Are Inflationary Shocks Regressive? A Feasible Set Approach

Layer 1 — Overview

Research Question. The paper asks whether inflationary shocks are regressive, and demonstrates that the answer depends critically on the source of the shock. A single aggregate inflation statistic conceals radically different distributional consequences depending on whether inflation is driven by an oil supply contraction or by expansionary monetary policy.

Framework. The authors develop a “feasible set approach” grounded in the envelope theorem. They show that the first-order money-metric welfare effect of any macroeconomic shock on a household is summarized by the present discounted value of changes to five components of the household’s budget constraint: (1) consumption prices, (2) wage income, (3) asset dividends, (4) asset prices, and (5) government transfers. Because the envelope theorem implies that endogenous substitution responses are not welfare-relevant to a first order, no assumption about the utility function’s form or the economy’s general equilibrium structure is required. The framework is valid for generic stationary shocks that do not directly shift household preferences.

Empirical Strategy. The welfare formula requires two inputs: (i) impulse response functions (IRFs) for all prices, dividends, wages, and unemployment, estimated using internal-instrument SVAR methods applied to two identified shocks — the Kanzig (2021) oil supply news shock (instrumented by oil futures surprises around OPEC announcements) and the Gertler-Karadi (2015) monetary policy shock (instrumented by fed funds futures surprises in 30-minute windows around FOMC announcements) — and (ii) cross-sectional data on consumption bundles, labor income, and asset portfolios from the CEX, CPS, SCF, and SIPP for three education groups (high school or less, some college, college-educated) across the full lifecycle. The baseline cross-section uses 2019 data. Shocks are normalized to produce comparable aggregate inflation responses: a 10% WTI oil price increase and a 25 basis point decline in the one-year Treasury yield each generate roughly 15–16 basis points of CPI-U inflation on impact, rising to approximately 34–35 basis points after two quarters.

Main Findings. Oil supply contractions are regressive and monetary expansions are progressive, and this divergence is primarily driven by the asset price channel, not the consumption price or labor income channels.

For the 10% oil supply shock: middle-aged households with high school education or less must be paid approximately $870 (around 2% of annual consumption) to be made whole relative to their pre-shock utility; college-educated middle-aged households, by contrast, gain the equivalent of approximately $833 (1.1% of annual consumption). Younger college-educated households (still net equity accumulators) gain around $572.

For the 25 basis point monetary rate cut: low-education households approximately break even (net welfare effect near $23), while middle-aged college-educated households must be paid approximately $4,051 (around 5.5% of annual consumption) to restore their pre-shock utility. Older college-educated households must be paid approximately $851.

Why asset prices dominate. Oil supply contractions reduce equity prices (S&P500 falls approximately 2% one year post-shock) and depress dividends (approximately 82 basis points), while leaving house prices and bond prices largely unaffected. Because middle-aged college-educated households are the primary accumulators of equities, they benefit from the price decline (cheaper future accumulation), making oil shocks progressive through this channel — but regressive overall once the consumption and labor income channels (both mildly regressive) are included. Monetary expansions do the opposite: equity prices rise approximately 3 percentage points on impact, house prices rise approximately 1.5% after three years, and dividends increase. These asset price increases hurt those in the accumulation phase — disproportionately middle-aged college-educated households — creating a progressive distributional pattern.

Consumption and labor income channels. Both shocks generate disproportionate inflation in motor fuel and fuel and utilities, and low-education households spend a larger share of their budget on these goods, making the consumption channel mildly regressive for both shocks. The labor income channel differs sharply: oil shocks raise unemployment (approximately 0.15 log points for low-education households two years post-shock) and reduce weekly earnings by 0.2–0.6 log points, mildly harming low-education workers; monetary expansions reduce unemployment (approximately 0.83 log points for low-education workers one year post-shock) and similarly benefit low-education households through the labor market, pushing toward progressivity.

Scope conditions. Results apply to short-run first-order welfare effects of identified stationary macroeconomic shocks (four-year horizon). The framework does not incorporate uncertainty shocks, preference shocks, or the role of hedging motives in portfolio choice. Results concern policy shocks rather than policy rules.

Robustness. Qualitative conclusions hold across six alternative specifications: incorporating borrowing constraints (with or without empirical death rates), adjusting for unemployment insurance replacement rates (approximately 6% true average replacement rate), allowing for log-linear trends in no-shock choices, and dropping aggregate CPI controls from IRF estimation.

Layer 2 — Q&A

Q1: What is the “feasible set approach” and how does it differ from prior work on inflation incidence? A: The feasible set approach measures welfare effects through changes in the household’s entire budget constraint — consumption prices, wage income, asset dividends, asset prices, and government transfers — rather than focusing on any single channel. Prior work either examined the Fisher channel (net nominal positions), or consumption price heterogeneity, or labor income responses in isolation. The key insight is that the envelope theorem implies substitution responses are not welfare-relevant to a first order, so the money-metric welfare change is simply the discounted sum of changes in the five budget constraint components evaluated at pre-shock choices, without requiring knowledge of the utility function’s form or the economy’s general equilibrium structure.

Q2: Why is the asset price channel — rather than consumption prices — the dominant channel in both shocks? A: Asset holdings are large relative to annual consumption (net worth averages $1.5 million for college-educated and $260,000 for high-school-educated households in 2019), so even modest percentage movements in asset prices generate large dollar welfare effects. By contrast, the budget shares on the goods most responsive to both shocks (motor fuel, fuel and utilities) are relatively modest, so the consumption channel, while mildly regressive, is quantitatively small relative to the portfolio channel. The portfolio channel accounts for roughly 0.5% of consumption gains for middle-aged college-educated households under the oil shock, while the consumption channel produces losses of only about 0.1% for college-educated and 0.25% for low-education households.

Q3: How does the direction of the equity price response differ between oil and monetary shocks, and why does this create opposite distributional effects? A: An oil supply contraction reduces equity prices (approximately 2% decline one year post-shock) and dividends (approximately 82 basis points decline), while a monetary expansion raises equity prices (approximately 3 percentage points on impact, approximately 4% higher after four quarters) and increases dividends. The welfare effect of asset price changes falls on those who trade the asset, not those who merely hold it at a constant level: middle-aged college-educated households are the primary net accumulators of equity, so falling prices benefit them (they can buy more cheaply) while rising prices hurt them. This is the principal reason oil shocks appear progressive through the portfolio channel — but regressive overall — while monetary expansions are regressive through the portfolio channel and progressive overall.

Q4: What are the precise welfare numbers for oil supply shocks by education group (baseline, ages 22–65)? A: From Table 3 (baseline row, lifecycle-weighted averages for ages 25–65): households with high school or less experience a welfare loss of approximately $798; those with some college experience a loss of approximately $816; and college-educated households experience a welfare gain of approximately $494. These numbers reflect the sum of the consumption, labor income, portfolio, and transfer channels over a 16-quarter horizon, discounted at the one-year Treasury yield.

Q5: What are the precise welfare numbers for monetary policy shocks by education group (baseline, ages 25–65)? A: From Table 3 (baseline row): households with high school or less experience a small welfare gain of approximately $23; those with some college experience a welfare loss of approximately $1,278; and college-educated households experience a welfare loss of approximately $3,055. These losses for college-educated households are driven overwhelmingly by rising equity and house prices that raise the cost of planned asset accumulation.

Q6: How does the life cycle interact with the distributional incidence of both shocks? A: There is substantial heterogeneity within education groups across the life cycle because asset accumulation and decumulation patterns are age-dependent. Under oil shocks, younger college-educated households (who are net equity accumulators) gain approximately $572, middle-aged college-educated households gain approximately $833, while older college-educated households lose approximately $69 (because they hold large equity positions and lose dividend income). Under monetary shocks, middle-aged college-educated households lose the most (approximately $4,051) because they are simultaneously accumulating equities and housing, both of which become more expensive. Older college-educated households lose less (approximately $851) because rising dividends on existing holdings partially offset the asset price cost. Low-education households are approximately flat across the life cycle under monetary shocks.

Q7: How does the consumption channel compare across education groups and across the two shocks? A: The consumption channel is mildly regressive for both shocks, but of similar absolute magnitude across the two shocks because both generate similar inflation in motor fuel and fuel and utilities — the goods with the largest price response. Low-education households spend a larger share on motor fuel and fuel and utilities; as a result, they lose approximately 0.25% of consumption from the consumption channel under the oil shock, compared with less than 0.1% for college-educated households. For monetary shocks, the consumption channel affects all household types roughly equally in proportional terms.

Q8: How does the labor income channel differ between oil and monetary shocks across education groups? A: Oil shocks raise unemployment disproportionately for low-education workers (approximately 0.15 log point increase after two years, roughly 0.68 standard deviations, compared with near-zero response for college-educated workers) and reduce weekly earnings by 0.2–0.6 log points across groups. Monetary expansions reverse this: a 25 basis point rate cut reduces log unemployment by approximately 0.83 log points for low-education workers and approximately 1.96 log points for college-educated workers after one year, with limited response in conditional wages. Thus the labor income channel pushes toward regressive incidence for oil shocks and toward progressive incidence for monetary expansions, though in both cases it is quantitatively smaller than the portfolio channel.

Q9: What is the role of housing in the portfolio channel? A: Housing behaves simultaneously as a durable consumption good and a financial asset. A house price increase raises welfare for households planning to decumulate (sell) housing (primarily older households) through the portfolio channel, but also raises the implicit rental cost for those who use housing — a negative consumption-side effect. Monetary expansions raise house prices by approximately 1.5% after three years. College-educated households accumulate housing at a faster rate and earlier in the life cycle than low-education households, making them more exposed to the cost of rising house prices during the accumulation phase. This amplifies the progressive pattern of monetary shocks through the portfolio channel.

Q10: How does the paper handle the dual role of durable goods (vehicles and housing)? A: Durable goods are treated as both a consumption good and a financial asset. The utility-relevant consumption price of a durable is proportional to the price times the depreciation rate per unit of use, capturing the “implicit rent” of ownership. On the asset side, the durable enters the portfolio channel like a zero-dividend financial asset. This allows the framework to correctly attribute, for example, that a rise in house prices hurts net accumulators (through the portfolio channel) while also raising the implicit cost of housing services (through the consumption channel), rather than treating house price appreciation as an unambiguous welfare gain for homeowners.

Q11: What happens to the main conclusions when borrowing constraints are introduced? A: Incorporating net worth constraints (with either constant or empirical death rates) dampens the portfolio channel for young and middle-aged college-educated households, because rising asset prices relax borrowing constraints for these households, partially offsetting the welfare cost of more expensive accumulation. Under constant death rates with borrowing constraints, college-educated households’ oil shock welfare gain falls from +$494 to +$76; under empirical death rates, it becomes a loss of -$394. For monetary shocks, the college-educated loss falls from -$3,055 to -$1,718 (constant death rate) or -$1,036 (empirical death rates). Despite these quantitative changes, the qualitative conclusion — oil shocks are regressive, monetary expansions are progressive — holds across all specifications.

Q12: What is the implication of these findings for the policy interaction between oil shocks and monetary tightening? A: If the monetary authority responds to oil-price-induced inflation with unexpected interest rate increases, it may exacerbate the distributional consequences of the initial oil shock. An oil supply contraction is already regressive (harming low-education households through consumption prices and labor market effects); a disinflationary monetary tightening would additionally harm low-education households through the labor income channel (higher unemployment, lower wages) while partially benefiting college-educated households through lower asset prices. The paper notes this policy interaction as noteworthy, while cautioning that the results concern identified policy shocks rather than policy rules.

Q13: How are the two shocks calibrated to be comparable? A: The oil shock is normalized to a 10% increase in WTI crude oil prices (approximately one standard deviation of monthly oil price growth). The monetary shock is normalized to a 25 basis point decline in the one-year Treasury yield — chosen because it generates approximately the same aggregate CPI-U inflation response as the oil shock (approximately 15–16 basis points on impact, rising to approximately 34–35 basis points after two quarters). This normalization allows the paper to attribute the different distributional outcomes to the source of inflation rather than to differences in the aggregate inflation magnitude.

Q14: What role does the transfer channel play, and for whom? A: The transfer channel is small relative to the other three channels for the vast majority of working-age households, because transfer income is less than $100 per month for most households under age 65. Social Security payments — the bulk of transfer income — are explicitly indexed to the CPI; the paper models them as moving with CPI with a one-year lag. The transfer channel exclusively benefits older households (those receiving Social Security), and its quantitative effect is modest even there. Transfer income is more than 20 times smaller than labor and asset income for prime-age households of all education groups.

Key Concepts

Feasible set approach. The paper’s organizing framework, in which the first-order welfare impact of a macroeconomic shock is measured by how the shock changes the household’s budget constraint (consumption prices, wage income, asset dividends, asset prices, and government transfers) evaluated at the household’s pre-shock choices. Substitution responses are not welfare-relevant to a first order by the envelope theorem.

Money-metric welfare gain. The willingness-to-pay measure used throughout: the welfare change from a shock divided by the household’s marginal utility of consumption at time zero, expressed in time-zero dollars. Interpreted as an equivalent variation — the amount the household must be paid or would give up to be indifferent to receiving the shock. Used because it places households with very different utility functions on a common dollar scale.

Portfolio channel. The component of the welfare formula capturing the effect of asset price and dividend changes on household welfare. Asset price changes are welfare-relevant only for households that trade (accumulate or decumulate) the asset: rising prices benefit sellers and harm buyers; falling prices benefit buyers and harm sellers. This is distinct from the “Fisher channel” in prior literature, which focuses on net nominal positions rather than on which households are in the accumulation versus decumulation phase.

Internal instrument SVAR. The time-series estimation procedure used throughout: the pre-estimated identified shock series (oil supply news or monetary policy surprise) is included as a variable ordered first in a recursive structural VAR for each outcome variable. This separates shock identification (using the published instruments and controls from Kanzig 2021 and Gertler-Karadi 2015) from IRF estimation for each outcome variable, allowing the use of the full available sample for each outcome series.

Oil supply news shock (Kanzig 2021). An identified supply shock to oil markets, constructed from changes in oil price futures in tight windows around OPEC production announcements. Used to capture exogenous cost-push inflation driven by supply constraints rather than demand.

Monetary policy shock (Gertler-Karadi 2015). An identified demand-side shock, constructed from federal funds rate futures surprises in 30-minute windows around FOMC announcements, instrumented into a monetary SVAR. Captures exogenous interest rate cuts that generate aggregate demand expansion and inflation.

Borrowing constraint wedge. An additional term that appears in the welfare formula when households face net worth constraints. Proportional to the Lagrange multiplier on the net worth constraint, it discounts future periods more heavily when constraints bind, and adds a term for the welfare value of relaxed constraints when asset prices rise. Identified from deviations from perfect consumption smoothing using CEX lifecycle consumption data.