Department of "Huh?!": John Cochrane and Ricardian Equivalence II

Paul Krugman wrote about a family that decides to borrow $100,000 and so trigger a contractor to build a new house which it then buys. He says that even under full Ricardian Equivalence on the order of 94% of the house construction and purchase is an addition to aggregate demand: A Note On The Ricardian Equivalence Argument Against Stimulus: If the house is newly built, that’s$100,000 of spending…. But the family has also taken on [$100,000 of] debt…. Its annual mortgage payment will be something like$6,000, so maybe you would expect a fall in spending by $6000 [under Ricardian Equivalence]; that offsets only a small fraction of the debt-financed purchase…. [T]his family is very much like the representative household in a Ricardian equivalence economy, reacting to a deficit financed infrastructure project like Lucas’s bridge… its reaction involves very little offset to the initial spending… John Cochrane, responding to this, writes: The Grumpy Economist: So, according to Paul, "Ricardian Equivalence," which is the theorem that stimulus does not work in a well-functioning economy… (Which it is not: an economy can be well-functioning and yet still have people immigrate and emigrate, die childless, fail to leave bequests, care about their descendants in other ways than seeking to maximize their subjective utility, etc., etc. And if any of those take place "Ricardian Equivalence" fails.) …fails because it predicts that a family who takes out a mortgage to buy a$100,000 house would reduce consumption by $100,000 in that very year… But that is not what Paul Krugman wrote. That is not at all what Paul Krugman wrote. What Paul Krugman wrote was that Bob Lucas did not understand Ricardian Equivalence, and that even under full Ricardian Equivalence a family that finds itself with an extra$100,000 of debt would reduce consumption by only $6,000 in that year. Cochrane has gotten Krugman's argument backwards. And then Cochrane repeats a part of Krugman's argument using the exact same numbers Krugman used: People who take out a$100,000 mortgage with $6,000 payments per year should spend about...$6,000 per year less on other things. Much of that $6,000 comes out of rent they are no longer paying on the house or apartment they moved out of, so there is not necessarily any change in their consumption of housing services. Some of the$6,000 goes to principal payments, which are a form of saving, allowing the household to put less in the bank. So, in fact they need not change consumption or saving at all!

How can anybody do this?