Since November 2015, Immigration NZ has approved 97 per cent of visa applications for such positions, with only 577 visa applications declined.
"The declined volume trend appears to be increasing slightly over time but numbers are very small, meaning little change has been noticed in the overall rate," the Mbie briefing to Goldsmith, presented in December and recently released, states.
"This initial information indicates that there are only low-levels of beneficiaries finding employment due to the front-loading process.
"Mbie and MSD will work together to undertake further analysis of outcomes, and consider the scope for operational and policy change to ensure that the front-loaded labour market test is performing as it should."
Immigration Minister Michael Woodhouse said the Mbie briefing was wrong.
"If the system was working, the proportion of successful applications would go up, not down. I think they have misunderstood the data."
The change was designed to help streamline the hiring process and reduce frustration for employers, Woodhouse said.
"It may well be that employers having put the process in place then did find there were New Zealanders available to do the job and then did not continue with the application for the visa. It follows that trend would not appear in the statistics given to Minister Goldsmith."
Immigration an election issue
Migration numbers for the year to January 31 showed a net migration gain of 71,300.
That's a record for a 12-month period and the first time in New Zealand's history the gain has topped 71,000.
NZ First leader Winston Peters has called for a drastic reduction in migration, saying New Zealanders are missing out on jobs and infrastructure is not coping.
Labour's immigration spokesman Iain Lees-Galloway said the net migration figures showed National had no plan for immigration and its impact on New Zealand.
But Prime Minister Bill English cited the large number of young Kiwis failing workplace drug tests as a reason not to further limit unskilled migrant numbers, despite 140,000 New Zealanders being out of work.
English said the Government was still getting "robust" complaints from businesses that they could not fill vacancies, especially the hospitality and horticulture industries.