Hi everyone,
I have a bit of a more general question related to the treatment of domestic and foreign bonds in multi-sector models. I have got models running with these specific features but I have always remained confused about whether the outcome was correct. For the purpose of this question, consider the following simplified cases:
- Two-sector, closed-economy RANK model
Suppose you only have representative agents. They can be employed in sector A or B. There is no income pooling, i.e., the ones working in sector A have a different budget constraint than those working in sector B.
In this specific setup, I gave the bonds in the respective budget constraints the subscript of the sector. Ricardians working in sector A hold b_{A,t}, Ricardians employed in sector B hold b_{B,t}. They both receive the same interest rate on holding bonds, i_t. Say that the population shares of these agents sum up to 1 (n_A + n_B = 1). I then closed the model with a bond market clearing condition where domestic bonds are in zero net supply. Log-linearized, this becomes: n_A\Delta b_{A,t} + n_B\Delta b_{B,t} = 0 (given that b_A and b_B = 0 in steady state, I use b_A\widetilde{b}_{A,t} = \Delta b_{A,t}).
This works, but is this the correct way to approach this? I’ve tried also with having just a single bond b_t in their budget constraints, but this usually leaves me with a missmatch in the number of variables and the number of equations in Dynare / instability or indeterminacy problems.
- Two-sector, small-open economy RANK model
Exactly the same question as above, but now for foreign bonds. For some reason, I have had better luck in this case with only defining a single foreign bond b_t^* in both budget constraints, and closing the model with an equation linking net foreign assets to net exports. Usually I can then leave out the nfa_t equation due to Walras’ law. I then check whether Walras’ law is satisfied for this equation by plugging in the respective IRFs, and generally this is the case.
So again; is this the correct way to approach this? If so, why is it that you have to treat these two cases so differently?
Thanks a lot in advance,
Alec Van Boven