Collin command gives you the option compute Eigenvalues and condition index without a constant (using the [, corr] option).
When assessing for multicollinearity between my independent variable should the "constant" variable be dropped?
As the test for multicollinearity is made between the independent variables in order to measure the relationship between them and how much it affects your regression model, I would think the results should be the same. I found this web page where they kinda address your question." The collin command displays several different measures of collinearity. For example, we can test for collinearity among the variables we used in the two examples above. Note that the collin command does not need to be run in connection with a regress command, unlike the vif command which follows a regress command. Also note that only predictor (independent) variables are used with the collin command."
Source: https://stats.idre.ucla.edu/stata/webbooks/reg/chapter2/stata-webbooksregressionwith-statachapter-2-regression-diagnostics/
Hope this helps.
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