Aggregation, Liquidity, and Asset Prices with Incomplete Markets
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
Models built to match how households really hold and spend money, with many "wealthy hand-to-mouth" households, are usually too complicated to solve once realistic aggregate shocks are added. This manuscript shows that one empirically motivated assumption -- idiosyncratic income risk rises when asset prices fall -- makes the model aggregate cleanly: each asset's total value is its frictionless single-household value times a constant capturing how useful it is for self-insurance. The payoff is a tractable theory in which liquidity premia, not risk premia, do most of the work explaining why safe bonds pay so little and why compensation for bearing pure risk looks smaller than standard models imply.
What this paper finds — and why it matters
This manuscript builds a tractable theory of asset pricing and household consumption behavior starting from the two-account incomplete-markets model of Kaplan and Violante (2014, 2022) – designed to match realistic, heterogeneous household-level consumption and asset-holding patterns, including large fractions of “wealthy hand-to-mouth” households – and extends it with aggregate shocks in a way that still permits a closed-form solution. The key move is to assume idiosyncratic risk speeds up whenever the representative-agent valuation ratio for aggregate output is low (a stylized version of the empirically documented countercyclical skewness of labor-income shocks); under this assumption, the aggregate value of each asset type equals its value in the corresponding frictionless representative-agent economy multiplied by a constant, asset-specific “liquidity factor” that is invariant to the process and history of aggregate shocks and can be recovered from the model’s steady state alone. Liquid assets carry a larger liquidity factor than illiquid ones because they additionally insure households against running out of funds before their next trading opportunity – a mechanism the authors show reproduces the “wealthy hand-to-mouth” pattern even for households with substantial wealth. Translated into expected returns, this produces liquidity premia that move inversely with valuation ratios, while risk premia and other second-moment properties of asset prices are unchanged from the representative-agent benchmark. Calibrating the model’s few sufficient-statistic moments to U.S. data, the authors argue the evidence points to small average risk premia and large, volatile liquidity premia: the model can quantitatively account for the gap between the high risk-free rate implied by low-EIS representative-agent models and the low return on Treasury bills, for why aggregate consumption Euler equations fit well for a zero-beta stock portfolio but poorly for Treasury bills, and for most of the predictability of excess stock returns.
Summary of a paper under review, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions. This is a working manuscript (version dated March 2026); the syllabus reading list cites an earlier circulated draft (2024) under the same title, and the DOI field uses the project’s no-DOI convention because the paper has not yet received a journal DOI.
Questions & answers
Q1. What gap in the existing incomplete-markets literature does the paper aim to close?
The paper starts from “canonical incomplete-market models with liquidity frictions (Kaplan and Violante (2014, 2022)),” which are “designed to explain the pattern of household-level consumption and asset-holding behavior (in particular, high and heterogeneous propensities to consume even for households with significant wealth), but are difficult to analyze in the presence of aggregate shocks” (Introduction, p. 2). The paper’s stated contribution is to “obtain aggregation results that allow us to solve them in closed form for general aggregate shocks,” so that models built to match rich micro-level heterogeneity no longer have to sacrifice tractability once aggregate shocks are introduced.
Q2. What is Assumption 1, and why is it described as necessary rather than incidental to the results?
Assumption 1 posits that the generator for idiosyncratic risk (and the arrival rate of trading opportunities) is scaled by the inverse of the representative-agent valuation ratio’s deviation from its steady state – “periods of low asset prices are periods of high idiosyncratic risk,” modeled “as a speeding up of the clock of idiosyncratic shocks” (Section 3.3, p. 11). The paper is explicit that this is not a simplifying convenience but the necessary ingredient: “Away from these [acyclical, constant-valuation] cases, valuation ratios are time-varying and aggregation would fail if idiosyncratic labor income risk were acyclical. Incorporating the realistic feature of countercyclical labor income idiosyncratic risk in this manner is precisely what is needed to obtain clean aggregation results” (p. 11), generalizing the special cases in Werning (2015) and Krueger and Lustig (2010), where constant valuation ratios (from log preferences or i.i.d. aggregate shocks respectively) let acyclical risk aggregate trivially.
Q3. What is the paper’s main aggregation theorem, and what economic content does the “liquidity factor” carry?
Proposition 1 shows that under Assumption 1, the incomplete-markets economy’s aggregate asset values equal their representative-agent counterparts times an asset-specific constant, and in the steady-state benchmark this constant is “larger for liquid assets… because they are better for consumption smoothing” (Section 3.2, p. 10). The authors describe the liquidity factor as broadly reflecting “precautionary saving, as in Aiyagari (1994),” but stress a key property that makes the theory usable: “the liquidity factor Λ_j is invariant to the history and the process for aggregate output, so it can be recovered by studying the steady state of the IM economy” (Introduction, p. 2) – meaning the aggregate-shock economy’s asset prices can be computed without ever solving the full dynamic incomplete-markets problem with shocks.
Q4. Mechanically, why do liquid assets carry a larger liquidity premium than illiquid ones?
The paper contrasts two household-level Euler equations (Section 3.2, equations 17-18): for an illiquid asset, the relevant horizon is the household’s next trading opportunity τ; for a liquid asset, it is the earlier of τ or τ′, the point at which the household would exhaust its liquid funds. “Liquid assets provide insurance against the event {τ′<τ} that the household runs out of liquid funds before the next trading opportunity, which is a high-marginal-utility state,” and this remains valuable “even for wealthy households, giving rise to the phenomena of the ‘wealthy hand-to-mouth’ (Kaplan and Violante, 2014)” – so households hold low-return liquid assets alongside higher-return illiquid ones because of a residual, positive probability of a liquidity shortfall, not because they are poor in the aggregate.
Q5. How does the model’s calibration attempt to remain agnostic about the deep cause of time-varying valuation ratios?
Rather than modeling why the valuation ratio moves, the paper calibrates only a handful of its moments directly – its volatility and its regression coefficients with output growth and asset returns – arguing that “all RA models that match these moments will generate the same predictions in their corresponding IM models with regards to aggregate Euler equations and excess return predictability” (Section 5.1, p. 23). This lets the theory “incorporate a variety of possibilities, including e.g. explanations based on long-run risk or belief distortions” for what ultimately drives valuation ratios, and similarly avoids taking a stand on the microeconomic source of average expected returns, since “Proposition 2 incorporates many possibilities, such as labor income risk, liquidity shocks and heterogeneous trading frictions” (p. 23).
Q6. What does the calibrated model imply about classic asset-pricing puzzles – the risk-free-rate puzzle and the equity premium puzzle?
On the risk-free-rate puzzle, the paper reports that its calibration’s implied representative-agent risk-free rate is 12.2%, “much higher than the average return of Treasury Bills,” and attributes essentially the entire gap to “a large liquidity premium (precautionary saving)” on safe bonds rather than to any failure of the standard Euler equation itself (Section 5.2, p. 24). On the equity premium, the paper reports the average return on a zero-beta stock portfolio (8.3%) is close to the average market return (8.1%), implying “the risk premium on the market is small on average,” consistent with “a flat securities market line (Black 1972)” – so “the model attributes most of the average excess return of the equity market over Treasury bills to differential liquidity premia” rather than to compensation for risk (p. 24).
Q7. How does the model reconcile the seemingly contradictory empirical facts about aggregate consumption Euler equations?
The paper lays out three facts in tension (Section 5.3, p. 24): the consumption Euler equation fits well using the zero-beta stock return, fits poorly using safe-bond returns, and does not describe individual households’ consumption at all. Because liquid assets carry a larger liquidity wedge than illiquid ones under the model’s aggregation result, “this wedge is larger for more liquid assets than for less liquid assets, and as a result can explain the empirical evidence on aggregate Euler equations” documented in a companion empirical paper by the same authors and a fourth coauthor (cited in-text as “Di Tella et al. (2025)”) – reconciling the good fit for stocks, the poor fit for bonds, and (via the model’s separation result) the very different behavior of individual households from the aggregate, all within a single closed-form framework (Section 5.3; Introduction, p. 3).
Q8. What is explicitly given up by this approach relative to fuller, numerically solved heterogeneous-agent asset-pricing models?
The authors state directly that their aggregation results “depend on absence of redistribution in response to aggregate shocks” – households experience heterogeneous capital gains depending on their portfolios, but once labor income and precautionary motives are accounted for, the distribution of consumption shares stays constant across aggregate states, so risk premia end up identical to the representative-agent benchmark (Introduction, p. 3). They position this explicitly as a trade-off relative to numerical approaches “capable [of] studying asset pricing in incomplete-market models” that do allow redistribution (citing Bhandari et al. 2023, Auclert et al. 2021, and Bilal 2023 – all elsewhere in this same reading list): “our approach has the advantage of sharp and intuitive analytical results, and the disadvantage of eliminating the redistributive effects of aggregate shocks in the model” (Introduction, p. 3).
Key terms in this paper
Definitions below follow the paper's own usage.
- Countercyclical idiosyncratic risk as a stochastic time-change
- the paper's Assumption 1, that the intensity of idiosyncratic shocks (and, in the paper's baseline case, the arrival rate of trading opportunities) is inversely proportional to the deviation of the representative-agent valuation ratio from its steady state, x(S) -- modeled as "a speeding up of the clock of idiosyncratic shocks" during periods of low asset prices, motivated by evidence (Guvenen et al. 2014) that the cross-sectional skewness of labor-income changes is countercyclical and correlated with stock-market valuations. The paper states this is exactly what is needed to obtain clean aggregation once valuation ratios are allowed to move, generalizing the acyclical-risk, constant-valuation special cases in Krueger and Lustig (2010) and Werning (2015).
- The aggregation theorem and the liquidity factor Λ_j
- the paper's central aggregation result (Proposition 1): under Assumption 1, the aggregate value of each asset type j in the incomplete-markets economy equals its value in the frictionless representative-agent economy times a constant, asset-specific liquidity factor, A_jt = A_RA,jt × Λ_j, where Λ_j is larger for more liquid assets (Λ_0 > Λ_1 for liquid versus illiquid) because liquid assets are more useful for smoothing idiosyncratic shocks; crucially, Λ_j is invariant to the process and history of aggregate shocks, so it can be recovered entirely from the model's steady state.
- Liquidity premium from insurance against running out of liquid funds
- the paper's explanation (Section 3.2) for why liquid assets earn systematically lower returns than illiquid assets even though both help smooth idiosyncratic risk: a household's Euler equation for an illiquid asset only prices risk up to its next trading opportunity τ, but for a liquid asset it prices risk up to min(τ, τ′), where τ′ is the (earlier) point at which the household would run out of liquid funds -- so liquid assets additionally insure against the high-marginal-utility event of hitting the liquidity constraint before the next trading opportunity, which "is true even for wealthy households," reproducing the "wealthy hand-to-mouth" phenomenon of Kaplan and Violante (2014).
- Liquidity-based reinterpretation of asset-pricing puzzles
- the paper's reinterpretation (Section 5) of several classic asset-pricing facts using its calibrated liquidity factors rather than risk premia: the gap between the high risk-free rate implied by a representative-agent model with low elasticity of intertemporal substitution and the low observed return on Treasury bills is attributed to a large liquidity premium on safe bonds (addressing the risk-free-rate puzzle of Weil 1989); the model can match a good empirical fit of the consumption Euler equation using the zero-beta rate on stocks but a poor fit using Treasury bill returns; and most of the market's average excess return over bills is attributed to differential liquidity premia rather than risk premia, consistent with a small average market risk premium (a flat securities market line, per Black 1972) while still allowing risk premia to be volatile or predictable.