A Demand System for Input Factors when there are Technological Changes in Production

Transcription

1 A Demand Syem for Inpu Facor when here are Technologcal Change n Producon

2 Movaon Due o (e.g.) echnologcal change here mgh no be a aonary relaonhp for he co hare of each npu facor. When emang demand yem one hould allow for uch echnologcal change. A he ame me, we wan o mpoe rercon on long run propere uch ha he yem can be ued for forecang. 2

3 Dpoon. Demand yem mple many conegrang relaonhp 2. Preenaon of a flexble demand yem 3. Show how a de-rended CVAR model approprae for pecfyng he yem 4. Emaon reul from a Norwegan producon ecor 5. Concluon 3

4 CES echnology wh only facor neural echnologcal progre Le v, be he ue of facor n perod ; p, he prce of facor ; p A, he aggregaed facor prce, x he producon level; v δ a drbuon parameer; σ he ubuon parameer; he cale elacy; θ he (facor neural) echnologcal level ( p, pa ) x, σ ln δ θ σ, 4

5 Co hare The log of he co hare for npu facor gven by σ lnδ n ( σ ) δ j lnδ j ( σ )( p, pa, ) j Th mple a aonary relaonhp beween he co hare and he relave prce of he facor. In a yem wh n npu facor here are n- ndependen co hare. Therefore, n h demand yem here are n- ndependen conegrang vecor. 5

6 Oher demand yem Oher facor demand yem, e.g. Tranlog, alo nvolve a aonary relaonhp for each cohare Wh Tranlog, he opmal co-hare wh: P, C V,, β p j, j β,, j j, j 0,, j j, j, u 6

7 7 A flexble demand yem A flexble demand yem. Smplfcaon: Aumng σ 2. Generalaon: Allowng he δ o be me-varan where A x p p v θ δ ln,,,,,,0,, 0 ln ln ε δ δ ε θ θ θ θ

8 8 Syem formulaon Syem formulaon Ung marx formulaon, he yem become We aume ha he procee of he error erm can be decrbed wh n-r common rend: n n A x con p p v, θ ε θ ε ( ) r n n A A :, υ ε ε θ

9 9 Emprcal formulaon Emprcal formulaon Conegraed VAR wh nerpreable effec of exogenou varable where ( ) ( ) ( ) Γ ' p Z Y Z Y Z Y ε µ β α [ ] ( ) [ ] µ β Z Y E Z Y E '

10 0 0 0 MA MA-repreenaon and repreenaon and heorecal demand yem heorecal demand yem The emprcal yem ha he followng MArepreenaon (confr. Granger rep. h.): We ee ha h concde wh heorecal demand yem: where P A A(A A) - A wh rank n-r. C Z Y Λ ε ι A n n A P x con p p v, θ ε θ ε

11 Daa ere 7 dfferen npu facor: labour elecrcy fuel oher npu facor buldng ranpor equpmen machnery For he la hree npu facor we ue nvemen daa and nvemen prce a proxe.

12 Co hare If he all δ were mendependen, all he co hare hould be aonary (when σ). From he graph we ee ha he co hare are no aonary. 2

13 Exogenou varable The vecor of exogenou varable conan: Noe: Z ( x ) ', When ncludng producon lke h, we mpoe a common facor rercon beween he npu facor and producon. Includng lagged dfference of producon (.e. x and x - ) n Z would remove h mpled rercon. Alo eaonal dumme could be ncluded. 3

14 Wha o e. The conegrang rank (number of common rend). 2. Rercon on. 4

15 Lkelhood rao e lkelhood LR r r r r r r r r p-value are baed on a Gamma drbuon uggeed by Doornk (998). 5

16 Teng rercon on lkelhood p-value θ No rer Scale-el (6).062 no rend (2) % (3) % θ (4) % Hypohe: Emaed wh GRaM θ 7 2, 7 6

17 Concluon Technologcal change n producon may ake place. Thee may lead o change n he opmal co hare. We ugge a yem where we allow for uch echnology change. In he emprcal analy we fnd le conegrang vecor han ndependen co hare, ndcang echnologcal change. Even wh reduced conegraon rank, we can mpoe and e he rercon ha here no rend n he co hare. 7