Cross posted on [Stackoverflow][1].
A while ago, I asked [this question][2], which was about correcting the standard errors when using IV/2SLS and the first stage has a tobit distribution, on which I got an amazing answer from jay.sf (example data at the bottom). He provided me with the following function:
vcov2sls <- function(s1, s2, data, type=2) {
## turn factor variables into dummies
DATA <- as.data.frame(model.matrix(phantom ~ ., transform(data, phantom=0)))
## list variable names
vn <- lapply(list(s1=s1, s2=s2), function(s)
c(all.vars(s$call)[1], colnames(model.matrix(s))[-1]))
## auxilliary model matrix
X <- cbind(`(Intercept)`=1, DATA[, c(vn$s1[1], vn$s2[-(1:2)]), F])
## get y
y <- DATA[, vn$s2[1]]
## betas second stage
b <- s2$coefficients
## calculate corrected sums of squares
sse <- sum((y - b %*% t(X))^2)
rmse <- sqrt(mean(s2$residuals^2)) ## RMSE 2nd stage
V0 <- vcov(s2) ## biased vcov 2nd stage
dof <- s2$df.residual ## degrees of freedom 2nd stage
## calculate corrected RMSE
rmse.c <- sqrt(sse/dof)
## calculate corrected vcov
V <- (rmse.c/rmse)^2 * V0
return(V)
}
It works great. Even when I want to use robust/clustered standard errors, that is not a problem, because `AER::tobit`, calculates the robust/clustered standard errors within the function:
tobit(y~x, left=12, right=33, data=DT, robust=robust, cluster=cluster)
However I want to use jay.sf's function, when the first stage is an `lm`, the clustering takes part in the summary ([source][3]), for example:
first_stage_ols <- lm(y~x, data=DT)
summary(first_stage_ols, robust=T)
Is there either, a way to correct the standard errors from within the lm function, or (replaced them in the result), or adapt the `vcov2sls` function to also account for robust/clustered standard errors?
# Example Data
DF <- structure(list(country = c("C", "C", "C", "C", "J", "J", "B",
"B", "F", "F", "E", "E", "D", "D", "F", "F", "I", "I", "J", "J",
"E", "E", "C", "C", "I", "I", "I", "I", "I", "I", "C", "C", "H",
"H", "J", "J", "G", "G", "J", "J", "I", "I", "C", "C", "D", "D",
"A", "A", "G", "G", "E", "E", "J", "J", "G", "G", "I", "I", "I",
"I", "J", "J", "G", "G", "E", "E", "G", "G", "E", "E", "F", "F",
"I", "I", "B", "B", "E", "E", "H", "H", "B", "B", "A", "A", "I",
"I", "I", "I", "F", "F", "E", "E", "I", "I", "J", "J", "D", "D",
"F", "F"), year = c(2005, 2010, 2010, 2005, 2005, 2010, 2010,
2005, 2010, 2005, 2005, 2010, 2010, 2005, 2005, 2010, 2005, 2010,
2005, 2010, 2010, 2005, 2010, 2005, 2005, 2010, 2005, 2010, 2010,
2005, 2010, 2005, 2005, 2010, 2010, 2005, 2005, 2010, 2005, 2010,
2005, 2010, 2005, 2010, 2010, 2005, 2005, 2010, 2010, 2005, 2010,
2005, 2010, 2005, 2010, 2005, 2010, 2005, 2010, 2005, 2010, 2005,
2010, 2005, 2010, 2005, 2010, 2005, 2005, 2010, 2005, 2010, 2005,
2010, 2005, 2010, 2005, 2010, 2005, 2010, 2010, 2005, 2005, 2010,
2005, 2010, 2010, 2005, 2010, 2005, 2010, 2005, 2005, 2010, 2005,
2010, 2010, 2005, 2010, 2005), sales = c(15.48, 12.39, 3.72,
23.61, 4, 31.87, 25.33, 7.64, -0.26, 2.9, 15.48, 12.39, 3.72,
23.61, 4, 31.87, 25.33, 7.64, -0.26, 2.9, 15.48, 12.39, 3.72,
23.61, 4, 31.87, 25.33, 7.64, -0.26, 2.9, 15.48, 12.39, 3.72,
23.61, 4, 31.87, 25.33, 7.64, -0.26, 2.9, 15.48, 12.39, 3.72,
23.61, 4, 31.87, 25.33, 7.64, -0.26, 2.9, 15.48, 12.39, 3.72,
23.61, 4, 31.87, 25.33, 7.64, -0.26, 2.9, 15.48, 12.39, 3.72,
23.61, 4, 31.87, 25.33, 7.64, -0.26, 2.9, 15.48, 12.39, 3.72,
23.61, 4, 31.87, 25.33, 7.64, -0.26, 2.9, 15.48, 12.39, 3.72,
23.61, 4, 31.87, 25.33, 7.64, -0.26, 2.9, 15.48, 12.39, 3.72,
23.61, 4, 31.87, 25.33, 7.64, -0.26, 2.9), industry = c("D",
"D", "E", "E", "F", "F", "F", "F", "D", "D", "E", "E", "D", "D",
"E", "E", "F", "F", "F", "F", "D", "D", "F", "F", "E", "E", "D",
"D", "D", "D", "E", "E", "F", "F", "D", "D", "E", "E", "E", "E",
"D", "D", "E", "E", "D", "D", "D", "D", "E", "E", "D", "D", "F",
"F", "D", "D", "D", "D", "E", "E", "D", "D", "E", "E", "D", "D",
"D", "D", "D", "D", "F", "F", "F", "F", "E", "E", "D", "D", "E",
"E", "F", "F", "E", "E", "F", "F", "E", "E", "F", "F", "D", "D",
"D", "D", "D", "D", "D", "D", "F", "F"), urbanisation = c("B",
"B", "A", "A", "B", "B", "A", "A", "C", "C", "C", "C", "A", "A",
"B", "B", "C", "C", "A", "A", "C", "C", "B", "B", "A", "A", "A",
"A", "A", "A", "A", "A", "A", "A", "C", "C", "B", "B", "B", "B",
"B", "B", "C", "C", "A", "A", "B", "B", "B", "B", "A", "A", "B",
"B", "A", "A", "A", "A", "B", "B", "C", "C", "A", "A", "C", "C",
"A", "A", "B", "B", "A", "A", "B", "B", "B", "B", "B", "B", "C",
"C", "A", "A", "A", "A", "A", "A", "A", "A", "C", "C", "A", "A",
"B", "B", "A", "A", "B", "B", "B", "B"), size = c(1, 1, 5, 5,
5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 2, 2, 2, 2, 5, 5, 1, 1, 1, 1, 5,
5, 5, 5, 4, 4, 5, 5, 5, 5, 4, 4, 2, 2, 5, 5, 1, 1, 1, 1, 2, 2,
1, 1, 2, 2, 5, 5, 1, 1, 3, 3, 2, 2, 2, 2, 5, 5, 4, 4, 1, 1, 5,
5, 2, 2, 5, 5, 2, 2, 2, 2, 4, 4, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3,
5, 5, 3, 3, 2, 2, 3, 3, 1, 1, 5, 5), base_rate = c(14L, 14L,
14L, 14L, 19L, 19L, 30L, 30L, 20L, 20L, 29L, 29L, 20L, 20L, 20L,
20L, 24L, 24L, 19L, 19L, 29L, 29L, 14L, 14L, 24L, 24L, 24L, 24L,
24L, 24L, 14L, 14L, 17L, 17L, 19L, 19L, 33L, 33L, 19L, 19L, 24L,
24L, 14L, 14L, 20L, 20L, 23L, 23L, 33L, 33L, 29L, 29L, 19L, 19L,
33L, 33L, 24L, 24L, 24L, 24L, 19L, 19L, 33L, 33L, 29L, 29L, 33L,
33L, 29L, 29L, 20L, 20L, 24L, 24L, 30L, 30L, 29L, 29L, 17L, 17L,
30L, 30L, 23L, 23L, 24L, 24L, 24L, 24L, 20L, 20L, 29L, 29L, 24L,
24L, 19L, 19L, 20L, 20L, 20L, 20L), taxrate = c(12L, 14L, 14L,
12L, 21L, 18L, 30L, 30L, 20L, 20L, 29L, 30L, 20L, 20L, 20L, 20L,
24L, 24L, 21L, 18L, 30L, 29L, 14L, 12L, 24L, 24L, 24L, 24L, 24L,
24L, 14L, 12L, 18L, 19L, 18L, 21L, 33L, 32L, 21L, 18L, 24L, 24L,
12L, 14L, 20L, 20L, 22L, 25L, 32L, 33L, 30L, 29L, 18L, 21L, 32L,
33L, 24L, 24L, 24L, 24L, 18L, 21L, 32L, 33L, 30L, 29L, 32L, 33L,
29L, 30L, 20L, 20L, 24L, 24L, 30L, 30L, 29L, 30L, 18L, 19L, 30L,
30L, 22L, 25L, 24L, 24L, 24L, 24L, 20L, 20L, 30L, 29L, 24L, 24L,
21L, 18L, 20L, 20L, 20L, 20L), vote = c(0, 0, 0, 0, 1, 1, 1,
0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1,
1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1,
1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0,
1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0,
1, 0, 1, 1, 1, 1, 0, 1, 1), votewon = c(0, 0, 0, 0, 1, 0, 1,
0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1,
1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1,
0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0,
1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0,
0, 0, 1, 1, 0, 1, 0, 1, 1)), class = "data.frame", row.names = c(NA,
-100L))
## convert variables to factors beforehand
DF[c(1, 2, 4, 5, 6, 9, 10)] <- lapply(DF[c(1, 2, 4, 5, 6, 9, 10)], factor)
s1.tobit <- AER::tobit(taxrate ~ votewon + industry + size + urbanisation + vote,
left=12, right=33, data=DF)
yhat <- fitted(s1.tobit)
s2.tobit <- lm(sales ~ yhat + industry + size + urbanisation + vote, data=DF)
lmtest::coeftest(s2.tobit, vcov.=vcov2sls(s1.tobit, s2.tobit, DF))
[1]: https://stackoverflow.com/questions/65627475/correcting-for-robust-clustered-standard-errors-within-the-lm-function-or-replac
[2]: https://stats.stackexchange.com/questions/491330/2sls-or-iv-with-a-tobit-distribution-in-the-first-stage
[3]: https://economictheoryblog.com/2016/08/07/robust-standard-errors-in-r-function/