Using Engel Curves to Estimate the Bias in the Australian CPI

The study investigates whether the Australian Consumer Price Index (CPI), a Laspeyres-type index known to suffer from substitution, outlet, new goods, and quality biases, accurately measures changes in the true cost of living (COLI). Relying on Engel’s law—that food budget shares decline as real total expenditure rises—the authors test if CPI-deflated food Engel curves from different years coincide once relative prices and demographics are controlled for. Systematic drift in these curves is interpreted as CPI mismeasurement. The purpose is to quantify the extent of overstatement in Australia’s CPI over 1975/1976–2003/2004 and to assess heterogeneity in CPI accuracy across demographic groups. Accurate inflation measurement is crucial for evaluating real GDP growth, productivity, real wages, income dynamics, and for policy uses such as indexation and monetary policy.

The paper reviews the Australian CPI’s evolution since its introduction in 1960, highlighting its Laspeyres construction with periodic reweighting and a major objective change in 1998 from a COLI for urban wage-earning households to a general household inflation measure, including removing interest charges and adding house purchase prices. Prior work applying Engel curve methods found the US CPI overstated inflation (Hamilton, 2001; Costa, 2001), consistent with the Boskin Commission’s estimate of roughly 1.1 percentage points annual bias. International applications show mixed evidence: overstatement in New Zealand and Canada, mixed or accurate performance in Norway. Engel-curve-based methods mainly capture substitution and outlet bias and generally provide lower-bound bias estimates, as they may not capture new goods or quality change biases. This study adopts and extends these methods to Australia.

The analysis uses food Engel curves estimated on Australian Bureau of Statistics (ABS) Household Expenditure Survey (HES) microdata from six survey waves: 1975/1976, 1984, 1988/1989, 1993/1994, 1998/1999, and 2003/2004. Food expenditures include food and non-alcoholic beverages consumed at home and away; total expenditure covers all major consumption categories. The food budget share is modeled using the Working–Leser specification: ω_ijt = φ + γ ln(p^f_jt/p^o_jt) + β ln(Y_ijt/p_jt) + X_ijt θ + μ_ijt, where relative food prices, real total expenditure, and household covariates enter, and μ_ijt is idiosyncratic error. Following Hamilton (2001), measured prices are decomposed into true price levels, CPI inflation, and measurement error; time dummies capture cumulative CPI mismeasurement δ_t relative to a base year (1984). Under the identifying assumption that bias in food and non-food prices is equal (r=1), cumulative CPI bias is inferred from δ_t via ε_t = δ_t/(-β), with a correction factor exp(-δ_t). A quadratic Engel curve extension (Costa, 2001) adds a squared log real expenditure term and is estimated by non-linear least squares to recover cumulative bias parameters. Data construction: multiple-family households were excluded, negative expenditures dropped, and the top/bottom 3% of expenditure and food share distributions trimmed per wave. Observations from ACT and NT were excluded where identifiable (1988 lacked state identifiers). The final sample comprises 30,132 households. Covariates include characteristics of the household reference person (sex, marital status, immigrant status, employment status including full-time, part-time, self-employed, indicator for age 65+), family characteristics (presence of dependent children and students, lone-parent indicator, household size top-coded at six), and state fixed effects. CPI series (total, food, non-food) from ABS were matched by survey period (third quarter) and state, rescaled to New South Wales in 1984 as the base. Semiparametric partially linear models were used for diagnostic checks of functional form. Sensitivity analyses tested robustness to excluding 1975 or 1988 waves, adding richer covariates (age bands and homeownership), using survey weights, and allowing the food price elasticity to vary with expenditure via interaction terms. Results were robust across these specifications.

- Full population: The CPI overstated the change in the cost of living. Quadratic Engel curve estimates imply cumulative bias of about 21% from 1984 to 2003 and 34% from 1975/1976 to 2003/2004, with average annual bias around 0.98% (quadratic) or 0.85% (linear) over 1984–2003; over 1975–2003, annual bias about 1.05% (quadratic) or 0.86% (linear). Estimated correction factors (quadratic): 1975=1.13 (SE 0.03), 1988=0.97 (0.03), 1993=0.96 (0.03), 1998=0.87 (0.02), 2003=0.79 (0.02), relative to 1984=1.00. - Subgroup heterogeneity (quadratic): • Singles: large overstatement—cumulative bias 34% (1984–2003) and 65% (1975–2003); average annual bias ~1.51% (1984–2003) and 1.80% (1975–2003). • Lone mothers: large overstatement—cumulative bias 26% (1984–2003) and 109% (1975–2003); average annual bias ~1.19% (1984–2003) and 2.67% (1975–2003). • Seniors: bias similar to full sample; cumulative bias 22% (1984–2003). • Couples without children: relatively accurate—cumulative bias ~3% (1984–2003), near zero or slightly negative long-run average. • Couples with children: modest overstatement—cumulative bias ~12% (1984–2003). • Working families: relatively accurate—cumulative bias ~6% (1984–2003); average annual bias ~0.11% (1975–2003). - The divergence between the official CPI and corrected COLI widened after 1998, coinciding with the CPI’s objective change and inclusion of house purchase prices amid rapid housing price growth. - F-tests reject the null that time effects are jointly zero, confirming statistically significant CPI mismeasurement.

By comparing CPI-deflated Engel curves across time while controlling for relative prices and demographics, the study attributes the systematic drift in food budget shares to CPI mismeasurement. The findings indicate that Australia’s CPI substantially overstates the true cost of living, implying that real incomes and real GDP per capita have grown faster than official statistics suggest. The heterogeneity across demographic groups shows that a single aggregate CPI does not function as a reliable COLI for all households: it notably mismeasures living-cost changes for singles and lone mothers but performs comparatively well for working families and couples, especially before 1998. The post-1998 divergence aligns with methodological changes to the CPI and rapid housing price increases, underscoring sensitivity to basket composition. These results are important for policy domains—benefit indexation, wage negotiations, and assessments of real living standards—where accurate COLIs matter, and suggest the value of group-specific COLIs.

The Australian CPI overestimated changes in the cost of living by roughly 1% per year on average over 1975/1976–2003/2004. Results are robust across linear and quadratic Engel curve specifications, alternative samples, weighting schemes, and models allowing price responsiveness to vary by expenditure. CPI mismeasurement is largest for singles and lone mothers, while couples and working families experienced relatively accurate CPI-based COLI changes. The paper recommends caution in interpreting the CPI as a COLI—particularly since 1998—and motivates the development of COLIs tailored to demographic groups and the use of multiple methodologies to track living costs.

- Engel curve approach captures mainly substitution and outlet biases; it may not reflect new product or quality change biases, so estimated CPI bias is a lower bound. - Identification relies on the assumption of equal bias in food and non-food prices (r=1) and uniform bias across regions; these cannot be tested directly. - Potential specification errors (e.g., omitted variables) that change over time could be conflated with CPI mismeasurement, though extensive covariates and sensitivity checks mitigate this concern. - The 1988 HES lacks regional identifiers, reducing variation for relative price identification in that wave. - Trimming and sample exclusions (e.g., ACT/NT, multiple-family households) may affect generalizability, although robustness checks suggest limited impact.