You might use the package systemfit to estimate simultaneous equations[1]. Systemfit does not explain how to test null coefficients together. The solution is simple. You juste have to compute a diagonal matrix of the dimension equals to the number of coefficients:
n = nrow(as.matrix(fit$coefficients))
Rmat <- matrix(0, nrow = n, ncol = n)
for (i in 1:n){ Rmat[i,i]=1}
linearHypothesis(fit,Rmat)
You replace the variable “fit” by the variable corresponding to your systemfit output. And there you are, you can get the results of your F test.
[1] You can refer as well to the vignettes to get a detailed explanation.
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