Using The Log Where It Does Not
Econometrical analysis is heart of any economic research. It won’t be fare if I do not give a glimpse about Econometrics; basically, econometrics is a special form of statistical analysis completely dedicated to the growth of economic research and in some cases it is distinguishable from standard statistical mathematics. The regime of econometrics is vast and new approaches are adding on day by day. Econometrics have the capability to give us subtle but meaningful insights through its computing and analytical power.
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.