Runs the system prior mode estimation of the DSGE model parameters. This function is similar to the posterior mode estimation function, except that only csminwel is supported. YADA can estimate the prior mode for the transformed parameters or for the original parameters for models that have a system prior density. This density acts like a likelihood function for the system prior mode estimation. Since some of the parameters may have restricted support, e.g., must be positive, it is convenient to transform such parameters to a scale where the support is the real line, e.g., through the logarithmic function. From a numerical optimization perspective such a transformation means that the optimization problem no longer needs to take equality or inequality constraints into account. At the same time, the Jacobian of the transformation needs to be taken into the log posterior function that we use in the optimization.
One interesting output from the system prior mode estimation is the Laplace approximation of the marginal likelihood of the system prior. This constant is needed when computing the full marginal likelihood conditional on the system prior features.
Additional Information
• | System priors are discussed in Section 4.4 of the YADA Manual. |
• | A details discussion of parameter transformations is found in Section 6 of the YADA Manual. |
• | A detailed description of the random walk Metropolis related algorithms can be found in Section 8.1 of the YADA Manual. |
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