Does anyone know how to obtain (the formula) the range of parameters with beta distribution? for example, in Smets and Wouters (2003), they said that with beta prior of mean = 0.75 and standard error = 0.05 for the calvo price parameters, the length of the contract (=1/(1-calvo), 1/(1-0.75)=4 quarters for the mean) ranges between 3 quarters to 8 quarters. I could not find this range using [0.75-20.05, 0.75+20.05].
Thanks for any help,
The beta is not the normal distribution. Hence, the rule of thumb with the two does not work. You can use en.wikipedia.org/wiki/Beta_distribution to compute the hyper-parameters. I guess it should be something along the lines of
mu=0.75; stdd=0.05; a = (1-mu)*mu^2/stdd^2 - mu ; b = a*(1/mu-1) ; x_low=betainv(0.05,a,b); x_high=betainv(0.95,a,b); calvo_low=1/(1-x_low) calvo_high=1/(1-x_high)
I may be wrong as only the lower bound fits.