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‘Metrics Monday: Combining Bits and Pieces of Likelihood to Study Behavior

I have mentioned a few times that there is an unspoken ontological order of things in applied work, wherein one first needs to take care of the problem of identification before one should worry about properly modeling the dependent variable’s data-generating process. In other words, before you obsess over whether you should estimate a Poisson or a negative binomial regression, your time is better spend thinking about whether the effect of your variable of interest on your dependent variable is properly identified.

This week, however, I wanted to move away from my usual focus on the identification of causal effects to look at the modeling of DGPs.

Let us take an example from the first article I ever published (and which, to this day, remains my most-cited article). In that article, my coauthor and I were interested in the marketing behavior of the households in our sample. In some time periods, some households happened to be net sellers (i.e., their sales exceeded their purchases), some households happened to be net buyers (i.e., their purchases exceeded their sales), and some households happened to be autarkic (i.e., their neither bought nor sold).

‘Metrics Monday: Fixed Effects, Random Effects, and (Lack of) External Validity

Very early mornings, before our entire households is awake, are when I get all of my professional reading done. Last Monday, I read a recent published paper in my discipline. I am remaining purposely vague about that paper, because the research question was interesting and the findings pretty useful; it’s just that the econometrics weren’t great.

Anyway, at some point the authors make the following argument:

  • Our random effects findings are almost identical to our fixed effects findings;
  • Random effects should be used with a random sample from a population of interest and fixed effects in the absence of such a random sample;
  • This means our (small, highly selected sample) is representative of the population of interest;
  • Thus, this means we can use findings from our (small, highly selected sample) to make inferences about the population as a whole.