Parker told the House the issue was that dead people were incapable of notifying the IRD that they had died. The way the IRD found out whether people had died was usually through a sporadic sharing of data with the Department of Internal Affairs.
National Party deputy leader Nicola Willis asked Parker whether he could be "confident that no deceased people have been paid the cost of living payment?"
Parker replied with a poem from James K Baxter, which he deduced to mean "in other words: after someone has died, they can't update their details to Inland Revenue".
"What Inland Revenue relies upon is periodic information that comes through from Internal Affairs, which is itself imperfect but the best that the country has."
Parker was unsure about the number of dead people who were having the payment deposited into their account.
"Probably around the same number as deceased people's bank accounts that get superannuation or unemployment or other payments," Parker said.
Willis said that "not only are London expats and French backpackers who haven't worked or lived in New Zealand for years receiving the payment, but now it has been revealed that dead people may have been paid out too".
"This is a total mess. Labour has a complete and utter disregard for taxpayers' money, not only spraying it overseas to people who are ineligible under the law but giving it to those who are literally unable to use it," Willis said.
Labour has been on the back foot over the cost of living payment this week, after it was revealed 800,000 of the 2.1 million people who are estimated to be eligible for the scheme are yet to actually claim it.
"While many dead people may have received this payment, many more Kiwis who actually need it have missed out," Willis said, noting "800,000 fewer people receiving the payment than was initially promised".
Labour insists the 800,000 people are likely to get their tax cuts, but only after they file their tax returns confirming their eligibility.
For the curious - the poem Parker recited was Baxter's High Country Weather:
Alone we are born
And die alone;
Yet see the red-gold cirrus
Over snow-mountains shine.
Upon the upland road
Ride easy, stranger:
Surrender to the sky
Your heart of anger.