I found a fix to my problem using the fastLm() from package RcppEigen, using
the Jacobi singular value decomposition (SVD) (method 4) or a method based
on the eigenvalue-eigenvector decomposition of X'X - method 5 of the fastLm
function



install.packages("RcppEigen")
library(RcppEigen)

n_obs <- 1500
y  <- rnorm(n_obs, 10,2.89)
x1 <- rnorm(n_obs, 0.00000000000001235657,0.000000000000000045)
x2 <- rnorm(n_obs, 10,3.21)
X  <- cbind(x1,x2)



bFE <- fastLm(y ~ x1 + x2, method =4)
bFE

Call:
fastLm.formula(formula = y ~ x1 + x2, method = 4)

Coefficients:
        (Intercept)                  x1                  x2 
9.94832839474159414 0.00000000000012293 0.00440078989949841 


Best,

Raluca





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