Treatment endogeneity without exclusion/instrumental variable

[Tanima Ahmed]

Dear Statalist,

My linear regression model has a continuous dependent variable, and an independent treatment variable (participated in the program=1 and 0 otherwise). I know my treatment variable is endogenous, because there is self selection in the program. However, given the one period cross sectional survey data, which was not designed for impact evaluation, I could not find any instrumental variable to model the selection process. After attempting to find an instrument several times, I am sure now I cannot find out to any exclusion / instrumental variable.

Without the exclusion/ instrumental variable, what methods are appropriate to deal with the self selection problem?
I know I can use heckman type correction, but my concern is:
1. Without exclusion variable how well the heckman type correction can solve the self selection bias?
2. Is there any other method that i can use?
3. If yes, how do I compare across the models and talk about which one is the better approach?

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

Many of these problems are simply not identified without an exogenous variable that influences treatment but not the outcome. In the old days, we taught a lot about how to figure out if a model is identified, although less is done now. Heckman and some treatment models are quite similar underneath. Some such models can be identified without an exogenous variable, but the identification is questionable depending for example on assumptions about differences in functional form.

[Attila Balogh]

The first step is to provide evidence on how the treatment group differs from the control group along the other covariates in your model. This will provide insight regarding selection on observable characteristics.

You may then employ matching methods to attempt moving towards the semblance of random assignment, provided that you have other covariates in your data.

Remember that OLS is still the best linear approximation to the conditional expectation function (Angrist and Pischke: Mostly Harmless Econometrics, 2009) and it will be a good benchmark in any case.