Sometimes obscuring models in some research activities make me anxious and pioneered me to think deeply about modeling issues. While attending a national seminar at a university I noticed a person presenting an econometric model with some indescribable move by making the natural logarithm operator common for all explanatory variables. Basically his model seems to be functionally miss-specified, i.e., the components of the model were erroneously presented. In this context, I am trying to reflect the dummies under the umbrella of natural logarithm.
Let’s kick off with the need for natural logs in a regression model. Natural logs are often used to show constant percentage regression models. For instance, with log wage dependent variable and education as
log(wage) = b0 + b1educ + u
a regressor we can say that wage increases by a constant percentage with every additional year of education. In addition, natural log can be used to obtain constant elasticity and semi elasticity regression model. In the above equation 100.b1 refers to as semi-elasticity of y with respect to x. if the education variable was log (educ), then we could have said b1 is elasticity of y with respect to x.
On the other hand, dichotomous or dummy variable is a kind of variable to show binary responses, i.e., either yes or no (0 or 1 similarly). But applying natural logarithm to a dummy variable is not a good idea as this may force the results to be biased. It is not meaningful as because natural log of 0, 1 is undefined and 0 respectively. Putting the log on the dummies basically an ignorance to basic mathematical theory and would be a point critical assessment. From my point of view, applying log to categorical variable is also avoidable; this may also lead to the same unsolved puzzle. A user of regression model is expected to have a fruitful decision-making abilities in deciding where to use these methods and where not. It is always better to leave dummy variable as it is should there be any appropriate need to change. If you have any particular view on this, putting up a comment would be appreciable.