# Can nonlinear equations use the steady-state values set by linear equations?

I want to do welfare analysis, so I must use a nonlinear model. But when I add the steady-state value of the logarithmic linearization model to the nonlinear model, the result shows that the residual error is not 0. What is the reason?nolinear1.mod (3.0 KB)

The model I imitated is IACOVIELLO (2005) “House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle”, and my model is a nonlinear equation.

No, since a log-linear model by definition has zero steady states for all varaiables. You have to calculate the steady state for the non-linear model in order to use it. Check the forum or the MMB, there should be versions of this model with steady states, I think.

I see that MMB has only linear models. The linear model only needs to solve the ratio of each endogenous variable to output. But the nonlinear model needs to solve the steady-state value of each endogenous variable.

I know how to solve it, I can first assume Y=1 in the model

I don’t have a solution to your problem, but may I kindly ask why you want to linearize your model and use the linear model to find steady-state? From my experience, a model has a unique and same steady-state whether you linearize the model or not, no? I always find steady-state using the non-linear equations, and it always works whether or not I linearize the model. Or maybe, I don’t understand your question.

Thank you for your answer. There is a problem with the steady-state value I calculated, although it works in the linear model. Now I have recalculated. He can work in both models.