Arrow-Debru securities in dynare

Hello everyone,

I have a puzzling question, I am building a two region model in dynare with complete markets. So there is international risk sharing between households in country A and households in country B. Here is my problem, because of Walras Law I know that one of my equilibrium conditions is redundant and therefore I choose to remove the budget constraint of households in country B. My question is then, how do I make dynare understand that my asset A_t in the budget constraint of households in country A is an Arrow security which is therefore for every state of nature ? In close or small open economy model I know that we solve this issue by just removing the budget constraint of households but in my case, I can only remove one budget constraint of households either in country A or B but then I have the issue just mentioned.

Thanks in advance for your answers.



I am not sure I understand the problem. The risk sharing condition already embeds that the ratio of marginal utilities across all states must be equal. Why do you think there is a link to the budget constraint? The constraint holds for all periods and states of the world. It does not involve expectations.

Dear Mr Pfeifer,

In fact in my model I have the equation of the IRS condition that states MU_t^a=MU_t^b rer_t (marginal utility at time t in country A is equal to marginal utility at time t in country B times the real exchange rate). But I also have the budget constraint of households in country A : c_t+ b_t/R_t + E(A_t Q_{t,t+1}) = A_t-1/pi_t + b_t-1/\pi_t+ wl+Tr_t-Tax_t (consumption + public bonds + arrow security is equal to arrow security at time t-1 + debt at time t-1 + wage revenue+ lump-sum transfers - lump sum taxes). I code this constraint in dynare as follows:
c+b/R+A/R=v+A(-1)/\pi+b(-1)/\pi+wl+Tr-Tax. My question was: do dynare understand the difference of nature between b and A ( b is just one asset while A is an Arrow security and is therefore the sum of all arrow security that insure against all state of the world). Is your previous comment saying that having the IRS condition stated above is enough for that ?

Thanks in advance for your reply Professor.



My understanding is that this should be sufficient. A here is not one asset but a full set.

Of course but my point was that in dynare b or A will have the same interpretation no ? in the sense that dynare does not know that A is a full set and b a single asset right ?

Yes, but I don’t think that matters in the end. What we care about is the risk sharing condition. Once that is properly encoded, we should only care about the value of the AD portfolio in the BC, not its composition.

Ok perfect, thank you very much Professor. I just have a last small question about the timing. In dynare, Arrow securities should be encoded as backward right ? I mean in the BC, we will have A and A(-1) ? Thanks again for your replies.

Yes, the budget constraint does not contain forward-looking elements.

Thank you very much Professor.

Have a good day.