"Mr Key has already written to the Remuneration Authority, which sets MPs' pay, asking it not to award a pay rise this year.
He also said he understood Governor-General Anand Satyanand was writing to the authority requesting no pay rise, "so I'm sure judges and the like will also take a similar view"."

I think the move borders on being unconstitutional, either by failing to accord judges a pay increase they are entitled to or for a member of the Executive to publicly champion that course of action.

Financial security of the judiciary is important element of the fundamental principle of judicial independence. As Joseph explains (Constitutional and Administrative Law, 2007, page 779):

"Judges' remuneration must not fall beneath a minimum level that could be perceived as exposing them to political pressure through economic manipulation."

Former Chief Justice Eichelbaum once noted that "guaranteed tenure of office for Judges, and adequate remuneration" was one of the essentials to support judicial independence ((1997) 6 Canterbury LR 421).

To a certain extent, this principle or convention has been expressly reflected in our constitution. Section 24 of the Constitution Act 1986 specifically directs that judges' salaries not be reduced:

24 Salaries of Judges not to be reduced
The salary of a Judge of the High Court shall not be reduced during the continuance of the Judge's commission.

(This provision has its origins in the Act of Settlement 1700 and which, as Palmer and Palmer put it (page 296), "was designed to protect the judges by removing the Crown's unfettered discretion to dismiss them".)

Whether this express protection would be breached by failing to increase salaries in line with inflation etc is unclear.

Authority from the United States suggests that such indirect, non-discriminatory reduction in salaries do not breach a similar protection (Joseph, 779). However, previously analysis in the New Zealand context has raised constitutional concerns about interference with judicial salaries:

- When previous attempts where made to voluntarily ask judges to request their salaries be reduced (1921) or for a request to be made for judges to voluntarily refund of their salaries (1932), such proposals were described as being "constitutionally improper" (Scott, The New Zealand Constitution, 1962, page 162).

- When changes were proposed to be made to the Government Superannuation Act, which would have seen a reduction in benefit entitlements for MPs and judge (1991), the then Solicitor-General - now Supreme Court judge - John McGrath, concluded that such specific changes directed at judges would be improper:

Such reductions would in effect diminish the security of judges in their office, which turns not only on their secure tenure as such but on undiminished remuneration during their tenure. As such the changes would be a measure detrimental to the independence of the judiciary, contrary to s 24 of the Constitution Act and in breach of the constitutional convention it articulates.

I'm not prepared, without more research and reflection, to definitively conclude that a wage freeze (effectively a reduction in salary in real terms) is unconstitutional per se. But it's fair to say that it is looks pretty dodgy at least, particularly as there seems to have been no explicit acknowledgement of the constitutional concerns it might raise.

And the public comments made by the Prime Minister championing such an approach might also be objectionable in their own right. Judicial independence and the separation of powers also requires constitutional actors to respect the underlying constitutional principles and sphere of responsibility. Ordinarily this manifests itself in the principle that Ministers should not express any views that could be regarded as reflecting adversely on the impartiality, personal views, or ability of any judge (Cabinet Manual, para 4.13). But it's not hard to see how the same principle would apply by analogy to encouraging approaches to judicial remuneration that might undermine judicial independence.

PS: People might also be interested in the two big Canadian cases on judicial remuneration, albeit operating in a slightly different matrix:
> http://csc.lexum.umontreal.ca/en/2005/2005scc44/2005scc44.html
> http://csc.lexum.umontreal.ca/en/1997/1997rcs3-3/1997rcs3-3.html