The RBA finds itself stuck between an overheated property market, which would seem to require higher rates to tame the "risks associated with high and rising levels of indebtedness", as governor Philip Lowe noted in his recent statement, and stubbornly low inflation, which would have the bank preferring to keep monetary policy as accommodative as possible.

Enter the jobs market. Last month the unemployment rate, as measured by the Australian Bureau of Statistics, climbed to 5.9 per cent, with a net loss of 6400 jobs from the economy. The poor numbers did much to dispel speculation that policymakers could be tempted to hike rates as soon as this year.

Those figures also moved the RBA boss to describe the labour market as "pretty soft", and to note that "we will want to see an improvement here before we can be confident that growth in the overall economy is strengthening". Mr Lowe will get his opportunity to do just that on Thursday, with the release of ABS employment figures for March.

"Trends in the labour market are particularly important to watch at the moment," CBA economist Kristina Clifton said. "While the RBA seems comfortable for inflation to be below target, they would be sensitive to a deterioration in labour market conditions."

NAB economist Tapas Strickland agrees that this week's labour figures "will take on greater than usual importance".

"The RBA [like the market] is holding faith to 'forward-looking indicators [which] still point to continued growth in employment over the period ahead'," Mr Strickland said, quoting Mr Lowe.

"How this divergence [between forward indicators and official jobs data] resolves itself will be crucial for the outlook for rates."

For now, the market is leaning towards lower, rather than higher rates. Fixed-income traders are pricing in just shy of a one-in-five chance of a rate cut by October, according to TD Securities. But the Canadian bank's rates strategist Annette Beacher highlighted the constraints on monetary policymakers at a time when regulators are intervening so energetically to take the heat out of property markets.

"The RBA can't possibly cut while APRA and ASIC try to cool housing demand," Ms Beacher said.

Meanwhile, property markets in the major cities continue to run hot. Sydney and Melbourne clearance rates jumped above 80 per cent over the weekend as the national volume of auctions reached its highest of the year.

Help for the RBA may be on its way. While the effects may not be immediately obvious, history suggests regulatory interventions in the housing market can and do dampen property price growth.

Caps on investor lending in 2015, combined with mortgage rate rises of around 0.27 percentage points from the four major banks slowed Sydney house price growth from 20 per cent in the year to April 2015 to zero in the year to April 2016, according to Westpac analysis, based on six-month annualised figures. The equivalent change in Melbourne was from 14 per cent to 4 per cent.

But Westpac chief economist Bill Evans said the latest moves in major lenders' mortgage rates was a more modest 0.17 percentage points, and the regulatory focus on interest-only lending, rather than investor lending. This suggests "the sharp slowdown in house price inflation in 2015 is unlikely to be repeated under the current set of policy and rate adjustments although some moderation in price pressures can be expected," Mr Evans said.

A further complication is that rising underemployment and weak wage growth is weighing on consumer confidence, something the Westpac sentiment survey for March should confirm on Wednesday. TD Securities' Annette Beacher notes that higher borrowing costs may "dampen" consumer confidence even further in the coming months.

This means that a desired cooling of the housing market may come at the cost of retail spending, and therefore economic growth. This could further complicate the RBA's task. Moderating house price growth and a firming economy are the ideal combination. This week will provide clues on whether governor Lowe's task is set to become simpler, or more complicated.