Ministers need to raise public sector pay to help retain skilled staff, the Institute for Fiscal Studies (IFS) economic research group has said.
More restraint "would take public pay to historically low levels relative to that in the private sector", it says.
Average weekly public sector pay has fallen by 4% in real terms in the past eight years, and "higher paid groups have fared least well", the IFS said.
But the government faces a conundrum as to how to fund pay increases.
Last week the government said the cap on public sector pay rises in England and Wales was to be lifted, with ministers getting "flexibility" to breach the longstanding 1% limit.
However, the government "is between a rock and a hard place" IFS senior research economist Jonathan Cribb told the BBC.
"If the government keeps the cap in place, it's harder to keep the staff it needs, but if it's increasing pay, that's going to cost a significant amount of money," he said.
Relaxing the pay cap and increasing public sector pay in line with inflation or private sector pay would cost public sector employers about £3bn a year in 2018-19, rising to about £6bn a year in 2019-20, the IFS research published on Wednesday suggested.
Because of the relative sizes of the workforces, the cost of increasing pay for police or the armed forces would be much smaller than increasing pay in the NHS, schools or the civil service, it added.
If ministers decide not to spend more money, they can either not increase pay, and face difficulties recruiting, retaining and motivating staff, or they can pay more out of existing budgets, but not be able to pay as many staff, Mr Cribb said.
However, if the government decides to give departments more money, it will have to either raise taxes, increase borrowing so future generations will pay, or find cuts elsewhere - for example, in the pensions budget, he added.
It would be fair to call this "a conundrum", Mr Cribb said.
Last week, chief secretary to the Treasury Elizabeth Truss said:
"We will continue to ensure that the overall package for public sector workers recognises their vital contribution and ensures that we can deliver world class public services, while also being affordable and fair to taxpayers as a whole."
Analysis: BBC economics correspondent Andy Verity
The IFS says that after allowing for inflation, public sector earnings have fallen by 4% under the coalition and Conservative governments.
While private sector pay was hit even harder in the immediate aftermath of the 2008 financial crash, it's been catching up.
Educated public sector workers such as teachers or senior civil servants are now paid less, by comparison to their private sector counterparts, than they were before the crisis.
The IFS says that if the public sector pay cap is kept it will become ever harder for schools, hospitals and other public services to attract and hang onto skilled staff - especially in the south-east where living costs are highest.
Public sector pay was frozen for two years in 2010, except for those earning less than £21,000 a year, and since 2013 rises have been capped at 1% - below the rate of inflation.
Last week, No 10 said the existing pay cap was at an end.
Police chiefs warned that making forces fund a pay increase themselves would put "financial pressure on already stretched budgets".
And unions said police getting a 1% rise plus a 1% bonus and prison officers a 1.7% rise would still be a real terms cut.
In August, UK inflation rose to 2.9%, its joint highest in more than five years, continuing to outpace wages.
The fall in the value of sterling since the EU referendum continued to be a major impetus for rising prices, the Office for National Statistics said.