Really interesting and useful thread re fixed vs random effects in ecology vs econ. This is something that I’ve focused on a lot over the past 5 years and it’s the overwhelming focus of my courses at @ICPSRSummer and #GSERM and I wanted to expand a bit (thread 1/)
There’s a fundamental difference in how econ deals with clustered/multilevel data and how most other fields do stemming from early intro of ANOVA into the field in the 1960s panel data 2/
Difference stems from misunderstandings of FE and RE, the nature of the Hausman test, the kinds of short panel data that economists tend to have, and relative ease of FE 3/
See Nerlove’s essay researchgate.net/publication/22… as well as biostat.umn.edu/~hodges/PubH84… and agfda.userweb.mwn.de/ALD_2015/downl… for more 4/
Econ historically argues that you can only look at the within group (time variant) effects generally and that between group effects are contaminating (biasing) within group betas 5/
This view was later retconned into a broader causal inference framework typified by Angrist & Pischke press.princeton.edu/titles/8769.ht… whereby within group-effects are “causal” and is the central way that it is framed in modern econ 6/
The Hausman test (1978) is one of several ways to test for this basic problem (also Mundlak test, joint F test, or LR test on random slopes) and shows if the effect of X on Y varies across groups 7/
Violation of the Hausman test means that effect of X on Y varies across groups. This variation is either cluster confounding (mismeasurement of 2 levels as 1) or a moderating effect of level 1 by level 2. 8/
Separating within and between group-effects is important outside of primarily predictive modeling either because you want to properly model DGP or you want to test individual effects in isolation (causal modeling) 9/
Traditionally, panel data econometrics has had two routes to solving this problem. FE where you cut out all between group variation via dummies or multilevel where you properly model within and between effects separately 10/
Most applied econ use FE for historical reasons w panel data econometricians often alternating between FE and multilevel (see Mundlak, Hausman, Greene, Hsiao, Nerlove) but rarely call what they are doing multilevel (see Hausman-Taylor, Mundlak devices, correlated RE models) 11/
Testing a between group effect in isolation a la experimental controls with FE is often very useful. I teach that it can be used as a benchmark for a structural approach modeling full DGP. 12/
Rotating through FE models (for within effects) and multilevel models (for a DGP approximation) is often crucial to know what you are doing 13/
There's often a bit of a confounding problem in language on causal inference and FE v RE. Causal inference is a theoretical interpretation of an effect given a design with justifiable leverage to make causal claims. 14/
The within-group estimates from a FE model do not automatically equate to actual causal inference! You are making an estimate of the common portion of an effect within sample that doesn’t vary over groups 15/
This ignores dynamics and joint causation problems need to be studied if you REALLY want to make causal inferences imai.princeton.edu/research/files… mattblackwell.org/files/papers/c… 16/
It ignores the fact that the pure within effect may not ever exist in isolation in reality and thus is always swamped in practice 17/
An isolated within group effect can be insignificant because the effect is + in some groups and – in others as a function of a group-level interaction 18/
It might not be significant because not much within group variance in X in data even though X definitely does matter in the DGP 19/
The FE approach is incredibly useful within context but it is often presented devoid of all context in econ 20/
Also in practice we don’t have to choose FE or RE agfda.userweb.mwn.de/ALD_2015/downl… and papers by Bell and Jones cambridge.org/core/journals/… 21/
There are also difficulties using it in nonlinear models because dummies break link functions see people.stern.nyu.edu/wgreene/nonlin… 22/
Econ solution to this kind of problem is to just use linear approximation but you have to be willing to talk about average and not local effects 23/
This also badly biases standard random effects (too small) and so makes direct comparison with multilevel models harder 24/
Wow threads are a lot of work...
I'm at'ing people who I've seen talk about parts of this or I cited here. @LauraEllenDee @bolkerb @polesasunder @AndrewJDBell @jebyrnes @jim_savage_ @economeager @matt_blackwell @marcfbellemare @CookieSci
I guess i should also you ahead and post a link to my @ICPSRSummer syllabus because there's a huge reading list on it icpsr.umich.edu/icpsrweb/sumpr…
