Open Journal of Statistics, 2013, 3, 173-178 doi:10.4236/ojs.2013.33019 Published Online June 2013 (http://www.scirp.org/journal/ojs) Application of Non-Linear Cobb-Douglas Production Function with Autocorrelation Problem to Selected Manufacturing Industries in Bangladesh Md. Moyazzem Hossain 1 , Tapati Basak 2 , Ajit Kumar Majumder 2 1 Department of Statistics, Islamic University, Kushtia, Bangladesh 2 Department of Statistics, Jahangirnagar University, Dhaka, Bangladesh Email: mmhrs.iustat@gmail.com, tapati555@yahoo.com, ajitm@ewubd.edu Received November 22, 2012; revised February 25, 2013; accepted March 4, 2013 Copyright © 2013 Md. Moyazzem Hossain et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ABSTRACT In developing counties, efficiency of economic development has been determined by the analysis of industrial produc- tion. An examination of the characteristic of industrial sector is an essential aspect of growth studies. The growth of a country can be measured by Gross Domestic Product (GDP). GDP is substantially affected by the industrial output. In- dustrial gross output is mainly a function of capital and labor input. If the effect of labor and capital input to output is at a satisfactory level in an industry or in a group of industries, then industrial investment will increase. As a result, the number of industries will increase, which will directly affect GDP and also will decrease the unemployment rate. This is why, industrial input-output relationship is so important for any industry as well as for the overall industrial sector of a country. To forecast the production of a firm is necessary to identify the appropriate model. MD. M. Hossain et al. [1] have shown that Cobb-Douglas production function with additive errors was more suitable for some selected manu- facturing industries in Bangladesh. The main purpose of this paper is to detect the autocorrelation problem of Cobb- Douglas production model with additive errors. The result shows that autocorrelation is presented in some manufactur- ing industries. Finally, this paper removes the autocorrelation problem and re-estimates the parameters of the Cobb- Douglas production function with additive errors. Keywords: Cobb-Douglas Production Function; Autocorrelation; Manufacturing Industry; Bangladesh 1. Introduction In the present times, production takes place by the com- bination forces of various factors of production such as land, labor, capital etc. In this connection, socialist coun- tries are using different patterns of level of factors of pro- duction for their respective industrialization policy ac- cording to the taste, demand and nature of their country- wide population, its size, location and environment. Bang- ladesh is a developing country. It is essential for Bang- ladesh to go for mass industrialization to strengthen the economy of Bangladesh for this purpose; of course our policy for industrialization must be well planned, well defined and well thoughtful. The development of eco- nomy is dependent on the industrial polices of the coun- try. By using production function we can get industrial policies especially indication about the nature of the pro- duction inputs used in the production function. The growth of a country can be measured by Gross Domestic Product (GDP). GDP is substantially affected by the industrial output. Industrial gross output is a function of capital and labor input mainly. If the effect of labor and capital input to output is at a satisfactory level in an industry or in a group of industries, then industrial investment will increase. As a result, the number of industries will increase, which will directly affect GDP and also will decrease the unemployment rate. This is why, industrial input-output relationship is so important for any industry as well as for the overall industrial sector of a country. Hoque [2], Bhatti [3], Baltagi [4], Bhatti and Owen [5], Bhatti [6], Bhatti et al. [7], Ingene and Lusch [8], Mok [9], Hossain et al. [10], Hajkova and Hurnik [11], Pra- jneshu [12], Antony [13], Hossain et al. [14], amongst others who have used linear regression models to mea- sure the log-linear Cobb-Douglas (C-D) type production processes. Hoque [2] used the survey data for Bang- ladesh to examine the relationship between farm size and Copyright © 2013 SciRes. OJS