Electricity in Economic Growth (1986) / Chapter Skim
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Appendix C: Econometric Model of Production and Technical Change
Appendix C: Econometric Model of Production and Technical Change
Pages 143-154
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From page 143... ...
EPRI EA-3482, Research Proj ect 1152-6, Final Report. Palo Alto, California: Electric Power Research Institute.
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From page 144... ...
Secondly, are formulate an error structure for the econometric model and discuss procedures for estimat ion of the Thorn parameter s. Our first step in formulating an econometric model of production and technical change is to consider specif ic forms for the sectoral price function {pil: qua 5 raO + ad In pi + AL In ~ + aE In PE + aN In ~ + aM In PM + aT · T + ~ ~(ln pE:)
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From page 145... ...
For the translog price functions the share elasticities with respect to price are constant. We can also characterize these forms of constant share elasticity or CSE price functions indicating the interpretation of the fixed parameters that enter the price functions.
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From page 146... ...
Our nest step in considering specif ic forms of the sectoral price functions {Pal is to derive restrictions on the parameters impl fed by the fact that the price functions are increasing in all five input prices and the concave in the five input prices. First, since the price functions are increasing in each of the five input prices, the value shares are nonnegative: vat 2 0 ~ .
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From page 147... ...
To impose concavity on the translog price functions the matrices {011 of constant share elasticities can be represented in terms of the their Cholesky factorizations: 21. The rate of change was introduced by Jorgenson and Lan (1983)
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From page 148... ...
i ~ t ~ t ~ i ~ i+} i ~ i ~ i+A i A i ~ i+A i ~ i A i A i ~ i+) i A i ~ i+> 1 ~ ~ ~ i ~ i ~ ~+6 i Under constant retorns to scale tho constant shero elasticitios satiefy ~ye motry rostrictions and restrictions implied by homogeneity of degree one of the price f~nction.
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From page 149... ...
Similarly, we can consider specific forms for prices of capital, labor, electricity, nonelectrical energy, and materials inputs as functions of prices of individual capital, labor, electricity, nonelectrical energy, and matcriale inputs into each industrial sector. Ve assume that the price of each input can be expressed as a translog function of the price of its components.
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From page 150... ...
The first is a nonrandom function of capital, labor, electricity, nonelectrical energy, and materials inputs and time; the second is an unobservable ransom distorbanec that is functionally independent of these variables. 's obtain an econometric model of production and technical change corresponding to the translog price function by adding random disturbances to all six cq~atione: Vet + B=1n pi+ p~Lln PL + ,~Eln PE + ,~Nln PN + liMln pi + B" · at+ L ~ BRL Pi ,l;Lln Pl; + Bj:;Eln PI + Bj:;Nln PN + ,l;Mln PM + ~ T+si VE=aE + 0~Eln PI + pLEln PL + ,pEln PI + BENln Pit ~ 0EMln pi + BiT T+8E V~a' + B1N18 Pi + ~LN1n PL + B N1D PE + BNNln PN + ~Mln PM BNT N V |
From page 151... ...
Finally, we assume that the random disturbances corresponding to distinct observations in the same or distinct equations are uncorrelated. Under this assumption that the matrix of random disturbances for the first four value shares and the rate of technical change for all observations has the Eronecker product form: V 'sx(1)
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From page 152... ...
. Tho covarianco matris of the average disturbances corresponding to the equatlon for tho rate of tochnical change for all observations, say Q, is a Laurent eatris: sT(2)
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From page 153... ...
We then calculate the' Cholesty factorization of the inverse matrix Q 1, Q-1 = LDL' , where L is a unit lower triangular matrix and D is a diagonal matrix with positive elements along the main diagonal. Finally, we can write the matrix T in the form:' .~ T = D1/2L, where D1/2 is a diagonal matrix with elements along the main diagonal equal to the square roots of the corresponding elements of D
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From page 154... ...
. _ Pi e I (i 1 2 To estimate the unknown parameters of the translog price function we combine the first four equations for the average value shares with the equation for the average rate of technical change to obtain a complete econometric model of production and technical change.
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