ESTIMATE OF POTENTIAL GROSS DOMESTIC PRODUCT USING THE PRODUCTION FUNCTION METHOD

Economeric Modelling Deparmen Igea Vrbanc June 2006 ESTIMATE OF POTENTIAL GROSS DOMESTIC PRODUCT USING THE PRODUCTION FUNCTION METHOD CONTENTS SUMMARY 1. INTRODUCTION 2. ESTIMATE OF THE PRODUCTION FUNCTION FOR CROATIA 2.1. Mehod 2.2. Daa 2.3. Esimae 3. CALCULATION OF POTENTIAL GDP 3.1. Calculaion of poenial GDP using esimaed labour and capial elasiciy 3.2. Calculaion of poenial GDP using income-based share of labour and capial in gross value added 4. COMPARISON OF GDP GAP OBTAINED BY THE PRODUCTION FUNCTION METHOD AND THE UNIVARIATE TECHNIQUES 5. CONCLUSION BIBLIOGRAPHY 1

SUMMARY This sudy is concerned wih he calculaion of poenial GDP using he producion funcion. The producion funcion mehod is a srucural approach o calculaion of poenial oupu and i is based on economic heory. The Cobb-Douglas funcion has been seleced as he producion funcion model. Poenial GDP has been calculaed by wo mehods. In he firs, poenial GDP has been calculaed using esimaed elasiciy of labour and capial, while in he second approach poenial GDP was calculaed using he income-based share of labour and capial in gross value added. In boh cases, poenial GDP was obained as he sum of poenial echnology (Solow residual rend), poenial employmen level and acual gross capial sock. The basic oucome of his research is esimaed elasiciy of GDP wih reference o labour and capial. The difference beween he esimaed models is he resul of he assumed echnological developmen over ime and resricion of parameers. Under boh models, labour elasiciy of approximaely 0.80 was obained boh under he assumpion of consan reurns on scale and when no such assumpion was applied. We herefore conclude ha he seleced series in he producion funcion model for Croaia will generae precisely his resul, unil a heoreically more jusified series of labour and capial inpus is consruced. The esimaed elasiciy of labour has been overvalued in comparison o our naional accouns, where he income-based share of labour during he 1997-2003 period was 0.64, and 0.36 for capial. The level of poenial GDP obained using he producion funcion approach was compared o acual GDP so ha an analysis of cyclical economic rends could be conduced and he saus of macroeconomic policy in he preceding period could be assessed. The GDP gap defined as he difference beween acual and poenial GDP ha resuled from he producion funcion was compared wih he gap obained using cerain simple saisical echniques. 2

1. INTRODUCTION There are a number of definiions of poenial oupu, and an equally number of mehods o quanify i. According o he so-called echnical definiion, poenial oupu is he level of producion where facors of producion are compleely uilised a he given level of echnology. Over he long run, poenial oupu reflecs he opimum poenial supply of an economy and faciliaes an esimae of non-inflaionary growh. Over he shor run, he difference beween acual and poenial oupu is refleced in he balance beween supply and demand and he poenial impac of economic growh on macroeconomic sabiliy indicaors, including inflaion. From he purely saisical poin of view, poenial oupu can be viewed as a rend or a smoohed componen of acual producion series. Alernaively, if we wish o bring economic reason ino he definiion, poenial oupu reflecs he possibiliies of an economy s aggregae supply ha are deermined by he level of echnology and available inpus (European Cenral Bank, 2000). According o he definiion of he OECD, for example, poenial oupu means he level of producion ha is consisen wih sable inflaion over he medium erm 1. This concep of poenial oupu is linked o he emphasis on conrolling inflaion ha is a key prioriy over he medium erm. The objecive of moneary policy in many counries is o mainain a low and sable inflaion rae. In his conex, measuremen of poenial oupu and is growh rae is vial. Growh of poenial oupu and he oupu gap can be very useful indicaors in assessing inflaionary pressures over he shor and medium erm. For hose formulaing economic policy, i is crucial o be able o observe on ime wheher poenial oupu growh rae has changed. If capial and labour force rends are relaively sable, he variabiliy of poenial oupu growh will be small (European Cenral Bank, 2000). Poenial oupu is no a direcly measurable variable and i mus herefore be esimaed using saisical and heoreical mehods. There is a wide range of empirical mehods for measuring poenial producion, beginning wih analysis of ime-series daa and rend-based analysis o more complex assessmens based on he producion funcion and producion-facor demand equaions. In his sudy, poenial oupu is calculaed on he basis of he producion funcion. The mos common srucural mehod o esimae he producion funcion is he Cobb-Douglas funcion 2. Since he Cobb-Douglas producion funcion is easily expressed in linear form, which is hen easy o esimae, he use of his funcion is sill very popular. This sudy is srucured so ha in he second secion GDP is explicily modelled in facor inpu erms, i.e. wih regard o echnology, labour and capial. Among he several models assessed, he mos accepable were seleced and heir elasiciy has been employed o calculae poenial GDP. Addiionally, poenial GDP was also calculaed using he incomebased share of labour and capial in gross value added derived from he naional accouns. In he fourh secion a comparison is made beween he GDP gap obained using he wo preceding mehods and he GDP gap obained using some simple saisical derending echniques. The principal resuls are subjec o commen in he conclusion. The moive underlying his research is he need o model he Croaian economy s supply side and he need o forecas GDP values for increasingly longer periods. There is also a beer 1 Torres and Marin (1990), p. 129. 2 Cobb C. W. and P. H. Douglas (1928). 3

saisical basis for facor inpus, paricularly capial, han here was in previous years. Measuremen of poenial oupu plays a vial role in various economic models because i is useful in disinguishing beween medium-erm rends and shor-erm cyclical rends in he economy. The oupu gap is, for example, used o obain esimaes of a cyclically adjused sae budge. I is also used o monior he progress of inernaional compeiiveness, where he oupu gap is employed o calculae he real exchange rae based on cyclically adjused labour uni coss. Addiionally, much research dealing wih he impac of he GDP gap on he naional economies of indusrial counries responds o he quesion of how inflaion responds o he GDP gap. 2. ESTIMATE OF THE PRODUCTION FUNCTION FOR CROATIA 2.1. Mehod There are a number of mehods o esimae poenial oupu ha are normally caegorised ino wo groups: saisical and srucural. In he firs group, he producion series is divided ino he rend and cyclical componens. The srucural mehod consiues an aemp o creae an explici supply model for a given economy relying on economic heory. Among he srucural mehods, he producion funcion mehod has a special place. The producion funcion can assume differen forms, bu mos ofen he Cobb-Douglas funcional specificaion is used. The Cobb-Douglas funcional formula represens a link beween oupu and producion inpus: α β Y = A L K, (2.1.1) where Y is aggregae oupu, L is labour inpu, K is capial inpu, A is he level of echnology and efficiency of is use, α and β represen producion facor elasiciy given labour and capial, while sands for ime. If he sum of elasiciies is one, α + β = 1, he producion funcion generaes consan reurns on scale. Or, saed mahemaically, he producion funcion should be linearly homogenous. This is he sandard producion funcion case, so insead of parameer β, he parameer 1 α is wrien. If he sum of elasiciies is less han one, α + β 1, he producion funcion generaes decreasing reurns on scale, while if his sum is greaer han 1, reurns are increasing. Logarihmic linearizaion simplifies he funcion and provides for clear separaion of coefficiens. Using logarihmic ransformaion, he Cobb-Douglas funcion assumes his form: lny = ln A + α ln L + β ln K. (2.1.2) Toal facor produciviy, also known as he Solow residual, is obained direcly from equaion (2.1.2) fp = ln( A ) = lny α ln L β ln K. (2.1.3) This means ha oal facor produciviy is deermined by he difference beween acual oupu and he weighed average of producion facors. To obain he mos accurae possible esimae of oal facor produciviy, correc measuremen of labour and capial inpus is required. 2.2. Daa The producion funcion has been esimaed for he 1997-2005 period based on quarerly daa. The shorcomings in he compleed research refer o firs and foremos o he shor period in which he link beween overall oupu in a given economy and he mos imporan producion inpus are deermined. Normally, such an analysis is applied o a much longer period and daa wih annual frequency. Oupu variable has been approximaed using gross domesic produc, 4

labour inpu is shown hrough a series of employmen figures, and capial inpu was obained using a series of gross capial sock figures. Char 1 shows rends in original and seasonally adjused real GDP values. The gross domesic produc series has exised since 1997 and i has been revised on several occasions. Daa revision raised GDP growh raes in period from 2001 o 2003 3. Daa for 2004 and 2005 are sill preliminary. Char 1. Gross domesic produc Base index, 1997 = 100 150 140 130 120 110 100 90 80 97 98 99 00 01 02 03 04 05 GDP GDP_SA Legend: GDP gross domesic produc, original daa GDP_SA gross domesic produc, seasonally adjused daa I is no possible o noe any remarkable cyclical regulariy in Croaian overall economic aciviy. Neverheless, analyical and descripive purposes required ime series division ino hree pars. An upward rend in economic aciviy during 1997 and firs hree quarer of 1998 was followed by depression in 1999. Second par, from he las quarer of 1999 o he hird quarer of 2004, was characerized by coninual and posiive GDP rend. The las par was signed by deceleraion of GDP movemen. Croaian economic aciviy was very dynamic from 1994 o 1997 having growh raes beween 5.9 and 6.8 percen. In 1997, GDP grew by 6.8 percen. Due o srong credi aciviy, main growh conribuions came from personal consumpion and invesmen. Expors were suppored by growing demand on main foreign rade markes. According o he supply side, growh in 1997 was a resul of coninual and dynamic posiive rends in consrucion and rade. Tourism, also srongly conribued o GDP growh in 1997. GDP growh rae slowed down o only 2.5 percen in 1998. Recession endencies sared in he las quarer of 1998. Such reverse developmens was a consequence of srucural problems in he economy, from privaizaion and corporae resrucuring o inadequae public consumpion srucure, banking crises, Kosovo' crises and relaively weak economic growh in main foreign rade parners. 3 Growh rae was increased by one percen poin in 2003. 5

Economic recovery regisered in he las quarer of 1999. I was deermined by srong personal consumpion growh and a slower growh of expors and public consumpion. Economic aciviy in rade, financial and commercial-service secor were srong while i had a negaive rend in consrucion and ranspor. From 2000 o he end of observed period, growh rend of economic aciviy coninued. Suppored by credi aciviy, remarkable conribuion o growh came from personal consumpion. Public infrasrucure invesmen improved GDP growh in 2002, 2003 and he firs half of 2004. Expors of goods and non-facor services were among major sources of growh as well. Reducion of invesmen caused a slowdown in overall economic aciviy in he second half of 2004. Faser GDP growh in 2005 compared wih he previous year was a resul of decreased negaive conribuion of ne expors. Weaker personal consumpion and invesmen slowed down domesic demand moderaely. Table 1. GDP growh raes (%) 1997 1998 1999 2000 2001 2002 2003 2004 2005 6.8 2.5-0.9 2.9 4.4 5.6 5.3 3.8* 4.3* Source: Naional Bureau of Saisics * Preliminary daa In his sudy, daa on oal employmen released by he Naional Bureau of Saisics was used for labour inpu. These daa include hose employed in legal eniies, hose employed in crafs and rades and free lances and insured persons - privae farmers 4. The economic recession only inensified he declining rend in employmen presen even earlier. The negaive rend was only sopped a he end of 2000. Char 2. Employmen Base index, 1997 = 100 106 104 102 100 98 96 94 97 98 99 00 01 02 03 04 05 EMP EMP_SA Legend: EMP oal number of employed, original daa EMP_SA oal number of employed, seasonally adjused daa 4 From he sandpoin of oupu analysis, labour inpu is bes measured by oal hours worked. This mus be a measure ha allows for changes in he composiion and qualiy of labour over ime. The leas recommended labour inpu measure is he number of employed. However, we only have annual daa on hours worked in legal eniies, and hese daa are released wih a wo-year delay. Monioring he labour marke based on The Labour Force Survey began in 1996, and i has a semi-annual frequency. 6

Economic recovery leaded o posiive rends on labor marke jus in 2001. Afer several years of is decline, employmen sared posiive rends owards he end of observed period. Employmen growh especially acceleraed in 2003. Due o deceleraion of overall economic aciviy as well as some mehodological changes employmen growh rearded in 2004. Insured persons - privae farmers decreased severe during 2004 conribuing oal employmen growh deceleraion. Toal employmen increased 0.8 percen in 2005 compared wih he previous year. Employmen in legal eniies, wih is sable average share of 78 percen, mainly deermined developmen of oal employmen, bu i could no be ignored posiive movemens of employmen in crafs and rades and free lances which increased is share from 13 o 18 percen in observed period. A he same ime, permanen declining of insured persons - privae farmers was regisered. Employmen reducion in agriculure resuled from persons' exclusion from pension insured regiser due o conribuion unpaid, bu no necessary from aciviy failure. In ha way, insured persons - privae farmers became unreliable indicaor of change in oal employmen. I can be assumed ha reducion in share of insured persons - privae farmers conribued o average produciviy level. Such people are usually less educaed and have a low level of produciviy. Char 3. Toal employmen componens 1200000 1000000 800000 600000 Employmen in legal eniies Employmen in crafs and rades and free lances Insured persons - privae farmers 400000 200000 0 1/97 5/97 9/97 1/98 5/98 9/98 1/99 5/99 9/99 1/00 5/00 9/00 1/01 5/01 9/01 01/02 05/02 09/02 01/03 05/03 09/03 01/04 05/04 09/04 01/05 05/05 09/05 In Croaia here sill are no officially released daa on capial sock. A preliminary esimae of capial sock levels for he 1999-2003 period was made by he Naional Bureau of Saisics. The calculaion conains daa on gross and ne capial sock, gross fixed invesmens and depreciaion. The daa were calculaed yearly and shown in curren prices and in 2003 prices. These daa are subjec o furher adjusmen. Gross capial sock in consan prices was aken as he capial inpu series. 5 5 In he conex of oupu heory, i is correc o use he flow of capial services for capial inpu. Some saisics agencies release he index of capial service volume as aggregae capial services. 7

Since he producion funcion for he years from 1997 o 2005 is being esimaed, he PIM (Perpeual Invenory Mehod) was used o esimae capial sock in he years in which here is no daa. The dynamics of capial sock was updaed using his formula: K = I + ( 1 δ ) K 1, (2.2.1) where K is capial sock, I is invesmen in fixed asses and δ is he depreciaion rae. Daa on invesmens were aken from he naional accouns, while he depreciaion rae is equal o he average weighed rae from he capial sock esimae for he 1999-2003 period, which was 3.1% 6. The depreciaion rae is low, regardless of wheher i is compared wih inernaional numbers or heory 7. Char 4. Gross capial sock in consan prices Base index, 1997 = 100 135 130 125 120 115 110 105 100 95 97 98 99 00 01 02 03 04 05 Due o exremely high road building invesmen in 2002 and 2003, capial sock level grew very quickly. The series of annual daa for capial sock was inerpolaed ino a series wih quarerly frequency using he Chow-Lin inerpolaion mehod 8. The fas upward rend of ha series sared earlier, in 2001. The usefulness of Chow-Lin mehod in pracice depends on he qualiy of he assumed regression model and he possible finding of a reference series ha forms a regression model wih a good approximaion of realiy. The reference series in our case was consruced using cumulaed quarerly invesmen series. Char 5 shows he share of invesmen in GDP and he growh rae in he period under analysis. Char 5. Growh rae and share of fixed invesmen in GDP 6 The depreciaion rae for Croaia is low due o he large share of buildings wih low depreciaion raes. In research relaed o Poland, for example, covering roughly he same period, he depreciaion rae was 5.5%, and 6.0% for he Czech Republic and 10% for Esonia. 7 For example, according o Nadiri and Prucha (1993), he depreciaion rae of capial sock in he US manufacuring secor was 5.9%. 8 Chow, G. C. and A.-l. Lin (1971). 8

30,0 30,0 25,0 20,0 15,0 Growh rae -lef (%) Share in GDP righ (%) 29,0 28,0 27,0 26,0 10,0 25,0 5,0 0,0-5,0 1 2 3 4 5 6 7 8 9 24,0 23,0 22,0 21,0-10,0 20,0 In 1999, he posiive invesmen rend ha aced as a srong impulse for GDP growh during he pos-war recovery years was inerruped. This rend was only reversed a he end of 2000. Posiive rends on he demand side and financing condiions encouraged invesmen in he subsequen years. One of he prime sources of financing for corporae invesmen was bank loans. Exremely high invesmen growh raes were achieved in 2002 and 2003. Besides privae secor aciviies, public invesmen in infrasrucure, i.e. highway consrucion, also increased considerably. Invesmens declined in he second half of 2004 afer he compleion of primary works on he Zagreb-Spli moorway. Since hen heir quarerly growh sayed a approximaely 5%. 2.3. Esimae The problem ha exiss in he original formulaion of he Cobb-Douglas funcion (equaion 2.1.1) is he impossibiliy of change in echnology. The sandard procedure of incorporaing he possibiliy of echnological change is o include he ime rend (T ). Technological change is encompassed in his manner, even hough i is assumed o be exogenous in he specificaion being esimaed. The Cobb-Douglas funcion can be reformulaed as Y = A( ) L α K β, (2.3.1) γ where A ( ) = Ae. A and γ are consans. γ is he measure of proporional change per period when he inpu level remains consan (i.e. proporional change in oupu which occurs as a resul of echnical progress). The equaion (2.3.1) is generally assessed as ln Y = a + γ T + α ln L + β ln K + ε, (2.3.2) where ε is he error erm. To esimae consan reurns on scale, i is simply necessary o es he hypohesis on he sum of parameers α and β. The form of he producion funcion was esimaed based on equaion 2.3.2. The objecive of esimaion was o deermine he producion funcion parameers, i.e. GDP elasiciy wih reference o labour and capial. The daa relaed o he 1997-2005 period, wih a quarerly frequency. The dependen variable in he model is real gross domesic produc, while he independen variables are he number of employed according o adminisraive sources and he gross capial sock expressed in consan prices. All hree variables are expressed in base indices, where he base is he 1997 average. 9

Esimaion was conduced wih variables expressed in levels. From he heoreical poin of view, coinegraion lieraure indicaes he superioriy of economeric esimaion a levels in comparison o esimaion of firs differences if he series are no saionary. The seasonal componen presen in gross domesic produc and employmen has been eliminaed prior o modelling. A naural logarihm was hen applied o all series. The logarihmic values of variables in he producion funcion model are shown in char 6. Char 6. Gross domesic produc, employmen and gross capial sock Logarihm of seasonally adjused daa 9, 1997 = 100 4.90 4.85 4.80 4.75 4.70 4.65 4.60 4.55 97 98 99 00 01 02 03 04 05 LGDP_SA LEMP_SA LGC Legend: LGDP_SA logarihm of seasonally adjused GDP series LEMP_SA logarihm of seasonally adjused employmen series LGC gross capial sock logarihm Resuls of esimaes of several alernaive producion funcion models for Croaia are shown in Table 2. Table 2. Esimaed producion funcion for Croaia Model 1 (linear T, cons. reurns on scale) Model 2 (T^1.5, cons. reurns on scale) Model 3 (T^0.56, cons. reurns on scale) Consan -0.0269 0.0013-0.0657 (0.0067) (0.0047) (0.0158) T 0.0064 0.0009 0.0280 (0.0009) (0.0001) (0.0055) LEMP_SA 0.8023 0.6940 0.6399 Model 4 (linear T, no resricions) Model 5 (T^1.1, no resricions) -0.7198-0.2469 (0.7492) (0.7760) 0.0061 (0.0009) 0.0043 (0.0007) 0.9341 (0.1691) 0.8385 (0.1668) (0.0908) (0.0806) (0.0988) LGC 0.2171 (0.0934) 0.2111 (0.0939) 2 R 0.9746 0.9730 0.9626 0.9753 0.9754 2 R 0.9731 0.9714 0.9603 0.9730 0.9731 * F ( 1,32) = 0. 8553 F 1,32) Wald es ( α + β = 1) ( = 0. 0860 * 9 The X12 mehod was used for seasonally adjusmen and a muliplicaive model was seleced. 10

D.W. 1.2630 1.2241 0.8317 1.3110 1.3173 The values in parenhesis relae o he sandard errors. * The null hypohesis on he uni sum of elasiciy of labour and capial wih significance of 5% canno be rejeced. The firs hree models were esimaed based on he assumpion of consan reurns on scale, while here are no resricions o parameers in he las wo models. Furhermore, he models differ in erms of inensiy of growh in echnological progress over ime. In model 1, a consan growh rae was assumed. In model 2 he echnology growh rae acceleraes wih ime, while in model 3 his rae slows down wih ime. The rend exponen in model 2 was seleced so ha labour elasiciy generally corresponds o he pracice of developed counries (approximaely 2/3). The rend exponen in model 3 was seleced so ha labour elasiciy is equal o he income-based share of labour from he naional accouns for Croaia. 10 The average value of his share in he 1997-2003 period was 0.64. Model 4 resuled in increasing reurns on scale and i has he highes labour elasiciy. The Wald es of parameer resricions showed ha he null hypohesis on he uni sum of labour and capial elasiciy wih significance of 5% canno be rejeced. Model 5 is he mos similar o model 1, he only difference being he slighly acceleraing growh of echnology over ime. In model 5 one canno paricularly rejec he null hypohesis on he uni sum of labour and capial elasiciy wih significance of 5%. The rend variable is saisically significan in all models. The Durbin-Wason saisic is lowes in model 3, indicaing ha residuals are posiively auocorrelaed or ha perhaps considerable explanaory variables in he model were omied. A posiive auocorrelaion of residuals is also presen in oher models, bu in lesser exen. The resuls of he esimae have shown ha direc esimaion of he producion funcion can produce α values ha grealy differ from he income-based share of labour in gross value added according o naional accouns, probably reflecing he fac ha he assumpion of perfec compeiion does no apply a he level of a given economy 11. Model 1 and model 2 were seleced o calculae poenial GDP in he subsequen secion. The values of parameers in model 1 are confirmed by model 5, in which here are no parameer resricions wih a sligh variance in he inensiy of rend. Model 2 was seleced due o he labour elasiciy which is presen in a large number of counries. Technology in model 1 assumes he form of a sraigh line and consan growh rae. The average quarerly growh of echnology was 0.64%, and 2.56% annually. Technology in model 2 developed exponenially wih average quarerly growh of 0.52% and annual growh of 2.09%. 3. CALCULATION OF POTENTIAL GDP 3.1. Calculaion of poenial GDP using esimaed labour and capial elasiciy 10 See secion 3.2. 11 For example, mos research shows ha he value of labour elasiciy in developed counries is approximaely 2/3, while capial elasiciy is approximaely 1/3. In he euro zone, from 1991 o 1997 he conribuion of capial growh o oupu growh was 67%, -13% o employmen growh, while he conribuion of he facor ha relaes o produciviy, including echnology, was 45%. 11

If inpus are a heir poenial levels, hen he producion funcion provides an esimae of poenial oupu and he oupu gap. Wih he Cobb-Douglas specificaion of he producion funcion, i is essenial o esimae he rend of componens of individual producion facors, excep capial. Since capial sock is an indicaor of oal capaciy, here is no jusificaion for smoohing ou his series in he producion funcion approach. The maximum conribuion of capial o poenial GDP is provided wih he full use of exising capial sock in he economy. By conras, i would no be desirable o incorporae curren employmen ino he definiion of poenial oupu, because labour inpu is subjec o powerful cyclical flucuaions. Esimaion of poenial GDP hus requires he eliminaion of cyclical componens from he labour facor and he oal facor produciviy Poenial GDP can be calculaed using he equaion: POT POT POT lny = ln A + α ln L + (1 α) ln K. (3.1.1) Toal facor produciviy is obained using equaion (2.1.3) or, alernaively, hrough he equaliy fp = c( 1) + c(2) * T + e. The Hodrick-Presco filer is applied o a series so calculaed o obain he poenial oal facor produciviy. When calculaing poenial employmen, a smoohed labour force series was used correced by he balanced rae of unemploymen. The non-acceleraing wage rae of unemploymen (NAWRU) was seleced for he equilibrium rae of unemploymen once, while he average rae of unemploymen in he analyzed period was seleced a second ime. Research has shown ha he equilibrium growh rae changes over ime, i.e. ha i is no consan, alhough i generally follows he acual rae of unemploymen (due o hyseresis and labour marke inelasiciy). The mehod specified by Elmeskov and Scarpea (1999) was used o measure he NAWRU ha varies over ime. Torres and Marin (1990) showed ha he NAWRU approach provides beer consisency beween he labour marke and he commodiies marke han he non-acceleraing inflaion rae of unemploymen (NAIRU) approach 12. Poenial employmen is calculaed using his equaion POT N L = LF (1 u ) (3.1.2) N where LF is he smoohed labour force (labour supply) series, while u is he smoohed NAWRU. The average level of labor force in Croaia according o The Labor Force Survey daa was 4.1 percen higher han he level from adminisraive source daa in observed period. Thus, poenial labor force from The Survey daa was higher compared wih he adminisraive 12 In he European Commission approach, Denis, McMorrow and Roeger (2002), he definiion of he maximum conribuion of employmen o poenial GDP is he employmen level consisen wih sable inflaion (NAIRU) or wages (NAWRU). Poenial employmen can be obained from smoohed labour force series derived hrough use of he HP filered rae of paricipaion in relaion o he working age populaion. Using a smoohed paricipaion rae ha leads o a less volaile labour supply series, poenial employmen is equal o labour supply minus he NAIRU esimae. One of he grea advanages of his approach is ha i generaes a series of poenial employmen ha is relaively sable, while a he same ime i also ensures ha year-o-year changes in series are closely linked o long-erm demographic rends and labour marke rends. 12

source daa. However, i could no be possible o use The Survey daa because of is semiannual frequency. Char 7. The Labor force according o The Survey and adminisraive source daa 1950 1900 LF - Survey LF - adminisraive (sae) LF - adminisraive (average) 1850 housand 1800 1750 1700 1650 1600 1996 II 1997 I 1997 II 1998 I 1998 II 1999 I 1999 II 2000 I 2000 II 2001 I 2001 II 2002 I 2002 II 2003 I 2003 II 2004 I 2004 II 2005 I 2005 II Labor force adminisraive daa was calculaed as a sum of oal employmen and regisered unemploymen. Tha series was growing by middle of 2002 even in period of recession. The growh was encouraged by unemploymen reaching he highes level in firs half of 2002. Employmen growh sared in he second half of 2001 could no overcome negaive endencies of unemploymen up o 2004 13. Char 8. Poenial GDP based on model 1 srucure. 13 The upward unemploymen rend was simulaed by economic aciviy deceleraion, crowded problems in some companies as well as acivaion of some necessary resrucuring processes. Growing rend of unemploymen coninued despie of recovery of he overall economic aciviy. The main cause of ha aribued o fas companies' resrucuring as well as he Croaian legislaion for defenders regisraion in he Croaian Employmen Service. A reversed rend of unemploymen concured wih sar of employmen inermediaion reform carried ou in he second half of 2002. Persons who did no saisfy he new crieria were already removed from he regiser. A quick reducion in unemploymen happened during 2003. Such unemploymen rend was also a resul of posiive employmen movemens, i.e. labor demand reinforcemen. A slowdown of economic aciviy a he end of 2004, conneced wih invesmen growh deceleraion in ranspor infrasrucure, caused a weak decrease of unemploymen. Bu, downward rend of unemploymen coninued in 2005. The impac of employmen inermediaion reform disappeared by he end of 2004. 13

4.9 4.8 4.7 4.6 4.5 4.4 97 98 99 00 01 02 03 04 05 GDP_POT_NAWRUHP1 GDP_POT_NAWRULAG1 GDP_POT_UNEMPRT1 GDP_POT_EMP1 Legend: GDP_POT-NAWRUHP1 Poenial GDP where poenial employmen is calculaed wih he NAWRU, and where expeced wages are derived using he HP filer on real wages GDP_POT_NAWRULAG1 Poenial GDP where poenial employmen is calculaed wih he NAWRU, and where expeced wages are shifed real wages GDP_POT_UNEMPRT1 Poenial GDP where poenial employmen is calculaed wih he average rae of unemploymen GDP_POT_EMP1 Poenial GDP where poenial employmen is calculaed using he HP filer on overall employmen The char shows ha he series of poenial GDP calculaed using he NAWRU concep and he naural rae of unemploymen almos overlap and ha heir levels are below poenial GDP, he poenial employmen of which is calculaed using an HP filer on overall employmen. Char 9. Poenial GDP based on model 2 srucure. 14

4.9 4.8 4.7 4.6 4.5 4.4 97 98 99 00 01 02 03 04 05 GDP_POT_NAWRUHP2 GDP_POT_NAWRULAG2 GDP_POT_UNEMPRT2 GDP_POT_EMP2 Legend: GDP_POT-NAWRUHP2 Poenial GDP where poenial employmen is calculaed wih he NAWRU, and where expeced wages are derived using he HP filer on real wages GDP_POT_NAWRULAG2 Poenial GDP where poenial employmen is calculaed wih he NAWRU, and where expeced wages are shifed real wages GDP_POT_UNEMPRT2 Poenial GDP where poenial employmen is calculaed wih he average rae of unemploymen GDP_POT_EMP2 Poenial GDP where poenial employmen is calculaed using he HP filer on overall employmen The nex char finally shows acual and poenial GDP rends according o he differen mehods. Char 10. Acual and poenial GDP 15

4.90 4.85 4.80 4.75 4.70 4.65 4.60 4.55 97 98 99 00 01 02 03 04 05 GDP_POT_EMP1 GDP_POT_EMP2 LGDP_SA Legend: GDP_POT_EMP1 Poenial GDP where poenial employmen is he HP filered number of employed, according o model 1. GDP_POT_EMP2 Poenial GDP where poenial employmen is he HP filered number of employed, according o model 2 LGDP_SA acual GDP The poenial GDP series where poenial employmen is a smoohed labour supply series adjused by he unemploymen rae is no shown in he char because hese lines are consanly below he level of acual GDP. Poenial GDP calculaed using model 1 and 2 is very similar. They show ha a cycle wih a posiive GDP gap can be observed in Croaia a he beginning of he analyzed period, in 1997 and 1998, and negaive during he recession period, in 1999 and 2000. During he subsequen period, in fac, he regulariy of a cycle canno be deeced, and acual GDP is very close o is poenial. We shall now specify some of he advanages and drawbacks o he producion funcion mehod in he esimaion of poenial oupu. One of he advanages lies in he fac ha i is possible o forecas poenial oupu by forecasing is componens, which are normally a our disposal. The producion funcion is quie flexible, because i can ake ino accoun differen assumpions abou echnology and i can encompass several of he advanages of he new growh heory, such as change in he qualiy of producion inpus. The basic drawbacks of he producion funcion approach o esimaing poenial oupu relae o he daa and rends of is inpu componen. Capial sock is normally no quie reliable or here are no daa on effecive work hours. Major flucuaions in produciviy levels and he labour supply make i difficul o liberae oal facor produciviy and labour supply rends. For example, here are differen views of how o model echnical progress. Similarly, here are alernaive views given he rend level of effecive labour supply ha depend on resisance on he labour marke. Differen assumpions abou hese rend componens will lead o very differen esimaes of poenial oupu. The Cobb-Douglas producion funcion represens a grea simplificaion of economic realiy. Furhermore, i assumes perfec compeiion on he producion inpus marke, i.e. he facors are homogenous. When poenial oupu is defined as maximum possible oupu, he siuaion 16

in which acual oupu exceeds poenial oupu does no exis. This shows ha use of capial sock in is enirey is impossible. The Solow residual is a considerable componen of he producion funcion, which is compued as he esimaed residual and as such i is economically inexplicable and is hus freely inerpreed. The esimae of poenial oupu includes a high degree of uncerainy. This is because i is a variable ha canno be measured. Addiionally, poenial oupu depends on variables ha canno be measured, such as he naural rae of unemploymen and he capial sock depreciaion rae. 3.2. Calculaion of poenial GDP using income-based share of labour and capial in gross value added Under perfec compeiion, where prices of producion facors are equal o heir marginal produc, parameer α from he Cobb-Douglas producion funcion (formula 2.1.1) should coincide wih he income-based share of labour in gross value added from he naional accouns. The elasiciy of capial is hen equal o 1 α. Since based on Croaia s naional accouns we know he shares of income generaed by labour and capial in gross value added according o ex-work prices from he 1997-2003 period, we shall use hem o calculae one more series of poenial GDP. In he subsequen period he average annual income-based share of labour in gross value added was 0.64, while he share of capial was 0.36 14. In he lieraure his approach o calculae poenial oupu is known as he growh accouning framework. Wih he given value α, oal facor produciviy is compued as ln A = lny α ln L (1 α) ln K, (3.2.1) or ln A = lny 0.64 ln L 0.36ln K. (3.2.2) Poenial GDP is once more calculaed according o formula 3.1.1. Poenial echnology is obained by applying he HP filer o he series (3.2.2), while poenial employmen is obained by applying he same filer o he employmen figure series. Char 11. Poenial GDP calculaed according o income-based shares of labour and capial in gross value added 14 The share of labour income in value added in developed economies is normally abou 2/3. I is 68% in he U.S. (Giorno e al., 1995), 67% in Canada (Dion and Kuszczak, 1997), 70% in England, 46% in Argenina (Barro and Sala-i-Marin, 1999), 48% in Chile (Barro and Sala-i-Marin, 1999), ec. According o he European Commission s work (2002a, 2002c), he assumed share of labour income is 0.65 for each counry. In he period in which we are esimaing poenial GDP, he share of labour income in Hungary was 0.65, 0.66 in Poland, and 0.50 in he Czech Republic. 17

4.90 4.85 4.80 4.75 4.70 4.65 4.60 4.55 97 98 99 00 01 02 03 04 05 GDP_POT_NACT LGDP_SA Legend: LGDP_SA acual GDP GDP_POT_NACT poenial GDP calculaed according o income-based shares of labour and capial in gross value added (from he naional accouns) Char 12 shows poenial GDP according o model 1, model 2 and according o income-based shares. A considerable overlap beween hese hree lines is noable. Char 12. Comparison of poenial GDP according o model 1, model 2 and he model wih income-based shares 4.90 4.85 4.80 4.75 4.70 4.65 4.60 4.55 97 98 99 00 01 02 03 04 05 GDP_POT_NACT GDP_POT_EMP1 GDP_POT_EMP2 Legend: GDP_POT_NACT Poenial GDP according o he model wih income-based shares GDP_POT_EMP1 Poenial GDP according o model 1. GDP_POT_EMP2 Poenial GDP according o model 2. 4. COMPARISON OF GDP GAP OBTAINED BY THE PRODUCTION FUNCTION METHOD AND THE UNIVARIATE TECHNIQUES The oupu gap is defined as he difference beween acual and poenial oupu. The posiive gap corresponds o excess demand in he economy, which make cause inflaionary pressure. If he gap is negaive, hen poenial oupu exceeds demand. The oupu gap canno be 18

mainained over he long run, because adjusmens of wages and prices will be esablished o reach a balance in which supply and demand are equal. In he economics lieraure here are differen explanaions of why acual and poenial oupu ofen diverge. According o one heory, acual oupu differs from poenial oupu because rigidiies in he economy imply a cerain period for prices and wages o adjus. In his case, he oupu gap is an imporan measure o balance overall demand and supply in he economy and i can provide useful informaion on price pressures. According o anoher heory, an economy is bes characerised by business cycle models, where acual oupu differs from end oupu because of occasional produciviy shocks. In his case, he oupu gap reflecs emporary deviaions provoked by adjusmen of oupu hrough echnological changes and unexpeced supply-side rends. 15 This secion conains a comparison of he GDP gap obained by he producion funcion wih he GDP gap obained using he linear rend mehod, he Hodrick-Presco filer and a modified Hodrick-Presco filer. 16 A comparison of hese variables can lead o a more credible conclusion on he curren posiion of he economy given is poenial, and a conclusion on business cycles in he preceding period. The GDP gap is calculaed as he difference beween acual and poenial GDP, and i is shown in percenages of acual GDP. Char 13. GDP gap according o differen poenial GDP calculaion mehods.020.015.010.005.000 -.005 -.010 97 98 99 00 01 02 03 04 05 GAP_HP GAP_HPMOD GAP_LT GAP_NACT GAP_EMP1 GAP_EMP2 Legend: GAP_HP - Poenial GDP obained by applying he HP filer o acual GDP GAP_HPMOD Poenial GDP obained by applying he modified HP filer o acual GDP GAP_LT Poenial GDP is a linear rend of acual GDP GAP_NACT Poenial GDP calculaed according o income-based shares from naional accouns GAP_EMP1 Poenial GDP calculaed using he producion funcion, model 1. GAP_EMP2 Poenial GDP calculaed using he producion funcion, model 2. 15 European Cenral Bank, 2000. 16 According o Bruchez, P.-A. (2003). The modified Hodrick-Presco filer solves he problem of bias in final poins, which is a shorcoming of sandard HP filers. 19

One can see ha he gap lines have a very similar shape, hey seem ranslaed and hey rarely inersec. According o all mehods, he economy move in he same direcion wih sronger or weaker inflaionary pressures. The saisical feaures of individual series of GDP gaps are provided in able 3. Table 3. Basic GDP gap saisics Mean Median Maximum Minimum Sd. deviaion GAP_HP -0.0000174-0.0003480 0.0148990-0.0054560 0.0038230 GAP_HPMOD -0.0003550-0.0006900 0.0146720-0.0054280 0.0037700 GAP_LT -0.0000262 0.0007910 0.0178450-0.0078420 0.0053050 GAP_NACT -0.0000135 0.0001340 0.0137540-0.0063930 0.0035130 GAP_EMP1-0.0000153 0.0000120 0.0142700-0.0052590 0.0035290 GAP_EMP2-0.0000141 0.0000975 0.013925-0.0060160 0.0034950 The mean is closes o zero, and his also means ha he closes proximiy beween acual and poenial GDP is in he GDP gap obained using he producion funcion mehod wih he income-based share from he naional accouns (GAP_NACT). The average deviaion of values of he series from is average, sandard deviaion, is he leas for he gap ha follows from he producion funcion, model 2, so he oscillaions in capaciy use are he leas in comparison wih oher mehods and inflaionary and deflaionary pressures are less inense han in oher mehods. The nex char shows he average GDP gap calculaed as he arihmeic average of he GDP gap series based on all mehods. Char 14. Arihmeic average of he GDP gap obained by differen mehods for calculaion of poenial GDP.016.012.008.004.000 -.004 -.008 97 98 99 00 01 02 03 04 05 GAP_AVERAGE Acual GDP was raher close o poenial GDP in he analyzed period, wih he excepion of 1997 and 1998, when very dynamic economic aciviy was recorded. The larges negaive gap was recorded 1999, 2000 and 2001, which have been characerised as recession or early recovery years. From mid-2002 o he end of he analyzed period, posiive gap values were recorded, excep in wo quarers: he las quarer of 2004 and he firs quarer of 2005. In he remainder of 2005, inflaionary pressures were somewha more significan. 20

5. CONCLUSION In his work he producion funcion has been seleced o esimae poenial GDP, since i has one major advanage over oher mehods, and ha is ha i creaes a relaionship beween oupu and producion inpus. Two basic procedures were used o calculae poenial GDP. In he firs, poenial GDP was calculaed using GDP elasiciy obained by regression wih reference o labour and capial, while in he oher case poenial GDP was calculaed using income-based shares of labour and capial in gross value added from he naional accouns. For he seleced labour and capial inpus, esimaed labour elasiciy in Croaia during he period from 1997 o 2005 was approximaely 0.80, while according o he naional accouns he income-based share of labour was 0.64. Poenial GDP was calculaed using he oal facor produciviy rend, he rend in he number of employed and acual gross capial sock. Toal facor produciviy in boh approaches was calculaed as he residual of acual GDP and he weighed sum of facor inpus. Poenial GDP obained using he producion funcion mehod wih he income-based shares from he naional accouns were bes adaped o acual GDP daa, and among he hree mehods i has he lowes gap sandard deviaion. The difference beween acual and poenial GDP is he GDP gap, and i has been compared wih he gap from cerain univariae echniques. The series of arihmeic GDP gap averages derived from he differen mehods shows ha in 1997 and 1998 very srong economic aciviy was recorded, and afer hese years GDP moved no far from is poenial, alhough an increasingly narrower link has been in effec from 2003 o he presen. Low-level inflaionary pressures have generally been presen over he pas few years. Coninued research is expeced o produce improvemens in he series of labour inpus given he educaional srucure. Aemps will be made o modify poenial employmen according o aggregaes from labour supply surveys. As for capial sock, a revision of daa is expeced soon in he direcion of changes o is srucure and increased depreciaion raes. In he nex phase of research, much more emphasis should be accorded o forecasing poenial GDP growh. 21

BIBLIOGRAPHY "Ausria: Seleced Issues and Saisical Appendix" (1998), IMF Saff Counry Repor 98/107 Babić, A. and T. Sučka (2000): "The oupu gap esimaed for Croaia for he period 1994-1999", Croaian Naional Bank, inernal Bank of England (2004): "Measuring oal facor produciviy for he Unied Kingdom", Quarerly Bullein, (spring) Bank of England (2001): "Measuring capial services in he Unied Kingdom", Quarerly Bullein, (auumn) Bank of England (2003): "Oupu and supply", Inflaion Repor, (November) Borić, V. (2005): "Odnos inflacije i nezaposlenosi u Republici Hrvaskoj", Docoral hesis, Faculy of Economics - Zagreb Bruchez, P. A. (2003): "A Modificaion of he HP Filer Aiming a Reducing he End-Poin Bias", Swiss Federal Finance Adminisraion Working Paper Chow, G. C. and A. - l. Lin (1971): "Bes Linear Unbiased Inerpolaion, Disribuion, and Exrapolaion of Time Series by Relaed Series", The Review of Economics and Saisics, Vol. 53, No. 4, 372-375 Cobb C. W. and P. H. Douglas (1928): "A Theory of Producion", American Economic Review, No. 18, p. 139-165 Darvas, Z. and A. Simon (1999): "Capial Sock and Economic Developmen in Hungary", Naional Bank of Hungary Working Paper 1999/3 De Brouwer, G. (1998): "Esimaing Oupu Gaps", Research Discussion Paper 9809, Reserve Bank of Ausralia De Masi, P. R. (1997): "IMF Esimaes of Poenial Oupu: Theory and Pracice", IMF Working Paper WP/97/177 Denis, C., K. Mc Morrow and W. Roeger (2002): "Producion funcion approach o calculaing poenial growh and oupu gaps - esimaes for he EU Member Saes and he US", European Commission Economic Papers, No. 176 Denis, C., D. Grenouilleau, K. Mc Morrow and W. Roeger (2006): "Calculaing poenial growh raes and oupu gaps - A revised producion funcion approach", European Commission Economic Papers, No. 247 Diewer, E. and D. Lawrence (1999): "Measuring New Zealand's Produciviy", Treasury Working Paper No. 99/5 Domar, E. D. (1961): "On he Measuremen of Technical Change", Economic Journal, LXX1, No. 284, December: 709-729 22

Doyle, P., L. Kuijs and G. Jiang (2001): "Real Convergence o EU income Levels: Cenral Europe from 1990 o he Long Term", IMF Working Paper WP/01/146 Elmeskov, J. and S. Scarpea (1999): "Is he NAIRU a reliable concep in he EU conex? Mehodological lessons from Member Saes experience and he novelies of he EMU seup", Seminar a he Commission of he European Communiies, Brussels England, A. S. (1988): "Tess of oal facor produciviy measuremen", OECD Working Papers No. 54, (June) European Cenral Bank (2000): "Poenial oupu growh and oupu gaps: concep, uses and esimaes", Monhly Bullein, (Ocober) Fraser, I. (2002): "The Cobb-Douglas Producion Funcion: An Anipodean Defence", Economic Issues, Vol. 7, Par 1, (March) "Hungary: Seleced Issues" (1999), IMF Saff Counry Repor 99/27 Jorgenson, D. W. and Z. Griliches (1967): "The Explanaion of produciviy Change", Review of Economic Sudies XXXIV (3), No. 99, July: 249-283 Kaz, A. J. and S. W. Herman (1997): "Improved esimaes of fixed reproducible angible wealh in he Unied Saes 1929-85, Survey of Curren Business, 69-92 Kolasa, M. (2003): "The Toal Facor Produciviy and he Poenial produc in Poland 1992-2002", Naional Bank of Poland Conference "Poenial Oupu and Barriers o Growh" "Measuremen of Capial Sock in Transiion Economies" (2003), OECD Occasional Paper 2003/1 Measuring Capial (2001), OECD Manual Measuring Produciviy (2001), OECD Manual Morrow Mc, K. and W. Roeger (2001): "Poenial Oupu: Measuremen Mehods, "New" Economy Influences and Scenarios for 2001-2010, A Comparison of he EU15 and he US, European Commission Economic Papers, No. 150 Oulon, N. and S. Srinivasan (2003): "Capial socks, capial services, and depreciaion: an inegraed framework", Bank of England Working Paper, No. 192 Pula, G. (2003): "Capial Sock Esimaion in Hungary: A brief descripion of mehodology and resuls", Naional Bank of Hungary Working Paper, No. 7 Roeger, W. and J. I. Veld (1997): "QUEST II. A Muli Counry Business Cycle and Growh Model", European Commission Economic Papers, No. 123 Roldos, J. (1997): "Poenial Oupu Growh in Emerging Marke Counries: The Case of Chile", IMF Working Paper WP/97/104 23

Room, M. (2001): "Poenial Oupu Esimaes for Cenral and Eas European Counries Using Producion Funcion Mehod", Esonian Naional Bank Samuelson, P. A. (1947): "Foundaions of Economic Analysis", Cambridge, MA: Harvard Universiy Press Sarel, M. (1997): "Growh and Produciviy in ASEAN Counries", IMF Working Paper WP/97/97 Scacciavillani, F. and P. Swagel (1999): "Measures of Poenial Oupu: An Applicaion o Israel", IMF Working Paper WP/99/96 Slevin, G. (2001): "Poenial Oupu and he Oupu Gap in Ireland", Cenral Bank of Ireland Technical Paper Solow, R. (1956): "A Conribuion o he Theory of Economic Growh", Quarerly Journal of Economics, pp. 65-94 Solow, R. M. (1957): "Technical Change and he Aggregae Producion Funcion", Review of Economics and Saisics, Vol. 39, No. 3, pp. 312-320 Sikus, D. (2003): "Measuring oupu gap in Lavia", Lavian Bank Working Paper, No. 2 Sysem of Naional Accouns (1993), Cenral Bureau of Saisics, Republic of Croaia Torres, R., P. Jarre and W. Suyker (1989): "Modeling business secor supply for he smaller OECD counries", OECD Deparmen of Economics and Saisics Working Papers, No. 71 (Ocober) Torres, R. and J. Marin (1990): "Measuring Poenial Oupu in he Seven Major OECD Counries", OECD Economic Sudies, No. 14 Zolkiewski, Z. and M. Kolasa (2003): "The Toal Facor Produciviy and he Poenial produc in Poland 1992-2002", Naional Bank of Poland Conference "Poenial Oupu and Barriers o Growh" 24