# Estimating finite sample bias for Instrumental Variables

Are there ways to estimate the finite sample bias with instrumental variables? I guess this would be conditional on assuming some structure to the problem and also would involve simulation, but, at least in applied econometrics papers, I have never seen people do it.

PS: If possible, the answer could be illustrated with R code.

Using the model with one regressor and many instruments(vector-matrix notation) $$y = x\beta +u$$ $$x = Z\gamma +v$$
$$B(\hat \beta_{IV}) = \frac {\operatorname{Cov}(u,v)}{\gamma'Z'Z\gamma}(K-2)$$
where $K$ is the number of instrument (the column dimension of matrix Z). Naturally, one uses the estimated quantities to calculate the above. This as a special case of results in A.L.Nagar (1959).