Can someone comment on the last post?
Interaction of fixed effects

Regression donkey here, refereeing paper and wanting to make sure of the interpretation of the interaction of two fixed effects. With panel data (say households i in state s at time t), the interaction of the state and time fixed effects \gamma_{s}*\lambda_{t} (is NOT the same as a statetime fixed effect \delta_{st} , right? The authors claim that the interaction term allows stateyear specific shocks, and that seems wrong to me. Am I right? Thanks!
Fine for op to ask this cause sometimes you get thrown off but there is way too much confusion in this thread.
Not the same. \delta_{st} allows stateyear specific shocks. It's nonparametric in the stateyear space. Their specification forces the stateyear surface into a hyperbolic parabaloid.
It's likely they messed up notation  they really want to interact the indicator variables for state, time to create the statetime indicator. Then you get \delta_{st} estimates as fixed effects. Estimating the parameters of a hyperbolic paraboloid is harder so I'm sure if they did this it would be obvious from the rest of the paper.

This is the worst thread in ejmmr history. Stateyet fe is the same as interacted state and year for if and only if you have a valid instrument for the endogeneity.
Go read some wooldridge or you all will fail the market horribly.My mistake. I think Hawaii became a state because of good surfing, maybe you can use waves as an instrument?

I feel like I'm taking crazy pills over here. Both of the following should yield the same results:
y = x + i.state#i.year
or
egen thing = group(state year)
y = x + i.thingLook at the notation in the original post. \gamma_{s}*\lambda_{t} or alternatively \delta_{st} are parameters to be estimated. Not indicator variables. If they were the latter then they'd yield identical fixed effects estimates, so your statement i quoted above is correct of course.

And yes, it will control for statespecific year shocks. That's because the interaction of state and year allows for a different, flexible time effect, which varies by state, in each year. Take a single example of that combination, say Nevada in 1990. That interaction will take a value of 1 only when both state = Nevada and year = 1990 are true. Just like a statebyyear FE generated using the group command will take a value of 1 only for observations that correspond to Nevada in 1990.

Good point. I'm reading this as though they are indicator variables.
But if it is a strict value interaction, then it makes no sense at all, because it will assign some value to the rank of states (which makes no sense). Using Stata's standard for indicator (i) vs. continuous (c) variables:
i.state#i.year ––> statespecific annual effects, flexibly controls for common annual shocks at the state level
i.state#c.year ––> statespecific trends, controls for common trends at the state level
c.state#c.year ––> makes no friggin' sense, since it would assume that the state variable has some interpretable numeric value, and now we're in log(NAICS) territoryI feel like I'm taking crazy pills over here. Both of the following should yield the same results:
y = x + i.state#i.year
or
egen thing = group(state year)
y = x + i.thingLook at the notation in the original post. \gamma_{s}*\lambda_{t} or alternatively \delta_{st} are parameters to be estimated. Not indicator variables. If they were the latter then they'd yield identical fixed effects estimates, so your statement i quoted above is correct of course.

Good point. I'm reading this as though they are indicator variables.
But if it is a strict value interaction, then it makes no sense at all, because it will assign some value to the rank of states (which makes no sense). Using Stata's standard for indicator (i) vs. continuous (c) variables:
i.state#i.year ––> statespecific annual effects, flexibly controls for common annual shocks at the state level
i.state#c.year ––> statespecific trends, controls for common trends at the state level
c.state#c.year ––> makes no friggin' sense, since it would assume that the state variable has some interpretable numeric value, and now we're in log(NAICS) territoryI feel like I'm taking crazy pills over here. Both of the following should yield the same results:
y = x + i.state#i.year
or
egen thing = group(state year)
y = x + i.thingLook at the notation in the original post. \gamma_{s}*\lambda_{t} or alternatively \delta_{st} are parameters to be estimated. Not indicator variables. If they were the latter then they'd yield identical fixed effects estimates, so your statement i quoted above is correct of course.
Haha not quite that bad. The states wouldn't be ordered arbitrarily, they would be ranked by which has the highest vs lowest \gamma. Same with years  you're interacting a fixed effect for each year, not the numeric value of the year. So you're fitting state*year onto the surface of a hyperbolic parabaloid y=\delta*\lambda. State identities and years would be arranged in unpredictable ways along the axes, since the axes are 'fixed effect' values associated with state and year. Whichn't make any sense to me still, but if i took some shrooms maybe i could come up with something.

Third year grad student here trying to understand twoway FE.
So suppose we have firmstateyear level data (denoted y_{fst}) and there are multiple firms within a stateyear. Then including stateyear FE (group(state year) or i.state#i.year in Stata) nonparametrically controls for stateyear shocks. That is we control for state level heterogeneity that varies by year (separate intercept for (state1, year1) and (state1, year2)) and also allows year effects to vary by state (separate intercept for (state1, year1) and (state2, year1)). So the variation left over to identify the remaining regression parameters is from firms within stateyear?
Someone clarify whether I am on the right track. Also given our data environment, would stateyear FE be generally preferred over state, year FE entering separately?