Prior Probability Interval for a Normal Distribution

Calculates the mean and variance of a normal prior probability interval. Given a lower and upper bound of a prior probability interval this function recovers the implied normal prior parameters. Useful for specifying informative priors on the steady-state parameters (elements of \(\Psi\)).

Usage

ppi(l, u, interval = 0.95, annualized_growthrate = FALSE, freq = 4)

Arguments

l

Numeric. The lower bound of the prior probability interval.

u

Numeric. The upper bound of the prior probability interval.

interval

Numeric. The prior probability mass within the interval. Default 0.95, i.e. 95%.

annualized_growthrate

Logical. If TRUE, treats l and u as bounds on the annualized steady-state growth rate and calculates the implied mean and variance on the corresponding quarterly/monthly scale. Useful if you are working with a variable diff(log(x)) (which may be scaled by 100). Default FALSE.

freq

Integer. The data frequency (e.g. 4 for quarterly). Only used when annualized_growthrate = TRUE. Default 4.

Value

A list with two elements: mean and var, giving the mean and variance of the implied normal distribution.

Details

Consider a CPI variable CPI <- data$CPI, observed at quarterly frequency. In the model, quarter-on-quarter inflation is used x <- 100*diff(log(CPI)). Suppose the prior belief is that annualized steady-state inflation lies between 1.7 and 2.3 with 95% probability (mean 2). On the quarterly scale used by x, this corresponds to a 95% interval of 0.425 to 0.575 (mean 0.5). Since it is typically more natural to elicit a prior on the annualized scale, the annualized_growthrate argument performs this conversion. See vignette("Homoscedastic-steady-state-BVAR") for usage in practice.

Examples

ppi(l = 1.7, u = 2.3, interval = 0.95)
#> $mean
#> [1] 2
#> 
#> $var
#> [1] 0.0234286
#> 
ppi(l = 1.7, u = 2.3, interval = 0.95, annualized_growthrate = TRUE, freq = 4)
#> $mean
#> [1] 0.5
#> 
#> $var
#> [1] 0.001464287
#>