An Empirical Analysis of Macrocosmic Response to Crude oil price volatility in. China by using the Input-output Models. Jing He *

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1 An Empirical Analysis of acrocosmic Response o Crude oil price volailiy in China by using he Inpu-oupu odels Jing He * Absrac. Alhough he use of he inpu-oupu price model has been widely appreciaed in public macroeconomics calculaion way, he dynamic model is no less wide spread and is used more in heory and han in pracice. From 1998 Chinese governmen reforms he price sysem of he domesic crude oil. When we exam he macroeconomic responses o oil price volailiy, he iniial model is ou of daa. In his paper a number of mehodological refinemens are proposed, including he formulaion, for he firs ime, of an exended price model, based on he discree ime funcions. The conribuion of his paper is wofold. Firs, we develop a new model of inpu oupu (IO) price analysis based on he discree ime funcions o measure he impac of oil price. Second, we apply he price volailiy model (PV) o explain he macroeconomic responses beween Jun 4, and Jun 4,24 ry o idenify he volailiy rae of price in he oher 9 secions effecs resuling from changes in oil price. This process enables us o esablish he feedback measure no only beween he oil prices and he price sysem bu also beween heory and applicaion. I is a grea advanage and an imporan ool for planners and decision-makers. Keywords: Inpu-oupu price models; dynamic; discree ime funcions; crude oil price 1. Inroducion Oil prices remain on imporan deerminan of global economic performance. The magniude of he direc effec of a given price increase depends on he share of he cos of oil in naional income, he degree of dependence on impored oil and he abiliy of end-users o reduce heir consumpion and swich away from oil. Naurally, he bigger he oil-price increase and he longer higher prices are susained, he bigger he macroeconomic impac. In his paper, we wan o develop a price dynamic model o measure he impac of he price volailiy of crude oil. China became he second larges oil consuming counry, surpassing Japan in, and has accouned for 4 percen of he world's oil-demand growh beween and 24. Beijing now impors one-hird of he oil i consumes. From 1998 he benchmark price of domesic crude oil Insiue of Sysems Science, Academy of ahemaics and Sysems Science, Chinese Academy of Sciences, Beijing 18, China, Hejing25@homail.com This research has been parially suppored by gran a Naional Naure Foundaion of China (No.71312).

2 2 Jing He will be in line wih he monhly FOB price plus ariff of similar crude oil on he inernaional marke and will be announced a he beginning of each monh by he Sae Developmen Planning Commission (SDPC) of China. Inpu oupu analysis is an imporan ools o measure he macroeconomic responses o oil price volailiy in China. I is now nearly 6 years since economiss firs ried o formulae an inpu-oupu price model. The firs version of Leonief s physical model was no associaed wih an explici price model (Leonief, 1966). The firs version of he dynamic IO price model, in which he sales of each indusry mus jus cover is curren coss plus he full cos of required new capial goods, was formulaed by Hawkins(Hawkins,1948).Leonief himself ignored he dynamic price heory in he firs published version of his dynamic quaniy heory (Leonief,1953).According o he firs definiion of he dynamic price heory as spelled ou by Georgescu(Georgescu,1951),he price of each commodiy mus cover is curren coss plus ineres on he value of he capial equipmen required per uni of oupu. Solow (Solow, 1959) referred o i as Roegen s docrine and fel i was more reasonable han Hawkins model (Bazzazan.F, ). The resul was a sysem of price and quaniy variables for boh he open and he closed economy under he assumpion of fixed echnical coefficiens and full uilizaion and ransferabiliy of capial goods from one secor o anoher. From he above price model, we can see ha he vas majoriy of price models rely on he fixed echnical coefficiens and he assumpion ha wages are apar of value added and value added is fixed even if he price of goods is changed, whereas in he real world he opposie is rue. The main aim of his paper is o provide answers o he following quesions: Wha scope is here o develop an IO price model based on he discree ime funcions, wih he variable in echnical and value added coefficiens? Wha difference does such model developmen make when i comes o he measuremen of impacs o crude oil price volailiy in China?

3 Dynamic Inpu-oupu price model 3 In answering hese quesions we will focus iniially upon he developmen of exended saic and dynamic inpu-oupu price models. We will hen urn our aenion o consrucing he models wih available and adjused daa. Finally, we will es he models in an invesigaion of he price impacs of crude oil price volailiy a he naional level in China. 2. Dynamic prices model by using IO analysis based on he discree ime funcion. The Dynamic prices model by using IO analysis based on he discree ime funcion model can be divided ino hree pars: forming model, impac model, and volailiy model. 2.1 The price forming model The Leonief price model is defined as a se of simulaneous linear equaions in which he price each producive secor of he economy receives per uni of is oupu mus be equal o he oal coss incurred in he course of is producion. Each equaion describes he balance beween he price received and he paymen made by each endogenous secor per uni of is producs. These coss usually comprise wages, ineres on capial and enrepreneurial revenues credied o households, axes paid o he governmen, and oher paymens by secors (Leonief, 1986). The simple Leonief price forming model is expressed as follows: P= I A A + A + A T 1 ( ) ( g v m) Ag + Av + Am = V (1) (2) Then: P = PA+ V (3) Where, P is a vecor of commodiy prices, A is he direc inpu coefficien, coefficiens of fixed asses depreciaion, A g Av is coefficiens of labor income & welfare, A coefficiens of social profis & Taxes. V is he added value coefficiens. is he is he odel (1) is a kind of saic price model. By adding he discree ime funcion in i, we can ge he dynamic price model. We pu ino some ime span and he backward lag is.+ denoes he ime span from he end of o he end of +.

4 4 Jing He The dynamic price model can be shown as follows: P () = P () A () + V () (4) 2.2 The price impac model The consrucion of an exended dynamic price model requires a number of assumpions o be made. These assumpions can be summarized as follows: The assumpion of he small and single counry is he presupposiion of our model. We assume China is a single and small counry in he inernaional marke and he domesic price of crude oil hardly affec he price in he oher counries. The assumpion is accord o he real marke where he domesic price of crude oil in he cerain monh is deermined by he price in he inernaional marke in he before monh. A disincion is made beween crude oil secor and non crude oil secors. A furher disincion is made beween he price in he secor adjusing he price forwardly and secors change he price passively. The pariioned marix is used hen (3) can be rewrien as follows: A A p = ( p p ) = ( p p )( ) + ( v v ) (5) A21 A22 Thus: P = PA + P A + V P = PA + P A + V (6) Where, P is he price vecor in secor n, P1 is he price vecor in secor We assume he fron K secors is he secors adjus he price forwardly, as well as he firs kind secors; he back n k secors is he secors change he price passively, as well as he second kind secors. P1 is he price vecor in he fron K secors. P 2 is price vecor in he back n k secors. The echnical coefficiens marix is divided ino four pars according o he secors in he secors K and n k, V1 is he added value coefficien vecor in he secors K. V2 coefficien vecor in he secors n k. is he added value 2.3 The price volailiy model

5 Dynamic Inpu-oupu price model 5 We selec he saring ime poin as hen P ( ) = P ( ) A( ) + P ( ) A( ) + V ( ) P( ) = P( ) A ( ) + P( ) A ( ) + V ( ) (7) Where, P 1( ) is he price vecor in he fron K secors a ime, P2( ) is price vecor in he back n k secors a ime, A11( ) is he echnical coefficiens of he fron secor K o he fron secor K a ime, A12 ( ) is he echnical coefficiens of he fron secor K o he back n k secors, A21( ) is he echnical coefficiens of he back n k secors o he fron secor K a ime, A22 ( ) is he echnical coefficiens of he back n k secors o he back n k secors a ime, V1 is he added value coefficien vecor in he secors K a ime. V2 is he added value coefficien vecor in he secors n k a ime. We assume: P () = P ( ) + P () A () = A ( ) + A () V () = V ( ) + V () P() (8) is he price volailiy vecor a ime, A() is he echnical volailiy coefficiens a ime, V() is he added value volailiy coefficien row vecor a ime. The backward lag beween and can be seleced a discreion in our empirical model in China he basic uni of is one monh and = 1 monh. Commonly he more ime in he back lag,he more change will occur in he volailiy parameer in Then: P() A () P ( ) + P () = [ P ( ) + P ()] A() + [ P ( ) + P ()] A() + V () (9) P( ) + P() = [ P( ) + P()] A () + [ P( ) + P()] A () + V () (1) Where, P () is he price volailiy a he ime in he fron K 1 secors. P() 2 is he price volailiy a he ime in he back n k secors. V (). A he ime poin of because P1 P 1 ( ) + P 1 ( ) is he price adjused forwardly by he inernaional marke price,so he equaion (9)don come ino exisence. The explain of he economic meanings come from he firs assumpion above of small and single counry. I means

6 6 Jing He P ( ) + P ( ) is no he inpu oupu equilibrium price in he fron K secors. While he back 1 1 n k secors are regarded as he secor adjusing he price passively, equaion (1) can come ino exisence. Thus: P()[ I A ()] = P( ) A () + P() A () + P( ) A () + V () P( ) (11) [ I A ( )] is reversible (we can ge he resul from he common economic sysem). If 22 We discuss as follows: When A ( ) = V () = (12) The meanings are he direc inpu coefficien and he added value coefficiens hold he line in shor ime inerval. Then: P()[ I A ( )] = P() A ( ) (13) In his secion we explore furher developmen of he exended price volailiy models in order ha hey may be used o measure he impacs of crude oil price volailiy. The model will also provide a measure of he impacs of crude oil price volailiy on producion prices wih he volailiy of he direc inpu and he added value coefficien. (13) come from hree assumpion:.china is a single and small counry in he inernaional crude oil marke.. he echnical coefficiens (A) will no change.. he value added coefficiens (V) will no change. The and can be accord o he fac a all. In our price model, when he ime span is long, he price in he oher secor will changed grealy. And he volailiy of price in he inernaional marke will affec he price in he domesic marke. any secors will adjus heir srucure of he producion by choosing he cheaper resources. Then he echnical coefficien of crude oil will changed grealy. Generally, longer he ime span is, greaer he change of he echnical coefficien will be, as well as he value added coefficiens. When A ( ) = V () (14) The economical meanings of his formula are ha he economical and echnological srucure will no be changed in shor imes. In our price model, we follow his assumpion when he

7 Dynamic Inpu-oupu price model 7 analysis span is shorer han 12 monhs. Because our calculaion base is Inpu-oupu able in July,, we will use he (14) o calculae he daa from July, o July,. Then: P()[ I A ( )] = P() A ( ) + V () (15) When A ( ) V () (16) In our price model, we follow his assumpion when he analysis span is longer han 12 monhs. Then: P ()[ I A ( ) A ()] = P( ) A ( ) + P() A ( ) + P() A () + P ( ) A () + V () (17) We can ge P 1( ) and P2( ) from (7),When [ I A22( )] [ I A11( )] 1 1 [ I A ( ) A ( )],{ I A ( )[ I A ( )] A ( )[ I A ( )] } is reversible (we can ge he resul from he common economic sysem).(17) can be rewrien as follows: P ( ) = {{ V ( )[ I A ( )] A ( )[ I A ( )] + V ( ) [ I A ( )] }[ I A ( )[ I A ( )] A ( )[ I A ( )] ] A ( ) + P( ) A ( ) + P( ) A ( ) + {{ V ( )[ I A ( )] A ( )[ I A ( )] + V ( )[ I A ( )] }[ I A ( )[ I A ( )] A ( )[ I A ( )] ] A ( )[ I A ( )] + V ( )[ I A ( )] } [ I A ( ) A ()] A () + V ()} (18) We can see from he analysis process ha (18) can be used o calculae he resul from July o July 24 because he change of V and A in our price model. We discuss he equaion (18): When A () A () = (19) The economical meanings of he assumpion is ha he echnological coefficiens of non crude oil secor assuming oil crude will change, while he echnological coefficiens of non crude oil secor assuming oher resources will no change. Then: [ I A ( )] P () = P ( ) A( ) + PA () ( ) + P () A() + V() (2)

8 8 Jing He Thus: P( ) = {{ V ( )[ I A ( )] A ( )[ I A ( )] + V ( )[ I A ( )] } [ I A ( )[ I A ( )] A ( )[ I A ( )] ] A ( ) P() A ( ) + P() A () + V ()}[ I A ( )] (21) The assumpion of (21) can be exended. When he price of crude oil secor changes is price accord o he inernaional marke, here are oher k-1 secors changing heir price forwardly. Then he price volailiy rae of he lef n-k secors can be calculaed from (21). 3. Empirical Analysis of he acroeconomic Responses o oil price volailiy in China Afer China's oil prices are pegged o he inernaional marke, he wellhead price of domesic crude oil will be abou equal o ha of impored producs. This new pricing sysem is a final move o free China's oil indusry from he planned economy and he sar of wha may be fierce compeiion on he inernaional marke. The dynamics of change in China price sysem are consequenly a projec wih a long ime span, disincive characer and complex srucure. The empirical analysis of he macroeconomic responses o oil price volailiy in China can give he useful decision suppor. 3.1 Daa issue Crude oil price volailiy rae daa Informaion abou oil prices is available wih a higher frequency such as on monhly or even daily basis. Because our model selec he lag as one monh, monhly oil price daa have he advanage of a large number of observaions, and hence allow for a more horough esing of he corresponding impac. The oil prices in inernaional marke beween Jun.4 o Jun.4 24 can be shown in Figure 1.The daa in he figure suggess ha oil prices in inernaional marke exhibi volailiy clusering jus by eyeballing he daa. Here, we ake a formal approach by exploring some summary saisics of he monhly oil price daa.the all counries spo price FOB is weighed by esimaed Expor volume. The volailiy rae is based as he daa on Jun.4,.

9 Dynamic Inpu-oupu price model Foreign Trade Inpu -Oupu (IO) ables of China. The process oulined in his work presens requiremen for IO ables. A foreign rade IO ables of China for 1995 Chen,24 is modified and shoren o 19 secors and is he main daa resource for our calculaion. The impor producion has been oulines separaely along wih he quaniies used in he inermediae inpu and final demand in Foreign Trade Inpu -Oupu (IO) ables of China. The syle of he able can be showed in able 1: 3.2 The price volailiy model We use he following formula: n i= 1 n i= 1 D D ij i i ij i i ( i 1,2,,n) X + Y = X = ( i 1,2,,n) X + Y = = Where, X ij is he square marix ( n (22) n ) of he iner-branch flows of inermediae uses. Each elemen of his marix is he oupu of he branch i earmarked for branch j, and is he inpu of he branch j o branch i, X i is he column vecor ( n 1 ) of gross oupu (oal producion). Yi is he column vecor ( n 1 ) of he final demand, i is he column vecor ( n 1 ) of he expor. The superscrip D is he domesic producion and is expor producion. The able has he advanage of a large number of observaions, and hence allow for a more horough esing of he imporance of lags in deermining variances. The ime series on oil prices can go back up o Jun.4,.We will apply our volailiy measure on monhly daa ha capures a longer ime span and use our measure o explain he macroeconomic response. Given our main objecive, he analysis of he impac of oil price. Given our main objecive, he analysis of he impac of oil price volailiy on he relaionship beween oil price and oher secors price, we need o esablish he price volailiy model due o he real saus in China. We regard he price in he secor of Crude oil in he foreign rade IOO ables as he average price of he crude oil. The price-forming model can be shown as:

10 1 Jing He D D A A ( ) ( ) A A ( ) V V P = P1, P2 = P1, P2 1, 2 ( 1, D D + P P A A + 2 ) A21 A22 A21 A22 (23) Here, he superscrip D is he domesic producion and is expor producion. P is a vecor of commodiy prices, A is he direc inpu coefficien. A V is he value added coefficien. We assume he fron K secors are he secors adjus he price forwardly, as well as he firs kind secors; he back n k secors are he secors adjus he price passively, as well as he second kind secors. The corresponding model of he price-forming model can be shown as: P = P A + P A + P A + P A + V D D D P = P A + P A + P A + P A + V D D D (24) Selec he basic ime poin, he model based on he discree ime funcions can be shown as: D D D P 1( ) = P 1( ) A11( ) + P2 ( ) A21( ) + P 1( ) A11( ) + P2 ( ) A21( ) + V1( ) D D D P 2( ) = P 1( ) A21( ) + P2 ( ) A22( ) + P 1( ) A12( ) + P2 ( ) A22( ) + V2( ) (25) We assume ha: P () = P ( ) + P () P () = P ( ) + P () D D D A () = A ( ) + A () V () = V ( ) + V () Due o he real saus in China, here is anoher assumpion: (26) There is only one secor adjus he price forwardly. We assume China is a single and small counry in he inernaional marke and he domesic price of crude oil hardly affec he price in he oher counries. The assumpion is accord o he real marke where he domesic price of crude oil in he cerain monh is deermined by he price in he inernaional marke in he before monh. Then we ge he formula as follows: P () = P( 1) I (27) Where, P () is he domesic price of crude oil in he cerain monh, P ( 1) I is he inernaional marke price in he before monh.

11 Dynamic Inpu-oupu price model 11 Due o he assumpion of single and small counry, we can make anoher assumpion ha he impor prices in he second kind of secors are no affeced by he impor price of crude oil. Tha D can be shoren as P () 1 P () 1. is affeced by P () 1 P enirely () 2 The ime lag in our model is one monh, which is oulined as = 1 P () = P ( ) + P () = P ( ) D D D P () 2 = We assume ha: (28) (29) is hardly affeced by (monh). Then: P () = α P ( ) 1 1 P () = β P ( ) D D 2 2 (3) α (%) is he growh rae of he inernaional marke price of he crude oil (see Table 2). β is he volailiy rae of he domesic price of he non-oil secors. The daa of α can be regards as he empirical daa. β is a row vecor. If I A () D 22 P ( ) 2 is reversible, hen β = { P ( )[ A ( ) + A ( ) + αa ( )] + P ( )[ A ( ) I] + P ( ) A ( ) + V ( )}[ I A ( )] P ( ) D 1 D (31) Then we can ge he main monh price volailiy rae ( β ) in 9 secors beween Jun 4, and Jun 4,24 in Table Conclusion This paper focuses on he Leonief price model, invesigaing ways in which i can be exended and exploring he effecs of such exensions in a policy analysis conex. The economies of oil-imporing developing counries would suffer mos from higher oil prices because our economies are more dependen on impored oil. In addiion, energy-inensive manufacuring generally accouns for a larger share of heir GDP and energy is used less efficienly. The economic simulus provided by higher oil price would be ouweighed by he depressive effec of higher prices on economic aciviy.

12 12 Jing He Table 1. Foreign Trade Inpu Oupu (IO) ables of China Inermediae Demands Final Demands Toal oupu and impor 1 2 n Consumpion Capial goods Expor Toal 1 Inermediae inpu of domesic producion 2.. n D X ij D Y i X i 1 Inpu Inermediae inpu of impor producion 2.. n X ij Y i i Primary inpu Toal inpu V j X j

13 Dynamic Inpu-oupu price model 13 Table 2. Crude Oil price volailiy rae and he oher 9 secors price volailiy rae Dae Jun 4, Jul 2, Aug 6, Aug 27, Sep 3, Oc 1, Nov 5, Dec 3, Dec 31, Jan 7, Feb 4, ar 3, Apr 7, ay 5, Jun 2, Jul 7, Aug 4, Sep 1, Oc 6, Nov 3, Dec 1, Jan 5, Feb 2, ar 2, Apr 6, ay 4, ay 25, Jun 1, Aug 3, Sep 7, Oc 5, Nov 2, Dec 7, Crude Oil Growh rae Price volailiy rae of each secor Price (US$ of Crude oil Oil & Elecriciy Agriculure Chemical Building Ferrous Heavy Passenger Commerce per barrel) (%) Refineries Indusries aerials eals ach. & Transpor Elecronics

14 Jan 4, Feb 1, ar 1, Apr 5, ay 3, Jun 7, Jul 5, Aug 2, Sep 6, Oc 4, Nov 1, Dec 6, Jan 3, Feb 7, ar 7, Apr 4, ay 2, Jun 6, Jul 4, Aug 1, Sep 5, Oc 3, Nov 7, Dec 5, Jan 2, 24 Feb 6, 24 ar 5, 24 Apr 2, 24 ay 7, 24 Jun 4, Jing He

15 Dynamic Inpu-oupu price model 15 Appendix Daa Sources: OECD inernaional secoral daabase OECD Srucural analysis daabase Energy Balances And own calculaions References Arrow, K. (1971).General Compeiive Analysis.pp2-8.San Francisco. CA. Holden-Day. Bazzazan. F & Baey, P.W.J. () The developmen and empirical esing of exended inpu-oupu price models. Economic Sysem Research.Vol.15,pp69-86 Chen,X.K.(24).Waer Conservancy Economy Inpu-Occupancy-Oupu Table of China and Is Applicaion. Inernaional Journal of Developmen Planning Lieraure.Vol.15, pp Chris, C. (1955).A review of inpu-oupu analysis, an Appraisal Sudies in Income and Wealh. pp Princeon Universiy Press. Ezra, D. (1989).Inpu-oupu and general equilibrium. Economic Sysems Research. Vol.11, pp Georgescu-Roegen, N.(1995). The aggregae linear producion funcion and is applicaion o von Nemann s economic model, in: T,C, Koopmans(ed), Aciviy Analysis of Producion and Allocaion(New Haven, Yale Universiy Press) Hawkins,D.(1948).Some condiions of macroeconomic sabiliy, Economeric,Vol.16, pp Leonief, W.(1966).Inpu-oupu Economics.pp33-54.New York, oxford Universiy Press. Liu,Q.Y.(1993). odels and mehods on economic sysem. pp17-36.bei Jing,Renin Press. Solow,R..(1959).Compeiive valuaion in a dynamic IO model, Economeric, Vol.27,pp3-53

16 16 Jing He Zhang, J.S. ().Non-linear dynamic inpu-oupu model and he dynamic CGE model. pp77-12.bei Jing,Tsinghua Universiy Press.