1 Universiy of Connecicu Economics Working Papers Deparmen of Economics Ocober 2005 Measuring Poenial Oupu and Oupu Gap and Macroeconomic Policy: The Case of Kenya Angelica E. Njuguna Kenyaa Universiy and KIPPRA Sephen N. Karingi Unied Naions Economic Commission for Africa Mwangi S. Kimenyi Universiy of Connecicu Follow his and addiional works a: hp://digialcommons.uconn.edu/econ_wpapers Recommended Ciaion Njuguna, Angelica E.; Karingi, Sephen N.; and Kimenyi, Mwangi S., "Measuring Poenial Oupu and Oupu Gap and Macroeconomic Policy: The Case of Kenya" (2005). Economics Working Papers hp://digialcommons.uconn.edu/econ_wpapers/200545
2 Deparmen of Economics Working Paper Series Measuring Poenial Oupu and Oupu Gap and Macroeconomic Policy: The Case of Kenya Angelica E. Njuguna Kenyaa Universiy and KIPPRA Sephen N. Karingi Unied Naions Economic Commission for Africa Mwangi S. Kimenyi Universiy of Connecicu Working Paper Ocober Mansfield Road, Uni 1063 Sorrs, CT Phone: (860) Fax: (860) hp://www.econ.uconn.edu/ This working paper is indexed on RePEc, hp://repec.org/
3 Absrac Measuring he level of an economy.s poenial oupu and oupu gap are essenial in idenifying a susainable non-inflaionary growh and assessing appropriae macroeconomic policies. The esimaion of poenial oupu helps o deermine he pace of susainable growh while oupu gap esimaes provide a key benchmark agains which o assess inflaionary or disinflaionary pressures suggesing when o ighen or ease moneary policies. These measures also help o provide a gauge in he deermining he srucural fiscal posiion of he governmen. This paper aemps o measure Kenya.s poenial oupu and oupu gap using alernaive saisical echniques and srucural mehods. Esimaion of poenial oupu and oupu gap using hese echniques shows varied resuls. The esimaed poenial oupu growh using differen mehods gave a range of.2.9 o 2.4 percen for 2000 and a range of.0.8 o 4.6 for Alhough various mehods produce varied resuls, hey however provided a broad consensus on he over-all rend and performance of he Kenyan economy. This sudy found ha firsly, poenial oupu growh is declining over he recen ime and secondly, he Kenyan economy is conracing in he recen years. Journal of Economic Lieraure Classificaion: N10, N17, O47 The auhors would like o acknowledge he valuable research assisance provided by Paul Gachanja; and he helpful commens from he paricipans of he 8h Annual Conference on Economeric Modelling for Africa (Universiy of Sellenbosch, Souh Africa, July 2003), paricularly from Adrian Pagan, John Muellbauer, Sephen Hall and Nelene Ehlers; also of John Randa from KIPPRA.
4 1 1.0 Inroducion Measuring he level of an economy s poenial oupu and oupu gap are essenial in idenifying a susainable non-inflaionary growh and assessing macroeconomics policies. Poenial oupu is considered he bes composie indicaor of he aggregae supply side capaciy of an economy and hus becomes an imporan subjec of research ineres (Denis, Mc Morrow and Roger 2002). Poenial oupu is he maximum oupu an economy could susain wihou generaing rise in inflaion (De Masi 1997). Is esimaed rend helps deermine he pace of susainable growh. Oupu gap 1 represens ransiory movemens from he poenial oupu. Is esimaes provide a key benchmark agains which o assess inflaionary or disinflaionary pressures and he cyclical posiion of he economy. When he acual oupu is greaer han he poenial oupu, his implies ha an economy is experiencing excess demand. This siuaion is ofen seen as a source of inflaionary pressures and calls for appropriae policy responses ha involve reducing aggregae demand such as reduced governmen spending and ighening of moneary policy. The reverse, which indicaes excess capaciy, may require easing of moneary condiions and oher policies o simulae demand. Poenial oupu and oupu gap have also direc relevance on governmen fiscal policy since governmen revenues and expendiures are affeced by he cyclical posiion of he economy (Donders and Kollau 2002). In an upurn, he budge balance will be more posiive owing o higher revenues and lower growh of expendiure. In a downurn, he opposie holds. In his case, poenial oupu and oupu gap can be used in he deerminaion of he cyclically adjused budge balance. A cyclically adjused budge balance is equal o he acual budge balance correced for divergences of acual from poenial oupu, and hus provides a measure of he governmen srucural fiscal posiion. Measuring poenial oupu and oupu gap is ofen associaed wih business cycle decomposiion mehods of separaing he rend or permanen componen of a series from is ransiory or cyclical componen (see iner alia Beveridge and Nelson 1981; Blanchard and Quah 1989; King, Plosser, Sock and Wason 1991; and Hodrick and Presco 1997). Poenial oupu corresponds o he rend or permanen componen while oupu gap is he ransiory or cyclical componen. Pagan (2003), however, argues ha such gaps are no business cycle 1 In general, oupu gap represens he difference beween he acual and he poenial oupu or he ransiory movemens from he poenial oupu, measured as a share of poenial oupu.
5 2 indicaors even hough hey are commonly labelled as such. Accordingly, a given level of an oupu gap is compaible wih being in eiher an expansion or a conracion. A number of echniques for measuring poenial oupu and oupu gap have been developed 2. However, many researchers believe ha none is compleely saisfacory. This is manifesed from he resuls of many empirical sudies showing ha differen mehodologies and assumpions for esimaing a counry's poenial oupu and oupu gap produce differen resuls (see for example de Brouwer 1998; Dupasquier, Guay and S-Aman 1999; Scacciavillani and Swagel 1999; and Cerra and Saxena 2000). The difficuly arises since neiher poenial oupu nor oupu gap is direcly observable. Moreover, hese measures mus be derived from heir hypohesized deerminans and oher informaion, such as observable variables ha are hough o be correlaed o he poenial oupu and oupu gap (Laxon and Telow 1992). The difficuly is compounded by he fac ha here is increasing evidence suggesing ha oupu series are bes characerized as inegraed series (Nelson and Plosser 1982). Therefore he presence of sochasic componen does no allow he poenial oupu o be reaed as simply a deerminisic componen. Based on he proposiions discussed above, i is believed ha measuring poenial oupu and oupu gap wih some degree of accuracy is essenial for he formulaion of sound macroeconomic policies. Hence, his sudy aemps o measure hisorical and curren Kenya s poenial oupu and oupu gap and deermine heir implicaions for boh moneary and fiscal policies. To dae, here have been no in deph sudies ha have sough o esimae Kenya s poenial oupu and oupu gap. This sudy is herefore crucial o a beer undersanding of he Kenyan economy. 1.1 The Oupu Trends in Kenya One of he common characerisics or sylized movemens of many economic variables is he presence of rend 3. Looking a Figure 1.1, i is eviden ha Kenyan GDP (Gross Domesic Produc) or oupu series displays a clear rend. The Kenyan real GDP a facor cos shows a generally upward rend, alhough i is inerruped by some marked declines, followed by he resumpion of posiive growh. I can also be observed ha here are obvious flucuaions around he oupu rend. Empirical invesigaions sugges ha for many counries oupu series 2 See a hisorical accoun from Laxon and Telow (1992). 3 See Enders (1995).
6 3 do no have a ime-invarian mean and herefore nonsaionary. However, by mere observaion of he Kenyan oupu plo in Figure 1.1, i is difficul o conclude wheher i is saionary or no. Figure 1.1 GDP a Facor Cos (In Consan 1982 Prices) Value (In Billion Ksh) Source of basic daa: KIPPRA-Treasury Macro Model, see Geda e al. (2001) and Huizinga e al. (2001). The growh in Kenyan real GDP as shown in Figure 1.2 is characerized by more or less regular flucuaions or cycles. Figure 1.2 indicaes ha he Kenyan economy conraced in four disinc periods ha is in , 1984, and These periods correspond o he firs oil crisis, drough, macroeconomic insabiliies in he economy characerized by high inflaion and anoher proraced drough, respecively. The recession in 2000 was deeper han he previous ones. In he lieraure, recessions are associaed wih negaive oupu gaps or excess capaciy. Furher, he cycles observed in he oupu growh seem o be repeaed every eigh o en years.
7 4 Figure 1.2 GDP Growh a Facor Cos a Consan 1982 Prices (In percen) Growh Raes (In percen) Source of basic daa: KIPPRA-Treasury Macro Model, see Geda e al. (2001) and Huizinga e al. (2001). Figure 1.3 Inflaion Rae a 1982 Base prices In percen Source of basic daa: Ryan 2002.
8 5 Since poenial oupu is relaed o inflaion, i is worh looking a is behaviour as well. The plo of he inflaion series is shown in Figure 1.3. Kenyan inflaion is also characerized by persisen flucuaions and in mos cases in he double-digis wih a highes rae of abou 46 percen in This hyperinflaion was due o excessive money supply growh during Kenya s firs muli-pary elecion 4. In he same period, oupu growh dropped o less han one percen. In he las four years of he sample period, inflaion seems o have sabilised a single digi. Despie he low inflaion rae, oupu growh in he las five years has been relaively low. The nex secion reviews various mehods of esimaing oupu poenial and oupu gap. 2.0 Review of Esimaion Mehods In his secion, some of he mos popularly used mehodologies for esimaing poenial oupu and oupu gap are reviewed. In general, he differen approaches o esimaing poenial oupu are classified ino wo: saisical derending and esimaion of srucural relaionships. The difference is ha he former approach aemps o separae he process ino permanen and cyclical componens while he laer isolaes he effecs of srucural and cyclical influences on oupu using economic heory (Cerra and Saxena 2000). Some of he derending mehods include he Hodrick-Presco filer and he unobserved componens mehods (univariae, bivariae, and common permanen and cyclical componens). The approaches for esimaing srucural relaionships include he linear mehod, srucural vecor auoregression (VAR) mehod and producion funcion mehod. 2.1 The Linear Mehod The simples way o esimae he oupu gap and poenial oupu is o use a linear rend. This mehod is based on he assumpion ha poenial oupu is a deerminisic funcion of ime and he oupu gap is a residual from he rend line. This mehod presumes ha oupu is a is poenial level on average, over he sample period 5. Hence rend in oupu, which represens poenial oupu, may be esimaed as = α ˆ + αˆ Trend y 0 1 (2.1) 4 This even is hough o be an afermah of he so-called Poliical Business Cycles where he main assumpion is ha policymakers can manipulae he economy o affec economic oucomes (Chorareas 1999). 5 This is conrary o he hrough-he-peaks mehod, which suggess ha poenial oupu is he maximum possible oupu. See Laxon and Telow (1992) for more discussion on he laer mehod including is weaknesses.
9 6 where y is oupu rend, ˆα i, i = 0,1 are esimaed coefficiens from he regression of he acual oupu on ime rend variable. Oupu gap is obained using c = y y (2.2) where c is he oupu gap, y is he acual oupu, 1, 2,, T is a ime index. y is he poenial oupu from (2.1), and = One of he major limiaions of his mehod is ha he long-run evoluion of he ime series is deerminisic and herefore perfecly predicable. Beveridge and Nelson (1981) argued ha if in fac he changes in economic series are a random process, hen he deviaion of he series from any deerminisic pah would grow wihou bound. Furhermore, o impose a deerminisic ime rend when one is no in fac presen may severely disor he apparen saisical properies of he resuling cycle or ransiory par of he series. Anoher criicism of his mehod is ha he esimae of he gap is found o be sensiive o he sample period used in he regression esimaion. For example, using Ausralian daa, de Brouwer (1998) found ha when he sample sars a he lowes poin in a recession, he slope of he sraigh line fiing he series became seeper, making he gap beween acual and poenial oupu a he end of he sample smaller 6. Therefore, i is imporan o carefully selec he saring period of he regression such as a period when he economy is basically in balance. The oher weakness of he above mehod is ha he assumpion ha poenial oupu grows a a consan rae ofen does no hold 7 (de Brouwer 1998). Since oupu growh can be decomposed ino growh of labour produciviy and of labour inpus, which in urn can be decomposed ino changes in populaion, labour force paricipaion and average hours worked, i is no jusified o assume ha hese componens are consan over ime, especially when an economy has undergone considerable srucural reform, or when here are major changes in improvemens in echnology. 6 This mehod also presens a problem in an inflaionary period (Laxon and Telow 1992). 7 As income level rises over ime, poenial oupu grows a slower raes due o diminishing marginal reurns o reproducible inpus, ceeris paribus.
10 7 2.2 The Hodrick-Presco Mehod The Hodrick-Presco mehod or Hodrick-Presco filer (Hodrick and Presco 1997), hereafer referred o as HP mehod, is a simple smoohing procedure. The main assumpion of his mehod is ha here is a prior knowledge ha growh componen varies smoohly over ime. The HP mehod operaes on a framework ha a given ime series, say expressed as he sum of a growh componen or rend componen or oupu gap c, ha is y (or oupu) may be y (or poenial oupu) and a cyclical y = y + c. (2.3) The measure of he smoohness of y is he sum of he squares of is second difference. The average of he deviaions of c from y is assumed o be near zero over a long period of ime. These assumpions lead o a programming problem of finding he growh componens by minimizing he following expression Min L = T = 1 T 2 y 1 ) = 2 2 c + λ ( y T 2 2 = ( y y ) + λ [(y y 1 ) (y 1 y 2 )]. (2.4) = 1 T = 2 The parameer λ is a posiive number, which penalizes variabiliy in he growh componen series. The larger he value of λ, he smooher is he soluion series. Moreover, as λ approaches infiniy, he limi of he soluions for equaion (2.4) is he leas squares of a linear ime rend model. On he oher hand, as he smoohing facor approaches zero, he funcion is minimised by eliminaing he difference beween acual and poenial oupu ha is making poenial oupu equal o acual oupu. In mos empirical work, he value of λ = 1,600 is chosen when using quarerly daa 8. 8 If he cyclical componens and he second differences of he growh componens were idenically and 2 2 independenly disribued normal random variables wih means zero and variances σ1 and σ 2, respecively, he * condiional expecaion of y would be he soluion o (2.4) when λ = σ 1 / σ2. I is believed ha a fivepercen cyclical componen is moderaely large, as is a one-eigh of one percen change in he growh rae in a quarer. Thus, λ = 5/(1/8) =40 or λ = 1,600 (Hodrick and Presco 1997).
11 8 The HP mehod has been used in a number of empirical sudies (see for example De Masi 1997; de Brouwer 1998; Scacciavillani and Swagel 1999; and Cerra and Saxena 2000). The populariy of his mehod is due o is flexibiliy in racking he characerisics of he flucuaions in rend oupu. The advanage of he HP filer is ha i renders he oupu gap saionary over a wide range of smoohing values and i allows he rend o change overime. Moreover, in mos sudies for developing counries, his mehod is preferred because of considerably less daa requiremens (see De Masi 1997). However, he HP mehod is also far from ideal. This mehod has been criicized and is weaknesses have been well documened in he lieraure (see Harvey and Jaeger 1993). The firs weakness of he HP mehod is ha changing he smoohing weigh (λ) affecs how responsive poenial oupu is o movemens in acual oupu (de Brouwer 1998). de Brouwer (1998) found ha a lower smoohing facor produces a 'smaller' esimae of he gap. For high smoohing facor, he esimae indicaes oupu above poenial, bu for moderae or low smoohing, he esimae suggess oupu below poenial. De Brouwer also found ha he cycles in oupu are sensiive o he smoohing weigh. Thus, an appropriae smoohing parameer (λ) is difficul o idenify. Anoher weakness of he HP mehod is he high end-sample biases, which reflec he symmeric rending objecive of he mehod across he whole sample and he differen consrains ha apply wihin he sample and is edges. This is especially a problem when one is ineresed wih he mos recen observaions in he sample for purposes of drawing conclusion for policy implemenaion and projecions for he immediae fuure. To couner his problem however, researchers use oupu projecions o augmen he observaions. The reliabiliy of measured poenial oupu and oupu gap would hen depend on he accuracy of he forecass used o avoid he end-sample bias. Finally, for inegraed or nearly inegraed series, i has been shown ha an arbirary value of smoohing parameer could lead o spurious cyclicaliy and an excessive smoohing of srucural breaks (Harvey and Jaeger 1993). 2.3 Unobserved Componens Mehod Univariae Beveridge-Nelson Mehod Anoher saisical approach for idenifying he permanen and ransiory componens of oupu involves he use of univariae saisical echniques such as he unobserved componens
12 9 approach suggesed by Beveridge and Nelson (1981) 9. Beveridge and Nelson inroduced a general procedure o decompose a nonsaionary series ino differen componens, which are sochasic in naure. The Beveridge-Nelson (BN) mehodology assumes ha any ime series, which exhibis he kind of homogeneous nonsaionariy ypical of economic ime series, may be decomposed ino wo addiive componens, a saionary series and a pure random walk. The saionary par and he random walk series are respecively, he ransiory and he permanen componens. The ransiory componen is a saionary process which represens he forecasable momenum presen a each ime period bu which is expeced o dissipae as he series ends o is permanen level. On he oher hand, he permanen componen is invariably a random walk wih he same rae of drif as he original daa and an innovaion, which is proporional o ha of he original daa. To follow he BN procedure, le he variable z denoe observaions on a paricular nonsaionary series and is firs difference w = z z -1. If he w s are saionary in he sense of flucuaing around a fixed mean wih sable auocovariance srucure, hen by Wold decomposiion heorem 10, w may be expressed as w µ + ε + λ ε +K (2.5) = 1 1 where µ is he long-run mean of he w series, he λ i s are consans, and he ε s are uncorrelaed random disurbances (or innovaions) wih mean zero and variance The decomposiion of z is guided by considering he relaion of he curren value z o he forecas profile for fuure z s. The forecas profile akes he place of a deerminisic rend as he benchmark for he locaion of he series and herefore for measuring he cyclical componen. The expecaion of ẑ (k) and is given by k 2 σ. z + condiional on daa for z hrough ime is denoed by ẑ (k) = E( z + k z 1, z ) = z + ŵ (1) + + ŵ (k) (2.6) since he z s can be expressed as accumulaion of he w s; and where ŵ (i) = µ + λi ε + λi + 1ε 1 + K (2.7) 9 Also suggesed by Wason (1986). A discussion is also found in Enders (1995). 10 If in a sysem, he only deerminisic componen is he mean erm, he heorem saes ha he sysem has a moving average (MA) represenaion (see Lukepohl 1993).
13 10 is he forecas of zero. w + i a ime since fuure disurbances ε are unknown bu have expecaion Subsiuing equaion (2.7) o (2.6) and gahering erms in each ε yields ẑ (k) = kµ + λ 1 z + ( ) k k+ 1 1 i ε + ( λ ) ε + K 2 i (2.8) Moreover, for a very long forecas horizons, k, equaion (2.8) is approximaely equal o ẑ (k) kµ + by virue of he convergence of λ z + ( ) ε + ( λ ) ε + K 1 i 1 2 i (2.9) Σ λi. I follows ha he forecas profile is asympoic o a linear funcion of k (he forecas horizon) wih slope equal o µ, he rae of drif of he series, and a level (algebraically he inercep) which iself is a sochasic process. Beveridge and Nelson inerpreed his level as he permanen componen expressed as z = λ z + ( ) ε + ( λ ) ε + K 1 i 1 2 i (2.10) The permanen componen of a series as defined in equaion (2.10) is he value he series would have if i were on ha long-run pah in he curren ime period. Beveridge and Nelson showed ha equaion (2.10) is equivalen o a random walk wih a drif and may be invariably expressed as z z = µ + ( ) λ 1 i ε. (2.11) By definiion, on he oher hand, he ransiory or he cyclical porion of z is he difference beween z s permanen componen and is curren value, ha is z z = ( ) λ 1 i 1 ε + ( ) K λ ε + 2 i (2.12) The BN decomposiion mehod is a sraighforward procedure o decompose any nonsaionary process ino a emporary and permanen componen. However, his mehod is no unique since i forces he innovaion in he rend and saionary componens o be perfecly correlaed (see Enders 1995). Anoher limiaion of his mehod is ha wihou addiional ad hoc resricions, he univariae characerizaions are compleely uninformaive of he underlying permanen and ransiory componens (Dupasquier e al. 1999).
14 11 Mulivariae Beveridge-Nelson Mehod The Beveridge and Nelson mehod can easily be exended ino he mulivariae decomposiion mehod (see Dupasquier e al. 1999). Le Z be an n 1 saionary vecor of variables. By he Wold decomposiion heorem, Z can be expressed as he following reduced form: Z = δ() + C(L) ε (2.13) where δ() is deerminisic, C(L) = i= 0 i CiL is a marix of polynomial lags, C 0 = I n is he ideniy marix, he vecor ε is he one-sep-ahead forecas errors in Z given informaion on lagged values of Z, E ( ε ) = 0, and E( ε ε ) = Ω wih Ω posiive definie. Here i is assumed ha he deerminanal polynomial C(L) has all is roos on or ouside he uni circle and hence, Z is saionary. Equaion (2.13) can be decomposed ino a long-run componen and a ransiory componen as: Z = δ() + C(1) ε + C*(L) ε, (2.14) where he long-run muliplier C(1) = C i=0 i and C*(L) = C(L) C(1). Assuming ha he firs elemen in Z is oupu, hen y = µ + C (1)ε + C (L) ε (2.15) y y y Now, poenial oupu is defined by he firs wo erms on he righ-hand side of equaion (2.15), ha is y = µ + C (1) ε. (2.16) p y y 2.4 Srucural Vecor Auoregression Mehod The srucural vecor auoregression (VAR) considers aside from oupu oher macroeconomic variables o esimae poenial oupu and oupu gap. By doing so, i does no consrain he shor-run dynamics of he permanen componen of oupu o a simple random walk process.
15 12 Dupasquier e al. (1999) suggesed ha i will ofen be useful for researchers and policymakers o include he dynamics of permanen shocks in poenial oupu since hey are more likely o reflec he producion capaciy of he economy. Tradiionally, he oupu is idenified wih he aggregae supply capaciy of he economy and cyclical flucuaions wih changes in aggregae demand. This mehodology was popularized by Blanchard and Quah (1989) where oupu was considered o be a linear combinaion of supply disurbances and demand disurbances. Blanchard and Quah assume ha he firs disurbances have a long-run effec on oupu while he oher have only emporary effecs on i. They used unemploymen o idenify he cyclical componen of he oupu. Blanchard and Quah found ha demand disurbances have a hump-shaped effec on oupu and unemploymen, which disappears afer approximaely wo o hree years, and ha supply disurbances have an effec on he U. S. oupu, which cumulaes over ime o reach a plaeau afer five years. They also concluded ha demand disurbances make a subsanial conribuion o oupu flucuaions a shor- and medium-erm horizons. From esimaion of he join process for oupu and unemploymen, and he idenifying resricions, one can form he demand componens of oupu and unemploymen. These are he ime pahs of oupu and unemploymen ha would have obained in he absence of supply disurbances. Similarly, by seing demand innovaions o zero, one can generae he ime-series of supply componens in oupu and unemploymen. From he idenifying resricion ha demand disurbances have no long-run effec on oupu, he resuling series of he demand componen in he level of oupu is saionary. Likewise, boh he demand and supply componens of unemploymen are saionary. King e al. (1991) exended he Blanchard and Quah model ino a hree-variable reduced form VAR sysem, which include oupu, invesmen and consumpion. King e al. used he long-run balanced-growh implicaion o isolae he permanen shocks in produciviy and hen o race ou he shor-run effecs of hese shocks. The economeric procedures rely on he fac ha balanced growh under uncerainy implies ha consumpion, invesmen, and oupu are coinegraed or relae in he long run. On he applicaion of he model using U.S. daa, King e al. found ha he resuls boh suppor and conradic he claim ha a common sochasic rend, i.e. he cumulaive effec of permanen shock o produciviy underlies he bulk of economic flucuaions. The US daa are consisen wih he presence of a common sochasic produciviy rend. Such a rend is capable of explaining imporan componens of flucuaions in consumpion, invesmen, and oupu. However, he common rend s explanaory power
16 13 drops off sharply when oher variables such as measures of money, he price level, and he nominal ineres rae are added o he sysem. The Model The srucural VAR mehodology can be used o esimae poenial oupu and oupu gap wih appropriae resricion imposed on oupu 11. Following Dupasquier e al. (1999), le Z be an n 1 saionary vecor including a n 1 -vecor of I(1) variables and a n 2 -vecor of I(0) variables such ' 1 ha Z = ( X, X ' 2 following reduced form: ). By he Wold decomposiion heorem, Z can be expressed as he Z = δ() + C(L) ε (2.17) where δ() is deerminisic, C(L) = i= 0 C i i L is a marix of polynomial lags 12, C 0 = I n is he ideniy marix, he vecor ε is he one-sep-ahead forecas errors in Z given informaion on lagged values of Z, E( ε ) = 0, and E( ε ε ) = Ω wih Ω posiive definie. Equaion (2.17) can be decomposed ino a long-run componen and a ransiory componen: Z = δ() + C(1) ε + C*(L) ε, (2.18) where C(1) = C i=0 i and C*(L) = C(L) C(1). C 1 (1) is defined as he long-run muliplier of he vecor X 1. If he rank of C 1 (1) is less han n 1, here exiss a leas one linear combinaion of he elemens in X 1 ha is I(0). In oher words, here exiss a leas one coinegraion relaionship beween hese variables. The model assumes ha Z has he following srucural represenaion: Z = δ() + Γ(L) η (2.19) 11 Generally called long-run resricions imposed on oupu (LRRO). This erm is used by Dupasquier e al. (1999) o generalize he mehod involving he srucural vecor auoregression used by Blachard and Quah (1989); King, e al. (1991) and ohers. 12 I is assumed ha he deerminanal polynomial C(L) has all is roos on or ouside he uni circle.
17 14 where η is an n-vecor of srucural shocks, E( η ) = 0 and E( η η ) = I n (a simple normalizaion). From he esimaed reduced form, he srucural form (2.19) can be recovered using he following relaionship: Γ 0 Γ 0 = Ω, ε = Γ0 η, and C(L) = Γ(L) 1 0 Γ. The long-run covariance marix of he reduced form is equal o C(1) ΩC(1). Equaions (2.18) and (2.19) gives C(1) ΩC(1) = Γ(1)Γ(1). (2.20) This relaion suggess ha he marix Γ 0 can be idenified wih an appropriae number of resricions on he long-run covariance marix of he srucural form. Le he log of oupu be he firs variable in he vecor Z. I is hen equal o: y = p p c y + Γy L) η + Γy (L) c µ ( η (2.21) where p η is he vecor of permanen shocks affecing oupu and c η is he vecor conaining shocks having only a ransiory effec on oupu. Poenial oupu is hen expressed as p y = p y + Γy L) p µ ( η. (2.22) Thus, poenial oupu corresponds o he permanen componen of oupu. The par of oupu due o ransiory shocks is defined as he oupu gap, ha is c y = c y L) c Γ ( η (2.23) Dupasquier e al. (1999) argued ha one advanage of he approach based on long-run resricions is ha i allows for esimaed ransiional dynamics following permanen shocks. Dupasquier e al. also provide evidence ha here is a saisically significan gradual diffusion process associaed wih permanen shocks.
18 The Producion Funcion Mehod An alernaive srucural approach o esimae poenial oupu and oupu gap is he use of aggregae producion funcion. This approach relaes poenial oupu o he availabiliy of facors of producion and echnological change (see for example Denis e al. 2002). Suppose ha oupu can be characerized as a Cobb-Douglas producion funcion as Y = L α K 1-α TFP (2.24) where Y is oupu, L is labour employed, K is capial sock, TFP is he oal facor produciviy and α is he labour share of income. TFP is defined as equal o (see Denis e al. 2002): TFP = ( E )( U α 1 α ) (2.25) α 1 α L E K L U K which summarises boh he degree of uilisaion (U) of facor inpus as well as heir echnological level (E). If inpus are equilibrium values, hen equaion (2.24) provides an esimae of poenial oupu. Wih he esimaed value of parameer 13 α, he TFP is given as: log(tfp ) = log(y ) αlog(l ) (1 α)log(k ) (2.26) where i is compued as a residual. A rend is hen fied o he residual, TFP, in order o obain an esimae of rend produciviy o be used in he esimaion of poenial oupu where a normal level of efficiency of facor inpus is assumed. The rend efficiency level is usually measured as he HP filered Solow Residual 14. To obain he poenial oupu, assumpion on he poenial employmen needs o be made. Mos sudies have differen assumpions on how o esimae poenial employmen (see for example de Brouwer 1998; Cerra and Saxena 2000; and Dennis e al. 2002). However, he main concern is o find he level of employmen ha is consisen wih non-acceleraing inflaion or he NAIRU (non-acceleraing inflaion rae of unemploymen). In Denis e al. (2002), poenial employmen is generaed from a smoohed labour force series, which is generaed by applying a HP filered paricipaion rae o he working age populaion figures. The smoohed 13 Usually by regressing log of Y on logs of L and K. 14 Since produciviy growh changes over ime, a simple linear rend is inappropriae.
19 16 paricipaion rae leads o a less volaile labour force series. Then, poenial employmen (L ) is compued o be he labour force (LF * ) minus he NAIRU esimaes 15, ha is L = LF * (1 NAIRU). (2.27) Formally, he poenial oupu (Y * ) is herefore given as: Y * = TFP * (L ) α (K) 1-α. The producion funcion approach can provide useful informaion on he deerminans of poenial growh. Despie he difficuly in esimaion, his approach is inuiively appealing and is widely used (see De Masi 1997; and Denis e al. 2002). One advanage of using producion funcion is ha i is capable of highlighing he close relaionship beween he poenial oupu and NAIRU conceps, given ha he producion funcion approach o calculaing poenial oupu requires esimaes o be provided of normal or equilibrium raes of unemploymen. Moreover, he producion funcion approach provides possibiliy of making forecass, or a leas building scenarios, of possible fuure growh prospecs by making explici assumpions on he fuure evoluion of demographic, insiuional and echnological rends. However, given he significan amoun of daa requiremen for his approach and a whole wide range of assumpions o derive variables, his mehod is difficul o use. Aside from difficul esimaion process, he producion funcion mehod has also several weaknesses (see Laxon and Telow 1992). For example, Laxon and Telow (1992) poined ou ha here has been no useful model of esimaing he produciviy and hence, esimaes are based on rend and herefore poenial oupu is essenially exogenous ime rends. Moreover, he problems of rend eliminaion for GDP are shifed o he rend esimaes of he inpus. Derending echniques such as he HP filer are used for smoohing he componens of he facor inpus. 3. Empirical Esimaes of Poenial Oupu and Oupu Gap The esimaion of poenial oupu and oupu gap for Kenya in his sudy uses a daabase from he KIPPRA-Treasury Macro Model 16 (KTMM) and Economic Surveys published by he Kenya 15 See for example Sraiger e al. (1996) and Debelle and Vickery (1997) for NAIRU esimaion. 16 The daabase are comprised of informaion colleced from differen sources mos of which are from official governmen records and largely from Kenya Cenral Bureau of Saisics (see Geda e al. 2001; and Huizinga e al. 2001)
20 17 Cenral Bureau of Saisics. The daa include annual informaion on GDP a facor cos, privae consumpion and capial sock all a consan 1982 prices from 1972 o 2001; labour force and inflaion 1986 based. Daa on no employed rae o proxy unemploymen rae and oal employmen were derived (see Appendix). The following sub-secions presen he esimaion resuls from differen mehodologies discussed in Secion The Linear Mehod The simples rend-cycle decomposiion mehod, which uses he linear mehod, yields he following equaion for esimaing Kenyan s poenial oupu: y = Trend (3.1) (0.6825) (0.0384) (s.e.) ( ) ( ) (-raio) R 2 = DW = The resuls show ha he coefficiens of he esimaed equaion are highly significan and ha he regression line is close o a perfec fi. However, he Durbin-Wason saisics show some evidence of auocorrelaion in he residuals, which implies ha he model is misspecified. The esimaes of poenial oupu based on he linear rend are shown on Figure 3.1. The figure shows ha poenial oupu in 2000 and 2001 are above he acual oupu wih growh raes of 2.4 percen for boh years (Table 3.1). According o his mehod, growh in Kenya s poenial oupu has been declining seadily over he period of he sudy (ie o 2001). This o a large exen suggess ha here have been unsusained and fruiless effors o achieve high growh raes. Moreover, susained negaive oupu gaps are observed in four periods: , , and wih lowes poins a -4.6 percen, -4.3 percen, -1.8 percen and -3.5 percen, respecively. Figure 3.1 also shows ha from , he Kenyan economy in mos cases was in excess capaciy while in he laer periods from , he reverse is observed. I is worh observing ha since 1996, here has been a prolonged period of declining oupu poenial. 3.2 The Hodrick-Presco Mehod For he Hodrick-Presco (HP) esimaions, wo alernaives for he smoohing parameer λ were considered namely: λ = 100 and λ = In boh cases, acual oupu is lower han poenial oupu in 2000 and 2001, which suggess ha Kenyan economy is currenly in excess capaciy (see Figure 3.2). Resuls from HP(100) showed ha poenial oupu growh is abou
21 percen in 2000 and 2001 while HP(1600) gave a poenial oupu growh of 2.3 percen in boh years. Negaive oupu gaps were also observed in he same period as in using he linear rend mehod. In mos cases, he peaks and roughs of HP(1600) are larger han HP(100). I can be observed ha he resuls of HP(1600) are closer o he linear mehod, which coincides wih oher empirical resuls. For example, he growh in he poenial oupu in he laer mehod is 2.4 percen while poenial oupu growh in he former is 2.3 percen in 2000 and This is no surprising since he higher he value of he smoohing parameer, he closer is esimaes o he ime rend. 3.3 Unobserved Componens Mehods Univariae Beveridge-Nelson Mehod For he univariae Beveridge-Nelson (UBN) decomposiion mehod he bes model ha fis he Kenyan oupu, is an ARIMA(0,1,2) based on simple diagnosic ess using Akaike-Informaion Crierion(AIC), Schwarz Crierion (SC) and he significance of coefficiens. The esimaed equaion is as follows: y = ε ε ε -2 (3.2) (0.4588) (0.1611) (0.1605) (s.e.) (5.0761) (5.1337) (3.4281) (-raio) The model esimae of he Kenya s poenial oupu closely racked he acual movemens in oupu (see Figure 3.3). This resul seems o conform o oher sudies (see Cerra and Saxena 2000) ha BN decomposiion ends o produce rend componens (ie. poenial oupu), which are close o he acual oupu. However, he BN mehod produced a highly volaile series of poenial oupu growh for he Kenyan economy. The resuls using his mehod had a poenial oupu growh of 4.6 percen in 2001 for he Kenyan economy 17, which is he highes rae compared o he esimaes of he oher mehods used in his sudy. On he oher hand, i produces a poenial oupu growh of 2.9 percen in The cyclical componen of oupu, which is he oupu gap, does no have disinc cycles compared o he HP and linear mehods. Much of he oupu gaps observed are negaive over he whole of he sudy period. 17 The World Bank also found an oupu poenial growh of around 4.6 percen for he Kenyan economy as conained in a draf Counry Economic Memorandum (CEM). This figure, however, was derived using panel regression resuls of differen counries and paid paricular emphasis on he correlaion of Kenyan s circumsances o hose of some of he counries in he panel resuls used in he CEM analysis.
22 19 Mulivariae Beveridge-Nelson Mehod The esimaes of he mulivariae Beveridge-Nelson (MBN) decomposiion mehod were derived by esimaing a vecor auoregressive represenaion of he variable Z, which is composed of he change in oupu ( y ) and he difference beween oupu and privae consumpion (y c ) represening he cyclical demand (see Dupasquier e al. 1999). Boh series are found o be saionary, I(0). Then, he esimaes of he VAR(2) model were invered o obain is vecor moving average represenaion. The number of lags of he VAR(2) model was chosen using he AIC 18.number The esimaes of Kenya s poenial oupu using MBN also racked he acual oupu very closely (Figure 3.4). The series of he poenial oupu growh is also highly volaile bu he peaks and roughs are shorer han is univariae counerpar. However, he cyclical componen of he MBN ends o be more reflecive of business cycles, alhough he daing periods do no coincide o he cycles of he HPs. The urning poins of he MBN seem o lag by one or wo periods o hose of he HPs. The MBN resuls showed ha acual and poenial oupu are almos a he same level in 2000 and The MBN esimaed a relaively lower poenial oupu growh of 1.6 percen and 1.2 percen, respecively in 2000 and Srucural Vecor Auoregression Mehod As in he MBN decomposiion mehod, a vecor auoregressive represenaion of he variable Z were firs esimaed and hen invered o derived is moving average represenaion. The idenifying resricions discussed in Secion 2 were used o recover he srucural innovaions. A similar se of variables from MBN esimaion was used in he srucural vecor auoregression (SVAR) esimaion ha is, he change in oupu ( y ) and he difference beween oupu and privae consumpion (y c ) represening he cyclical demand, herefore Z = [( y (y c) ] (see Dupasquier e al. 1999). The mehodology assumes ha oupu in firs differences follows a saionary sochasic process responding o wo ypes of srucural shocks namely permanen (supply, ε s ) and ransiory (demand, ε d ). As in Dupasquier e al. (1999), i is assumed ha demand does no have a long run effec on oupu, which implies ha he marix of long-run coefficiens C(1) is upper riangular. The long-run represenaion for variable Z is given as: 18 The likelihood raio es ends o give a higher number of lags while he SC ends o give a lower number of lags. Since he number of observaions is limied, a rade off beween he wo crieria is used, ha is he AIC.
23 20 y (y c) C = C (1) (1) C C (1) ε (1) ε s d (3.3) where C 12 (1) is assumed o be zero, which implies ha oupu is affeced only by supply shocks. The assumpions on he covariance marix and he long-run resricion on oupu were used as he idenifying resricions o recover he srucural disurbances. The impulse-response funcion (Figure 3.5) based on VAR(2) model shows ha supply shocks have posiive long-run effec on oupu while demand shocks end o have shorer effecs. However, resuls showed ha supply shocks do no have permanen effec on oupu as responses diminish wih ime. The srucural VAR resuls show ha esimaes of poenial oupu also follow closely he movemens of he acual oupu (Figure 3.6). This approach produced esimaes of poenial oupu growh of 1.3 percen and 0.8 percen for 2000 and 2001, respecively. The VAR poenial oupu growh for 2001 is he lowes esimae compared wih he oher mehods (Table 3.1). However he series of poenial oupu growh resembles some degree of similariy o he movemen of he acual growh series. The esimaed oupu gaps using srucural VAR showed some small bu more frequen cycles and showing more negaive oupu gaps over he sample period even in he earlier period. 3.5 The Producion Funcion Mehod In he esimaion of poenial oupu using producion funcion approach, several variables or informaion are needed. The basic ones are he oal facor produciviy (TFP), poenial employmen (L * ), and capial sock. The capial sock is given using he KTMM daa while he TFP and L * were derived 19. The TFP is he calculaed residual from he regression of he log of oupu on log of capial and log oal employmen. The HP mehod was applied o he calculaed residual o obain an esimae of rend produciviy. Several forms of he Cobb- Douglas producion funcion were esimaed 20. The model, which excludes echnology, yields he bes esimaion resuls for α, he share of labour in oupu, which was found o be equal o around Similar esimaions for he European counries found an esimae of 0.62 (see Dennis e al 2002). I is also noeworhy o menion ha a more recen U.S. daa showed ha he raio of labour income o oal income is abou 0.70 (see Mankiw 2000). Hence, he 19 See Appendix B for procedures in he derivaion of daa used in he esimaion of poenial oupu using producion funcion mehod.
24 21 esimaed α = 0.76 seems o be reasonable for he Kenyan case. In he esimaion of poenial employmen, an esimae of NAIRU is necessary. In his sudy, he procedure from Debelle and Vickery (1997) was adaped and resuls are given in Appendix B. The esimaed series of poenial oupu from he producion funcion approach follows he movemen of he acual oupu closely in mos periods ha is from 1974 up o 1999 (Figure 3.7a). A wider gap was observed beween acual and poenial oupu in periods beween 1990 o 1994 and 1998 o The period was dominaed by posiive oupu gap, which implies ha he Kenyan economy was mos of he ime operaing a excess demand. Consequenly, his paricular period is when Kenyan inflaion was also rising. Since poenial oupu is he susainable non-inflaionary level of oupu, is esimaes during he same period reflec a downward pressure on poenial employmen due o high inflaion, which made he esimae of poenial oupu o be lower han he acual oupu. On he oher hand, he period was dominaed by negaive oupu gap, which implies ha here is excess capaciy in he economy. The calculaed poenial oupu growh, in mos cases, is characerized by regular small flucuaions. However, he flucuaions become volaile in he 1990s (Figure 3.7b). These resuls also reflec he highly volaile inflaion in Kenya during he same period. One ineresing resul is ha he growh in poenial oupu excep in , is generally declining owards he end of he sample period, which copies similar rend from he oher mehods. The resuls of he esimaed oupu gaps as proporion of he poenial oupu from he producion funcion approach are given in Figure 3.7c. Like he resuls using oher mehods, he esimaed series shifs from posiive o negaive quadrans from ime o ime and records negaive oupu gap in he las few years of he sample period. However, he flucuaions are no regular and here are no definie cycles in he series. 4.0 Summary and Conclusions This sudy aemps o esimae Kenyan poenial oupu and oupu gap using differen mehods namely he linear ime rends, HP mehod, univariae and mulivariae Beveridge- Nelson, he srucural VAR and he producion funcion approach. Each mehod has 20 Models, wih and wihou echnology as one of he explanaory variables, were esimaed. Technology in he form of Harrod-nueral and Hicks-nueral echnical progress were boh considered.
25 22 advanages and disadvanages as discussed in Secion 2. The esimaion resuls for he values of poenial oupu level and is growh, and he oupu gap vary from mehod o mehod, however resuls from mos mehods seems o be consisen wih one anoher, which means ha a consensus may be buil on how he Kenyan economy has been performing in erms of is poenial capaciy and growh. Poenial Oupu Growh Tables 3.1 and 3.2, respecively, summarize he poenial oupu growh in 2000 and 2001, and he average five-year growh from 1973 o Esimaes of poenial oupu growh in 2000 using differen mehods ranged from 2.9 (UBN) o 2.4 (linear mehod) percen, while in 2001 he range is 0.8 (SVAR) o 4.6 (UBN) percen (see Table 3.1). The univariae Beveridge- Nelson (UBN) gave resuls ha are exreme in boh years, ha is he lowes growh in 2000 and he highes growh in Alhough he magniudes of growh are differen from mehod o mehod, all resuls show a decline in poenial growh from 2000 o 2001, excep for he case of he UBN mehod. From Table 3.2, i can be furher observed a generally declining rend in poenial oupu growh over he sample period. The average growh in gave a range of 5.03 (HP100) o 6.42 (UBN) percen. In he same period, he growh esimaes from all mehods are higher han all heir corresponding resuls of five-year growh averages from in 1981 o Similarly, each mehod esimae of he average growh in ranging from 0.84 (UBN) o 2.61 (SVAR) percen is he lowes compared o he corresponding five-year average growh in each mehod for all years. Esimaes of poenial oupu growh in 2001 from each mehod are consisenly lower han each of he corresponding five-year averages in he earlier years. This observed general declining rend in he growh of poenial oupu was also observed in he acual oupu or he Kenyan GDP growh. Acual oupu grew a an average of 5.82 percen in and reduced o 1.99 percen in while a growh rae of 1.20 percen was recorded in Oupu Gap To derive a good insigh, he esimaes of he oupu gap from he differen mehods may be compared o he expeced oupu gap in he Kenyan economy wih respec o he differen imporan economic evens boh domesic and inernaional evens. These are he firs oil shocks ha occurred in ; he coffee boom in ; he second oil crisis in 1979; he drough in 1984; he beginning of he implemenaion of he srucural adjusmen program
26 23 (SAP) in 1986; and he rising inflaion in he beginning of he 1990s. During he periods of oil crisis and drough, negaive oupu gaps may be expeced since hese shocks would have lowered economic aciviy due o higher coss of producion and lower revenues. Hence, acual oupu is lower han poenial oupu. On he oher hand, he periods of coffee boom, implemenaion of SAP 21 and rising inflaion may have increased aggregae demand due o expansion in economic aciviy or increased money supply in he economy. In hese cases, posiive oupu gap may be expeced. The esimaes of oupu gap series using linear rend, HPs and he producion funcion approach end o follow he expeced paern (see seleced plos of oupu gaps, Figure 4.1). The esimaes from boh he univariae and mulivariae Beveridge-Nelson mehods conradic hese expecaions. The esimaes from he srucural VAR, on he oher hand, did no mach he full expecaions. Towards he end of he 1990s only he oupu gap esimaes using producion funcion mehod urn negaive and coninue is course unil he beginning of 2000s. Oupu gaps from HPs and linear rend urn negaive in 2000 and All he oher esimaes follow he negaive direcion in The posiive oupu gaps around he middle of 1990s are more difficul o explain. However, he inroducion of various srucural reforms in 1993 such as he removal of price conrol, impor licenses and foreign exchange conrol may have had lag effecs on simulaing higher growh. However, slow growh in acual oupu persised unil he beginning of 2000s. Declining Oupu Growh Poenial and Economic Recession Alhough various mehods produce varied resuls, hey however provided a broad consensus on he over-all rend and performance of he Kenyan economy. This sudy found ha firsly, poenial oupu growh is declining over he recen ime and secondly, he Kenyan economy is conracing in he recen years. This rend is observed from he simples of he measures, which uses he linear rend of he economy s growh performance as he measure of poenial oupu. These consisen resuls on he decline in poenial oupu are indicaive of capial desrucion in mos of he period covered by he sudy and he sagnaion of he join produciviy of labour and capial in he economy. The imporan poin is ha whaever mehodology is employed o esimae boh measures, i is clear ha he poenial oupu growh of he economy has been falling and esimaed o be currenly a around 2.4% on he basis of he Hodrick-Presco and linear mehods. This growh rae is confirmed by he five- year 21 This program was financed by he World Bank.
27 24 average poenial growh raes ( ) arrived a using he srucural VAR and producion funcion echniques. There was also a broad degree of consisency ha exiss in all mehods in erms of he sign and he size of he oupu gap. While his sudy has confirmed he exisence of negaive oupu gap in he recen pas, i does however raise an imporan issue, which can easily be ignored. Tha is, due o he declining oupu growh poenial of he economy over he years, he oupu poenial is no as large as one migh hink. This is an imporan resul wih major implicaions on he exen o which expansionary fiscal policy and a relaxed moneary policy can be uilized in he shor erm o seer he economy owards is poenial oupu growh raes. The Sagnaion of he Mulifacor Produciviy One of he mehods used in his sudy involved he esimaion of an aggregae producion funcion of he Kenyan economy. The producion funcion approach no only allowed he deerminaion of he shares of labour and capial in oupu bu also he produciviy of hese wo facors. The sudy showed ha he labour share of income is around 0.75 and ha of capial is approximaely The esimaed share for labour facor is slighly higher han he 0.7 ha has been esimaed for he Unied Saes and 0.65 for he Euro area economies. In hinking abou growh, he mos imporan esimaes are hose of he oal facor produciviy of capial and labour, which capures he conribuion o growh of echnological advances. In simple erms, oal facor produciviy when viewed wih respec o a facor such as labour shows he oupu per worker. This sudy has found ha oal facor produciviy has been conribuing very lile o economic growh and is growh has been declining in he las decade (see Figure 4.2). Conclusions and Implicaions for Moneary and Fiscal Policy This sudy ends o favour he resuls derived from he HP mehod, as hey are beer reflecion of he realiy. Moreover, since here is less daa used and fewer assumpions made using his mehod, hus he sudy believes ha here are fewer errors in he HP resuls. The esimaes from he MBN and srucural VAR could be fauled in he case of Kenya from he residual naure in which consumpion (an imporan variable in he series used in he esimaion) is arrived a in he consrucion of he Kenyan Naional Accouns. Here, he Balance of Paymens (BOP) and invesmen surveys are lumped in he residual, which consiue he consumpion-expendiure figure. On he oher hand, alhough he use of producion funcion is
A Probabilisic Approach o Wors Case Scenarios A Probabilisic Approach o Wors Case Scenarios By Giovanni Barone-Adesi Universiy of Albera, Canada and Ciy Universiy Business School, London Frederick Bourgoin
Morningsar Invesor Reurn Morningsar Mehodology Paper March 3, 2009 2009 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion by
CEPREMAP WORLD GROWTH AND INTERNATIONAL CAPITAL FLOWS IN THE XXI s CENTURY A prospecive analysis wih he INGENUE 2 model by he INGENUE TEAM Michel AGLIETTA and Vladimir BORGY (Cepii), Jean CHATEAU (Ocde),
FORECASTING TECHNIQUES ADE 2013 Prof Anoni Espasa TOPIC 1 PART 2 TRENDS AND ACCUMULATION OF KNOWLEDGE. SEASONALITY HANDOUT February 2013 MAIN FACTORS CAUSING TRENDS Increases in populaion. Seady inflaion.
Gene Squares 61 40- o 2 3 50-minue sessions ACIVIY OVERVIEW P R O B L E M S O LV I N G SUMMARY Sudens use Punne squares o predic he approximae frequencies of rais among he offspring of specific crier crosses.
Economic Growh wih Bubbles AlberoMarin,andJaumeVenura March 2010 Absrac We develop a sylized model of economic growh wih bubbles. In his model, financial fricions lead o equilibrium dispersion in he raes
The Universiy of Reading THE BUSINESS SCHOOL FOR FINANCIAL MARKETS Sources of Over-Performance in Equiy Markes: Mean Reversion, Common Trends and Herding ISMA Cenre Discussion Papers in Finance 2003-08
Wha he Puck? an exploraion of Two-Dimensional collisions 1) Have you ever played 8-Ball pool and los he game because you scrached while aemping o sink he 8-Ball in a corner pocke? Skech he sho below: Each
PERFORMACE ATTRIBUTIO FOR EQUITY PORTFOLIOS Performance Aribuion for Equiy Porfolios Yang Lu and David Kane Inroducion Many porfolio managers measure performance wih reference o a benchmark. The difference
COMPETITION BETWEEN MULE AND WHITE- TAILED DEER METAPOPULATIONS IN NORTH-CENTRAL WASHINGTON E. O. Garon, Kris Hennings : Fish and Wildlife Dep., Univ. of Idaho, Moscow, ID 83844 Maureen Murphy, and Seve
A Sable Money Demand: Looking for he Righ Moneary Aggregae Pedro Teles Federal Reserve Bank of Chicago, CEPR. Ruilin Zhou Pennsylvania Sae Universiy January, 2005 Absrac In his paper, we argue ha M1 is
Mehods for Esimaing Term Srucure of Ineres Raes Iskander Karibzhanov Absrac This paper compares differen inerpolaion algorihms for consrucing yield curves: cubic splines, linear and quadraic programming,
The -es 1//008 P331 -ess 1 Wha We Will Cover in This Secion Inroducion One-sample -es. Power and effec size. Independen samples -es. Dependen samples -es. Key learning poins. 1//008 P331 -ess A Research
Being Agains Bea Andrea Frazzini and Lasse H. Pedersen * This draf: Ocober 5, 2010 Absrac. We presen a model in which some invesors are prohibied from using leverage and oher invesors leverage is limied
MODEL SELECTION FOR VALUE-AT-RISK: UNIVARIATE AND MULTIVARIATE APPROACHES By SANG JIN LEE Bachelor of Science in Mahemaics Yonsei Universiy Seoul, Republic of Korea 999 Maser of Business Adminisraion Yonsei
Scienific Journals Mariime Universiy of Szczecin Zeszyy Naukowe Akademia Morska w Szczecinie 214, 39(111) pp. 122 127 214, 39(111) s. 122 127 ISSN 1733-867 The safe ships rajecory in a resriced area Zbigniew
San Francisco Sae Universiy Micael Bar ECON 560 Fall 207 Miderm Exam 2 Tuesday, Ocober 3 our, 5 minues Name: Insrucions. Tis is closed book, closed noes exam. 2. No calculaors or elecronic devices of any
chaper KINEMATICS IN ONE DIMENSION Secion 2.1 Displacemen Secion 2.2 Speed and Velociy 1. A paricle ravels along a curved pah beween wo poins P and Q as shown. The displacemen of he paricle does no depend
INSTRUCTIONS OR USE This file can only be used o produce a handou maser: Use Prin from he ile menu o make a prinou of he es. You may no modify he conens of his file. IMPORTNT NOTICE: You may prin his es
Urban Transpor XIII: Urban Transpor and he Environmen in he 21s Cenury 347 Urban public ranspor opimizaion by bus ways: a neural nework-based mehodology M. Migliore & M. Caalano Deparmen of Transporaion
Proceedings of he 2010 Join Rail Conference JRC2010 April 27-29, 2010, Urbana, Illinois, USA JRC2010-36236 WHO RIDE THE HIGH SPEED RAIL IN THE UNITED STATES THE ACELA EXPRESS CASE STUDY Zhenhua Chen The
ANALYSIS OF RELIABILITY, MAINTENANCE AND RISK BASED INSPECTION OF PRESSURE SAFETY VALVES Venilon Forunao Francisco Machado Mechanical Engineering Dep, Insiuo Superior Técnico, Av. Rovisco Pais, 049-00,
Avoiding Componen Failure in Indusrial Refrigeraion Sysems By Tim Kroeger, segmen markeing manager indusrial refrigeraion, Asia Pacific & India The aricle caegorises and gives examples of ypical componen
Overreacion and Underreacion : - Evidence for he Poruguese Sock Marke - João Vasco Soares* and Ana Paula Serra** March 2005 * Faculdade de Economia da Universidade do Poro ** (corresponding auhor) CEMPRE,
EXAMINING THE FEASIBILITY OF PAIRED CLOSELY-SPACED PARALLEL APPROACHES Seven J. Landry and Amy R. Priche Georgia Insiue of Technology Alana GA 30332-0205 ABSTRACT Paired closely-spaced parallel approaches
Cenre for Invesmen Research Discussion Paper Series Discussion Paper # 08-0* Momenum Profis and Time-Varying Unsysemaic Risk Cenre for Invesmen Research O'Rahilly Building, Room 3.0 Universiy College Cork
2017 World of Coal Ash (WOCA) Conference in Lexingon, KY - May 9-11, 2017 hp://www.flyash.info/ Wha is a Pracical (ASTM C 618) SAI--Srengh Aciviy Index for Fly Ashes ha can be used o Proporion Concrees
An Alernaive Mahemaical Model for Oxygen Transfer Evaluaion in Clean Waer Yanjun (John) He 1, PE, BCEE 1 Kruger Inc., 41 Weson Parkway, Cary, NC 27513 Email: firstname.lastname@example.org ABSTRACT Energy consumpion
Proecing he African Elephan: A Dynamic Bioeconomic Model of Ivory Trade G. Cornelis van Kooen Deparmen of Economics Universiy of Vicoria P.O. Box 1700, Sn CSC Vicoria, BC V8W 2Y2 Canada Email: email@example.com
December 2010 Version 1 ITG Dynamic Daily Risk Model for Europe 2010 All righs reserved. No o be reproduced or reransmied wihou permission. 121610 29140 These maerials are for informaional purposes only,
Real-ime Sochasic Evacuaion Models for Decision Suppor in Acual Emergencies ARTURO CUESTA, DANIEL ALVEAR, ORLANDO ABREU and DELFÍN SILIÓ Transpors and echnology projecs and processes Universiy of Canabria
American Fisheries Sociey Symposium 35:275 283, 2003 2003 by he American Fisheries Sociey A Saisical, Age-Srucured, Life-Hisory-Based Sock Assessmen Model for Anadromous Alosa A. JAMIE F. GIBSON 1 Acadia
Is he Decline in he Frequency of Draws in Tes Mach Cricke Derimenal o he Long Form of he Game? # Liam J. A. Lenen * Deparmen of Economics and Finance La Trobe Universiy Absrac The frequency of draws in
Breeding Incenive Programs and Demand for California horoughbred Racing: he radeoff Beween Quaniy and Qualiy by Marin D. Smih Deparmen of Agriculural and Resource Economics Universiy of California, Davis
Asse and Liabiliy Managemen by CADES, a manager of public deb Name Deparmen & affiliaion Mailing Address e-mail address(es) Phone number 331 55 78 58 19, 331 55 78 58 00 Fax number 331 55 78 58 02 Eric
1 h Inernaional Conference on Sabiliy of Ships and Ocean Vehicles 591 SIMULATION OF WAVE EFFECT ON SHIP HYDRODYNAMICS BY RANSE Qiuxin Gao, Universiy of Srahclyde, UK, Gao.firstname.lastname@example.org Dracos Vassalos,
AMURE PUBLICATIONS Working Papers Series N D-20-2006 < A Cos-Benefi Analysis of Improving Trawl Seleciviy: he Nephrops norvegicus Fishery in he Bay of Biscay > Claire MACHER */** Olivier GUYADER * Caherine
Economic Analysis Working Papers.- 7h Volume Number 11 MULIVARIAE RISK-REURN DECISION MAKING WIHIN DYNAMIC ESIMAION Josip Arnerić 1, Elza Jurun, and Snježana Pivac, 3 Universiy of Spli, Faculy of Economics,
MICKAËL MALLINGER- DOGAN is an assisan vice presiden, Illiquid Asses Analics, a Harvard Managemen Compan in Boson, MA. email@example.com MARK C. SZIGETY is vice presiden and head of Quaniaive Risk
Proceedings of he ASME 28h Inernaional Conference on Ocean, Offshore and Arcic Engineering OMAE29 May 31 - June 5, 29, Honolulu, Hawaii OMAE29-79385 ANALYSIS OF THE TUNNEL IMMERSION FOR THE BUSAN-GEOJE
Revisa Caarinense da Ciência Conábil, ISSN 1808-3781 - eissn 2237-7662, Florianópolis, SC, Brazil, v. 16, n. 48, p. 81-98, May/Aug. 2017 doi: 10.16930/2237-7662/rccc.v16n48.2376 Available a hp://revisa.crcsc.org.br
Auomaic air-main charging and pressure conrol sysem for compressed air supplies Type PCS A module from he sysem -vacorol Swiching on-off a compressed air uni in a compressed air supply generally akes place
COMPARING SIMULATED ROAD SAFETY PERFORMANCE TO OBSERVED CRASH FREQUENCY AT SIGNALIZED INTERSECTIONS Janailson Q. Souza Research Assisan, Deparmen of Transporaion Engineering, Universidade Federal do Ceará,
The Trade Performance Index Technical noes May 27 Mare Analysis Secion Inernaional Trade Cener (ITC) Geneva, Swizerland 1 ACKNOWLEDGEMENTS The Trade Performance Index has been developed a ITC s Mare Analysis
Zelio Conrol Measuremen elays FNCTIONS These devices monior he levels of conducive liquids. They conrol he acuaion of pumps or valves o regulae levels; hey are also suiable for proecing submersible pumps
Skills Workshee Mah Skills Acceleraion Afer you sudy each sample problem and soluion, work ou he pracice problems on a separae shee of paper. Wrie your answers in he spaces provided. In 1970, Don Big Daddy
Reexamining Spors-Senimen Hypohesis: Microeconomic Evidences from Borsa Isanbul Ka Wai Terence Fung +, Ender Demir, Chi Keung Marco Lau And Kwok Ho Chan * Absrac This paper examines he impac of inernaional
Card, carro and gasoline he flagship programs/policies o reduce povery and inequaliy in Indonesia Arief Anshory Yusuf SDGs Cener, Universias Padjadjaran, Indonesia Cener for Susainable Developmen Goals
www.sakshieducaion.com Time & isance The raio beween disance () ravelled by an objec and he ime () aken by ha o ravel he disance is called he speed (S) of he objec. S = = S = Generally if he disance ()
CHARACTERIZATION AND MODELING OF A PROPORTIONAL VALVE FOR CONTROL SYNTHESIS Osama. OLABY, Xavier. BRN, Sylvie. SESMAT, Tanneguy. REDARCE and Eric. BIDEAX Laboraoire d Auomaique Indusrielle - hp://www-lai.insa-lyon.fr
Journal of Mahemaical Finance 7-8 Published Online November (hp://wwwscirporg/journal/jmf) hp://dxdoiorg//jmf Opimal Variaional Porfolios wih Inflaion Proecion raegy and Efficien Fronier of Expeced Value
The curren issue and full ex archive of his journal is available a www.emeraldinsigh.com/0960-0035.hm Analysis of he bullwhip effec wih order baching in muli-echelon supply chains Maloub Hussain College
Dual Boos High Performances Power Facor Correcion (PFC) C. Aaianese, Senior Member, IEEE - V. Nardi, Member, IEEE - F. Parillo - G. Tomasso, Member, IEEE Deparmen of Auomaion, Elecromagneism, Compuer Science
WORKING PAPER 2006-03 Resource Economics and Policy Analysis (REPA) Research Group Deparmen of Economics Universiy of Vicoria A Dynamic Bioeconomic Model of Ivory Trade: Deails and Exended Resuls G. Cornelis
HKS Sysem sysem consising of 3 series for opimum colour fideliy and colour ideniy Base colour ink series for sheefed offse Produc feaures The HKS colour sysem consiss of he 3 spo colour ink series: Novavi
IB PHYSICS Name: DEVIL PHYSICS Perio: Dae: BADDEST CLASS ON CAMPUS CHAPTER TEST REVIEW, LESSONS 4- TO 4-5 S. Waer waves a he surface of a pon pass a floaing log of lengh L. The log is a res relaive o he
Developmen of Urban Public Transi Nework Srucure Inegraing Muli-Class Public Transi Lines and Transfer Hubs Zhenbao Wang 1, Anyan Chen 2 1College of Civil Engineering, Hebei Universiy of Engineering Handan,
AN ANALYSIS OF THE ECOMIC EFFECT OF A ROAD DIET IN ELIZABETHTOWN AND GEORGETOWN, KENTUCKY MARCH 2014 This repor was produced a he reques of he Ron Sco, Ciy Manager for Danville, Kenucky, under he supervision
Chaper. Liew Sau Poh Wave moion Ouline. Progressive Waves. Wave Inensi.3 Principle of Superposiion.4 Sanding Waves.5 Elecromagneic Waves Objecives a) inerpre and use he progressive wave equaion, = a sin
4. mezinárodní konference Řízení a modelování finančních rizik Osrava VŠB-U Osrava Ekonomická fakula kaedra Financí.-. září 008 On conveiy of SD efficiency ses - no shor sales case Miloš Kopa Absrac his
Managing he abundance of bison in Yellowsone Naional Park winer 2012 Chris Geremia P. J. Whie and Rick Wallen Sepember 12 2011 EXECUTIVE SUMMARY Background Yellowsone Naional Park (YNP) developed a plan
EFFECTS OF WIND SPEED ON WIND TURBINE AVAILABILITY S. Faulsich 1, P. Lyding 1, P. J. Tavner 2 1 Fraunhofer Insiue for Wind Energy and Energy Sysem Technology (IWES) 2 Energy Group, School of Engineering,
Please read How o Complee a Risk Assessmen before compleion EVENT OR ACTIVITY BEING RISK ASSESSED (add name of even where relevan) NAME OF DEPARTMENT Squad Training Neball DATE OF COMPLETION OF RISK ASSESSMENT
Issue Dae: June 6 15 Revision B June 2010 RECOMMENDAION FOR INERCHANGEABE UD BO AND A END UD FOR AI EC 6A FANGE ECHNICA REOR R501 Revision B AWHEM publicaions may be use by anyone esiring o o so. Every
hp://www.ransnav.eu he Inernaional Journal on Marine Navigaion and Safey of Sea Transporaion Volume 8 Number 3 Sepember 214 DOI: 1.12716/22.214.171.124 Coefficiens of Propeller-hull Ineracion in Propulsion Sysem
Souhern Illinois Universiy Carbondale OpenSIUC ublicaions Deparmen of Zoology 2003 Chronic Wasing Disease in Deer and Elk: a Criique of Curren Models and Their Applicaion Eric M. Schauber Souhern Illinois
Clemco Indusries Corp. ISO 9001 Cerified 6 cuf Classic Blas Machines Exclusively from... SIMPLE, RUGGED, RELIABLE More han 75 years of reliable field service have made Clemco blas machines he preferred
Chaper 30 Reading Guide Chaper 30 Reading Guide A Second Global Conflic and he End of he European World Order A Second Global Conflic and he End of he European World Order Name: Name: Name: Due Dae: Wednesday,
Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Normalizaion vs. denominaion 1 h JRC Annual Training
Sensors and Acuaors A 144 (2008) 354 360 Conens liss available a ScienceDirec Sensors and Acuaors A: Physical journal homepage: www.elsevier.com/locae/sna A micro-robo fish wih embedded SMA wire acuaed
SCI. AR., 65 (): 75-8 SCIENIA ARINA 2 Populaion size and exploiaion of gian squid (Dosidicus gigas D Orbigny, 835) in he Gulf of California, exico* ENRIQUE ORALES-BOJÓRQUEZ, AGUSÍN HERNÁNDEZ-HERRERA 2,
Making he connecion Glen Smale discusses racing engine con rod echnology wih specialis manufacurers from around he world Making he connecion necessary beween he op end and he boom end of he racing engine
This is he pre-proof acceped version of he manuscrip, he full version can be accessed for free here. Improvemen of individual camouflage hrough background choice in ground-nesing birds Auhors: Marin Sevens*1,
An Auonomous Blimp for he Wall Following Conrol. Seung-Yong Oh *,**, Chi- Won Roh *, Sung- Chul Kang *, Eun-ai Kim ** * Inelligen Roboics Research Cener, Korea Insiue of Science an echnology, Seoul, Korea
Journal of Ecological Engineering Volume 17, Issue 5, Nov. 016, pages 90 95 DOI: 10.1911/998993/65454 Research Aricle OPTIMAL ENERGY SOURCE FOR AN ENVIRONMENTALLY-FRIENDLY GO-KART Pior Zbigniew Filip 1,
EUROPEAN USERS 400V 50Hz SUPPLY DETAILS ARE INCLUDED WITH ELECTRICAL CON- TROL BOX. DISREGARD SUPPLY WIR- ING DETAILS IN THIS MANUAL 14,000 POUND CAPACITY COMMERCIAL GRADE FOUR-POST LIFTS IMPORTANT SAFETY
Your consent to our cookies if you continue to use this website.