Coub Douglas function of Pakistani economics

7/23/2019 Coub Douglas function of Pakistani economics

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Seminar in Economic Policy Ahmed Faizan Kashmiri (Std 14447) 0333-3820172

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Can we Interpret Pakistan`seconomic Insights by a coub

douglas production Function?

Abstract

Can aggregate production model of economy like Pakistan is justifiable with the help of a coub-

douglas model. Whether we can compute the insight on relationships that existed between the

inputs and outputs, simply by drawing functions of production in this arrangement, we have

used data from inputs and outputs and applied regression models to test the framework in an

economic simulation. Conclusive relationship was observed, justifying that economic variationsin outputs of Pakistani economics can be explained and estimated by a coub Douglas function

with reliable effectiveness.

Introduction

Computing a function to justify the relationship between factors of productions was primarily a

micro level phenomenon, it provided basis for justification of answering the most difficult

questions ever raised by any economist.

As the economic school of thought gained evolution this principle was started to answer the

Macro level productions outputs related anomalies, however the models were always criticized

and skeptics emerged with a question that whether the function of specific model represent

true economic relationship or not.

One of such model was Coub-Douglas Model of production which described the aggregate

production in a function and can be used to justify the economic phenomena on a macro level

but still the questions evolves that whether it fits the variable of the country level economic


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scales. Its applicability to asses depends from country to country depending upon the strength

of data availability. We therefore decided to test the model on Pakistan economic indicator in

order to find whether our production related researches can or cannot be done using subject

model.

Literature Review

Cob Douglas function (Charles W Cobb, Paul H Douglas, 1928) discovered relationships between

Labor, capital and product. It is one of the frequently used functions for computing aggregates

of outputs/productions. It represents real relationship among variables of productions (capital,

tech-change & wages) as wage impact turns constant most of the time (Franklin M. Fisher, Oct

1970).(Herbert A Simon & Ferdinand K Levy, 1970) also affirmed strong pragmatic evidences of

the economic relationship after simulating diverse applications of this function with aggregate

production in their critically analytical research work.

The effectiveness and reliability of the function was further confirmed by working papers of the

central bureau of statistics of Norway, where they analyzed Noted Elasticities of Variables in

different Industrial Sectors to alter the Output at optimum level (Vidar Ringstad, 1967).

Although there were few researchers who argued the idea of using Cob-Douglas function as

appropriate aggregate production function ,one of such example is (Pol Antr`as,2004) it argued

that a Cobb-Douglas specification of the U.S. aggregate production function may be misleading.

Controlling for biased technological change, the elasticity of substitution between capital


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and labor is likely to be considerably below one, and may even be lower than

0.5. This contrasts with the results of Berndt (1976).

It is notable that relationship discovered and explained during different subsets for growth

projections and Production outputs model based on Coub Douglas, CES function and Knowles

assumptions (Richard R Nelson, 1964).

(Robert Sollow, 1957) concluded that Technical change during that period was neutral on average.

Gross output per man hour doubled over the interval, the aggregate production function, corrected for

technical change, gives a distinct impression of diminishing returns, but the curvature is not violent.

Studies (Joan Robinson, 1954) further discovered that, The rate of production on capital will

tend to be higher, and real wages lower if: the more plentiful are the technical opportunities

for mechanizing production; the slower is the rate of capital accumulation in relation to the

growth of population; the weaker is the force of competition and the weaker is the bargaining

power of the workers, when competition is weak.

GDP is used as development indicator which is very similar to aggregate production in a coub

Douglass arrangement, Real GDP tends to underestimate the increase in real domestic income

and welfare when the terms of trade improve. An improvement in the terms of trade is similar

to a technological progress, but when computing real GDP, the national accounts treat the

former as a price phenomenon and the latter as a real event.(Ulrich Kohli,2004)


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In most of studies it was found that cob Douglas expression can be used effectively to judge the

relationship of the variables of production in relation to the aggregate level of production. A

model based on such assumption can affirm an economic relationship and its significance.

Hypothesis

With evidences from the primitive researches we concluded the following hypothesis to test

H1: A coub Douglas function can explain all the relationship between economic variable in

economics of Pakistan and justify aggregate production.

H:A coub Douglas function cannot explain all the relationship between economic variable in

economics of Pakistan and justify aggregate production.

Model

The crux of this research paper is to simulate the aggregate production function on economic

level with relational to inputs provision made through economic indicators data made available

by the government of Pakistan and World Bank.

Assumptions are made on the modified form of mathematical function of cob Douglas

(production function),

Y F(K,E L)

Where:

Eis competence of labor, in use as an indicator of the level of technology

(manufacturing practice and scientific awareness etc)

Y -- The level of output (GDP). L -- The economy's labor supply (No of workers)


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K -- The economy's capital stock (Gross Capital formation).

The core purpose of the research is to gain insight of a real relationship between dependent

variables (wage, capital and technological advancements) and their impacts in relation to the

relevant GDP of the period.

The Assumption is made simple if the GDP is the total production of any country it can be

termed as output = Y that resembles the total output as suggested by Coub and Douglas in their

production function.

Keeping the aggregate technology as constant (Limitation due to UN 2008 reporting model of

adopted by Govt of Pakistan for macroeconomic reporting) we can test the relational

significance of labor and capital pass into economy. The actual gross domestic product however

can serve as a benchmark for comparative analytical rationale if the relationship further tested

for CES techniques.

Data

Time Series data is selected from 19902010

from Pakistan economic indicators.

Due to Limitation in availability of data the

data set is constrained to 21 years.


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Methodology

Periodic/historic data can be analyzed to test the significance of independent variables over the

dependent variables by using Statiscal techniques i.e. regression analysis (Least Square

Method), Granger causality test for checking overall auto correlations existences (if any).

Analysis & Findings

A regression analysis using least square was conducted. Ordinary least squares are a

statistical technique that uses model data to approximate the true population

association between two variables. It constructs a line that minimizes the computation

of the squared plumb distances from the line to the pragmatic data points. The findings

were:


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Regression analysis are not free from the problem of auto correlation where by the

error terms of the variables often get interrelated and the results may seems vague if it

exists. Granger causality test was performed in order to check if the problem exists the

findings were :

Interpretation of Results

i.

Hypothesis is supported by evidence. The relationship between data is real and reliable.

ii. P values for the variables tested in less than .1 that is conventionally treated as

significant. It tells how likely it is that the coefficient for that independent variable

emerged by chance.

iii. t stat compares the error suggested by the null hypothesis to the standard error of the

estimate here in our case the T stats value are greater than 1.96 having probability

under or equal 0.05 suggests that the independent variables are significant predictors of

dependent variables.


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iv. R square resulted 0.99 while adjusted R Square is 0.98 implies that 98% of variation in

responses can be explained by variables .it proves the model as whole have highly

reliable relationship.

v. Overall significance of the model is judged by F Stats value and Prob F indicators; F stats

show a high value of 922 and Prob F results 0.000 indicates there is no chance for all of

regressive parameters can be zero.

vi. No autocorrelation existed among variables of the model.

Conclusions

The imminent of economic relationships in economy of Pakistan can be computed with

accuracy by a coub douglas function styled function; one can practically estimates the trends of

possible output with ratios and build optimum production analysis by the this model of

production function. The study represented that the aggregate production of economic inputs

in Pakistan represented in real relationship by such functional form.

So the answer to the Title is YES it can .


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References

A Note on the cob-Douglas Function ,Herbert A Simon & Ferdinand K Levy, The Review of

Economic Study Vol 30 ,No 2 (1963)

AGGREGATE PRODUCTION FUNCTIONS AND THE EXPLANATION

OF WAGES: A SIMULATION EXPERIMENT, by Franklin M. Fisher No. 61 October, 1970 Source:

LIBRARY OF THEMASSACHUSETTS INSTITUTE OF TECHNOLOGY

ECONOMIES OF SCALE AND THE FORM OF THE PRODUCTION FUNCTION

Progress Report No 6, prepared by Vidar Ringsted, Source: Scholars.Google.com,WORKING

PAPERS FROM THE CENTRAL BUREAU OF STATISTICS OF NORWAY Oslo, 7 June 1967

Is the U.S. Aggregate Production Function Cobb-Douglas? New Estimates of the Elasticity of

Substitution by Pol Antr`as, Contributions to Macroeconomics 4(1): article 4. Harvard

University ,April 2004 Source: http://nrs.harvard.edu/urn-3:HUL.InstRepos:3196325

A Cross-Country Empirical Investigation of the Aggregate Production Function Specification

by JOHN DUFFY Department of Economics, University of Pittsburgh

& CHRIS PAPAGEORGIOU Department of Economics, Louisiana State University

published : Journal of Economic Growth, 5: 87120 (March 2000) Kluwer Academic Publishers.

Printed in the Netherlands JEL classification: O40, O47 Source: Scholars.Google.com

Aggregate production function & Medium range growth projections By Richard R Nelson ,

American Economic Review Vol 54,No 5 (Sep 1964 )


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The Production Function and the Theory of Capital By Joan Robinson The Review of Economic

Study Vol 21 ,No 2 (1953-54)PP 81-106

Real GDP, real domestic income, and terms-of-trade changes by :Ulrich Kohli Journal of

International Economics 62 (2004) 83106 ,JEL classification: O11; O41; C43; F11

World Bank Economic indicator database & Labor Survey of Pakistan (Govt of Pakistan ,Various

years)

Technical Change and the Aggregate Production Function

Author(s): Robert M. Solow Source: The Review of Economics and Statistics, Vol. 39, No. 3 (Aug.,

1957), pp. 312-320

A theory of production BY Charles W Cobb,Paul H Douglas Mar 1928,The American Economic

Review Vol 18 Issue 1 Source : Jstor.org

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Coub Douglas function of Pakistani economics