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Given a balanced two-period panel data, with lets say 1000 observations on 500 individuals.

When you estimate a pooled OLS regression and first-differences regression is there a standard in the economics literature on how you should report number of observations.

It seems most natural for me to report 500 observations in the case of first-differences.

This might seem trivial. But better follow any standard if it exists.

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    $\begingroup$ I don't see how this could be reported as anything other than 500 observations. If you ran a fixed effects regression it would be 1,000 observations but would also have 500 more parameters. $\endgroup$ – BKay Mar 9 '17 at 16:33
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It is reasonable to show both observations and number of units of analysis. For instance, take this example of an article in the American Economic Review:

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There is the row Observations, and the row Countries. The latter is the unit of analysis. As the data is a longitudinal panel, there are multiple observations per country. As the panel is unbalanced, the number of observations is generally not a multiple of the number of countries (e.g. for Pooled OLS (column 1), $945/150=6.3$).

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It is conventional to report both the total number of observations (1000 in your case) and the number of groups (500 in your case). If you want or are allowed to report only one number as the number of observations, it is suitable to report 1000 for POLS because POLS doesn't mind the fact that it is a panel data set. For FD, it is slightly confusing to me to say that the number of observations is 500. I would probably ask again of the writer what 500 means.

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