I am estimating an instrumental variable regression (IV) where Y is my dependent, X my variable of interest, and Z the dicotomous instument.
I am interestend in verifying if the coefficient estimate of X is actually a Local Average Treatment Effect (LATE) or a Average Treatment Effect (ATE).
In order for the IV to produce a ATE the monotonicity assumption must old. That is no observation in the sample must be a defier(do the opposite of what they are supposed to do). Simply, Z has a causal effect on X.
For the case of LATE, the instrument Z has a heterogeneous effect on X.
Convincingly arguing monotonicity of the instrument on the instrumented is not a simple task. However, I see that in R there exists the function 'ATE' from the homonimous package which computes ATE exploiting a matching technique.
Can someone explain the rationality behind this function and how to apply it for my case. Moreover, how do I check that my coefficient equals the LATE or ATE?
The ATE function acutally requires the dicotomous treatment vector, a numeric vector of the output of interest and a matrix object for the covariates to be used for the matching.
What actually the function does is to compute the mean effect for both the treated and not treated. It is able to do so because each treated is matched with a non-treated with the highest degree of similarity in the covariates.
The output of ATE mainly gives a difference in means, with a correspondent p-value where HP_null: mean of treated and mean non-treated are the same.
Going back to my specific example. I want to check if the effect of my instrument is monotonic for the treated on the instrumented variable.
In R i run:
ate <- ATE(df$X, df$Z, socio_matrix, ATT = TRUE)
where socio_matrix is a matrix of socio-economic individual characteristics.
the output is the following:
Estimate StdErr 95%.Lower 95%.Upper Z.value p.value E[Y(1)|T=1] 0.5820551 0.0071496 0.5680420 0.5960681 81.410 < 2.2e-16 *** E[Y(0)|T=1] 0.2147127 0.0052483 0.2044262 0.2249992 40.911 < 2.2e-16 *** ATT 0.3673423 0.0083993 0.3508799 0.3838047 43.735 < 2.2e-16 ***
This signals that on average the treated are likely to show higher values of the outcome (instrumented variable). The average treatment effect on the treated is 0.36 (compared to their counterfactual, the non-treated)
What are the conclusions for my IV strategy?