Does the Phillips Curve Lie Down as We Age?
What this paper finds — and why it matters
Layer 1: Overview
Research question and motivation: The paper asks whether population aging flattens the Phillips curve through a previously unexplored channel — age-related differences in the elasticity of substitution across product varieties. Existing work on demographics and monetary policy emphasizes wealth, liquidity, and life-cycle savings channels. The authors instead argue that if older consumers are less willing to substitute across varieties of goods (i.e., they have a lower elasticity of substitution), then firms selling to them have more market power, adjust prices less responsively to marginal cost, and the slope of the Phillips curve falls. Because advanced economies are simultaneously aging and exhibiting a flattening Phillips curve, this offers a structural, demographically-driven explanation.
Data and empirical strategy: The empirical analysis uses barcode (UPC) level retail purchase data from the NielsenIQ Homescan Consumer Panel, 2004-2019. The panel is rotating and nationally representative, surveying between 40,000 and 60,000 households per year (average 57,355 households/year), capturing over 900 million transactions and 1,117 product modules. Purchases are aggregated into five age groups (25-34, 35-44, 45-54, 55-64, 65+) within more than 1,000 disaggregated product modules. The elasticity of substitution within modules is estimated by age using the Feenstra (1994) / Broda and Weinstein (2006) supply-and-demand identification (applied as in Jaravel 2019), with Equation (4) estimated by weighted least squares and aggregate elasticities formed as expenditure-share-weighted averages of module elasticities. Each module must have at least 20 purchasing households.
Main quantitative findings: The youngest cohort (25-34) consistently has the highest elasticity and the oldest (65+) the lowest; the middle groups (35-64) are non-monotonic. Median elasticity is 5.73 for the oldest and 7.02 for the youngest, in line with prior estimates (Broda-Weinstein 2010, Hottman et al. 2016). The maximum gap (oldest vs. youngest) is 1.29 for medians and 1.55 for means — larger than the 0.375 difference Faber and Fally (2022) find between richest and poorest income quintiles. A decomposition (Table 1) attributes the 65+ vs. 25-34 gap to one-third lower within-module elasticities and two-thirds a composition effect (older baskets weighted toward lower-elasticity products); for other age groups vs. 65+, 55-60% comes from the within-module elasticity term. The age pattern survives income controls and is most pronounced in the top two income quartiles (over 70% of expenditure share), so the authors conclude the age gradient is not driven by income.
Mechanism and theory: They extend a Rotemberg (1982) price-adjustment model to multiple consumer types. The log-linearized Phillips curve slope (Eq. 7/19) is the population-weighted average elasticity, sum_a (sigma_a - 1) s_a / phi. A lower share-weighted average elasticity flattens the curve: firms facing less price-sensitive (older) demand have more market power, can delay price changes, so inflation responds less to marginal cost. They note this does not hold in a first-order Calvo approximation with constant returns, but show in an Online Appendix menu-cost model that for empirically relevant parameters a lower elasticity reduces the probability of price adjustment, extending the result.
Quantitative exercise: Calibrating phi = 122 to match a 2022 Phillips-curve slope of 0.055 (the Gagliardone et al. 2023 midpoint of an estimated 0.05-0.06 range), then feeding in 1984 consumption shares yields a slope of 0.056 — a 2.3% reduction over 1984-2022. Benchmarked against the literature’s roughly 50% (halving) decline in the slope (Furlanetto and Lepetit 2024), the demographic channel accounts for about 4.5% of the observed flattening (2.3/50 = 4.5). The authors describe this as not large but a genuine contributing factor.
Layer 2: Deep Dive
What is the identification strategy for the elasticity of substitution, and what are the main threats to it?
They use the Feenstra (1994) and Broda-Weinstein (2006) double-difference approach. For each product module they specify a CES demand equation relating changes in expenditure shares to changes in prices (slope -(sigma_m - 1)) and an inverse supply equation. Differencing both relative to a reference barcode k eliminates the time-varying intercepts (alpha_mt, phi_mt). Assuming the differenced demand and supply errors are uncorrelated, the two are combined into a single moment condition (Eq. 4) involving squared and cross-product terms of differenced prices and shares, estimated by weighted least squares; sigma_m and the inverse supply elasticity omega_m are backed out from the estimated theta coefficients subject to sigma_m > 1 and omega_m > 0. The key identifying assumption is the orthogonality of demand and supply shocks (changes in unobserved quality vs. supply-side shocks). A second threat the authors directly address is that age correlates with income, so age differences in elasticity could reflect income; they rebut this by re-estimating within income halves. They use only continuing barcodes (present in t and t-1) to measure period-to-period changes, and exclude non-UPC ‘magnet’ items like fresh produce.
How is the age effect distinguished from an income effect?
Income in the Homescan data is reported in discrete bins with a two-year lag, so the authors instead construct per-capita expenditure as an income proxy (following Faber and Fally 2022), regressing log total expenditure on household-size dummies and household attributes and netting out size effects; an appendix table shows this proxy is monotonically increasing in reported income bins. Re-estimating elasticities within the lower and upper 50% of the (expenditure-proxied) income distribution (Table 2), the falling-with-age pattern remains apparent conditional on being high income — indeed the gap across ages is even starker at higher incomes. Since upper-income households account for the large majority of expenditure within each age group, the pooled estimates track the upper-income pattern. The authors conclude the age gradient stems from a factor of age unrelated to income.
What are the two channels behind the age-elasticity gap, and how are they separated?
A decomposition (Table 1) splits the overall elasticity gap between each younger group and the 65+ group into (i) a ‘difference from sigma’ term that varies module elasticities while holding expenditure weights fixed (older people have lower elasticities within the same modules), and (ii) a ‘composition’ term that holds module elasticities at the 65+ values and varies expenditure weights (older baskets tilt toward lower-elasticity modules). For the largest gap (65+ vs. 25-34), about one-third is the within-module elasticity effect and two-thirds is composition; for the other age groups vs. 65+, 55-60% is the within-module elasticity effect.
Why does a lower elasticity flatten the Phillips curve mechanically in the model?
In the multi-type Rotemberg model the non-linear pricing FOC (Eq. 5) scales marginal cost by consumption weighted by each cohort’s elasticity. Log-linearizing around zero-inflation steady state gives a slope equal to the share-weighted average (sigma-bar - 1)/phi. A lower sigma means products are less substitutable, firms have more market power and are less sensitive to marginal-cost changes, so they can absorb cost changes or delay passing them through without losing demand — making larger but less frequent price changes. Marginal cost must move relatively more to generate the same inflationary pressure, hence a flatter curve. As the old (lower sigma) consume a rising share of output, sigma-bar falls and the curve flattens.
Doesn’t the Calvo model undercut the result, since elasticity doesn’t enter its Phillips-curve slope?
To a first-order approximation around zero-inflation steady state with constant returns to scale, the elasticity of substitution does not affect the Calvo Phillips-curve slope, because the price-adjustment probability is exogenous and independent of pricing power. The authors address this two ways. First, with decreasing returns the Calvo slope does depend on elasticity (a higher elasticity flattens it via marginal-cost dispersion), an effect absent under Rotemberg because there is no price/cost dispersion. Second, and more importantly, in a one-period menu-cost model (Online Appendix B) they show the firm’s willingness to pay the fixed cost and update prices is increasing in sigma for empirically relevant parameters (6 < sigma < 11, phi around 0.5 implying a 5-10% profit share). Since Calvo is a special case of dynamic menu costs, a lower elasticity maps to a lower adjustment probability and thus a flatter curve, so the result extends beyond Rotemberg.
What does the quantitative exercise actually compute, and what are its limits?
It is explicitly not a full-scale evaluation — it was added at a reviewer’s suggestion. They write the five-group slope (Eq. 8), calibrate phi = 122 so that 2022 elasticities and consumption shares reproduce a slope of 0.055 (Gagliardone et al. 2023 midpoint of 0.05-0.06, estimated from Danish firm-level marginal-cost data 1999-2019), then substitute 1984 consumption shares (holding elasticities fixed) to get 0.056. The resulting 2.3% slope decline, divided by the roughly 50% decline the literature reports (Furlanetto-Lepetit 2024 survey, with large uncertainty), gives about 4.5% of the observed flattening. The exercise varies only consumption shares, not the estimated elasticities themselves, over time, and the literature’s 50% benchmark is itself uncertain.
What heterogeneity is documented beyond the age gradient?
By income (Table 2): at lower income, mean elasticities rise slightly until 55-64 and are lowest for 65+; at higher income the age differences are starker than pooled. Median elasticities across income but within age are similar for ages 45+, but below 45 the lower-income group has smaller elasticities than the upper-income group. By year (Appendix Table 6): elasticities by age and year are reported for 2004-2019, with the oldest group lowest in essentially every year. The number of estimable modules differs across groups (e.g., Age 25-34: 378; 35-44: 632; 45-54: 743; 55-64: 768; 65+: 742), with fewer modules at younger and lower-income groups due to the 20-household threshold.
How does this paper relate to and differ from closely related prior work?
It departs from the wealth/liquidity HANK literature (Kaplan-Violante 2018, McKay-Wolf 2023) and from age-and-monetary-policy work that runs through wealth and savings: Eggertsson et al. (2019) on aging savers pushing down the natural rate, Berg et al. (2021) on age-dependent interest-rate sensitivity via wealth, Leahy-Thapar (2022) on the age structure of entrepreneurs, and Juselius-Takats (2021) on demographics affecting the level of inflation. Closest is Mangiante (2023), who shows older households’ baskets are weighted toward higher-price-rigidity products; this paper instead emphasizes that older households are themselves intrinsically less price-sensitive (lower within-module elasticity), a distinct price channel. It is consistent with Bornstein (2021) (older consumption more persistent) and Aguiar-Hurst (2007) (older households shop more, pay lower prices). It also speaks to the structural-stability literature (Rubio-Ramirez and Fernandez-Villaverde 2007): the aggregate elasticity is not a fixed structural parameter but depends on demographic composition.
What are the policy implications and their scope conditions?
Because the monetary-policy transmission mechanism depends on the Phillips-curve slope, ignoring the age distribution can bias the conduct and assessment of monetary policy efficacy; transmission will also have heterogeneous effects across age groups; and, all else equal, aging advanced economies should expect a flattening Phillips curve. Scope conditions: the channel is qualitatively important but quantitatively modest (about 4.5% of the observed flattening); the estimate covers retail/UPC purchases only and excludes services (where older households spend more and where price rigidities are higher per Cravino et al. 2022 and Mangiante 2023, so the composition effect may be understated); the flattening result is model-dependent (clean under Rotemberg, requiring the menu-cost argument to extend to Calvo); and the normative implications for optimal monetary policy are left as an open question.
What robustness checks and caveats does the paper provide?
Income re-estimation within income halves; per-capita expenditure validated as an income proxy against reported bins; a 20-household-per-module threshold; use of continuing barcodes only; exclusion of magnet items; year-by-year elasticity estimates (Appendix Table 6) showing stability of the ranking; the menu-cost extension to address Calvo; and explicit acknowledgment that services are missing from the data and that the quantitative benchmark (50% slope decline) is uncertain. The authors note the middle age groups are non-monotonic, so the result is a young-vs-old contrast rather than a strictly monotone age gradient.