Does using mixed-frequency data enhance the strength of parameter identification?
That question is ill-posed. Relative to what? A model where you do not observe the data at the highest frequency? In that case, the answer would be yes. Having more data generally helps with identification.
Thank you, Professor. May I also ask if there are any specific algorithms used in Dynare for Bayesian estimation when dealing with mixed-frequency data? If so, could you please tell me which paper proposed the algorithm adopted by Dynare?
There is no special algorithm. Mixed frequency data is simply a special case of using the Kalman filter to construct the likelihood function, where the Kalman filter infers the states even if some information is missing.
Dear Professor,
I am currently working with a very large set of observed time series. Based on my understanding of state-space model theory, when employing mixed-frequency data—specifically, combining annual and quarterly observations—one typically needs to augment the state vector to include lagged values of the high-frequency state variables (i.e., the lags that would not be required if all data were quarterly). I am concerned that this expansion of the state vector would substantially increase both spatial complexity (memory requirements) and temporal complexity (computational cost) in my Bayesian estimation procedure.
To mitigate this issue, I am considering performing an internal interpolation of my annual-frequency data prior to estimation, so that all series can be treated as quarterly observations. Could you kindly suggest any theoretically sound and practically reasonable interpolation algorithms for this purpose? While reviewing discussions in various forums, I noticed that the Denton method appears to be generally discouraged in modern applications.
You will get additional states related to the low frequency variables, not the high-frequency ones if their definition backward-looking variables. Say you only observe GDP at annual frequency. In that case
Y_annual=Y_quarter+Y_quarter(-1)+Y_quarter(-2)+Y_quarter(-3),
which introduces three states. Whether that really slows down estimation significantly it something you should try, particularly with respect to algorithmic options like fast_kalman_filter.
I would usually not attempt to interpolate the data. How are you going to infer four missing quarterly values from one annual observation in a way that is consistent with the model you are trying to estimate? The Kalman filter would exactly do that.