I have a conceptual question in terms of econometrics.

I understand for example that the primary goal of econometrics is to use estimated parameters to calculate the average change in the dependent variable conditional upon a unit change in the independent/explanatory variable(s).

However, may I ask if this 'unit change' is represented by the standard deviation, or in fact is representative of a 1% change?

Any feedback/discussion on this would be appreciated,



You can use summary statistics to compare the one unit change to the standard deviation and could say that it represents a 1, 1.2 2 etc. standard deviation change. For example, if in the regular form: $$y_i=\beta_{0}+\beta_{1}x_i+u_i$$ say $\beta_{1}=6$ and from your summary statistics, the standard deviation of $y$ is 3, you could in turn explain the coefficient as: "A one unit change in $x$ is associated with a 2 standard deviation change in $y$, ceteris paribus".

To interpret the unit change as a 1% change, you can convert the coefficient to read it in terms of percents relative to the levels of $x$ and $y$ or, to much more convenience, you can run the model in log-log form: $$\log(y)_i=\beta_{0}+\beta_{1}\log(x)_{i}+u_i$$ In this form, $\beta_{1}$ is the percentage change in $y$ from a 1% change in $x$. Exactly what you are looking for! $$\beta_{1}=\frac{\%\Delta y}{\%\Delta x}$$ where the denominator is usually a 1% change.

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  • $\begingroup$ Thanks Brennan. Just need clarifcation on the matter - much appreciated. $\endgroup$ – Andrew Coyle Aug 29 '19 at 8:43
  • $\begingroup$ No problem! If you are satisfied with the answer please accept it as it helps get the site off of beta! $\endgroup$ – Brennan Aug 29 '19 at 23:20

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