Production Function of Companies - The Case of Macedonia and Albania

Transcription

1 Vol. 5, No. 3, 2015, Production Function of Companies - The Case of Macedonia and Albania Besa Xhaferi 1 Abstract The purpose of this study is to empirically analyze production function and productivity for companies in Albania and Macedonia. The main contribution to knowledge derived is the evidence for describing productivity. The main hypothesis of the study is: companies in respective countries possibly do not operate at their minimum cost. The aim of the study is to measure productivity function and scale of economies for small and medium sized enterprises in transition countries respectively in Albania and Macedonia. The research on productivity is large both at micro and macro level and the research is build on using different approaches of measuring productivity and therefore is also subject to different measurement challenges and problems. For empirical analyses data are extracted from BEEPS dataset and a Cobb- Douglas production function is estimated. We estimate an equivalent linear function of logarithms of Cobb- Douglas production function. The resulting estimated coefficients of the Cobb-Douglas production function are output elasticity s of respective inputs and in our estimation output elasticity of capital is 0.46 and output elasticity of labor is Keywords: production function, elasticity, labour, capital JEL: D24; C35; C51 1. Introduction This paper is organized as follows: Section 1 summarizes main findings and the origins of Cobb- Douglas production function; Section 2 presents estimation method and results; main conclusions of the research are highlighted in Section 3 also further research areas and limitations of the study are identified. Discussion on Cobb- Douglas Production Function Beginning with the work of Cobb and Douglas (1928) production function estimation studies originate since 1928 with tendency to prove that production functions are linear homogenous functions. The Cobb- Douglas production function is discussed widely on economic and econometric grounds and yet is widely used for estimation purposes. The regression to be estimated in this section is based on a Cobb Douglas production function, with the dependent variable growth of sales. The purpose is to observe only behavior of labor input and capital. A second regression is log of sales, where more variables are included. Mathematically we can express the Cobb Douglas production function as: Y = A * L a K (1-a) Equation 1 Since the exponents on labor and capital sum up to 1, the production displays constant returns to scale. Rewriting equation 1 we get: A = Y / L a * K (1-a) Equation 2 Where A is the total product output per unit of each of the inputs. In linear form we can express the general production function as: 1 PhD in Economics, Lecturer at State University of Tetova 2015 Research Academy of Social Sciences 213

2 B. Xhaferi ln Y = ln A + a * ln L + (1-a) * ln K Equation 3 While if we want to look at growth instead of levels of output we take the derivatives and get the form: dy / Y = da / A + a * dl / L + (1-a) * dk / K Equation 4 So that we can account for the percentage changes of output caused by percentage changes of each input, when knowing that A can be calculated as residual. The underlying econometric Cobb-Douglas production function that describes output by two inputs: respectively labor and capital, can be written as: lny = β 0 + β L lnl + β K lnk + u Equation 5 The β parameters describe respective input elasticity s of output and the sum of parameters represent returns to scale which we denote with R. Additionally to Ark s (2002) definition that productivity is a measure of effectiveness, we note that productivity is a measure of both effectiveness and efficiency and that is how it differs from profitability. Schools of firm profitability are identified in Stierwald (2009). Grosskopf (2002) reviews productivity measurement and decomposition and suggest that productivity should be directed to economic growth literature from frontier productivity measurement. TFP growth estimation assumes that the units are efficient otherwise the estimation is biased also human capital is important for accuracy of measurement (Maudos et al.,1999). Moreover they note the importance of human capital in measuring productivity growth in macro level in OECD countries using dataset of World Penn Tables. Bhanumurthy (2002) note that Cobb-Douglas production function may be used not just because of ease of computing, but also because the problems that may arise with its estimation, may be addressed with corresponding remedies. Felipe and Adams (2005) note that the aim of aggregate production function is producing distribution income accounting identity. They discuss aggregation problems of production function and note that Cobb- Douglas production is the most ubiquitous form of theoretical and empirical analysis. Chambers (1998) discusses input, output and productivity measures and develop Benet Bowley measures transformation which are translation invariant. Douglas (1967) in his Comments on the Cobb-Douglas production function answers to the critics and explains how their production function started from the intuition of Euler theorem but faced most caustic criticism from neoclassicists, institutionalists, econometricians and statisticians. He ends the comments challenging researchers with the question: There is law and relative regularity everywhere else- why not in production and distribution? (Douglas, 1967, p.22). Without taking sides advocating Douglas or the critics and trying to answer who is right and who is wrong, one thing is sure their paper raised the voice for consistent and better data collection especially for capital which on the other hand made possible further research in different fields. Douglas (1948) accepted two critics: one of independently determining exponentials in the production function (Durand, 1937) and broadening the field of investigation (Hitherto) and they find agreement in exponential values between the results for US, Australia and South Africa. He concludes that this is not the final say and yet there is much to be done in the road ahead regarding production function. In order to check the benefits from productivity in international trade gains Harrison (1994) discuss productivity competition and trade reform. He underline that previous research found that free-trade can increase growth, though the relationship between trade reform and productivity growth is inconclusive due to that how productivity is measured. He finds strong positive correlation between trade reform and productivity for the panel sample of manufacturing firms undertaken in their study. Bernard and Jones (1996) do not find evidence of productivity convergence in OECD countries but they raise the question of comparison between countries and over time. Diewert (1991) discuses measurement issues on productivity Productivity measurement is discussed in Dean (1999). Diwert (2008) makes suggestions to agencies for data improving in relation to productivity measurement and also suggest that balance sheet information should be public. 214

3 Regarding above theoretical considerations we suggest the estimation of the following function models: Log sales= β 0 + β L LnLAB+ β K lncapital + u Log sales= β 0 + β L LnLAB+ β K lncapital + β I lnintermediate +β E lnelectricity+u 2. Cobb- Douglas Estimation The very first estimated micro production function is in agricultural studies. A production function is an empirical relationship between inputs employed and outputs produced. Economists relate input and output since 1800 ( Levinsohn and Petrin, (2000)). Sandelin (1976) notes that there are different dates regarding to the origins of Cobb-Douglas production function and suggest that the origins go back in Wicksteed (1984) while it is often stated that the origins date in Wicksell (1901). The very first estimation of input-output relationship was in Cobb and Douglas (1928). Their work was object of discussions among researchers criticizing and giving credit to the same. Despite the critics Douglas continued working on the theory of production for two decades and estimating both time series and cross section. Later it was generalized and extensively used especcialy after Solow (1957) for estimating economic growth both in microeconomics and macroeconomics. Theoretically a less restrictive estimation than Cobb-Douglas is a translog production function. We estimate an equivalent linear function of logarithms of Cobb-Douglas production function. Cobb-Douglas production function may be estimated in the state level, industry level, firm or plant level. In this study we are estimating Cobb-Douglas for manufacturing industries. Allocation of resources in the production process is important because they address productivity and are a response to market demand. We estimated a two-input model: Sales=f (labor, capital) Equation 6 The above equation expresses that the production of outputs a function of labor (LAB) and capital. The definition of output in our case is the value of sales, the definition of labor is only the number of full time employees and we aggregate the capital measure form the net book value of machinery &equipment and as well as land&buildings. Capital is usually the most problematic measure in production function studies since data for it are usually not readily available and researchers use their own measures of diverse aggregation components. The properties that such production functions follow are that we include the inputs required for the production and an increase in an input translates with an increase in the output and they can exhibit increasing, constant or decreasing returns to scale. A Cobb-Douglas representation of the production function, given our variables of interest is stated as in equation 7: Sales = β 0 LAB β 1CAPITAL β 2 Equation 7 An equivalent linear function as a logarithmic representation of Cobb-Douglas production function can be stated as follows: Log sales= β 0 + β L LnLAB+ β K lncapital + u Equation 8 The allocation problem of inputs for the production process is mainly management decision but it should be based on optimization. The residual of this equation is the logarithm of total factor productivity. We have estimated Cobb-Douglass production function for a sample industry data in Albania and Macedonia substracted from BEEPS dataset. We recall the definition of variables in the underlying model: the dependent variable is the logarithm of sales, labor is the number of full time employees in the company and capital is the net book value of machinery and equipment as well as land and buildings. The elasticity coefficients obtained from the estimates are approximately 0, 7 for labor and 0, 4 for capital and they are both significant at conventional levels of significance. 215

4 B. Xhaferi We performed the diagnostic testing for multicolinarity and heteroscedscity and results that the model does not suffer from multicolinearity but it has the heteroscedascity problem. Heteroscedascity problem is usually present in cross-section data but it does affect only estimator s efficacy and does not affect the bias of estimators. We performed different types of hetersoscedascity tests such as: Breusch- Pagan; Cameron- Trivedi and White test and they all suggest that out model is heteroscedastic. As a result we performed White corrected standard errors and interpret these coefficients. Table 1 Cobb-Douglas Estimation Regressor Coefficient O.L.S. Estimation S.E. t- ratio p value O.L.S. Results based on White s Heteroscedasticity adjusted S.E. s S.E. t- ratio p value LN_CAP 0.46*** LN_LABOUR 0.78*** CONS 3.85*** Source: authors calculation Note: level by significance *** for 1%; ** for 5% and * for 10% statistical significance From the results we can write the estimated equation in the log-linear form: lnsales= LAB+0.46 capital The estimated equation in its multiplicative form is: Sales=46.99LAB 0.78 CAPITAL 0.46 This production shows that the output elasticitie s of labor and capital in the manufacturing sector and is interpreted as follows: holding the labor constant, an one percent increase in the capital input leads on the average to a 0.46 percent increase in the output; similarly, holding the capital and constant, an one percent increase in the labor input leads on the average to a 0.78 percent increase in the output. Alternatively we can interpret the estimate that a 10% increase in capital will increase the output by 4, 6% which implies that there are decreasing returns to capital. Similarly a 10% increase in labor will lead to 7.8% increase in output and again implies that there are diminishing returns to labor as well. The resulting estimated coefficients are output elasticity s of respective inputs. In our estimation output elasticity of capital is 0.46 and output elasticity of labor is Thus, our results are in accordance with the economic theory which tells us that marginal products of capital and labor are both positive, and both these inputs individually exhibit diminishing returns. The results suggest that labor contributes more than capital in the output i.e. in order to add output the distribution of input goods should be toward labor in order to have higher increase in the output level. Thus our estimates are evidence of applied Cobb-Douglas production function with statistically valid results. The mathematics for proving that Cobb-Douglas production function is homogenous is simple: We introduced sales= f( labor, capital) and then we have the general form of the production function: Sales = AL β LK β K and after estimation we obtained the following result: Sales=46.99LAB 0.78 CAPITAL

5 If we increase both inputs with o constant let s say 10 the resulting increase in output will be: A times respectively Returns to scale in the industry are obtained summing up the elasticitie s in coefficients in equation above. The obtained value of 1.24 suggests that firms are experiencing positive economies of scale of 0.24, on average. This implies that increasing all the inputs (labor and capital) will lead to a more than proportional increase in sales. Increasing returns to scale at the coefficient level of 1.24 indicates that if the inputs are increased by 100 percent the output will increase by 124 percent. Capital labor ratio may be one of the explanations for these increasing returns to scale. Another explanation may be the costs of production. Some studies report that countries with high capital labor ratio are more efficient than the ones with lower ratio. The drawback of this consideration is that they do not capture factor prices and factor endowment which may be crucial for factor allocation. The positive economies of scale suggest that industries can produce and export at competing prices and may grow employing more inputs. If this is the case these firms may generate revenues for the economy. Decreasing returns to scale means that the industry is inefficient. Bhanymurthy (2002) discusses that Cobb- Douglas production function should be used not just because it is a simple tool as critics suggest but because of advantages it possesses in handling multiple inputs in its generalized form. For these purpose we will have a closer look to the four-input model estimation. We construct again a Cobb-Douglas production function but beside two inputs that we had in the previous model respectively labor and capital we add cost of materials and intermediate goods ( intermedite) and the electiricity input ( cost of electiricity) and have the following equation: Log sales= β 0 + β L LnLAB+ β K lncapital +β I lnintermediate+β E lnelectricity+u Estimation results of the above equation are presented in Table 2: Table 2 Model Estimation LN_SALES COEF STD.ERR T P> t 95% CONF. LN_labour.529** LN-CAPITAL.272*** LN_INTERMEDIATE LN_ELECTRICITY.669*** _CONS Source: authors estimation Note: level by significance *** for 1%; ** for 5% and * for 10% statistical significance INTERV AL Before starting with inference we performed diagnostic testing for the assumptions of classical linear regression model. The variable inflation factor suggests that the model does not suffer of any multicolinearity problems. Felipe and Adams (2005) suggest that Cobb-Douglas production function may suffer from multicolinearity so we have tested for it. We performed different types of hetersoscedascity tests such as: Breusch- Pagan; Cameron-Trivedi and White test and they all suggest that out model is heteroscedastic. The econometric literature related to this type of problem offers remedial measures such as white heteroscedastic corrected standard errors or estimation with GLS. We performed white heteroscedastic corrected standard errors for our model and noticed that the sign and significance of parameter coefficients do not change and the differences in the model with no corrections and the model with correction are relatively small. As a consequence we choose to interpret the heteroscedascity corrected 217

6 B. Xhaferi model at robust parameters estimation as shown in Table 3. Because of the consequences and drawbacks of GLS (which we do not intend to discuss in this work) we do not use GLS which is usually suggested only when the significance of variables changes when corrected with white heteroscedatic corrected standard errors. Table 3 Heteroscedascity Corrected Estimation, Robust LN_SALES COEF ROBUST STD.ERR T P> t 95% CONF. INTERVA L LN_labour.529** LN-CAPITAL.272*** LN_INTERMEDIAT E LN_ELECTRICITY.669*** _CONS Source: Authors estimation Note: level by significance *** for 1%; ** for 5% and * for 10% statistical significance Our multiplicative Cobb-Douglas model may be described as follows: Sales=1.13LAB 0.53 CAPITAL 0.27 INTERMEDIATE 0.07 ELECTRICITY 0.67 According to the results the variables in the model are significant at conventional significance levels, except the intermediate materials input. The corresponding elasticity coefficients of the inputs in the model are: for labor; for capital and approximately 0.7 for electricity. The output elasticity of intermediate goods used in the production is relatively small and result insignificant in conventional levels of significance. The evidence is in accordance with the theory since the model estimation displays positive and decreasing returns to inputs. The elasticity of output with respect to production factors imply that if capital (labor, electricity) increases by 1%, the output increases by 0.46%, (0.122%, 0.699%) respectively on average, ceteris paribus. Again the coefficient on labor is larger compared to capital but smaller than electricity, an input added in this model. The results suggest that firms are experiencing increasing returns to scale on average. Increasing returns to scale results both in the original 2-input Cobb-Douglas production function and the 4-input production function. Again increasing returns to scale suggest that a 1% increase in the inputs leads to more than 1% increase in output. Further more the resulting increasing returns may suggest that firms do not operate with minimum costs, respectively they are not Pareto efficient. Additionally we performed another test to test the elasticity of substitution estimating: Log Q/L = β 0 + β Log w; Where w = real wage rate, Q/L = labor productivity and β = elasticity of substitution. Wage is measures as monthly compensation of full time employee. The results are shown in table below: 218

7 Table 4 Estimating Elasticity of Substitution Labor-productivity COEF STD.ERR T P> t 95% CONF. INTERVA L LN_wage 1.03*** _CONS -3.8*** Source: Authors estimation Note: level by significance *** for 1%; ** for 5% and * for 10% statistical significance The estimation results suggest that the elasticity of substitution is unitary; on average a percentage point increase in wage will result with a percentage point increase in labor productivity. According to Klein s viewpoint if elasticity of substitution is near about unity a Cobb-Douglas production function can be estimated. Wage rates have impact on labor productivity. We suggest that incentives related to wage levels in these countries are same as incentivizing labor productivity which on the other hand is evidence that using wage incentive instruments is aligning companies goal and may not lead to principle agent problem. Again this is evidence that labor productivity may be explained by employee earnings. The general idea is in line with Lazear that wages may be as incentives for increasing labor productivity. We may propose that recognized forms of financial participation both theoretically and empirically, that result with increased productivity may be used in transition countries for their expected potential benefits. Examples of this kind are employee share ownership and profit sharing. The introduction of Financial Participation in transition countries can be identified with the privatization process; it was a bridge for the transformation of the ownership of state owned enterprises. In recent years there is no evidence that these countries are incentivizing and creating a legal framework for such schemes. Increasing wages that may potentially increase labor productivity is a desirable outcome for both employees and employers and is not a Principle-Agent problem. In line whith this we propose: 1. Aligning the goals of the Principle and the Agents will lead to increased productivity; 2. Linking the effort with income may increase the performance. 3. Conclusion Studies on productivity have as stakeholders the employees, owners and the government. The literature on productivity is diverse and looking at different aspects of productivity. In the firm level being productive may be understood as incentivizing employees to work efficiently while in the macro level studies on productivity we may be interested in GDP and employment. Most of macroeconomic studies finish noting the limitations on macroeconomic studies and suggesting micro studies to capture the channels to which business climate enhances growth (Durlauf et al. (2008); Straub (2008); Pande and Udry (2005).Micro data in studying productivity are important in different fields of economics: microeconomics, macroeconomics, labor economics, international trade and industrial organization. According to empirical research we find that variables correlated with productivity are: institutional change, technological progress, IT investment, innovation and Cross section production function is analyzed therefore there is urge for a micro panel dataset so that researchers will be able to look far beyond the scope of the provided research here. The evidence from estimated Cobb-Douglas production function is that companies in Macedonia and Albania show increasing returns to scale and the sign of corresponding input elasticities are in line with the theory. The urge of the necessity of micro panel dataset is especially for transition countries because this limitation results with the scarcity of research in this kind of countries who need policy recommendation in order to improve and grow economically. 219

8 B. Xhaferi Policy recommendation that respective institutions should follow is to encourage firms to show increasing returns to scale or constant returns to scale or identify the firms operating with increasing returns to scale and incentivize them to stay in the business. Government policy should be to attract efficient firms. As a consequence of the transition process and privatization which is the case of both Macedonia and Albania it is expected that in the short run there will be a large number of small and medium enterprises, but on the other perspective as both countries are adhering the EU in order to survive in the open market economy they should be competitive and productive. The legislation and policy response therefore should be in line with the international market. Finally the awareness of policy makers should be focused that both productive firms and productive workers should be incentivized otherwise we encourage them to seek better off opportunities somewhere else. Policies should be oriented toward: 1. Aligning the goals of the Principle and the Agents will lead to increased productivity; 2. Linking the effort with income may increase the performance. Costs will depend on productivity which responses to the law of diminishing marginal returns and our findings in this work are in line with theory and give supporting evidence for our hypothesis. The estimation suggest that policies regarding employee incentivizing for working more productively, employing adequate skilled workforce, incentivizing and subsidies for innovation and R&D may improve the productivity in the countries referenced. Cobb-Douglas production function is used extensively in productivity studies and such a function is estimated in the thesis. The very first estimation of input-output relationship was in Cobb and Douglas (1928). Their work was object of discussions among researchers criticizing and giving credit to the same. We estimate an equivalent linear function of logarithms of Cobb-Douglas production function. The resulting estimated coefficients of the Cobb-Douglas production function are output elasticity s of respective inputs and in our estimation ( after testing and correcting for multicolinearity and heteroscdedascity) output elasticity of capital is 0.46 and output elasticity of labor is In the four input Cobb-Douglas estimation the corresponding elasticity coefficients of the inputs in the model are: for labor; for capital and approximately 0.7 for electricity. Thus, our results are in accordance with the economic theory which tells us that marginal products of capital and labor are both positive, and these inputs individually exhibiting diminishing returns. The results suggest that labor contributes more than capital in the output i.e. in order to add output the distribution of input goods should be toward labor in order to have higher increase in the output level. Thus our estimates are evidence of applied Cobb-Douglas production function with statistically valid results. Finally our results are in line with the theory and we provide supporting evidence for Schumpeterian view and Lazears theory of incentive wages. The empirical evidence in the study suggests that the enterprises in respective countries are experiencing increasing returns to scale. The positive economies of scale on the other hand suggest that industries can produce and export at competing prices and may grow employing more inputs. If this is the case these firms may generate revenues for the economy. This study is subject to some limitations which are mainly related to lack of data. The first limitation is that the study does not capture industry and country differences; secondly; examination is done by using cross section data; thirdly we do not calculate total factor productivity and its convergence within industries and countries. We propose and suggest that further research should be done using a trans-log production function or taking the Levinshon-Petrin approach. This approach is a technique that uses the cost of material as a proxy of companies information about productivity. Another approach that may be applied is Olley and Pakes if the dataset has information about investment which is their proxy for companies information about productivity. Concluding we may state some suggestions for the road ahead are to pursue the following approaches: Legros and Galia (2011)-simultaneous equations; Levinshon-Petrin approach; Olley and Pakes approach; Translog production function and comparative studies. 220

9 The problem of availability of data for large samples and longer time periods is a limitation for conducting studies on productivity. Therefore we suggest that preparing questionnaire and colecting micropanel dataset may be helpful in solving estimation and comparison models in productivity studies. In closing I would like to add that increasing productivity is multilevel complex framework and a better understanding of the problem may be attained by disaggregating the problem in micro level studies. References Bernard AB, Jones CI (1996) Comparing apples to oranges: productivity convergence and measurement across industries and countries. Am Econ Rev 86(5): Bhanumurthy, K. V. (2002). Arguing a case for the Cobb-Douglas production function. Review of Commerce Studies, 20, 21. Chambers, R. G. (1996). A new look at exact input, output, and productivity measurement. Department of Agricultural and Resource Economics Working Paper, Cobb, C. and Douglas, P. (1928) A theory of production, American Economic Review,vol 18, issues 1, p Dean, E. R. (1999). Accuracy of the BLS Productivity Measures, The. Monthly Lab. Rev., 122, 24. Diewert, Walter Erwin (2008) What Is To Be Done for Better productivity Measurement International Productivity Monitor, 2008, 16, Douglas, P. H. (1948). Are there laws of production?. The American Economic Review, 38(1), i-41. Douglas, P. H. (1967). Comments on the Cobb-Douglas production function. InThe Theory and Empirical Analysis of Production (pp ). Columbia University Press. Felipe, J., & Adams, F. G. (2005). " A Theory of Production" The Estimation of the Cobb-Douglas Function: A Retrospective View. Eastern Economic Journal,31(3), Grosskopf, S. (2003). Some remarks on productivity and its decompositions. Journal of Productivity Analysis, 20(3), Harrison, A. E. (1996). Productivity, imperfect competition and trade reform Theory and evidence, 36(1994), Levinsohn, J. and A. Petrin (2000) Estimating production functions using inputs to control for unobservables NBER WP Maudos, J., Pastor, J. M., & Serrano, L. (1999). Total factor productivity measurement and human capital in OECD countries. Economics letters, 63(1), Sandelin, B. (1976). On the origin of the Cobb-Douglas production function.economy and History, 19(2), Solow, Robert (1957), "Technical Change and the Aggregate Production Function" The Review of Economics and Statistics 39, pp Stierwald, A. (2009). Determinants of Firm Profitability - The Effect of Productivity and its Persistence, 61(0). 221