You run a first stage regression in R, where Z1 and Z2 are the instrumental variables. D1 and D2 are exogenous dummy variables, and X1 and X2 are exogenous continuous variables. # Run the first stage regression to check instrument relevance first <- lm(Y~ Z1 + Z2 + D1 + D2 + X1 + X2, data = dta) You could test for instrument relevance by:

A,Testing the hypothesis that the coefficients on Z1, Z2, X1, and X2 are jointly equal to zero using the R code: lht(first,c("Z1","Z2","X1","X2")). If the F-statistic from this hypothesis test is > 10, we will believe the instruments are probably relevant. Note we are explicitly omitted the dummy variables, since the coefficients on these variables cannot be tested.

B,Create a new variable in R, equal to 1 if both Z1 and Z2 are greater than 0, and 0 otherwise. If the mean of this new variable is greater than 0.05, we will reject the instrument relevance at the 5% level of significance.

C,Simply look at the Model Fit for the first regression above, that is Model Fit: F(6,N), where N is the number of observations. If the F-statistic from this hypothesis test is > 10, we will believe the instruments are probably relevant.

D,Testing the hypothesis that the coefficients on Z1 and Z2 are jointly equal to zero using the R code: lht(first,c("Z1","Z2")). If the F-statistic from this hypothesis test is > 10, we will believe the instruments are probably relevant.