Hi,

In many papers, the dependent variable is transformed by taking natural log. For instance, consider the following model:

Code:
log(Y) = α + β X1 + ε
I understand that the interpretation of β is the percentage change in Y for a given unit change in X. However, some papers comment on the direction of relationship between X and Y (and not Log (Y)) on the basis of sign of β.

Through a simple simulation exercise, I have found out that it may be erroneous to comment on the direction of relationship between Y and X on the basis of sign of β in the above equation. Specifically, the signs of Cov (X,Y) and Cov (X, Log (Y)) may be different.

Please let me know if my finding is correct.