Inflation is expected to rise, boosted by higher tobacco taxes and prescription charges.
The Consumer Price Index for the first three months of the year is released on Wednesday, when ASB Bank expects a quarterly increase of 0.6%, bringing the annual rate of inflation to 1.1%.
That's just inside the bottom end of the Reserve Bank's 1% to 3% target band.
ASB senior economist Jane Turner said construction costs and rents are also picking up, particularly driven by the rebuilding of Christchurch, though outside that, demand pressures remain subdued.
She said the March quarter increase has been driven by administrative charges including the tobacco tax increase on 1 January and also a reduction in health care subsidies.
But aside from that, Ms Turner said there has been a pick up in construction costs as Canterbury starts to be rebuilt and also continued growth in rentals being driven by supply shortages in Auckland and Canterbury.
Outside of the housing and rental markets there are indications that demand remains quite subdued, in the December quarter there was evidence of aggressive discounting.
Ms Turner said overall price pressures remain subdued and will not be a concern for the Reserve Bank at the moment.
While the economic recovery is picking up pace, Ms Turner expects the Reserve Bank to start raising the official cash rate from its record low of 2.5% from March next year.