State by Year Fixed Effects and Annual State Controls

[Trevor Andrew]

In my econometric model the identifying variation is at the state, year, and factory level. When I include state (i.state) fixed effects, year (i.year) fixed effects, state by year fixed effects (i.state#i.year), and state-level controls that change over time (e.g. state unemployment rate), stata does not drop unemployment rate due to collinearity. However I thought that state-by-year fixed effects perfectly absorb state-level controls that change over time. Am I doing something wrong coding wise or am I thinking wrong about the relationship between state-by-year fixed effects and state-level controls that change over time?

[Andrew Musau]

You do not show your command and output, so I am just speculating here. If you include these fixed effects as indicators in the regression, Stata probably drops one indicator instead of the state unemployment rate variable. But the fact that you see a coefficient on the state unemployment rate does not mean that the coefficient is identified. Two ways of seeing this are:

1. to change the base categories of each of the indicators and check whether the coefficient on the state unemployment rate changes.
2. install reghdfe (SSC) and absorb all the indicators, leaving out the state unemployment rate variable and to note that it is omitted due to collinearity.

If neither of these happens, then you are mistaken in believing that the variable is invariant within state-year. To check this, you can

gen stateyear= c.state#c.year
xtset stateyear
xtsum state_unemployment_var

and check whether the within standard deviation is 0 (meaning that it is invariant within state-year).

[Trevor Andrew]

Andrew Musau thanks! Method 1, 2, and 3 worked perfectly. I should have added the output. The output shows that stata drops the interaction between the last state and year. It's good to know that stata randomly drops variables in case of collinearity.