How we tested the Census against house prices

How each figure in What the Census says about house prices was found and tested. Every number below is written from the analysis’s results file by the page’s build, from official data under open licences (ABS).

The data

• Census: every cell of the 2021 Time Series Profile, which gives 2011, 2016 and 2021 on 2021 boundaries: 1,582 measures for each SA2 and 2,309 for each council after shares were taken of their proper totals and near-empty cells dropped; and 187 measures aligned across the Censuses from 1991 for each state (ABS). The ABS publishes no time series for suburbs, so suburbs are joined to SA2s through 117,170 mesh blocks, weighted by dwellings (ABS Mesh Block Counts).
• Prices: suburb medians from Valuer-General Victoria (2014–2025) and South Australia (2014–2025, yearly figures weighted from quarters); 549 SA2s priced (Victoria 453, Adelaide 96), where at least 60% of dwellings sit in priced suburbs. Victoria’s 79 councils from 1995. State indexes from 1986, spliced from ABS series (ABS).
• Migration: net overseas, interstate and natural increase by state from 1981; net overseas migration by country of birth by state 2004–05 to 2024–25 (ABS).

Census housing costs as a stand-in for prices

Correlation within each state, number of areas in brackets (ABS; Valuer-General Victoria).

Every measure, three screens

Each of 1,580 SA2 measures, by rank correlation within state: found in Victoria with the false discovery rate held at 5%; held in South Australia (same sign, p < 0.05); and held in the other period (ABS; SA). The strongest ten of each, near-duplicates and the rent and mortgage bands left out; labels are the ABS’s own.

Price level, 2021

Growth 2016–21, from 2016 values

Growth 2016–21, from the change 2016–21

Victoria’s councils over 30 years

Of 2,307 measures, 126 kept one sign of relationship with growth across 2011–16, 2016–21 and 2021–25, against 577 expected by chance; 3 were significant all three times. Growth in one five years against the next (Valuer-General Victoria):

All 546 councils, housing-cost growth 2011–21

Found in NSW, Queensland and the NT, held in the other states: 485 found, 295 held, 258 also held in 2016–21; 86% agreed in sign (ABS). Strongest ten:

States

Eight states over six five-year periods from 1991, state and period effects removed, 2,000 shuffles within period: 6 of 181 starting levels significant after the false discovery rate (9 would pass p < 0.05 by chance), none without the Northern Territory (ABS; ABS prices).

Each year from 1988 to 2025, state and year effects removed (ABS):

Country of birth

These measure where populations grew and settled, not how any group behaves. Most country-of-birth series rise and fall with total migration, which follows visa settings, the economic cycle and border closures; arrivals include renters, students and temporary residents as well as buyers. Each is therefore shown after controlling for total population growth. SA2s: of 25 countries, 6 significant in 2016–21 after the false discovery rate, 0 held in 2021–25 (ABS).

State by year, 50 countries, each as net overseas migration of people born there as a share of the state’s population, partial on total population growth (ABS):

The models, tested

Ridge regression of annualised SA2 price growth 2016→2021 on 15 Census variables (2016 values; chosen on the training data only by within-state rank correlation, skipping any correlating above 0.85 with one already chosen), the log 2016 price level and a South Australia indicator; penalty by 5-fold cross-validation in SA3 blocks. Tested on 2021 values → growth 2021→2025, a period the model never saw. Its 15 measures, chosen on 2016–21 alone:

• Persons Management and commerce Age 25 34 years (−0.58)
• Persons Bachelor Degree Level Age 25 34 years (−0.55)
• Couple family with children Social marital status of parents Married in a registered marriage Number of dependent children usually resident One (−0.55)
• Persons Agriculture environmental and related studies Total (+0.54)
• Persons Bachelor Degree Level Age 20 24 years (−0.54)
• Persons per square kilometre (2021 boundary, ASGS area) (−0.54)
• Semi detached row or terrace house townhouse etc Three bedrooms Number of persons usually resident in family households Four (−0.54)
• Persons Management and commerce Total (−0.53)
• Persons Information technology Total (−0.52)
• Separate house Number of persons usually resident Two (+0.52)
• Highest non school qualifications Certificate Level Total Persons (+0.52)
• Age group of parent Total Number of children ever born Four children (+0.51)
• Separate house Total Number of persons usually resident in group households Two (+0.50)
• Financial and insurance services Persons (−0.50)
• Persons 15 19 years Employed Worked full time (+0.50)

Calibration on 2021–25, by fifth of the model’s picks: predicted against actual relative growth, points a year (Valuer-General Victoria; SA).

Chosen on the 2021→2025 out-of-sample test, a period neither model saw: relative R² 0.481 for the price level alone (with a state term) against 0.29 for the Census and price-level ridge model. The illustration therefore uses the price level alone: within each state, how far an area's 2025 median sits above or below the state's, refitted on both periods.

States

Financial-year state price growth relative to the average of the states that year. Two variants: on population growth and the NOM rate (relative the same way) with a constant per state; and on relative population growth alone, with no state constants. Each fitted 1988–2015 and tested 2016–2025; the better one on the test illustrates 2025–26 to 2027–28 with the Centre for Population's 2025 projections. The illustration uses the variant with the better out-of-sample R² against the state average over 2016–2025: population growth and NOM with a constant per state (0.213 against 0.173).

What the results cannot show

• Areas, not people. Every result compares places. A measure that marks expensive suburbs says nothing about any resident, and country-of-birth measures mark where people live, not what they do.
• Boundaries. The Census series is on 2021 boundaries; a suburb’s price reaches its SA2 through a dwelling-weighted join, and suburb medians are not SA2 medians. Before 2011 only states align.
• The 2021 Census was taken in lockdown, with few students and visitors, and the 2016–21 prices include the move from inner cities in 2020–21.
• Nominal dollars, and medians that move with the mix of homes sold; South Australia’s yearly medians are weighted from quarters.
• Prices for two states only. New South Wales licenses its sales data for non-commercial use only; Queensland, Western Australia, Tasmania, the Northern Territory and the ACT publish none openly.
• Many tests. Thousands per screen; the false discovery rate, a second state and a second period are the guard. The Northern Territory’s price series is the weakest, so state results are shown without it too.

Sources

1. ABS, Census DataPacks: 2021 Time Series Profile (SA2, LGA, state, Australia), 2006 and 2001 Time Series Profiles, 1996 Basic Community Profile, 2021 General Community Profile. CC BY 4.0.
2. ABS, ASGS Edition 3 allocation files, Mesh Block Counts 2021.
3. Valuer-General Victoria, property sales statistics; Government of South Australia, Metro median house sales. CC BY 4.0.
4. ABS, Total Value of Dwellings, Residential Property Price Indexes, House Price Indexes (6416.0).
5. ABS, National, state and territory population, Overseas Migration, Australia’s Population by Country of Birth.
6. Centre for Population, 2025 Population Statement. CC BY 3.0 AU.