A model with weights


I am interested in modeling aggregate CPI as the weighted sum of its components. To do so, I need to incorporate the weights, but I am unsure about the best way to implement them in Dynare. One option is to treat them as constant parameters, but then I will ignore the changes that occur every few years. Another option is to make them endogenous variables driven by corresponding shocks, and then use the historical weights as observables. This might work, but it also has several drawbacks. The likelihood will be distorted, the computational cost will be higher, and there might be other issues.

Does anyone have a better suggestion?


That’s tricky. Because even if you use time-varying weights, an approximation of the nonlinear system will happen. I think you need to decide which approximation error is more important.

I think I can make the best of both (the least bad). I can make each weight to be:
wI,t=\mu_i+ ei,t
while ei,t is an exogenous shock, and \mu_i is the sample mean of the weight. That way, the linearization around the steady state will be around the sample mean. right?

The problem is not the approximation of w_{l,t}, but of arising products like w_{l,t}q_{lt}