1
$\begingroup$

I have a problem with my co-author, we do not agree on the inerpretation of the regression coeffcients. In our regression (part of a more complicated model, which does not matter here) we defined the dependent variable as log difference, that is, ln(Gt) - ln(Gt-1), where G are local investment. The most relevant independent variable is in level (St, surcharge of a tax). We are struggling with the interpretation of the regression coefficient, beta, on St. In my opinion, an increase in St of one unit leads t a beta percentage points increase in G; while he interprets it in percentage terms.

Could help us?

$\endgroup$
3
$\begingroup$

You have marginally (excluding other variables except the intercept) $$ \log \left(\frac{G_t}{G_{t-1}}\right) = \beta \ \cdot \mathrm{Surcharge} + C $$ meaning

$$ G_t = G_{t-1} \cdot \exp \left(\beta \ \cdot \mathrm{Surcharge}\right) \cdot e^C $$

Here $e^C$ has the interpretation of a `base rate' of growth. A marginal unit increase in $\mathrm{Surcharge}$ yields a multiplication by $e^\beta$. You can interpret this as a $e^\beta$-percent growth (or decrease, if $e^\beta$ < 1) since the last measured value $G_{t-1}$, after the base rate has been applied. For example, an estimated $\hat{\beta} = .5$ would mean the previous value $G_{t-1}$ is first multiplied by the basal rate $e^C$, and then is additionally multiplied by $e^{\hat{\beta}} \simeq 1.648$, a $165\%$ growth compared to the base-rate growth (or a $65\%$ increase with respect to basal growth).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.