Model specification to obtain steady state in two agent RBC style model

Hello everybody,

We are trying to construct a model to analyse a policy measure in rental markets in Germany, more specifically a rent cap (“Mietpreisbremse”) implemented to control the rise in rents. Our research question is: What are the effects of a rent cap on the construction sector, rent prices and output in the economy?

To do so, we started from the model used by Rubio and Mora-Sanguinetti ( Recent reforms in Spanish housing markets: An evaluation using a DSGE model , 2014) (A Iacoviello type model with a construction sector and the savers providing rental services to the borrowers) and stripped it from its open economy and its New Keynesian (NK) features. We leave out the the open economy part for the sake of simplicity and the NK features because we think we do not need them to answer our research question.

In our RBC-type model, we need to include some sort of bonds, so that agents in our models face an intertemporal trade-off between consumption in the current and in subsequent periods.
We considered the options (a) agents buy bonds and firms make debt that are equal in equilibrium and (b) landlords (agents that can buy housing to transform it into rental services) lend money to tenants (agents that draw utility from both owner-occupied and rented housing), inspired by Iacoviello type models (but without a collateral constraint for tenants). We opted for option (b) because option (a) would mean adapting the production functions in the consumption and housing sector in order to incorporate capital as a means of production.

As we have not been able to obtain steady-state values for our model, we wanted to ask for guidance. More specifically:

  1. Is our way of including bonds sensible?
  2. Are we considering the right model equations in our code?
  3. Is our modelling strategy of including landlords and tenants sensible? Landlords and tenants can be distinguished by the parameter value of the discount factor beta (beta_landlords > beta_tenant to encourage borrowing) features that landlords can buy housing to produce rental services (see landlord’s budget constraint) and tenants draw utility from owner-occupied housing and rental services

We uploaded our dynare code and a PDF explaining the model and the equations we included in our code.

AdvMacroMethodsPresentation_1304.pdf (250.1 KB)
RBC_Construction_1404_bonds_forum.mod (7.5 KB)

Thank you very much in advance!

I am not sure I am following. The reason that the Iacoviello setup leads to a well-defined steady state despite two agents with different discount factors is the presence of a binding collateral constraint. It’s the resulting Lagrange multiplier that makes the two Euler equations hold in the presence of only one common interest rate.