Optimal Long-Run Fiscal Policy with Heterogeneous Agents

The paper opens by noting that, despite the success of Bewley-Aiyagari-Huggett heterogeneous-agent models at matching micro facts (buffer-stock saving, life-cycle consumption profiles, MPCs, labor supply) and their central role in modern macro, “little is known about their normative properties”: how a planner should trade off capital versus labor taxation, how much public debt to use given its self-insurance benefits to households, how progressive taxes should be given that precautionary saving mitigates the usual equity-efficiency trade-off, and whether higher inequality calls for more government debt (Introduction, p.1). The authors attribute the gap in the literature to “the computational complexity of heterogeneous-agent models, especially when embedded in an optimal policy problem” (p.1), which their new method is designed to overcome specifically for the long-run (steady-state) piece of the problem.

The paper characterizes the Ramsey steady state (RSS) – the long-run steady state of the full-commitment optimal (“Ramsey”) tax plan – using a “sequence-space” representation of aggregate household behavior, in which aggregate asset demand A_t and labor supply N_t at date t are written as functions of the entire sequences of past and future after-tax interest rates and wages, building on the sequence-space methods of Auclert, Bardoczy, Rognlie and Straub (2021) (Introduction, pp.2-3). From these sequence-space functions the authors define “discounted elasticities” – e.g., e_{N,w}, the response of the present value of labor supply to a permanent, fully anticipated, one-time increase in wages – which they describe as “potentially estimable in micro data” and useful “sufficient statistics” for household behavior in the optimal-tax problem, generalizing related objects in Piketty and Saez (2013) and Straub and Werning (2020) (p.3).

The paper derives a pair of necessary optimality conditions that must hold at any Ramsey steady state of the (labor-only) economy: one assuming the co-state multiplier on the government’s implementability constraint converges to a finite limit, and a second that explicitly allows for an exploding multiplier, in the spirit of Straub and Werning (2020) (Introduction, p.3; Section 3). The first condition “is best thought of as equating benefits and costs from the planner choosing to provide more liquidity (raising r, benefiting households) financed by higher labor taxes (lowering w, hurting households),” balancing the liquidity benefit against the labor-supply disincentive effect of lower wages and the redistributive cost of moving resources from the average worker to the average saver (p.3).

Evaluating the Ramsey steady-state optimality condition numerically for a standard log-separable-preferences calibration of the U.S. economy, the authors find “that the benefit from marginally increasing interest rates and increasing labor income taxes is always strictly positive. Thus, a Ramsey steady state does not exist,” and the economy’s optimal policy instead “tends towards immiseration, with labor taxes approaching 100% and real consumption converging to zero” (Introduction, pp.3-4; Section 4). Even in variants where a Ramsey steady state can be shown to exist, results “point to immiseration” in the sense that the steady state involves labor income tax rates “above 90%” – described by the authors as “near-immiseration” rather than a moderate optimal tax rate (p.4).

The authors identify the discounted labor-supply elasticity e_{N,w} as “the main force towards immiseration in the model”: in their calibrations e_{N,w} is negative, meaning that a permanent, fully anticipated fall in the after-tax wage actually raises aggregate labor supply, “as agents rationally anticipate greater future labor taxes, they raise their hours in the present. This turns the traditional labor supply cost of high labor taxation into a benefit” (Introduction, p.3). Because higher labor taxes therefore do not carry the usual efficiency cost of discouraging work – and instead, in this anticipatory sense, encourage it – there is nothing internal to the model’s household-behavior margin to stop the planner from raising labor taxes indefinitely, which is what produces the drift toward full confiscation.

No – in Section 6, extending the baseline labor-only economy to include capital and capital income taxes (directly following the Aiyagari 1995 environment) yields a pair of closely analogous Ramsey steady-state optimality conditions, and “again, no Ramsey steady state exists. Instead, our results point to immiseration again,” with the added finding that “Lagrange multipliers diverge, breaking the modified golden rule of capital accumulation” (Introduction, p.4). The paper thus explicitly connects and contrasts its results with Aiyagari (1995) – which established that incomplete markets alone push the modified golden rule off track (requiring a positive long-run capital tax) but did not find full immiseration – by showing that once labor taxation and the planner’s full-commitment Ramsey problem are analyzed together with the paper’s discounted-elasticity approach, even the modified-golden-rule benchmark itself can break down.

Very robust along most dimensions the authors check, but not to the choice of preferences: as long as household preferences are consistent with balanced growth (King, Plosser and Rebelo 1988), the paper finds either a Ramsey steady state very close to immiseration (labor taxes above 90%) or no Ramsey steady state at all, and this holds “for a variety of different income processes, for different assumptions on initial government debt or government spending, and for models with lump-sum transfers and progressive taxes” (Introduction, p.4; Section 5). The exception is preferences: with additively separable preferences and an elasticity of intertemporal substitution (EIS) above 1, “we can always find Ramsey steady states… with labor income taxes strictly below 100%,” because a high EIS “dampens the negative wealth effect that higher labor taxes have on labor supply, pushing e_{N,w} into positive territory”; conversely, an EIS below 1 pushes labor taxes back toward 100% (p.4). Greenwood-Hercowitz-Huffman (GHH) preferences also escape immiseration entirely, “as wealth effects on labor supply are entirely absent with these preferences” (p.4). The authors additionally find that “bond-in-utility” models – often used as a more tractable stand-in for full heterogeneous-agent models – “have conceptually similar predictions for Ramsey steady states as our full-blown Aiyagari model,” including immiseration in a standard log-separable version, while standard overlapping-generations models and Woodford (1990)-style alternating-income-state economies generally do not immiserate, a contrast the paper’s optimality conditions help explain (p.4).

They anticipate two reactions and address both directly: first, that immiseration might be an artifact of assuming full commitment – which they concede could change the planner’s chosen outcome under limited commitment or a more patient social discount factor, but “this will not change the fact that households themselves would still want immiseration in the long run, only that the planner cannot deliver it to them”; second, and more fundamentally, that the negative sign of e_{N,w} plausibly has “the wrong sign relative to what it should be empirically” (Introduction, p.4). The authors state they “suspect” that if household behavior were modified to dampen unrealistic anticipatory responses to distant future wage changes – along the lines of the bounded-rationality/myopia approaches in Garcia-Schmidt and Woodford (2019) and Gabaix (2020) – “e_{N,w} would flip its sign to be positive, making immiseration no longer optimal,” and they explicitly flag this as “a fruitful avenue for future work” rather than presenting immiseration as a considered policy prescription (p.4).

The paper positions itself as most closely related to Aiyagari (1995), Acikgoz, Hagedorn, Holter and Wang (2018), Chien and Wen (2022), and Dyrda and Pedroni (2023), stating that “relative to these papers, our paper develops a new method to characterize Ramsey steady states, and demonstrates how in many standard cases (though not all) immiseration is optimal” (Introduction, p.4). It also distinguishes its full-commitment, coincident-discount-factor approach from Aiyagari and McGrattan (1998), which considers an infinitely patient planner who ignores transition dynamics; from Boar and Midrigan (2022), who solve a transition-inclusive planning problem but restrict attention to constant tax rates; from LeGrand and Ragot (2023), who derive analytical results in a Woodford-style alternating-income-states economy but endow the planner with income-state-dependent welfare weights that differ from household preferences; and from Davila, Hong, Krusell and Rios-Rull (2012), who study constrained-efficient allocations under individual-specific capital taxes/subsidies rather than the economy-wide tax schedules studied here (p.4).