Ascari, Magnusson and Mavroeidis (2021) showed, using weak-identification-robust inference on US quarterly aggregate data, that the consumption Euler equation imposes only very weak restrictions on the intertemporal-substitution parameter, and that aggregate time series cannot distinguish among the microeconomic mechanisms (habits, liquidity constraints, limited participation, recursive preferences) that all generate a small aggregate Euler-equation slope. The open problem they pose is to find new sources of identification — household or panel data, better measures of the unobserved return on wealth, cross-sectional moments, or higher-frequency observations — and to quantify the specific bias channels left unresolved by their analysis (proxy error from using stock-market returns for the return on wealth, time aggregation, hyperbolic discounting, durable-goods nonseparability, consumption commitments, richer borrowing constraints), so that the elasticity of intertemporal substitution and the mechanism set are identified with inference robust to weak identification. No resolution is known in the literature to date: later work extends the same robust toolkit to other equations and countries, exploits other countries' data, or refines measurement, but no study yet demonstrates discrimination of the aggregate mechanisms or robust identification of the US aggregate EIS from new information sources.

Background

The consumption Euler equation is the first-order condition of a consumer who allocates consumption over time in a standard intertemporal-optimization model; in its log-linearized form it relates expected consumption growth to the real interest rate through the elasticity of intertemporal substitution (EIS), the fraction by which planned consumption growth responds to a change in the expected return on saving. The EIS governs the strength of the consumption channel in monetary-policy models and is the central preference parameter of consumption-based asset pricing. Since Hansen and Singleton's (1982) generalized method of moments (GMM) studies, the standard empirical approach regresses consumption growth on a return and instruments for the return; a long literature found small, unstable aggregate estimates. The problem is that the return is nearly unpredictable, so the instruments are only weakly correlated with it — a weak-instrument problem that invalidates conventional GMM inference. Weak-identification-robust methods — inverting tests built on the Anderson–Rubin statistic, which exploits only the restriction that the instruments are uncorrelated with the consumption shock and so remains valid however weak the instruments are, and related conditionally robust score statistics in the spirit of Kleibergen's conditional inference — deliver valid confidence sets regardless of instrument strength, at the price of possibly wide sets. Applying such methods to US quarterly real consumption data, Ascari, Magnusson and Mavroeidis (2021) found that the robust confidence sets for the EIS are so wide that the aggregate data are nearly uninformative: they cannot reject very small or large EIS values, and they cannot distinguish among structural mechanisms — consumption habits (utility depends on past consumption), hand-to-mouth or liquidity-constrained households (consumption tracks income), limited asset-market participation (only some households hold the interest-bearing asset, as documented for stockholders versus non-stockholders by Vissing-Jørgensen (2002)), and recursive preferences (Epstein–Zin utility separating risk aversion from the EIS) — because all of these aggregate to a small Euler-equation slope. The authors' companion works applied the same toolkit to investment (Ascari, Haque, Magnusson and Mavroeidis, 2024) and to open economies (Haque and Magnusson, 2020, 2023), reaching the same frontier. Independent strands provide the ingredients a resolution would need but not the resolution itself: quasi-experimental micro estimates of the EIS from UK mortgage notches (Best, Cloyne, Ilzetzki and Kleven, 2020), and administrative Norwegian data measuring household-level returns to wealth (Fagereng, Guiso, Malacrino and Pistaferri, 2020) — the kind of measurement that could replace the stock-market return used as a proxy for the unobserved return on wealth rtWr_t^W. The unresolved question is how, and whether, the identification frontier can be moved beyond what US aggregate time series deliver.

Problem Statement

As stated by Ascari, Magnusson and Mavroeidis (2021): US aggregate quarterly data, analyzed with weak-identification-robust methods, cannot identify the elasticity of intertemporal substitution (EIS) or distinguish among the structural mechanisms — habits, liquidity constraints, limited asset-market participation, recursive preferences — that generate the small observed aggregate Euler-equation slope. The open problem is to move this identification frontier: determine what the EIS and the mechanism set are, using new sources of identification beyond the US aggregate time series, with inference that remains robust to weak identification. The open problem also includes quantifying, where feasible, the bias channels the source paper explicitly leaves unresolved: the magnitude and direction of proxy error from using stock-market returns for the unobserved return on wealth; the effect of time aggregation on the coverage of weak-IV-robust tests in quarterly data; and the quantitative effect of hyperbolic discounting, durable-goods nonseparability, consumption commitments, and richer borrowing constraints on robust aggregate Euler estimation. For the information sources considered, the question also asks whether and how much the identification frontier moves, including when a proposed source cannot improve identification.

References

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