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Assume that there are two variables $x$ and $y$ and they both have trend.
For example,
(case 1) During covid-19, government spending($x$) and inflation($y$) are both increased
(case 2) A productive firm has high labor productivity($x$) and investment($y$)
and of course, they does not represent 100% of the following propositions
due to the self-selection problem:
(case 1) government spending increases prices
(case 2) investment increases labor productivity

When we use times series data we must control this endogeneity.
However if we use panel data this self-selection problem can be solved?
If it is true how it could be possible?

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1 Answer 1

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Panel data in of itself cannot solve this problem.

One way to see this is that there may be some omitted variable that influences both. So even if you observe countries/firms over time if there is an omitted variable it will probably co-move as well over time. Same reasoning holds across countries/firms.

One way to solve this and to estimate the true relationship is to come up with some instrument(z) for which an exclusion restriction holds, i.e. that it only influences y through x.

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  • $\begingroup$ Sorry it took some time to reply your answer. I think panel data analysis especially fixed effects model can fix self-selection problem if the bias caused by self-selection can be treated like a fixed effects term($u_i$). And from what I've looked up panel data analysis is the method which is used to deal with such problems. $\endgroup$
    – guest
    Commented Jan 2 at 14:58

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