A Stochastic Frontier Cost Function Approach - Assignment Example

Name, Instructor, Course, Date, Stochastic Frontier Analysis Using Shazam Question 1 constructing a stochastic production frontier (a) Estimate the stochastic frontier production function based on Cobb-Douglas and translog functional forms, using the time-varying option. In the Cobb Douglas and translog functional forms, Yn = xn + (Vn – Un) ,n=1,...,N, Yn = xn + (Vn – Un) ,n=1,...,N, Yn = production ( log of the production) of the n-th firm; Xn = a k1 vector transformations of the input quantity of the n-th firm  is an unknown parameters; the Vn is random variable assumed to be iid. N(0,V2), In inefficiencies, the Frontier Analysis comes out as a theoretical-practical framework, with the objective of contributing on the definition /estimating production frontiers. This Frontier comes from remote influences. However, the literature that influenced it’s development directly, has been the theoretical framework on pro­duction efficiency. Linear programming parametric method of SFA, stochastic frontier con­siders production frontier as a random shock. The OLS (Ordinary Least Squares) method provides a simple test for the identification of the presence of technical inefficiency in the data. The error term is symmet­ric and the data does not evidence technical inefficiency. The term quantifies the technical inefficien­cy or the distance in relation to the efficiency frontier. The technical ineffi­ciency presence may be directly tested by the residuals of OLS if the most efficient estimate, presents a value of 0. If it is positive, it will make the value in the brackets of exponential term to be non-negative and not smaller than unity. Technical inefficiency will present declining effects as time goes by (positive ef­fects on the technical efficiency with time). In contrast, a negative value will cause inefficiency to be inclining with time (persistent inefficieRiverancy) The log likelihood ratio test LR at a significance level of 5% established the use of the Cobb Douglas specification and rejected the translog model. (b) Test whether the Cobb-Douglas functional form is an adequate representation of the data. Which functional form would you select to use and why? Maximum 200 words. The Cobb–Douglas and translog functional forms should be estimated and then undergo testing to establish whether they are adequate representation of the involved data, according to the specification of the translog model. The study sample size can allow us to do it as a result of the degrees of freedom. The stochastic frontier analysis used to investigate the link between the variables have assumed the appropriateness of the Cobb–Douglas form. They also found Cobb–Douglas to be as good as translog as a representation of the relationship of the independent and dependent variables. Where, Yi is the quantity of electricity output, Xa is a vector of input quantities and, b is a vector of parameters ε i is an error term defined as: εi = Vi – Ui i = 1, 2, … n farms …………………………….… (2) c) Using the functional form of choice, comment on the significance of the four input variables in influencing maize output on the frontier How do these estimates compare with those obtained for the average producer? d) Test for any change in mean technical efficiency over time and comment on the results. Maximum 100 words. The Maximum-Likelihood ML method helps in testing for the the estimation of the parameters in the frontier production function. The ML requires the numerical maximization of the likelihood function. The individual mathematical expectation (technical efficiency)TE = exp (-ui) of the variables could only be evaluated/ predicted under the distributional assumptions of the underlying technical inefficiency. When the UIS are i.i.d and the assumption is that they are half-normal random variables, the ML Estimator to find the mean technical efficiency is by substituting ML estimators for the parameters in the equation. This is because the sample’s technical efficiencies may be predicted. e) Re-run the model using the efficiency effects model and including the five efficiency variables outlined above. Interpret results for the efficiency variables, reporting any management implications from the technical efficiency estimates obtained. Maximum 300 words. In order to make an estimation of the frontier production function estimate, the data is created in the Frontier form referred to as ‘Model 2’. The variables included 1. Age of the household head 2. Education of the household head 3. Household size 4. Number of adults in the household 5. Percentage of area classified as upland fields The translog had 14 x variables with 3 z variables. He values in the instruction file are self-explanatory. The log-likelihood function for the model was calculated to -17.988 while the value for the OLS fit is -38.999. This is less than the value in the full frontier model. Therefore, the generalized likelihood-ratio to test the absence of a technical inefficiency effect in the frontier may be calculated as follows LR = -2{-38.999- (-17.988) }= 42.02 This is the LR test of one sided error. Given that this value exceeds 10.371, it is significant. For the degrees of freedom that equal five, this is the critical value, therefore, we reject the null hypothesis. The ML estimate for Y is 0.9999999 given an estimated 0.0035 standard error. The results in the Frontier are consistent to the fact that the y-value is greater than zero. Despite this, the y estimate is not different from one (significantly). Therefore, the y-estimate may not be significantly different from one. This means that the stochastic model may not be different from the deterministic frontier (significantly) given that there are random errors inside the production function The estimate for the “age of the household head” coefficient is negative in the model for inefficient effects. This means that the large rice farms have smaller inefficiency effects. It is interesting to establish whether the true value is zero given that the ML estimate is small relative to the standard error. Question 2 constructing a stochastic cost frontier Use the file a2q2.dta, which contains one year of data on the production of electricity by a sample of 100 electricity utilities. Undertake the following tasks using FRONTIER: (a) Estimate the stochastic frontier cost function based on Cobb-Douglas using the efficiency effects model and including the three efficiency variables: average age of workers; average education attainment of workers; and size of operations. Comment on the significance of the quantity and price variables in influencing the cost of power on the frontier. Maximum 300 words. An inefficient in the stochastic frontier cost function is a deviation from the frontier. In this case the one sided error is required in order to represent this. The stochastic frontier cost model in this case permits the inefficiency effects into a function of the set of explanatory variables. In which case, they are parameters that are simultaneously within the stochastic frontier. This approach is stochastic and the observations appear to be off the frontier due to the inefficiency, or as a result of random shocks/ measurement errors. The cost of investing in the electricity firm in the area i is represented by the stochastic frontier cost function, written as: Ci = C(yi, wi) + (Vi + Ui) (1) In determining the electricity output given three variables the mean value for the 100 respondents is estimated to be 0.677, and a range from 0.214 to 0.951. This means that the output may be increased by an average of 29.7%. The technical efficiency is calculated by finding the expectation of technical efficiency. First of all, from the tables, the LR accepts the null hypothesis which is that the Cobb-Douglas is the appropriate model. The second test is to find out whether the inefficiency effects can be included in the model. Since the inefficiency matter, we need a stochastic frontier. If this was not the case we would use the augmented average production function. This is because the firm would be in operation under a technically efficient frontier. In equation (1), the Vi parameter is taken to be independent and also identically distributed random errors. This is in a normal distribution of a mean of zero and unknown variance σ2V, and independent of Ui. Ui -non-negative unobservable random variables related with cost inefficiency, that are considered to be independently distributed as truncations at 0 of the N(mi, σ2U) distribution, mi is an effects vector, of population areas, with mi=ziδ. Cost inefficiency affects the error term and has the following two components: 1. cost inefficiency effect 2. Statistical noise. The error components signify 2 totally diverse sources of random variation in cost intensities that cannot be described from output or input prices. The cost inefficiency effects, Ui, may be: Ui = ziδ + Wi (2) b) Report and discuss any management implications from the technical efficiency estimates obtained. Maximum 300 words. The stochastic Frontier offers some estimation and technical efficiency scores. However, this may lack the necessary policy implications if the studies fail to find out the source of inefficiency. The frontier program helps estimate the variation in inefficiency using maximum likelihood. In this model, the unexplained systematic cost differences arise from the inefficiency. Regardless, the residual cost differences may also entail output factors which were not captured accurately by the employed measures. The cost differences cannot be considered efficiency differences. This allows us to come up with two explanatory factors: 1. Environmental 2. Control Environmental variables help in the testing of the inefficiency sources. The control variable helps to find the inefficiency. The results in the tests show that the relationship between the electricity and the variables is highly correlated. This shows that not only does the average age of workers affect the power, but also the size of operations and the education of workers. The LR tests helped in the decision making process of the null hypothesis about Cobb Douglas function. A zero null hypothesis is rejected. The test to establish whether the inefficient effects are a function of explanatory variables rejects the null hypothesis. This confirms the joint effect of the variables towards the cost inefficiency. The Cobb Douglas cost function of have parameters which represent the cost elasticity’s. There was a high multicollinearity of the Cobb Douglas frontier. References Puig-Junoy Jaume, Ortun Vicente, “Cost Efficiency in Primary Care Contracting: A Stochastic Frontier Cost Function Approach,” University of Pompeu Fabra Sept 2013 Web. July 2002 http://www.econ.upf.edu/~puig/publicacions/paper6.pdf Read More