### American Journal of Theoretical and Applied Statistics

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### Estimating the Determinants of Firm Innovation Inefficiency Through the Conditional Mean of Innovation Inefficiency Given a Composite Error

The present paper demonstrates that the estimations of the determinants of firm innovation inefficiency can be obtained through the conditional mean of innovation inefficiency given a composite error. We extract the estimations of the determinants of firm innovation inefficiency by replacing the true parameters in the equation of the conditional mean of innovation inefficiency given a composite error with Maximum Likelihood estimations from the Stochastic Frontier Approach. This is an alternative method for the estimation of the determinants of firm inefficiency besides those which are existent in the relevant literature. Based on statistical theory and algebra, we first present the case where innovation inefficiency is assumed to be distributed as a truncated normal with a nonzero constant mean. Second, we focus on the case where innovation inefficiency is assumed to be distributed as a truncated normal with a mean that varies across firms. There, we show that all the change in the error term of the Stochastic Frontier Knowledge Production Function originates from innovation inefficiency. The latter is modelled as having two components: a) a function of some firm-specific characteristics (variables) and b) random component. Then, we advance to the estimations of the determinants of firm innovation inefficiency via a generalized Stochastic Frontier Approach (generalized production frontier approach). Finally, we replace the true parameters in the equation of the conditional mean of innovation inefficiency given a composite error with Maximum Likelihood estimations from the generalized production frontier approach.

Innovation Inefficiency, Firms, Conditional Mean Estimator, Stochastic Frontier Models

APA Style

Kanellopoulos, V. (2023). Estimating the Determinants of Firm Innovation Inefficiency Through the Conditional Mean of Innovation Inefficiency Given a Composite Error. American Journal of Theoretical and Applied Statistics, 12(6), 180-186. https://doi.org/10.11648/j.ajtas.20231206.14

ACS Style

Kanellopoulos, V. Estimating the Determinants of Firm Innovation Inefficiency Through the Conditional Mean of Innovation Inefficiency Given a Composite Error. Am. J. Theor. Appl. Stat. 2023, 12(6), 180-186. doi: 10.11648/j.ajtas.20231206.14

AMA Style

Kanellopoulos V. Estimating the Determinants of Firm Innovation Inefficiency Through the Conditional Mean of Innovation Inefficiency Given a Composite Error. Am J Theor Appl Stat. 2023;12(6):180-186. doi: 10.11648/j.ajtas.20231206.14

Copyright © 2023 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 1 Farrell M J (1957) The measurement of productive efficiency. Journal of the Royal Statistical Society, Series A 120(3): 253-290. 2 Kalirajan K P and Shand R T (1985) Types of education and agricultural productivity: A quantitative analysis of Tamil Nadu. Journal of Development Studies 21(2): 232-243. 3 Alvarez R and Crespi G (2003) Determinants of technical efficiency in small firms. Small Business Economics 20(3): 233-244. 4 Pestana Barros C and Dieke P U C (2008) Technical efficiency of African hotels. International Journal of Hospitality Management 27(3): 438-447. 5 Page J M (1980) Technical efficiency and economic performance: Some evidence from Ghana. Oxford Economic Papers 32(2): 319-339. 6 Pitt M and Lee L F (1981) The measurement and sources of technical inefficiency in the Indonesian weaving industry. Journal of Development Economics 9(1): 43-64. 7 Kumbhakar S, Ghosh S and McGuckin J T (1991) A generalized production frontier approach for estimating determinants of inefficiency in U. S. dairy farms. Journal of Business & Economics Statistics 9(3): 279-286. 8 Reifschneider D and Stevenson R (1991) Systematic departures from the frontier: A framework for the analysis of firm inefficiency. International Economic Review 32(3): 715-723. 9 Battese G and Coelli T (1995) A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Economics 20(2): 325-332. 10 Zeebari Z, Mansson C Sjolander P Soderberg M (2023) Regularized conditional estimators of unit inefficiency in stochastic frontier analysis, with application to electricity distribution market. Journal of Productivity Analysis 59(1): 79-97. 11 De Borger B, Kerstens K Moesen W and Vanneste J (1994) Explaining differences in productive efficiency: An application to Belgian municipalities. Public Choice 80(3-4): 339-358. 12 Jondrow J, Lovell K C A Materov I S and Schmidt P (1982) On the estimation of technical inefficiency in the stochastic frontier production function model. Journal of Econometrics 19(2-3): 233-238. 13 Pellegrino G and Piva M (2020) Innovation, industry and firm age: are there new knowledge production functions? Eurasian Business Review 10(1): 65-95. 14 Catozzella A and Vivarelli M (2007) Beyond the Knowledge Production Function: The role of R&D in a multi-faceted innovative process. Jena Economic Research Paper No. 2007-087. 15 Ramani S, El-Aroui M-A and Carrere M (2008) On estimating a knowledge production function at the firm and sector level using patent statistics. Research Policy 37(9): 1568-1578. 16 Stevenson R (1980) Likelihood functions for generalized stochastic frontier estimation. Journal of Econometrics 13(1): 57-66. 17 Aigner D, Lovell K C A and Schmidt P (1977) Formulation and estimation of stochastic frontier production function models. Journal of Econometrics 6(1): 21-37. 18 Kumbhakar S, Parmeter C and Zelenyuk V (2020) Stochastic Frontier Analysis: Foundations and Advances II. In S. Ray R. Chambers and S. Kumbhakar (eds.) Handbook of Production Economics (pp. 1-40). Singapore: Springer. 19 Wang W S and Schmidt P (2009) On the distribution of estimated technical efficiency in stochastic frontier models. Journal of Econometrics 148(1): 36-45. 20 Badunenko O, Henderson D and Kumbhakar S (2012) When, where and how to perform efficiency estimation. Journal of the Royal Statistical Society. Series A (Statistics in Society) 175(4): 863-892. 21 Andor M, Parmeter C and Sommer S (2019) Combining uncertainty with uncertainty to get certainty? Efficiency analysis for regulation purposes. European Journal of Operational Research 274(1): 240-252. 22 Tsionas M G (2021) Optimal combinations of stochastic frontier and data envelopment analysis models. European Journal of Operational Research 294(2): 790-800.