Addressing Temporal Limitations in Panel Data Analysis: A Fixed Effects Regression Approach

[Maria Isabel]

I'm currently working with STATA on a panel data analysis using the xtreg command. My model is structured as follows: xtreg dependent_var independent_var _It*, fe i(cve) robust cluster(cve). I aim to incorporate control variables, X, to account for various characteristics that might influence my estimation. However, I face a challenge: the analysis covers the period from 2010 to 2020 (with dependent and independent variables available quarterly for all years), but my control variables, X, are only available for 2007.

Incorporating fixed effects causes these characteristics to be omitted since STATA does not take into account variables that are constant over time in a fixed effects model. One suggestion I received was to create an interaction term between X and the period, essentially X*Period, to introduce a trend for these variables over time. However, I'm unsure about how to implement this strategy effectively and whether it's a valid approach.

I would appreciate any advice on how to proceed with incorporating my control variables into the model, especially considering their limited temporal scope.

[Clyde Schechter]

I don't think this approach is sound unless there is a good reason to believe that this X variable really has an effect on your dependent variable that grows linearly with time over a long period of time (from 2007 to 2020). Things that work that way in the real world exist, but are pretty rare. The idea of doing this is especially disturbing since the one year for which X data are available is not even within the interval covered by your panel data. So you would be extrapolating--which is hazardous under the best of circumstances.

I would say that unless you can get contemporaneous data on X, you should just forget about it. If there is theoretical reason to believe that X would then be an important source of omitted variable bias, then I think you have to go back to square one and come up with a new plan or find a new data source.

[Maria Isabel]

I appreciate your insightful response greatly. I've discovered additional variables that are available at five-year intervals (2005, 2010, 2015, and 2020), and I'm curious if they could be incorporated into my analysis. If so, could you provide an example of the procedure to follow in Stata? Finding variables on a quarterly basis, which corresponds to the temporal resolution of my study, poses a significant challenge, as does securing annual data at the municipal level.

[Clyde Schechter]

The variables that you can get at 5 year intervals are probably workable. You will have to find a way to fill in the gaps to match the quarterly periodicity of your other data--how to do that depends on what the variable are and how they can best relate to your outcome variable. Perhaps linear interpolation, perhaps just applying the 2010 value to everything between 2010 and 2014, perhaps there is some other model for doing it. It really depends on what the variables are and what is known about their variation over time. It is much more of a substantive question than a statistical one.

You might also want to consider whether you really are gaining much with your quarterly data. Given that there are other important variables that are difficult to even get data on annually, you might be better off aggregating your existing quarterly data up to annual. Again whether one does that by means, or mins, or maxes, or medians, or something else, is a substantive question.

Once you have resolved these substantive issues, it will be possible to provide help with coding the solutions in Stata. You can post back then and set out your specific plan for harmonizing/synchronizing your data sets. You will also need to show examples from the data sets. The only really helpful way to do that is with the -dataex- command. If you are running version 18, 17, 16 or a fully updated version 15.1 or 14.2, -dataex- is already part of your official Stata installation. If not, run -ssc install dataex- to get it. Either way, run -help dataex- to read the simple instructions for using it. -dataex- will save you time; it is easier and quicker than typing out tables. It includes complete information about aspects of the data that are often critical to answering your question but cannot be seen from tabular displays or screenshots. It also makes it possible for those who want to help you to create a faithful representation of your example to try out their code, which in turn makes it more likely that their answer will actually work in your data.

[Maria Isabel]

Thank you very much for your guidance; I'll start working on it. Your assistance has been invaluable.

[Jeff Wooldridge]

I took the original suggestion to be to interact the period dummy variables with X. That’s actually a good strategy. In fact, that’s exactly what the new xthdidregress command does with time constant controls. It relaxes the parallel trends assumption. You can’t estimate the effect of X overall, but you can see if the effects change across t. So put in i.year#c.X and not c.year#c.X.

[Clyde Schechter]

Jeff Wooldridge I know we sometimes have conflicting viewpoints that reflect our disciplinary backgrounds. But I'm really puzzled by your advice in #6. What you are proposing is to estimate yearly shocks during the interval from 2010 to 2010 on the effect of a single value of something, whose own time evolution we have no information about at all, that was measured once in 2007. I can't see how that makes sense in any context. What am I missing here?

[Jeff Wooldridge]

Suppose X is unemployment in 2007, and an opportunity zone program rolls out starting in 2009 based on 2007 unemployment across census tracts. Both the probability of being a zone and the relationship between 2007 unemployment and later years can change over time. Putting in i.year#c.X solves the nonrandom assignment (selection) problem. I’m not interested in those coefficients. They’re controls. This is exactly what the latest in diff-in-diffs does.

[Clyde Schechter]

OK, that's a good example. Thanks.