Suppose I have the following relation:
X(t+1) = Alpha + Beta*Y(t) + …
Based on the theoretical model beta is assumed to be negative, i.e., the relationship between X and Y is negative. So I want to define priors such that the support of the posterior distribution reflects that. However, as far as I know Dynare does not allow truncated normal distribution.
So I was wondering if I could use the following trick: rewrite the equation such as:
X(t+1) = Alpha - Beta*Y(t) + …
And then use a Gamma Distribution for Beta. In this case beta will assume a positive number, but in the model a “positive” beta means that the correlation of X and Y is negative, as it is supposed to be.
My question is: the posterior mean/mode will be a positive number, of course, but can I interpret this number as a “negative” number in the spirit of the model?
For example, after the estimation I get beta =0.5. So that means that the correlation between X and Y is -0.5! Am I correct?