### 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

Received: Oct. 17, 2023    Accepted: Nov. 03, 2023    Published: Nov. 11, 2023

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Abstract

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.

 DOI 10.11648/j.ajtas.20231206.14 Published in American Journal of Theoretical and Applied Statistics ( Volume 12, Issue 6, November 2023 ) Page(s) 180-186 Creative Commons This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. Copyright Copyright © The Author(s), 2024. Published by Science Publishing Group
Keywords

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

References
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• 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

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title = {Estimating the Determinants of Firm Innovation Inefficiency Through the Conditional Mean of Innovation Inefficiency Given a Composite Error},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {12},
number = {6},
pages = {180-186},
doi = {10.11648/j.ajtas.20231206.14},
url = {https://doi.org/10.11648/j.ajtas.20231206.14},
abstract = {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.
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AB  - 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.

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Author Information
• Department of Economics, University of Patras, Patras, Greece

• Section