Variance Decompositions

Calculate the forecast error variance decomposition of the original observed variables and for the levels data determined via the data construction file. Parameter values are given by the initial or the posterior mode values, or a sample from the prior or the posterior distribution of the parameters. In the event that a sample from the posterior is selected, the number of parameters in the sample is determined by the number of post burn-in posterior draws and the percentage use of posterior draws for impulse responses, variance decompositions and other functions of the parameters. These values are set in the posterior sampling frame on the Options tab.

The decompositions can be performed for all individual measurement errors, structural shocks, and the signal extraction error, where the latter error occurs when the DSGE model includes measurement errors and some of the state variables are unobserved. Alternatively, YADA performs the decomposition for the measurement errors, the shock groups, and the signal extraction error. The shock groups are set on Actions menu.

To solve the variance decompositions, it is sometimes necessary to use a Riccati equation solver. The Riccati equations can in this case be expressed as:

P1 = FP1F' - FP1H[H'P1H + R]-1HP1F' + B0B0' ,

where P1 is the expected value of the time varying covariance matrix of the state variables at t+1 minus the optimal forecast of these state variables using the data until period t and conditional on this data. The matrix F is the state transition matrix, while B0 is the matrix that maps the structural shocks into the state variables. Finally, H maps the state variable into the observed variables in the measurement equations, while R is the covariance matrix of the measurement errors. Once the Riccati equations have been solved for P1, all other variance decompositions can be calculated.

Th Riccati equation solver is not used when P1 = B0B0' provides a solution to the equation. This case seems likely to occur when R = 0 and the number of structural shocks does not exceed the number of observed variables.

Additional Information

•	A more detailed description about forecast error variance decompositions can also be found in Section 11.4 of the YADA Manual.

•	A more detailed description about the Riccati solver can also be found in Section 11.5 of the YADA Manual.

NOTE: Variance decompositions are only available if you have the Control System Toolbox installed.

Page url: http://www.texlips.net/yada/help/index.html?variance_decompositions.htm