Brash was Governor of the Bank for almost 14 years, during which he was able to tame New Zealand's historically high inflation. He helped usher in the bank's modern inflation targeting regime, an innovation pioneered in New Zealand and now imitated at many central banks around the world.
Brash left the bank for a political career, leading the National and Act Parties.
Brash said the Government's 2022 Budget, announced a fortnight ago, was "clearly unhelpful" in fighting inflation, and could force Orr into hiking rates faster.
"Both monetary policy and fiscal policy influence the level of total demand. The stronger the fiscal policy is, the stronger government spending is relative to its tax revenue, the stronger Adrian Orr's response has to be - and that's just the way it is," Brash said.
CPI inflation is currently at 6.9 per cent. The Budget announced $5.9 billion worth of new operating spending, plus a $1b cost of living package.
Treasury's BEFU forecasts said domestic inflation pressures were being "driven by strong domestic demand pushing up against constrained supply, which in turn has been compounded by the Russian invasion of Ukraine".
Treasury advice on the $350 payments that formed the centrepiece of the cost of living package warned they were likely to add to inflation pressures in the short term.
The bank itself, in its Monetary Policy Statement released last week, said "Government spending, as outlined in the 2022 Budget, is very high".
Brash said if the Government had announced less spending in Budget 2022, the Reserve Bank would not have had to announce such a fearsome round of interest rate hikes.
"The general consensus around economists is that had the Budget been less stimulatory than it in fact turned out to be, monetary policy would not be so tight, and forecast to be tighter," Brash said.
The bank itself denied this, Orr saying the Budget was not a "trigger point" for its OCR decision.
"What we saw from the Budget last week was an upward tick in demand pressure coming from the Government in the near term, more than was anticipated from the half-year economic update but relatively small beer compared with all the other drivers going on," Orr said.
Orr had a dollar each way in statements made later in the week, saying Government spending "is putting upward pressure on aggregate demand and hence inflation now," but "over the course of the projection period [Government spending] starts to have a negative impulse", meaning spending levels would begin to dampen inflationary pressure.
The bank's chief economist Paul Conway said "the overall impact of [Budget 2022] on the OCR track is negligible".
Brash said when it came to using fiscal policy or monetary policy to fight inflation, the Government has a political choice to make, which was who should wear the pain.
"The two are two sides of the same coin. The more the Government stimulates, the more Adrian Orr has to tighten monetary policy - put up mortgage rates effectively, and it's really effectively a question of who pays the cost of getting inflation down: is it the homeowner with the big mortgage, seeing his interest rates go higher, or is it other people who don't get the benefit which they would otherwise get from Government spending?" Brash said.
Brash said it was, however, "desirable" that house prices come down. Rising interest rates have pushed house prices down this year, and both Treasury and the Reserve Bank are forecasting further falls.
The Government has said it will announce $4.5b of new operating spending in next year's Budget, giving it the second largest operating allowance of all Labour's Budgets.
Brash said the Government will be tempted to spend more in election year, defying the Reserve Bank and Treasury's forecasts of fiscal tightening, and adding to inflation.
Brash said a big Budget next year would cause the bank to hike the official cash rate above 4. The OCR has not risen above 3.5 since it was slashed in 2008 to fight the global financial crisis.
"If the Government has a big Budget next year going into the election, which in historical terms wouldn't be a surprise, [Orr]'s going to go above 3.9, I'd be pretty confident," Brash said.
National has accused the Government's fiscal policy of making homeownership unaffordable.
National's Housing spokesman Chris Bishop released a statement on Sunday morning saying the Reserve Bank's most recent Monetary Policy Statement "will make for chilling reading for mortgage holders, with the central bank predicting the interest rate on one and two-year mortgages will hit 6 per cent next year".
"This will mean a major hit for Kiwi budgets. A household that has borrowed $700,000 would face annual interest costs of $42,000, meaning they would have to pay more than $800 a week before they even begin to reduce the actual loan," Bishop said.
"The pressure will be especially great for those who have recently entered the property market, with the Reserve Bank acknowledging that many first-time buyers from 2021 will find it difficult to pay their mortgages and cover their other expenses," he said.
The Bank's Monetary Policy Statement published research saying new buyers were paying more of their disposable income in mortgage servicing than at any point since the last months of the Clark Government, when the OCR was above 8.
The bank modelled the share of median household disposable income required to service a new 30-year mortgage on a median-priced house with a loan-to-value ratio of 80 percent at the average two-year mortgage rate, and found new buyers were having to pay more than 55 per cent of their disposable income servicing a loan.
Before the pandemic, this figure was 35 to 40 per cent. For most of National's time in office, the figure hovered between 35 and 45 per cent.
"Kiwis are already paying more to cover their loans than they have in a long time," Bishop said.
"According to the Reserve Bank, the share of disposable income required to service a new mortgage is approaching 60 per cent, the highest it has been since before the Global Financial Crisis, under the Clark Government," he said.