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I recently got a comment that I should use dynamic panel data model instead of a static one because my outcome is likely to be serially correlated. I guess it makes sense for my application, but it also got me thinking that this criticism is probably valid for virtually all economic outcomes observed in a panel setting. Consider demand, supply, unemployment, income, education, growth, inflation, interest rates, debt, bond prices, productivity etc. For all these variables, I would intuitively say that the status in the previous period is among the most important determinants of the realizations in the current period.

So, in practice how do we decide between a static and a dynamic panel specification?

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The issue OP raises has always bothered me. Now I think it all depends on the purpose of the study and whether we want to control for $y_{it-1}$ or not. There are examples against dynamic models.

As one example, suppose that we want to measure how much a collusion increased the price (damage estimation). Do we want to include $\ln p_{it-1}$ in that case? I don't think so, because $p_{it-1}$ can also be affected by the collusion and the lagged dependent variable would eat up most of the collusion effect. Most treatment effects will be similar.

As another example, suppose that we want to determine how poverty is related to observed characteristics (by means of cross-individual comparison [BE] or temporal comparison [FE] or both [RE or POLS]). Do we want to control for last year's income in the equation for this year's income? I wouldn't do it. My goal is to explain how the observed characteristics (not previous income) determine current income. I don't want to control for $y_{it-1}$, and dynamic models would be inappropriate.

Above are two examples, and I believe there are many others.

BTW, I would like to add that serial correlation in $e_{it}$ does not necessarily suggest a dynamic model. Correct specification of a static model does not require serial uncorrelatedness in $e_{it}$. A static model can be perfectly well specified even when $e_{it}$ is serially correlated as long as the regressors (or the instruments) are strictly exogenous with respect to $(e_{i1}, \ldots, e_{iT})$, the idiosyncratic errors.

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