Hi all,

I have read a few threads regarding this topic (e.g. https://www.statalist.org/forums/for...uous-variables) but have not yet found an answer to my question. Apologies if the identical question has already been answered.

I have a count dependent variable (Y) (linear TWFE results are shown, but marginal effects from Poisson are virtually identical), which I have regressed on two continuous variables (X1 and X2) and their interaction.

The summary statistics of the variables are:

Code:
    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
  Y |    373,763    .1933016    2.363418          0        502
X1 |    373,763    .5695304    .6594848          0      4.364
X2 |    373,763   -2246.553     773.906   -3651.53    316.896
These are the results:

Code:
HDFE Linear regression                            Number of obs   =    373,763
Absorbing 3 HDFE groups                           F( 141,   7317) =    1955.95
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.0578
                                                  Adj R-squared   =     0.0292
                                                  Within R-sq.    =     0.0016
Number of clusters (token1)  =      7,318         Root MSE        =     2.3286

                                                       (Std. err. adjusted for 7,318 clusters in ID)
--------------------------------------------------------------------------------------------------------
                                       |               Robust
                            Y | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------------------------------+----------------------------------------------------------------
                        X1 |  -.5015123   .1355351    -3.70   0.000    -.7672003   -.2358244
                                       |
c.X1#c.X2 |  -.0002419   .0000586    -4.13   0.000    -.0003567    -.000127

//The coefficient on X2 alone is perfectly collinear with the fixed-effects
I am fully aware that the economic significance of a coefficient depends on the field, research question, etc. However, what is the methodology / logic to assess the economic significance of an interaction term between two continuous variables?

For instance, one often compares the magntiude of the coefficient on a dummy variable to the mean of the dependent variable to assess economic significance, and whether the effect is large enough to be "interesting". Similarly, what would one compare the coefficient on c.X1#c.X2 to in order to assess its magnitude?

Please let me know if my question is unclear, I would happy to rephrase it.