A model of expenditure shocks
What this paper finds — and why it matters
A common observation from account-level bank data is that low-income, low-liquidity households often use additional income to repay debt rather than consume, and that household-level consumption is extremely volatile even though aggregate consumption is smooth. This paper formalizes these patterns using four new facts from the PSID: household consumption is as volatile as income (contradicting PIH); the correlation between household consumption and income growth is only about 0.2 (low); consumption growth is negatively autocorrelated (contradicting both PIH and habit models); and—a finding new to the literature—the cross-sectional correlation between consumption and income growth is far smaller among households experiencing high consumption episodes than in the full sample. The paper proposes an explanation based on stochastic consumption thresholds: unanticipated shocks such as medical expenses or vehicle repairs create time-varying minimum-consumption floors whose violation incurs large utility costs, inducing households to prioritize expenditures on these needs over income-responsive consumption and to rebuild savings after the shock. This mechanism increases the welfare cost of income fluctuations by an order of magnitude relative to standard models.
Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Q1. What are the four empirical facts and why do they challenge standard models?
Fact 1: for the average PSID household, consumption is as volatile as income; Fact 2: the correlation between consumption growth and income growth is about 0.2; Fact 3: household consumption growth is negatively autocorrelated; Fact 4 (new): the cross-sectional correlation between consumption and income growth is far smaller among households with high consumption than in the full sample. Fact 1 contradicts the permanent income hypothesis (PIH), under which consumption should be smoother than income. Facts 1 and 2 together cannot both be explained by liquidity constraints (which would tie consumption to current income, producing a high correlation) or by very persistent income shocks (same problem). Fact 3 contradicts habit models (which generate positive autocorrelation) and is inconsistent with PIH (which implies zero autocorrelation). Fact 4 is novel: in standard models the level of consumption barely affects the income-consumption growth relationship, so this fact requires a new explanation.
Q2. What is the expenditure shock mechanism, and how does it rationalize the four facts?
The model introduces stochastic, time-varying consumption thresholds—representing unavoidable expenditures such as medical emergencies, vehicle breakdowns, or appliance repairs—that, if violated, incur large utility costs; this forces households to prioritize meeting these minimum needs over income-proportional consumption. When a threshold shock hits, consumption jumps to meet it regardless of current income (explaining volatile, income-disconnected consumption). After the shock the household rebuilds savings, reducing consumption below its long-run level (generating negative autocorrelation). During high-consumption episodes (threshold shocks), income and consumption growth are decoupled (explaining Fact 4). Meanwhile, without a threshold shock, households are saving to self-insure against future shocks (explaining why low-income households save rather than consume when income rises).
Q3. What does the model imply for the welfare cost of income fluctuations?
The stochastic thresholds increase the welfare cost of income fluctuations by an order of magnitude relative to standard consumption models, because households must maintain precautionary buffers against the risk of hitting a threshold and being unable to meet it. The large welfare cost arises from two sources: the direct cost of violating a threshold (large utility penalty), and the precautionary motive it creates, which forces households to save at the expense of current consumption utility even when no threshold shock is present.
Q4. What empirical evidence does the paper use and what is the scope of the findings?
The PSID (post-1999 comprehensive consumption module) provides panel data on total household consumption and income; the authors use this to document all four facts, including the novel Fact 4. The negative autocorrelation of consumption growth (Fact 3) is documented in the prior literature (Blundell et al. 2008) as indicative of preference shocks or measurement error, but the paper’s model gives it a structural interpretation as evidence of expenditure shocks. The finding that consumption is volatile yet disconnected from income (Facts 1 and 2) is robust to restricting attention to nondurable consumption, ruling out durable goods as the driver. The results hold at the household level; aggregate consumption is smooth because household threshold shocks are largely idiosyncratic and average out.
Key concepts
stochastic consumption threshold : a time-varying, unanticipated minimum consumption level (representing unavoidable expenditures like medical emergencies or vehicle repairs) whose violation incurs large utility costs; the paper’s key modeling innovation.
expenditure shock : an unanticipated increase in the required minimum consumption level, representing events that force households to spend on necessities regardless of current income or savings; the proposed explanation for the four empirical facts about household consumption dynamics.