Steady state of an endowment economy with taxation

[Taikuri15]

Hi,
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,
Taikuri

[jpfeifer]

Your Euler equation is wrong. If

Code: Select all

r=1/beta;


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

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(1+r)


suggesting it is a net interest rate. Using

Code: Select all

r=1/beta-1;


solves the issue.