Efficiency estimation of Heat and Power Stations with production frontier models (deterministic production frontier and stochastic frontier models).

Use your Heat and Power Stations sample with data on fuel inputs (in tonnes) and energy outputs (electricity (in MWh = 1000kWh) and heat (in GCAL). To apply parametric model of technology you have to aggregate two outputs (electricity and heat) in a single output. It might (but not have to) be the volume of energy produced by the Heat and Power Station measured in GJ (gigajoule), where 1 MWh = 3.610⁹J = 3.6 GJ, 1 GCal = 4.1868GJ.

To accomplish the tasks the following data on Heat and Power Station operation is needed:

The volumes of fuels consumption (gas and oil) expressed in logarithms, i.e. Ln (gas) and Ln (oil);

The volumes of energy supplied expressed in logarithms, i.e. Ln (energy);

The estimates of parameters for the average production function describing relationship between the fuel inputs and the energy produced for external consumption specified as follows: , where y - volume of energy produced for external consumption (output variable); x₁ - volume of consumption of natural gas, x₂ - volume of consumption of furnace oil; A, a, b-production function parameters.

The tasks:

1.

You have to construct the deterministic production frontier (DPF) from the average production function estimated from your sample data. To construct DPF use the following method for estimation of the DPF parameters:

where- the residual calculated for observation (unit) i in average production function estimated from the data sample with OLS, N - number of observations (production units).

2.Calculate technical efficiency estimate for every Heat and Power Station in a sample on the basis of constructed DPF.

3.Construct Stochastic Production Frontiers (SPF) using Stata software package[1] assuming different types of technical inefficiency distributions (gamma distribution[2], truncated normal distribution[3], half normal distribution[4], and exponential distribution[5]).

4.Calculate the estimates of parameters of DPF and SPFs constructed for different distributions of technical inefficiency. Submit estimation results for DPF and SPF models in the following table

The parameters Estimates (t-statistics)

DPF

SFA (expon)

SFA (hnorm)

SFA (tnorm)

SFA (gamma)

ln gas

ln oil

const

Compare and evaluate the empirical models.

[1] In computer class (room 105) you may try again to install sfcross module as follows:

1.Open stata

2.Type in command line: net install sfcross, all from(http://www.econometrics.it/stata).

If that will not work, then use frontier module and omit calculations for gamma distribution.

[2] https://en.wikipedia.org/wiki/Gamma_distribution

[3] https://en.wikipedia.org/wiki/Truncated_normal_distribution

[4] https://en.wikipedia.org/wiki/Half-normal_distribution

[5] https://en.wikipedia.org/wiki/Exponential_distribution