# Tank model Labor supply

Hello everyone,

I am trying to understand the TANK Model of Tirelli and Ferrare (2019). The economy is populated by two types of agents: Ricardian HHs, who can access the bond market, receive dividends from firm profits in addition to labor wages and capital income, and Non-Ricardian HHs who are hand to mouth and live only on labor income. Below I report their budget constraints, which are equations (4) and (5) in the paper, respectively.

Non-Ricardian agent
c_t^{rt}=w_t h_t^d

Ricardian agent
c_t^o+K_{t+1}^o-(1-\delta)K_t^o+\frac{M_{t+1}^o}{P_t}=r_t^kK_t^o+w_th_t^d+d_t^o+R_t\frac{M_{t}^o}{P_t}

What confuses me is labor income. The paper defines h_t^d as aggregate labor demand. How is it possible that w_th_t^d appears without distinction in both budget equations? This seems very strange to me and I cannot explain it. Mathematically speaking looking at the budget constraint of the Non-Ricardian agent, this implies that all labor income is used to finance the consumption of these agents, but obviously this cannot be true.

I would be very happy to receive if possible an insight from you.

Thank you for your help

Elsewhere in the model w is indexed by labor type, but these indexes are missing the resource constraints. Labor demand, as you point out, has to be carved up somehow. If the w’s for each labor type added to 1, they could serve this purpose. (Just a thought - I have not worked this through.)

Thank you for the answer. Yes, true elswhere w is indexed by labor type j, but this has to do with the Calvo wage setting. I am relatively sure, it is not related to the HH typ

I guess you can only ask the authors what they did there. The equations and the descriptions in the paper strike me as inconsistent in the way you describe. Either there are typos, unstated assumptions, or there is a mistake in the model.

Hello

Thank you for the answer.

Ah! I’m sure you are right. Then I agree with jpfeifer, ask the authors. They claim to have solved this model in dynare but they don’t make the mod file available and they don’t give us a clear list of input equations, either.