Hi, I’m currently estimating a model with 6 moment equations and 6 parameters (call x1,x2,x3 and c1,c2,c3). The x’s are identified by the first 3 moments but also appear in the 3 other equations. The c’s only appear in the 3 last moments.
When I first wrote down the model, I started with the 3 initial moments and the x’s fits were pretty good (using a simulated dataset). However, when I introduced the 3 other moment equations, the fit of the c’s were really good but x3 got bad. I tried reparametrizing and making the code more sampling-efficient but I feel like I reached a limit.
What I’d like to know is if there is a way to restrict the estimation of the x’s to only the first three moments and the c’s to only the last three equations (like plugging the estimated x’s into these moments under the hood). I’m pretty sure this could be easily done separating the model into two. However, ideally I would like to keep the whole estimation in the same Stan model since I believe if I separated the models, the standard error computations for c’s would get messy because of error propagation. Is there a way to implement these moments restrictions within the same model? Thanks in advance!