# How to assess economic significance in a log-log OLS model?

I ran an OLS regression in log-log form and got statistical results (coefficients and their standard errors). How can I now assess whether these results are economically significant? I also calculated the usual descriptive statistics for the variables in the model (mean, median, minimum, maximum, standard deviation). Should I somehow relate the OLS results to the descriptive statistics, and if so, how?

A fictitious example for illustration

regression results:

Y = 4 + 5*X + u


descriptive statistics:

Variable     Min  Mean  Median   Max   standard deviation
Y           2.00  4.00    4.20   6.00  0.60
X           3.00  4.00    3.80   7.00  0.20


The ultimate question is: Is an effect of 5 economically significant? For example, would it possible to say that 5 is economically significant because it causes a change in Y that is more than 8 standard deviations? (coefficient on X / standard deviation of Y = 8.333)

• I say this is on-topic here. No, statisticians are not the ones to decide if economists should see $5$ as important, but the techniques to investigate that absolutely are within the purview of Cross Validated.
– Dave
May 21, 2022 at 15:32

Consider e.g., a simple linear regression in which $$Y$$ would refer to yearly income (in \$) and $$X$$ to years of schooling of the individuals in your sample. If the goal of your analysis was to identify variables that can be altered by individuals with the goal to increase income by at least $$1000$$ \$, a coefficient of $$5$$ would not be deemed economically "significant", since one would need to add $$200$$ additional years of schooling. If you knew that people had the possibility to do five more years of schooling, and the coefficient for $$X$$ would be $$250$$, one could argue that years of schooling are economically significant.