How To Calculate Price Elasiciy Per Capia Per Capi

Transcription

1 Price elasiciy of demand for crude oil: esimaes for 23 counries John C.B. Cooper Absrac This paper uses a muliple regression model derived from an adapaion of Nerlove s parial adjusmen model o esimae boh he shor-run and long-run elasiciies of demand for crude oil in 23 counries. The esimaes so obained confirm ha he demand for crude oil inernaionally is highly insensiive o changes in price. March Organizaion of he Peroleum Exporing Counries 1

2 The auhor is from he Deparmen of Economics a Glasgow Caledonian Universiy, Scoland Organizaion of he Peroleum Exporing Counries OPEC Review

3 CRUDE OIL CONTINUES o occupy a pre-eminen posiion a he hear of he world economy. I is he mos imporan source of energy, accouning for some 40.6 per cen of primary energy consumpion, and i is he raw maerial for he inernaional perochemical indusry. Over he 30-year period from 1971 o 2000, world crude oil consumpion increased by 46 per cen, from 2,412 o 3,519 million onnes per annum. Of his oal, he Unied Saes of America currenly consumes jus in excess of 25 per cen. One would have expeced he large oil price rises of he 1970s o have provided a very srong incenive for he more efficien use of oil, hrough he developmen and exploiaion of new echnology. The accompanying able shows he average annual rae of growh of oil consumpion per capia, along wih he average annual rae of growh of real GDP per capia over he period for 23 economies. A comparison of hese wo figures provides a crude measure of any improved efficiency. More precisely, if oil consumpion has grown a a slower rae han real GDP, hen, ceeris paribus, he rae of oil consumpion in he producion of GDP mus have declined. Of course, i may be he case ha GDP growh is now being fuelled by he relaively less energy-inensive service secor, raher han he more energy-inensive indusrial secor, bu, wih his cavea in mind, i is sill ineresing o make he comparison. All 23 economies experienced posiive real economic growh o varying degrees, and 13 of hese showed negaive average growh in oil consumpion. Of he en for which average growh in oil consumpion was posiive, seven recorded a higher rae of economic growh. Newly indusrializing China is a prominen example. In only hree economies, namely Greece, Korea and Porugal, did growh in oil consumpion exceed economic growh. Thus, in general, as economies have subsiued more energy efficien capial sock and/or have expanded heir less energy-inensive service secor, heir consumpion of crude oil has exhibied a downward rend. Anoher imporan quaniy moniored by policy-makers is he price elasiciy of demand for crude oil. This measures he responsiveness or sensiiviy of oil demand o changes in price. Economeric esimaes, derived from a variey of saisical procedures and covering various differen periods, sugges ha his price elasiciy is very low in boh he shor and he long run. The US Federal Energy Office, for example, esimaed ha he long-run price elasiciy of demand in consuming counries ranged from 0.2 o 0.6, wih ha of he USA recorded a 0.5 (see Kalymon, 1975). A priori, one would expec shor-run price elasiciies o be even lower, given he ime-lag necessary o respond o significan price changes. Thus, for example, Brown and Phillips (1989) esimaed he long-run price elasiciy for he USA a 0.56, which is similar o ha repored above, while he corresponding shor-run elasiciy was esimaed a Given he criical imporance of price elasiciy of demand for pricing policy, his paper will aemp o provide boh shor-run and long-run esimaes of his quaniy for all 23 counries lised in he able. March Organizaion of he Peroleum Exporing Counries 3

4 Table Demand for crude oil Oil consumpion Real GDP % growh % growh Price elasiciy per capia per capia Shor-run Long-run Ausralia Ausria Canada China Denmark Finland France Germany Greece Iceland Ireland Ialy Japan Korea Neherlands New Zealand Norway Porugal Spain Sweden Swizerland Unied Kingdom Unies Saes of America The calculaions for China and Souh Korea are based on he period Mehodology The approach used o model crude oil demand was o specify a parial adjusmen equaion o accoun for he difficuly and cos of changing echnology in he shor run. The heoreical underpinning for his procedure is provided in he appendix. The equaion esimaed ook he following form: where: Ln D = Ln α + βln P + γln Y + δ Ln D 1 + ε (1) Organizaion of he Peroleum Exporing Counries OPEC Review

5 D = per capia consumpion of crude oil in year P = real price of crude oil in year Y = real GDP per capia in year ε = assumed random error erm Ln= naural logarihm α, β, γ, δ are coefficiens o be esimaed An aracive feaure of such a log-linear model is ha he coefficien β can be inerpreed as he shor-run price elasiciy of demand and β (1 δ ) as he long-run price elasiciy of demand. The mos serious esimaion problem wih any specificaion conaining a lagged dependen variable is he high probabiliy of serial correlaion. Deecion of serial correlaion wih he familiar Durbin-Wason saisic is invalid in such circumsances and, accordingly, he Breusch-Godfrey Lagrange muliplier es was used insead. Thereafer, in he presence of serial correlaion, he Cochrane-Orcu ieraive procedure was employed o esimae he coefficiens, using annual daa for he period Oil consumpion and price daa were supplied by Briish Peroleum, while real per capia GDP was compued from saisics published by he Inernaional Moneary Fund. The esimaed equaion for he USA is presened below, for illusraive purposes: Ln D = Ln P Ln Y Ln D 1 (2) (3.39) (4.06) (6.54) R 2 = 0.91 F = LM = saisics are shown in parenheses. The adjused R 2 figure and he overall F saisic indicae ha he model fis he daa very well. The esimaed coefficiens have he expeced a priori signs and he associaed -saisics indicae ha hese coefficiens are all saisically significan a he one per cen level. The esimaed shor-run price elasiciy of demand is 0.06, while he long-run price elasiciy of demand equals 0.06 (1 0.87) or Noe ha hese values are very close o he esimaes for he USA repored by oher analyss. This same model was esimaed for he oher 22 oher counries and he esimaed elasiciies are presened in he able. The resuls (a) All esimaed shor-run elasiciies sugges ha oil demand is highly price-inelasic in he shor run. Only wo esimaes do no have he expeced negaive sign, namely China and Porugal, bu he -saisics (0.05 and 1.20, respecively) indicae ha hese wo coefficiens are no saisically differen from zero anyway. March Organizaion of he Peroleum Exporing Counries 5

6 (b) As expeced, all long-run elasiciies are greaer han he corresponding shor- run values. Ineresingly, for he G7 group of counries, namely Canada, France, Germany, Ialy, Japan, he Unied Kingdom and he USA, he long-run elasiciy falls wihin he range 0.18 o Clearly, his corresponds very closely o he range of 0.2 o 0.6 esimaed by he US Federal Energy Office. References BP Saisical Review of World Energy, Briish Peroleum, various issues. Brown, S.P.A., and Phillips, K.R., Oil Demand and Prices in he 1990s, Federal Reserve Bank of Dallas Economic Review, January Inernaional Financial Saisics, Inernaional Moneary Fund, various issues. Kalymon, B.A., Economic incenives in OPEC oil pricing policy, Journal of Developmen Economics, Vol.12, No.4, Organizaion of he Peroleum Exporing Counries OPEC Review

7 Appendix Consider a hypoheical economy, which is seeking o reduce is consumpion of crude oil. Suppose, for illusraive purposes, i has succeeded in reducing is oil consumpion from 125 unis in year 1 o 110 unis in year, bu, ideally, wans o reduce consumpion o 100 unis. Because of echnical rigidiies, his furher reducion canno be accomplished wihin a single period. Only a parial adjusmen can be made each period, and he enire move o he new desired long-run level will be spread over several periods. The following adapaion of Nerlove s parial adjusmen model allows us o capure he above siuaion and, a he same ime, o esimae long-run price elasiciies from available shor-run daa. Le he long-run demand funcion for crude oil in he economy be given by: D and le he gradual adjusmen process be expressed as: D D L L S b D = D L c = ap Y e 1, S d where 0 < d 1 (1A) (2A) where: D L = long-run demand for oil as a year D S = shor-run demand for oil in year P = reall price of oil in year Y = real GDP per capia in year e = random error erm and a, b, c, d are parameers,where: b = long-run price elasiciy of demand for oil d = coefficien of adjusmen In he simple arihmeical example above, equaion (2A) becomes: = 125 or: d = (0.8) d, from which d = Solving for D L in equaion (2A), we obain: March Organizaion of he Peroleum Exporing Counries 7

8 D L DS = d ( D S ) 1, 1 1 d (3A) Subsiuing his value for D L in equaion (1A), we obain: DS d ( D 1, S) 1 1 d b c = ap Y e from which: ( 1 d) b1 ( d) c( 1 d) d ( 1 d) D = a P Y D e S 1,S (4A) Taking logs of boh sides of equaion (4A), we obain: Ln D S = (1 d) Ln a + b(1 d) Ln P + c(1 d) Ln Y + dlnd 1,S (5A) + (1 d) Ln e Equaion (5A) above is in he same form as equaion (1) in he ex and is is heoreical underpinning.the shor-run price elasiciy of demand is given by b(1 d), which corresponds o β in equaion (1). Similarly, he long-run price elasiciy of demand is given by b, which is equivalen o β (1 δ) in equaion (1) Organizaion of he Peroleum Exporing Counries OPEC Review