Estimation of marginal abatement costs for undesirable outputs in India's power generation sector: An output distance function approach.

2

+ γ t^t + 0.5 *γ tt^t

In equation (xvi), x = (x₁ x₂, x_N) denotes inputs, and y = (y₁ y₂, y_M)
corresponds to both the desirable and undesirable outputs. In the model
У = (У1 y₂,     y_i) are the desirable outputs while y = (y_i+1 y_M)

represent the undesirable outputs. In our model fuel (F), capital (K) and
labour (L) are the three inputs while the output consists of desirable
output, electricity (Y) and undesirable output, CO2 emission (P)
generated by the power plants. A time variable t is introduced to reflect
technical change. In order to reduce the number of parameters to be
estimated the terms corresponding to the product of time variable (t) and
logarithms of other variables are excluded by assuming a neutral
technical change.

The parameters of the equation (xvi) are computed by using the
linear programming technique as suggested by Aigner and Chu (1968).
Theoretically the value of the output distance function D₀ (x, y) cannot
exceed unity and it must be less than or equal to unity (assuming there
are no measurement errors). Formally,

(xvii) KK ln D₀^k (x, y)≤0          ∀k= 1,2,......,K.

where k = (1, 2, ......, K) indexes individual observation. Now if we add

a non-negative error term to equation (xvii), it can be rewritten as:

(xviii) KK ln D₀^k (x, y) + ε ^k = 0

where ε, (ε ≥0) denotes the non-negative residual or the error term.

Next we choose the ‘fitting’ criterion to be the minimum absolute error
of errors is as small as possible (Hetemaki, 1996). The parameters of the
translog output distance function can be obtained by solving the following
problem:

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