Hi all – I’ve put together a little Heckman selection type model. It seems to run OK, but in simulation I’m finding the correlation parameter rho is biased towards 1. @bgoodri or @jonah (or others) might have some ideas on what to do. The Stan code: // saved as heckman_correction.stan functions {…

Sorry, yes that is what I meant – your preferred solution in the case of cov(X,e) ≠ 0 and a possibly invalid Z. Valid external instruments are a rare animal. Swamy claims that it is simply impossible to find one (I’m not sure if I buy that extreme view… I would say “extremely difficult”): Swamy, P…

Sorry for bumping this topic, but this type of model has been discussed a few times over the past years and I liked this implementation by @James_Savage . As far as I can see this initial issue was not really addressed here (“bias” in rho), so if someone digs this up in the future this might be help…

Hey @Max_Mantei – have you tried replicating the simulation above with your change? (Sorry, don’t have time to dive back into this right now).

Hey, I didn’t systematically test this. However, it seems that the second parametrization generally recovers lower values of rho. This comes at the cost that it doesn’t sample that well (also, I think that \alpha_1 +Z\gamma should go into the inverse Mills ration, and not p, right? This also leads t…

Max, rtrangucci’s model above addresses the bias problem. In simulations I have run, it recovers all the parameters very well with great coverage properties and I didn’t notice bias in rho. If you spot any issues with rtrangucci’s model though please update me/us as I am about to use it for a paper …

Just somewhat related, but I’m working with a similar (though more simple) model, and I found that identification/reliability improved considerably once I had covariates that could predict the probabilities. Might consider adding that to the simulation to see if it makes a difference.

Hi Rachael! I think everything @rtrangucci posts is correct. And yes, as far as I can see the problem I mentioned is addressed in his approach (in a quite elegant way). Good luck with your paper! Max

@bgoodri Two years later and a search of the forum turned up this post. I’d be curious to know if there are further insights at this point, as the use of the inverse Mills ratio seems highly variable across fields and applications.

Just adding a bump here. I am excited to see the extension of these econometric models into Stan.

Heckman selection model code + simulation

Modeling

James_Savage May 7, 2021, 6:14pm 31

In any case, I tagged you in completely the wrong old thread–clearly projected to the same node in my brain by the presence of @rtrangucci

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Heckman selection model code + simulation

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