Replacing ricardian household's budget constraints with non-ricardian household budget constraints in the model's equilibrium equations gives wrong results

In chapter 7 of Celso Jose Costa Junior’s book, I get different and wrong results when I drop budget constraints (for Ricardian households) from the equilibrium equations of the model, and rather replaces it with budget constraints for non-Ricardian households. In chapters 5 and 6, the book uses budget constraints for non-Ricardian households though, instead of budget constraints for Ricardian households.

I understand from this forum that you can’t use both constraints due to Walras law. But not sure why they give different results.

Here is the log linearised equation for Ricardian households budget constraints:

Pss*CRss*((P+CR)*(1+tau_css)+tau_css*tau_c) + Pss*IPss*((P+IP)
*(1+tau_css)+tau_css*tau_c) + (Bss/RBss)*(B-RB) = Wss*LRss
*(1-tau_kss)-tau_kss*tau_k) + Bss*B(-1) + omegaR*TRANSss*(TRANS+P);

And here is the log linearized equation for nonricardian households budget constraints:

Pss*CNRss*((P+CNR)*(1+tau_css)+tau_css*tau_c) = Wss*LNRss*((W+LNR)*(1-tau_lss)-tau_lss*tau_l) 
+ (1-omegaR)*TRANSss*(TRANS+P);

Non ricardian households do not own capital and do not invest in bonds.

Here is the associated mod file (original.mod (7.6 KB)) for the case when ricardian budget constraint is used. And here is the mod file (original1.mod (7.5 KB) ) for the case when non-ricardian budget constraint is used.

Any help is very much appreciated.

It’s only equivalent if the information in the equation you leave out is really contained in the other ones. So if the rest of the model in that chapter differs from the previous ones, that could explain it.

Hi Prof. Pfeifer,

Thanks for the reply. Indeed the model in this chapter is different from the other chapters as it contains the public sector.

So it is not just about dropping one budget constraint, but dropping the irrelevant one…not easy to spot though, which one is irrelevant. Any hint on how to do that? Or perhaps there exist some conventional way.

It’s not about budget constraints, but about market clearing. See e.g.

In the end, it depends on your model setup.