A THEORETICAL FRAMEWORK FOR KENYA'S CENTRAL BANK MACROECONOMETRIC MODEL

Transcription

1 AFRICA GROWTH INITIATIVE WORKING PAPER 10 MAY 2013 A THEORETICAL FRAMEWORK FOR KENYA'S CENTRAL BANK MACROECONOMETRIC MODEL Maureen Were Anne W. Kamau Moses M. Sichei Moses Kipui

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3 Maureen Were is a researcher a he Cenral Bank of Kenya, Kenya School of Moneary Sudies (KSMS) Research Cenre/Research Deparmen, Nairobi. Anne W. Kamau is an Africa research fellow a he Africa Growh Iniiaive of he Brookings Insiuion and a he Cenral Bank of Kenya, KSMS Research Cenre/ Research Deparmen, Nairobi. Moses M. Sichei is he head of research a he Commission on Revenue Allocaion bu was formerly a he Research Deparmen of he Cenral Bank of Kenya. Moses Kipui is a senior researcher a he KSMS Research Cenre, Cenral Bank of Kenya. Absrac The macroeconomeric model was developed as a ool ha would aid he Cenral Bank of Kenya (CBK) in forecasing key economic variables in a consisen manner. The economy is modeled in line wih economic heory and srucure of Kenya's economy. The moneary secor, which is he main focus of he model, is highly disaggregaed o capure he various relaionships ha exis beween he moneary secor and he real economy. The exernal, real and fiscal secors are no as highly disaggregaed and have been incorporaed ino he model o capure he ransmission channels and he impac of moneary policy. This working paper gives he heoreical foundaions upon which he CBK macroeconomeric model is buil. The heoreical framework is discussed wih he aim of delineaing he model s underlying logical srucure and he heoreical base for is core behavioral equaions. Acknowledgemens: The auhors are graeful o Njuguna Ndung u, John Randa and he exernal model reviewers Alemayehu Geda, John Weeks and Sephen Karingi for heir criical commens on he iniial draf of his paper. They would also like o hank he Africa Growh Iniiaive exernal peer reviewer for he valuable commens on he previous version of his paper. The auhors are, however, responsible for any errors and omissions. The views expressed in his paper do no necessarily represen he official posiion of he CBK. For any quesions or commens on his paper, you can reach Anne Kamau a kamauaw@cenralbank.go.ke, Maureen Were a sikalimw@cenralbank.go.ke, Moses Sichei a moses.sichei@crakenya.org, and Moses Kipui a kipuim@ksms.or.ke.

4 CONTENTS 1. Inroducion An Overview of he Model...4 The Srucural Model...4 Moneary Policy Transmission Mechanisms...7 The Deails of he Moneary Secor and Is Links wih he Oher Secors The Theoreical Base of he Modeled Equaions...11 The Demand for and Supply of Money Ineres Rae Modeling Inflaion Deerminaion...17 The Consumpion Funcion...20 The Privae Invesmen Funcion The Exernal Accoun Conclusion...27 Appendices...28 References...30 Endnoes...35

5 LIST OF TABLES Table 1. Summary of Core Secors and Equaions...11 LIST OF FIGURES Figure 1. Logical Framework and Srucure of he Model...4 Figure 2. Submarkes: Quadrans...6 Figure 3. Transmission Mechanisms...8 Figure 4. Deails of he Moneary Secor and Is Links wih Oher Secors... 10

6 A THEORETICAL FRAMEWORK FOR KENYA'S CENTRAL BANK MACROECONOMETRIC MODEL Maureen Were Anne W. Kamau Moses M. Sichei Moses Kipui 1. INTRODUCTION This paper presens he heoreical framework for he Cenral Bank of Kenya (CBK) macroeconomeric model. In addiion, i highlighs he heoreical base for he model s main behavioral equaions. The jusificaion for he model relaes o is usefulness in aiding he policymaking process a he CBK. I is expeced ha he model will suppor he Moneary Policy Commiee (MPC) and Research Deparmen in furher undersanding how he economy works hrough he complex ineracions of various economic agens. The conduc of moneary policy requires fairly accurae analyses and forecass backed up by sound economic heory and a raionale ensuring ha effecive moneary policy is formulaed and implemened. In his regard, he model will provide consisen shor-erm forecass of key macroeconomic variables such as economic growh and inflaion. In addiion, he model will be helpful in evaluaing he impac of various shocks and policies on he economy. The MPC may also use he model as an insrumen o help in srucuring is communicaion wih he public on he raionale behind is decisions. This paper is organized as follows. The res of Secion 1 discusses he ype of macro model developed, Secion 2 presens he model s logical and heoreical framework and illusraes he linkages beween he moneary submodel and he oher blocks of he model, Secion 3 discusses he heoreical foundaions of he model s behavioral equaions, and Secion 4 concludes. Wha Type of Model? Whereas here are differen varians of economic models, wo ypes of macroeconomic models sand ou for macroeconomic policy analysis and forecasing: dynamic sochasic general equilibrium (DSGE) models and macroeconomeric models. The choice beween hese wo caegories in a given siuaion depends on a number of facors: he purpose for which he model is needed, he level of deail and complexiy required, and daa availabiliy, among oher facors. The wo ypes of models complemen each oher because no single model can adequaely answer all economic policy quesions or address all needs. DSGE models are a fairly recen developmen, whereas macroeconomeric models dae back o 1940s and 1950s, when he emphasis was on consrucing quaniaive models ha could help o describe he dynamics observed in ime series economic daa. 2 GLOBAL ECONOMY AND DEVELOPMENT PROGRAM

7 Macroeconomeric models are mos suiable for forecasing and policy analysis. Unlike univariae saisical modeling, macroeconomeric models provide a comprehensive srucural view of he enire economy in a coheren and consisen manner wih he level of deail required for policy analysis. Many cenral banks rely on macroeconomeric models for economic projecions and analysis, even in cases where hey have oher ses of models. 1 However, macroeconomeric models came under srong criicism in he 1970s following he Lucas (1976) and Sargen (1981) finding ha he model coefficiens were likely no invarian o policy shifs or srucural changes. This was compounded by Sims s (1980) argumen abou lack of clearly idenified assumpions ha deal wih simulaneiy among macro variables. Despie Lucas s criique, many cenral banks coninued o rely on reduced-form saisical/macro models for forecasing economic variables (Galì and Gerler 2007). has become widespread across he globe, especially in counries ha have adoped an inflaion-argeing framework. However, a number of limiaions have been noed for hese models. Firs, hey end o perform poorly in erms of quaniaive predicions/projecions since hey are no suied for economic forecasing. Second, DSGE models are echnically more difficul o solve and analyze, and heir use in several cenral banks, paricularly in developing African counries, is sill consrained by capaciy. Third, hey absrac from secoral deails, making i difficul o sudy ineracions beween individual agens. Fourh, given he srong assumpions (e.g., complee markes), criics have argued ha hey can be misleading and are unable o describe he highly nonlinear dynamics of economic flucuaions. The validiy of hese assumpions in poor and developing counries wih less developed and incomplee markes is also quesionable. Fifh, hey may oversae individual raionaliy and foresigh and he degree of homogeneiy. DSGE models are suiable for analyzing business cycles and he cyclical effecs of moneary policy since hey emphasize he dynamics of he economy. They promise major benefis for raional policymaking process. DSGE models are relaively new, having arisen in he 1980s and 1990s as a resul of wo ypes of lieraure ha emerged in response o he shorfalls of radiional macroeconomic modeling: real business cycle (RBC) heory (Kydland and Presco, 1982 and 1990) and New Keynesian heory. These sough o provide microeconomic foundaions for he Keynesian conceps (Galì and Gerler 2007). The RBC models assume flexible prices, while he New Keynesian School assumes price rigidiies. These ypes of macroeconomic models place greaer emphasis on micro foundaions and heoreical coherence. DSGE models begin by specifying a se of economic agens (households, firms, governmens), each assumed o make opimal choices, in a way ha clears every marke. The use of DSGE models a cenral banks To overcome he challenges and shorcomings of relying on one model, he use of muliple models (i.e., a suie of models) has also become popular wih cenral banks. Given he curren forecasing needs and he needs of he MPC, he prioriy was o firs develop a simple macroeconomeric model wih solid forecasing performance as par of he overall sraegy for developing a suie of models for he CBK. This was furher moivaed by he need o develop a macroeconomeric model wih a sysemaic framework enailing a deailed moneary secor and how i relaes o he oher secors of he economy. The laer is made possible by he flexibiliy provided by he macroeconomeric ype of models, in erms of heir ease of applicaion and abiliy o describe economic relaionships based on empirical daa and economic heory. To effecively execue is primary ask of formulaing and conducing moneary policy and is secondary role of promoing economic growh and employmen, he CBK akes cognizance of he srucural economic inerlinkages in he economy. A THEORETICAL FRAMEWORK FOR KENYA'S CENTRAL BANK MACROECONOMETRIC MODEL 3

8 2. AN OVERVIEW OF THE MODEL The Srucural Model The srucure of he model can be summarized using a flowchar, as shown in Figure 1. The figure shows he srucural inerlinkages of he model and capures he ineracion beween he various secors of he economy (blue boxes). I also shows he ineracion beween markes ha is, beween he financial marke and oher markes. The whie boxes denoe differen domesic prices deermined in he model (consumer price, exchange rae and domesic ineres raes). For insance, he ineracion of money demand and money supply deermines domesic ineres raes. Excess money demand acs as one of he riggers of moneary policy acions. The CBK follows he moneary-argeing framework, where i conrols quaniies (money sock) o affec he prices in he economy. Reserve money (RM) is he operaing arge and is under he CBK s conrol. Broad money, or he money supply (M3), is he inermediae arge and is relaed o reserve money hrough he money muliplier. CBK uses M3, given ha i is perceived o conain all he insrumens used o influence policy (currency, demand deposis, quasi-money and foreign currency deposis). Acions on he fiscal side have implicaions on domesic ineres raes (e.g., hrough he price effec of crowding ou or hrough he effecs on he reurn o governmen securiies relaive o oher asses). Aggregae demand, price level, exchange rae and ineres raes deermine money demand. 2 Oher markes ha is, he exernal secor Figure 1. Logical Framework and Srucure of he Model Money Demand Excess Money Demand Money Supply World Ineres Raes World Prices Govermen Secor Domesic Ineres Raes Nominal Exchange Rae Consumer Price Non-Tradable Tradable Real Exchange Rae Domesic Demand & Supply Oupu Gap Wages Exernal Secor 4 GLOBAL ECONOMY AND DEVELOPMENT PROGRAM

9 and he governmen/fiscal secor are represened in he brigh blue boxes. Unlike he KIPPRA Treasury Macro Model (KTMM), 3 which was designed wih a deailed governmen secor o mee he governmen s needs in he naional budgeary and planning process, he CBK model has a more deailed moneary secor ailored o he needs of he moneary policy process. The nominal exchange rae is deermined in he foreign exchange marke by he differenials beween domesic and world ineres raes, as well as beween he domesic price and world prices. For insance, a rise in domesic ineres raes relaive o foreign ineres raes will lead o an appreciaion of he local currency. The real exchange rae follows by definiion (i.e., from he nominal exchange rae, he foreign price and he domesic price level). The (real) exchange rae has an impac on he expors and impors of goods and services in he exernal secor. World price and foreign ineres raes are exogenous (gray boxes). A he aggregae level, he model closely follows he aggregae demand (AD) aggregae supply (AS) framework. In he shor run, income is deermined in he real economy from he demand side, ha is, aggregae demand. Toal demand equals he sum of final consumpion expendiures by households, invesmen (capial formaion), governmen expendiure and expors less impors. On he supply side, i is assumed ha oupu is produced in accordance wih a consan elasiciy-of-subsiuion producion funcion wih capial and labor as key inpus. Producion leads o demand for labor and invesmen goods. Business enerprises produce goods and services ha are sold in he domesic as well as global markes. The demand for labor and wages is deermined in he labor marke. There is a wage-price spiral ha can lead o a vicious cycle in which business owners raise prices o proec profi margins from rising coss, while wageearners push for higher nominal wages o cach up wih rising prices o preven real wages from falling. This may be riggered by higher aggregae demand relaive o supply, or he effec of supply shocks such as inernaional oil price hike. Consumer price is domesically deermined hrough he ineracion of AD and AS, as well as by excess money having an impac on he price of nonradables. The difference beween acual and poenial oupu is known as he oupu gap. Theoreically, his gap is given by he difference in oupu beween shor-run equilibrium, where AD inersecs AS, and he long-run AS, which refers o he naural rae of oupu. 4 The producion secor pays ne axes o he governmen. Households sell heir labor in he labor marke and receive income in form of remuneraion, as well as dividend paymens and ransfers from he governmen. They pay axes and spend heir ne income (disposable income) o buy goods and services. Governmen spending consiss of governmen expendiure (consumpion and invesmen) and ransfers o households. The Quadran Approach Insead of using he flowchar/logical framework o summarize he macro economy, he alernaive approach is he use of he four-quadran IS LM BP framework (see Figure 2). 5 The money marke falls in he firs quadran, while he ineracion beween AD and AS is shown in he second quadran. AD is downward sloping, while AS is upward sloping. Among oher facors, he gap beween he AS and AD (oupu gap) deermines he price movemen. The foreign exchange marke is capured in he hird A THEORETICAL FRAMEWORK FOR KENYA'S CENTRAL BANK MACROECONOMETRIC MODEL 5

10 Figure 2. Submarkes: Quadrans (IV) r r: Ineres Rae (I) LM BOP Exernal and inernal balance LM 1 r 0 r 1 E: Exchange Rae E E 1 E 0 45 Y: Oupu IS Y 0 Y 1 Y AD AD 1 p 0 p 1 (f(e)) AS (III) P P: Price (II) quadran. A rise in domesic price leads o depreciaion of nominal exchange rae. Given he uncovered ineres pariy (UIP) assumpion, a policy ha leads o lower ineres raes (relaive o foreign ineres raes) depreciaes he domesic currency. The fourh quadran is abou he inernal and exernal balance. The differen prices (general domesic price, ineres raes and exchange rae) are he main adjusing componens. Basic Seup Quadran I: Goods and he Money Marke The IS curve is a combinaion of poins where he ineres rae (r) and oupu (Y) inersec in he goods marke. 6 The goods marke is in equilibrium along hose poins. I is negaively sloped o indicae ha higher ineres raes reduce invesmen spending, which in urn reduces aggregae demand and income. The LM curve, conversely, shows a combina- 6 GLOBAL ECONOMY AND DEVELOPMENT PROGRAM

11 ion of ineres raes and oupu derived in he money marke where money demand equals money supply. Along his curve, he money marke is in equilibrium. The demand for money is demand for real balances. The curve is upward sloping, implying ha demand for real balances increases wih increases in income when he money supply is fixed. A he inersecion of he IS and LM curves, he goods and money markes are in equilibrium. Quadran II: Aggregae Demand and Aggregae Supply The AD and AS curves inersec a a general equilibrium price level. The AD curve is derived from he IS LM equilibrium income a differen price levels. The AS curve reflecs he economy s price adjusmen mechanism. The AS curve is upward sloping in he shor run bu verical in he long run, as i is expeced ha equilibrium in he labor marke remains he same a differen price levels. The labor marke does no respond o surprises immediaely, hence he upwardsloping AS curve in he shor run, due o nominal rigidiies such as he sicky wage seup. Quadran III: The Foreign Exchange Marke The diagram assumes a small, open economy where a floaing exchange rae regime is followed. In he foreign exchange marke, he endogenous variable in Quadran III is he exchange rae, E, whereas he exogenous variables are he domesic ineres rae (r d ), he foreign ineres rae ( r f ), he expeced exchange rae E e, domesic prices (P d ) and foreign prices (P f ). The value of he equilibrium exchange rae is affeced by domesic and foreign raes of reurn in he marke. Quadran IV: The Balance of Paymens The inernal equilibrium is achieved hrough Y = C(y) + I(r) + G + X(e) Z(e,Y) and he Ms/p = L(r) + k(y). An appreciaion of he exchange rae, e, requires a decrease in governmen expendiures o have an inernal equilibrium. An appreciaion of e worsens he curren accoun balance posiion bu increases oupu (Y) hrough he muliplier effec. In order o counerac he change in Y, governmen spending has o decline. An exernal balance is aained hrough he balance-of-paymens (BOP) equilibrium of an open economy. This may be defined by BOP = X(p,e,y) Z (p,e,y) + F(r). The endogenous variable in Quadran IV is he balance of paymens, and he exogenous variables are prices (P), he exchange rae (E) and income (oupu) (Y). Above he BOP curve, as governmen spending increases, rade deficis and hence balance-of-paymens deficis arise. As a resul, he governmen mus uilize is foreign reserves o preserve he exchange rae. The CBK modeling approach closely follows he Keynesian and monearis lines of hough, in which fiscal and moneary policy can be used o raise he level of oupu and employmen in he economy in he shor run. I conains feaures of he New Keynesian economics ha emphasize sicky or sluggishness in wages and prices o explain why moneary policy affecs producion aciviies in he shor run and he new classical models ha shed ligh on how households and firms make decisions over ime. Combining he differen srenghs of compeing approaches is expeced o yield robus resuls boh in erms of he heoreical underpinnings and pracical applicaions of he model. Moneary Policy Transmission Mechanisms Moneary policy ransmission mechanisms describe how policy-induced changes in he nominal money sock or he shor-erm nominal ineres rae have an impac on real variables, such as aggregae oupu. 7 For insance, he MPC changes he Cenral Bank Rae (CBR) from ime o ime o signal he moneary A THEORETICAL FRAMEWORK FOR KENYA'S CENTRAL BANK MACROECONOMETRIC MODEL 7

12 Figure 3. Transmission Mechanisms Shor-Term Ineres Rae Long-Term Ineres Rae Expecaions Moneary Policy Bank Lending Balance Shee Bank Reserves Asse Prices Equiy & Real Esae Privae Secor Loans Adverse Selecion Moral Hazard Domesic Demand Toal Demand Domesic Inflaionary Pressures Inflaion Ineres Rae Differenials Exchange Rae Capial Accoun Ne Expor Exernal Demand Impor Prices policy sance i is following. This is represened in Figure 3, and he differen ransmission channels are briefly explained here. Ineres rae channel: Through his channel, he policy-induced increase in he shor-erm ineres rae (i.e., he policy rae) influences he oher shor-erm raes as well as long-erm ineres raes, such as he lending rae. As a resul of increased lending raes, firms cu back on heir invesmen expendiures, as he real cos of borrowing over he horizons has increased. Households also cu spending on consumpion of durables due o he higher coss of borrowing. This leads o a fall in aggregae demand and, consequenly, lower inflaionary pressures (see Mishkin 1995; Ireland 2005). Exchange rae channel: When domesic ineres raes rise relaive o foreign ineres raes, under he UIP assumpion, equilibrium in he foreign exchange rae marke would require a gradual depreciaion of he domesic currency (Ireland 2005). This expeced fuure depreciaion iniially requires an appreciaion of he domesic currency, which makes home-produced goods more expensive relaive o foreign-produced goods. Ne expors fall, leading o a fall in oal demand. The rise in he domesic ineres rae above he foreign ineres rae also aracs capial inflows, which lead o an appreciaion and, depending on he magniude of foreign direc invesmen, also have implicaions for aggregae oupu. The precise impac of a change in he official rae on exchange raes may, hus, be uncerain. 8 GLOBAL ECONOMY AND DEVELOPMENT PROGRAM

13 The credi channel works in wo ways: Firs, he credi channel affecs he bank lending channel and, second, i affecs he balance shee of households and firms. When he cenral bank reduces he money sock by reducing he quaniy of reserve money, he bank s reserves decline, hence reducing he amoun banks have available for lending ou. Conversely, he reducion in he money sock leads o a worsening of households and firms balance shees hrough he fall in asse and equiy prices. This reduces he ne worh of he borrowers. Banks hen need o screen borrowers in order o avoid adverse selecion and hen monior he borrowers o reduce moral hazard. This process reduces he amoun of loans given by he banks. Adverse selecion and moral hazard are driven by informaion imperfecions in he marke. In boh cases, he effecs would reduce domesic demand, oal demand and evenually oupu. Key assumpions are ha bank loans are firms principal sources of funds, for which few close subsiues exis. shee and expecaions channels are no modeled in he model since hey are no well developed. Deails of he Moneary Secor and Is Links wih he Oher Secors In broad overview, Figure 4 combines Figure 1, he srucural model, and Figure 3, he ransmission mechanisms of moneary policy, o oher secors in he economy. The figure provides a more deailed breakdown of he moneary secor of he model, illusraing he cenral role ha moneary policy insrumens play and he main channels hrough which moneary impulses influence oher facors such as credi o he privae secor in he economy. As before, he oher secors are he fiscal, exernal and real secors. The flowchar furher shows he relaionship beween he growh in he money supply and overall inflaion and oupu in he real secor. The ulimae objecive of he cenral bank is o ensure price sabiliy. The changes in he policy rae may influence expecaions abou he fuure pah of real economic aciviy and he confidence wih which hose expecaions are held. Changes in percepion are likely o affec paricipans in he financial markes as well as economic agens in oher markes (Bank of England 1999). However, i is hard o predic he direcion in which such effecs work. For insance, a rise in he CBR may be inerpreed o imply ha he MPC assumes he economy is likely o be growing faser han previously hough, which gives a boos o expecaions of fuure growh and enhances confidence. Bu he acion can also be inerpreed o imply he need o slow he growh in order o hi he inflaion arge, hus yielding expecaions of low fuure growh and lower confidence. Some previous sudies on moneary policy ransmission mechanisms in Kenya have shown ha he bank lending channel is sronger han all he oher channels. The balance Moneary policy acion can be riggered by various facors ha are deemed o have implicaions for inflaion or employmen. These include demand-driven inflaionary pressures ha arise as a resul of excess money demand in he economy, as illusraed in Figure 4. The moneary auhoriies hen use various insrumens o conduc moneary policy operaions in a moneary argeing framework. Some moneary policy ools of operaion include open marke operaions (OMO), he cash reserve raio (CRR), he CBR and he forex. A he CBK, he repo raes and CBR are he mos frequenly used insrumens. The CBR is used o provide signals o he marke of he moneary policy sance ha he CBK is pursuing. Given he erm srucure of ineres raes, he ransmission mechanism is expeced o be from he shor-erm raes o he long-erm raes (he green arrows). I is hus expeced ha he CBR coordinaes he move- A THEORETICAL FRAMEWORK FOR KENYA'S CENTRAL BANK MACROECONOMETRIC MODEL 9

14 Figure 4. Deails of he Moneary Secor and Is Links wih Oher Secors Money Supply Excess Money Demand Money Demand COB Deposis mm POLICY Shor erm raes RM Tools OMO CBR Repo Inerbank CRR Forex Term Aucion Inflaion Moneary Impored NFA CBK ODC NCG CBK ODC PSC CBK ODC OIN CBK ODC Long-erm raes Deposi Raes Lending Raes Real Secor Expecaions Exernal Secor Exchange Rae Curren Accoun Capial Accoun Fiscal Secor Tbill Rae Revenue Expendiure Real Secor mens of shor-erm raes which evenually affec he long-erm raes such as he lending rae. The long-erm lending raes would affec credi o he privae secor and ha will lead o an increase in money supply. Credi o he privae secor also affecs invesmen demand in he real secor. Overall inflaion is primarily influenced by changes in he prices of impored goods and services, produciviy developmens, excesses in money demand and price expecaions. Wage rae flucuaions also play an imporan role in price deerminaion. The money supply is deermined via he money muliplier, mm, and reserve money, RM, and disaggregaed by sources ha is, ne foreign asses (NFA), ne credi o governmen (NCG), credi o he privae secor (PSC) and oher iems ne (OIN). Each is a summaion of wo componens, for CBK and oher deposiory corporaions (ODC). The CBK componens add up o reserve money. The NFA is deermined in he exernal secor, ha is, hrough he BOP accouns. NCG is deermined in he governmen secor by he governmen s borrowing requiremens ne of governmen deposis a he CBK. This is he same approach ha underlies he curren moneary program a he CBK. On he liabiliies side, money demand is composed of currency ouside bank (COB) and deposis. Deposis can be furher disaggregaed ino demand deposis, quasi-deposis and foreign currency deposis. 10 GLOBAL ECONOMY AND DEVELOPMENT PROGRAM

15 3. THE THEORETICAL BASE OF THE MODELED EQUATIONS The economy is modeled a he macro level, which is in line wih he modeling approaches employed in hese ypes of models. In accordance wih he underlying heoreical framework ha blends he New Keynesian and Keynesian radiions, he model allows for nominal and real ineria as well as he role of aggregae demand in deermining oupu in he shor run. In he long run, he economic variables graviae oward heir corresponding supply-side-deermined seady saes or equilibrium levels. The model capures he Kenyan economy as a small, open economy. The key variables are deermined in he model as endogenous variables. The main secors considered and he main core equaions esimaed are summarized in Table 1. The equaions have been developed in line wih he heoreical framework laid ou in his paper. The secors (moneary, exernal, real and fiscal secor) are as described from he flowchars given as Figures 1 hrough 4. The following subsecions discuss he heories underpinning he core equaions in Table 1. Table 1. Summary of Core Secors and Equaions 8 SECTOR CORE EQUATIONS Money marke MONETARY SECTOR A equilibrium, aggregae money demand (M D ) equals money supply (M S ). The deviaion beween he wo, depending a wha level he economy is operaing, has implicaions on inflaion and hence riggers moneary policy acion. M S is deermined via money muliplier (mm), i.e., as a produc of mm and reserve money (RM). This equals money sources (NFA + NCG + PSC + OIN). NFA is ne foreign asses, NCG is ne credi o Governmen, PSC is privae secor credi and OIN is oher iems ne. The ransmission mechanism works hrough he domesic ineres raes, i.e., from policy rae (r CBR ) o shor-erm raes (inerbank rae(r in ), repo/reverse repo) o long-erm deposi rae (r D ), lending rae (r L )) o he real secor (privae invesmen). The credi channel works via he privae secor credi. Treasury bill rae (TBR), which is considered a medium-erm rae, is a risk-free rae and alernaive rae of reurn. r CBR is policy rae deermined by he MPC. On he liabiliies side (demand side), money (M3) is disaggregaed ino currency ouside banks (COB) and Bank Reserves (BR). BR is furher decomposed ino is componens (cash in ills, required reserves and excess reserves). M S = mmrm, where mm is money muliplier M S = NFA + NDA + OIN Where NFA = NFA CBK + NFA ODC and NDA = NCG + PSC + OPC PSC = f(lending rae, GDP, credi o public secor) M D = f(rgdp, CPI, TBR, US TBR and exchange rae) COB = f(rgdp, CPI, TBR) Excess reserves = f(inerbank rae, TBR, governmen deposis) r in = f(r CBR, excess reserves, governmen deposis) TBR = f(r in, price expecaions (lagged CPI), GDP, NSE index) r L = f(tbr, real GDP) Deposi rae = f(inerbank rae, TBR, GDP, NSE index) The repo and reverse repo operaionalize he r CBR A THEORETICAL FRAMEWORK FOR KENYA'S CENTRAL BANK MACROECONOMETRIC MODEL 11

16 BOP accouns EXTERNAL SECTOR SECTOR CORE EQUATIONS Core accouns of BOP are he curren accoun (CA), capial and financial accoun (KA). Under curren accoun, expor/impor of goods and expor/ impor of services is deermined separaely. Expor of goods (X goods ) is deermined based on small counry assumpion as a funcion relaive price (weighed expor price as a raio of world non-fuel commodiy price index) and income of Kenya s key rading parner. Impor of goods (M goods ) is deermined by domesic income and relaive price (weighed producer price index of rading parners(source counries for impors) relaive o domesic price (CPI), while impor of services is a funcion of domesic income. BOP = KA + CA X goods = f(relaive price, weighed income of rading parners) X services = f(weighed income of rading parners, poliical sabiliy index) M goods = f(relaive price, real GDP) M services = f(weighed GDP of rading parners, real GDP) e = f(p, P*, r r*, CA) Foreign asse marke Ideniies and bridge equaions link he capial accoun o he money supply process and impor and expor demands o he real secor for consisency. Exchange rae (e) is one of he fundamenal prices in he model. A modified PPP (i.e., domesic price (P), foreign price (P*) and ineres rae differenial (r r*)) deermines he exchange rae in he long run. Changes in hese variables ogeher wih he curren accoun balances (CA) capure he shor run dynamics. Ineres rae differenials absorb deviaions from he PPP. Aggregae demand REAL SECTOR Aggregae demand (AD) equals oal available supply in he economy (AS). AD is derived as a summaion of privae consumpion (C), invesmen demand (I), governmen expendiure (G) and expors (X) less impors (M). C, I, X and M are endogenously deermined as behavioral equaions. X and M are already deermined in he exernal secor. Invesmen funcion is an eclecic of flexible acceleraor and neoclassical heories. C = (GDP, ineres rae(r L ) I = f(ineres raes, r L, GDP, privae secor credi, SC, as a share of oal credi) CPI = f(excess money demand, impored inflaion, wage inflaion and oupu gap) CPI/inflaion is modeled as emanaing from differen markes/sources (i.e., money marke, impored inflaion, oupu gap). 12 GLOBAL ECONOMY AND DEVELOPMENT PROGRAM

17 Expendiure, revenue and defici financing FISCAL/GOVERNMENT SECTOR SECTOR CORE EQUATIONS Mos of he fiscal variables, especially on he expendiure side, are reaed as semi-behavioral or exogenous. On he revenue side, income ax is modeled based on income elasiciy while he value-added ax (VAT; local and impored) is a funcion of consumpion and impor of goods and services. Once oal revenues (ax and nonax revenues) and levels of expendiures are deermined, fiscal defici is derived as a residual. Income ax = f(gdp) VAT = f(privae consumpion, impor of goods and services) The link o moneary policy can be capured hrough variables ha affec he balance shee of CBK, and by implicaion he reserve money. Specifically, his includes (ne) governmen deposis a CBK. The Demand for and Supply of Money The Demand for Money The demand for money is rooed in he classical quaniy heory of money, as ariculaed in he work of Fisher (1911b). The Fisher equaion of exchange has been modified over ime o become PY M D (1) V Using k o represen inverse velociy, his equaion becomes M D kpy (2) This equaion of exchange saes ha he level of nominal income (PY) deermines he quaniy of money ha people demand. However, his formulaion assumes ha ineres raes have no effec on he demand for money. I is his assumpion wih which Keynes (2006) disagrees in his paper, which argues ha ineres raes affec he demand for real balances, as specified in (3): M d f Y i P, (3) where Y is real income and i is he nominal ineres rae. Combining he Fisher equaion of exchange and Keynes s formulaion and aking ino accoun ha Kenya has a small, open economy wih a floaing exchange rae he CBK model posulaes money demand as a funcion of real GDP, he price level, nominal ineres raes and he nominal exchange rae: M d Y P i E (4) where M d denoes nominal demand for money, 9 Y is real GDP, i is he nominal ineres rae, and E is he nominal exchange rae. The ineres raes are marke deermined hrough he forces of money demand and money supply. Movemens in he nominal exchange rae are assumed o affec he demand for money. Money Supply The CBK follows a moneary-argeing framework o implemen moneary policy. The operaing arge is reserve money, and he CBK conrols reserve money o influence he broad money supply hrough he money A THEORETICAL FRAMEWORK FOR KENYA'S CENTRAL BANK MACROECONOMETRIC MODEL 13

18 muliplier process. The CBK s balance shee is represened by (5): RM = e.nfa + NDA (5) Equaion 6 shows he relaionship beween he money supply and reserve money in (5). 10 The money supply in he CBK model is hus defined as a funcion of reserve money and he money muliplier: M s where mm RM (6) s M is he broad money supply, 11 mm is he money muliplier, and RM is reserve money. 12 The money muliplier can be described generally as mm = 1 + cc cc + rr, cc = cu d = f c (.) f d (.) and rr is he reserve-deposi raio, which is assumed o be exogenous. 13 In an open economy, wih he LM curve represening he money marke equilibrium M d = M S, he ineres rae moves o clear he money marke; hus, nominal ineres raes are a funcion of he money supply, real GDP, prices, he repo rae, he volume of Treasury bills and he exchange rae. In equilibrium, he demand-for-money equaion is sufficien o show he dynamics of he ineres rae, given ha he ineres rae is an invered form of money demand: i s Y P E M (7), The Moneary Policy Reacion Funcion As early as 1898, Wicksell argued ha he objecive of he cenral bank should be o mainain price sabiliy, which in heory could be realized if he ineres rae were se such ha i was equal o he economy s naural rae of ineres. Given ha he naural rae was an unobservable and absrac concep, he argued ha a simple policy rule ha responded sysemaically o prices would suffice. The CBK currenly describes is moneary policy framework in erms of arges on moneary aggregaes. Under he financial programming framework being used, assumpions of economic growh and inflaion arges enable he desirable growh pah of moneary aggregaes arges on a monhly and quarerly basis. However, wih he formaion of he MPC, he CBK seems o be laying is emphasis on he policy insrumen (he CBR) o signal he policy direcion. This implies ha i is also feasible o consider modeling a Taylor-ype of moneary policy rule. In modeling he moneary policy reacion funcion, herefore, boh aspecs need o aken ino consideraion. The approach follows Berg e al. (2010), in which he CBK implemens an acive moneary policy ha responds boh o inflaionary pressure and oupu flucuaions. As such, he moneary policy reacion funcion, wih he moneary aggregae as he insrumen, could be specified as ΔM T * = ΔM (m m * ) 1 + (π π * ) δ(e (π +1 ) π * ) γ(y y * ) (8) This ineres rae, furher, gives us he link beween he foreign exchange markes and he money marke, given ha he ineres rae differenial is one of he deerminans of he exchange rae. * Where ΔM is he long-run equilibrium change in money base, m is real money balances, π is acual inflaion in ime, π * is he arge or long-erm rae of inflaion, y is acual oupu and y * is poenial oupu. E is he expecaion a ime, abou wha 14 GLOBAL ECONOMY AND DEVELOPMENT PROGRAM

19 he variable will be in he following period. Finally, m * is he real money balance, which ensures ha (π π * ) = 0 and (y y * ) = 0. By choosing a paricular growh arge for moneary aggregae in (8) above ex ane, he CBK implicily has chosen a shor-erm ineres rae ha is muually consisen wih he chosen money arge hrough he money demand funcion specified in (4). For example, o derive he implicaion of (8) for he relevan nominal ineres rae involves solving for he nominal ineres rae by subsiuing (8) in he money demand funcion specified in (3) (for a similar approach, see Berg e al. 2010). This yields (9): The Fisher Equaion The Fisher equaion is a heory of ineres rae deerminaion whereby he nominal ineres rae is equal o he real ineres rae plus he expeced level of inflaion. This relaionship is capured in he equaion i = r + π e (10) where i is he nominal ineres rae, r is he real ineres rae, and π e is he expeced rae of inflaion. Shorerm ineres raes, herefore, depend on expeced inflaion in he near fuure, while longer-erm ineres raes depend on expeced inflaion in he more disan fuure, if he invesmen was worhwhile. r p = r * + π * + φ 1 + (E (π +1 ) π * ) + φ 2 (y y* ) (9) where r p is he policy rae and r * is some noional equilibrium (naural) ineres rae, and boh are in nominal erms. The reacion funcion in (8) and (9) above posulaes a Taylor-ype, forward-looking moneary policy framework ha reacs o deviaions of inflaion from is long-run pah and flucuaions of oupu from is full poenial. The parameers in (8) could be derived from he esimaion of he demand funcion (4) and he weighs ha he MPC aaches o he deviaions of inflaion from he arge and oupu from he arge. Ineres Rae Modeling Several heories have been advanced o explain how ineres raes are deermined. These include he Fisher equaion, Keynes s liquidiy preference, and he erm srucure heories, which include he expecaions hypohesis, marke segmenaion heory and liquidiy premium heory. The Loanable Funds Theory Wicksell s loanable funds heory implies ha he equilibrium ineres rae will be deermined by he demand and supply condiions in he marke for loanable funds. Thus, marke ineres raes are deermined by he facors ha conrol he supply of and demand for loanable funds. These funds are financial asses, which mainly comprise bank loans and household savings. The marke for loanable funds brings ogeher households, business firms, governmen and foreigners as eiher borrowers or savers. The inersecion of he supply and demand curves generaes an equilibrium ineres rae ha clears he marke for loanable funds. A equilibrium, naional savings equal domesic savings plus ne foreign invesmen. The supply-for-loans funcion is upward sloping, implying ha he suppliers of loanable funds will supply more as he reurn on heir savings increases. Conversely, he demand schedule is downward sloping, implying ha borrowers will demand for loans as he price for loans declines. Since borrowers seek loans o expand capial in order o produce more goods and services, hey assess he cos of loanable funds (he ineres rae) vis-à-vis he addiional rev- A THEORETICAL FRAMEWORK FOR KENYA'S CENTRAL BANK MACROECONOMETRIC MODEL 15

20 enue from he addiional capial (he rae of reurn on capial). Hence, borrowers demand for addiional capial (loans o expand capial) will coninue o grow so long as he reurn on he borrowed funds exceeds he ineres rae on he borrowed funds, and will sop a he poin where he ineres rae equals he rae of reurn on capial. Tha is, a company s demand coninues o grow so long as he rae of reurn on is capial coninues o increase. Keynes s Liquidiy Preference According o he liquidiy preference heory, he marke rae of ineres is deermined by he demand for and supply of money balances. This heory saes ha people demand money for ransacions, as a precauion and for speculaive purposes. The ransacion demand and precauionary demand for money increase wih income, while he speculaive demand is inversely relaed o ineres raes because of he forgone ineres. The supply of money is deermined by he moneary auhoriy (i.e., he cenral bank), by he lending of commercial banks and by he public preference for holding cash. This is consisen wih he liquidiy preference heory of he erm srucure of ineres raes, whereby ineres raes are expeced o increase as he mauriy profile of securiies increases. This is so because he longer he mauriy, he greaer is he uncerainy; and herefore he premium demanded by invesors o par wih cash increases as he mauriy profile increases. The expecaion, herefore, is ha forward raes should offer a premium over expeced fuure spo raes since hose who are risk-averse demand a premium for securiies wih longer-erm mauriies. A premium is offered by way of greaer forward raes in order o arac invesors o longer-erm securiies. Consequenly, curren ineres raes reflec expeced inflaion raes, income (GDP) and expeced money supply changes: i = f(gdp, m s, π e ) (11) The Expecaions Theory of he Term Srucure According o expecaions heory, long-erm ineres raes are averages of expeced fuure shor-erm ineres raes. Thus, a reurn on a wo-year securiy should be equal o he anicipaed reurn from invesing in wo consecuive one-year securiies: (1 + R 2 ) 2 = (1 + R 1 )( +1 r 1 ) (12) where R 1 and R 2 are, respecively, he known annualized rae on one-year and wo-year securiies and +1 r 1 is one-year ineres rae ha is anicipaed in ime +1. This can be generalized o n periods, so ha an n - year securiy should offer a reurn ha is equal o he expeced reurn from invesing in n consecuive oneyear securiies: (1 + R n ) n = (1 + R 1 ) ( +1 r 1 ) ( +2 r 1 ) ( +n r 1 ) (13) where +n r 1 is he one-year ineres rae ha is anicipaed as of ime +n and R n is he known annualized rae on an n -year securiy. Ineres Rae Modeling for he CBK Macroeconomeric Model The ineres rae equaion for he CBK model incorporaes all he aspecs of he hree heories discussed above. In addiion, based on he MPC s marke survey which indicaes ha lenders ake ino accoun shor-erm raes (inerbank, Treasury bill raes) in he lending rae he ineres rae equaion is modeled as 16 GLOBAL ECONOMY AND DEVELOPMENT PROGRAM

21 j On he basis of he Harberger model, which makes i p q r s v i 1ii 2 RGDP i 3CPI i 4 Depr i 5Tbillr ii i j RGDP j k CPI k l Depr l mtbillr m ipossible 1 o jinver 0 he real money k 0 balances lfuncion 0 o p q m0 r s v 4 Depr i 5Tbillr ii i j RGDP j k CPI k l become Depr l a price mequaion, Tbillr m we obain i1 j0 k 0 l0 m0 r s v RGDP j k CPI k l Depr l mtbillr m (14) k 0 l0 m0 P 1M 2 y 3i (16) Where i is he overall weighed average lending rae of commercial banks; RGDP is real oupu; CPI is he consumer price index; Tbill is he average 91-day Treasury bill rae and Depr is he overall weighed average deposi rae of commercial banks. Impored Inflaion Modeling impored inflaion follows eiher he purchasing power pariy (PPP) or he UIP condiion or a combinaion of he wo. Inflaion Deerminaion Inflaion in open economies resuls from differen disequilibria in many markes specifically, he domesic money marke, exernal/foreign markes and he labor marke. Thus we recognize ha inflaion emanaes from hree main sources in he CBK model: excess money supply, foreign prices and cos push facors. The heory of PPP requires ha nominal exchange raes move o equalize he price of goods and services across counries. There are wo versions of he PPP: he absolue version (law of one price) and he relaive version. Following he relaive PPP heory, inflaion rae differenials beween wo counries or regions are offse hrough inverse changes in he nominal exchange rae so ha purchasing power raio beween he wo remains consan. The Monearis Model of Inflaion The monearis views inflaion as always and everywhere a moneary phenomenon (Friedman 1963). Furher, macroeconomic heory proposes ha growing he money supply in excess of real growh causes inflaion. This is also he resul from he Harberger (1963) model, which assumes ha prices adjus o excess money supply in he money marke. I is on he basis of his assumpion ha i is possible o inver he real money demand equaion as a price equaion in equaion 15: P = f (M, y, i) (15) where P is he price level, M is he nominal money supply, y is real GDP, and i is he nominal ineres rae. The relaive PPP is formally expressed as e c p p (17) * * where p is he log of he domesic price level, p is he log of he foreign price level, e is he log of he spo nominal effecive exchange rae (i.e., he Kenya shillings price of a uni of foreign currency) and c is a consan represening he permanen deviaion from absolue PPP due o produciviy differenials and oher facors. Since goods arbirage is slow, PPP represens a longer-erm relaionship han equaion 17 suggess. There are a number of facors ha could drive he exchange rae emporarily away from he PPP. These include commodiy prices, differen ineres rae srucures, relaive growh differenials and speculaive price A THEORETICAL FRAMEWORK FOR KENYA'S CENTRAL BANK MACROECONOMETRIC MODEL 17

22 movemens. Whenever here is a deviaion from PPP, i is expeced ha he exchange rae will move smoohly oward resoring relaive PPP, as shown in equaion 18: α[p p * e c] = i m i m* + u (21) Rearranging, Δe +1 = α[p p * e c] (18) where 0 1. e p p * m m i i k 0 1 * where k c u (22) Conversely, he heory of UIP requires ha if ineres raes in Kenya are higher han similar ineres raes in he Unied Saes, hen invesors will have an incenive o purchase Kenyan asses. UIP can be expressed algebraically as E m m e m e i i u * (19) where E = is he expecaion on he basis of all informaion available a ime, i m = is he yield on domesic m* asses wih mauriy m a ime, i = is an equivalen foreign ineres rae, and u = is he risk premium associaed wih holding Kenya shilling asses. The available evidence shows ha PPP and UIP have been rejeced individually due o a failure o recognize he sysemaic relaionship beween he wo condiions. Following Choy (2000) we combine PPP and UIP as follows. Assuming raional expecaions, equaion 18 can be rewrien as E (e +m ) e = α[p p * e c] (20) The exchange rae expecaions also feaure in he UIP condiion in equaion 19. If we assume ha PPP forms he basis of he expecaions in he UIP assumpion, we can subsiue equaion 20 for expecaions in equaion 19; In he real world, he relaionship in equaion 22 is no deerminisic. Speculaive aciviy or commodiy price movemens could, for insance, lead o a susained and significan deviaion from equaion 22. Thus equaion 22 can be viewed as an equilibrium condiion oward which prices, ineres raes and he exchange rae end o move in he long run ha is, prices, ineres raes and he exchange rae are coinegraed: * m m m* e 3 6 ~ (0) 1 1 p p i i i I k (23) Equaion 21 can be furher relaxed in hree ways o ake ino consideraion he weak form of PPP and UIP. Firs, we are no concerned wih meeing he acual magniudes saed in equaion 22 bu raher he direcion. Second, he analysis akes ino consideraion he small counry assumpion, whereby exernal variables are reaed as weakly exogenous. Finally, crude oil prices are added as an addiional variable given he fac ha Kenya is a ne imporer of oil. Wages and Inflaion There are hree differen levels of wage formaion in Kenya: unionized, compeiive and adminisered. This implies ha he observed wage is a funcion of compeiive, adminisered and bargained wages, which can be explained by differen heories of unemploymen. Firs is he efficiency wage heory, in which here is a cos as well as a benefi o he firm of paying lower 18 GLOBAL ECONOMY AND DEVELOPMENT PROGRAM

23 wages (e.g., he model of Shapiro and Sigliz 1984). The second are he conracing models (explici and implici conracs). Under implici conracs, here is a long-erm relaionship beween firms and workers. Firms do no hire workers afresh every period bu, raher, many jobs involve long-erm aachmens and considerable firm-specific skills acquired by workers. This model implies ha wages do no have o adjus o clear he labor marke each period. Thus, workers are conen o say in heir curren jobs as long as he salary hey expec o obain is preferable o he ouside job opporuniy. This model is applicable o some labor, especially in cenral and local governmen, as well as some privae firms. The hird model is he insider-ousider model, which assumes ha here are wo groups of poenial workers. The firs group is he insiders who have some connecion wih he firm a he ime of bargaining, and hus he wage conrac akes heir ineres ino accoun. The second group are he ousiders who have no iniial connecion wih he firm bu who may be hired afer he conrac is se. This model assumes ha he ousiders and insiders wages are linked. The fourh model is he bargaining heory of wages, which holds ha wages, work hours and condiions are dependen on he relaive bargaining srenghs of he paries involved in he agreemen. The deails of wage bargaining are presened by Huizinga e al. (2001) (see appendix 2). The differen bargaining srucures show differen relaionships beween an increase in he real consumpion wage and he real produc wage (see Flanagan, Moene and Wallersein 1993). Under markup pricing, wih increases in wages in one secor and no ohers, oupu price will increase bu he impac on he consumer price will be smaller. Conversely, if bargaining is cenralized so ha wages rise in mos of he economy, hen he increase in real produc wages will be similar o he increase in he consumpion wage. The price wedge also depends on he exen of produc marke compeiion. If a paricular indusry is exposed o inense foreign compeiion, produc prices canno be increased as much, even hough domesic wages rise. However, since he consumpion baske conains impored goods and services, foreign rade and he domesic service secor will also influence he price of real consumpion wages. If a naionwide wage increase iniially affecs a highly exposed indusry wih oupu prices already a or above he compeiive foreign rade levels, he indusry has hree opions. Firs, i can reduce employmen unil he marginal cos equals he compeiive price. Second, i can increase labor produciviy. Or hird, i can close down he indusry wih regard o labor produciviy. I is imporan o make a disincion beween a rise in labor produciviy due o echnological progress or an eliminaion of previous excess capaciy. In Kenya, here are formal collecive wage bargaining agreemens, and here are also adminisered minimum wage guidelines. The governmen legislaes minimum wages hrough wage guidelines, inroduced in 1973, o guide he Indusrial Cour in adjudicaing rade dispues. The governmen made some changes in Wage guidelines were liberalized, allowing workers and employers greaer freedom in wage negoiaions for maximum compensaion for rises in he cos of living. The wage guidelines give consideraion o produciviy and performance in addiion o changes in he cos of living as refleced by he inflaion rae. The empirical equaion for esing is in he form pc, py, a2rer a3r 3 w pc, pr a0 a1, (24) A THEORETICAL FRAMEWORK FOR KENYA'S CENTRAL BANK MACROECONOMETRIC MODEL 19