using lasso to test heterogeneous policy effects

[Karen Arulsamy]

Hi,

I am studying the effect of a policy reform on the outcomes of individuals with and without poor mental health. To do this, I regress the outcome on mental health + post policy period + mental health*post policy period + controls. There are 13 control variables that capture individual level characteristics. The interaction term captures the effect of the policy for those with poor mental health.

Then, I would like to compare the differential effect of the policy across mental health and the control variables via post policy*characteristic interaction terms. Since there are lots of variables which could lead to the multiple hypothesis testing issue, I would like to use lasso to do this. The idea is that lasso selects the interaction variables that are most relevant in predicting the outcome and from there, I can compare the effects of the policy across the remaining variables i.e. the coefficients on the interaction variables.

Can I get some advice on :
1) Whether the base lasso (lasso2) is sufficient?
2) Whether I should use cross-validation, AIC, BIC or EBIC in implementing the lasso procedure in this case?

Many thanks
Karen

[George Ford]

search telasso

[Jeff Wooldridge]

telasso allows you to estimate ATE and ATET with treatment effect heterogeneity, but it doesn't allow you to estimate how these TEs change with the covariates. How much data do you have? If the sample size is not small, it's not a big deal to just use basic regression adjustment by interacting the treatment with the 13 variables and see which ones seem to matter. You can't use teffects because, like with telasso, this only reports the ATE or ATET. But it's easy to do it directly with regress.

[Karen Arulsamy]

Hi Jeff,
Many thanks for responding to my question. The regressions are run separately for male and female respondents so I have 22,845 observations for males and 20,592 observations for females.

[Jeff Wooldridge]

I don't think there's any need to use lasso in this case. You can estimate the separate equations for males and females and include 13 interactions with the three indicators. This looks like a difference-in-differences design. Is it panel data?