Empirical Example- Returns to Scale in Electricity supply.pdf

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Empirical Example- Returns to Scale in Electricity supply.pdf

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Empirical Example- Returns to Scale in Electricity supply

Empirical Example: Returns to Scale in Electricity Supply Walter Sosa-Escudero Econ 507. Econometric Analysis. Spring 2009 February 10, 2009 Walter Sosa-Escudero Empirical Example: Returns to Scale in Electricity Supply Classic paper: Nerlove (1963), analyzed in detail in Hayashi (2000). Problem: returns to scale in a regulated industry (electric power supply). See Hayashi for a discussion of the underlying institutional framework. Data: 145 in 44 states. Variables: total costs, factor prices (wage rate, price of fuel, and the rental price of capital), and output. Walter Sosa-Escudero Empirical Example: Returns to Scale in Electricity Supply Economic problem: cannot just look at costs vs. output. Factor prices interact with output. Cobb-Douglas technology: Qi = A1xα11i x α2 2i x α4 3i Qi: output xj : factors Ai: ‘firm heterogeneity’: unobservable differences in production efficiency. r ≡ α1 + α2 + α3 measures degree of returns to scale. Walter Sosa-Escudero Empirical Example: Returns to Scale in Electricity Supply Cost function: TCi = r (αα11 α α2 2 α α3 3 ) ?1/rQ1/ri p α1/r 1i p α2/r 2i p α3/r 3i Taking logs: lnTC1 = μi + 1 r lnQi + α1 r ln p1i + α2 r ln p2i + α3 r ln p3i, μi ≡ ln [r (αα11 αα22 αα33 )] The linear econometric model is: lnTC1 = β1 + β2 lnQi + β3 ln p1i + β4 ln p2i + β5 ln p3i + i with β2 = 1/r, β3 = α1/r, β4 = α2/r, β5 = α4/r. μ ≡ E(μi), i ≡ μi ? μ, so E(i) = 0. Walter Sosa-Escudero Empirical Example: Returns to Scale in Electricity Supply Role of classical assumptions Linearity: is a consequence of the Cobb-Douglas tecnology (in logs). Strict exogeneity: factor prices are given to the firm independently of efficiency. Ouput: if prices are set independently of efficiency, Ok. If prices are set to cover costs: unobserved efficiency is related to ouput. No multicollinearity: Ok Firm spillovers might harm the no-serial correlation assumption. Heteroskedasticity very likely to be present. Careful. Walter Sosa-Escudero Empirical Example: Returns to Sca