Download Bayesian Estimation of DSGE Models by Edward P. Herbst, Frank Schorfheide PDF

By Edward P. Herbst, Frank Schorfheide

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Vice versa, if h(θ) is outside of the interval [δl , δu ], then the best choice for the adversary is to set λ = −∞. The econometrician has an incentive to choose a short interval that covers h(θ). Now suppose neither player knows h(θ) and both players minimize their posterior expected loss under the same distribution p(h(θ)|Y ). 23) = (δu − δl ) + max− λ P(δl ≤ h(θ) ≤ δu |Y ) − (1 − α) . 23) is the shortest connected interval with coverage probability 1−α. The shortest connected interval can be computed based on equally weighted draws as follows: sort the draws h(θi ) in ascending order to obtain the sequence h(i) ; for i = 1 to N α minimize h( N (1−α) +i) − h(i) with respect to i.

The distributions are typically parameterized such that the plausible range for each parameter corresponds to a 90% or 95% credible interval. A joint prior distribution for θ could then be obtained from the product of marginal distributions, possibly truncated to ensure the existence of a unique stable DSGE model solution over the domain of the prior. Generating prior distributions for a high-dimensional parameter vector as the product of marginal distributions could have undesirable consequences.

In the former case, it consists of a lower bound δl and an upper bound δu . Let δ = [δl , δu ] and consider the following two-player game between the econometrician and an adversary. The econometrician chooses δ and the adversary chooses a scalar parameter λ ∈ R− . 22) where I{x ≤ a} is the indicator function that equals one if x ≥ a and equals zero otherwise. If δl ≤ θ ≤ δu then the factor post-multiplying λ is positive for α > 0 and the adversary minimizes his loss by setting λ = 0. Vice versa, if h(θ) is outside of the interval [δl , δu ], then the best choice for the adversary is to set λ = −∞.

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