Predict using felm output with standard errors

Question

Is there way to get predict behavior with standard errors from lfe::felm if the fixed effects are swept out using the projection method in felm? Th

Answer 1

After conversations with several people, I don't believe it is possible to obtain an estimate the distribution of yhat=Xb (where X includes both the covariates and the fixed effects) directly from felm, which is what this question boils down to. It is possible bootstrap them, however. The following code does so in parallel. There is scope for performance improvements, but this gives the general idea.

Note: here I do not compute full prediction interval, just the SEs on Xb, but obtaining the prediction interval is straightforward - just add the root of sigma^2 to the SE.

library(DAAG)
library(lfe)
library(parallel)

model1 <- lm(data = cps1, re74 ~ age + nodeg + marr)
yhat_lm <- predict(model1, newdata = data.frame(age=40, nodeg = 0, marr=1), se.fit = T)

set.seed(42)
boot_yhat <- function(b) {
  print(b)
  n <- nrow(cps1)
  boot <- cps1[sample(1:n, n, replace=T),]

  lm.model <- lm(data=demeanlist(boot[, c("re74", "age")], list(factor(boot$nodeg), factor(boot$marr))), 
                 formula = re74 ~ age)
  fe <- getfe(felm(data = boot, re74 ~ age | nodeg + marr))

  bootResult <- predict(lm.model, newdata = data.frame(age = 40)) + 
    fe$effect[fe$fe == "nodeg" & fe$idx==0] + 
    fe$effect[fe$fe == "marr" & fe$idx==1]
  return(bootResult)
}

B = 1000
yhats_boot <- mclapply(1:B, boot_yhat)

plot(density(rnorm(10000, mean=yhat_lm$fit, sd=yhat_lm$se.fit)))
lines(density(yhats), col="red")