Adrien Auclert | Macro Paper Warehouse

Demographics, Wealth, and Global Imbalances in the Twenty-First Century

A popular argument — the “asset market meltdown” of the 1990s, revived as the “great demographic reversal” — holds that once the old start running down their savings, aging will push interest rates back up. This paper argues the opposite, and its central object is the compositional effect: the direct impact of a changing age distribution on log wealth-to-GDP, holding the age profiles of wealth and labor income fixed. In the authors’ baseline overlapping-generations model that statistic is a sufficient statistic for the change in wealth-to-GDP in a small open economy, and aggregated across countries — combined with asset supply and demand semielasticities obtained from further sufficient-statistic formulas — it pins down the general equilibrium effect on returns, wealth and global imbalances. Measuring it from 2019 UN population projections and household surveys for 25 countries, they find it positive everywhere between 2016 and 2100, ranging from 17 log points in Sweden to 45 in China and 56 in India, with a wealth-weighted global average of 31.7; the driver is that the old hold much more wealth than the young and on average do not dissave much as they age. In their central case, with an elasticity of intertemporal substitution of 0.5 and a unit elasticity of capital-labor substitution, the world return falls by 1.07 percentage points by 2100, global wealth-to-GDP rises by 8.9 log points (456% to 498% of world GDP), and net foreign asset positions diverge sharply — India’s rising by 179 percentage points of GDP and Germany’s falling by 56. The magnitudes depend on those two parameters (the return falls by between 0.58 and 2.45 percentage points across the range considered), the projections are taken as given rather than explained, indirect effects such as changes in technology or market structure are ruled out, and the authors report that rising government debt “can mitigate or even undo” the effect on real interest rates.

Determinacy and Large-Scale Solutions in the Sequence Space

This paper studies the mathematical structure of sequence-space Jacobians – the derivative operators, mapping perfect-foresight paths of shocks to paths of aggregate outcomes, that underlie the increasingly popular “sequence-space” approach to solving macroeconomic models with rich heterogeneity. The authors prove that under general conditions these Jacobians are “quasi-Toeplitz operators”: a Toeplitz operator (whose matrix has constant diagonals, reflecting time-invariant responses to well-anticipated shocks) plus a compact correction that captures the extra effect of a shock’s not being anticipated before the initial date, and that vanishes for shocks announced sufficiently far in advance. They establish two structure theorems – that the Jacobian of any stationary heterogeneous-agent block is quasi-Toeplitz, and, more generally, that the solution operator of any expectational linear difference equation satisfying standard stability conditions is quasi-Toeplitz – implying that quasi-Toeplitz structure is close to universal in sequence-space macroeconomics. The authors exploit this structure in three ways. First, they derive a “winding number” test, building on Onatski (2006), that determines whether a sequence-space system has a unique solution, suffers from indeterminacy, or has no solution at all, by counting how many times a related complex-valued “symbol” function winds around the origin; they show this test agrees with the classic Blanchard-Kahn root-counting criterion when applicable, but extends to a much broader class of models, including heterogeneous-agent models with no finite-dimensional canonical form, and they show the test holds “generically” for quasi-Toeplitz operators, addressing a genericity critique previously raised by Sims (2007) against Onatski’s original test. Second, they show that quasi-Toeplitz structure can be exploited computationally to sharply reduce the cost of avoiding truncation error, either by using the (cheap-to-compute) Toeplitz part of a Jacobian’s inverse as a preconditioner for iterative solvers such as GMRES, or by representing the compact correction term with a low-rank approximation. Third, and most strikingly, they apply these methods to solve a heterogeneous-agent, multi-country fiscal policy model in which 190 countries trade according to a realistic, asymmetric bilateral trade network – a sequence-space system with roughly 190,000 unknowns at each of 1,000 time periods, far too large to solve by direct matrix inversion – in just 12 iterations and under three seconds on a laptop, versus an extrapolated multi-year cost for a comparable state-space solution method. Throughout, the paper’s applications center on stationary models (technically, Jacobians mapping into the space of square-summable sequences), explicitly excluding representative-agent models with a unit root in consumption, which the authors flag as a limitation and direction for future work.

Excess Savings and Twin Deficits: The Transmission of Fiscal Stimulus in Open Economies

This paper studies the effects of debt-financed fiscal transfers in a general-equilibrium, heterogeneous-agent model of the world economy, merging a closed-economy HANK fiscal model (Auclert, Rognlie and Straub 2018) with an open-economy HANK model (Auclert, Rognlie, Souchier and Straub 2021) and, going beyond a small-open-economy assumption, letting fiscal deficits move the world interest rate as in Frenkel and Razin (1986). Its central analytical result is that fiscal deficits are eventually financed entirely by foreigners – in the long run, a country’s public debt increase leaves its private wealth unchanged and is absorbed one-for-one abroad (Proposition 1) – but that this happens only gradually. In the short run, because households have high, realistic marginal propensities to consume (MPCs) and spend mostly on home-biased domestic goods, almost all of a fiscal deficit shows up as a rise in the deficit country’s own private saving (“excess savings”), while the current account deteriorates only slowly (a “slow-motion twin deficit”), with a transition speed set jointly by the matrix of intertemporal MPCs and the degree of home bias. The paper shows analytically that the world economy decomposes into an aggregate, closed-economy-like response to the world-average fiscal shock and a small-open-economy-like response of each country’s deviation from that average, and it tests this prediction against cross-country data on private savings, current accounts and fiscal deficits since the start of the Covid pandemic, finding that a simple cross-sectional regression coefficient closely matches the model’s calibrated prediction after five quarters. A quantitative extension with 26 asymmetric countries and an explicitly estimated Covid demand shock replicates these patterns and finds that fiscal deficits, not the pandemic shock itself, account for the large majority of observed excess savings.

Exchange Rates and Monetary Policy with Heterogeneous Agents: Sizing up the Real Income Channel

Introducing heterogeneous households with realistic, empirically-documented marginal propensities to consume into an otherwise-canonical small open economy New Keynesian model (the representative-agent, complete-markets “RA-CM” model of Galí and Monacelli 2005) changes how depreciations and monetary policy affect output. Beyond the standard expenditure-switching channel, in which a cheaper currency shifts domestic and foreign spending toward home goods, the heterogeneous-agent (HA) model adds a “real income channel,” through which a depreciation’s rise in import prices lowers households’ real income and induces them to cut consumption, and a Keynesian multiplier that feeds any output change back into income. The balance between these forces is governed by the trade elasticity χ (the sum of the import and export price elasticities): at χ = 1, the real income channel and multiplier exactly cancel and household heterogeneity is irrelevant to the exchange rate shock’s effects; below χ = 1, the real income channel can dominate, and for a sufficiently low trade elasticity, output falls on impact – a “contractionary depreciation” – something the paper shows is quantitatively powerful only when high marginal propensities to consume are combined with incomplete markets (the HA-IM case), not in representative-agent or two-agent models with the same average MPC. An analogous neutrality result holds for domestic monetary policy shocks at χ = 2−α (nesting the Cole-Obstfeld unitary-elasticity case); away from it, monetary easing can “steal demand from the future” by financing a current spending boom with a current account deficit that must later be repaid. A calibrated quantitative extension – adding delayed substitution (a Calvo-style adjustment friction that generates a rising, J-curve-shaped trade elasticity), sticky import/export prices, non-homothetic consumption baskets, and unequal incidence of aggregate income shocks across households, calibrated broadly to Mexico – finds that depreciations are contractionary for about a year and expansionary thereafter, and that the resulting policy dilemma (whether a central bank facing capital outflows should hike rates to defend the currency or cut rates to support demand) can go either way depending on the trade elasticity.

Fiscal and Monetary Policy with Heterogeneous Agents

This paper reviews the Heterogeneous-Agent New Keynesian (HANK) literature that has emerged over the past decade, combining the canonical incomplete-markets model of income and wealth inequality (in the Bewley-Huggett-Aiyagari tradition) with the New Keynesian model of price and wage rigidity used to study monetary and fiscal policy. Rather than surveying disparate models, the authors build a single “canonical HANK model” – with sticky wages, flexible prices, and endogenous consumption-saving choice only (no endogenous labor supply) – calibrated to match realistic average marginal propensities to consume (MPCs) and a realistic wealth distribution, and use it to organize the field’s central results. Studying fiscal policy first, they show that a balanced-budget increase in government spending produces an output multiplier of exactly 1, identical to a representative-agent (RA) model, regardless of household heterogeneity (Proposition 1) – but a deficit-financed tax cut has much larger and more persistent effects in the heterogeneous-agent (HA) model than in either a representative-agent or two-agent (TA) model, because households partially save the tax cut, building up “excess savings” that low-MPC, poor households then spend down over time, an effect that “trickles up” toward wealthier households as it winds down. Turning to monetary policy, they show a subtler result: when steady-state government debt is zero, a monetary policy shock has an identical aggregate effect on output in HA, TA, and RA models (Proposition 2, generalizing a result first obtained by Werning 2015), because higher marginal propensities to consume are offset by lower sensitivity to future interest rates. Heterogeneity does not necessarily change the size of monetary policy’s aggregate effect, but it does change its transmission mechanism: decomposing the consumption response shows that “indirect” effects from labor income, capital gains, and government transfers dominate the “direct” interest-rate effect on saving decisions, a finding the authors attribute to Kaplan, Moll and Violante (2018). The paper then surveys a wide set of extensions – cyclical income risk, government debt maturity, nominal (rather than real) assets, behavioral frictions, the fiscal theory of the price level, illiquid two-account models, endogenous portfolio choice, and additional demand components such as investment and durable goods – and closes by noting that the literature has not yet reached a comparably mature theory of optimal monetary and fiscal policy in HANK models, in part because an unrestricted heterogeneous-agent economy typically lacks a well-defined Ramsey steady state to serve as a benchmark.

Higher-Order Perturbation in Sequence Space: the Certainty Correspondence

Sequence-space methods have made first-order solutions of heterogeneous-agent models with aggregate shocks fast, by exploiting “certainty equivalence”: to first order, aggregate risk is neutral, so the response to a one-time, perfect-foresight (“MIT”) shock is the same as the true stochastic impulse response. But that restriction to first order rules out any role for precautionary behavior, welfare effects of risk, or history- and size-dependent responses – exactly the questions a growing literature wants to ask of these models. This paper shows how to go beyond first order in the sequence space by establishing a “certainty correspondence”: nearly all the terms in the second- and third-order Taylor expansion of the model’s full nonlinear sequence-space solution – including the risky steady state and the interaction between shock size and shock history – can be computed purely from perfect-foresight (“MIT shock”) impulse responses, differentiated with respect to shock size and shock timing, without ever manipulating the derivatives of the underlying equilibrium system directly. Combined with a “one-shot principle” that lets each order of the general-equilibrium solution be obtained by evaluating equilibrium conditions on the previous order’s solution and applying a single already-computed inverse Jacobian, this makes third-order solutions of large heterogeneous-agent models computationally practical: an unreduced HANK model with roughly 5,000 idiosyncratic grid points needs only about 300,000 terms at third order in the sequence space, versus a state-space alternative that would require roughly 62 trillion terms and could not be stored on a computer. Applying the method to a quantitative HANK model, the paper finds the fiscal (transfer) multiplier is about four times larger when a sequence of shocks has pushed output several percent below steady state than when output is above steady state, consistent with empirical evidence on state-dependent fiscal multipliers. Applying it to a menu-cost model with strategic complementarity, the paper finds the responsiveness of inflation to nominal marginal cost is significantly steeper when trend inflation is already high, echoing recent findings on nonlinear Phillips curves. Extensive accuracy checks – against third-order state-space perturbation on a small model, and against a global Bellman solution in partial equilibrium – show the third-order sequence-space solution tracks both closely, and in fact tracks the global solution more closely than the perfect-foresight solution does, because it captures the effect of aggregate precautionary saving on marginal propensities to consume that a purely perfect-foresight calculation misses.

Managing an Energy Shock: Fiscal and Monetary Policy

This paper studies the macroeconomic effects of energy price shocks on energy-importing economies using a heterogeneous-agent New Keynesian small open economy model, extending Auclert, Rognlie, Souchier and Straub (2021b) to add an imported energy good. Its central finding is that once households have realistically high marginal propensities to consume (MPCs) and the short-run elasticity of substitution between energy and other goods is realistically low, a rise in world energy prices depresses real income enough to cause a domestic recession, even if the central bank keeps the real interest rate constant – in sharp contrast to complete-markets representative-agent models, where the same shock is always expansionary because it only triggers expenditure switching toward domestic goods. Building on this framework, the paper studies three questions in turn: whether the shock triggers a self-reinforcing wage-price spiral (it can, but this never actually protects real wages, which fall by the amount the shock dictates regardless); how effective unilateral versus coordinated monetary tightening is at curbing imported inflation (largely ineffective alone, materially effective in coordination, creating a free-rider problem among energy-importing central banks); and how fiscal policy – energy subsidies, and targeted or untargeted transfers – can shield an individual country from the shock (effectively, especially via subsidies) while imposing negative externalities on other energy importers through the world energy market (again, especially via subsidies, which blunt the substitution away from energy that would otherwise restrain world energy demand).

Micro Jumps, Macro Humps: Monetary Policy and Business Cycles in an Estimated HANK Model

This paper builds and estimates a Heterogeneous-Agent New Keynesian (HANK) model that simultaneously matches two sets of moments the prior literature could not reconcile: “micro jumps” – the large, immediate marginal propensity to consume (MPC) out of a transitory income shock documented in household data (Fagereng, Holm and Natvik 2018) – and “macro humps” – the hump-shaped, delayed peak response of aggregate output to an identified monetary policy shock. Representative-agent models with habit formation can match the macro hump but feature MPCs far too low to match the micro jump; existing heterogeneous-agent models match high MPCs but produce an aggregate response to monetary policy that peaks immediately, failing to display a hump. The paper resolves this tension by adding “sticky expectations” (following Carroll, Crawley, Slacalek, Tokuoka and White 2018) – households update their beliefs about future aggregate variables only infrequently, though they always observe current prices and income – to an otherwise standard incomplete-markets model with long-term debt, illiquid assets, and investment adjustment costs, estimated using the sequence-space impulse-matching methodology of Auclert, Bardóczy, Rognlie and Straub (2019) to jointly fit Christiano-Eichenbaum-Evans-style monetary policy impulse responses and Smets-Wouters-style aggregate time series. Two central findings follow. First, investment plays an outsized role in monetary transmission: eliminating the investment response cuts the cumulative five-year output response by over 80%, far more than investment’s roughly 40% direct accounting share of GDP, because a rise in investment raises labor income which, given high MPCs, is largely spent, generating a consumption-investment feedback loop absent from representative-agent or simple two-agent models (which, even calibrated to the same average MPC, lack the right intertemporal-MPC profile and show almost no such amplification); by the same logic, fiscal policy turns out to be comparatively unimportant for monetary transmission once the model is calibrated with realistic five-year-duration long-term government debt and a gradual, rather than balanced-budget, fiscal adjustment rule. Second, when the model is extended with a full set of seven orthogonal shocks and re-estimated on 1966-2018 US data, investment shocks explain about 65% of business-cycle-frequency output variation and 55% of consumption variation (versus about 15% and near-zero, respectively, in the estimated representative-agent counterpart), because the same high-MPC investment-consumption complementarity that amplifies monetary transmission also lets investment shocks generate the procyclical consumption-investment comovement that representative-agent models have struggled to explain since Barro and King (1984).

Monetary Policy and the Redistribution Channel

This paper formalizes and measures a “redistribution channel” through which monetary policy affects aggregate consumption – distinct from, and additional to, the standard income and substitution channels present in representative-agent models. Building on Tobin’s (1982) intuition that “aggregation would not matter if… marginal propensities to spend… were the same for creditors and for debtors,” Auclert identifies three specific sources of redistribution set in motion by a monetary expansion: an earnings heterogeneity channel (unequal gains from higher aggregate income), a Fisher channel (unexpected inflation reallocating wealth between nominal creditors and debtors), and an interest rate exposure channel (real rate changes reallocating wealth according to the duration mismatch between a household’s maturing assets and liabilities, captured by a new measure called “unhedged interest rate exposure,” or URE). The paper’s central theoretical result decomposes the first-order response of aggregate consumption into five terms – the two channels present in representative-agent models plus these three redistributive channels – each governed by a sufficient statistic: the cross-sectional covariance between household marginal propensities to consume (MPCs) and the household’s exposure to the relevant aggregate shock. Using household survey data from Italy and the United States, employing three different established methods for measuring MPCs, the paper finds that all three covariances point in the amplifying direction – households who gain from an accommodative monetary shock tend to have higher MPCs than those who lose – with the interest-rate-exposure channel comparable in magnitude to the conventional substitution channel for empirically plausible values of the elasticity of intertemporal substitution, while the Fisher channel, though correctly signed, turns out to be quantitatively modest.

MPCs, MPEs, and Multipliers: A Trilemma for New Keynesian Models

This paper shows that New Keynesian models with frictionless labor supply cannot simultaneously match three well-established macro and micro facts: high average marginal propensities to consume (MPCs, about 0.25 quarterly), low average marginal propensities to earn (MPEs, between 0 and 0.04 annually), and fiscal multipliers that are moderate under accommodative monetary policy (0.6 to 2). Using standard consumer theory, the authors show at the individual level that the ratio of MPE to MPC is governed by a “complementarity index” (CI) between consumption and labor in preferences, together with the Frisch elasticity and the elasticity of intertemporal substitution (EIS): matching high MPCs and low MPEs simultaneously requires CI close to 1, as under Greenwood-Hercowitz-Huffman (GHH) preferences. But in a representative-agent New Keynesian model with a constant real interest rate, they derive an exact formula showing the fiscal multiplier equals 1/(1 - (1-tau)CI), where tau is the steady-state labor wedge; separable preferences (CI = 0) give Woodford’s (2011) multiplier of exactly 1, while GHH preferences (CI = 1) give a multiplier of 1/tau, typically 5 or more under standard calibrations – far outside the empirically plausible range. Solving a quantitative heterogeneous-agent New Keynesian (HANK) model with flexible “GHH-plus” preferences that span the full range of complementarity, calibrated to always match the target MPC, the authors show numerically that no value of the complementarity parameter can deliver both an acceptable MPE and an acceptable cumulative fiscal multiplier at once – the trilemma survives, and is robust to varying the EIS, the Frisch elasticity, the markup, and the progressivity of financing taxes. The authors’ proposed resolution is to introduce nominal wage stickiness and demand-determined labor, which mechanically sets every household’s MPE to zero regardless of preferences, freeing the model to use separable preferences (CI = 0) to simultaneously match high MPCs and a moderate multiplier (1.21 on impact, 1.18 cumulative in their calibration).

New Keynesian Economics with Household and Firm Heterogeneity

This paper extends the Heterogeneous-Agent New Keynesian (HANK) research program, which over the past decade has studied how idiosyncratic income risk and borrowing constraints reshape monetary and fiscal transmission through household consumption, to the investment side of the economy by building a parallel canonical model of heterogeneous firms. The authors develop a firm model in the tradition of Khan and Thomas (2013) and Ottonello and Winberry (2020), in which firms face idiosyncratic productivity risk and choose investment subject to capital adjustment costs, a collateral constraint on borrowing, and a non-negativity constraint on dividends. They define a firm-level “marginal propensity to invest” (MPI) – the response of investment to a one-time, unexpected increase in cash flow – as the direct analogue of the household marginal propensity to consume (MPC), and show that financially constrained firms have a strictly positive, sometimes greater-than-one MPI (because new capital can be pledged as collateral for further borrowing), while unconstrained firms follow the standard Q-theory prediction of a zero MPI. Because there is no broad quasi-experimental evidence on MPIs comparable to what exists for MPCs, the authors calibrate the distribution of MPIs indirectly, obtaining an unweighted average MPI of 0.50 but a much smaller size-weighted MPI of 0.05, reflecting a strong negative correlation between firm size and financial constraint in their calibration. This distinction matters for policy transmission: a uniform, deficit-financed transfer to firms stimulates aggregate investment strongly, governed by the large unweighted MPI, while the indirect general-equilibrium effect of higher aggregate demand on cash flows – and hence on investment – operates through the much smaller size-weighted MPI, so that in their calibrated response to a monetary policy shock, this indirect “cash flow” channel accounts for only about 13% of the total investment response, with the bulk still coming from the traditional direct effect of interest rates on firms’ discount rates. When heterogeneous households and heterogeneous firms are combined in the same model, the authors document “aggregate demand complementarities”: because a transfer to firms raises aggregate demand and therefore household income, which stimulates further consumption by high-MPC households, the total output response to a firm transfer is roughly 20% larger than in a model with heterogeneous firms alone. The paper closes by systematically mapping the concepts of the heterogeneous-household literature onto their firm-side analogues – target buffer-stock assets versus target capital, precautionary saving versus constraint-avoidance behavior, MPCs/iMPCs versus MPIs/iMPIs – to organize an agenda of open questions, chief among them the need for direct empirical estimates of firm-level MPIs to discipline these new mechanisms the way quasi-experimental MPC estimates have disciplined the household side.

Optimal Long-Run Fiscal Policy with Heterogeneous Agents

How should a government that can fully commit to taxes and debt forever set long-run fiscal policy in an economy where households self-insure against uninsurable income risk by saving, as in Aiyagari (1995)? This paper introduces a new method for characterizing the long-run (“Ramsey”) steady state of such dynamic optimal-taxation problems, built on recently developed “sequence-space” representations of aggregate household behavior: household asset demand and labor supply at any date are written as functions of entire anticipated future paths of after-tax interest rates and wages, which lets the authors define “discounted elasticities” – present-value responses of household aggregates to a permanent, fully anticipated, one-time change in a price – as interpretable, potentially estimable sufficient statistics for the optimal-tax problem. Evaluating the resulting Ramsey steady-state optimality condition numerically for standard calibrations of a labor-only Aiyagari economy with the balanced-growth household preferences typically used in heterogeneous-agent macro models, the authors find that the condition is never satisfied at any finite tax rate: the marginal benefit of raising interest rates (providing more liquidity for precautionary saving) financed by higher labor taxes never turns negative, so optimal policy points toward “immiseration” – labor income taxes rising toward 100% and real consumption collapsing to zero – rather than converging to an interior steady state. Where a Ramsey steady state does exist under alternative parameterizations, it typically still involves near-confiscatory labor tax rates above 90%. The authors trace this result to a specific, counterintuitive channel: the discounted elasticity of labor supply with respect to the after-tax wage is negative in these calibrations, so households, anticipating that future taxes will keep rising, work more today rather than less, turning what is normally understood as the efficiency cost of labor taxation into an apparent benefit for the planner. This finding is robust across a wide range of income processes, initial government debt levels, government-spending levels, lump-sum-transfer and progressive-tax variants, and to extending the model to include capital and capital income taxes following Aiyagari (1995) directly, where the same near-immiseration or non-existence result reappears alongside a breakdown of the modified golden rule of capital accumulation. The one dependable escape route the paper identifies is a change in preferences: additively separable preferences with an elasticity of intertemporal substitution above 1, or Greenwood-Hercowitz-Huffman (GHH) preferences that eliminate wealth effects on labor supply altogether, both push the discounted labor-supply elasticity into positive territory and restore a reasonable interior Ramsey steady state. The authors are explicit that they regard the immiseration result as revealing an implausibly strong anticipatory response of household behavior to distant future tax changes, rather than a literal policy recommendation, and flag dampening these anticipation effects (in the spirit of Garcia-Schmidt and Woodford 2019 and Gabaix 2020) as a promising direction for future work.

The Intertemporal Keynesian Cross

This paper replaces the textbook static Keynesian cross – where aggregate consumption depends only on current after-tax income – with an “intertemporal Keynesian cross” derived from microfounded consumption-saving models in which households respect their intertemporal budget constraints. The key theoretical object is the matrix of intertemporal marginal propensities to consume (iMPCs), which generalizes the scalar mpc: entry Mts gives the consumption response at date t to an anticipated income change at date s. The authors prove that, assuming monetary policy holds the real interest rate constant, this matrix M is a sufficient statistic for the general-equilibrium output response to any path of government spending and taxes. Using Norwegian administrative lottery-winner data and Italian survey data, they find that consumption responds not only strongly to an income shock in the year it arrives (an average annual MPC around 0.5) but also substantially in the following year (an iMPC around 0.18) – a pattern inconsistent with representative-agent models (which cannot match the high initial MPC) and with standard two-agent models (which match the initial MPC but predict a much smaller follow-on response). Only a heterogeneous-agent model with both a liquid and an illiquid asset (“HA-two”) fits this pattern along with the data on how post-shock savings accumulate and how spending responds to capital gains. The financing of fiscal policy turns out to be decisive: when spending is balanced-budget (financed by contemporaneous taxes), the multiplier is exactly 1 regardless of iMPCs, but when spending is deficit-financed, the multiplier depends entirely on the interaction between iMPCs and the path of primary deficits – and only the HA-two model, among those considered, generates multipliers strictly above 1 both on impact and cumulatively, in the paper’s stylized environment and, after extending the model to include capital, sticky prices, and a realistic Taylor rule, in its full quantitative HANK model as well (multipliers there run from about 0.3 under a balanced budget up to about 1.3 under substantial deficit financing).

Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models

This paper proposes a general and highly efficient method for solving and estimating general-equilibrium heterogeneous-agent models with aggregate shocks in discrete time. Building on Reiter (2009)’s idea of perturbing a heterogeneous-agent model to first order in aggregates, the authors write the linearized equilibrium conditions not in the state space (as Reiter does) but in the “sequence space” – as a system relating perfect-foresight paths of aggregate variables – so that the size of the resulting linear system no longer depends on the size of the underlying distributional state space. The paper’s central objects are sequence-space Jacobians: derivatives of the mapping from aggregate input sequences (such as interest rates or wages) to aggregate output sequences (such as consumption or investment), which the authors show are “sufficient statistics” summarizing everything about household or firm heterogeneity relevant for general equilibrium. Their main technical contribution is a “fake news” algorithm (Proposition 1) that computes these Jacobians using a single backward iteration and a single set of forward-iterated expectation vectors, rather than the costly direct approach of repeating a full backward-then-forward solve separately for a shock at each date – lowering the computational cost by a factor of roughly T, the number of periods considered, which is typically 300 to 1,000 in practice. These heterogeneous-agent Jacobians are then combined with the Jacobians of the model’s other equilibrium conditions – represented as a directed acyclic graph of blocks – via the chain rule, to obtain full general-equilibrium impulse responses essentially instantaneously. The authors verify the method’s accuracy by showing it reproduces the Reiter method’s solutions, using automatic differentiation in both methods, to within machine precision on models small enough for Reiter to remain feasible. They then develop two applications that this speed makes newly practical: full-information, likelihood-based Bayesian estimation of heterogeneous-agent models (by recovering an MA representation, computing autocovariances analytically, and applying the Kalman filter, while reusing Jacobians across repeated likelihood evaluations), and the computation of nonlinear perfect-foresight transitions via a quasi-Newton method that reuses the steady-state Jacobian at every iteration. Applied to three canonical models of increasing complexity – a Krusell-Smith neoclassical model, a one-asset New Keynesian HANK model, and a two-asset New Keynesian HANK model – the methods compute all heterogeneous-agent Jacobians in under 11 seconds, obtain posterior-mode estimates in under nine minutes, and trace out full posterior distributions via Markov Chain Monte Carlo with 200,000 draws in under twelve hours even for the most complex two-asset model – estimation exercises the authors describe as previously out of reach for the literature.

When do Endogenous Portfolios Matter for HANK?

Most heterogeneous-agent New Keynesian (HANK) models assume households hold a fixed, exogenously given mix of assets – a simplification that is natural because standard first-order or “MIT shock” solution methods leave portfolio choice genuinely indeterminate, but one that sidesteps the fact that agents who perceive aggregate risk and can invest in several assets have a well-defined optimal portfolio near the steady state. This paper develops a new sequence-space method for solving jointly for these “zeroth-order” endogenous portfolios and for the model’s impulse responses, extending the fake-news-algorithm machinery of Auclert, Bardóczy, Rognlie and Straub (2021) with a second-order perturbation of the household portfolio problem evaluated just before shocks realize. When there are at least as many assets as aggregate shocks, optimal portfolios reduce to a simple risk-sharing test – marginal utility must respond proportionally across households to any aggregate shock – and the correction this implies for the model’s sequence-space Jacobians uses the same objects as the ordinary, exogenous-portfolio computation. Applying the method to a simple HANK model with a stock and a bond, the authors find that endogenous portfolios leave the aggregate effects of balanced-budget government spending shocks and of monetary policy shocks unchanged relative to the standard exogenous-portfolio (100%-stock) benchmark, because in both cases the exogenous portfolio already happens to satisfy (or trivially bypass) the risk-sharing condition. Deficit-financed fiscal transfers are different: because such transfers disproportionately raise the consumption – and lower the marginal utility – of poor, high-marginal-propensity-to-consume (high-MPC) households, optimal hedging induces poor agents to take large short positions in the booming stock market, cutting the baseline calibration’s impact transfer multiplier from 0.2 to 0.08 and its cumulative multiplier from 0.77 to 0.53. This result is sensitive to how much gross portfolio exposure is allowed: realistic short-sale and leverage constraints (stocks between -100% and 200% of net worth) bring the multiplier back close to the exogenous-portfolio benchmark, and adding more shocks than assets (incomplete markets) likewise pulls results back toward the exogenous-portfolio case when the additional shocks are hard to hedge. A parallel exercise with nominal assets shows the same logic working in the opposite direction: when households start out highly exposed to a Fisher (debt-deflation) channel, optimal portfolios shrink that exposure toward empirically plausible levels and substantially dampen the response to monetary shocks. The authors conclude that endogenous portfolios can matter a great deal for HANK results, but only when high-MPC agents are permitted to take large gross positions to hedge aggregate risk – a scope condition the paper is explicit about throughout.