[Econometrics] Logarithmic Functional Forms In Linear Regression(Adv, Disadv)

^log(y) = ^β0 + ^β1*log(x1) + ^β2*X2

 

There are some advantages and disadvantages when we transform a linear regression function into a logarithmic functional form. When △DV per one unit IDV change is large, a logarithmic approximation is convenient to measure the change. We can estimate the percentage change of DV. 

 

Not only that, when y > 0, models using log(y) as the DV often satisfy the CLM assumptions more closely than models using the level of y. Strictly positive variables often have conditional distributions that are heteroskedastic or skewed. Another potential benefit of using logs is that taking the log of a variable often narrows its range. This is particularly beneficial when we measure large monetary values, such as firms' annual sales or baseball players' salaries. Narrowing the range of the DV and IDV can make OLS estimates less sensitive to outlying.

 

* There are some standard rules of thumb for taking logs.

- when a variable is a positive dollar amount, the log is often used. ex) wages, salaries, firm sales and firm market value

- population, the total number of employees, and school enrollment

- variables that are measured in years such as education, experience, tenure, age

- variables that are proportion or percent such as the unemployment rate, the participation rate

  -> in this case, we can interpret results with percentages point change.

 

One limitation of the log is that it cannot be used if a variable takes on zero or negative values. In cases where a variable y in nonnegative but can take on the value 0, log(1+y) is sometimes used. Technically, however, log(1+y) cannot be normally distributed. Another drawback of using log is that it is more difficult to predict the original variable. This model allows us to interpret log(y) not y.  

 

 

 

 

Resource : Jeffrey M. Woolderfige, "Introductory Econometrics : A Modern Approach 5th edition"