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For instance, income elasticity may be known to be less than 1 for some countries, or autocorrelation is known to be between -1 and 1. Either way, a Bayesian approach allows us to combine that external information with what we observe in the current data to form a more realistic view of the economic process of interest.
As a quick introduction to Bayesian analysis, we use an example, described in Hoff (2009, 3),
of estimating the prevalence of a rare infectious disease in a small city. A small random sample of
20 subjects from the city will be checked for infection. The parameter of interest 2 [0; 1] is the
fraction of infected individuals in the city. Outcome y records the number of infected individuals in
the sample. A reasonable sampling model for y is a binomial model: yj Binomial(20; ). Based
on the studies from other comparable cities, the infection rate ranged between 0.05 and 0.20, with
an average prevalence of 0.10. To use this information, we must conduct Bayesian analysis. This
information can be incorporated into a Bayesian model with a prior distribution for , which assigns
a large probability between 0.05 and 0.20, with the expected value of close to 0.10. One potential
prior that satisfies this condition is a Beta(2; 20) prior with the expected value of 2=(2+20) = 0.09.
So, let’s assume this prior for the infection rate , that is, Beta(2; 20). We sample individuals
and observe none who have an infection, that is, y = 0. This value is not that uncommon for a small
sample and a rare disease. For example, for a true rate = 0.05, the probability of observing 0
infections in a sample of 20 individuals is about 36% according to the binomial distribution. So, our
Bayesian model can be defined as follows:
Now fit your Bayesian VAR models with bayes: var.
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