Hello Johannes,

Hope all is well.

We are trying to estimate a parameter in a univariate local linear trend model for US GDP in annual frequency starting in 1979.

If we use the data in approximate percent form, that is, the first difference of real GDP is defined as y_dif(t) = y(t) – y(t-1), where y(t) = 100 * ln( Y), then we get (this is in line 159 of the log file “Model1_data_in_percent_form.log”) that the prior mode is 0.6729, and so we wonder what we are missing since we were expecting the prior mode to be 0.5 because that is the prior mean and the distribution is symmetric.

If we instead use the data in decimal form, that is, without the 100, or as the first difference of real GDP defined as y_dif(t) = y(t) – y(t-1), where y(t) = ln( Y), then we get (as in line 213 of the log file “Model1_data_in_percent_form.log”) that the prior mode is 0.9900 (again different from 0.5) and that the log data density is NaN so the parameter cannot be estimated.

We have also run other versions of the model that can estimate a parameter when data is used in both, percent and decimal form. In these cases the reported prior and the estimated posterior depend on the form the data is used. We have also run other versions of the model that do estimate the parameter when the data is in decimal form but do not estimate it when the data is in percent form.

Please what is our blind spot, why is the reported mode different from the mean? Why is it that the model may run with the data in one way and not in the other? Why is it that the estimated posterior depends on the form the data is used?

We are attaching the model, the executable code, the data and to log files with the results.

Best regards and happy holidays,

Javier

Run_Model1.m (362 Bytes)

Model1.mod (1.1 KB)

Data_in_decimal_form.xls (29.5 KB)

Data_in_percent_form.xls (29.5 KB)

Model1_data_in_decimal_form.log (9.6 KB)

Model1_data_in_percent_from.log (8.4 KB)