10th Global Conference on Business & EconomicsISBN : 978-0-9830452-1-2
ANALYSIS OF THE FACTORS AFFECTING PRODUCTIVITY USING NON PARAMETRIC REGRESSION METHOD
NURAY TEZCAN
Asst.Prof.Dr.
Halic University
Faculty of Management
Emekyemez Mah. Okçu Musa Cad.
Mektep Sok. No: 21
Sishane/İSTANBUL
Phone: 00 90 532 700 81 46 , Fax: 00 90 212 297 31 44
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ANALYSIS OF THE FACTORS AFFECTING PRODUCTIVITY USING NON PARAMETRIC REGRESSION METHOD
Asst.Prof.Dr. Nuray Tezcan, Halic University, Turkey
ABSTRACT
The aim of this study is to determine the factors affecting productivity of non- parametric regression. Productivity, basically, is defined as relationship between output-which is obtained from production process- and input which is used to create output.Productivity increaseis an important indicator of the economy and the market value of the firms. Therefore, it is crucial for the business management to determine and control the factors affecting productivity.This study investigates the factors affecting productivity through using non-parametric regression method. In the study, Turkey’s Top 500 Industrial Enterprises are used.As a result, return on assets (ROA) and sales are found statistically significant. Also it has been showed that results obtained with non-parametric regression analysis are better than that of parametric regression analysis.
INTRODUCTION
Productivity, basically, is defined as relationship between output which is obtained from production process and input which is used to create output. It is an important measure since it represents production process. Many indicators are used to measure productivity. Labor productivity, which is the ratio of added value to number of the employees, is one the main measure used in the literature. However, there is a debate about the measurement of added value. The gross added value versus the net added value debate is a dispute over depreciation. Net added value is gross added value minus depreciation. According to the some academic writers gross added value should be used since depreciation account is a provision and it belongs to shareholders. Another advantage of using gross value added is that it cannot be manipulated because it does not changefirm to firm. ( Bao and Bao, 1989) Therefore in his study, gross value added is selected.
The importance of productivity growth has been discussed by numerous studies.At the firm level productivity growth demonstrates that resources have been used efficiently and this situation causes decrease in the costs. A firm, therefore, can reduce the prices of its products while maintaining or increasing profit margins. At the national level, productivity is one of the main determinant of economic growth and progress. Productivity growth provides to decrease in rate of inflation and it also develops the competitiveness of domestic firms.Productivity growth, therefore, increases the wealth of a nation.( Bao and Bao, 1989)
This study is organized as follows: After introduction part; literature review will be provided. Then data, sample, estimation method and empirical results will be explained. In the last section conclusion and discussion will be given.
LITERATURE REVIEW
Financial performance and size of the firms' debt structure, ownership, corporate governance, export behavior, innovative activities are factors affecting productivity and there are numerous studies that focus on these topics in the literature.
Studies that examine relationship between productivity and leverage have given us different results. According to the some of these, there is a negative relationship between variables and debt ratio affect productivity negatively and less productive firms should not increase this ratio to solve this problem. (Nunes et.al, 2007 ) Nonetheless, in the other study with two stage, efficieny score was obtained using Data Envelope Analysis then, was researched that these scores affect the profitability or not. As a result, leverage affects efficiency and efficiency affects profitability positively too. (Mok et. al, 2007 ) One study that explores relationship between profitability and leverage emphasized that there is negative relationship. Also, results has been supported by tests in this study (Saibal, 2009)
In the literature, there are many studieson the relationship between productivity and other variables. Positive relationship is found between productivity and ownership but relationship that both size and independence of the management board is found to be insignificant (Adewuyi and Olowookere, 2009). Another, it has been indicated that, increasing productivity in the public enterprises grows, nonethelessincreasing of profitability comes true delayed.(Zhang et.al, 2002). The main point is that profitability does not mean productivity at all times and vice versa. (Hitt and Brynjolfsson,1996). Fernandes (2008) and Yaşar et. al. (2006) investigated effects of export behavior on productivity. As a result, they emphasize the positive impact of this factor on firm performance and they justify that exporting firms are more productivity than non-exporting firms.Some studies evaluate the relationship between innovation and productivity. Janz et. al.(2008) indicate that there is a positive relationship between variables and results differ in terms of country. Also, the other studies prove that the close linkage between the capability of innovation and competitiveness.
In the studies stated above, various methods have been conducted to explain relationship between variables. In this study, non-parametric regression method is utilized. By doing this, usability of this method has been displayed in the determining of relationship between variables at the business management area.
RESEARCH METHODOLOGY
Data and Variables
The data used in the analysis is constructed through firms which are Turkey’s Top 500 Companies listed by ICI for the year of 2007. At the beginning of study, data set is consisted of 500 firms however, 92 of them are cancelled because of outliers and missing values. Therefore, final data set covers total of 408 firms. After calculating various financial ratio, then the natural logarithm to the base “e” is used for these variables. S-PLUS 6.1. ve R 2.9.0 are employed to analyze the data.
Labor productivity that is defined as the ratio of gross value added to number of employees is employed as dependent variable and the independent variables are stated as below.
1.Return on Sales (ROS)= Income / Sales
2.Return on Equity (ROE)= Income / Equity
3.Return on Asset (ROA)= Income / Total Assets
4.Leverage= Total Debt/Equity
5.Total Sales (in thousand TL)
6.Total Asset (in thousand TL)
7.Export (in thousand TL)
Limitations of the Study
Main limitation in the analysis is that there are a few financial information declared by ICI. Although several factors affecting productivity like financial performance, leverage, firm size and export are employed, however, some of important variables are not contained in the analysis due to lack of data Especially absence of data regarding capasity usage ratio, innovative activities and level of corporate governance avert more detailed explanations. In addition, ownership variable has not been used because there are a few public firms in comparison with private firms.
Method
Non-parametric regression analysis is selected as method for determining for relationship between variables. Parametric regression method, namely Ordinary Least Square (OLS) regression, is commonly used in the statistical data analysis. In this method, however, form of regression function is determined in advance and it requires strong assumptions like normality of the error term and homoscedasticity. If these assumptions are violated then parametric estimates may be inconsistent and cause misleading explanations whereas non-parametric regression does not require these assumptions. Also, it provides flexibility in revealing relationship between variables. Briefly, it is defined as “let the data speak for itself”. An important distinctive feature is emphasized that parametric regression estimates unknown regression coefficients while non-parametric counterpart estimates unknown regression curve. (Hardle et all. 2004) In addition to this, in non-parametric analysis it has been assumed that regression function has feature of smoothness like continuity and differantiability (Eubank,1990). Nonetheless, non-parametric regression have some disadvantages. First, this tecnique is theoretically more complex than the parametric counterpart so there may be difficulty in interpretationing of results. Second, it is computationally intensive and the data used in the analysis should be have many observations, however there is no exact number about this issue in the literature. (Yatchew, 1998) Also, in multiple non-parametric regression, as the number of predictors increases, the number of points in the local neighborhood of a focal point tends to decline rapidly. Therefore, local neighborhood is decreased to include fix number of observations. Depending on this, the quality of estimates distorts. (Fox, 2000).
Kernel regression is based on nonparametric density estimation using kernel functions. Kernel functions are necesserily symmetric around 0 and integrate to 1, and their estimates represent densities and they don’t depend on any choice of origin (Hardle, 1990)
observations
where , unknown smooth function, ε denotes a random term with mean zero and variance defines the variation of Y around its mean, .
, Kernel function that symmetric probability distribution function,
, non-negative bandwidth that controls size of local neighbour
When is estimated by locally weighted averaging, Nadaraya-Watson estimator is obtained. (Nadaraya, 1964 and Watson, 1964). This estimator is stated as below
(1)
In parametric regression analysis coefficient of determination, namely , is an indicator for determininig goodnees of the model prediction. Also, unit-free measure of goodness-of-fit for nonparametric regression models can be calculated and this measure defined as follows:
(2)
; Value of dependent variable for observation i.
; Fitted value of dependent variable for observation i.
; Arithmetic mean of dependent variable
; The number of observations.
This measure will always lie in the range with the value 1 denoting a perfect fit to the sample data and 0 denoting no predictive power of the non-parametric regression model. (Hayfield and Racine, 2008). Also, obtained from non-parametric regression model is directly comparable to the unadjusted provided from parametric regression model (Racine, 2008)
In non-parametrik regression analysis, the most important issue is bandwith selection . Bandwidth selection is basically covers trade-off between biased and variance of estimation. “Optimal bandwidth” has been obtained by minimizing the mean integrated squared error (MISE).(Dinardo and Tobias, 2001) There are various methods to determine bandwidth like cross-validation and plug-in in the literatüre. In this study, “Cross Validation (CV) method is used and also variables covered in the model are tested to determine significant or not. Within this purpose, “Nested Pivotal Bootstrapping” method is used. (Racine, 1997).
To employ non-parametric regression, different estimation methods can be used. Kernel Regression, Local Regression or Spline Smoothing are commonly known methods in the literature. In this study, Kernel Regression, namely Nadaraya-Watson (N-W) estimator is utilized and also parametric regression (OLS) is employed for the same data. After doing this, results obtained both methods are compared.
Empirical Results
In this study, to determine factors affecting productivity multiple non-parametric regression analysis was used. First of all, non-parametric regression model is composed single variable then other variables are added one by one to increase goodness of model prediction. However on the contrary parametric regression analysis, as number of variables increase, goodness of model can decrease. Therefore many models are formed and during this process, either coefficient of determination is found to be very low or even model has high , some variables are obtained to be insignificant in the model. After several trying, final model is stated as below.
Labor Productivity ~ (ROA + Sales)
This model has the highest value and both variables of the model are statistically significant. Results obtained from analysis are displayed as Table 1.
<Table 1>
As can be seen Table 1, ROA and sales are found statistically significant and is calculated as 38%. Also, standart error of the model is 0,6316.
After conducting non-parametric regression, this time parametric regression is employed to imagine difference between models with same variables.
<Table 2>
As can be seen Table 2, parametric regression model significant at 0,001 level. and is calculated as 32%. Also, standart error of estimation is 0,8354. In addition, to generalize results whole population, partial regression coefficients are tested and both variables are found to be significant.
According to the results, ROA and sales are effective factors on productivity and this result is consistent with the theory. ROA percentage shows how profitable a company's assets are in generating revenue and this ratio gives an indication of the capital intensity of the company. The other variable sales is accepted as indicator of firm size in the finance literature. Increasing in these indicators is desirable situation all firms. Besides, it has been stated that these indicators have been affecting productivity of the firms’ positively.
The other result provided from this study is about method. Coefficient of determination obtained with non-parametric regression analysis are better than that of parametric regression analysis, respectively 38% and 32% and standart error of the non-parametric model is less than that of parametric model, respectively 0,6316 and 0,8354.
CONCLUSION and DISCUSSION
Productivity is a vital indicator both in determining efficiency of the firms’ and in increasing welfare of country. Therefore investigating factors that being effected on productivity is crucial issue in the literature. On this account the aim of this study is to explore these factors. Also, to display usability of non-parametric regression method in the solving problems about business management area.
In this study, nonparametric regression analysis is conducted as method in the determining relationship between variables and labor productivity is employed as dependent variable while financial performance of the firms’, size, leverage and export behavior are used as independent variables. Due to lack of data for some variables such as ownership structure, level of corporate governance, innovation activities and capasity usage ratio could not cover in the analysis. According to the non-parametric regression analysis, ROA and sales are found to be statistically significant. In addition, parametric regression is employed to the same data. Coefficient of determination obtained with non-parametric regression analysis are better than that of parametric regression analysis, respectively 38% ve 32%. However, these ratios are not high which means that other variables affecting productivity must be included in the model.
It has been noted that, non-parametric regression analysis is not unique method for explaining relationship among variables.This method a good option for more complicated models and can be used in situation that assumptions are not satisfied .
REFERENCES
Adewuyi, A. O.&Olowookere A. E., (2009), ‘Impact of Governance Instruments on the Productivity of Nigerian Listed Firms’, The Icfai University Journal of Corporate Governance, pp. 51–74.
Bao, B. H.& Bao, B. H., (1989), ‘An Empirical Investigation of the Association between Productivity and Firm Value’, Journal of Business Finance and Accounting, Vol. 16, pp. 699–717.
Dinardo, John & Justin Tobias (2001); “Nonparametric Density and Regression Estimation”, Journal of Economic Perspectives, Volume 15, No:4, pp.11–28.
Eubank R.L., (1990), Nonparametric Regression And Spline Smoothing, Second Edition
Fernandes A. M., (2008), “Firm Productivity in Bangladesh Manufacturing Industries”, World Development, Vol.36, No.10, pp.1725-1744
Fox John, (2000), Nonparametric Simple Regression: Smoothing Scatterplots, Sage University Paper Series No: 07–130
Hardle W.,Müller M.,Sperlich S.&Werwatz A., (2004); Nonparametric and Semiparametric Models: An Introduction, Springer Series in Statistics
Hardle Wolfgang (1990) Applied Nonparametric Regression, Cambridge University Press
Hitt L. M.&Brynjolfsson E., (1996) “Productivity, Business Profitability and Consumer Surplus:Three Different Measures of Information Technology Value”, Management Information Systems Quarterly, Vol.20, No.2, pp.121-142
Janz, N., Lööf, H.& Peters, B., (2008), ‘Firm Level Innovation and Productivity – Is There a Common Story Across Countries’, Center for European Economic Research, Working Paper Series.
Mok, V., Yeung, G., Han, Z. & Li, Z., (2007), ‘Leverage, Technical Efficiency and Profitability: An Application of DEA to Foreign Invested Toy Manufacturing Firms in China’, Journal of Contemporary China, Vol. 16, pp. 259–274
Nadaraya E.A., (1964) “On estimating regression”, Theory of Probability and Its Applications, 9, 141–142
Nunes, P. M., Sequeira, T. N.&Serrasqueiro, Z., (2007), ‘Firms’ Leverage and Labour Productivity: A Quantile Approach in Portuguese Firms’, Applied Economics, Vol. 39, pp. 1783–1788.
Racine Jeffrey, (2008), “Nonparametric Econometrics: A Primer” , Foundations and Trends in Econometrics, Vol. 3, No.1, s.47
Saibal, G., (2009), ‘Productivity and Financial Structure: Evidence from Indian High-Tech Firms’, Munich Personal RePEc Archieve, MPRA Paper No. 19467.
Watson G.S.; (1964), “Smooth Regression Analysis”, Sankhya Ser. A, 26, 359–372
Tristen Hayfield & Jeffrey Racine (2008) “Nonparametric Econometrics: The np Package”; Journal of Statistical Software, Volume 27, Issue 5, s.10
Racine Jeff, (1997), “Consistent Significance Testing for Nonparametric Regression”, Journal of Business&Economic Statistics, Vol. 15, No. 3,pp.369–378
Yaşar, M., Nelson, C.& Rejesusu, R., 2006), ‘Productivity and Exporting Status of Manufacturing Firms’, Review of World Economics, Vol. 142, pp. 675–694.
Yatchew Adonis, (1998), “Non-Parametric Regression Techniques in Economics” Journal of Economic Literature
Zhang, A., Zhang, Y. & Zhao, R., (2002), ‘Profitability and Productivity of Chinese Industrial Firms: Measurement and Ownership İmplications’, China Economic Review, Vol. 13, pp. 65–88.
TABLES
Table 1: Results of Non-Parametric Regression Analysis
Dependent Variable / Labor ProductivityIndependent Variable / ROA
Sales
Number of Observation / 408
Standart Error of Model / 0,6316
Bandwidth
ROA / 1,1707
Sales / 0,6210
R 2 / 0,3839
p-value
ROA / 2,22e-16*
Sales / 2,22e-16*
*significant statistically at 0,001 level
Table 2: Results of Parametric Regression Analysis
Dependent Variable / Labor ProductivityIndependent Variable / ROA
Sales
Number of Observation / 408
Standart Error of Estimation / 0,8354
Durbin-Watson Statistics / 1,973
F-value / 96,79
R 2 / 0,323
p-value / 0,000
*significant statistically at 0,001 level
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October 15-16, 2010
Rome, Italy