In many empirical models within finance, one needs to decide whether to use variables as their levels or their changes. In this post, I briefly go over reasons why one may choose one versus the other.
The first consideration is the stationarity of the variables in question.
Specifically, one should avoid regressing levels on levels is when $y_t$ and $x_t$ are not stationary in the following model:
$$ y_t = a + bx_t + e_t $$
where $y_t = y_{t-1} + v_t$ and $x_t = x_{t-1} + w_t$ and $v_t, w_t$ are each IID normal.
In this case, we often have:
Cointegration is one possible way of handling spurious regression, widely used in the macroeconomics literature. In this case, it is safe to run an OLS regression.