text: For the same reason that the highest mountain in the world is at least as high as the highest mountain in US.\n\nUnrestricted model includes the restricted one as a special case, i.e. as a subset of coefficients that go into it. Most estimation choose coefficients that minimize the error. Wider set of coefficients to choose from means that errors cannot increase. \n\nProof: If you have an estimate from restricted model, the coefficients are still valid for unrestricted model & generate same error. If some unrestricted coefficients give you lower error, good; if not - you still have restricted estimate and it's error.