Question

How do you interpret a regression coefficient, which has log differences as both independent and dependent variable.

For example, log(y_t+1)-log(y_t) = alpha+beta{log(x_t+1)-log(x_t)}+......

Is it “1 percent increase in the growth rate of x affects the growth rate of y by beta percent.”?

Answer 1

The standard interpretation of coefficients in a regression analysis is that a unit change in the independent variable results in the respective regression coefficient change in the expected value of the dependent variable while all the predictors are held constant.

Answer to question asked:

Interpretation of a log transformed variable is done as follows:

In instances where both the dependent variable and independent variable are log - transformed variables, the relationship is referred as elastic in econometrics and the coefficient of log X is referred to as elasticity.

In regression setting, we interpret the elasticity as the percent change in y (the dependent variable), while x (the independent variable) increases by 1%.

We interpret the coefficient as the percent increase in the dependent variable for every 1% increase in the independent variable.

For example:

in the case of

1% increase in the growth rate of x increases the growth rate of y by %.

In terms of effects of changes in X on Y (both unlogged):

(i) Multiplying X by e will multiply the expected value of Y by

(ii) To get the proportionate change in Y associated with a p% increase in X, calculate:

and take

.