Measurement of Labour Productivity Through Stochastic Process: A Study in Organised Manufacturing Sector of Odisha, India

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1 Autralian Journal of Baic and Applied Science, 6(9): , 22 ISSN Meaurement of Labour Productivity Through Stochatic Proce: A Study in Organied Manufacturing Sector of Odiha, India Satya Ranjan Nayak, 2 M.K. Hota, 3 Dr. Sudhakar Patra and 4 Mr. Madhumita Samal Faculty of Economic and Buine Adminitration, Gandhi Intitute for Technological Advancement, Bhubanewar, At: Badaraghunathpur, Po: Madanpur, Dit: Khordha, Odiha., India, Pin: Aociate Profeor of Mathematic, Gandhi Intitute for Technological Advancement, Bhubanewar, Odiha.India. 3 Profeor of Economic, Ravenhaw Univerity, Cuttack, Odiha, India 4 At. Profeor. Of Economic, Gandhi Intitute for Technological Advancement, Bhubanewar, Odiha., India, Pin: Abtract: Labour productivity i not of contant magnitude, but it evolve with time. The proce grow in the beginning of economical work unit but it reache at it limit with repect to time. Any economical unit provide growth of labour productivity and in future, it may be replaced by more perfect economical unit to enhance the growth of labour productivity. The main component of the labour productivity i the improvement of the efficiency parameter that i engineering and technology. The growth of economy of a country or efficiency of production ytem generally depend on it level of education, cience, technology and trategic management.thi paper preent a new analytical approach with the help of Stochatic proce for calculating labour productivity uing the data of Economy urvey of Odiha, 2-, publihed by the State Govt. of Odiha, India. The role of educated worker to accept the technological change which lead to improvement of total factor productivity (TFP) i alo conidered in thi paper with the help of advanced calculu. Key word: labour productivity, educated worker, total factor productivity (TFP), tochatic procee and Markov chain. INTRODUCTION It i well known that economic growth, a a mean to enhancing the welfare of people, depend on the ue of both the factor of production uch a capital and labour with the efficiency in reource ue. It i often referred to a productivity. Recent development indicate the growing importance of productivity, particularly for the Indian economy at it preent tage of development. The involvement of technological progre to modern economic growth and riing per capita income in the highly developed countrie i widely acclaimed and acknowledged. Long-run economic growth i utained through continuou rie in productivity and required fundamental non-reverible tructural change. The production tructure ha grown mature and technologically ophiticated acro and within ector. The growth of economy of a country or efficiency of production ytem generally depend on it level of education, cience, technology and trategic management. A well educated, killed and developed work force mut be required for the growth of a country production level which alo include production facilitie. Education at all level contribute to economic growth through imparting general attitude, dicipline and pecific kill neceary for a variety of workplace. It alo contribute to economic growth by improving health, reducing fertility and poibly by contributing to political tability. The major importance of the educational ytem to any labour market would depend majorly in it ability to produce a literate, diciplined, flexible labour force via high quality education. Conequently, with economic development new technology i applied to production, which reult in an increae in the demand for worker with kill and better education. The manufacturing ector of Odiha which contitute 62 percent of it total indutrial ector, play a greater role in generating employment and upporting the large cale indutrie a well a mall and medium cale indutrie (SMI S ).The majority of the manufacturing enterprie from mall cale to medium cale grouped together are called Micro, mall and medium enterprie (MSME ). It i encouraging to note that the number of mall cale indutrie (SSI) and MSME unit et up during a year ha been increaing over the year but their contribution to value- added and value of fixed aet are far le than that of large cale indutrie. The main caue behind thi may be a low level of labour productivity and poor input quality. So thi paper trie to tudy the impact of technological progre and change in the indutrial tructure on the productivity growth of Correponding Author: Satya Ranjan Nayak, Faculty of Economic and Buine Adminitration, Gandhi Intitute for Technological Advancement, Bhubanewar, At: Badaraghunathpur, Po: Madanpur, Dit: Khordha, Odiha., India, Pin: atyaranjan.nayak76@gmail.com 53

2 Aut. J. Baic & Appl. Sci., 6(9): , 22 the manufacturing ector of the tate of Odiha, India and alo predict the future trend of Total factor productivity. Review of Literature: Dr. Shri Prakah and Ritu Sharma(2) 4 in a tudy of Impact of Technology on Production in Indian Economy evaluated the impact of change in technology on output with relation to economic factor which influence final demand. They evaluated the growth/output effect of technological change by the change in input coefficient matrix, an in Input-Output Model. The model i ued for examining growth effect with the change in technology a reflected by change in matrix, A. The model i: X t = (I-A t ) - * f t Where X t = Gro output vector; A t = Technology matrix; f t = Final demand vector; t= Time, (I-A) - = Leontief invere, and A i the technology matrix. Finally they had found that output grow with the change in technology. Manoj Kumar Dah, Gaurav Kabra and Ajay Singh (2) 3 in a tudy on Productivity Growth of Manufacturing Sector in India an Inter-State Analyi etimated the total factor productivity growth of the manufacturing indutrie of different tate of India uing the Tranlog production function. They examined the extent of employment concentration in Oria manufacturing indutrie relative to all India to know the tructure and growth of regitered manufacturing factory ector. They ued total factor productivity a the meaure of productivity which i defined a the difference between the rate of growth of output and rate of growth of combined input i.e. labour (L),Capital (K) and time (T) repreenting technical progre. Maiti and Mitra (2) 8 have conidered education, pecifically, enrolment ratio in engineering and management tudie, a a proxy for available kill formation. They argue that with higher level of education, the quality of labour and thereby their employability in the formal ector of the economy would be enhanced which meaure the kill content of the work force. Idri Jajri and Rahmah Imail (29) 7 in a tudy of Technical Progre and Labour Productivity in Small and Medium Scale Indutry in Malayia oberved that technical progre i a complement with more killed labour but a ubtitute with le killed labour. They examined the effect of technical progre on labour productivity uing a Human capital method developed by Cörver (994) which i baed on the Cobb-Dougla production function. Finally they viewed that technical progre will have a poitive effect on labour productivity. Sabuj Kumar Mandal and S. Madhewaran(29) 9 in a working paper (26) of Intitute for Social and Economic Change (ISEC) titled Technological progre, cale effect and total factor productivity growth in Indian cement indutry: Panel etimation of tochatic production frontier tudied on Total Factor Productivity (TFP) growth in Indian cement indutry during the period to 26-7 uing company level data and applying Stochatic Frontier Approach. TFP growth i decompoed into technical progre (TP), technical efficiency change (TEC) and change in cale component (SC) with a view to gaining ome inight into the ource of productivity growth of thi indutry in the pot reform era. The finding how that TFP growth i mainly driven by SC and TP and not by TEC, ince TEC i time invariant in nature. Nichola F. R. Craft(23) 2 in a tudy of Quantifying the Contribution of Technological Change to Economic Growth in Different Era: A Review of the Evidence found firt that the etimate of TFP growth that reult from tandard growth accounting i not necearily a good indicator of the contribution made by technological change to economic growth. The dicrepancy can go either way and ha varied coniderably both over time and alo acro countrie. Second, even the mot powerful new technologie have modet impact on productivity growth in their early tage. Thi i eaily undertood in the context of growth accounting which make explicit the weight to be attached to new type of capital and production. He critically reviewed Solow method and Cobb-Dougla production function in thi regard. Humphrey (997) 6 give an outline of hitorical development of the concept and mathematical formulation of production function before the enunciation of Cobb-Dougla function in 928. Paul Dougla, on a abbatical at Amhert, aked mathematic profeor Charle W. Cobb to ugget an equation decribing the relationhip among the time erie on manufacturing output, labor input, and capital input that Dougla had aembled for the period , and thi led to their joint paper. Productivity Growth and Technological Change: Productivity i a relationhip between production and the mean of production or more formally a relation of proportionality between the output of a good or ervice and input which are ued to generate that output. Thi relationhip i articulated through the given technology of production. 53

3 Aut. J. Baic & Appl. Sci., 6(9): , 22 Productivity growth i crucially affected by technological change. Their relationhip i o cloe that the two term are often ued interchangeably. Productivity i a wider concept, even though a crucial one technological change i only one of the many factor which affect productivity growth. Other are being ocial, cultural, educational, organiational and managerial factor. Better management of worker and machine and appropriate incentive tructure can increae production and/or reduce cot. But thee are different from technological change. It i not eay or traight forward to dientangle the effect of technological change from ocial and cultural factor. Mathematical Formulation of Model Specification: There are a good number of procedure exit to meaure the total factor productivity (TFP) in indutrie (may be mall cale or large cale). Generally, TFP a a meaure of productivity i defined a the difference between the rate of growth of output and the rate of growth of combined input i.e. Mathematically:, P i Total factor productivity, V(t) i output and f(k,l) i the aggregate function of two input i.e. Capital(K),Labour(L) and time (t) which i repreenting the evolution of technical progre. Thu, () Keeping Capital ( K ) a contant, for ; which atifie the idea of Law of variable proportion. The Law tate that; keeping ome input factor fixed and any change in other variable input lead to change in output for a certain limit. A good number of tudie are made on productivity growth in both developed and developing countrie with the help of number of exiting production function like Cobb-Dougla production function, CES production function, VES production function, Tranlong production function etc. But in thi paper an attempt ha been made to meaure labour productivity with the help of tochatic proce and Markov chain. Then, the developed idea ha been verified numerically with the help of the data ource and a uitable example i alo cited in it. To formulate the idea, we have taken here the help of Johann Von Thünen exponential production function and derived the function a (2) K=Capital, L * = effective labour, A= Efficiency parameter and T= Technology a i are the parameter aociated with repective factor having their meaning at i =, 2, 3. It i pertinent to note that an effective labour can be defined a employment in three categorie of work: management and profeional, technical and upervior, and finally, direct production group. Thu the effective labour likelihood function can be defined a: * L = Lll. 23 l L Quantity of labour, l Number of worker in management and profeional group, l2 Number of worker in technical and uperviion group and l Number of worker in production group (mainly the phyical worker) 3 The total number of worker in production group i.e. type which conit of both educated and noneducated worker. Before defining educated worker, it i neceary to know the importance of educated 532

4 Aut. J. Baic & Appl. Sci., 6(9): , 22 worker in indutrie. To upport any technical change for the growth of manufacturing ector Odiha, only educated worker will be effective enough to adopt the change. The employment of above defined educated worker will reduce the depreciation amount of fixed capital a well a the plant and machinery of the production unit. It i alo oberved from the tudy that the educated worker are cautiou and able enough to ue and handle the machinerie, o that the depreciation amount occurring through wrong operation and miue of machine will be certainly low. Definition: Educated worker can be defined a the worker with no technical education (indutrial or vocational training, diploma or degree engineering) but with formal chool education (matriculation/ th tandard) o that they are more able to adapt the technological change and can ue new production technique more proactively. On the bai of the above, we have claified the above tated type of worker a: l = l + l 3 3m 3n l 3m = phyical worker without any chool education l 3n = worker with formal chool education (educated labour category a tated above) The reulting production function will be:. = and. Thu; = A A Which uffice the above claification theoretically ignifie that the total production increae with repect to the claification and reduction of the parameter. Etimation Reult: The obervation of the tudy reveal that from 2 to 2 in the manufacturing ector of Odiha, the growth of total factor productivity (TFG) i minimum and fluctuating with the average of.378 and it i only due to le expoure to technical progre (Table- ). Table : No. of Regitered indutrie, value of output, value of input and Net value added. Depreciation. PERIOD VALUE OF VALUE OF DEPRECIATION NET VALUE TFP( O/I) INPUT(RS) OUTPUT(RS) (RS, CRORE) ADDED (RS/CRORE) Source: Economic Survey of Odiha, India,

5 Aut. J. Baic & Appl. Sci., 6(9): , 22 After urveying more than mall and medium cale indutrie a a ample, it i recorded that near about 4% to 5% worker are working in thee indutrie without having formal chool education. Though it i dicued that educated worker can allocate the input optimally and efficiently, o a a reult it will increae the output.a the educated worker are killed enough to handle the machinerie carefully o the depreciation occurring due to accident, wrong ue and mihandling will be reduced. So a precribed model Table -2 i prepared with the help of correlation and regreion analyi to verify our dicuion with reference to the Table -. Table 2: (Numerical verification). PERIOD VALUE OF INPUT(RS) VALUE OF OUTPUT(RS) TFP( O/I) Source: Author calculation *The above reult for the new output i obtained by the regreion analyi, taking output a dependent variable[y] and input a independent variable [X]. The regreion line equation i Y= X It i alo oberved that the output level i increaing a well a the average value of TFP i increaed from.378 to.542. Meauring Total Factor Productivity Through Stochatic Proce: Since in an indutry (mall or large cale); the total production for future year depend upon the preent financial year but not on the pat, thu the production procee follow the Markovian property and the proce i a Markov chain. The analytical tudie to increae the labour productivity of mall cale indutrie a dicued in the preceding ection, i verified by the tochatic proce in thi ection. The model i formulated and mathematically jutified with uitable example with numerical data taken from the data ource. Formulation: A an S valued tochatic proce i a probability pace ( Ω,, P) together with random variable: Xt : Ω S, for t = {,,2,... } ; Ω Sample pace, ΡΩ ( ) power et of Ω, P Tranition probability, and S State pace; the problem of labour productivity i formulated a follow. By replacing the phyical labour with le number of educated labour ( l3n < l3) if the production i increaing in preent year, then the probability that it will increae in next year be p and if the production i decreaing in preent year, then the probability that it will be increaed in next year be q. Referring to the above tated model, the tate-pace i conit of only two tate and a defined below: : if the production i increaing in preent year, then will increae in next year, : if the production i decreaing in preent year, then will increae in next year. A a reult, ince the tate tranition probabilitie: 534

6 Aut. J. Baic & Appl. Sci., 6(9): , 22 { +,,...,, } { t+ j t i} ;,,. p = p X = X = X = X = X = ij t j t v t i = p X = X = i j = only depend on the preent tate but not on the pat tate. Thu, the collection: X t : t =,,2,3,... ; { } i a Markov chain and the correponding tate tranition matrix i: P = State p p q q. (State-Tranition Diagram) To oberve the labour productivity for a long period of year, we have extended our tudie to the long-run propertie of Markov chain in thi model by taking the help of Chapman-Kolmogorov 5 equation: ( n) ( m) ( n m) pij = pik pkj ; i, j =, and m < k = which ignifie the labour productivity for Applying the algebraic method, the recurrence relation: P ( n) = P. P = P n ( n ) = P. P = P n ( n ). P n n n, ubequent year. tep tranition matrix Moreover, ince the formulated Markov chain i irreducible; thu ( ) lim p n exit and converge to a pecific value π (ay). n ij n j p i the n (n) ij tep tranition probabilitie (n) P can be computed by the following That i, for large (year after year) the total production will attain a contant value (Steady-tate) one tage of law of variable proportion. However, when the production attain the teady-tate; to oberve the production proce for future trend, we have determined the expected firt paage time f and which can be computed from the teady-tate production probabilitie f jj = ; j =,. π j π j a: Numerical Verification: To verify numerically, we have conidered the ource date given in Table- and the author calculation given in Table-2. Since in Table-2 with the bae year a 24-5, the calculated probabilitie are p =.5 and q =.4 ; thu the one tep tate-tranition matrix obtain a: P = State and therefore ubequently by applying the Chapman-Kolmogorov equation, the proce attain the teady tate after ix year i.e. the total production will be contant which i a jutification of law of variable of proportion. The 6-tep tranition matrix i given a: jj 535

7 Aut. J. Baic & Appl. Sci., 6(9): , 22 P (6) = State Since here the tate are communicative and recurrent; repreenting the production for future year, thu the production will be increaed in a periodical form if the proce attain teady tate after ome year of production which ha been viewed by computing the firt paage time f jj. Here and f f = 2.25 =.799 year year which ignifie that after attaining the teady-tate, in an interval of will be increaed year ; the total production Concluion: Thi tudy mainly focue on improvement of labour productivity in manufacturing ector of Odiha which comprie of maximum number of medium and mall cale indutrie. To improve the labour productivity, it i indeed neceary to accept and make ue of advanced technology. But due to lack of educated worker, the total factor productivity grow at a lower pace which ultimately hamper the profit level of indutrie. For overall improvement of the indutrie of Odiha, it i concluded that at leat the formal chool education, vocational education, engineering education mut be given top mot priority by the government o that it lead to the acceptance and aborption of the technological change to compete in the global market. The paper develop analytical equation for calculating the labour productivity rate, which include the equation of productivity rate of technology which i only poible through educated worker. Conequently, manufacturing ector of Odiha need killed and educated worker to become an important ource of growth and development of the economy. REFERENCES Corver, F., 996. The Impact of Human Capital on Labour Productivity in the Manufacturing Sector of the European Union, Reearch Centre for Education and the Labour Market, ROARM-996/2E, Univerity of Limburg. Craft, Nichola F.R. Craft, 23. Quantifying the Contribution of Technological Change to Economic Growth in Different Era. Working Paper No. 79/3, Department of Economic Hitory, London School of Economic, pp: -3. Dah, Manoj Kumar, Kabra, Gaurav and Singh, Ajay, 2. Productivity Growth of Manufacturing Sector in India an Inter-State Analyi, European Journal of Scientific Reearch, 44(3): Dr. Shri Prakah and Sharma, Ritu, 2. Impact of Technology on Production in Indian Economy International Conference on Education, Reearch and Innovation IPEDR vol.8 ((2) IACSIT Pre, Singapore, pp: Hiller, Frederick S. and Lieberman, J. Gerald, Operation Reearch Tata Mc Graw Hill Education pvt. Ltd. New Delhi, Eighth Edition. Humphrey, T.M., 997. Algebraic Production Function and their Ue before Cobb-Dougla, Federal Reerve Bank of Richmond Economic Quarterly, 83(): Jajri Idri and Imail Rahmah, 29. Technical Progre and Labour Productivity in Small and Medium Scale Indutry in Malayia European Journal of Economic, Finance and Adminitrative Science, 5: Maiti, D., A. Mitra, 2. Skill, Informality, and Development, IEG working paper No.36. Mandal, Sabuj Kumar and Madhewaran, S., 29. Technological progre, cale effect and total factor productivity growth in Indian cement indutry: Panel etimation of tochatic production frontier working paper (26) of Intitute for Social and Economic Change (ISEC), Bangalore, pp: -2. Thünen, J.H. von, 93. Der iolierte Staat in Beziehung auf Landwirthchaft und National okonomie. 3 volume: Ficher, Jena, Germany. 536

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