A solution to log of dependent variables with negative observations
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A solution to log of dependent variables with negative observations Mustafa U. Karakaplan1 Levent Kutlu2 Mike G. Tsionas3,4 ●
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Abstract Negative observations pose a problem in econometric models that apply log-transformation to the data. We propose a simple yet effective solution to this problem by extending the domain of numbers to the set of complex numbers. In particular, this approach suggests that we can replace the negative values with their absolute values and estimate this transformed model with conventional estimation methods. Moreover, we extended this approach to logs of independent variables with negative observations as well. Using our method, we estimated the profit efficiencies of the US banks and illustrated that different treatments for observations with negative profits (loss) may lead to substantially different efficiency estimates. We also showed the importance of controlling bank heterogeneity when estimating efficiency. 1234567890();,:
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Accepted: 1 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Keywords Complex Regression Log of Negative observation Loss Profit Function Translog Function US Banks ●
1 Introduction Log-transformation of variables is widely used in econometric analysis when we are interested in relative (multiplicative) changes or have a skewed error term. Moreover, some widely used models theoretically require logtransformations such as translog model for profit function. One of the difficulties in applying this transformation is that the dataset may contain negative observations for the dependent variable as the logarithm of a negative number is not defined in the real number set. In this study, we propose a simple yet effective solution to this problem. In particular, we suggest extending the domain of numbers from the real
* Levent Kutlu [email protected] 1
Department of Finance, University of South Carolina, Darla Moore School of Business, 1014 Greene Street, Columbia, SC 29208, USA
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Department of Economics and Finance, University of Texas Rio Grande Valley, 1201 W University Dr, Edinburg, TX 78539, USA
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Lancaster University Management School, Bailrigg LA1 4YX, UK
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Montpellier Business School, 2300 Avenue des Moulins, 34080 Montpellier, France
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numbers to the complex numbers.1 This way the logarithm of a negative observation would still be defined in this extended domain. This approach suggests that we can estimate the parameters of a model with log-transformed dependent variables via conventional econometric methods by simply replacing the logarithm of the variable by the logarithm of absolute value of this variable and adding a negative-profit dummy variable to the model. Log-transformation is used in many different areas of economics, however, for the sake of illustration, we concentrate on the production literature, which utilizes this transformation extensively.2 In particular, we consider profit function estimation as an illustration of our methodology. Translog profit function is a commonly used p
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