Specifying multiple fixed effects in felm - r

Question

I am trying to estimate a following model:
y_{it} = \alpha + \beta x_{it}+\eta_i+\gamma_t+group_i\times \eta_t+\epsilon_{it}
#Clear everything and load the needed libraries:
rm(list=ls())
library(data.table)
#Define nr of individuals:
nr_ind<-1000
#Define time periods
nr_time<-5
#Define groups:
nr_groups<-2
#Create individual indicators:
pers_id<-rep(1:nr_ind,each = nr_time)
time_id<-rep(1:nr_time,nr_ind)
data<-data.table(pers_id=pers_id,time_id=time_id)
#Create time varying regressor:
data<-data[,x:=rnorm(1,0.01),by=c("pers_id","time_id")]
#Create time effect:
data<-data[,mean_x_time:=3*mean(x),by=c("time_id")]
#Create fixed effect:
data<-data[,mean_x_person:=1.5*mean(x),by=c("pers_id")]
#Create group varying time effect:
data_group<-data.table(pers_id=1:nr_ind,group=sample(c("M","F"),nr_ind,replace=TRUE))
data<-merge(data,data_group,by="pers_id",all.x=TRUE)
data<-data[,group_effect:=ifelse(group=="M",mean_x_time+mean_x_time^2+0.03,0)]
#Define the model:
data$y<-0.1+0.3*data$x+data$mean_x_person+data$mean_x_time+data$group_effect+rnorm(dim(data)[1])
data<-data[,time_id:=as.factor(time_id)]
data<-data[,group:=as.factor(group)]
model<-felm(y~x|pers_id+time_id*group,data=data)
When I then type:
getfe(model)
I obtain an error, which is an expected result given that pers_id and group are collinear. and as far as I understand what felm does it creates:
pers_id+time_id+group_id+time_id:group_id
Currently I can do something like this:
interaction_term<-interaction(data$time_id,data$group)
data$interaction_term<-as.character(interaction_term)
data$dummy_1<-ifelse(as.character(data$interaction_term)=="1.M",1,0)
data$dummy_2<-ifelse(as.character(data$interaction_term)=="2.M",1,0)
data$dummy_3<-ifelse(as.character(data$interaction_term)=="3.M",1,0)
data$dummy_4<-ifelse(as.character(data$interaction_term)=="4.M",1,0)
data$dummy_5<-ifelse(as.character(data$interaction_term)=="5.M",1,0)
model<-felm(y~x+dummy_2+dummy_3+dummy_4+dummy_5|pers_id+time_id,data=data)
But this is a little bit clumsy and becomes infeasible when I have a lot of time periods. So my question is, whether it is possible somehow in felm specify felm(y~x|f1:f2) and have only interaction effect, i.e. f1:f2 and not f1+f2+f1:f2

Answer 1

The construction a*b is not supported in the fixed-effect part of formulas in felm. That field is not parsed with the ordinary parser. Mainly due to the fact that expressions like f*x where f is a factor and x is a numeric would create havoc. I.e. it would create fixed effects like x + f + f:x, but x, being a numeric, should normally be treated as an ordinary continuous variable, i.e. be put in the first part of the formula. This is of course possible to do automatically, but is not currently supported by felm. Neither is f*g with two factors. What actually happens then, I don't know.
The parser is quite simplistic, it consists of letting : be an infix function of two variables, and the fixed-effect part of the formula is then eval'ed in the model frame. The function : creates an interaction factor if both its arguments are factors. It works recursively, so things like f:g:h with three factors also works (by chance, rather than by thought). If one of the arguments is a numeric, it creates an lfe-internal structure so that the expression is treated as an interaction between a factor and a continuous covariate.
In short, there is very limited formula-functionality in the fixed-effect part of the formula. Full interaction '*' is not supported. Only things like time_id:group, or time_id:group + time_id + group.
There is currently an error in getfe() which may lead to an obscure error message if an interaction between two factors is specified in the fixed-effect field to felm. (It's an idiotic error; expressions like attr(f,'x') matches partially on 'x', and I haven't specified exact=TRUE, so it matches something it shouldn't, deep inside lfe). This will be fixed in the next version which is due in a week or so.
This mess is due to the fact that the syntax f:x was introduced in the fixed-effect field to support interaction between a factor f and a continuous covariate x. Interaction between two factors was implemented as an afterthought.