Applied Economerics and Inernaional Developmen. AEID.Vol. 6-2 (2006) THE INFLATION-CAPACITY UTILIZATION CONUNDRUM: EVIDENCE FROM THE CANADIAN ECONOMY TSOULFIDIS, Leferis * DERGIADES, Theologos Absrac In his paper we develop a new, simple and, a he same ime, general mehod for he esimaion of he rae of capaciy uilizaion (CU). This mehod draws on he sandard heory of economic growh and makes use of he srucural vecor auoregression (SVAR) sysem of equaions esimaing echnique wih long-run resricions. The measure of CU ha we derive for he Canadia n economy displays a similar profile wih he corresponding survey measure. The resuls of he economeric analysis, however, show ha he explanaory conen of he SVAR measure wih regard o he acceleraion of inflaion exceeds ha of he survey, especially when i comes o he pos-1990 years. JEL Classificaion: C22, E31, E32, E37 Key Words: Capaciy Uilizaion, Inflaion, Economic Growh, SVAR 1. Inroducion The rae of CU is one of he prominen economic variables in macroeconomic heory and also a variable used for policy purposes especially when dealing wih problems relaing o inflaion and is acceleraion. In he las decade economic analyss have quesioned he close connecion of CU and inflaion for many OECD counries, as inflaion is much lower compared o ha of 1980s, while CU coninues o vary a relaively high levels. This phenomenon has been paricularly pronounced in he Canadian economy since 1990s (Baylor, 2001). The problem in invesigaing his phenomenon is ha capaciy oupu is an unobservable and herefore a heoreical and, a he same ime, a poliically sensiive variable; as a consequence, here are various mehodologies ha are used for is approximaion, none of which, however, is unequivocally acceped. From hese mehodologies he mos popular one is based on surveys which are conduced on regular ime inervals. The managers of firms in he surveys are supposed o give heir esimaes of acual use of heir capaciy in relaion o a raher vaguely defined noion of normal capaciy. There is no doub ha surveys, despie heir deficiencies, remain he mos direc mehod for he esimaion of CU, and governmens ogeher wih businesses ake hese esimaes ino accoun in he conemplaion of heir policies. The survey daa for Canada exends back o he year 1963, as a consequence our empirical invesigaion of he relaionship beween CU and inflaion can be deailed enough since he quarerly daa allow for he more appropriae incorporaion of inflaionary dynamics and also may lead o more general conclusions since we have a sufficienly long ime period. * Leferis Tsoulfidis is Associae Professor of Economics a he Universiy of Macedonia, Greece, e-mail: ln@uom.gr and Theologos Dergiades is Lecurer of Economics a Ciy College, Greece, e- mail: dergiades@ciy.academic.gr. Names are randomly ordered. 73
Applied Economerics and Inernaional Developmen. AEID.Vol. 6-2 (2006) The remainder of he paper is organized as follows: secion 2 reviews he lieraure on he relaionship beween CU and acceleraion of inf laion. Secion 3 lays down he underlying heory of our proposed alernaive model. Secion 4 discusses he economeric specificaion of he acceleraion of inflaion ogeher wih he resuls of he analysis. Finally, secion 5 presens he conclusions a nd makes some remarks regarding fuure research effors. 2. Lieraure Review I is commonplace ha when CU increases, compeiion over resources inensifies and generaes inflaionary pressures. This proposiion alhough so simple neverheless i is exremely difficul o prove empirically, precisely because here is no single and undispued measure of CU, whose variaion would provide signals abou he movemen of inflaion. Perhaps he bes index of CU in his kind of empirical research is he survey measure which for he years before he 1990s displayed such a close associaion wih he variaions of inflaion ha a new erm was invened known as NAICU, he nonacceleraing inflaion rae-capaciy uilizaion rae (McElhaan, 1978 and 1985). The underlying idea behind he selecion of his acronym was ha NAICU evenually o replace he popular non-acceleraing inflaion rae-unemploymen rae (NAIRU), since NAICU is a much broader index for i includes he slack of all resources, while NAIRU is resriced o only he unemploymen of labor. The economeric analysis for boh he US and Canada showed ha if he rae of CU exceeds he 82 percen hreshold level hen inflaionary pressures sar being developed (McElhaan, 1985; Fougère, 1993; Garner, 1994; Corrado and Maey, 1997). In he recen years, however, i has been shown ha his saisical relaion no longer holds firmly in he daa of he USA and especially of Canada. More specifically, Emery and Chang (1997) using quarerly daa for he US economy and he survey measure of CU of Federal Reserve Board found ha for he period 1967-1996 he inflaion rae acceleraes when he rae of CU exceeds he 82 percen borderline level. Moreover, by breaking heir oal period ino wo subperiods (1967-1982 and 1983-1996), hey found ha while he relaionship holds firmly for he 1967-1982 period, bu no for he 1983-1996 period. However, when hey used for he measuremen of he acceleraion of inflaion he producers insead of he consumers price index hey found ha here is sill evidence of a significan posiive relaionship in he pos-1982 period, bu no as srong as ha of he pre-1982 period. The resuls wih he survey measure of CU for he Canadian economy were more dramaic han hose of he US economy. In fac, afer he year 1986 he measure of CU rae is rising exceeding he 82 percen hreshold level and he inflaion rae during he same ime period is falling making he Canadian economy an ideal case sudy. As a resul, Baylor (2001) derived negaive conclusions wih respec o he CU rae as an explanaory variable of he acceleraion of he inflaion rae for he pos-1986 years for he Canadian economy. Various hypoheses have been pu forward for he explanaion of he conundrum of high capaciy uilizaion raes and low inflaion raes. One explanaion claims ha he 74
Tsoulfidis, L. and Dergiades, T. The inflaion-capaciy uilizaion conundrum survey measure of CU coninues o be represenaive of he rue sae of aggregae demand and is low explanaory power mus be blamed on exernal facors, such as he globalizaion process, rapid echnological progress and a more forward looking moneary policy (Baylor, 2001). Anoher possible explanaion aribues his incongruence beween survey measures of CU, for he Canadian economy and low inflaion raes o he mismeasuremen of CU, especially when dealing wih recen years. I is possible ha recen observaions are oversaed, and ha, in searching he relaionship furher, i is possible o discover ha CU coninuous o be a reliable predicor of he acceleraion rae of inflaion. In his line of research i is argued ha he curren high raes of CU mus be revised o he downward direcion so as o resore he predicive conen of survey measures of CU o he pre-1990 years (Baylor, 2001). We do no know o wha exen such revisions are possible or desirable, since surveys by heir very consrucion have buil in subjecive elemens which are no easy o remove by beer quesionnaires. Furhermore, surveys are no based on economic heory; we herefore oped for an alernaive measure of CU which is designed o accoun precisely for he effecs of changes in he producion condiions drawing on boh economic heory and he appropriae for his ask economeric echnique. 3. An alernaive esimaing mehod The model of CU ha we propose is based on he close connecion beween profis and invesmen. The idea is ha invesmen spending is mainly financed hrough profis and invesmen mus always be undersood as a facor whose variaions exer an effec on he economy s producion capaciy. This idea can be raced in he simple Kaldorian growh model which can be saed in he following erms: P 1 I = and Y s Y P 1 = I s (1) where, P sands for profis, Y is oupu, s is he desired propensiy o save and I is invesmen. The connecion beween he Kaldorian model and he CU rae is ha as long as invesmen increases and exers pressure on profis he economy expands a high raes and he CU rae is expeced o increase, a resul which is manifesed in a rising price level. If by conras, he amoun of invesmen falls shor of he amoun of profis and herefore invesmen does no exer pressure on profis i follows ha capaciy is underuilized, a resul which implies a slow down of he inflaion rae. From he above i follows ha overuilizaion of capaciy is accompanied by he acceleraion of inflaion. The converse is rue in he case where here is underuilizaion of he economy s capaciy. I follows ha here mus be a naural level of CU, where here is neiher acceleraion nor deceleraion of invesmen aciviy and so, oher hings equal, here is no pressure on he inflaion rae o move o eiher direcion. This siuaion can be hough of as he seady sae of he economy, ha is, he case where he growh rae of profis equals o he growh rae of invesmen and ha wih he warraned growh rae. 75
Applied Economerics and Inernaional Developmen. AEID.Vol. 6-2 (2006) In erms of Harrod s growh model where he warraned growh rae (g w ) is defined as: Y Y = g w = s v (2) from which we can derive ha invesmen and oupu grow pari passu, ha is according o he raio of he desired propensiy o save o he acceleraor coefficien (v ), ha is, he desired capial-oupu raio. In fac, saring from Kaldor s seady sae condiion where: P I = P I (3) and by invoking he consiuens of Harrod s model, ha is he acceleraor principle I = v Y and he muliplier I = s Y, we derive ha: P I = P I Y = Y = s v (4) I follows ha in any paricular ime period he acual amoun of invesmen will be differen from ha required for he mainenance of he above equilibrium condiion, which is idenified wih he mainenance of he normal capaciy uilizaion rae. The inuiive idea here is ha in he long run profis consiue he source of invesmen aciviy which is mainly responsible for he flucuaions of he level of economic aciviy. Consequenly, i is imporan o disenangle he demand shocks, and in his way o isolae he deviaions of acual invesmen spending from wha is required o mainain he above equilibrium condiion. The raio of acual invesmen o he normal or equilibriummainaining invesmen defines he degree of CU. The same esimaes, of course, can be derived by simply adding hese growh rae deviaions o he acual oupu in order o ge he normal or capaciy level of oupu. The raio of acual o he so-derived normal level of oupu gives he same rae of CU. 4. The rae of cu as an explanaory variable of he acceleraion of inflaion As we have argued CU is a heoreical variable and as such i canno be measured in any direc way, as for example is he case of GDP and is componens. In addiion, CU is a poliically sensiive variable perhaps more sensiive han unemploymen because i gauges he percenage of available resources ha remains idle in a sense. Consequenly, policy makers migh be criicized for no aking he appropriae measures o correc any imbalances beween aggregae demand and supply. While i is rue ha, as a heoreical concep, CU canno be measured in any direc, and a he same ime generally acceped way; however, in our view here mus be crieria such ha o help for he selecion of a single measure of CU. A similar problem exiss in he unemploymen saisics, which are also poliically sensiive and here is no absolue agreemen as o who mus be considered employed, unemployed and ou of he labor force. However, over he years a consensus has been formed and here is a single official unemploymen rae repored. Wih regard o 76
Tsoulfidis, L. and Dergiades, T. The inflaion-capaciy uilizaion conundrum he rae of CU, we hink ha a consensus migh be formed on he basis of cerain crieria among hem one may include he cos of consrucing such an index, he generaliy of he index such ha i can be used for inerindusry analysis wihin a counry or across counries, and of course is explanaory conen wih respec o he acceleraion of inflaion mus be saisfacory for all periods and sub-periods of he analysis. Turning now o he mos crucial crierion for selecing he appropriae measure of CU, which is is explanaory power wih regard o he acceleraion of inflaion. We observe ha he popular survey mehod published by he Saisics of Canada failed o give saisfacory resuls for he Canadian economy in he pos-1990 years, where he survey measure of CU (solid line) and he inflaion rae (doed line) followed differen direcions (see Figure 1). Figure 1. Survey Measure of CU vs. Inflaion 100 95 90 85 80 75 70 65 60 65 70 75 80 85 90 95 00 05.14.12.10.08.06.04.02.00 -.02 In our proposed measure of CU we use quarerly daa of profis and invesmen for he Canadian economy for he period 1963:1 o 2005:2 1. In a preparaory sep and prior o he esimaion of he reduced form of VAR equaions we need o ensure ha boh variables are saionary. In fac, for boh profis and invesmen we found ha we canno rejec he hypohesis of I(1); however, by aking heir difference in logs we conver hem o saionary. For his purpose we use he Augmened Dickey-Fuller along wih he KPSS ess, boh of which rejec he hypohesis ha he growh raes of profis and invesmen are I(1). The resuls of he saisical analysis are displayed in Table 1 below: 1 The daa are from OECD Saisical Compendium, where profis are approximaed by he gross operaing surplus deflaed by he GDP deflaor and invesmen is approximaed by Gross Fixed Capial Formaion deflaed by he corresponding deflaor. 77
Applied Economerics and Inernaional Developmen. AEID.Vol. 6-2 (2006) Table 1. Uni Roo Tess Variables ADF* es saisic KPSS** LM-Sa. Invesmen Growh Profi Growh -9.149583-11.29258 0.088003 0.057294 Criical values for differen levels of significance for ADF and KPSS es. 1% criical value -3.584743 0.739000 5% criical value -2.928142 0.463000 10% criical value -2.602225 0.347000 * The Schwarz informaion crierion used for he lag selecion on Augmened Dickey-Fuller es and he maximum lag lengh was se o nine. ** The Barle Kernel specral esimaion mehod was seleced for Kwiakowski-Phillips- Schmid-Shin es. A correcly specified SVAR model requires is variables no only o be of he same order of inegraion bu also no o display an equilibrium relaionship, ha is o say, he variables involved should no be coinegraed 2. For his reason he Johansen (1988) coinegraion es is applied assuming he exisence of linear deerminisic rend in he daa. The resuls (see Table 2) show ha he wo variables (real gross invesmen and real gross operaing surplus) are no coinegraed. As a consequence, we can safely make use of hese wo variables in our SVAR sysem of equaions. Table 2. Johansen Coinegraion Tes Resuls 5% Criical Values Trace Saisic Max.-Eigen Saisic Trace Max-Eigen 3.230137 3.229190 15.41 14.07 The null hypohesis suggess ha here are zero coinegraing vecors (H 0 : r = 0).Boh Trace es and Max-Eigenvalue es indicae no coinegraion a 5%. Anoher relaed issue for he specificaion of he bivariae reduced form of he SVAR model is he deerminaion of he opimal lag lengh, which in our case was based principally on he Likelihood Raio es. Opimal lag lengh selecion is crucial, since a sufficien number of lags prevens he possibiliy of serial correlaion and leads o unbiased esimaes of srucural componens. All he order selecion crieria, displayed in Table 3, sugges ha he opimal lag lengh for he esimaed VAR is equal o 1. 2 Naurally, since he purpose of SVAR specificaion is o exrac an equilibrium relaionship beween he variables involved. 78
Tsoulfidis, L. and Dergiades, T. The inflaion-capaciy uilizaion conundrum Table 3. VAR Lag Order Selecion Crieria Lag LogL LR FPE AIC SC HQ 0 683.23 NA 4.93E-07-8.84-8.80-8.83 1 697.05 27.1* 4.34E-07* -8.97* -8.85* -8.92* 2 700.04 5.78 4.40E-07-8.96-8.76-8.88 3 702.00 3.74 4.51E-07-8.93-8.65-8.82 4 705.53 6.63 4.54E-07-8.92-8.57-8.78 5 709.18 6.79 4.56E-07-8.92-8.49-8.74 6 710.60 2.58 4.72E-07-8.89-8.37-8.68 7 714.30 6.69 4.74E-07-8.88-8.29-8.64 8 716.84 4.51 4.84E-07-8.86-8.19-8.59 9 721.01 7.30 4.83E-07-8.87-8.12-8.56 10 722.48 2.53 4.99E-07-8.83-8.00-8.50 * indicaes lag order seleced by he crierion. LR: sequenial modified LR es saisic (each es a 5% level), FPE: Final predicion error, AIC: Akaike informaion crierion, SC: Schwarz informaion crierion, HQ: Hannan-Quinn informaion crierion Finally, by imposing he resricion ha he long-run effec of he growh of profis on he growh of invesmen is negligible we can idenify he elemens of A(0) marix (see he Appendix) and, herefore, recover he srucural residuals. I is imporan o poin ou in his connecion ha aggregae demand shocks are due o profi changes, for example, higher profis lead o higher invesmen spending and aggregae supply shocks are due o invesmen changes. Once, he srucural residuals have been recovered, he nex sep is o isolae he variaion of invesmen growh which is aribued o aggregae demand shocks (i.e., he invesmen gap). The way o do his is by merely accumulaing he series of he srucural demand residuals. The esimaes of CU (solid line) are displayed in Figure 2 along wih he inflaion rae (doed line). In a comparison of Figures 1 and 2, we observe ha he wo compeing measures of CU display a similar paern, which however canno be idenified wih he usual measures of linear associaion such as for example he correlaion coefficien. I is possible for he wo measures o be perfecly correlaed and a he same ime he indicaed sae may be alogeher differen almos for he whole sample period, signifying his way mismach of he informaion conveyed by each measure wih respec o he acceleraion of inflaion. Thus, in our case wha is more ineresing is o idenify wheher or no he wo measures coexis in he same sae for a considerable period of ime. This ype of informaion is obained by an alernaive es based on he non-parameric concordance saisic (Harding and Pagan 2002), which deermines he proporion of ime ha he wo measures are in he same sae (e.g. overuilizaion or underuilizaion). In our case, we suppose ha here is overuilizaion, when he CU measure is above he NAICU hreshold level (approximaely 82%) and vice-versa. The concordance saisic presened in Table 4 indicaes ha more han wo-hirds of he ime he wo measures coexis in he same sae 3. Turning now o he firs sub-sample he ime he wo measures spend ogeher 3 This porion of ime (0.668711) is considered prey high especially when observaions are quarerly. 79
Applied Economerics and Inernaional Developmen. AEID.Vol. 6-2 (2006) increases (0.737373), suggesing ha he wo measures should perform equally well in explaining he acceleraion of inflaion. Finally, focusing on he las sub-sample we observe a sharp decrease in he value of he concordance saisic, a resul ha indicaes ha he wo measures coexis in he same sae for a lesser proporion of ime and so heir explanaory power wih regard o he acceleraion of inflaion is expeced o differ Figure 2. SVAR Measure of CU vs. Inflaion 96 92 88 84 80 76 72 68 64 65 70 75 80 85 90 95 00 05.14.12.10.08.06.04.02.00 -.02 Table 4. Concordance Saisics Concordance Saisic 4 Period Saisic Value p-value 1965:2 2005:2 0.668711 0.019* 1965:2 1989:4 0.737373 0.018* 1990:1 2005:2 0.557377 0.021* * The concordance saisic is significan a he 5 percen level. 4 The concordance saisic is given by he following formula: T T 1{ ( 1,, ) (1 1, )(1, ) = = } C = T S S + S S ij i j i j where T is he sample size, S i and S j are binary variables aking he value of one when each of he CU measures is greaer han he NAICU (approximaely 82%) and zero oherwise. For esing he significance of he concordance saisic i is acually esed he a coefficien in he following momen condiion: Ε(( S S ) ( S S ) a) = 0 i i j j The GMM esimaion echnique applied for he esimaion of he above equaion using he Barle kernel wih a fixed bandwidh of 3. For furher discussion on he concordance saisic, see Hall and McDermo (2004). 80
Tsoulfidis, L. and Dergiades, T. The inflaion-capaciy uilizaion conundrum We observe ha in he 1990s he survey measure of CU (Figure 1) is above he average CU of approximaely 82 percen. By conras, he CU measure derived by our SVAR model (Figure 2) is higher han he hreshold level of 82 percen, mos of he ime, in he 1970s and unil he middle of 1980s and remains below he 82 percen for mos of he years hereafer. Thus, i comes as no surprise ha he explanaory power of he SVAR measure of CU wih regard o he acceleraion of inflaion exceeds ha of he survey for he Canadian economy in he pos-1990 years. Bu in such circumsances he economeric analysis is he mos appropriae o disenangle he exac relaions among he variables. For his purpose we esed he following economeric specificaion: 3 2 βι i γ j j δ1 3 i= 1 j= 1 (5) Inf = c+ CU + Inf + Z + u Where, inf refers o he acceleraion of CPI inflaion, CU is he rae of CU, Z is he acceleraion in he crude oil price inflaion, c, βγ, and δ are parameers o be esimaed, u is he disurbance erm and is ime. The acceleraion of he price of oil is designed o capure direcly he various price shocks, we have also esed dummies o capure he changes in he policies of he Bank of Canada in he early 1990s, a dummy also was used o capure he effecs of he wage and price conrols in he decade of 1970s, bu boh dummies did no prove o be saisically significan. In wha follows by assuming ha he acceleraion of inflaion is zero and seing he supply shock and he disurbance erms equal o zero, we can deermine he value of he NAICU from he erm c /( β1 + β2 + β3). The resuls of he regression equaion (5) are displayed below in Table 5, Table 5. Alernaive Measures of CU and he Acceleraion of Inflaion SVAR measure of CU, Model 1 Dependen Variable Acceleraion of Inflaion Variable / Sample 1965:2-2005:2 1965:2-1989:4 1990:1-2005:2 c -2.951 (0.85)* -4.963 (0.81) -2.261 (0.35) CU -1 0.376 (3.04) 0.295 (1.96) 0.522 (2.25) CU -2-0.533 (3.12) -0.591 (2.98) -0.435 (1.30) CU -3 0.192 (1.55) 0.355 (2.37) -0.059 (0.25) Inf -1-0.435 (5.83) -0.397(4.12) -0.495 (4.05) Inf -2-0.367 (4.93) -0.356 (3.67) -0.390 (3.22) Z -3 0.004(1.49) 0.002 (0.67) 0.006 (1.44) Adjused R 2 0.236 0.220 0.225 NAICU c /( β1 + β2 + β3) 81.64 (4.76)** 82.93 (3.58)** 81.50 (6.20)** *Absolue values of -saisics are given in parenheses, **Sandard errors 5 81
Applied Economerics and Inernaional Developmen. AEID.Vol. 6-2 (2006) Table 5 (coninued). Alernaive Measures of CU and he Acceleraion of Inflaion Survey measure of CU, Model 2 Dependen Variable Acceleraion of Inflaion Variable / Sample 1965:2-2005:2 1965:2-1989:4 1990:1-2005:2 c -8.70 (-2.37)* -10.88 (2.67) -5.560 (0.71) CU -1 0.265 (1.95) 0.487 (2.98) -0.014 (0.05) CU -2-0.142 (0.63) -0.558 (1.97) 0.391 (1.00) CU -3-0.015 (0.11) 0.205 (1.23) -0.310 (1.21) Inf -1-0.468 (6.24) -0.435 (4.42) -0.465 (3.81) Inf -2-0.367 (4.93) -0.356 (3.67) -0.390 (3.22) Z -3 0.004(1.49) 0.002 (0.67) 0.006 (1.44) Adjused R 2 0.230 0.246 0.189 NAICU c /( β1 + β2 + β3) 81.57 (1.62)** 80.91 (1.54)** 83.17 (5.03)** *Absolue values of -saisics are given in parenheses, **Sandard errors 5 The resuls of economeric analysis show ha in he case of he Canadian economy he measure of CU based on he SVAR esimaing echnique displays a consisenly saisfacory explanaory power of he acceleraion of he inflaion rae. In each subsample for model 1, adjused R 2 remains roughly consan in he hree periods of our analysis and in all periods he lags in he CU are saisically significan. As a resul, he esimaed NAICU remains approximaely he same over he differen periods and is in he range of 82%. Turning now o he resuls of model 2, when he survey measure of CU is used as an explanaory variable of he acceleraion of he inflaion rae, we observe ha he adjused R 2 displays high variabiliy and he worse is ha is value drops during he las period of he analysis. Similarly he values of he -raios signify ha he rae CU of he survey measure is no longer a saisically significan explanaory variable of he acceleraion of he inflaion rae in he las period of our analysis. From he above saisical analysis of he compeing models, i follows ha model 1 performs beer han model 2 especially during he mos recen sample period, where he survey measure fails o give saisfacory resuls. Bu in order o infer safer conclusions abou he superioriy of a model over anoher, furher economeric esing is needed. For his reason a number of esing procedures are used o reach o he proper specificaion. Specifically, alernaive model selecion crieria, ou-of-sample forecasing and coefficien sabiliy esing are uilized o jusify our model selecion process. For his purpose eigh differen model selecion crieria are presened in Table 6. Clearly, all 5 In he esimaion of NAICU since boh he numeraor and denominaor of he fracion - c /( β + β + β ) are esimaed parameers, i follows ha he sandard error of he above erm 1 2 3 should be approximaed from he marix of esimaed covariances of he coefficiens (Kmena, 1986, pp. 485-490). More specifically, he esimaed variance of he NAICU will be: Var(NAICU) ( f / β)' E( βˆ β)( βˆ β)' ( f / β ) 82
Tsoulfidis, L. and Dergiades, T. The inflaion-capaciy uilizaion conundrum crieria lend suppor o he idea ha model 1 is preferred for he whole sample period and also for he crucial second sub-sample period. Only for he firs sub-sample here is evidence ha model 2 performs slighly beer. Table 6. Model Selecion Crieria for Non-Nesed Models Period 65:2-05:2 65:2-89:4 90:1-05:2 Crierion* Model 1 Model 2 Model 1 Model 2 Model 1 Model 2 Akaike 5.001 5.043 3.182 3.079 6.448 6.751 Schwarz 5.718 5.766 3.689 3.569 8.199 8.583 HQ 5.281 5.325 3.379 3.270 7.086 7.418 Rice 5.021 5.063 3.200 3.096 6.645 6.957 Shibaa 4.983 5.025 3.167 3.064 6.306 6.602 GCV 5.011 5.053 3.191 3.087 6.538 6.844 FPE 5.001 5.043 3.182 3.079 6.454 6.757 SGMASQ 4.793 4.833 3.030 2.932 5.800 6.072 *A model is preferred when is crierion value (for all crieria) is lower han he crierion value of he compeiive model. Anoher way o compare he alernaive models is o assess heir forecasing performance. Two models ha appear o fi he daa equally well can perform quie differenly in a pseudo ou-of-sample forecasing exercise (Sock and Wason 2003, p. 475). For his reason he wo alernaive specificaions for he whole sample period are used in order o forecas he acceleraion of inflaion for he las en years of he sample, which is from he firs quarer of 1994 o he second quarer of 2005. The forecasing performance of he wo compeing models is depiced in Figure 3. Clearly, model 1 (Figure 3a), which conains he SVAR CU measure, consisenly follows he paern of he observed acceleraion of inflaion. Using now model 2 o make a forecas for he same period (Figure 3b), afer mid-1996 displays an upward bias. Figure 3. Pseudo Ou-of-Sample Forecasing of Inflaion, Models 1 and 2 12 8 6 8 4 4 2 0 0-2 -4 95 96 97 98 99 00 01 02 03 04 (a) -4 95 96 97 98 99 00 01 02 03 04 (b) 83
Applied Economerics and Inernaional Developmen. AEID.Vol. 6-2 (2006) We also esimaed Theil s Inequaliy Coefficien for boh models (Table 7). Since he value of his coefficien is lower for model 1 i follows ha is forecas performance is higher han ha of model 2. Furhermore, he covariance proporion also displayed in Table 7 is much higher for model 1, suggesing ha a much larger amoun of he forecasing errors is aribued o random facors 6. Finally, he mean absolue error and he roo mean square error favored model 1. Table 7. CPI Inflaion Forecas Evaluaion. Crierion Model 1 Model 2 Theil Inequaliy Coefficien 0.573989 0.592359 Bias Proporion 0.153589 0.763709 Variance Proporion 0.057153 0.033329 Covariance Proporion 0.789258 0.202962 Mean Absolue Error 1.872351 5.560154 Roo Mean Squared Error 2.466358 6.328946 A final sep of our analysis is o examine for boh models he sabiliy of he esimaed coefficiens. For his reason he N-sep forecas es is employed in order o spo he exac ime, where he break ook place wihou using any prior informaion. By visual inspecion of Figures 1 and 2, possible daes for srucural change are 1990:1 and 2001:1 for boh models. Specifically, for model 1 (Figure 4a) we marginally rejec he hypohesis of no srucural change for 0.1 level of significance, bu for model 2 (Figure 4b) he hypohesis of no srucural change is clearly rejeced a 0.05 level of significance. Overall, we may say ha he esimaed parameers of model 1 behave in a more sable way han hose of model 2. Figure 4. N-Sep Forecas Tes for Parameer Sabiliy, Models 1 and 2 12 8.00 8 4 0-4.00 4 0-4.05-8.05-8.10.10.15 1975 1980 1985 1990 1995 2000 2005.15 1975 1980 1985 1990 1995 2000 2005 (a) (b) 6 Noe ha he bias, variance, and covariance proporions add up o one. For a "good" forecas, he bias and variance proporions should be small so ha mos of he bias should be aribued o he covariance proporions. 84
Tsoulfidis, L. and Dergiades, T. The inflaion-capaciy uilizaion conundrum 5. Conclusions The main objecive of his paper has been he developmen of an alernaive, and a he same ime reliable measure of Capaciy Uilizaion (CU), based on he sandard heory of economic growh and he SVAR sysem of equaions esimaing echnique. The soderived measure of CU for he Canadian economy is conrased o ha of he popular survey echnique employed by he Saisic s of Canada. The comparison shows ha he measure of CU derived from he SVAR model no only replicaes, o a grea exen, he survey measure of CU, bu moreover, i does ha in a simple, general and heoreically sensible way. Furhermore, our measure of CU gives resuls wih respec o he acceleraion of he inflaion rae, which are consisen hroughou he period of analysis. By conras, he survey measure of CU no longer is a saisically significan explanaory variable of he acceleraion of inflaion rae. By conras, he forecasing performance of our proposed model was higher han ha of he survey measure. And in a period of ime where here is skepicism as o he usefulness of he concep of CU as a resul of is failure o predic inflaion and is acceleraion in he 1990s, he findings of our proposed model migh be a promising alernaive o he curren salemae. References Baylor, M. (2001) Capaciy Uilizaion and Inflaion: Is Saisics Canada s Measure an Appropriae Indicaor of Inflaionary Pressures? Deparmen of Finance Working Paper 2001-06. Blanchard, O. J. and Quah, D. (1989) The Dynamic Effec of Aggregae Demand and Supply Disurbances, American Economic Review 79, 655 673. Corrodo, C. and Maey, J. (1997) Capaciy Uilizaion, Journal of Economic Perespecives 11, 151-167. Emery, K.M. and Chang, C.P. (1997) Is here a Sable Relaionship Beween Capaciy Uilizaion and Inflaion? Federal Reserve Bank of Dallas Economic Review, Firs Quarer, 14-20. Fougère, M. (1993) Le Taux D uilisaion de la Capacié Comme Mesure de Tension Inflaionnise, EAFD. Garner, A. (1994) Capaciy Uilizaion and US Inflaion. Economic Review, Federal Reserve Bank of Kansas Ciy, Fourh Quarer. Hall, V.B. and McDermo, C.J. (2004) Regional business cycles in New Zealand: Do hey exis? Wha migh drive hem? Mou Working paper, 04-10. Harding, D. and Pagan, A. (2002) Dissecing he Cycle: A Mehodological Invesigaion, Journal of Moneary Economics 49, 365-381 Johansen, S. (1988) Saisical Analysis of Coinegraion Vecors, Journal of Economic Dynamics and Conrol 12, 231-54. 85
Applied Economerics and Inernaional Developmen. AEID.Vol. 6-2 (2006) Kmena, J. (1986) Elemens of Economerics, 2 nd Ediion, Macmillan, New York. McElhaan, R. (1978) Esimaing a Sable-Inflaion Capaciy Uilizaion Rae, Federal Reserve Bank of San Francisco Economic Review, Fall, 20-30. McElhaan, R. (1985) Inflaion, Supply Shocks and he Sable-Inflaion Rae of Capaciy Uilizaion, Federal Reserve Bank of San Francisco Economic Review, Winer, 45-63. Sock, J. and M. Wason (2003), Inroducion o Economerics, Inernaional Ediion, Addison Wesley. Appendix: The Srucural VAR Model For he esimaion of he rae of CU we use he SVAR mehodology wih long-run resricions. This mehodology was iniially advanced by Blanchard and Quah (1989) and since, i has been used in a number of applicaions. We suppose ha hese wo variables are affeced by he same srucural shocks, which come eiher from he demand or from he supply side of he economy. The srucural model can be wrien in erms of a moving average represenaion of curren and pas srucural residuals. DI = a ( nu ) + a ( nu ) 11 1 n 12 2 n n= 0 n= 0 (6) where DP = a ( nu ) + a ( nu ) DI and 21 1 n 22 2 n n= 0 n= 0 (7) DP denoe he growh raes of invesmen and profis and a ( n) sand for he individual coefficiens. Fina lly, u1 and u 2 represen he srucural residuals, which are considered o be serially uncorrelaed and heir covariance marix equals o he ideniy marix: T Euu ( ) = I =Σ (8) 2 u Equaions (6) and (7) in marix represenaion can be wrien as follows: DY =A(L)u (9) DY is he vecor of endogenous variables, u is he vecor of srucural residuals and A(L) is a (2x2) marix, where is elemens A ij are polynomials in he lag operaor. In order o idenify he srucural residuals, we esimae an unresriced VAR model of he form: DY = T (L) DY 1 + e (10) Given ha he sochasic process is saionary, (10) can be rewrien as an infinie moving average process: 86 ij
Tsoulfidis, L. and Dergiades, T. The inflaion-capaciy uilizaion conundrum DY = CLε ( ) (11) Where C(L)=(I 2 T (L)L) 1. Thus, hrough relaions (9) and (11) he srucural residuals are conneced o he esimaed residuals in he following way: ε = A(0) u (12) Equaion (10) implies ha he covariance marix of he esimaed residuals will be: E( εε T ) [ (0) ( (0) ) T ] (0) ( T ) (0) T (0) (0) T = EA u A u = A Euu A = A A =Σ ε (13) Our purpose is o esimae he four elemens of A(0) marix, so a sysem of a leas four equaions is required. From he symmeric, posiive definie covariance marix of he esimaed residuals Σ, he nex hree equaions could be derived: ε a (0) + a (0) = var( ε ) (14) 2 2 11 12 1 a (0) + a (0) = var( ε ) (15) 2 2 21 22 2 a (0) a (0) + a (0) a (0) = cov( ε ε ) (16) 21 11 22 12 2 1 The above hree equaions conain four unknown parameers, ha is, he elemens of he desired A(0) marix; consequenly, his sysem of equaions canno be solved. For he deerminaion A(0) marix, one more equaion is needed. Combining equaions (9), (11) and (12) we ge: ALu ( ) = CLε ( ) ALu ( ) = CLA ( ) (0) u AL ( ) = CLA ( ) (0) (17) A resricion should be imposed o he elemens of he marix A(L) in order o specify one more equaion. By ransforming he marix A(L) o a lower riangular we essenially eliminae he long-run effecs of demand shocks on invesmen. More specifically, we have: C ( La ) (0) + C ( La ) (0) = 0 (18) 11 12 12 22 Now, i is possible o esimae all he elemens of A(0) marix and naurally o recover he srucural residuals hrough he esimaed residuals. In he moving average represenaion he change in invesmen can be expressed as a linear combinaion of curren and pas srucural shocks: 87
Applied Economerics and Inernaional Developmen. AEID.Vol. 6-2 (2006) DY = A ( Lu ) + A ( Lu ) (19) 11 1 12 2 The change in invesmen growh due o demand-side shocks is defined as he invesmen gap and is equal o he second par of he righ-hand side of equaion (19). In paricular, he invesmen gap is given by: A12( Lu ) 2 (20) Based on he above esimaed invesmen gap we can exrac he equilibrium mainaining invesmen spending. Journal published by he Euro-American Associaion of Economic Developmen. hp://www.usc.es/econome/eaa.hm 88