I am trying to estimate a simplified version of a two-sector (consumption and investment) model in which goods are differentitaed in each sector and require shopping. Shopping effort influences the amount of varieties obtained in each sector, and demand plays a productive role, as in Bai, Rios-Rull, and Storesletten 2019. The price of the investment basket is the numeraire. Capital is immobile betweeen sectors, and there are second-order quadratic investment adjustment costs.
As observable variables, I use output, investment, labor productivity, and the relative price of investment. There are shocks to general technology, investment-specific productivity, general shopping, investment-specific shopping, labor supply, and the discount factor.
As this is a multisector model, we need to control for movements in relative prices across the sectors in mapping model investment and output to the data. Accordingly, we take the steady state relative price as the base.
The inclusion of the relative price of investment triggers a stochastic singularity error:
Error using initial_estimation_checks initial_estimation_checks:: The forecast error variance in the multivariate Kalman filter became singular.
I briefly note that this formulation is a simplified version of a richer model which does not feature this error. I understand the problem is that the model implies that one observable variable is a linear combination of others, so that the model is completely rejected, but I cannot detect how this would arise. Any tips in diagnosing the source of stochastic singularity would be most appreciated.
I attach the mod file and the observables.mat file. The latter includes several additional variables unused in the current simplified model.