Introduction and Calculation of the physical production function for the Iran economy

The production function is the technical relation of converting inputs into products. The production function is a completely physical concept and simply shows the relationship between output and production inputs. Regarding the selection of key production factors, in the initial research, has been highlighted work role and physical capital, along with other factors, but the use of energy has not been sufficiently addressed as a major input of production. Considering that energy use is necessary at all stages of production and there is no production possibility without energy consumption, in the last few decades research has been carried out to investigate the role of energy in production functions. Some have used physical laws to justify the use of energy in economics and production. In the present study, the production function called "physical production function" is introduced by the definition of work in physics, which suggests that capital interactions with labor and energy are separated. Thompson (2016) states that the output elasticity of energy is twice that of labor. Energy is underpaid relative to productivity suggesting monopsony power in the energy market. In contrast, overpaid labor faces elastic own substitution. Capital is characterized by inelastic substitution. Changes in the price of energy induce substitution toward labor but little substitution toward capital.
Considering that the production function is an important economic tool in economic analysis, in this study, the production function is introduced and estimated, which is influenced by the separate interactions of capital with labor and energy. Also, in this study, along with the estimation of the physical production function for the Iran economy during the period of 1974-2016, have been used other of two production functions; Cobb Douglas and Translog production function is used to compare and determine the more reliable econometric results.
Findings: In this study, in order to select the appropriate production function for the Iran economy, we will estimate the Cobb-Douglas, Translog and physical production functions, then the significance of the coefficients as well as the conformity and compatibility of parameters and elasticities are considered by economic theories, according to Thompson (2016), and finally, by using of the correct diagnosis tests of the model, the proper production function is selected.It should be noted that different states are considered for estimation production functions in order to obtain the best possible results, including the method of ordinary least squares and error correction method, with considering energy input in production functions.
The results of the model diagnostic and the accuracy tests as well as the variables coefficients in the estimation of functions indicate that the physical production function has a more suitable pattern than other two functions for the Iran economy. Among the production inputs, physical capital (0.85%) and labor force (1.95%) have the greatest impact on production. The effect of labor force increase on production (except to Translog) have a ​​positive and significant and in the physical production function of this coefficient is 1.95%. Energy in physical production function estimation have a share of 0.90%.
Separate capital-labor interactions with labor and energy have led to more reliable econometric characteristics as well as more sensible economic outcomes. Among production inputs, physical capital have the greatest impact on production, which indicates the importance of investments in the country's economy, which should be optimally and with planning in the infrastructure of the country. Because it has the ability to move the manufacturing sector in an optimal combination of labor and technology, and, with the trade boom improving living standards and economic growth. Meanwhile, Iran has suffered from lack of investment and production from the beginning of the planning process and the development path. The results of the estimation of the physical production function emphasize capital and its interaction with other inputs.