COBB-DOUGLAS PRODUCTION FUNCTION.
Introduction
Some economists define very basic aim of econometrics as ‘to put empirical flesh and blood on a theoretical structure. ’ A more lengthy definition is that of Samuel at al, who describes econometrics as, ‘the application of mathematical statistics to economic data to lend empirical support to the model constructed by mathematical economists and to obtain numerical estimates.
The economists deduce or predict certain relationships between two or more economic data series. Obvious examples are the consumption function, demand curve and employment function. Econometrics concern with quantifying such relationship and finding values for the parameters contained in them, testing any theories implied such relationships and using relationships as a basis for quantitative prediction or forecast.
In this assignment I have choose Cobb-Douglas production function. The Author has proven that this theorem could be applied in a case of Bangladeshi economy. But here I am concern with testing this function in the content of Malaysia.
Problem Statement
There was an econometric model developed by two experts C.W Cobb and D.H Douglas in 1920’s. Since they are from the old school and had come with there idea.
They came with a function which is expressed mathematically as
P = ALαKβu,
Where it defined as P=out put, K= capital, L= labor and A as the constant. α and β , are positive parameters.
Taking log of both sides of equation, the function transforms to a log-linear form as:
lnP =lnA + α lnL+ β lnK+ lnu
since this model have been develop to check the production function of the developing country , I here tried to check whether it can be applied to Malaysian content.
Research Objectives
Even though my reference term paper is about the elasticity of labor and capital with respect to all the industry in the economy, here I tried to narrow down my research to find out the truth behind my chosen economic model. Here I m going to test this econometric model based on the out put which is supposed to be equal with the sum of labor force employed and the investment which is spend on the economy.
The C-D production function could be evaluated from different angles but here as to make it simple and work out it easily with my level I stick with the basic model it self rather then going for an evaluation from different angles.
This function is applied many researchers to find the output. It could be to find the labor output or agricultural output as well as industry output. But this research is to check the out put of the economy as a whole in the content of Malaysia.
Literature Review
1. Here is an article quoted from a journal where they are concerned with doing an income model. But we see that their approach of finding total out put produce in an economy in other word GDP is totally different. I believe that this is the direct approach where steps involved in it are more than the C-D production function.
The model simulated is relatively simple and represents an extension of the model presented by Smith. 1 In the strictest sense, simplicity is important to an aggregate analysis. Suits indicate that for purposes of exposition the smaller and less complex the model the better it will be. 2 The establishment of the model on a conceptual basis is of prime importance. An expansion of the model can always he pursued at some later time of policy which would enable them to maintain inventory at a constant level in either an expanding or contracting economy. GNP is then obtained by aggregating consumption, investment and the demand for inventory. Thus, the model which is demand oriented serves to illustrate the dynamics of the multiplier and the damping effects of the inventory feedback mechanism.
Given a desired level of inventory, some fixed investment and the GNP from the previous time period, values are calculated for the present consumption and the residual non consumed output investment (inventory).Thus, the composition of successive levels of GNP is determined through the system of equations, which compose the basic model. These equations are shown below.
i. Yt = Ct-i + It-I + Dt-i
2. C + cY +C
t t o
3. It + Ift + Int
4. Int + Yt - (Ct + I~)
5. K n = K n I n
t t-i + t
6. D = K d - K n
t t t
7. S = Y C
t t t
where
Y Gross National Product
t
C Consumption
t
I Actual Investment
t
D Actual Inventory Demanded
t
c Marginal Propensity to Consume
C Autonomous Consumption
o
if Fixed Investment
t
I n Added Investment as Inventory
t
K n Actual[ Ending Inventory
t
2- According to Marjan Senjur paper he has concentrated on the level of expenditure by the government or the government spending and its impact of the economy.
Here is had used the circular flow of income as his methodology and he explained what happens when government increase it’s spending to the GDP given that other factors remains constant. His findings conclude that
Grossman (1990) established a slightly negative effect on economic growth, with great fluctuations between countries. Diamond (1990) could not find any empirical relation between the size of public expenditures and the rate of economic growth. This is also our finding. Out of these findings, with different results; we can state that it is not possible to give a reliable statement about the relation between public expenditures and economic growth. A possible explanation for this is that the problem was not formulated correctly. As Barro (1990) has already stated, such results show that, in general, countries choose the right public expenditure rate.
On average the actual PE rate is growth neutral, and, therefore, empirical results of regression of rates of growth and share of public expenditures, or of rates of growth of public expenditures, do not show correlation.
3-Accoring to Economic Issues, Vol.7, and Part 1, March 2002 paper a re-examination of the original time-series data sets used by Professor Douglas and associated researchers to establish the existence of an aggregate production function is undertaken. Particular attention is paid to the issue of whether the data provide deductive support for the ‘Laws of Production’ as claimed by Douglas (1948). Various statistical methods are used to analyze the data to see if the claims of Douglas are justified. Only the New South Wales data and to a lesser extent the New Zealand data yield results that support the assertions of Douglas - hence the Antipodean defense
In the same paper they author had quoted that the fact that on the basis of fairly wide studies there is an appreciable degree of uniformity, and that the sum of the exponents approximates unity, fairly clearly suggests that there are laws of production which can be approximated by inductive studies and that we are at least approaching them. (pp. 20-1).
This gives us the hint that sometimes C_D production function could not be applied to some industry. Only from one geographic area they are able to come with the right fit.
4-This apparent empirical strength of aggregate production functions is often interpreted as support for neoclassical theory. But there is neither theoretical nor empirical basis, for this conclusion. We already know that such functions cannot be derived theoretically, except under conditions which neoclassical theory itself rejects (e.g. the simple labor theory of value) (Garegnani, 1970). Moreover, Fisher (1971) discovered through simulation studies that the aggregate data generated by microeconomic production functions were not generally well fitted by aggregate production functions; there the functions which did best fit this data are not neoclassical in nature (this is a common finding, e.g. Walters, 1963); and that in simulation runs where the wage share happened to be roughly constant and aggregate Cobb-Douglas production functions happened to work well, this goodness of fit was puzzling because it held even when the theoretical conditions for aggregate production functions were flagrantly violated.
These guys actually support the Cobb-Douglas theory since they have faced it difficult to analyze regression using some other production function given by famous authors.
5- Dr.Khalid did a research on Cobb-Douglas production function and his conclusion and recommendations are
i. Although Cobb-Douglas production function shows physical output as the Douglas labor and capital inputs, this article prove that monetary Model is good alternative to Real Model (Physical Model) at least in Egyptian tourism sector.
ii. Cobb-Douglas production function in Monetary Model may be good formula in services sectors.
iii. Cobb-Douglas production function with intercept has good results than Cobb-Douglas production function without intercept.
iv. The Egyptian tourism sector is more sensitive for regional and national security, but it is disappear in Cobb-Douglas production function
Over all I conclude that Cobb-Douglas production function had been tested by my individual and researches and it is proven to be attractive and widely used in the economies. On the other hand this is not the case for some researchers since there is more then two factors (labor and Capital) when finding the out put. As said above in Egyptian case tourism is heavily depends on the level of internal securities provided since Middle East in not safe from the operating militias group like Al-Qaeda.
Construct your econometric model.
Since in this paper I have decided to test on the C-D production function, fist of all I have gathered data about the three components that is required to run this econometric model. Since the availability of data is limited this paper has only focused on the data collected during 1985-2005 from Malaysia.
P L K
1985 77470.000 5653.300 23124.000
1986 71594.000 5760.100 18865.000
1987 81085.000 5983.900 17904.000
1988 92370.000 6175.800 22726.000
1989 105233.000 6390.900 30599.000
1990 119081.000 6685.000 39348.000
1991 135124.000 6891.000 49126.000
1992 150682.000 7047.800 55191.000
1993 172194.000 7383.400 66937.000
1994 195461.000 7618.000 78664.000
1995 222473.000 7645.000 96967.000
1996 253732.000 8399.500 107825.000
1997 281795.000 8569.200 121494.000
1998 283243.000 8602.750 75982.000
1999 300764.000 8830.500 65841.000
2000 343215.000 9291.250 87729.000
2001 334404.000 9357.000 83345.000
2002 362012.000 9543.000 83764.000
2003 395017.000 9870.000 87089.000
2004 450152.000 9987.000 91818.000
2005 495239.000 10064.800 98930.000
From the above date P is the Gross Domestic Product (GDP) which is taken from t he statistic provided by the Malaysian government. And the L refers to the Employment where counts number of people who are employed and working is. It does not count on the number of people who are in the working age group but not working or unable to find a job.
When I was looking for a K which is believed to be the level of investment in the economy I have come across couple of figures. But I have chosen the Gross Fixed Capital Formation as K since this is the most accurate data available.
The Gross Fixed Capital Formation is a flow value. It is usually defined as the total value of additions to fixed assets by resident producer enterprises, less disposals of fixed assets during the quarter or year, plus additions to the value of non-produced assets (such as discoveries of mineral deposits, or land improvements).
Normally these assets are tangible assets, but in some cases they are intangible intellectual property including artwork and software. The debate continues about the exact definitional boundaries. The main asset types are plant & machinery, equipment, vehicles, land improvements and buildings.
Then in order to make the calculation easier what I did was to log on each figure. For example (in excel =log (77470).). Here is the logged table for P, L and K.
P L K
1985 4.889134 3.752302 4.364063
1986 4.854877 3.76043 4.275657
1987 4.908941 3.776984 4.25295
1988 4.965531 3.790693 4.356523
1989 5.022152 3.805562 4.485707
1990 5.075842 3.825101 4.594923
1991 5.130732 3.838282 4.691311
1992 5.178061 3.848054 4.741868
1993 5.236018 3.868256 4.825666
1994 5.29106 3.881841 4.895776
1995 5.347277 3.883377 4.986624
1996 5.404375 3.924253 5.032719
1997 5.449933 3.93294 5.084555
1998 5.452159 3.934637 4.880711
1999 5.478226 3.945985 4.818496
2000 5.535566 3.968074 4.943143
2001 5.524271 3.971137 4.92088
2002 5.558723 3.979685 4.923057
2003 5.596616 3.994317 4.939963
2004 5.653359 3.999435 4.962928
2005 5.694815 4.002805 4.995328
From those data then I ran the OLS regression equation with eviews software and the findings are here.
Dependent Variable: P=GDP
Method: Least Squares
Date: 09/12/07 Time: 17:49
Sample: 1985 2005
Included observations: 21
Variable Coefficient Std. Error t-Statistic Prob.
L=labor 2.83572 0.121723 23.29645 0
K=NFCF 0.129905 0.038305 3.391331 0.0033
A=Integer -6.35108 0.324183 -19.591 0
R-squared 0.994283 Mean dependent var 5.297508
Adjusted R-squared 0.993648 S.D. dependent var 0.26821
S.E. of regression 0.021376 Akaike info criterion -4.72156
Sum squared resid 0.008225 Schwarz criterion -4.57234
Log likelihood 52.57633 F-statistic 1565.366
Durbin-Watson stat 1.532652 Prob(F-statistic) 0
Therefore our function is In P = -6.35108 + 2.83572 In L + 0.129905 In K
Interpretation of the table:
Integer:
When all independent variable is 0 the dependent variable is -6.35108. However there is no economic meaning.
Labor or Employment:
Other independent variable remains constant if 1% increases in Labor force or employment will lead to a 2.83% increase in the P or Gross Domestic Output.
Capital or Gross Fixed Capital formation:
If other independent factors remain constant 1% increase in the K or capital will lead to a 0.13% increase in the GDP.
R-squared:
The two regressors L-Labor and K-GFCF explain 0.994283 or 99.4283 percent of the variation in the P-GDP. The estimated regression line fits the data quite well. The R2 value of 0.994283 means that about 99% percent of the
Variation in the (log of) output or GDP is explained by the (logs of) L-labor and K-capital.
Durbin-Watson statistic
The Durbin-Watson statistic is a test statistic used to detect the presence of autocorrelation in the residuals from a regression analysis. The value of Durbin-Watson statistic should be reasonable from 0 to 4. A value of 2 indicates there appears to be no autocorrelation. Small values of d indicate successive error terms are, on average, close in value to one another, or positively correlated. Large values of d indicate successive error terms are, on average, much different in value to one another, or negatively correlated. It means that 1.532652 value is smaller than 4. Therefore the value of Durbin-Watson statistic is can be explained by the 2 independent variables.
Year Actual Fitted Residual Residual Plot
1985 4.88913 4.85631 0.03282 | . | . * |
1986 4.85488 4.86788 -0.013 | . * | . |
1987 4.90894 4.91187 -0.00293 | . *| . |
1988 4.96553 4.9642 0.00133 | . * . |
1989 5.02215 5.02314 -0.00099 | . * . |
1990 5.07584 5.09274 -0.0169 | . * | . |
1991 5.13073 5.14264 -0.01191 | . * | . |
1992 5.17806 5.17691 0.00115 | . * . |
1993 5.23602 5.24509 -0.00907 | . * | . |
1994 5.29106 5.29272 -0.00166 | . * . |
1995 5.34728 5.30888 0.0384 | . | . * |
1996 5.40438 5.43078 -0.0264 | *. | . |
1997 5.44993 5.46215 -0.01221 | . * | . |
1998 5.45216 5.44048 0.01168 | . | * . |
1999 5.47823 5.46458 0.01365 | . | * . |
2000 5.53557 5.54341 -0.00784 | . * | . |
2001 5.52427 5.5492 -0.02493 | * | . |
2002 5.55872 5.57372 -0.015 | . * | . |
2003 5.59662 5.61741 -0.02079 | .* | . |
2004 5.65336 5.63491 0.01845 | . | *. |
2005 5.69481 5.64867 0.04614 | . | . *|
References.
• The effects of Randomly Generated Disturbances and Fiscal Policy on an Aggregate Demand Macro economic model
University of Akron
Akron, Ohio 44325
P. d. Kuzdrall
University of Western Ontario
London, Ontario CANADA N6A 3
• Public expenditure rate and economic growth by Marjan Senjur-Faculty of Economics, University of Ljubljana, Slovenia
• The Cobb-Douglas Production Function: An Antipodean Defense? Iain Fraser1: Economic Issues, Vol.7, Part 1, March 2002- 39
• Hamburg production function by Anwar Shekh
• An Estimation of Cobb-Douglas production function in Egyptian Tourism Sector by Dr Khalid from Zagazig university
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