TSCS and TWFE

[Piku Sarkhel]

Dear All:
I am analysing a panel of 152 countries over a period of 12 years. I intend to estimate the influence of x on an age standardized outcome (say disease burden) y over time. Initially I chose to estimate the model using TWFE (two way fixed effects ) .
I used xtreg y x yeardummies , fe .
However, I find that there are some problems with the TWFE (as cited in the literature) as it combines both TS and CS variations and this creates the problem of identification. My question is should TWFE pose a problem if we are looking at TSCS association between x and y? I mean if we are not hinting at causality ? If there's a problem what would be some alternative estimators that I can use .
Also what if I want to run the panel data model with only time fixed effects. I can't use the noconstant option with xtreg.
Any help in this regard would be greatly appreciated.

[Maxence Morlet]

Regarding your second question, if you want to remove the unit fixed effects (I wonder why but if you need to investigate something) exploit the FWL theorem and use a normal regression, specify the time fixed effects as dummies.

The identification assumption of TWFE is that, conditional on controls, time and unit fixed effects, the regressor of interest is uncorrelated with unobserved heterogeneity. In TWFE with e.g. states and time, you exploit state-by-time variation and you cannot have state-by-time fixed effects. Therefore you must assume that conditional on your fixed effects, your regressor of interest, which varies by state and time in my example, is conditionally uncorrelated with e.g. selective immigration across states that also changes with time, e.g. as employment opportunities evolve between states. This would be unobserved state-by-time heterogeneity.

In the classic TWFE, fixed effects wipe out all time-invariant unobserved heterogeneity, while time fixed effects ensure that time-varying common shocks are addressed. The variation that remains is across units and time.