General questions on how to solve steady state in nonlinear equations

I met with an issue in my code that the expected result cannot be generated. I am wondering if it’s because of the way I am using for steady state solutions, my model includes lots of sectors independently. In order to solve the steady states from these groups of equations, I follow lots of paper method that sacrifices the degree of freedom from exogenous variable parameters for critical values like gdp normalization Y=1 or sector ratio like Y1/Y2=1. My question is very simple. If I took this method that most of other papers use, will it affect my calibration later ? How people deal with this problem in calibration for comparative statistics ? If their simulation codes could only be solved with normalized output ? Do they control play with different normalization to fix the exogenous variable parameterized values ? Not sure if I explain my questions clearly or not, but if anyone has experience on these issues. I would be happy to learn your knowledge. Thanks

If your model features constant returns to scale, then the scaling with TFP is arbitrary. It does not matter whether you normalize when you consider percentage deviations from steady state.

Many thanks, Johannes. Can I ask another question about impulse response function interpretation ? Basically, I set up an expression for stock return as ret(t)=Price(t)/(Price(t-1)-Dividend(t-1)) and make experiment on exogeneous shock occurs at t. Then, I draw the impulse response curve for exogenous x on ret (ret could be obtained through Euler Equation). I am wondering whether I should interpret this return as realized return (risk that materialized at t) or expected return since dynare conducts lots of simulation experiment that starts from t-1 and average the response with large number of simulations , so according to large laws of number, it should be explained as expected value (expected return) ? I am prone to the second one but really want to hear of your advice on this.

Best
Yi

Sorry, but you need to more carefully explain what you are doing. Where does the large number of simulations come in?

BTW, professor, I have a second question regarding estimation procedure. I notice that Dynare now has a new block to help deal with moment matching problem like SMM. Do you know where I could find references to this part ? I plan to match target moments when the code issue is solved. I want to have some template for moment matching part. Ideally, if it could match with multi sector model that will be better. Thanks !

There are various examples at tests/estimation/method_of_moments · master · Dynare / dynare · GitLab

Professor, do you know where I could find references for the option settings of the template codes ? The template codes are well structured but both the video and the template have no details about the parameter setting instructions. It will be very helpful if possible. Thanks !

Sorry, professor, I have one more question for the RBC template code you provide. In the RBC running, the final result doesn’t have estimation for standard errors of estimators (NAs), but as far as I know in SMM or GMM should include direct or indirect inferences on this part. Is there anyway that I can adjust the option to show these parts ? Like the screenshot, it seems that the block could only show the conclusion on overidentification but not the estimator inference.

Best
Yi