Can this selection issue (for multiple years) be addressed by the Heckman model?

[Kailin Gao]

Dear Statalists,
I collected data from an online platform in 2018 (platform data hereafter). Members need to pay an annual fee to remain at the platform. The platform data show how long the firm has been on the platform, e.g. from 1 to 18 years. I matched the platform data with firm census data from 2000-2016 (the latest census I can have is from the year 2016). So there are two selection issues when using the matched data:
1) Firms that exit entirely from the market, or simply exit from the online platform before 2018 won't be observed in the platform data. I only observe platform survivors.
2) Firms established from 2017-2018 won't be observed in the matched data.

These two selection issues are a little complicated. I am not sure whether it can be solved by the Heckman selection model as the selection is for multiple years. Any suggestions would be appreciated!
Thanks,
Kailin

[Maxence Morlet]

Suppose you measure an outcome only if the firm has paid access to the platform, and you have data on variables that may predict whether a firm would pay in order to access said platform. In this case, a Heckman model would be very useful (see here for an example of an application of the Heckman model: http://repec.business.uzh.ch/RePEc/i...5_lhwpaper.pdf).

Your second issue pertains to censored data, where we do not know the true value of a variable. This would lead to the use of a tobit model,

Your first issue could be addressed by competing risks model to predict market exit (see Thomas, 1996 concerning competing risks models).

In any case, OLS here is likely to be biased so I would not recommend it if you're after any form of causal inference.

[Kailin Gao]

Suppose you measure an outcome only if the firm has paid access to the platform, and you have data on variables that may predict whether a firm would pay in order to access said platform. In this case, a Heckman model would be very useful (see here for an example of an application of the Heckman model: http://repec.business.uzh.ch/RePEc/i...5_lhwpaper.pdf).

Your second issue pertains to censored data, where we do not know the true value of a variable. This would lead to the use of a tobit model,

Your first issue could be addressed by competing risks model to predict market exit (see Thomas, 1996 concerning competing risks models).

In any case, OLS here is likely to be biased so I would not recommend it if you're after any form of causal inference.

Thanks a lot Maxence! Very clear and helpful comments. Let me think about it.
Kailin