The HAUSMAN option on the FIT statement incorrectly computes the Hausman statistic and corresponding p-value for all comparisons except for the OLS vs. 2SLS comparison. For all other comparisons:

OLS vs. SUR
OLS vs. 3SLS
2SLS vs. 3SLS

the sign of the Hausman test statistic is opposite of what it should be, which then causes the p-value to be incorrect.

The sign of the test statistic is opposite of what it should be due to the manner in which a component (q) of the statistic is calculated. For example, in the 2SLS vs. 3SLS comparison, q should be calculated as:

beta_2SLS - beta_3SLS.

However, PROC MODEL computes q as:

beta_3SLS - beta_2SLS.

To circumvent the problem for the aforementioned cases, use the PROBCHI function in the DATA step to compute the correct p-value. The correct p-value can be calculated as:

p_value = 1 - probchi(m,df);

where m is the Hausman statistic computed by PROC MODEL, but modified with the opposite sign, and df are the degrees of freedom associated with the statistic as provided in the PROC MODEL output.

Note that negative m statistics result in an invalid argument to the PROBCHI function and may be due to an insufficient sample size or model misspecification.