To interact or multiply dummy variables in Stata, you can use the factor variable notation, which allows you to specify interactions using # or ## symbols. For example, if you have a dummy variable for country (country_dummy) and a dummy variable for year (year_dummy), you can interact them by typing country_dummy#year_dummy in your regression command. This will create a new dummy variable for each combination of country and year.

Alternatively, you can use the tabulate command with the generate option to create new dummy variables for each interaction term. For example, if you type tabulate country_dummy year_dummy, generate(country_year), Stata will create a new set of dummy variables named country_year1, country_year2, etc., that correspond to each cell of the cross-tabulation table. Then you can include these new dummy variables in your regression command.

However, when you interact dummy variables, you need to be careful about collinearity issues, which may cause some interaction terms to be dropped from the regression. To avoid this problem, you may want to use the allbaselevels option or change the reference level of your dummy variables using the ib prefix.