Normal-Wishart Prior

[apopescu]

Hi,

I have some questions and issues with the way the NIW prior is implemented, including in EViews 9.

1. Is it not clear to me whether you are implementing the independent Normal - Wishart or the natural conjugate NIW. The manual seems to suggest that it is the conjugate, but is is not clear and there seem to be several mistakes (Ch 18, p 596).

2. It is not clear to me why EViews allows the user to only specify 2 hyperparameters, miu1 and lambda1, instead of the 4 which characterize this prior. It is also unclear how the variance of theta, which should be of the Kronecker form, can be written as lambda1*I. Also, strangely, lambda1 going to 0 implies a more non-informative prior, when it should actually mean a very tight prior.

I would be very grateful if you could provide the references as to how this prior was implemented.

Thanks & regards,

Adina

[EViews Esther]

Hi Adina,

Yes, EViews implemented the conjugate Normal-Wishart prior and derived the analytical posterior results.

The current EViews allows you to specify only 2 hyperparameters, mu1 and lambda1, for the coefficients Normal prior. The Wishart prior values are fixed as S = identity (scale matrix) and nu = m (degree of freedom) for calculation convenience.

Since EViews specifies the coefficient covariance prior as V0 = lambda1 * identity, the kronecker form becomes Sigma kron V0 = lambda1 (Sigma kron identiy), which may be undesirable restriction.

I thank you for your observation and I will incorporate your suggestions in the documentation.

Best,
Esther