 4.1 Inroducion Aggregae inflaion dynamics depends on he dynamics of disaggregaed inflaion dynamics. Bu his naural resul alone does no help in our ask of undersanding he forces behind inflaion dynamics and paricularly inflaion persisence. Anoher resul of he aggregaion process is ha he persisence of aggregaed daa will have a il owards he mos persisen individual series. Cecchei and Debelle (2006) offer a good explanaion for his resul and also a graphical illusraion of i. Granger (1980) and Zaffaroni (2004) give a more heoreical explanaion abou he consequences of aggregaion of individual series. In hese papers, he imporance of he disribuion of individual persisence parameers is commonly expressed as he individual series being saionary or no having a mass in disribuion a he uni roo poin. 4.2 Inflaion Persisence in Disaggregaed Daa wihou Common Facors In his sub-secion we esimae inflaion persisence for disaggregaed daa. Several papers have demonsraed ha aggregae inflaion persisence is larger han disaggregaed inflaion persisence. We calculae disaggregaed inflaion persisence for 342 producs using IPCA daa during 3Q1999 o 1Q2010. Since 1995 here has been hree changes in IPCA componens: In 1996, in 1999 and The iems in he 1999 and 2006 poll are prey much similar bu he iems in he 1996 poll are very differen and were no included in his analysis. The 1999 poll had 511 iems and he 2006 poll had 384 iems. There are 341 common iems among hese wo samples. Among hese 341 iems, 9 were excluded due o lack of dynamics and unreliable resuls from he auoregressive models used in esimaion. Mos of hese iems are moniored prices where price changes occur seldom and several enries are zeroed. Due o his, he AR(1) or AR(4) models used were no reliable. In order o check for common iems we used he iems coding provided by IBGE. The final sample consiss of 332 inflaion series from 3Q1999 o 1Q2011. The able bellow presens he descripive saisics of he disaggregaed daa. As one can see in such able, he median inflaion is close o he aggregae inflaion (boh weighed, original daa or unweighed) and is much more volaile and presens less auocorrelaion han he aggregae inflaion. Klenow and Krisosov (2008) presen similar resuls for US inflaion daa: In heir sample, he persisence of inflaion is much larger in he aggregae han in he disaggregaed daa. The same resuls were found by Clark (2006) also using daa for US inflaion. 12

13 Table 3: Summary Saisics of Disaggregaed Inflaion Daa Mean Sd Dev Corr(,-1) Agreggae 1,65% 1,12% 0,447 Unweighed Aggregae 1,97% 1,50% 0,252 Minimum -1,92% 0,67% -0,545 Median 1,77% 2,80% 0,072 Maximum 12,06% 50,33% 0,843 In his secion we esimae several simple models of inflaion dynamics (or Phillips curves) by using disaggregaed daa. The objecive of hese esimaions is o undersand he differences in inflaion persisence in differen inflaion groups. This is imporan due o he impac ha highly persisen series can have on he aggregaed daa. Granger (1980), Zaffaroni (2004) and Pesaran (2003) have shown ha under cerain assumpions, he dynamics of he aggregaed daa can be analyzed from he disaggregaed daa. In paricular, by considering a simple AR(1) model for inflaion dynamics in disaggregaed daa, Granger (1980) shows ha he aggregaed daa can presen long memory. This resul was laer refined by Zaffaroni (2004) and Pesaran (2003). We will use some resuls presened in Pesaran (2003) o discuss our disaggregaed resuls and is implicaion for aggregaed inflaion persisence. Debelle and Cecchei (2008) discuss in a much less rigorous way he impac of aggregaion of inflaion series wih differen persisence on aggregaed inflaion dynamics. The general resuls of hese papers can be summarized as follows: a) assuming independence of all disaggregaed inflaion series, he aggregaed inflaion persisence will be deermined by he disribuion of he inflaion persisence of he individual series and b) also depending on he disribuion of he individual series, he aggregaed series can display long memory. The resul expressed in (a) is very inuiive while (b) is no. In boh cases, a bea disribuion is used o characerize he disribuion of he AR(1) parameers for individual series and i is possible o show ha he presence or no of long memory can be inferred from specific parameers of he bea disribuion. The able bellow presens he resuls for several specificaion of he Phillips. In all cases, excep for model 5, we presen he coefficiens for he aggregaed specificaion and also he mean and median coefficiens of he disaggregaed specificaion. We will focus our discussion on models 1, 2 and 5. Each model presens esimaions resuls for individual inflaion iems specificaions as follows: Le π i, be he inflaion rae of produc i a he quarer (one of he 332 producs we are using in his secion as we defined in he beginning of his sub-secion). We esimae produc specific Phillips curves similar o equaions (1) o (4) for each produc i. This can be wrien as: E π, = λ π, 1 + φπ 1, 4 + βπ 1 + γ y 1 + u,, i=1,...,332 (9) i i i + i For each specificaion, we presen he mean and he median of he AR(1) coefficien and also he mean and he median of he individual coefficiens of he oher explanaory variables. The aggregaed row represens he coefficien esimaed by using he aggregaed inflaion daa, boh weighed and unweighed. The resuls are no exacly he same as in able 2 for headline inflaion due o he differen sample periods: In able 2, we esimaed he models using he whole sample (1Q95 o 1Q11) and for disaggregaed daa we are using jus daa from 3Q99 o 1Q11 (his is he daa available for disaggregaed daa). We esimaed he equaions one a once by using a simple rouine wrien o esimae each of he 332 equaions and hen sore he coefficiens in a specific marix. 13

14 The esimaion resuls in model 1 shows ha inflaion persisence in disaggregaed daa is much smaller han in aggregaed daa. This resul is similar o he one repored by Clark (2006) and also Klenow and Krysosov (2005) for US daa. The inclusion of he oupu gap in he inflaion equaion lowers he persisence of inflaion boh in aggregaed daa equaion and in disaggregaed daa. In opposiion o wha happens o inflaion persisence, he impac of he oupu gap is larger in disaggregaed daa han aggregae daa. In model 4 we also add inflaion expecaion and commodiy prices in he inflaion equaion. The resuls indicae a larger role for expeced inflaion han lagged inflaion. The impac of oupu gap is lower han in model 2 and he impac of commodiy prices is small. This low impac of commodiy prices can be considered a puzzle since boh exchange rae movemens and also commodiy prices inflaion are considered relevan variables in inflaion dynamics almos everywhere. In model 5 we included he lagged aggregaed inflaion as an explanaory variable. The reason behind his is quie simple: Indexaion mechanisms are almos always relaed o lagged aggregaed inflaion and i is considered a convenional wisdom ha several indexaion mechanisms are sill in pracice in Brazil no only among moniored or regulaed prices bu also among free prices. The resuls of model 5 conradic his convenional wisdom: Expeced inflaion is more imporan han lagged inflaion as an explanaory variable for disaggregaed inflaion dynamics. E E The esimaed impac of expeced inflaion is lower when we consider π 2, + 4 insead of π 1, + 4. Our inerpreaion o his resuls is ha expeced inflaion incorporaes several price adjusmens announced in advance and also some macro rends or common facors in he sense of Granger (1987) already known o affec inflaion in he nex quarer. In oher words, our measure of expeced inflaion 4 may be a he same ime a driving force of inflaion and a variable ha is being impaced by curren inflaion. If his is rue, his could be an imporan cause of inflaion persisence in Brazil. Neverheless we recognize ha his explanaion is jus enaive and we consider his hypohesis as a direcion for furher research on inflaion persisence in E E Brazil. If we run a regression of he variaion in inflaion expecaion ( π, + 4 π 1, + 4 ) on he variaion of he L L underlying level of inflaion ( π π ), we find regression coefficiens as large as 0.5 by using core inflaion. When using headline inflaion, he impac is lower - close o E E L L, + 4 1, + 4 (0,072) 1 π π = 0,504( π π ) + e (10) 4 This is also he measure commonly used by he Cenral Bank. 14

15 Table 4 Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8* AR(1) Aggregae 0,477 0,505 0,344 0,098 0,438 Unweighed Agg. 0,351 0,370 0,182 0,032 0,232 Disaggr. Mean 0,129 0,118 0,050 0,091 0,030 Disaggr. Median 0,154 0,143 0,041 0,055 0,016 Oupu gap Aggregae 0,099 0,038 0,036 0,059 0,048 0,071 0,058 Unweighed Aggregae 0,209 0,125 0,127 0,155 0,118 0,158 0,144 Disaggregaed Mean 0,161 0,149 0,115 0,139 0,118 0,158 0,144 Disaggregaed Median 0,086 0,042 0,055 0,072 0,067 0,081 0,061 Commodiy Prices Aggregae 0,074 0,066 0,078 0,080 0,046 Unweighed Aggregae 0,096 0,099 0,094 0,098 0,060 Disaggregaed Mean 0,010 0,097 0,094 0,098 0,060 Disaggregaed Median -0,008 0,062 0,058 0,057 0,030 Expeced inflaion (-1) & (-2) Aggregae 0,285 0,318-0,002 0,354-0,071 0,149 Unweighed Aggregae 0,354 0,342 0,076 0,461-0,097 0,151 Disaggregaed Mean 0,314 0,312 0,115 0,461-0,096 0,151 Disaggregaed Median 0,308 0,311 0,179 0,331-0,042 0,113 Lagged Aggreg. Inflaion Aggregae -0,026 0,147-0,020 Unweighed Aggregae -0,080 0,144-0,044 Disaggregaed Mean -0,080 0,144-0,044 Disaggregaed Median -0,010 0,167 0,022 *Idenical o model 7 exceps for he Inclusion of a dummy variable for 4Q02 and 1Q03 The impac of differen weighs is aribued o differen iems in he aggregaion process as fig. 3 shows. There is no correlaion beween he weigh of each iem and is esimaed persisence. The disribuion of inflaion persisence in model 1 is depiced in fig. 4. The disribuion is skewed o he lef wih mean of and median of These values are much lower han he AR(1) coefficien from he aggregaed equaion (close o 0.5). The persisence of unweighed aggregaed inflaion is lower han he persisence of weighed inflaion (he weighed inflaion is curren daa informed by IBGE). In he nex secion we compare his disribuion wih he Bea disribuion and he values upon which a long memory in aggregaed series could arise. The figures 5, 6, 7 and 8 presen he esimaed coefficiens for expeced inflaion, lagged inflaion, oupu gap and he R 2 of each equaion in model 5. The figures jus make i easier o see he impac of each variable in disagreed inflaion dynamics as summarized in able 4. In he appendix we provide more inflaion regarding he mean and median for oher groups of inflaion componens, like he exclusion core inflaion (which excludes foods and moniored prices) and also services inflaion. This is imporan since hese wo groups have been subjec o scruiny by policy makers, marke paricipans and also he press. 15

16 Figure 3: AR(1) Persisence (model 1) x Weigh Figure 4: AR(1) Persisence (Model 1) For each graph we presen he esimaed coefficien in he y axis followed by he group from which he specific produc belongs o. We did no wrie he exac name of he produc because i would be almos impossible for anyone o read i. Therefore, he several bars labeled food are indeed he several producs belonging o he food group in he same order as presened by IBGE in is inflaion (IPCA) releases. For example, he very firs bar represens he coefficiens for rice ( group) and he las bar represens elecommunicaion handse (COMMUNICATION group). Since he communicaion group has only 5 producs, in mos graphs he las label ha appears is EDUCATION. In figure 8 we presene he R 2 for model 6. The explanaory power is lower for disaggregaed daa han for aggregaed inflaion daa. By using model 6, he mean R 2 is jus The resul is very differen from he ones observed by oher auhors using a similar daase for oher counries. For insance, he mean R 2 in Gianoni e al (2010) is jus 0.15 when using a facor model 5 for disaggregaed daa. The R 2 rises close o 0.70 when using aggregaed daa. In Chudik and Pesaran (2011) he esimaed R 2 varies from 0.36 o 0.39 by using an auoregressive model for disaggregaed daa and he esimaed R 2 rises o values beween 0.48 and 0.56 when he auhor includes common facors in he esimaed model. Gianonni e al (2010) use US daa and Chudik and Pesaran (2011) use daa from Germany, France and Ialy. Figure 5: Expeced inflaion coef. (model 6) Figure 6: Lagged inflaion coef. (model 6) 1,0 0,8 0,6 0,4 0,2 0,0-0,2-0,4-0,6-0,8 HOUSING HOMEAPP HOMEAPP HOMEAPP APPAREL APPAREL TRANSPORT TRANSPORT HEALTHCARE HEALTHCARE PERSERVICES PERSERVICES EDUCATION 1,0 0,8 0,6 0,4 0,2 0,0-0,2-0,4-0,6-0,8-1,0 HOUSING HOMEAPP HOMEAPP HOMEAPP APPAREL APPAREL TRANSPORT TRANSPORT HEALTHCARE HEALTHCARE PERSERVICES PERSERVICES EDUCATION 5 The facors are exraced from a large daase of macroeconomic variables. Mos of he variables are economic aciviy indicaors. The nominal ineres rae is also used as a facor. 16

17 Figure 7: Oupu gap coef. (Model 6) Figure 8: R 2 (Model 6) 0,8 0,6 0,4 0,2 0,0-0,2-0,4-0,6 HOUSING HOMEAPP HOMEAPP HOMEAPP APPAREL APPAREL TRANSPORT TRANSPORT HEALTHCARE HEALTHCARE PERSERVICES PERSERVICES EDUCATION 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 HOUSING HOMEAPP HOMEAPP HOMEAPP APPAREL APPAREL TRANSPORT TRANSPORT HEALTHCARE HEALTHCARE PERSERVICES PERSERVICES EDUCATION Figure 9 shows he dispersion of he esimaed coefficien of lagged inflaion and expeced inflaion on disaggregaed inflaion dynamics. There is a clear negaive relaion beween he coefficiens: Iems wih srong response o lagged inflaion presen a low response o expeced inflaion. This resul was somehow expeced: When inflaion is sable, he sum of coefficiens of lagged inflaion and expeced inflaion mus no exceed one in modulus 6. The esimaed impac of inflaion expecaion is usually larger han he impac of lagged inflaion (boh las 12 monhs cumulaed inflaion and he AR(1) coefficien). Among he several differen esimaed equaions, he lagged inflaion coefficien is larger han he esimaed coefficien on expeced inflaion in almos 80 equaions ou of 332. The producs ha show greaer impac of lagged inflaion are evenly disribued across he several inflaion groups. Figure 9: Dispersion of expeced inf. coefficien (X-axis) and lagged inf. coefficien (Y-axis) In almos 40 equaions ou of 332 he sum of coefficiens on lagged inflaion and expeced inflaion exceeds one in modulus. We did no perform any es o check if he sums are saisically differen from one. 17

18 4.3 Inflaion Persisence in Disaggregaed Daa: The Relevance of Common Facors A possible explanaion for he low R 2 of he esimaed equaion in he previous sub-secion is he presence of common facors a he cross-secion of he esimaed model. This problem was firs sudied by Granger (1987). The presence of common facors a he cross secion can explain he exisence of a good fi of saisical models a he aggregae level bu almos no fi a he disaggregaed level. Le us consider a simple dynamic linear model for disaggregaed daa: π = λ π + α η + u (11) i, i i, 1 i i, Where π i, is he inflaion rae in he iem i a he ime inerval and η is he common facor for all iems a. This model is similar o he ones presened previously excep for he inclusion of a common facor η a every cross-secion. There is a large lieraure on esimaion and inference in such kind of specificaion and we will no review he differen approaches and resuls from his lieraure 7. Coakley e al (2002) propose using principal componens echniques o consruc insrumens for η. Pesaran (2006) proposes he average of he disaggregae variable, π π 1 = N i i,, as an insrumen for η. This approach is similar o model 6, model 7 and model 8 in our previous esimaions. The difference is ha we used he lagged (and aggregaed) dependen variable insead of conemporaneous aggregaed variable. We will use he principal componens approach o derive he common facor a he cross-secion of our daa. In order o do so, we will used model 1 and model 5 residuals o esimae he principal componens. In model 1 we incorporaed no macro srucure o each individual inflaion series whereas in model 5 we incorporaed several variables ha could be a proxy for he common facor. This could indicae higher and lower bonds common facors. However, he wo facors are prey much similar o a correlaion close o 0.9. Due o his resul, we will only presen resuls wih he use of he common facor exraced from residuals of model 5. Afer exracing he common facor, we esimae he model again by using he augmened equaion: π = λ π + α f + u (11 ) i, i i, 1 i i, Where f is he common facor exraced from he residuals of model 5. Overall, he inclusion of he common facor does no cause grea changes in he esimaed coefficiens of he model. When we use he common facor ino model 6, he common facor is almos always non-significan and he model resuls do no change much: The esimaed coefficiens on lagged and expeced inflaion are very similar and he R 2 is also similar. When we include he common facor ino model 1, he resuls change bu no much. There is a sensible increase in he R 2 bu his can be explained by he simple srucure of he model and is lack of macroeconomic variables as explanaory variables. The -saisic is larger han wo for several producs indicaing his common facor is significan in mos regressions. 7 Coakley e al (2002) and Chudik and Pesaran (2011) are he mos similar research we found. Pesaran (2006) presens a more heoreical discussion of he subjec. 18

19 4.4 Relaion o long memory models In he las years several papers esimaed long memory models for aggregaed inflaion daa on he grounds of he resuls presened by Granger (1980) 8 : Assuming a simple auoregressive model for disaggregaed daa, he aggregaed daa may presen long memory depending on he disribuion of he auoregressive coefficiens of disaggregaed daa. This resuls is no only applicable o inflaion bu for any aggregaed daa. See Pesaran (2003) and Zaffaroni (2004) for more examples. Le yi represen he value of he y variable observed a ime for i-h individual 9. Thus le us consider ha he dynamics of his variable follows an AR(1) model for all individuals: yi = λi yi, 1 + ui, i=1,2,..., N, =1,2,..., T (12) Therefore, le us assume λ i follows a Bea disribuion of he second ype on he range (0,1): f 2 B( p, q) 2 p 1 2 q 1 ( λ) = λ (1 λ ), 0 λ 1 (13 ) In his case: j B( p + j / 2, q) λ = B( p, q) (14 ) And for a large j: j q λ = ( p + j / 2) (15) N In his case, he aggregaed daa, Y = y / N will presen long memory when 0<q<1. i= 1 i By using he resuls from he previous secion for disaggregaed daa, we could approximae a Bea disribuion for he AR(1) coefficiens as a form o esimae he parameers p and q of he Bea disribuion and check if i is consisen wih long memory models for aggregaed inflaion daa in Brazil. Usually, he long memory hypohesis is esed direcly from he aggregaed daa. In some circumsances, for insance in our small sample of quarerly inflaion daa, his approach can be considered an alernaive o he more radiional ess of long memory in ime series daa. I is clear from figure 4 ha he case proposed iniially by Granger (1980) does no apply o our esimaion resuls. The disribuion of he λ ' s are no resriced o he inerval [0,1] and he Bea disribuion canno be applied. I does no mean ha aggregaed inflaion does no have long memory. The generalizaion of long memory proposiion is no an easy ask and we do no inend o do i in his paper. 8 Pesaran (2003) and Zaffaroni (2004) presen some refinemens of he Granger (1980) resuls. 9 This explanaion for he long memory resul arising from aggregaion is based in Pesaran (2003). 19

20 5 Inflaion Persisence in Emerging Markes In his secion we sudy inflaion persisence in oher developing counries. The sample of counries we use is based in wo aspecs relaed o he hisory of hese counries. Firsly, we include in our sample counries wih a hisory of high inflaion in he recen pas, paricularly in he 90 s. Secondly, we include in our sample counries ha inroduced a clear sraegy o pursue moneary sabiliy, in paricular by using he inflaion arge regime. These counries resemble Brazil and are more prone o show he same problems in dealing wih inflaion cycles and also inflaion expecaions. Therefore, high inflaion can lead o several mechanisms of indexaion similar o he ones observed in Brazil and hus lead o high inflaion persisence. Table 5: Summary Saisics of Emerging Markes Inflaion Headline Inflaion Core Inflaion Mean Sd Dev Corr(,-1) Mean Sd Dev Corr(,-1) Chile 3,8% 1,8% 0,443 2,3% 1,2% 0,337 Czech Republic 4,0% 2,4% 0,174 3,9% 2,6% -0,019 Hungary 8,9% 3,9% 0,643 8,5% 4,0% 0,734 Israel 3,6% 2,5% 0,362 3,3% 2,6% 0,379 Mexico 10,1% 5,5% 0,760 9,6% 5,3% 0,775 Poland 6,4% 3,6% 0,650 6,0% 3,3% 0,869 Turkey 29,3% 12,2% 0,849 29,1% 12,1% 0,913 Souh Africa 5,6% 2,1% 0,592 n.a. n.a. n.a. Colombia 8,7% 4,0% 0,411 5,2% 1,9% 0,045 Peru 4,0% 2,0% 0,565 n.a. n.a. n.a. Brazil 7,3% 2,7% 0,714 7,3% 2,7% 0,714 Mean 8,3% 3,9% 0,560 8,4% 4,0% 0,527 Median 6,4% 2,7% 0,592 6,0% 2,7% 0,714 Source: OECD and auhors calculaion Table 6 presens he resuls for inflaion persisence esimaes for our sample of developing counries. The esimaed inflaion persisence is larger in Brazil han for mos of oher developing counries considered in our sample. Only Poland shows inflaion persisence larger han he one esimaed for Brazil. I is imporan o noice he low inflaion persisence for mos of he counries. This resul seems o indicae ha inflaion persisence is similar for mos of he counries. The difference in inflaion dynamics among emerging counries and developed counries may lie on oher aspecs of he inflaion dynamics and no on persisence. 20

21 Table 6: Inflaion persisence esimaes for emerging markes Headline Inflaion Core Inflaion ξ AR(4) ξ AR(4) Chile 0,151 0,375 0,223 0,295 Czech Republic -0,076 0,174 0,328 0,505 Hungary 0,482 0,508-0,041 0,236 Israel -0,226 0,022 0,226 0,404 Mexico 0,438 0,423 0,488 0,487 Poland 0,543 0,670 0,708 0,650 Turkey 0,393 0,411 0,209 0,198 Souh Africa 0,368 0,448 n.a. n.a. Colombia 0,310 0,412 0,461 0,682 Peru -0,052 0,033 n.a. n.a. Brazil 0,594 0,598 0,681 0,692 Mean 0,266 0,370 0,365 0,461 Median 0,368 0,412 0,328 0,487 Several auhors have used Hansen (1999) boosrap mehod o esimae he mean of he auoregressive coefficiens in dynamic models like he ones we have esimaed so far. The firs reason o use Hansen (1999) is he bias in OLS esimaion. The second reason is o consruc confidence inervals o he esimaed coefficiens. Considering hese reasons we have also used Hansen (1999) mehod for emerging markes inflaion (using his mehod also make i easier o compare our resuls wih hose repored by oher auhors). All models were esimaed including boh a consan and a ime rend. The ime rend is no a dummy variable as in he previous esimaion (resuls from able 6). This makes he resuls no direcly comparable. A possible fuure refinemen of his esimaion would be o reduce he esimaion inerval o exclude he sabilizaion period in mos counries (usually from 1995 o 2000). The consan erm and rend coefficiens were no repored. The complee esimaion resuls are presened in he appendix. In able 7 we repor he resuls of emerging markes esimaes. In figure 10 we show boh coefficiens esimaes for boh emerging and developed counries. Using his alernaive esimaion procedure, inflaion persisence is lower han average in Brazil and no higher as in oher cases. This can be a resul of he esimaed model, which did no allow for srucural break or a dummy rend variable. In many emerging markes, he esimaed 90% confidence inerval for ρ is very large. Again, his can be a resul of he pos sabilizaion period, which could have made he coefficiens unsable in he firs par of our sample. The esimaed confidence inerval for emerging markes is usually larger o he esimaed for developed counries by Levin and Piger (2004): in our 11 counries sample, he average inerval is 0.51while in he Levin and Piger (2004) sample of 12 counries, he average inerval is Using Hansen (1999) mehod, he inflaion persisence is higher for all counries bu Brazil. This resul was expeced since OLS esimaion of auoregressive models are biased downward as expressed by Hansen (1999) among ohers. 21