Curbing migrant workers' benefits will do very little to slow immigration to the UK, a senior member of the Office for Budget Responsibility cautioned.
The withering assessment of Prime Minister David Cameron's central EU renegotiation demand was given to MPs by respected economist Sir Stephen Nickell.
Mr Cameron is engaged in a battle with other leaders over his demand the UK be able to deny migrants in-work benefits for four years - which he says would cut the flow of foreign job-seekers.
Sir Stephen said the OBR had not done any detailed analysis of the consequences of the squeeze as it was not yet Government policy so fell outside the watchdog's remit.
But asked for his personal opinion, he told the Treasury Select Committee: "Changing the benefit rules for EU migration so that they become more difficult to obtain - you are asking me what impact that is likely to have.
"In my opinion: not much."
Asked if he could expand, he said: "I have no idea because I have not investigated it.
"I am prepared to say that any changes to benefit rules are unlikely to have a huge impact on migration flows.
"But to go further and start trying to analyse the actual consequences is not within our remit."
Sir Stephen, a former member of the Bank of England Monetary Policy Committee, did however say there was "quite a lot of evidence that the differential in job opportunities, the differential in pay, is a significant factor in migration flows ... around the world."
He spoke out shorty after Work and Pensions Secretary Iain Duncan Smith insisted that the door remains open for Britain to secure its welfare demand after European Council president Donald Tusk said there was "no consensus" among the EU's 28 member states on it.
Mr Tusk said on Monday that the other 27 national leaders would need to "hear more" from Mr Cameron before coming to a conclusion on the issue, which he described as the "most delicate" element of the renegotiation of Britain's membership ahead of the in/out referendum promised by 2017.
The comment was widely interpreted as an indication that concessions may be needed from the Prime Minister, who has himself said that he is "open to different ways of dealing with this issue".
But Mr Duncan Smith said that Mr Tusk's letter was "carefully drafted to say that the door is still open" to discussions on Britain's proposal and he was "upbeat" that Mr Cameron will be successful.
Asked what alternatives to the four-year ban he would personally be ready to accept, the Work and Pensions Secretary replied: "That they agree with us. That's an alternative to the way the EU sometimes goes about its business."
Several European leaders have cautioned that the UK scheme would breach the principle that benefit rules should not discriminate against non-native workers from other EU states.
But Mr Duncan Smith insisted that in private, ministers from countries such as Germany and France had agreed that there was "something fundamentally wrong" about a system which makes migrants eligible to claim benefits immediately on arrival in a country where they have made no contribution to the welfare system.
"As usual, it is the British who have to make the case, but behind closed doors they all agree it is an issue," he said.
Asked whether he expected Mr Cameron to make concessions to reach agreement on a reform package at a Brussels summit in February, Mr Duncan Smith said: "My general sense is that the case is still there and the Prime Minister is still going to make it. I remain upbeat."