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)

Statistical and economic significance are not the same concept. Broadly speaking, statistical significance in a regression tells you if a variable has an effect on the outcome variable (depending on the confidence level one defines). It does not matter what kind of data or model is used. On the contrary, economic "significance" depends on the context of your analysis.
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.
To wrap up, while statistical significance is clearly defined and gives you information about the statistical properties of your estimates, economic "significance" depends on the context and goal of your analysis. You need to define what you consider economically "significant" based on the research question at hand.
