Steady-state file

[Bhaskar]

Hi,

I’m trying to compute steady state using a steady state file and I’m running into a problem while entering the steady state equations. I’m unsure as to how I can define my variables? Variable ‘w’ is a function of variable ‘l’ but variable ‘l’ is also a function of variable ‘w’.
Since my system is highly non-linear, it’s very hard to express most variables in terms of parameters.
Not sure how to proceed.

[jpfeifer]

There are many posts on this. See e.g.

Advice finding a tricky steady state

For such models, the way to go is a mixture. You reduce the problem to at most a handful of equations solved numerically (e.g. a nonlinear function of labor) and the rest is computed analytically.

[Bhaskar]

So it’s okay if I don’t enter equations in the steadystate file as the SS versions of the equations as they appear in my mod file? When I tried solving the system numerically, I did reduce the system from about 20 odd equations to about 15. Can I just enter those in the the steadystate file?

[jpfeifer]

You need to provide a full steady state for all variables. But you can of course attempt to solve a subset numerically and then the rest analytically.

[Bhaskar]

I went through some steadystate resources and a lot of them have expressed variables in terms of labour. Is there any significance of expressing variables like that? Dr Mutschler’s RBC model on his website also follows the same process. But I’m struggling to understand the logic behind choosing labour. Or can one choose any variable? Like consumption or output

[jpfeifer]

There are two common approaches:

1. You fix labor to a particular value and compute the disutility parameter that causes the steady state to hold at the particular value for hours worked. E.g.

Steady-state negative Frisch Elasticity

The Frisch elasticity is still a parameter. I don’t understand what you are doing. When you calibrate labor in steady state, the disutility parameter needs to be adjusted accordingly. But that is different from the Frisch elasticity. See e.g. which features a unit Frisch elasticity, but sets the labor disutility parameter phi to have labor as 1/3

2. It is often possible to reduce the problem of steady-state finding to a single equation in labor (plugging in for consumption in the budget constraint based on the labor FOC). That equation is often rather easy to solve because you know that the value should be between 0 and 1.