To Calculate the J-Statistic You Regress the A $R ^ { 2 }$

Short Answer

To calculate the J-statistic you regress the a. squared values of the TSLS residuals on all exogenous variables and the instruments. The statistic is then the number of observations times the regression $R ^ { 2 }$
b. TSLS residuals on all exogenous variables and the instruments. You then multiply the homoskedasticity-only $F$ -statistic from that regression by the number of instruments.
c. OLS residuals from the reduced form on the instruments. The $F$ -statistic from this regression is the $J$ -statistic.
d. TSLS residuals on all exogenous variables and the instruments. You then multiply the heteroskedasticity-robust $F$ -statistic from that regression by the number of instruments.