Given my "acknowledged statistical ignorance", I tried to find a *solution
*in this forum...
And this is not primarily a statistical issue, it is an issue about the
Hausman test in the R environment. 

I cannot imagine, no one in this forum has ever done a Hausman test on OLS
regressions.
I read in the systemfit package and found only this example referring to
2SLS and 3SLS regressions: 

data( "Kmenta" )
eqDemand <- consump ~ price + income
eqSupply <- consump ~ price + farmPrice + trend
inst <- ~ income + farmPrice + trend
system <- list( demand = eqDemand, supply = eqSupply )
## perform the estimations
fit2sls <- systemfit( system, "2SLS", inst = inst, data = Kmenta )
fit3sls <- systemfit( system, "3SLS", inst = inst, data = Kmenta )
## perform the Hausman test
h <- hausman.systemfit( fit2sls, fit3sls )
print( h )




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