SMM estimates Sensitive to Moment Ordering

Hello all,

I’m replicating Aguiar & Gopinath (2007) using Dynare’s method of moments command. Since the model has a stochastic trend but the target moments come from HP-filtered data, I’ve implemented an SMM approach by modifying the objective_function.m and get_data_moments.m files in the dynare/matlab/+mom/ folder.

My approach: After simulating the detrended model, I reconstruct non-stationary series by building up the technology level (log_Y_t = log_y_t + log_X_{t-1}), apply the one-sided HP filter, and compute the 11 moments exactly as in the data. Both model and data go through identical transformations.

The estimation runs and gives reasonable results (objective function around 0.7), but I’ve encountered a strange issue: when I change the ordering of the moments, the parameter estimates change drastically. Mathematically, the GMM criterion should be invariant to moment ordering as long as the weighting matrix is reordered consistently, which I’m doing.

I’m using two-stage GMM with identity weighting in stage 1 and the optimal HAC weighting matrix in stage 2. I’ve double-checked that both the moment vector and the weighting matrix are reordered together.

I’ve attached my mod file and the modified objective_function.m and get_data_moments.m files (only the SMM section was changed in objective_function.m). Has anyone encountered this before? Is there something about how Dynare handles moment ordering that I’m missing, or could there be an issue with my HAC variance-covariance matrix computation?

Any insights would be greatly appreciated!

objective_function.m (25.1 KB)

get_data_moments.m (7.2 KB)

mod_file.mod (5.8 KB)

Thanks!

You did not provide the data file.

data_cycle_is_trend.xls (439 KB)

Dear Professor,

I took my data from Gita Gopinath’s page (Data and Codes | Gita Gopinath), which was the same used by both the authors. I worked with the deseasonalized data, took the necessary transformations to match with the moments provided in the paper.

Thank You

What you describe indeed looks strange and is most likely related to an inconsistent re-ordering between empirical moments, model moments and the rows and columns of the weighting matrix.