# The question about two country model and the international risk-sharing condition

Hi，
model2.mod (2.9 KB)
model1.mod (2.8 KB)

Thanks a lot for your time. I am learning the two-country model, which involves international risk-sharing conditions. In the textbook, both domestic and foreign families can save money at home and abroad. So there are four equations about domestic and foreign interest rates, as follows:

betaEt{(C(t+1)/C(t))^(-sigma)(P(t)/P(t+1))}=1/R(t);

betaEt{(C(t+1)/C(t))^(-sigma)(P(t)/P(t+1))*(e(t+1)/e(t))}=1/Rx(t);

betaEt{(Cx(t+1)/Cx(t))^(-sigma)(Px(t)/Px(t+1))}=1/Rx(t);

betaEt{(Cx(t+1)/Cx(t))^(-sigma)(Px(t)/Px(t+1))*(e(t)/e(t+1))}=1/R(t);

The four equations are collinear, and the international risk-sharing conditions can be obtained by combining the four equations:

(Cx(t)/C(t))^(-sigma)=Q(t), which Qt represents the real exchange rate.

Two interest rate equations and an international risk-sharing condition are written into the code, and the model can operate normally. The specific code is model1.

My question is: since the international risk-sharing condition is derived from the interest rate equation, can I choose three interest rate equations to make the model work normally? I try to replace the international risk-sharing condition with the third interest rate equation and construct the program model2.Only one equation of the two programs is different, and the others are exactly the same.
But when I tried to run the model, I found that the BK condition of the model was not satisfied and there was a unit root.
Why can the model work normally when two interest rate equations and one international risk sharing condition are selected, but there will be unit roots when three interest rate equations are selected? Can anyone explain why? Thank you!

Hi, have any scholars seen my question? I sincerely ask for your help.