# 'One Unit Change in the Explanatory Variable'

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,

Best,

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.