The first difference of the logarithm of $Y _ { t }$ equals
A) the first difference of Y .
B) the difference between the lead and the lag of Y .
C) approximately the growth rate of Y when the growth rate is small.
D) the growth rate of Y exactly.

Question

The first difference of the logarithm of $Y _ { t }$ equals
A) the first difference of  Y .
B) the difference between the lead and the lag of  Y .
C) approximately the growth rate of  Y  when the growth rate is small.
D) the growth rate of  Y  exactly.

Quizplus · Accepted Answer

The first difference of the logarithm of $Y_t$, $\log(Y_t) - \log(Y_{t-1})$, approximates the growth rate of $Y$ when the growth rate is small, due to the properties of logarithms and the fact that $\log(1 + x) \approx x$ for small $x$.

The First Difference of the Logarithm Of YtY _ { t }Yt​

The First Difference of the Logarithm Of $Y _ { t }$