Steady state of an endowment economy with taxation

I’m trying to run my first model with Dynare so I appreicate your help and patience.

The set-up is very simple. A stochastic endowment economy with an exogenous fixed interest rate. The only bit of extra is that there is taxation that depends non-linearly on income. Taxation is positive with the (given) steady state value of endowment but could in general become negative (income subsidy) if the endowment realisation is very low.

I would like to simulate the model to generate paths for consumption, assets and the endowment realisation. However, matlab complains: “Impossible to find the steady state. Either the model doesn’t have a steady state, there are an infinity of steady states, or the guess values are too far from the solution” . This is even though I have computed one particular exact steady state as the initial value. Why doesn’t matlab converge to that? I suppose there are an infinity of steady states if consumption and assets can be chosen freely, but this is a general issue and shouldn’t preclude finding a particular one if starting at it (or very close to it)?

Is this type of problem meaningfully analysed with Dynare or should I use general Matlab coding to find the solution to the dynamic programming problem via value function iteration?

Thanks for your help,
endowment.mod (488 Bytes)

Your Euler equation is wrong. If

then r is a gross interest rate. But in the Euler equation you have

suggesting it is a net interest rate. Using

solves the issue.