Significance of a variable - Regression Model alternatives I am looking at cross-sectional data. I have a dependent variable and a set of independent variables. 
Specifically, I want to assess whether a binary variable has a significant influence on the dependent variable. 
The typical approach would be to just do this via constructing and estimating a cross-sectional regression model. But are there valid alternative approaches?
 A: Actually regression analysis is generally not a good approach to say anything about influence. It is never free of omitted variable problem. Regression analysis might tell only about correlation, and due to your interpretation and argumentation is wether correlation is enough argument for causality.
If you are really looking to tell something about influence, what you are looking for is causal inference and methods capable of saying something about causality.

Here are some ideas of what you can do, when your variable of interest is binary:


*

*Maybe your binary variable was randomly assigned by you, and what you run is in fact an experiment - you do not need any regression analysis there. Just simple mean/median comparison.

*Sometimes, variable was not randomly assigned by you, but you can insist, that it was randomly assigned by nature. If possible you should run some placebo tests, and proceed as before.

*If none of the above is valid, you can run simple regression and make sure, that you included every possible variable, that correlates with both your variable of interest and the outcome (confounding factors). Often it is the best you can do.

*Maybe you can find an instrumental variable. Sometimes, rather with lots of luck, all your problems may just disappear and 2SLS solves everything.

*You can try matching methods. This depend on the setting. Sometimes it is possible to use something like spatial regression discontinuity design. PSM is another try, but as simple regression it does suffer omitted variable problem, when you do not fully know the selection process of your variable (CIA assumption violated).

*If all you could do so far was regression, you should at least try to extend your data with more time periods. At least two points of time allow to run Difference-in-Differences (DD) method. Panels are often even better, and with use of past values as an instrument you can insist on desired influence.
