Estimating treatment effects on multiple outcomes

[ghoetker]

Hello all,

I hope someone can point me to resources (within or beyond the Statasphere) relevant to the following. I am interested in the effect of a treatment T on two outcomes, Y and Z. Thus,

Y =   aX + bT + cXT + u
Z =   dX + fT + gXT + v

T = 1(hX + kZ + e > 0), estimated by logit or probit.

I am not willing to assume that corr(e, u) = corr(e, v) = 0. The issue of whether corr(u, v) = 0 or not is a headache for another day at this point.

To make this concrete, let Y be income, Z be training opportunities taken and T be union membership. Let everything be continuous and normally distributed for simplicity.

I'm stuck on how to estimate the treatment effect for union membership here. Beyond the question of which command to use, my conceptual hangup is that a person only gets to choose one union status, but that choice is potentially correlated with both income and training opportunities given (non)-membership in a union. Because of that, modeling the two outcomes separately seems problematic.

I'm more comfortable (perhaps wrongly) with how I'd handle this if I could assume conditional independence. I think that I could apply any of the teffects commands to Y and Z separately.

Any suggestions would be very much appreciated. Thank you.

Glenn

[Phil Bromiley]

You didn't get a quick answer so let me offer my 2 cents worth.

I would think you would be fine if you include T and XT in the selection equation. Then the treatment controls for the potential influence of those factors on the treatment which is what you're worried about. You could then estimate this as two separate heckman estimates which would implicitly let the errors of the two outcome questions correlate. Another way to do this would probably be a selection model in GSEM.

[ghoetker]

Thank you, Phil, for the thoughts. I'll give them a try!