I have panel data where firms disappear from failure and mergers. Conditional on existing as a stand alone firm, I observe all firms. However, I am differencing two periods (Late - Early), and the probability of being in the second period partly depends on X. I am interested in: $$ y_{late, i} - y_{early, i} = \beta_0 + \beta_1 * (x_{late, i} - x_{early, i}) + \epsilon_i $$

I am concerned about the selection bias biasing my results. My intuition is that this is a special case of sample selection, and therefore that if the disappearance is randomly done or determined solely by the value of $x$ that the resulting estimates are unbiased. Alternatively, if the sample is determined by the value of $y$ then the resulting estimates are biased.

I believe I am safe here because in my setting, censoring is driven by $x$ and little based on $y$.

Are there special concerns due to the panel setting or the use of differencing? Are there key references in this area for dealing with this issue? I couldn't find anything specific to the panel setting in Cameron and Trivedi (2005).


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