Correcting for robust/clustered standard errors within the lm function or replacing the results

Question

Cross posted on Stackoverflow with a bounty of 200.

EDIT:

I think I have to clarify this question a little bit more. So what I am looking for, is a function in which I can provide both the vcov matrix (the vcov2sls), and have robust and clustered standard errors. However it seems that they both pertain to the same vcov matrix option. So if I supply one, I already have to make sure the se's are clustered and robust.. So I guess I am essentially asking how I can make the vcov2sls function have robust and clustered errors. Obviously any other solution leading to the same practical outcome would be great as well.

END OF EDIT

A while ago, I asked this question, 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), 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?

EDIT: I know that also lmtest:coeftest exists, but I want to able to use weights. See this link. I am having trouble figuring out if this is possible in lmtest:coeftest .

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))