Multinomial Logit Fixed Effects: Stata and R

Question

I am trying to run a multinomial logit with year fixed effects in mlogit in Stata (panel data: year-country), but I do not get standard errors for some of the models. When I run the same model using multinom in R I get both coefficients and standard errors.

I do not use Stata frequently, so I may be missing something or I may be running different models in Stata and R and should not be comparing them in the first place. What may be happening?

So a few details about the simple version of the model of interest:

I created a data example to show what the problem is

• Dependent variable (will call it DV1) with 3 categories of -1, 0, 1 (unordered and 0 as reference)

• Independent variables: 2 continuous variables, 3 binary variables, interaction of 2 of the 3 binary variables

• Years: 1995-2003

• Number of observations in the model: 900

In R I run the code and get coefficients and standard errors as below.

R version of code creating data and running the model:

## Fabricate example data 
library(fabricatr)
data <- fabricate(
  N = 900,
  id = rep(1:900, 1),
  IV1 = draw_binary(0.5, N = N),
  IV2 = draw_binary(0.5, N = N),
  IV3 = draw_binary(0.5, N = N),
  IV4 = draw_normal_icc(mean = 3, N = N, clusters = id, ICC = 0.99),
  IV5 = draw_normal_icc(mean = 6, N = N, clusters = id, ICC = 0.99))

library(AlgDesign)
DV = gen.factorial(c(3), 1, center=TRUE, varNames=c("DV"))
year = gen.factorial(c(9), 1, center=TRUE, varNames=c("year"))

DV = do.call("rbind", replicate(300, DV, simplify = FALSE))
year = do.call("rbind", replicate(100, year, simplify = FALSE))

year[year==-4]= 1995
year[year==-3]= 1996
year[year==-2]= 1997
year[year==-1]= 1998
year[year==0]= 1999
year[year==1]= 2000
year[year==2]= 2001
year[year==3]= 2002
year[year==4]= 2003

data1=cbind(data, DV, year)
data1$DV1 = relevel(factor(data1$DV), ref = "0")

## Save data as csv file (to use in Stata)
library(foreign)
write.csv(data1, "datafile.csv", row.names=FALSE)

## Run multinom
library(nnet)
model1 <- multinom(DV1 ~ IV1 + IV2 + IV3 + IV4 + IV5 + IV1*IV2 + as.factor(year), data = data1)

Results from R

When I run the model using mlogit (without fixed effects) in Stata I get both coefficients and standard errors.

So I tried including year fixed effects in the model using Stata three different ways and none worked:

1. femlogit

• factor-variable and time-series operators not allowed
• depvar and indepvars may not contain factor variables or time-series operators

2. mlogit

• fe option: fe not allowed
• used i.year: omits certain variables and/or does not give me standard errors and only shows coefficients (example in code below)

* Read file
  import delimited using "datafile.csv", clear case(preserve)
  
* Run regression
    mlogit DV1 IV1 IV2 IV3 IV4 IV5 IV1##IV2 i.year, base(0) iterate(1000)

Stata results

3. xtmlogit

• error - does not run
• error message: total number of permutations is 2,389,461,218; this many permutations require a considerable amount of memory and can result in long run times; use option force to proceed anyway, or consider using option rsample()

Answer 1

Fixed effects and non-linear models (such as logits) are an awkward combination. In a linear model you can simply add dummies/demean to get rid of a group-specific intercept, but in a non-linear model none of that works. I mean you could do it technically (which I think is what the R code is doing) but conceptually it is very unclear what that actually does.

Econometricians have spent a lot of time working on this, which has led to some work-arounds, usually referred to as conditional logit. IIRC this is what's implemented in femlogit. I think the mistake in your code is that you tried to include the fixed effects through a dummy specification (i.year). Instead, you should xtset your data and then run femlogit without the dummies.

xtset year
femlogit DV1 IV1 IV2 IV3 IV4 IV5 IV1##IV2

Note that these conditional logit models can be very slow. Personally, I'm more a fan of running two one-vs-all linear regressions (1=1 and 0/-1 set to zero, then -1=1 and 0/1 set to zero). However, opinions are divided (Wooldridge appears to be a fan too, many others very much not so).