With panel data we can control for entry exit decisions of firms while estimating their TFP. However, in case of developing countries often data is just cross sectional. Endogeneity bias can be controlled using IV method. However I am not sure how to control for selectivity bias.
Please refer to the article
"Internet Appendix for Firm Level Productivity, Risk, and Return"
by
Ayse Imrohoroglu and Selale Tuzel
at
http://www-bcf.usc.edu/~tuzel/TFP_InternetAppendix_July8.pdf
Syed -
This is not an application with which I am really familiar, but I wonder if perhaps you may have some kind of quantitative data available on every member of the population which might be considered as a measure of size? If you are collecting quantitative data, and were trying to avoid bias and generally improve "representativeness" by say, taking a stratified random sample perhaps, or other such random design (strata often being very useful for either design based or model based methods), you could perhaps use auxuliary/regressor/size data to pick a more 'balanced' sample, with respect to that size measure. [Estimated variance of prediction errors could be helpful. Remaining estimation bias would still impact the 'calculation' of the estimated variances of the prediction errors through inflated sigma.]
[Sometimes, with firms, for estimating totals, IF that is of interest, one may want to concentrate on the largest ones, keeping all influences on total errors in mind.]
If you are not able to obtain either a random (preferably stratified) sample, nor a reasonably balanced (by auxiliary variable size ... preferably stratified) sample for your regression, but are simply 'stuck' with available data to input to your regression model (which I assume you are using), then you can still study where you are missing 'representativeness,' by using such a size measure, to help you interpret possible impacts. Perhaps you could consider poststratification by size.
I assume that you are looking at regression modeling anyway, and are just trying to guard against model failure.
But I am not familiar with this area of application (TFP), so I took a look at the internet, and found these lecture notes, which looked promising:
http://www.soderbom.net/lecture15final.pdf
The first "topic" in those notes, by Mans Soderbom, is "How to estimate regressions if your sample
is not random, in which case there may be sample selection bias...." On page 3, he says that sample selection bias can be considered a special case of endogeneity bias, so I'm not sure that this is what you are trying to investigate. Also, not looking further at the attachment, I wonder if perhaps it might get into the use of information that you do not have. I don't know. But I thought you might want to look at it. It appears extensive and might have a reference or two of interest.
Perhaps I have misunderstood your question ... but at least I learned a little by taking a moment to look into this. :-)
Best wishes - Jim.
Maybe you can try tu build clusters of interest that could have the selection bias and apply dummy variables to these clusters. These dummy variables could mitigate the selection bias in the estimators. Best wishes,
Greg
How about doing something similar as advised by Wooldridge here:
http://www.statalist.org/forums/forum/general-stata-discussion/general/1295287-heckman-sample-selection-and-instrumental-variable-iv-or-simultaneous-equations-model
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