# 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.

dear DoubleBass.I’ve never understood, can we find the steady state after we linearize it. We still have to do it before we linearize it.

Hi heroluotao,

you do need to find the steady state before (log-)linearizing, since the model is linearized around the non-stochastic steady state. Afterwards, the model variables - in case of log-linearization - are percentage deviations from steady state. Hence their interpretations changes and their “new” steady state, ie the one of the new log-linear variables, is zero.

thanks for your answer.can we still find the steady state value after linearization. For example, if the steady-state values of consumption and output appear after linearization, can I directly substitute them with the realistic ratio of consumption and output?

No, you cannot do that. The model steady state is a function of the structural parameters. If you put in an arbitrary number, this number will be inconsistent with the parameters of the model.

After log-linearization, only some of the equations have steady-state variables. We just need to figure out the steady state variables of some of the equations？Thank you very much for your answer

Yes, that is usually the case.

dear jpfeifer.I found in the linearization process that some parameters were eliminated, which did not play a role in the model. My question is whether these parameters need to be calibrated.

No, if something drops out of the model, it’s value does not matter anymore.