I'm looking at social origin effect on occupational attainment (in terms of ISEI) in three different countries (Sweden, Germany and the UK). I have run three individual regressions and found variations in the effect but want to test whether this variation is statistically significant.

A study of the same issue in 12 European countries - by Christina Iannelli (2002) - uses a regression model which include all the countries as dummy variables. Here the effect of the country variables are statistically significant and the study concludes that there is a 'substantial' difference between the countries but is this a valid way to do it? I mean, does this test whether the effect of social origin varies significantly between the countries? Or should I include an interaction term between country and social origin?

Moreover, a similar study (Bernardi and Ballarino 2016) compare the same effect in 14 European countries (done by different scholars and datasets in each country) and compare the results without testing whether the country variance is statistically significant. The study emphasizes the 'common patterns' more than the differences, but can one compare country differences without testing whether these are significant?