I have a question regarding 3SLS in STATA, using reg3 command. I hope
you can share me your thoughts.
I am trying to replicate the results of a paper, in which it specifies
only V2, V3, V6 as exogenous variables.
I try the following command in STATA
reg3 (V1 V1_lag V2 V3 V4) (V5 V1 V6 V4)
And I found that STATA treats V1 and V5 as endogenous variables and the
rest as exogenous ones. Note that V1_Lag is lagged variable for V1, and
V4 = V1_Lag - V5_Lag
In order to explicitly specify the exogenous variables, as the authors
did in their paper, I try the following command
reg3 (V1 V1_lag V2 V3 V4) (V5 V1 V6 V4) endog(V1 V1_Lag V4 V5) exog(V2
However, STATA tells me that "Equation is not identified -- does not
meet order conditions". I am wondering how can I get around by only
specifying V2, V3 and V6 as exogenous variables?
3SLS is a systems estimator in which the number of endogenous variables is equal to the number of equations. If you have two eqns, you cannot have more than two endog vars. It makes no sense to consider the lagged value of something (or the difference of two lagged values) as endogenous--there is no way that they can be determined at time t if they are dated (t-1).
In your original specification, v1_lag and v4 = L.v1-L.v5 could be considered predetermined variables since they involve lagged endogenous variables. That would make the system recursive; if we consider v2, v3, v6 to be exogenous, then the first eqn may be estimated via OLS since it does not contain endogenous variables on the RHS. The second eqn requires instrumental variables (2SLS or 3SLS) since it has v1 on the RHS. It is overidentified since v2, v3, and v1_lag are available instruments, excluded from this equation, and only one instrument is needed. It seems to me that your original reg3 command is correct, and the authors' claim that only v2, v3 and v6 are exog may be semantic: the other instruments in the system (v1_lag and v4) are predetermined.