Forecasting and Monetary Policy Analysis in Low-Income Countries: Food and non-food Inflation in Kenya

Transcription

1 WP/13/61 Forecasing and Moneary Policy Analysis in Low-Income Counries: Food and non-food Inflaion in Kenya Michal Andrle, Andrew Berg, R. Armando Morales, Rafael Porillo and Jan Vlcek

2 2013 Inernaional Moneary Fund WP/ IMF Working Paper Research Deparmen Forecasing and Moneary Policy Analysis in Low-Income Counries: Food and non Food Inflaion in Kenya Michal Andrle, Andrew Berg, R. Armando Morales, Rafael Porillo and Jan Vlcek * Auhorized for disribuion by Andrew Berg March 2013 This Working Paper should no be repored as represening he views of he IMF. The views expressed in his Working Paper are hose of he auhor(s) and do no necessarily represen hose of he IMF, IMF policy or of DFID. Working Papers describe research in progress by he auhor(s) and are published o elici commens and o furher debae. Absrac We develop a semi-srucural new-keynesian open-economy model, wih separae food and nonfood inflaion dynamics, for forecasing and moneary policy analysis in low-income counries and apply i o Kenya. We use he model o run several policy-relevan exercises. Firs, we filer inernaional and Kenyan daa (on oupu, inflaion and is componens, exchange raes and ineres raes) o recover a model-based decomposiion of mos variables ino rends (or poenial values) and emporary movemens (or gaps) including for he inernaional and domesic relaive price of food. Second, we use he filraion exercise o recover he sequence of domesic and foreign macroeconomic shocks ha accoun for business cycle dynamics in Kenya over he las few years, wih a special emphasis on he various facors (inernaional food prices, moneary policy) driving inflaion. Third, we perform an ou-of-sample forecas o idenify where he economy and herefore policy was likely headed given he inflaionary pressures a he end of our sample (2011Q2). We find ha while impored food price shocks have been an imporan source of inflaion, boh in 2008 and more recenly, accommodaing moneary policy has also played a role, mos noably hrough is effec on he nominal exchange rae. The model correcly prediced ha a policy ighening was required, alhough he acual ineres rae increase was larger. We discuss implicaions for he use of model-based policy analysis in low income counries. JEL Classificaion Numbers: E52, E58, F47, O23 Keywords: Moneary Policy, Forecasing, Food Prices, Kenya, Low-Income Counries Auhor s Address: mandrle@imf.org ; aberg@imf.org ; amorales@imf.org ; rporillo@imf.org ; janvlcekacz@gmail.com * The Inernaional Moneary Fund and OGResearch. mandrle@imf.org; aberg@imf.org; amorales@imf.org; rporillo@imf.org; janvlcekacz@gmail.com. We hank Enrico Berkes for ousanding research assisance. Will Clark also conribued. This working paper is par of a research projec on macroeconomic policy in low-income counries suppored by he U.K. s Deparmen for Inernaional Developmen. All errors remain ours.

3 2 Conens Page I. Inroducion... 4 II. Kenya: Inflaion Developmens and Moneary Policy III. The Model A. Price Indices and Relaive Prices B. Trends in Relaive Prices C. Oupu and Real Ineres Raes D. Philips Curves E. Exchange rae (UIP) F. Moneary policy rule G. Foreign Block IV. Applying he model for policy analysis in Kenya A. Calibraion and Daa B. Impulse Response Analysis C. Filering Kenyan Daa Through he Model D. A Model Based Inerpreaion of Recen Hisory The Period The Period V. Applying he model for macro forecasing in Kenya A. In sample forecasing properies B. Ou of-sample forecasing VI. Discussion VII. Conclusion VIII. References IX. Appendixes Appendix I. Deriving Phillips Curves from Micro Foundaions Appendix II. Daa Series Appendix III. Solving and Using he Model Solving and Simulaing he Model Kalman filer & Smooher... 37

4 3 X. Tables Table 1. Calibraion Table 2. Calibraion (coninued) Table 3. Calibraion (coninued) Table 4. In-sample model forecass (MF) vs. random walk (RW), RMSE raios XI. Figures Figure 1. Food and Non food Inflaion, Kenya Figure 2. Domesic and Inernaional Food Prices (in US$) Figure 3. Shor Term Ineres Raes, Kenya Figure 4. Impulse Response Funcions, = Figure 5. Impulse Response Funcions, = Figure 6. Impulse Response Funcions, = Figure 7. Impulse Response Funcions, = Figure 8. Trend/Gap Decomposiion, Relaive Prices Figure 9. Trend/Gap Decomposiion, GDP Figure 10. Trend/Gap Decomposiion, Real Ineres Raes Figure 11. Shock Decomposiion, Oupu Gap Figure 12. Shock Decomposiion, Non-Food Inflaion Figure 13. Shock Decomposiion, Food Inflaion Figure 14. Shock Decomposiion, Headline Inflaion Figure 15. Shock Decomposiion, Nominal Depreciaion Figure 16. Real Marginal Coss Decomposiion Food Price Inflaion Figure 17. Cenral Bank Rae Repo Raes Figure 18. Impulse Response Funcions, Global Food Crisis Figure 19. Condiioned hisorical simulaions, Seleced Variables Figure 20. Model Forecas versus Acual Daa... 62

5 4 I. INTRODUCTION Cenral banks in many sub-saharan African (SSA) counries find hemselves a a crossroads. During he firs half of he 2000s, SSA counries succeeded in re-anchoring inflaionary expecaions, reducing median inflaion in he region from 15 percen in 2000 o 6 percen in In he conex of fiscal based sabilizaion effors, many SSA counries adoped policy regimes cenered on arges for reserve and broad money and considerable managemen of he exchange rae. 2 While de faco flexibiliy was and has always been he norm money arges are frequenly missed in eiher direcion he adopion of such arges was mean o signal ha he cenral bank was holding he line, i.e., ha sabilizaion effors were on rack and ha fiscal pressures on moneary policy were conained. More recenly however, he region has been buffeed by large exernal shocks, saring wih he firs food and fuel crisis of , spillovers from he global financial crisis in and he laes spike in commodiy prices. These shocks have resuled in large swings in inflaion. 3 In some cases he moneary policy response has been erraic. 4 More generally here has been an acknowledgemen among policy makers ha exising regimes wih heir almos exclusive emphasis on money arges and arge misses have no provided a useful framework for hinking abou hese shocks, heir effecs on inflaion and he economy, and he role of policy decisions in offseing or amplifying hem. In addiion, oher facors srucural changes ha enhance he role of marke signals, increasing insabiliy in money demand, greaer exposure o inernaional capial flows have also called ino quesion he adequacy of exising regimes. In ligh of hese challenges, some cenral banks in he region have moved o, or have announced he adopion of, inflaion forecas argeing (IFT), a forward looking regime in which he inflaion forecas is he inermediae arge of policy, and a shor erm ineres rae ofen serves as he operaional arge. 5 Under his regime, cenral bank effors are focused on undersanding (and explaining o he public) why inflaion may currenly deviae from he arge, and deermining wha policy decisions may be necessary o bring he inflaion forecas back in line. While oher SSA cenral banks are no planning o formally adop IFT in he immediae fuure, many are ineresed in adoping cerain elemens of inflaion argeing. One such elemen is he developmen of in house forecasing and policy analysis sysems (FPAS). IFT cenral banks make ample use of hese frameworks o discipline heir policy analysis. Specifically, he FPAS framework: (i) collecs and helps organize high frequency daa; (ii) uses a simple quarerly projecion model of he economy ha incorporaes policymakers views abou he ransmission mechanism and he relevan shocks; and (iii) 2 See IMF (2008). 3 See World Economic Oulook Fall 2011, Chaper 3. 4 See Benes and ohers (2012) for a discussion of Zambia s moneary policy responses during he crisis. 5 Wih he excepion of Souh Africa, Ghana was he firs SSA counry o formally adop inflaion argeing in The Bank of Uganda has also recenly announced he adopion of an Inflaion Targeing Lie regime.

6 5 helps develop a consisen, model based macroeconomic forecas, including wih measures of uncerainy and alernaive scenarios. 6 The purpose of his paper (and is companion piece) is o provide a blueprin of an FPAS for low income counries (LICs), wih an applicaion o Kenya. In his paper we exend exising frameworks o include an explici role for food prices, in ligh of he imporance of hese shocks in recen years. In he companion paper we hen incorporae moneary aggregaes and money arges in he analysis, wih an eye on hose counries where money arges may coninue o play some role in he policy framework. The papers inended audience is all hose concerned wih he analysis of moneary policy in low income counries, especially economiss working in he modelling division of cenral banks in sub-saharan Africa. The papers are no mean o cover he enire range of exercises and analyses ha can be underaken wih such frameworks, bu raher o zoom in on some ha are relevan for he Kenyan case. Exising FPAS frameworks are based on new Keynesian open economy models, which embody he fairly general view ha aggregae demand and moneary policy maer for oupu dynamics in he shor run. Unlike heir Keynesian predecessors, hese models are buil on micro foundaions and raional expecaions. 7 A heir core, hey consis of a forward looking IS equaion, a hybrid Phillips curve, a moneary policy rule and an uncovered ineres pariy equaion. 8 An imporan feaure of hese models is he emphasis on gaps in oupu and he real exchange rae deviaions beween observed values and rend or poenial componens as drivers of inflaion. Considerable effor herefore goes oward disinguishing gaps from rend. We exend he sandard framework by inroducing wo separae Phillips curves, one for food and one for non food. The disaggregaion requires ha special aenion be paid o various relaive food prices: boh he domesic and he inernaional relaive price as well as he deviaion beween he wo. I also calls for a careful reamen of rends in hese relaive prices, which we explicily underake here, for wo reasons. Firs, rends in relaive prices have implicaions for he consisency beween secoral inflaion raes and he inflaion arge (oward which headline inflaion evenually converges). Second, deviaions beween relaive prices and heir rend becomes an imporan source of inflaionary pressures, boh secorally and in he aggregae, as hese gaps ener he Phillips curves direcly. The Kenyan case is represenaive of he challenges SSA counries have faced in recen years. As figure 1 indicaes, Kenya experienced large swings in inflaion, firs increasing o 16 percen in mid 2008, falling back o under 4 percen in mid 2010, only o increase again o almos 20 percen a he end of While movemens in inernaional food prices accoun for some of hese flucuaions, moneary policy may have also played a role, wih shor erm 6 For a horough discussion of he pracical implemenaion of FPAS frameworks in IFT cenral banks, see Laxon and ohers (2009). 7 See Clarida, Gali and Gerler (1998) and Gali and Monacelli (2002), among many ohers. 8 See Berg, Karam and Laxon (2006) for an overview of he sandard FPAS model

7 6 ineres raes falling from 6 percen in 2009 o abou 1 percen by early Disenangling he role of exernal facors versus he conribuion of moneary policy decisions (and oher domesic facors) is an imporan ask of moneary policy analysis, a ask our FPAS is suied o address. We use he framework o run a number of exercises. Firs, we filer seleced macroeconomic daa from Kenya hrough he model, in order o recover a model based decomposiion of mos series ino gap and poenial/rend componens. The filraion exercise also serves o recover he sequence of macroeconomic shocks ha, according o he srucure of he model and our own view of recen hisory, accoun for business cycle dynamics over he las few years. This allows us o discuss he quaniaive significance of various facors (inernaional shocks, moneary policy) in explaining inflaion developmens. This process is ieraive: as we have a prior opinion on he relaive imporance of various shocks, we repea he filraion o adjus he calibraion of he model unil a consisen view of he economy emerges; his ieraion also helps us adjus our own views in ligh of he empirical evidence. Second, we assess he performance of he model wih in sample hisorical forecass and he analysis of impulse response funcions. Finally, saring from where our daa ends (3rd quarer 2011), we perform an ou of sample forecas o idenify where he economy and herefore policy was likely headed given he inflaionary pressures a he ime. Our resuls are he following. Firs, no surprisingly, we find ha impored food shocks have accouned for some of he inflaion dynamics in Kenya, boh in 2008 bu also recenly. Domesic food shocks (harves shocks) were also relevan. We also find ha accommodaive moneary policy played an imporan role, boh in and recenly. In , he CB experienced good luck : domesic inflaionary pressures were compensaed by disinflaionary forces associaed wih he global recession, wihou a need for ighening. The 2011 inflaionary spike was differen in ha such forces were no presen. Ineresingly, our exercise indicaed ha shor erm ineres raes needed o increase, i.e., policy needed o be ighened o offse hese inflaionary pressures, which is exacly wha he cenral bank of Kenya (CBK) implemened by he end of The coincidence beween he laer response and he model s forecas validaes he use of he model for policy analysis in LICs. We acknowledge ha he exension of FPAS ype frameworks o low income counries is no unconroversial. I is someimes argued ha such counries lack: adequae financial marke developmen, sufficienly srong (or well undersood) moneary policy ransmission channels, and various insiuional prerequisies, as well as he requisie inflaion forecasing abiliy. These shorcomings, according o his view, would invalidae he applicaion of an FPAS ype framework o LICs, and more generally would call ino quesion he overall effeciveness of moneary policy in sabilizing aggregae demand ha is implici in such frameworks. We believe ha here is sill a lo o learn abou he moneary ransmission mechanism in LICs, bu also ha here is a lo o gain by applying sandard FPAS frameworks o LICs, once hese are suiably calibraed o reflec he relaive srengh of various ransmission channels and exended o include LIC specific shocks. The abiliy o use such a model o provide a coheren sory abou he sae of he Kenyan economy and signal he direcion of ineres

8 7 rae changes validaes our claim. More generally, our experience wih Kenya demonsraes ha he above challenges represen opporuniies o sharpen he analysis and formulaion of policy raher han reasons o avoid rying. Our paper is organized as follows. Secion II presens an overview of recen developmens in he Kenyan economy. Secion III inroduces he model. Secion IV presens resuls from he filering exercise, while Secion V discusses forecasing. Secion VI discusses some possible reasons behind he moneary policy response in recen years and draws some policy lessons for moneary policy in LICs. Secion VII concludes. II. KENYA: INFLATION DEVELOPMENTS AND MONETARY POLICY In his secion we provide a brief overview of Kenya s economy, is recen inflaion hisory and moneary policy developmens. Kenya is he fourh larges economy in Sub-Saharan Africa (SSA) and he sixh mos populaed counry, wih esimaed 40 million inhabians, and a GDP per-capia of US$ 1,700 as of 2011 (in PPP erms). Growh has averaged abou 5 percen over he las decade; hough i slowed during he global financial crisis. Kenya sands ou for is services secor, mos noably financial services and elecommunicaions (wih a conribuion o GDP of above 60 percen), and for is widespread use of mobile phone based paymen ransfers. 75 percen of he populaion relies on agriculure for food and income (a large share of which a subsisence levels), which also accouns for percen of oal expors (ea, coffee and horiculure). The rade balance has been in defici over he las few years, wih remiances, foreign direc invesmen, and official flows providing he bulk of he financing. Porfolio inflows have been increasing over ime, mosly o he sock marke (banks, elecommunicaions and energy), hough wih a noable slowdown during he global crisis. Kenya s de jure moneary policy anchor has radiionally been reserve money argeing, alhough arges on ne domesic asses have become more prominen recenly (in he conex of an IMF program), and he cenral bank has been paying increasing aenion o shor erm ineres raes. The counry mainains a managed floa, wih foreign exchange rae operaions, reflecing in par he role of he CBK as banker o he governmen and he magniude of official FX flows, providing mos of he liquidiy injecions in recen years. I is difficul o idenify inervenions designed specifically o influence he exchange rae, wih considerable volailiy in he laer variable. On he fiscal fron, he governmen s deb lies a abou 45 percen of GDP, despie no having benefied from deb relief as mos counries in he region. Insead, abou half of he governmen deb is in domesic currency, hanks o he rapid developmen of he governmen securiies marke. The fiscal defici has hovered a around 5 percen of GDP in recen years bu is consisen wih he governmen s medium erm deb sraegy, suppored by ax revenue equivalen o abou 20 percen of GDP (among he highes in SSA).

9 8 Kenya has experienced large swings in inflaion in recen years. Headline inflaion acceleraed from around 3 percen a he beginning of 2007 o 16 percen by mid 2008, and afer having fully reversed by mid 2010, climbed again o almos 20 percen by end Inflaion dynamics were accouned for by boh food and non food (see Figure 1). Alhough Kenya s share of food in he consumer baske is somewha below he average for low-income counries (38 vs. 50 percen respecively), i is exposed o changes in impored food prices: 40 percen of he oal cereal consumpion (of abou 5 million meric ons, chiefly maize) is impored. This influence can be seen by comparing he Kenyan food price index (measured in dollars) wih a price index of inernaional food commodiy prices (see Figure 2): he wo series display considerable comovemen, especially during he food crisis. 9 Policy challenges were compounded by domesic shocks and he downurn of he global economy in he period , among hem: A poliical crisis ha followed he December 2007 general elecions, resuling in major economic disrupions. During he crisis, over 1,000 people were killed and more han 350,000 (abou 1 percen of he populaion) were displaced. Poliical insabiliy ook a oll on economic aciviy and exacerbaed inflaionary pressures in early A drough in he las monhs of 2008 ha aggravaed he decline in maize producion and increased food insecuriy defined as he size of he populaion ha does no have access o or canno afford sufficien food by abou 47 percen. The governmen declared a food emergency for an esimaed 10 million Kenyans. The significan impac of sharp oil price flucuaions on domesic prices for an oil imporer like Kenya. The impac of he global financial crisis ha iniially dampened Kenya s exernal demand, curailing expor growh, ourism receips, remiances and privae capial flows. Official foreign exchange reserves fell by almos US$ 800 million (abou 20 percen of he sock of reserves) beween mid-2008 and early 2009, and Kenya had o borrow from he IMF Exogenous Shock Faciliy. I is difficul o characerize he CBKs de faco moneary policy framework. I mainained an inflaion arge of 5 +/- 2 percen. 10 In erms of insrumens, i injeced liquidiy hrough foreign exchange purchases and also conduced open marke operaions. Is reserve money arges have ofen been missed and subsequenly adjused, so ha hey in hemselves have no dicaed moneary policy. 11 From 2009 hrough 2011, reserve growh was consisenly higher 9 Coinegraion beween he wo series is rejeced. Regressing he Kenyan index on he inernaional one (in firs differences) generaes a pass hrough coefficien of Under he Cenral Bank of Kenya Ac, he Miniser of Finance ses he price sabiliy arges of he Governmen. In pracice, he arge is se in coordinaion beween he Minisry of Finance and he CBK. 11 For he purposes of he ongoing Exended Credi Faciliy (ECF) program wih he IMF (in place since January 2011), he CBK also ses a ceiling on ne domesic asses (NDA) and a floor for ne inernaional reserves (NIR). There is an implied indicaive arge for reserve money.

10 9 han argeed, explained by he CBK in erms of is objecive of increasing financial inermediaion (hrough higher broad money growh) and hus supporing economic aciviy. The effeciveness, or a leas ransparency, of moneary policy was hampered by he operaional framework in place. The CBK mainained a so-called policy rae mean o signal he sance of policy. This rae was he Cenral Bank Rae or CBR, a which i sood ready o lend o banks overnigh wihin is sanding faciliy program. In pracice he rae was no relevan for he financial sysem: sizeable injecions of liquidiy resuled in a large decline in inerbank raes, which fell o 1 percen while he CBR sood a 6 percen. Moreover he CBK employed repo and reverse repo operaions o manage liquidiy, wih he raes associaed wih hese operaions delinked o he CBR and moving in line wih he inerbank rae. Inflaion sared o accelerae significanly in 2011, reaching almos 19 percen in November. The Shilling depreciaed by 15 percen in he six monhs hrough November 2011 as inflaion expecaions deerioraed. In response o hese developmens, he CBK reduced foreign exchange purchases and suspended he provision of liquidiy hrough reverse repos. As inerbank raes sared o spike up (see Figure 3), commercial banks began o exploi arbirage opporuniies from he expeced depreciaion by borrowing from he CBK s overnigh discoun window and building up foreign exchange posiions. In an effor o sem he incipien crisis, he CBK raised he CBR hrough he second half of 2011 and evenually resriced he use of he discoun faciliy, bu wihou a clear communicaion sraegy, which resuled in even larger increases in he inerbank rae. Facing his insabiliy, and he increase in inflaion, he CBK modified is operaional framework in Sepember 2011, wih a view o making he CBR useful as a signal of policy. I increased he CBR o 18 percen by December 2011 from 6.25 in Sepember. In addiion, he CBR became he pivo rae for boh repos and reverse repos; i.e., hese operaions would ake place a he CBR rae plus or minus a margin. The overnigh rae was se a he CBR rae plus 600 basis poins, o eliminae is role as a regular source of funding. Since his reform and policy shif, inflaion has been declining seadily, hough i remains above he 5 percen arge, sanding a 13 percen as of April In sum, Kenya fis he descripion of many SSA cenral banks in IMF (2008): i pursued an inflaion objecive in he conex of a managed floa, bu wih a variey of insrumens and inermediae arges, including some uneven aenion o moneary aggregaes. In his paper we choose o simplify by characerizing he sance of policy in erms of a single ineres rae. For mos of he period, his rae is based on he raes a which open marke operaions for liquidiy provision or wihdrawal were acually underaken (he repo or reverse repo raes). For he mos recen period, he CBR serves as an appropriae indicaor of he policy sance in erms of ineres raes. In a companion paper, we explore he role of money aggregae arges explicily. Such an analysis may shed ligh on some of he policy developmens during he period under sudy. However, our undersanding is ha he CBK auhoriies and marke paricipans now generally undersand he policy sance in erms of he CBR. Given he objecive of his paper of providing a pracical framework for policy analysis going forward, and he fac ha our applicaion of his approach has no revealed major gaps requiring he inclusion of money, we have been saisfied wih his approach.

11 10 III. THE MODEL In his secion we describe all he equaions of he model, i.e., hose ha describe he ineracion of gap erms (business cycle movemens) and hose ha describe movemens in poenial values or rends. In erms of general noaion, for any given variable x a bar (x) denoes ha variable s rend or poenial value. A gap erm added o he variable (xgap) denoes deviaion from rend or poenial. A dela ( ) in fron of he variable indicaes changes from one period o he nex, excep for inflaion raes which are denoed wih a π. Finally, an aserisk denoes a foreign variable. Before presening he model i is useful o briefly menion is properies. The model is srucural, in ha each equaion has economic inerpreaion, and general equilibrium, in ha he model s equaions joinly deermine he dynamics of inflaion, oupu, shor erm ineres raes and he real exchange rae. I is also sochasic: he sysem of equaions is subjec o various shocks, he variance of which can help derive measures of uncerainy in he baseline forecas. Expecaions of fuure variables maer for macroeconomic oucomes and are raional, in he sense ha hey depend on he model s own forecas. Despie hese somewha complex feaures, he core economics embedded in he model are simple: aggregae demand and moneary policy maer for inflaion. One addiional commen abou he gap/rend decomposiion. Jus like he new-keynesian models on which hey are based, FPAS models emphasize oupu and real exchange rae gaps as drivers of inflaion. However, unlike more srucural/dsge ype models, FPAS frameworks are agnosic abou he srucural origin and comovemen properies of real rends. As will be shown below he descripion of rends is limied o he specificaion of auoregressive processes, based on long run properies of he daa, which grealy simplifies he applicaion of he model. A. Price Indices and Relaive Prices We begin by defining price indices and various relaive prices. Firs, he headline price index (p cpi, all prices are in logs) is he weighed sum of food (p f ) and non food prices (p nf ): π cpi p cpi = 4(p cpi = wp f + (1 w)p nf, p cpi 1) = wπ f + (1 w)π nf, π 4,cpi = p cpi p cpi 4, where w is he weigh of food, π is he quarerly inflaion rae (annualized) and π 4 is he year on year inflaion rae.

12 11 The firs relaive price is he domesic price of food relaive o non food: rlp = p f p nf. The second relaive price is he domesic price of food relaive o he inernaional price of food measured in local currency: ( ) dev = p f p f + s, where p f is he inernaional price of food (in dollars) and s is he nominal exchange rae (shillings per dollars). dev measures he exen of he deviaion beween domesic and foreign food prices. As will be show laer, wheher his deviaion creaes pressures for domesic food price inflaion in order o cach up wih inernaional prices depends on wheher he deviaion reflecs emporary or long erm facors. The hird relaive price is he inernaional price of food relaive o he inernaional CPI (p cpi ): rlp = p f p cpi. The fourh relaive price is he real exchange rae, which is given by he inernaional CPI (measured in domesic currency) minus he domesic CPI: z = s + p cpi p cpi. Noe ha, by consrucion, all four relaive prices are relaed, as follows: z = (1 w)rlp rlp dev. The above relaion also holds specifically for he gaps and rend componens of hese relaive prices. For reasons ha will become clear laer, we also define wo alernaive real exchange rae measures, a food and a non food real exchange rae. Each of hese relaive prices can also be derived using z and rlp : z f = s + p cpi p f = z (1 w)rlp. z nf = s + p cpi p nf = z + wrlp. B. Trends in Relaive Prices All relaive prices are decomposed ino gap and rend componens: x = xgap + x, for x = rlp, rlp, dev, z, z f, z nf. We only need o define sochasic processes for hree relaive price rends, as rends for he oher relaive prices will follow from he above relaions. We assume firs order

13 12 auoregressive processes in firs (annualized) differences for he domesic relaive price of food (rlp), he inernaional relaive price of food (rlp ) and he real exchange rae (z): rlp = θ rlp rlp 1 + (1 θ rlp ) rlp + ε rlp. rlp = θ rlp rlp 1 + (1 θ rlp ) rlp + ε rlp. z = θ z z 1 + (1 θ z ) z + ε z. The above specificaion meris wo commens. Firs, he rend value of dev (dev ) will drif, as implied by he sochasic rends of rlp, rlp and z. This drif implies he long run value of domesic food prices is unrelaed o he long run value of inernaional food prices: rend changes in inernaional relaive food prices rlp will simply resul in an equal and offseing increase in dev, wihou any implicaion for rend changes in domesic relaive food prices rlp. This is a sronger assumpion han lack of coinegraion. While his disconnec may seem exreme, i only applies o long run movemens in relaive prices and no o gap movemens, which as we will see accoun for much of he dynamics in inernaional food prices in he las few years. As will be shown below, i is also based on he observed rend movemens in dev. Second, he exisence of relaive price rends has implicaions for he inflaion raes of cerain price indices, even if he inflaion rae for he headline index is (evenually) deermined by he inflaion objecive. As he relaive price of food is eiher growing or decaying along a sochasic rend (depending on he sign of rlp ), nominal food prices will end o grow a a differen rae han non food prices. Specifically, for any ime varying inflaion objecive π, implici arges for food and non food inflaion mus be as follows: π f = π + (1 w) rlp, π nf = π w rlp. In addiion, he long run (annualized) nominal rae of depreciaion mus be consisen wih he process for rend real exchange raes and domesic and foreign inflaion arges: s = z + π π. C. Oupu and Real Ineres Raes Quarerly (non agriculural) oupu is divided ino is gap and poenial componens, y = y + ygap, where poenial oupu follows a random walk wih ime varying drif g : y = g + ε y, g = τ g g + (1 τ g ) g 1 + ε g. Thus here can be boh i.i.d. and persisen shocks o he growh rae, which allows for more flexibiliy in maching he daa. The oupu gap is given by a hybrid IS curve. I depends on

14 13 real moneary condiions (rmc) and foreign demand (ygap ), as well as pas and fuure oupu gaps: ygap = β 1 ygap 1 + β 2 E (ygap +1 ) β 3 rmc 1 + β 5 ygap + ε ygap. Real moneary condiions are composed of he real ineres rae gap (rrgap) he difference beween acual real ineres raes ( rs E (π+1) ) cpi and neural real ineres raes (rr ) and he real exchange rae gap: rmc = (1 β 4 )rrgap + β 4 ( zgap ). Noe ha neural raes follow an AR(1) process: rr = ρ rr rr 1 + (1 ρ rr )rr + ε rr. D. Philips Curves We inroduce wo Philips curve, one for non food prices and one for food prices. As described in Appendix A, boh can be derived from micro foundaions. The non food Philips curve is of he form: π nf π nf where and = λ 1 (E (π+1) π nf nf )+(1 λ 1 λ 2 ) (π nf π imp 1 π nf )+λ 2 (π imp = π cpi + s, π imp = π cpi + s rmc nf = λ 4 ygap + (1 λ 4 )z nf gap, nf, πimp )+λ 3 rmc nf This specificaion allows emporary changes in impored inflaion o have a direc effec on non food inflaion, as capured by he erm λ 2 (π imp nf, πimp ). I also makes non food inflaion sensiive o expeced fuure and lagged changes of iself, as well as changes in real marginal coss in he non food secor (rmc nf ). These are given by a weighed sum of he domesic oupu gap and he real exchange rae gap in erms of food prices. 12 The Philips curve for food prices has a similar srucure: +ε πnf, π f π f = b 1 (E (π+1) f π f ) + (1 b 1 b 2 ) (π f 1 π f ) + b 2 (π imp π imp ) + b 3 rmc f + ε πf, where rmc f = (1 b 4 b 5 ) ygap + b 4 z f gap b 5 devgap. 12 As shown in he appendix, his specificaion can be derived from microfoundaions by assuming ha he producion of non food requires a domesic inpu, e.g., labor, and impored goods. In his case, changes in he domesic cos of producion are capured by changes in he oupu gap, while changes in he impored cos are represened by he real exchange rae gap. Noe ha, in wo secor models, wha is inflaionary in each secor is no he real exchange rae gap per se bu he cos of impored goods relaive o prices in ha secor, which is why z nf gap eners he equaion and no zgap.

15 14 In addiion o poenially differen calibraions, he main difference relaive o non food inflaion is ha real marginal coss also depend on emporary deviaions beween domesic and inernaional food prices (devgap ). This exra erm implies ha emporary increases in inernaional food prices will be inflaionary, as hey open a gap relaive o domesic food prices ha will be closed (in par) by increases in domesic food prices. 13 E. Exchange rae (UIP) We assume ha uncovered ineres pariy (UIP) holds: 4(zgap zgap e ) = (rrgap rrgap ) + prem + ε s, where prem measures persisen movemens in he risk premium associaed wih holding domesic currency, which follows an AR(1) process wih coefficien ρ prem, and ε s measure one ime errors in exchange rae valuaion. Real exchange rae expecaions are allowed o deviae emporarily from raional expecaions: zgap e = ϕe (zgap +1 ) + (1 ϕ)zgap 1. F. Moneary policy rule We assume ha he cenral bank moves he ineres rae in response o endogenous developmens in he economy, as follows: [ ( ) ] rs = γ 1 rs 1 + (1 γ 1 ) rr + π +1 + γ 2 π 4,cpi +4 π cpi +4 + γ3 ygap + γ 4 sgap + ε rs. The cenral bank also specifies a sochasic process for is inflaion arge: π = ρ π π 1 + (1 ρ π )π + ε π. While his specificaion may appear surprising why would he cenral bank subjec is inflaion arge o persisen flucuaions? i is mean o capure relaively low frequency movemens in inflaion. These movemens end o reflec changes in he cenral bank s willingness o olerae cerain levels of inflaion and have been proven o capure an imporan elemen of inflaion dynamics in developed and emerging markes As proved in he appendix, his addiional erm is microfounded by assuming ha he producion of he domesic food baske also requires impored food, in addiion o domesic labor and impored non food iems. 14 See Smes and Wouers (2003) and Ireland (2007), among ohers.

16 15 G. Foreign Block The dynamics of he model are complee wih he he foreign block, a se of six equaions ha describes he comovemen of exernal variables: ygap = β 1ygap 1 + β 2ygap +1 β 3rrgap 1 + ε ygap, π cpi = λ 1π cpi +1 + (1 λ 1) π cpi rs = γ 1rs 1 + (1 γ 1) [ rr + π + γ λ 2ygap + ε π ( π 4, cpi +4 π cpi) + γ3ygap rlpgap = ρ f rlpgap 1 + ε rlp, rr = ρ rr rr 1 + (1 ρ rr ) rr + ε rr,, ] + ε RS, and he process for he rend in he inernaional relaive price of food described earlier. Noe ha inernaional food inflaion is given by π f = π cpi + rlp. IV. APPLYING THE MODEL FOR POLICY ANALYSIS IN KENYA Having described he model, we now presen various model based exercises for Kenya. We begin by describing he calibraion and our daa se. We hen provide impulse response funcions for seleced shocks. We describe he filraion exercise, wih an emphasis on wo relaed issues: he decomposiion of macro variables ino heir rend and gap componens, and he hisorical decomposiion of recen business cycle dynamics in Kenya by he relevan shocks. A. Calibraion and Daa Calibraion We presen he calibraion in ables 1-3. Our choice is guided by he following principles. Firs, some of he parameers of he model (average growh raes of relaive prices and oupu, real ineres raes, average inflaion arge) reflec Kenyan averages or, in he case of he inflaion arge, he explici objecive of he cenral bank. Oher parameers reflec our views abou srucural feaures of he Kenyan economy. In he IS curve, he relaively large backward looking erm and small forward looking erm reflec our view ha expecaions of fuure developmens play a relaively small role in oupu dynamics. The small sensiiviy of oupu o ineres raes (given by β 3 (1 β 4 ) = 0.06) is consisen wih he view ha he ineres rae channel is likely o be small in LICs (see Prachi and ohers (2011)), while he relaive imporance of he real exchange rae gap in rmc indicaes he exchange rae channel is relaively sronger. In he case of he wo Phillips curves, non food inflaion is more sensiive o he oupu gap, wih he sensiiviy given by λ 3 λ 4 = 0.1, han food inflaion, wih he sensiiviy given by

17 16 b 3 (1 b 4 b 5 ) = The same holds regarding sensiiviy o he real exchange rae: i equals λ 3 (1 λ 4 ) = 0.1 in he non food secor bu only b 3 b 4 = 0.04 in he food secor. On he oher hand, food inflaion is quie sensiive o emporary gaps beween inernaional and domesic food prices (devgap ): a 1 percen widening of he gap ignoring expecaions of fuure values of devgap resuls in an immediae 0.07 percen increase in food prices. The effec is wice as large (0.13) once expecaions abou fuure gaps are incorporaed ino curren prices. The calibraion of he moneary policy rule is relaively dovish, wih large smoohing of ineres raes and a relaively small response o increases in expeced inflaion. The calibraion also allows for some response o nominal exchange rae movemens (an imporan issue in LICs) bu no response o he oupu gap. The calibraion for he res of he world is aken from applicaions of similar gap models o he US economy. Finally, he las se of parameers are calibraed based on he model s abiliy o deliver plausible inerpreaions of recen macro dynamics. The parameers ha fall in his caegory are primarily he AR coefficiens of mos exogenous variables, as well as he variances of he shocks which are lised in Table 3. As is explained in he appendix, he filraion exercise depends on he relaive variance of he shocks, since here are more shocks han observables, so he choice of hese as well as he AR coefficiens help deermine he model s accoun of Kenya s business cycle. For example, if shocks o he rend real exchange rae are considerably more volaile han emporary shocks o he risk premium, hen he model will inerpre mos movemens in he real exchange rae as reflecing rend movemens raher han gap movemens. To pin down hese parameer values, we sar wih an iniial calibraion, assess he model based decomposiion of he daa, and ierae unil he model based sory looks plausible. 15 Daa The daa is described in appendix II. The daa is of mixed frequency, and goes from he beginning of 2000 o Two series are worh discussing in some deail. The shor erm ineres rae used in he model monhly series, averaged ino quarers differs from he CBK policy rae, since he laer did no reflec he rue sance of moneary policy for reasons discussed in Secion II. Insead, we choose he rae ha bes capures he policy sance. From 2000:1 o 2009:1, and from 20011:5 o 2011:6, we use he repo rae as he cenral bank was mainly wihdrawing liquidiy from he money marke. From 2009:3 o 2011:4 we use he reverse repo rae since he cenral bank was mainly injecing liquidiy. In 2009:2 we used he average of he wo as he cenral bank was engaging in boh operaions hrough he monh. 15 I is feasible o esimae he model hrough Bayesian mehods (as for example in Berg, Porillo, and Unsal (2010) for a similar model). However, for operaional purposes he ieraive process is preferable, a leas a firs. I helps he operaor undersand he mechanisms of he model and in paricular he mapping beween calibraions and he inerpreaion of hisory. I also allows he operaor o embody views of he ransmission mechanism derived from oher sources, such as he judgmen of policymakers. And i avoids he danger of overfiing, in paricular of aemping o fi episodes when he operaor knows (or should know) ha here really were large unexpeced and un modeled evens, e.g. fiscal shocks, movemens in he risk premium from global evens, or droughs or rios ha emporarily drove food prices.

18 17 The second series of ineres is he CPI series and is componens. There have been various changes in mehodology in he consrucion of price indices in Kenya. Previous CPI inflaion series suffered from upward biases, especially in food price infaion, in par reflecing he use of a chained arihmeic mean formula (he Carli index). The Kenya Naional Bureau of Saisics swiched o a geomeric mean formula in 2009, for boh food and non food prices, and reroacively revised he aggregae CPI index (bu no he subindexes) up o To consruc a consisen series ha would go back o he beginning of our sample, we esimaed a bias coefficien from he period where he alernaive indices (from he wo mehodologies) overlap and applied he correcion o he older series. B. Impulse Response Analysis We begin our assessmen of he model by analyzing how a one percen emporary increase in inernaional relaive food prices (ε rlpgap = 1) affecs Kenyan inflaion, according o various specificaions of he model. The purpose of his exercise is o highligh various aspecs of he ransmission mechanism. Figure 4 plos impulse responses for inernaional food price inflaion as well as domesic food and CPI inflaion (all presened on a year on year (YoY) basis) for wo cases. Resuls are presened in deviaions, i.e., movemens in inflaion raes above or below heir long run value. By consrucion, emporary changes o inernaional relaive food prices have very shor lived effecs on inernaional food inflaion, since hey resul in one ime increases in he food price level, which hen declines over ime. This is refleced in he large drop in YoY inernaional food price inflaion afer four quarers. However, he effec on domesic inflaion is longer lived, since i akes longer for he increase o be (incompleely) passed on o domesic food prices. In he firs case (lef quadran), we assume ha moneary policy does no respond and ha he nominal exchange rae does no depreciae. 16 The increase in inflaion can be hough of as he firs round effec of shocks o inernaional food prices. In his case, he shock has a large effec on food inflaion bu no effec on non food, so he impac on headline is given by he weigh of food in he CPI. In he second case (righ quadran), we allow for moneary policy o respond, in which case he cenral bank raises ineres raes as inflaion increases. This policy ighening leads o an incipien decline in he oupu gap, which, all else equal, creaes pressures for boh non food and food inflaion o decrease. In addiion, he increases in ineres raes resuls in a emporary appreciaion of he currency, which also reduces inflaion by reducing producion coss in boh secors. The increase in inflaion is herefore smaller. Noe ha he direc effec of moneary policy can also be analyzed wih a moneary policy shock (ε RS = 1), shown in Figure 5. Consisen wih he previous discussion, he shock 16 To generae his scenario, we simulae a subse of he model where he oupu gap is always se o zero and he nominal ineres rae says consan, in which case he nominal exchange rae hrough uncovered ineres pariy does no depreciae. As acual real ineres raes are declining, his exercise implicily assumes a decrease in equilibrium real ineres raes o mainain he oupu gap closed.

19 18 resuls in an increase in he oupu gap, a decline in boh componens of inflaion and a nominal and real depreciaion. Figure 6 shows he effecs of an increase in he rend componen of inernaional relaive food prices (ε rlp = 1). In his case, he increase in inernaional food inflaion is more persisen, bu as described in he model secion here is no effec on domesic food and headline inflaion, regardless of he moneary policy response or he srucure of he economy. In sum, hese experimens show ha in our model some shocks o inernaional food prices have inflaionary effecs and some do no. In he former, we have disinguished a direc effec operaing hrough he srucure of he food secor: he exposure o inernaional food prices and he parameers of he Phillips curve. We have also analyzed an indirec effec relaed o he moneary policy response, which in his case mues he impac on inflaion. A similar resul applies o he oher shocks in he model, which we will no discuss in heir enirey for he sake of breviy. All non rend shocks will have an effec on inflaion since hey affec gap erms, and he moneary policy response will play a role in he propagaion of he shock. 17 Shocks o rend componens are no inflaionary, wih wo qualificaions. The firs qualificaion is a posiive shock o he rend componen of he domesic relaive price of food (ε rlp = 1), shown in Figure 7. In his case, here would be an increase in he food inflaion rae, a decrease in non food inflaion rae, bu no change in he headline inflaion rae (and no moneary policy response). The second excepion concerns a shock o equilibrium real ineres raes (ε rr, no shown), which would have an impac on economic aciviy and inflaion because of he slow adjusmen in he moneary policy rule. Acual real ineres raes would no keep up wih equilibrium raes, hus opening a gap in real moneary condiions. C. Filering Kenyan Daa Through he Model We now use he model o inerpre he join movemen of macro variables in Kenya. To do so, we filer he daa hrough he model using he Kalman smooher described in Appendix III. The Kalman filer and smooher are recursive algorihms used o esimae a sequence of unobserved sae variables whose dynamics are described by a sae space model a vecor auoregression of order one (VAR(1)) based on he observaions of a sequence of oher variables which are linearly relaed o hem. In our case, he sae variables are rend and gap componens and he shocks heir dynamics are joinly described by he VAR(1) represenaion of he model soluion and he observables are he acual series. The use of he Kalman smooher o esimae rends and gaps implies ha he esimaes a any poin in ime draw on informaion from he enire sample, e.g., he esimae of he oupu gap 17 One such shock is he one ha appears in he food Phillips curve. This shock can capure variaions in food inflaion due o emporary real facors, such as large variaions in he weaher ha affec he producion of food, or changes in food ariffs, subsidies or axes. Undersanding how hese facors affec food inflaion and by how much is an imporan area of research and meris furher work.

20 19 in 2005:Q1 depends on movemens in inflaion (and oher observed variables) from boh before and afer 2005:Q1. This feaure is convenien when rying o undersand hisorical episodes, hough i also implies ha he economis doing he exercise can have a clearer picure of pas macro developmens han policy makers a he ime. We will focus primarily on wo main oupus: a decomposiion of mos series ino a rend (or poenial) and a gap componen, and a decomposiion of he curren value of any variable ino he differen shocks responsible for is dynamics. Decomposiion ino rends and gaps We begin he analysis by looking a he model s four main relaive prices (z, rlp, rlp, dev ), which are displayed in Figure 8. Kenya s real exchange rae (z ) has appreciaed over ime (see upper lef quadran), which in he model is accouned for by a smooh rend appreciaion. The real exchange rae also displays some noiceable spikes, especially in 2008, accouned for by movemens in he gap (he difference beween he wo series). The inernaional relaive price of food (rlp, boom lef quadran) also displays a relaively smooh posiive rend, wih large movemens in he gap. Of paricular ineres are he large increase in inernaional food prices in and he more recen spike, which in our model are mainly accouned for by shocks o he inernaional food price gap, alhough he rend also increased. A differen sory emerges for he domesic relaive price of food (rlp, upper righ quadran). The rend componen also increases over ime, hough i slows down a he onse of he period before acceleraing afer ha. The acual domesic relaive price of food falls in early 2007, so ha mos of he increase in food inflaion observed in 2008 can be inerpreed as caching up relaive o he rend. rlp falls below rend again in 2010, hough he gap is smaller. The deviaion beween domesic and foreign food prices (dev, boom righ quadran) oscillaes widely, wih he crisis and he more recen spike opening up large negaive gaps. Given he role of dev in he food Phillips curve, we can foresee hese gaps will be inflaionary. Figure 9 plos he ime series for GDP. Oupu experienced fas growh during , wih a six percen average growh and 7 percen peak in 2007, before dropping o 2 percen in Given our assumpion abou he volailiy of shocks o poenial, poenial oupu displays a smooh pah, alhough i accouns for mos of he growh observed in Mos of he acceleraion and deceleraion of oupu around 2007 is explained by movemens in he oupu gap, which peaks during ha ime bu hen conracs unil i closes in mid 2009, in he mids of he global financial crisis. The gap opens up again from 2010 onwards. Finally, he real ineres rae (see Figure 10) displays large movemens: largely posiive from 2001 o early 2003, hen largely negaive unil mid 2005 and again from mid 2007 unil he end of he sample. Mos of hese movemens are accouned for by movemens in he real ineres rae gap. In sum, he rend/gap decomposiion has idenified various periods wih sizeable gaps in oupu, relaive prices and real ineres raes. As hese gaps have inflaionary effecs, in he

21 20 nex subsecion we accoun for some of hem and for he resuling changes in inflaion in erms of he model s shocks. Decomposiion ino shocks Wih he help of he Kalman smooher, we decompose he dynamics of each series boh observed and unobserved ino he differen esimaed shocks and iniial condiions (see Appendix III). Since we have 18 differen shocks, we regroup hem ino seven groups: Shocks ha hi he oupu gap: ε ygap, ε rr. Shocks ha hi secoral inflaion raes: ε πf, ε πnf, ε rlp. Shocks ha affec he inernaional relaive price of food: ε rlp, ε rlpgap. Shocks relaed o moneary policy: ε RS, ε π. Shocks ha direcly affec he exchange rae: ε S, ε prem, ε z. Shocks ha originae in he res of he world: ε ygap Oher (iniial condiions). 18, ε π, ε RS, ε rr The regrouping should no be inerpreed oo sricly, as some of he groups can overlap: some shocks o he exchange rae reflec changes in inernaional marke condiions and may be relaed o developmens in he world economy. More generally, he model remains highly sylized and is likely o miss oher ransmission mechanisms which may be imporan in cerain hisorical episodes. Esimaed shocks may herefore correlae as a resul. I is imporan o reierae ha shocks affec he model variables in a number of ways. In some cases, he effec is sraighforward o undersand. For example, shocks o he oupu gap will have a direc posiive effec on ha variable. In oher cases, he inerpreaion is no simple. For example, shocks ha persisenly raise inflaion would in principle have a posiive impac on he oupu gap since, by raising expeced inflaion, hey lower he real ineres rae. However, his effec is more han offse by he fac ha moneary policy endogenously responds o increases in inflaion, which hen ighens real moneary condiions and resuls in a real appreciaion, boh of which reduce he oupu gap. I is imporan for he model s user o undersand he differen channels hrough which shocks affecs variables. Finally, an imporan cavea o he shock based analysis is he imporance of own shocks, i.e., shocks ha direcly affec an observed variable (like emporary shocks o food and non food inflaion ε πf and ε πnf ). In general, hese will soak up wo ypes of movemens in ha variable. The firs ype of movemen has an economic inerpreaion, e.g., negaive shocks o he food harves will resul in an increase in food inflaion, and will show up in ε πf. 18 As previously discussed, shocks o poenial oupu do no affec inflaion and are herefore ignored in his analysis.