Last updated on November 2, 2025
My paper with Dan Millimet titled “On the (Mis) Use of the Fixed Effects Estimator” has been accepted and is now forthcoming at the Oxford Bulletin of Economics and Statistics. If you want a link to a .pdf of the accepted version of the paper or to a Stata .do file showing you how to use the alternative estimators we discuss in the paper, scroll all the way to the end of this post. If you want a bit of storytelling about how this paper came about, and what it does, read on.
I forget when Dan and I first discussed this, but this paper was born out of the two of us connecting and bonding over social media during the pandemic. Since about 2014, I had had in mind the idea that if you have, say, 10 years worth of longitudinal data on workers, why was the default way to deal with that to use one individual fixed effect per worker? Why not two fixed effects per worker–one for years 1 to 5, and one for years 6 to 10? Why not more than two? What is the optimal number of fixed effects per unit of observation when you have a “long” panel? At some point, Dan and I discussed this and realized we had both been thinking about the same thing, and so we set to work on this paper. (It’s really Dan’s paper, I was just along for the ride. And while Dan likes to joke that he’s not really an econometrician, he just plays one on TV, I think that’s just humility speaking.)
This is especially important for two reasons. First, if you have only a handful of observations over time per unit of observation (say, you follow workers over two, maybe three years), then yes, you can probably argue that individual fixed effects do a good job of purging the error term of unobserved heterogeneity that is correlated with the covariates because said heterogeneity is arguably time-invariant given that individuals do not change that much over the span of two or three years.
But we are not the 1990s anymore: We now have access to much longer panel data sets, and as one adds additional observations over time to a panel data set, there is a lot less that remains time-invariant, and fixed effects become much less useful for identification. In the limit, as the number of time periods goes to infinity, the fixed effects estimator does no better than a pooled OLS. As we note both in this article and in our article earlier this year in the Journal of Economic Perspectives on Yair Mundlak and the fixed effects estimator, this is something that Mundlak himself recognized in his seminal 1961 article in the Journal of Farm Economics (now the American Journal of Agricultural Economics), in which he brought to economics the first application of the fixed effects estimator.
So far so good. But this brings us to the second problem: Why did the fixed effects estimator become the de facto way to deal with heterogeneity in panel data among the reduced-form applied micro crowd, a crowd that is notoriously picky about and likely to cry foul at identification, especially when there are much better options (e.g., first differences) to account for the fact that, in this sad Heraclitean world of ours, although an individual today might be comparable to herself last year, that same individual today is much less likely to be comparable to herself ten years ago?
For whatever it is worth, this is a particularly egregious problem in political science, where scholars often rely on cross-country fixed effects over periods of time in excess of 25 years. But what does remain constant over time for an entire country? Climate and topography can change. Cultures certainly change as well. Even a country’s borders can change in 25 years! So if you always were skeptical of cross-country longitudinal studies but could never quite put your finger on why, here is your huckleberry.
(The funny thing is that when we submitted this to a leading political science journal, we were told by the editor, with my own emphasis: “[W]e feel that the contribution is not strong enough for a top general interest journal … [w]e also feel that the research design and empirical strategy remain underdeveloped.” I am no political scientist, so I cannot assess how valid the former statement is. But when I wrote to the editor in charge about the latter statement, asking whether we were talking about the same paper since our paper is not your usual application to a research question, and thus does not really have a research design or identification strategy, I never heard back from them…)
In this article, we show how the fixed effects estimator can (and often does) break down with ever-longer panels, and we discuss alternative (and often better) means of dealing with heterogeneity in panel data including first differences, of course, but also interactive fixed effects as well as novel rolling estimators. We then illustrate our point with Monte Carlo simulations and by replicating four sets of results published in leading journals—with only one such set of results turning out to be robust.
Here is the accepted version, and here is the abstract:
Data that span multiple units and time periods allow controlling for time-invariant heterogeneity correlated with the covariates. While researchers can do this in different ways, the fixed effects estimator—also known as the within estimator, and equivalent to the least squares dummy variable approach—has become the default choice. But when time-invariant attributes are not invariant to time—that is, when they are not invariant to the length of the panel—the fixed effects estimator can be considerably biased as researchers incorporate additional time periods. We show that, in finite samples, first-differencing and novel rolling estimators can offer researchers a practical alternative to the fixed effects estimator in this case. These estimators are simple to implement and can significantly reduce bias relative to the fixed effects estimator under certain data-generating processes. Most importantly, researchers should always provide results from multiple estimators. We illustrate this with simulations and four replications.
If you would like to use the alternative estimators to fixed effects we discuss in the paper, you can find a Stata template in this .zip file.