最近在学习一篇论文，论文中有一个递归方程，如下所示。

RM = α0 +  Σα1 Cost of RM  +  Σα2 Cost of AM + Σ α3 Controls + μ

AM = γ0 + Σγ1Cost of RM  +  Σγ2 Cost of AM  + γ3 unexpected RM +  Σγ4 Controls + μ

在最后的稳健性检验里作者对这个递归方程中RM的外生性进行了豪斯曼检验。原文如下：Specifically, in the first stage, I regress AM and RM on the exogenous variables (i.e., the costs associated with the two earnings management approaches and the control variables) in the equation system and obtain instruments for AM and RM as the predicted values from the first-stage regressions. In the second stage, I regress AM on the exogenous variables, the instrument of RM and RM itself.
我想问一下具体的第二步检验是按照等式(1)还是等式(2)进行？

AM = γ0 + γ1 RM + γ2 Pred_RM+  Σγ3 Cost of AM +  Σγ4 Controls + μ (1)

AM = γ0 + γ1 RM + γ2 Pred_RM+  Σγ3 Cost of AM + Σγ4 Cost of RM + Σγ5 Controls+ μ (2)

如果联立方程是这样的，豪斯曼检验怎么做？

RM = α0 + α1 AM + Σα3 Cost of AM + Σα4 Controls + μ

AM = γ0 +γ1 RM + Σγ3 Cost of AM + Σγ4 Controls + μ

谢谢各位！