Growth Rates

Growth Rate

The growth rate $g_t$$\large g_t$ of a variable $X$$\large X$ at time $t$$\large t$ is given by,

This means the ratio of consecutive terms is given by,

Growth Rate of Product

The growth rate $g_t$$\large g_t$ of the product of variables $X$$\large X$ and $Y$$\large Y$ at time $t$$\large t$ is given by,

Annualized Growth Rate

The annualized growth rate $g_t$$\large g_t$ of a variable $X$$\large X$ at time $t$$\large t$ is given by,

where $n$$\large n$ is the number of samples per year.

For monthly data, $n=12$$\large n = 12$.

For quarterly data, $n=4$$\large n = 4$.

Logarithm & Growth Rate

The growth rate $g_t$$\large g_t$ of a variable $X$$\large X$ at time $t$$\large t$ is related to the natural logarithm of the variable:

The growth rate $g_t$$\large g_t$ of the product of variables $X$$\large X$ and $Y$$\large Y$ at time $t$$\large t$ is related to the natural logarithm of the variable: