The Intermingling of Micro and Macro

A synthesis report bridging the SOTA micro and SOTA macro reports. Prepared 2026-05-26. Cross-references: companion reports 01 (micro foundations), 02 (general equilibrium), 03 (macro: RBC/NK/inflation), and 05 (policy and empirics) in this series.

Executive summary

For most of the last hundred years, micro and macro behaved like two separate disciplines stapled together inside the same department. Micro studied utility-maximizing households, profit-maximizing firms, and Walrasian equilibria. Macro tracked aggregates — GDP, unemployment, inflation — and used reduced-form equations whose parameters were estimated, not derived. The two halves intermingled awkwardly in the textbook: micro produced demand curves and supply curves, macro graphed AD and AS without asking whether either really aggregated up.

Three intellectual shocks broke that division and created the modern micro-macro synthesis:

1. The Lucas critique (1976) killed the assumption that estimated macro relationships are policy-invariant, forcing macro to derive its equations from deep parameters of preferences and technology. This launched the microfoundations program and the DSGE tradition that dominated 1980–2010.
2. The Sonnenschein–Mantel–Debreu theorem (1972–1974) proved that rational micro agents do not in general aggregate into a well-behaved excess-demand function. This is the formal obstacle that representative-agent macro silently assumes away.
3. The heterogeneous-agent revolution — Krusell–Smith 1998, Kaplan–Violante 2014, and especially Kaplan–Moll–Violante 2018 "Monetary Policy according to HANK" — replaced the representative consumer with a continuum of households facing idiosyncratic income risk and incomplete insurance. Once you do this, micro estimates of marginal propensities to consume become first-order inputs to macro multipliers, monetary policy redistributes rather than just stimulates, and fiscal policy can be deeply expansionary even when Ricardian equivalence "should" hold.

A parallel revolution in production-network macro — Gabaix 2011 on granularity, Acemoglu–Carvalho–Ozdaglar–Tahbaz-Salehi 2012 on input–output linkages, Baqaee–Farhi 2019, and the COVID supply-chain literature — established that aggregate fluctuations can have purely microeconomic origins, propagated through the network structure of firms and sectors. The "law of large numbers" assumption that idiosyncratic shocks wash out is empirically false because firm size is Zipf-distributed and sectoral linkages are sparse and asymmetric.

Together these literatures have produced a new core of "usable macroeconomics" (Auclert 2025) in which:

• the fraction of households who are hand-to-mouth is a macro parameter as important as the intertemporal elasticity of substitution;
• the size distribution of firms and structure of the input–output table are macro parameters as important as TFP shocks;
• the distribution of income, debt, and wealth matters not just for normative inequality questions but for the positive transmission of monetary and fiscal policy;
• partial-equilibrium micro estimates are essential inputs to macro models but never enough on their own — the synthesis requires sequence-space methods that re-aggregate micro responses into general-equilibrium dynamics.

Three concrete payoffs are visible by 2026:

• Fiscal multipliers from deficit-financed transfers are much larger and more persistent than RANK predicted. The Auclert–Rognlie–Straub "intertemporal Keynesian cross" (JPE 2024) shows multipliers above 1 emerge naturally once intertemporal MPCs are matched to micro evidence.
• Monetary policy works as much through redistribution as through intertemporal substitution. Cutting rates transfers wealth from savers to borrowers and from fixed-income to floating-income households; the high-MPC recipients spend, and aggregate demand rises through what Kaplan–Moll–Violante call indirect channels rather than the Euler-equation direct channel of the textbook.
• The 2020–2024 pandemic-and-inflation episode is the first major business cycle to be analyzed in real time with HANK and disaggregated network models. The Baqaee–Farhi family of models attributes the inflation burst to a combination of sectoral demand shifts (goods over services), sectoral supply disruptions (lockdowns, chips, shipping), and aggregate demand support (fiscal transfers amplified by high-MPC recipients).

The micro-macro synthesis is incomplete. Live debates in 2024–2026 ask whether rational expectations is tractable in heterogeneous models at all (Moll 2025), whether full HANK is overkill once you allow behavioral discounting and TANK (Bilbiie 2024), whether the empirical iMPC consensus is robust to recent disagreements about distributional statistics (Auten–Splinter vs Piketty–Saez–Zucman), and whether agent-based macro can supplant DSGE for crisis prediction (Farmer–Axtell 2025).

Research brief

• Topic: How the two halves of economics intermingle in theory and practice. This is a synthesis bridging the standalone micro and macro reports in the series.
• Audience: A highly capable self-learner. Foundational terms (utility, preferences, IS-LM, NK Phillips curve, marginal cost) are assumed defined in the companion micro and macro reports.
• Recency policy: Heavy weight on 2021–2026 (HANK consolidation, intertemporal MPCs, pandemic supply-chain inflation, distributional national accounts debate); moderate 2016–2020 (HANK emergence, granularity, network origins); foundational classics where they remain load-bearing (Lucas 1976, SMD 1972–1974, Kydland–Prescott 1982, Acemoglu et al. 2012, Gabaix 2011).
• Math policy: Algebra in body, calculus and dynamic programming skipped with "Study this next" callouts. Worked TANK example, worked Leontief 2×2 example, worked MPC-aggregation example.
• Source policy: AEJ:Macro, JPE, Econometrica, NBER, JEP synthesis (Auclert/Kaplan–Moll–Violante surveys are particularly valuable), Fed and BIS working papers, Annual Reviews, Conversable Economist, Bank Underground, Liberty Street, Cochrane.
• Decision the report supports: Building a research-grade mental model of how modern macro reasons about micro causes, so the reader can navigate Fed speeches, NBER papers, and the academic literature on policy.

Key findings

1. Micro and macro are no longer parallel disciplines. The 2010s and 2020s closed the gap that the Lucas critique opened in the 1970s. The modern frontier writes down explicit micro decision rules for heterogeneous households and firms, simulates them at scale (Aiyagari-style stationary distributions plus aggregate shocks), and reads off macroeconomic responses using the sequence-space Jacobian machinery of Auclert et al. (Econometrica 2021). The HANK class has become "the new core of usable macroeconomics" per Auclert's 2025 essay.

2. Aggregation is hard and was always hard. Sonnenschein–Mantel–Debreu showed in the 1970s that micro rationality places almost no restrictions on aggregate excess demand — "anything goes." Representative-agent macro evaded this only by assuming that aggregate behavior looks like a single rational consumer. HANK does not solve SMD; it sidesteps it by computing aggregate responses numerically from a known distribution of agents.

3. MPC heterogeneity is a first-order macro fact. Empirical MPCs are bimodal: a substantial share of households spend 30–60% of a windfall within a quarter, while another share spend almost nothing. Roughly one-third of US households are hand-to-mouth by the Kaplan–Violante–Weidner (2014) criterion, including a large group of "wealthy hand-to-mouth" who hold illiquid assets (homes, retirement accounts) but no liquid buffer. The representative-agent intertemporal Euler equation cannot reproduce this and therefore badly mis-prices fiscal transfers and tax rebates.

4. Monetary policy is largely redistribution. Kaplan–Moll–Violante (AER 2018) show that in a HANK model with realistic MPC distribution, the indirect channel — labor-demand and income effects on high-MPC households — accounts for most of the consumption response to a rate cut, while the direct channel (Euler-equation intertemporal substitution by patient savers) accounts for nearly all of it in RANK. Auclert (AER 2019) decomposes the redistribution into earnings heterogeneity, Fisher (debt revaluation), and interest-rate exposure channels.

5. Fiscal policy works through iMPCs, not period-MPCs. Auclert, Rognlie, and Straub's "Intertemporal Keynesian Cross" (JPE 2024) shows that the dynamic response of consumption to a transfer is summarized by a vector of intertemporal MPCs — how much extra is spent in each future quarter from a dollar today. Empirical iMPCs are higher and more front-loaded than RANK or TANK predict, and matching them generates multipliers above 1 on deficit-financed government spending.

6. Aggregate fluctuations have granular and network origins. Gabaix (Econometrica 2011) shows the law of large numbers fails when firm size is fat-tailed (Zipf): the largest 100 US firms explain roughly one-third of US GDP-growth variation. Acemoglu et al. (Econometrica 2012) show that input–output linkages amplify sectoral shocks asymmetrically, with hub sectors driving aggregate volatility. Carvalho, Nirei, Saito, and Tahbaz-Salehi (QJE 2021) document a 0.47 percentage-point reduction in Japanese GDP growth from supply-chain propagation of the 2011 Tōhoku earthquake.

7. Beyond Hulten in non-linear network economies. Baqaee–Farhi (Econometrica 2019) extend Hulten's theorem to second order, showing that in the presence of complementarities and reallocation frictions, microeconomic shocks have effects on aggregate output that depart sharply from their cost-share weights. Their disaggregated Keynesian COVID model (AER 2022) decomposes pandemic-era inflation into sectoral supply, sectoral demand, and aggregate demand shocks — formalizing what Powell and Lagarde had been saying in plain English.

8. The "rise of market power" connects micro structure to macro stagnation. De Loecker–Eeckhout–Unger (QJE 2020) document rising aggregate markups from ~21% above marginal cost in 1980 to ~61% in 2016, driven by the upper tail of the markup distribution. Autor–Dorn–Katz–Patterson–Van Reenen (QJE 2020) link this to the rise of superstar firms with low labor shares. Philippon's Great Reversal (2019) and Mian–Straub–Sufi's "Indebted Demand" (QJE 2021) connect rising concentration and inequality to falling natural rates, secular stagnation, and the demand-side amplification of inequality.

9. Behavioral macro modifies, not replaces, the synthesis. Gabaix's "Behavioral New Keynesian" (AER 2020) introduces a cognitive discount factor that makes agents myopic toward the distant future, resolving the forward guidance puzzle and bringing model dynamics closer to data without abandoning rational-expectations infrastructure. García-Schmidt and Woodford (AER 2019) propose reflective equilibrium as an alternative to perfect foresight. Recent work (Pfäuti–Seyrich 2024) combines behavioral discounting with HANK and finds the two interact powerfully.

10. Live front of 2024–2026: Bilbiie's THANK framework (RES 2025) argues that a tractable two-agent model captures most of what HANK delivers, provided you parameterize cyclical inequality correctly. Moll (2024–2025) challenges whether rational expectations is even tractable in HANK once you allow aggregate risk and non-linearities, suggesting learning-based or temporary-equilibrium alternatives. Agent-based macro (Farmer, Dosi, Hommes) has had a post-COVID revival showing that bottom-up simulation can match macro moments without DSGE's equilibrium assumptions.

11. Distributional accounts are now contested macro statistics. Piketty–Saez–Zucman's Distributional National Accounts (QJE 2018) made it possible to consistently allocate every dollar of national income across the distribution and to track top-share growth alongside GDP. Auten–Splinter (2024) reach much flatter conclusions using different tax-data assumptions. The dispute is not purely statistical: HANK and indebted-demand models rely on which set is right when calibrating wealth distributions for macro analysis.

12. Synthesis insights that neither half shows alone:

• Cyclical incidence: Recessions concentrate income losses on high-MPC households, which amplifies the downturn — visible only when you allow MPC heterogeneity. RANK predicts smooth Euler-equation-driven dynamics.
• Forward guidance puzzle: RANK predicts implausibly large stimulus from far-future rate promises. HANK (via discounting from limited self-insurance) and behavioral macro (via cognitive discounting) both shrink the effect into the realistic range — they reach the same destination by different routes.
• Fiscal-monetary interaction: In HANK, the size of a monetary expansion depends on whether the deficit it implies is financed by lump-sum taxes (RANK-like) or distortionary ones (which redistribute). Pure Ricardian neutrality is not just empirically wrong; it requires conditions HANK shows are never met.
• Network-amplified inequality: A shock to a sector hub doesn't just spread to downstream sectors — it concentrates wage losses on workers in those sectors, who tend to have high MPCs, generating a second-round aggregate-demand collapse on top of the supply propagation.

Detailed analysis

This section walks through the conceptual structure of the modern micro-macro synthesis in roughly historical and logical order: the Lucas critique that made microfoundations necessary, the SMD theorem that made them hard, the RBC→NK→HANK lineage that built them, the production-network literature that complemented them, the empirical "identified moments" approach that disciplined them, and the live debates that contest them.

1. The Lucas critique: why micro became macro's grammar

In 1972 the dominant macroeconomic technology was a large structural econometric model — the FRB-MIT-Penn model, the Wharton model, the OECD's INTERLINK. These models were estimated equation-by-equation from historical data: a consumption equation in current income and lagged income; an investment equation in the cost of capital; a Phillips curve in inflation and unemployment. Once estimated, the model could be simulated under alternative policy paths to forecast the effect of, say, a permanent tax cut or a permanent shift in monetary policy.

Robert Lucas's 1976 "Econometric Policy Evaluation: A Critique" demolished this enterprise in three pages of argument. The critique runs as follows. The historical regression coefficients are not deep parameters of preferences or technology. They are reduced-form coefficients that already embed the policy regime in force during the sample. They reflect how households and firms optimized under the anticipated policy environment — what the Federal Reserve was expected to do, what tax rates were expected to be, what inflation was expected to average. Change the policy rule, and the optimizing agents will re-derive their decision rules. The estimated parameters will shift. Counterfactuals using the old parameters will be systematically wrong (Lucas 1976, PDF; see also the Wikipedia summary).

The example most often used in classrooms is the Phillips curve. The 1960s Phillips curve fit by Samuelson and Solow appeared to offer a stable trade-off between unemployment and inflation. By 1976 — the year of Lucas's paper — that trade-off had visibly broken down: high unemployment and high inflation coexisted, the regression had drifted. Lucas's interpretation was not that the underlying micro behavior had changed but that the expectations regime had: once policymakers were known to be willing to inflate to chase low unemployment, workers and firms built that expectation into wage and price setting, and the apparent trade-off vanished.

The methodological consequence was decisive. To do counterfactual policy analysis legitimately, you must build a model whose parameters are policy-invariant: tastes, technology, information structure. From these you derive optimal decision rules conditional on the policy rule, aggregate, and read off equilibrium dynamics. Change the policy rule and re-derive. This is what we call microfoundations, and it is what the next forty years of macro tried to deliver.

The Lucas critique was decisive in three ways:

• It killed the structural-econometric-model industry in academic macro within a decade (it survived in policy institutions, where backward-looking forecasting was useful even when counterfactuals were not).
• It established that rigorous policy analysis requires a model built from agents who optimize against the policy rule.
• It made internal consistency — every equation derived from the same primitives — a methodological commandment in mainstream macro.

A subtle further consequence: the Lucas critique applies equally to any model that estimates a non-structural relationship and then uses it to evaluate a policy that changes the relationship. This includes reduced-form fiscal-multiplier estimates that ignore monetary response, reduced-form Phillips curves that ignore anchoring of expectations, and even calibrated HANK models whose income-process parameters were estimated under a different policy regime. Modern HANK practitioners are well aware of this, and the sequence-space Jacobian methodology (Auclert et al. 2021) is explicitly designed to update the response to any new policy rule without re-estimating the deep parameters.

The Phillips curve as the canonical Lucas-critique example

To make the abstraction concrete, walk through the Phillips curve. The 1960s reduced-form regression looked like:

$$\pi_t = \alpha - \beta u_t + \epsilon_t$$

— inflation $\pi_t$ as a downward-sloping function of unemployment $u_t$. Estimated on 1948–1968 US data, $\beta$ was a stable positive coefficient. Samuelson and Solow's famous 1960 paper invited policymakers to read this as a menu: choose lower unemployment, accept higher inflation; choose lower inflation, accept higher unemployment.

The Lucas-Friedman critique, anticipated by Friedman (1968) and formalized by Lucas (1976), is that $\beta$ is not a deep parameter. It depends on the expected inflation rate, which depends on the policy regime. The microfounded relationship is:

$$\pi_t = E_t[\pi_{t+1}] + \kappa \cdot (\text{output gap}_t) + \text{markup shock}_t$$

— the New Keynesian Phillips curve. The reduced-form $\beta$ from the 1960s regression confounded three things: the structural slope $\kappa$, the policy regime's effect on expectations, and the joint distribution of output gap and unemployment under that regime. Change the regime — say, the Fed commits to inflation targeting — and $E_t[\pi_{t+1}]$ becomes anchored. The reduced-form $\beta$ shifts. The "menu" disappears.

This is precisely what happened in 1968–1980: the apparent Phillips trade-off broke down as the Fed accommodated inflation and expectations un-anchored. After 1985, under Volcker–Greenspan inflation-credibility, the curve flattened again — but with the new property of stable low inflation. The 1968 reduced-form coefficient was useless for the 1990 policy environment.

The right response was not "abandon Phillips-curve thinking" but "rebuild it from primitives that don't change with policy" — the price-setting friction (Calvo), the marginal-cost driver of inflation, the rational forecast of future inflation. This is the New Keynesian Phillips curve, and it is robust to policy-regime changes by construction, because it derives from the micro problem of a price-setting firm under sticky-price frictions.

The deeper implication: macro is now applied general-equilibrium analysis

The Lucas critique is sometimes taught as a technicality. Its deeper implication is profound. Before Lucas, macroeconomics could be done with reduced-form regressions and ad-hoc behavioral equations. After Lucas, legitimate macro analysis requires:

1. A model of decision-making by every agent type (households, firms, government, central bank).
2. A specification of how those decisions aggregate under market-clearing.
3. A specification of the information and expectations structure.
4. A derivation of how the model behaves under different policy rules.

This is what microfoundations and DSGE deliver — and what HANK extends to incorporate distributional heterogeneity. The 40-year project from Lucas 1976 to HANK 2018 is, at its core, the rebuilding of macro on micro foundations because the Lucas critique made anything else illegitimate.

"Study this next" — rational-expectations equilibrium. The Lucas critique presupposes that agents form rational expectations of the policy rule — they know the rule and use it correctly. This is itself a contested assumption (see Moll 2024, Pfäuti–Seyrich 2024) but a working understanding requires fixed-point reasoning and dynamic programming. After algebra, the next book is Sargent's Macroeconomic Theory or Ljungqvist–Sargent's Recursive Macroeconomic Theory for the formal treatment.

2. The aggregation problem: Sonnenschein–Mantel–Debreu

If micro is rigorous and macro is just micro aggregated, you might expect to be able to start from a population of utility-maximizing households and derive a downward-sloping market demand curve, a stable equilibrium, and a comparative statics that supports textbook reasoning.

You cannot. The Sonnenschein–Mantel–Debreu (SMD) theorem, proved in stages by Sonnenschein (1972, 1973), Mantel (1974), and Debreu (1974), shows that the aggregate excess-demand function of an exchange economy populated by utility-maximizing rational consumers is essentially unrestricted beyond three trivial conditions: continuity, homogeneity of degree zero in prices, and Walras's law (the value of excess demand sums to zero). Any function meeting those three conditions can be realized as the aggregate excess demand of some economy of rational consumers (Wikipedia: Sonnenschein–Mantel–Debreu theorem).

The colloquial label is the "anything goes theorem." The technical content is more sobering: the standard restrictions on individual demand (the Slutsky matrix is symmetric and negative semi-definite) do not aggregate. Wealth effects across heterogeneous households can produce aggregate demand curves that slope upward, have multiple equilibria, are unstable under Walrasian tâtonnement, and admit no representative consumer.

For macro, three implications matter:

1. There is no general theorem that a representative-agent model is a legitimate aggregation of a population of heterogeneous agents. Conditions exist (Gorman 1953: linear Engel curves, identical except for intercept), but they are restrictive and empirically rejected. The representative-consumer assumption is a modeling shortcut, not a theorem.
2. Comparative statics that look obvious in partial equilibrium need not survive aggregation. A tax cut that increases demand for good A may, through general-equilibrium repricing, raise or lower demand for good B in ways that depend on the joint distribution of preferences and wealth.
3. Stability and uniqueness of equilibrium cannot be assumed. Outside of special cases (gross substitutes, weak axiom of revealed preference for aggregate demand), equilibrium may be non-unique, unstable, or both. This is the foundation underneath modern debates about multiple equilibria in macro (sunspot equilibria, self-fulfilling debt crises, equilibrium selection in HANK).

SMD did not stop macro from building representative-agent models — it just clarified that the representative agent is a modeling assumption with no general theoretical backing. The HANK revolution can be read as an empirical answer to SMD: rather than impose aggregation and hope, you simulate the cross-section explicitly.

Philosophical implications of SMD

SMD has three philosophical implications that the modern synthesis takes seriously:

(i) The fallacy of composition is structural, not behavioral. The classical SMD-style fallacy is exemplified in the "paradox of thrift": if every household decides to save more, aggregate saving may fall because aggregate income falls. The micro-rational behavior (save more during uncertainty) produces a macro-undesirable outcome. SMD generalizes this insight: there is no general theorem that micro rationality plus market clearing produces well-behaved macro outcomes. The fallacy of composition is the rule, not the exception.

(ii) Equilibrium selection becomes a substantive question. If SMD permits multiple equilibria, the macroeconomist must explain why one rather than another is realized. This invites self-fulfilling-prophecy mechanisms (Cole–Kehoe sovereign-default crises, sunspot-driven banking panics, Mertens–Ravn fiscal-cliff equilibria), expectations-coordination devices, and game-theoretic refinements that have become standard in modern macro and finance.

(iii) Identification of "the" macroeconomic effect is harder than identification in micro. A micro econometrician identifying the wage elasticity of labor supply can rely on cross-sectional variation under partial-equilibrium assumptions. A macro econometrician identifying the effect of a fiscal stimulus on output cannot — because the general-equilibrium consequences of the stimulus may shift the very mechanisms being measured. This is what the "identified moments" approach (Nakamura–Steinsson 2018) tries to recover: cross-sectional, geographically-bounded identification that has macro-relevant external validity precisely because it's quasi-experimental at the micro level.

Why HANK doesn't "solve" SMD

A careful reader notices: HANK has a continuum of heterogeneous agents. Doesn't this fall directly under SMD's "anything goes" verdict?

Yes. HANK does not solve SMD in any deep sense. What HANK does is compute aggregate behavior for a specific, empirically-anchored heterogeneous economy, without assuming aggregation. The aggregate demand curve of a HANK economy is whatever the simulation says it is — which may indeed have peculiar shapes, multiple equilibria, or instabilities. Modern HANK practitioners spend considerable effort verifying determinacy of equilibrium (under the Taylor principle, modified for HANK) and tracking stability under realistic shocks. SMD is the warning that this work is necessary; HANK is the methodology that can do it.

"Study this next" — Gorman aggregation. The classical aggregation result is Gorman aggregation: if all households have indirect utility of the Gorman polar form, aggregate demand behaves as if generated by a representative consumer. The conditions are restrictive (in particular, parallel-linear Engel curves), and the failure of these conditions is exactly what HANK exploits. See Mas-Colell, Whinston, and Green's Microeconomic Theory, Chapter 4 for the formal treatment.

3. The microfoundations program: triumph and discontent

Between 1976 and 2008, macroeconomics was reorganized around the imperative of microfoundations. The result was a sequence of nested model families:

• Lucas islands models (1970s) — agents with island-specific information, monetary surprises generating real effects through signal-extraction.
• Real Business Cycle models (Kydland–Prescott 1982) — a representative household and firm optimize, technology shocks drive business cycles in a frictionless competitive equilibrium (Kydland–Prescott 1982 "Time to Build"; see Rebelo's survey).
• New Keynesian models (1990s–2000s) — add sticky prices à la Calvo and monopolistic competition à la Dixit–Stiglitz, generating monetary non-neutrality and an active role for stabilization policy.
• DSGE models (Smets–Wouters 2003, 2007) — the workhorse of central banks: rich enough to fit data, microfounded enough to do counterfactual policy analysis.

Each generation deepened the micro story. RBC's representative consumer maximized expected utility from consumption and leisure over an infinite horizon under known technology shocks. NK added a monopolistic-competition friction in the goods market and Calvo price-setting friction in the price-setting layer. Smets–Wouters added a dozen real and nominal rigidities (habit formation in consumption, capital adjustment costs, wage stickiness, indexation) and shocks (markup, risk-premium, government-spending, monetary).

The methodological triumph was real. Central banks could now do counterfactual policy analysis with internally consistent models. The Lucas critique was respected: change the Taylor rule and re-solve. Estimation became respectable through Bayesian methods (An–Schorfheide 2007). Comparative welfare analysis became possible because everything was anchored in the representative household's utility function.

The methodological discontent was also real and concentrated in three lines of critique:

1. False-precision critique (Caballero 2010). Ricardo Caballero, in "Macroeconomics after the Crisis: Time to Deal with the Pretense-of-Knowledge Syndrome" (JEP 24(4): 85–102), argued that the DSGE core had become "mesmerized with its own internal logic" and had "confused the precision it has achieved about its own world with the precision that it has about the real one" (NBER WP 16429; AEA link). His complaint is not that microfoundations are wrong, but that the specific microfoundations chosen — representative agent, complete markets, frictionless intermediation — became reified into a "new reality" that hid the actual sources of fragility revealed in 2008.

2. Aggregation critique (the SMD point in modern dress). Hugo Sonnenschein's theorem from 1973 came back to bite: there is no theoretical reason the aggregated economy should look like a single rational consumer. By assuming so, RBC and NK were making a behavioral assumption disguised as a technical one.

3. Distributional critique. Representative agents have no distribution. Inequality cannot exist in a single-agent economy. But the post-2008 economy was distinguished by debt distribution (Mian–Sufi), wealth concentration (Piketty), and labor-market polarization (Autor). A model that assumed homogeneity was structurally incapable of representing the central diagnostic facts of the crisis.

The response to these critiques was not "abandon microfoundations" — that would have re-opened the Lucas critique — but "deepen microfoundations to include heterogeneity, frictions, and distribution." This is the HANK program, and it is the dominant frontier of 2020s macroeconomics.

4. RBC → NK → HANK: the genealogy of modern macro

It helps to lay the three families side by side.

Real Business Cycle (RBC)

• One representative household, infinite-lived, with constant-relative-risk-aversion utility over consumption and leisure.
• One representative firm with constant-returns Cobb–Douglas technology.
• Competitive labor and goods markets. Flexible prices.
• Exogenous total-factor-productivity shocks drive fluctuations.
• Calibrated rather than estimated. Policy has no role: government spending is wasteful, monetary policy is super-neutral.

Key insight: a substantial fraction of US business-cycle volatility could be reproduced by TFP shocks in a frictionless competitive equilibrium. The model "matched" the standard deviations and correlations of US macro aggregates without invoking aggregate demand shocks at all.

Key limitation: monetary policy doesn't matter (against the entire Volcker disinflation), labor-supply elasticities required are implausibly high, the implied "recession is just an efficient response to a bad technology shock" view sat poorly with the experience of mass unemployment.

The algebraic core of RBC, stated without dynamic-programming machinery, is a single-good economy where the representative consumer chooses consumption $c_t$, capital $k_{t+1}$, and labor $\ell_t$ to maximize expected discounted utility:

$$E_0 \sum_{t=0}^{\infty} \beta^t , u(c_t, 1 - \ell_t)$$

subject to the budget constraint $c_t + k_{t+1} - (1 - \delta) k_t = z_t f(k_t, \ell_t)$, where $z_t$ is a TFP shock with persistence. The first-order conditions yield an Euler equation (consumption today versus tomorrow), a labor-leisure trade-off (current real wage versus marginal utility of leisure), and capital accumulation. Solving means finding policy functions $c(k, z)$, $\ell(k, z)$, $k'(k, z)$. Simulating the model under stochastic $z$ produces time series for output, consumption, investment, and hours that can be compared to data — "moment matching" calibration in Kydland-Prescott style.

The intellectual victory of RBC was twofold. First, it showed that internally consistent macroeconomic dynamics could be built up from first principles without ad-hoc behavioral equations. Second, it raised the bar: any subsequent macro theory had to provide micro-level decision rules and aggregate them rigorously. The intellectual cost was that the simplest RBC was a frictionless competitive equilibrium with no role for money, no involuntary unemployment, no inflation, no aggregate demand. Re-introducing these phenomena drove the next 30 years of research.

New Keynesian (NK)

• Same representative household.
• Monopolistically competitive firms à la Dixit–Stiglitz produce differentiated varieties.
• Calvo price-setting friction: only a fraction of firms can re-optimize prices each period.
• Monetary policy follows a Taylor rule; nominal interest rates are the policy instrument.
• Resulting Phillips curve relates inflation to the gap between marginal cost and steady-state level (the "New Keynesian Phillips curve").

The canonical three-equation NK model is:

• IS curve: output gap depends on expected future output gap and real interest rate.
• NKPC: inflation depends on expected inflation and output gap.
• Taylor rule: nominal rate responds to inflation and output gap.

Key insight: monetary policy has real effects through Euler-equation intertemporal substitution. Cutting the real rate makes consumers want to consume more today. The Taylor rule, properly designed (Taylor principle: respond more than one-for-one to inflation), produces determinate equilibrium and stabilization properties consistent with the Great Moderation.

Key limitation: representative agent → no distribution, no MPC heterogeneity, no role for fiscal policy beyond government spending. The model also generates the forward guidance puzzle: a credible promise to keep rates low far in the future has implausibly large effects today, because the rep agent intertemporally substitutes across all dates.

The compact three-equation New Keynesian model (Galí 2015 is the canonical textbook) is:

• IS curve: $x_t = E_t x_{t+1} - \sigma^{-1}(i_t - E_t \pi_{t+1} - r^n_t)$ (output gap depends on expected future gap and real rate gap from natural rate)
• NKPC: $\pi_t = \beta E_t \pi_{t+1} + \kappa x_t$ (inflation depends on expected inflation and output gap)
• Taylor rule: $i_t = \phi_\pi \pi_t + \phi_x x_t$ (policy rate responds to inflation and output gap)

Three equations in three unknowns: output gap $x$, inflation $\pi$, nominal rate $i$. The model is a tractable workhorse for monetary-policy analysis. Welfare can be computed from the household's utility function. Optimal policy can be characterized analytically (Taylor principle: $\phi_\pi > 1$ for determinacy).

The empirical workhorse versions — Smets-Wouters (2003 for the euro area, 2007 for the US) — add capital accumulation, habit formation in consumption, wage stickiness, indexation, and a dozen shock processes. These models are estimated using Bayesian methods on time-series data and are the operational tools of the Fed, ECB, and many central-bank research departments.

The NK model's three structural pathologies that motivated HANK:

• Forward guidance puzzle. A credible promise to keep the rate $\bar{\epsilon}$ basis points below normal for $T$ periods has output and inflation effects that grow without bound in $T$. Empirically the effects are an order of magnitude smaller.
• Discount-factor puzzle. The Euler equation's intertemporal elasticity, calibrated to match the natural rate of interest, implies an implausibly high willingness to substitute consumption across periods.
• Fiscal-multiplier puzzle. Under Ricardian equivalence, deficit-financed transfers have zero aggregate effect. Empirically, US fiscal multipliers from federal transfer programs are estimated at 1.5–2 in cross-state regressions (Chodorow-Reich 2019).

HANK addresses all three by adding constrained households.

Heterogeneous Agent New Keynesian (HANK)

• Continuum of households with idiosyncratic income risk, incomplete insurance markets, and one (or two) assets to smooth consumption.
• New Keynesian goods-market and price-setting structure preserved.
• Aggregate fluctuations driven by monetary, fiscal, or other shocks, propagating through both rep-agent-style intertemporal substitution and through redistribution and MPC-weighted indirect channels.
• Solved numerically: Aiyagari steady state for the cross-section, plus aggregate shocks added via Krusell–Smith (1998) or, in modern practice, sequence-space Jacobian methods (Auclert et al. 2021).

The flagship paper is Kaplan, Moll, and Violante 2018, "Monetary Policy according to HANK" (AER 108(3): 697–743; PDF; AEA link). Two design choices distinguish KMV from earlier HA models:

1. Two-asset structure: households hold a liquid asset (low return, no transaction cost) and an illiquid asset (high return, transaction cost). This generates a realistic distribution of liquid and illiquid wealth and, crucially, populates the wealthy hand-to-mouth group (Kaplan–Violante–Weidner BPEA 2014) — households with substantial illiquid wealth (houses, retirement accounts) but little liquid buffer, who exhibit high quarterly MPCs despite being not-poor.
2. Realistic income process: idiosyncratic earnings calibrated to match income-volatility evidence, producing precautionary saving and a wealth distribution consistent with the Survey of Consumer Finances.

In KMV's HANK, indirect effects of monetary policy — the labor-demand response that raises income at high-MPC households — dominate. Direct effects — Euler-equation intertemporal substitution — are small because most consumers either can't borrow (constrained) or are well-insured against rate shocks (deep-pocketed savers). The contrast with RANK is stark: in RANK, direct effects are ~95% of the transmission; in HANK they are ~20%.

A central technical contribution of the KMV agenda is computational: rather than try to track the entire wealth distribution as a state variable (the Krusell–Smith approach, which approximates it by a few moments), KMV-style HANK exploits the structure of optimal consumption rules to derive analytic responses to aggregate shocks.

"Study this next" — Aiyagari steady states and the Bewley–Huggett–Aiyagari class. The micro core of HANK is the Aiyagari (1994) model: a continuum of agents facing idiosyncratic income risk, with a borrowing constraint, who save in a single risk-free asset. The steady state is a fixed-point: aggregate capital implies an interest rate, which determines individual policy functions, which determine the stationary distribution of wealth, which must aggregate to the assumed capital stock. Solving this requires dynamic programming (Bellman equation, value-function iteration, endogenous grid methods). Ljungqvist–Sargent's Recursive Macroeconomic Theory chapters on incomplete markets is the canonical pedagogy.

TANK as the analytical bridge

Full HANK is computationally heavy and conceptually slippery. TANK — the Two-Agent New Keynesian model — splits the population into two groups:

• A fraction $1-\lambda$ of households are savers: they have access to assets, smooth consumption à la rep-agent.
• A fraction $\lambda$ are hand-to-mouth: they consume their entire current after-tax income each period.

TANK keeps the analytical clarity of RANK while capturing the essential MPC-heterogeneity channel that drives HANK's distinctive predictions. Galí, López-Salido, and Vallés (2007) and Bilbiie (2008) launched the modern TANK literature; Bilbiie's "Monetary Policy and Heterogeneity: An Analytical Framework" (Review of Economic Studies, forthcoming 2025; paper) consolidates the framework into "THANK" — a tractable HANK with cyclical inequality, self-insurance, and realistic intertemporal MPCs that can be solved in closed form.

The pedagogical payoff: in TANK, you can solve algebraically for the aggregate consumption response to a transfer, fiscal multiplier, and amplified forward-guidance effect (Bilbiie's TANK NBER chapter 2024). We work out the TANK transfer multiplier in the Mathematical Foundations section below.

5. The sequence-space Jacobian: how micro and macro re-combine

The technical innovation that made the HANK research program scalable is the sequence-space Jacobian (SSJ) methodology of Auclert, Bardóczy, Rognlie, and Straub (Econometrica 89(5): 2375–2408, September 2021; paper; GitHub toolkit).

The conceptual trick is to think about the model in sequence space rather than state space. State-space methods (the older Krusell–Smith approach) require tracking the cross-sectional distribution of wealth as part of the state, which is high-dimensional and computationally brutal. Sequence-space methods instead compute, around the deterministic steady state, the Jacobian of aggregate outcomes (consumption $C_t$, investment $I_t$, output $Y_t$, ...) with respect to aggregate inputs (interest rate $r_t$, income $Y_t$, taxes $T_t$, ...) viewed as time paths rather than current values.

Intuitively: at the steady state, ask "how would aggregate consumption in period $t$ change if interest rates were perturbed in period $s$?" Compute this for every $(t, s)$ pair and assemble the answer into a matrix. That matrix — the sequence-space Jacobian — is all you need to compute the response of the model to any small aggregate shock under any policy rule.

Three properties make SSJ revolutionary:

1. Modularity: you compute Jacobians of micro blocks (household consumption, firm investment, central bank rule, government budget) separately and then chain them together via matrix multiplication. Re-using the household Jacobian, you can compute responses to monetary policy, fiscal policy, sectoral demand shifts, anything.
2. Speed: solving a representative household problem at the steady state and computing its perturbation is much faster than simulating the full distribution.
3. Insight: the Jacobian decomposition makes the direct vs indirect channels in HANK transparent. The direct channel is the diagonal of the consumption-w.r.t.-rate Jacobian. The indirect channel runs through the income Jacobian times the consumption-w.r.t.-income Jacobian.

The SSJ approach also clarifies a key conceptual point: the macro response is, exactly and not just approximately, the time-summed micro impulse response weighted by the shock path. Or in the formula taught in the Mathematical Foundations section below: aggregate consumption response = $\sum_s J_{ts} \cdot$ shock$_s$.

"Study this next" — perturbation methods in dynamic equilibrium. The mathematical apparatus is multivariate calculus applied to functional equations. Auclert et al.'s online appendix and the shade-econ/sequence-jacobian GitHub repo include both formal derivations and Python notebooks; the natural prior reading is Adda–Cooper's Dynamic Economics for the discrete-time recursive techniques.

6. Intertemporal MPCs and the intertemporal Keynesian cross

Once you have SSJ, you can read off a quantity that is empirically observable and theoretically central: the intertemporal MPC (iMPC).

The iMPC is a vector: it answers, "if a household receives an extra dollar today, how much do they consume today, next quarter, next year, and so on?" Empirical iMPCs from JPMC data (Parker–Souleles–Johnson–McClelland 2013 AER 103(6): 2530–53; AER link), Broda–Parker, and European HFCS data show a distinctive pattern:

• The on-impact MPC is substantial (12–30% of a transfer spent on non-durables within the first quarter; 50–90% including durables and vehicles).
• The MPC decays slowly: there's persistent extra spending for several quarters.
• The iMPC is much higher than RANK predicts (where the MPC out of a permanent-income-equivalent transfer is roughly the real interest rate, i.e. 1–3% per quarter).
• It's even higher than TANK predicts (since TANK has a lump-and-spend pattern, not a decay pattern).

Auclert, Rognlie, and Straub's "Intertemporal Keynesian Cross" (JPE 132(12), 2024; JPE link; NBER WP 25020) shows the macro implication: the aggregate output response to fiscal policy is a function only of the iMPC vector and the deficit path. Specifically:

aggregate output response $= M \cdot$ deficit path

where $M$ — the intertemporal Keynesian-cross multiplier matrix — is built from the iMPC vector. Match the empirical iMPC, and deficit-financed fiscal multipliers come out above 1, even cumulatively over many quarters. Use the RANK iMPC, and multipliers are well below 1. The difference is not a free parameter; it's a measurement.

The intertemporal Keynesian cross also gives a unified vocabulary for old debates:

• Balanced-budget multiplier (Haavelmo): close to 1 in HANK, as in RANK, because the spending and the tax cancel out in the iMPC algebra.
• Deficit-financed multiplier: well above 1 in HANK, well below 1 in RANK, because the future tax burden discounted by the iMPC vector is much smaller than the present transfer (since iMPCs decay and rep-agent MPCs are tiny).
• Forward-guidance puzzle: shrinks in HANK because high-MPC households face binding constraints today and don't intertemporally substitute much from far-future rate cuts.

7. Auclert's redistribution decomposition

A complementary contribution is Adrien Auclert's "Monetary Policy and the Redistribution Channel" (AER 109(6): 2333–67, 2019; AEA link; PDF). Auclert decomposes the redistribution effects of a monetary expansion into three channels:

1. Earnings heterogeneity channel. Different households' earnings respond differently to monetary policy. If labor income at the bottom is more cyclical than at the top — as the empirical evidence suggests — then a rate cut redistributes earnings toward higher-MPC households, amplifying the aggregate consumption response.
2. Fisher channel. Unexpected inflation transfers real wealth from creditors (low MPC: rich, old) to debtors (high MPC: mortgaged households). A monetary expansion that raises inflation expectations triggers this revaluation.
3. Interest-rate exposure channel. A change in the real rate has different income effects on households with different maturity-mismatch structures. Households with floating-rate debt (or short-duration assets) gain from rate cuts; those with long-duration fixed-income assets lose.

Each channel runs in the opposite direction in RANK (where Ricardian equivalence neutralizes most of them). In HANK, they sum and amplify the rate cut's effect on aggregate consumption. Crucially, the empirical sign and magnitude of each channel can be measured from micro data; this is the "identified moments" approach that disciplines the model.

8. The Annual Review consolidation (Auclert, Rognlie, Straub 2025)

The most authoritative recent survey is Auclert, Rognlie, and Straub's "Fiscal and Monetary Policy with Heterogeneous Agents" (Annual Review of Economics 17: 539–562, 2025; Annual Reviews link; NBER WP 32991; PDF). Their headline message is two-part:

"Monetary and balanced-budget fiscal policy have similar aggregate effects as in the standard New Keynesian model, while deficit-financed fiscal policy is much more expansionary."

This is the modern consensus, and it is a remarkable consensus. HANK does not overturn RANK on monetary policy in the aggregate — it changes the decomposition (direct vs indirect channel) and the distributional incidence, but not the headline output and inflation responses. HANK does overturn RANK on deficit-financed fiscal policy: where RANK predicts Ricardian neutrality, HANK predicts powerful aggregate effects, because the wealthy hand-to-mouth and the constrained spend the transfers in ways that swamp the discounted future-tax burden.

The survey emphasizes:

• The benefits of sequence-space methods for solving HANK efficiently.
• The role of behavioral frictions (cognitive discounting) in complementing rather than substituting for HANK.
• The importance of cyclical income risk (Storesletten–Telmer–Yaron 2004 evidence that earnings risk is countercyclical) in amplifying recessions.
• Maturity structure of debt and the nominal/real composition of household balance sheets as additional sources of heterogeneous transmission.

9. Granularity: Gabaix's idiosyncratic-shocks-don't-average-out result

Switch tracks now to the firm side of the micro-macro synthesis. The traditional macro view of firm-level shocks was that they cancel out in aggregation: the law of large numbers means that with $N$ independent firms, aggregate volatility scales as $1/\sqrt{N}$, which is tiny for the millions of US firms. Aggregate fluctuations therefore must come from aggregate shocks — TFP, monetary, fiscal.

Xavier Gabaix's "The Granular Origins of Aggregate Fluctuations" (Econometrica 79(3): 733–772, May 2011; Econometric Society link; PDF) showed this is empirically wrong. The argument is concise:

• The law of large numbers requires either independence or that the size distribution have a finite second moment.
• US firms are Zipf-distributed: the largest firms are extremely large relative to the median; the size distribution has approximately a power-law tail with exponent close to 1.
• For Zipf-distributed firms, $\sigma_{aggregate}$ does not decay as $1/\sqrt{N}$. It decays as $1/\ln N$, which is much slower. Idiosyncratic firm shocks remain a non-negligible share of aggregate volatility even at the size of the US economy.

Quantitatively: Gabaix shows the idiosyncratic movements of the largest 100 US firms explain about one-third of variation in US output growth. A new iPhone product cycle, an Exxon refinery accident, a Walmart inventory-system upgrade — these are macroeconomic events.

Carvalho and Grassi's "Large Firm Dynamics and the Business Cycle" (AER 109(4): 1375–1425, April 2019; AEA link) extends the granular hypothesis to a fully dynamic setting where firm-level entry, growth, and exit shocks generate aggregate persistence, volatility, and time-varying second moments — purely from the bottom up.

"Study this next" — power laws and Zipf distributions. The mathematical foundation is the theory of stable distributions and power laws. Gabaix's other survey, "Power Laws in Economics and Finance" (Annual Review of Economics 2009), is the standard reference. The empirical workhorse is Pareto's law: the fraction of firms larger than size $s$ scales as $s^{-\alpha}$ with $\alpha \approx 1$, a deeply non-Gaussian distribution in which the largest firms dominate aggregate behavior.

10. Production networks: Acemoglu–Carvalho–Ozdaglar–Tahbaz-Salehi

The complementary mechanism is input–output (I-O) network propagation. Acemoglu, Carvalho, Ozdaglar, and Tahbaz-Salehi's "The Network Origins of Aggregate Fluctuations" (Econometrica 80(5): 1977–2016, September 2012; Econometric Society link; PDF) shows that the network structure of inter-sectoral input supplies matters as much as firm size for aggregate volatility.

Intuition: a sector that supplies inputs to many other sectors — like energy, transport, semiconductors — is a hub. A shock to a hub propagates downstream through its direct customers and further downstream through its customers' customers, in a cascade. If hubs exist (and empirically they do — the US I-O network is highly asymmetric), idiosyncratic sectoral shocks to hub sectors generate aggregate volatility that would not exist if every sector were equally connected.

The mathematical structure is captured by the Leontief inverse $L = (I - A)^{-1}$, where $A$ is the input-output matrix (entry $A_{ij}$ = share of sector $j$ inputs in sector $i$'s production). The $(i, j)$ entry of $L$ measures sector $j$'s total importance (direct and indirect) as a supplier to sector $i$. The column sums of $L$ give what Carvalho and Tahbaz-Salehi (Annual Review of Economics 11: 635–663, 2019; Annual Reviews link; PDF) call influence vectors: the share of aggregate volatility a sector contributes when shocked.

The empirical companion to this theoretical literature is Carvalho, Nirei, Saito, and Tahbaz-Salehi's "Supply Chain Disruptions: Evidence from the Great East Japan Earthquake" (QJE 136(2): 1255–1321, May 2021; QJE link; PDF). The authors use firm-level supplier-customer data to trace how the 2011 Tōhoku earthquake — geographically localized, exogenous, and well-dated — propagated through Japan's production network. The result: a 0.47 percentage-point reduction in real GDP growth from supply-chain spillovers, more than four times the direct damage. Upstream and downstream effects are roughly equal in magnitude. The paper is the canonical empirical demonstration that input–output network propagation is real, large, and quantitatively significant.

We work out a 2×2 Leontief example by hand in the Mathematical Foundations section below.

11. Beyond Hulten: non-linear network economics

Hulten's theorem (1978) is the foundational result for linearized I-O analysis: to a first-order approximation, the macro effect of a sector-specific productivity shock equals the sector's cost-share in GDP. This is the "Domar weight" result and it underpins growth accounting.

Baqaee and Farhi's "The Macroeconomic Impact of Microeconomic Shocks: Beyond Hulten's Theorem" (Econometrica 87(4): 1155–1203, July 2019; Econometric Society link; PDF) shows that Hulten's first-order result is brutally inadequate at second order in real economies. Two features matter:

1. Complementarities in production. If electricity and labor must be combined in roughly fixed proportions (low elasticity of substitution), then a shock to electricity has much larger effects than its cost share suggests because labor cannot substitute.
2. Reallocation frictions. Markets re-allocate resources sluggishly across sectors. In the short run, the aggregate effect of a sector shock is amplified.

Baqaee and Farhi formalize this with non-parametric, structural elasticities at the second order. The intuition is "network propagation interacts with curvature": when production functions have low elasticities (Leontief technology in the limit), sectoral shocks are amplified by the network in a way that linear Domar weights miss completely.

Application to COVID-era inflation

Baqaee and Farhi's "Supply and Demand in Disaggregated Keynesian Economies with an Application to the Covid-19 Crisis" (AER 112(5): 1397–1436, May 2022; SSRN; AEA) extended the framework to a disaggregated Keynesian model with input–output linkages and applied it to the pandemic. Key findings:

• Lockdowns generated sectoral supply shocks (some sectors couldn't operate); these had macro effects much larger than their cost share suggested because of complementarities.
• Consumption baskets shifted from services to goods (sectoral demand shock).
• Aggregate fiscal transfers added aggregate demand on top.
• The combination explains the size, timing, and sectoral composition of the 2021–2022 US inflation burst much better than either pure-supply or pure-demand stories.

This is a paradigmatic micro-macro intermingling: the inflation aggregate is computed bottom-up from sectoral price changes weighted by their network position and consumption shares. The aggregate Phillips curve is an emergent property, not a primitive.

Bernanke and Blanchard's "An Analysis of Pandemic-Era Inflation in 11 Economies" (NBER WP 32532; Brookings) reaches a complementary conclusion using a reduced-form decomposition: supply shocks dominated the initial inflation burst, but tight labor markets and nominal wage gains became increasingly important as supply disruptions faded.

12. The "identified moments" approach: how micro causal estimates discipline macro

The bridge from micro evidence to macro models had, until recently, been treated as an art. Calibration matched a few moments (capital-output ratio, average hours worked); estimation fit time series. Neither directly used the explosion of micro causal-inference work that the Card-Angrist credibility revolution produced in the 1990s and 2000s.

Nakamura and Steinsson's "Identification in Macroeconomics" (JEP 32(3): 59–86, 2018; AEA link; PDF; NBER WP 23968) crystallized a new approach: use identified macro moments — credible causal estimates from natural experiments, cross-sectional variation, or regression-discontinuity designs — as moments to match in structural estimation of macro models.

Examples that have become standard inputs to macro:

• Cross-state fiscal multipliers from the American Recovery and Reinvestment Act and other regional variation. Chodorow-Reich's "Geographic Cross-Sectional Fiscal Spending Multipliers: What Have We Learned?" (AEJ:Economic Policy 11(2): 1–34, May 2019; AEA link; NBER WP) finds a preferred cross-sectional multiplier of 1.8.
• Mian–Sufi housing-debt evidence: cross-county variation in the housing bust × ex-ante leverage predicts consumption collapse. This estimates a causal MPC out of housing wealth that is then used to calibrate HANK-style household behavior.
• MPC from stimulus payments: Parker–Souleles–Johnson–McClelland use the random timing of the 2008 stimulus payments to estimate household-level MPCs from a temporary transfer.

The methodological commitment is: the micro estimate enters the macro model as a target, not as a free parameter. If the model can't match the cross-state fiscal multiplier (a moment), it's mis-specified, regardless of how well it fits aggregate time series. This is the modern empirical disciplining of microfoundations.

"Study this next" — structural macro estimation. The toolkit ranges from generalized method of moments (GMM) for identified-moment matching to Bayesian likelihood-based estimation of DSGE models. An–Schorfheide's Journal of Econometrics 2007 survey is the formal Bayesian DSGE reference; Hansen–Heckman's Journal of Economic Perspectives 1996 "The Empirical Foundations of Calibration" is the philosophical statement of the calibration tradition that identified-moments matching modernizes.

13. The Mian–Sufi housing-debt thesis

A particularly influential demonstration of the identified-moments approach is Mian and Sufi's House of Debt (2014, University of Chicago Press; based on their academic work in QJE, AER, and Econometrica). The argument:

• Households entered the 2007–2009 recession with historic levels of mortgage debt, concentrated among lower-net-worth households.
• The housing bust destroyed housing wealth most aggressively at the bottom of the wealth distribution (because leverage amplifies wealth losses).
• High-MPC, low-wealth households cut consumption sharply.
• The consumption collapse — not financial-sector contagion alone — drove the recession.

The empirical methodology is cross-county: counties with higher ex-ante household leverage saw bigger consumption drops, bigger auto-sales drops, bigger employment losses, in proportion to local housing-price declines. The exclusion restriction is housing supply elasticity (Saiz 2010) as an instrument for housing-price changes.

The macro implication is exactly HANK-shaped: the recession was deeper than a representative-agent model predicts because the wealth losses landed on high-MPC households, who could not borrow to smooth and instead cut spending sharply. This finding has been built directly into HANK calibrations (Kaplan–Mitman–Violante 2020 quantify the housing-wealth-effect contribution to the 2007–2010 collapse using a HANK model with housing).

13b. Financial intermediation: from Bernanke-Gertler-Gilchrist to the post-2008 frontier

A parallel synthesis runs through the financial system. The traditional NK model treated the banking sector as a passive veil between the central bank and the real economy. The 2008 crisis and the European sovereign-debt crisis exposed this as inadequate.

The Bernanke-Gertler-Gilchrist financial-accelerator tradition (BGG 1999 Handbook of Macroeconomics chapter; building on Bernanke-Gertler 1989 AER) introduced borrower-lender information asymmetries into the NK model. Firms with weak balance sheets face external-finance premia that rise during downturns, creating a feedback loop: low net worth → high cost of capital → low investment → low income → low net worth. This is a micro friction — the costly-state-verification problem of Townsend (1979) — with macro amplification properties.

The Gertler-Karadi (2011, 2013) banking-friction framework extended this to a constrained banking sector: banks face a leverage constraint tied to their net worth, so shocks to bank net worth (asset write-downs, deposit runs) tighten credit supply throughout the economy. This is the canonical microfoundation for "unconventional monetary policy" — large-scale asset purchases, lending facilities — that the Fed deployed in 2008–2009 and 2020.

The He-Krishnamurthy (2013) intermediary-asset-pricing tradition flips the perspective: instead of treating intermediaries as a friction on firm financing, treat them as the marginal investor whose risk-taking capacity drives asset prices. When intermediary equity is depleted, risk premia spike across all risky asset classes — a micro fact about who is at the margin of asset markets, with macro consequences for the cost of capital throughout the economy.

The synthesis with HANK and production-network macro is incomplete but active. Three-friction models that combine household heterogeneity (HANK), firm heterogeneity (Khan-Thomas, Ottonello-Winberry), and intermediary heterogeneity (Gertler-Karadi, He-Krishnamurthy) are computationally heavy and operationally rare, but they are the natural endpoint of the synthesis. The Bank of England's UK-HANK model (BoE 2026) is an attempt in this direction, with detailed housing and mortgage blocks; the Reserve Bank of Australia's RDP 2025-04 is another.

The deeper lesson: the 2008 crisis re-opened the question of whether the aggregate household and firm data are sufficient for macro analysis, or whether the micro structure of intermediation — who holds what risks, how networks of exposures propagate stress — is a first-order driver of macro outcomes. The post-2008 consensus is that intermediation matters, but the integration of intermediation with HANK and network macro is unfinished business.

14. Heterogeneous firms in macro: Khan–Thomas, Ottonello–Winberry

A parallel literature applies the heterogeneity insight to firms. Two landmark contributions:

• Khan and Thomas's "Idiosyncratic Shocks and the Role of Nonconvexities in Plant and Aggregate Investment Dynamics" (Econometrica 76(2): 395–436, March 2008; Wiley link) studies a model where firms face fixed costs of adjusting capital. Investment is lumpy at the firm level (long periods of inaction punctuated by bursts), and aggregating produces aggregate-investment dynamics that depend on the distribution of firms' distance from their target capital level.
• Ottonello and Winberry's "Financial Heterogeneity and the Investment Channel of Monetary Policy" (Econometrica 88(6): 2473–2502, November 2020; Wiley; PDF) shows that firms with low default risk (high distance-to-default) are more responsive to monetary policy. The intuition is the opposite of the textbook financial-accelerator: financially constrained firms cannot expand even when borrowing costs fall, so their investment is less interest-elastic. The most monetary-policy-responsive firms are the healthy ones.

Both contributions confirm the central HANK message in the firm dimension: aggregating across heterogeneous units gives qualitatively and quantitatively different answers than the representative-firm benchmark. The investment response to monetary policy is bigger or smaller depending on the distribution of firms over financial states.

15. Distributional national accounts and the inequality-macro link

Piketty, Saez, and Zucman's "Distributional National Accounts: Methods and Estimates for the United States" (QJE 133(2): 553–609, 2018; QJE link; NBER WP 22945) introduced a methodology that allocates 100% of national income to individual adults using a combination of tax records, surveys, and national-accounts identities. The goal: produce growth rates by income decile that aggregate consistently to the national-accounts GDP. This made it possible to ask "growth for whom?" rather than just "growth at the aggregate."

The PSZ DINA project has produced some of the most influential narratives of post-1980 American macroeconomic history:

• The top 1% income share roughly doubled from 1980 to 2014.
• The bottom 50% experienced near-zero real income growth over decades.
• These distributional patterns are first-order facts that any macro narrative must reconcile.

The methodology is contested. Auten and Splinter's "Income Inequality in the United States: Using Tax Data to Measure Long-Term Trends" (2024 version; reply to PSZ; 2025 update) reach much flatter conclusions about the rise in top shares, arguing that PSZ's allocations of underreported business income, retirement savings, and corporate retained earnings inflate the trend. Piketty, Saez, and Zucman's reply (PSZ 2024 technical note) defends the original methodology.

This is not a footnote: macro models that build in inequality as a driver of macro dynamics (Mian–Straub–Sufi "Indebted Demand", QJE 2021) are sensitive to which series is right. If inequality has risen sharply (PSZ), the demand-suppression mechanism of indebted demand is potent. If inequality has been roughly flat (Auten–Splinter), the mechanism is weaker. The micro-macro intermingling is thus normatively contested through a technical dispute about distributional accounting.

15b. The inequality-growth relationship: from Kuznets to Chetty

A cross-cutting question in the micro-macro intermingling is whether inequality affects long-run growth. Three threads in the recent literature:

(i) Inequality lowers demand and natural rates. This is the indebted-demand thesis (Mian-Straub-Sufi 2021) discussed above. The micro mechanism is heterogeneous propensities to save; the macro consequence is suppressed natural rates and secular stagnation.

(ii) Inequality affects long-run growth through human-capital investment. Chetty, Hendren, Kline, and Saez's "Where is the Land of Opportunity? The Geography of Intergenerational Mobility in the United States" (QJE 129(4): 1553–1623, 2014; QJE link; PDF) used 40 million tax records to document substantial geographic variation in intergenerational mobility: a child born to parents at the 25th percentile in Seattle has outcomes equivalent to a child born at the median in Atlanta. The follow-on paper, Chetty and Hendren's "The Impacts of Neighborhoods on Intergenerational Mobility" (QJE 133(3): 1107–62, 2018; QJE link), used moves between commuting zones to show that two-thirds of the cross-county variation reflects causal place effects.

The macro implication: areas with lower upward mobility have lower long-run growth in the children of the disadvantaged, which compounds into lower aggregate productivity over a generation. If inequality is sustained because of low mobility — and not just because of high concentration at the top — then policies that improve mobility (early-childhood education, school quality, neighborhood diversity) have macro-growth payoffs in addition to normative-welfare payoffs.

(iii) Inequality may affect growth through innovation incentives. Aghion-Akcigit-Hyytinen-Toivanen (2020 QJE) document that inventors come disproportionately from high-income families, but conditional on parental income, the income elasticity of becoming an inventor is sharper at higher income (the "lost Einstein" effect). Reducing this gradient could raise the aggregate stock of inventors and accelerate growth.

The synthesis here is that inequality is not merely a normative concern, and not merely a demand-side aggregate-fluctuation concern (as in indebted demand), but a long-run supply-side concern through human-capital accumulation. The macro growth literature is slowly absorbing these micro mobility findings, but the integration remains incomplete.

16. Market power, superstars, and macro stagnation

A complementary strand connects rising firm-level market power to macro stagnation:

• De Loecker, Eeckhout, and Unger's "The Rise of Market Power and the Macroeconomic Implications" (QJE 135(2): 561–644, May 2020; QJE link) documents aggregate US markups rising from ~21% above marginal cost in 1980 to ~61% in 2016, driven by the upper tail of the distribution. Profit rates rose from ~1% to ~8% over the same period.
• Autor, Dorn, Katz, Patterson, and Van Reenen's "The Fall of the Labor Share and the Rise of Superstar Firms" (QJE 135(2): 645–709, May 2020; QJE link; NBER WP 23396) shows that sales have concentrated within industries among a small number of high-markup, low-labor-share "superstars." As these firms grow, the aggregate labor share falls — even though within-firm labor shares change little.
• Philippon's The Great Reversal: How America Gave Up on Free Markets (Harvard University Press, 2019) argues that US product markets have lost competition relative to Europe, and that rising concentration explains a meaningful share of the decline in US business investment and dynamism.

The macro implication runs through several channels:

• Higher markups raise the gap between marginal cost and price, which lowers labor's share and the natural rate of investment.
• Concentration may reduce business dynamism (entry, exit, reallocation), slowing aggregate productivity growth.
• Profits accrue to wealthier households who save them, depressing aggregate demand.

This is a synthesis story: a micro fact (firm-level markups) explains macro trends (falling labor share, slowing investment, low natural rates). It is not yet settled — De Loecker's markup measurement methodology has been challenged by Traina (2018) on the treatment of selling, general, and administrative expenses — but it has reshaped the way the labor-share decline is discussed.

17. Indebted demand: how distribution links to secular stagnation

A direct synthesis paper is Mian, Straub, and Sufi's "Indebted Demand" (QJE 136(4): 2243–2307, November 2021; QJE link; Straub PDF). The argument:

• Top-income households save more out of permanent income than middle-income households. (This is the empirical motivation; intuitively, the rich consume a smaller share of their lifetime income.)
• Rising inequality therefore lowers aggregate demand at any given interest rate, pushing the natural rate down.
• Households respond by borrowing — financial deregulation makes credit easy — sustaining demand in the short run.
• But debt service eventually crowds out consumption, sustaining low natural rates persistently. The economy can be trapped in a debt trap with zero or negative natural rates.

Mian–Straub–Sufi's model unifies the savings-glut hypothesis (Bernanke 2005), the inequality-and-stagnation hypothesis (Summers 2014), and the household-debt hypothesis (Mian–Sufi 2014) into a single quantitative framework. The micro mechanism — different MPCs by income — drives a macro outcome — secular stagnation.

The policy implications are HANK-shaped: redistribute toward high-MPC households to escape the debt trap; financial regulation should consider its macro-stabilization function, not just micro-prudential safety.

18. Behavioral macro: adjusting expectations, not microfoundations

A separate route to fixing RANK's empirical pathologies is to keep the representative agent but replace rational expectations with bounded rationality or behavioral discounting.

Gabaix's "A Behavioral New Keynesian Model" (AER 110(8): 2271–2327, August 2020; AEA; PDF; NBER WP 22954) introduces a single parameter — cognitive discounting — that captures myopia toward distant future events. Agents underreact to news about events far in the future, in roughly the way human survey responses suggest they do. This single modification resolves:

• The forward-guidance puzzle (agents discount the distant-future rate cut more heavily).
• The fiscal-multiplier puzzle (agents discount the distant tax burden more heavily, making deficit-financed fiscal more powerful — same effect as HANK).
• The Phillips-curve flattening puzzle (cognitive discounting makes firms less responsive to current marginal-cost shocks because they expect them to fade).

García-Schmidt and Woodford's "Are Low Interest Rates Deflationary? A Paradox of Perfect-Foresight Analysis" (AER 109(1): 86–120, January 2019; AEA link; PDF) attacks the "neo-Fisherian" prediction that pegging rates at zero is deflationary. They propose a process of reflective equilibrium in which agents iteratively refine their forecasts. Under reflection, low rates are expansionary (the traditional view), not deflationary (the neo-Fisherian perfect-foresight result). The mechanism teaches a deep lesson: equilibrium-selection problems in macro can be illuminated by modeling explicitly how expectations form.

Pfäuti and Seyrich's "A Behavioral Heterogeneous Agent New Keynesian Model" (2024 working paper; PDF) combines the two: cognitive discounting and heterogeneous agents. The combination is potent — inflation rises 67% more on impact than in either model alone, because cognitive discounting interacts with the unequal exposure of constrained households to inflation.

The conceptual point: HANK and behavioral macro are substitutes for some puzzles (both resolve the forward-guidance puzzle) but complements for others (cyclical inequality plus inattention generates dynamics neither alone can produce).

Level-k thinking and macro

A more cognitively realistic alternative to rational expectations is level-k thinking, imported from game theory (Stahl-Wilson 1995, Nagel 1995). The idea: instead of imposing fixed-point rationality, agents reason finitely many steps ahead.

• Level-0 agents are non-strategic (use a default rule or current state).
• Level-1 agents best-respond to a population of level-0s.
• Level-k agents best-respond to level-(k-1)s.

In a macro context (Farhi-Werning 2019, Iovino-Sergeyev 2023), the forward-guidance puzzle disappears because finite-k agents do not chain expectations indefinitely; the equilibrium path of inflation and output stops well short of the rational-expectations explosion.

Level-k thinking also illuminates the expectation-formation problem that survey data document: households' inflation forecasts cluster around personal experience, lagged values, and salient prices (gas, groceries) rather than around the Fed's announcements (Coibion-Gorodnichenko 2015). This is consistent with shallow-depth reasoning rather than full-information rational expectations.

Heterogeneous expectations in agent-based macro

Cars Hommes's "behavioral heterogeneous expectations" framework (CeNDEF Amsterdam) populates the economy with multiple forecasting rules (e.g., fundamentalists, chartists, naive) and lets evolutionary selection determine which rules survive. The result is a macro economy that can exhibit endogenous boom-bust cycles, regime switching, and complex non-equilibrium dynamics that neither RANK nor HANK can produce.

The frontier (Hommes 2021, JEL) integrates such heterogeneous expectations into both representative-agent and HANK frameworks. The empirical payoff is calibrating models to experimental data on forecasting behavior (Hommes's "learning-to-forecast" experiments) rather than to aggregate moments. The methodological cost is moving away from analytical tractability toward simulation.

19. Agent-based macro: the post-COVID revival

A more radical alternative to DSGE is agent-based macroeconomics (ABM). Where DSGE models start from equations and impose equilibrium, ABM starts from heterogeneous behavioral rules for individual agents and simulates the resulting dynamics. Equilibrium, if it emerges, emerges from the bottom up.

Long associated with Doyne Farmer (INET Oxford), Giovanni Dosi (Sant'Anna, Pisa), and Cars Hommes (CeNDEF Amsterdam), ABM was a fringe enterprise within mainstream macro through the 2010s. The post-COVID period brought a partial revival:

• ABM models successfully forecast the macroeconomic impact of UK lockdowns in 2020 (INET Oxford writeup).
• The Austrian central bank used ABM to forecast medium-run effects of COVID lockdowns.
• Axtell and Farmer's Agent-Based Modeling in Economics and Finance: Past, Present, and Future (2025) provides a comprehensive survey.

The intellectual appeal: ABM does not require representative agents, equilibrium, or rational expectations. It allows non-linearities, financial-network cascades, and emergent crises that DSGE struggles to represent. The methodological cost: ABM is computational rather than analytical; validation is harder; comparative statics are noisier.

The current consensus (as of 2025–2026) is that ABM and HANK/DSGE are complementary tools. HANK provides analytical tractability and policy-counterfactual rigor; ABM provides flexibility for crisis simulation and complex-network dynamics. The CCB-class central banks (Bank of England, ECB) experiment with both.

20. The 2024–2026 frontier: live debates

Several debates are unresolved and active in the period leading up to and including 2026:

(a) How much heterogeneity matters: HANK vs TANK vs THANK

Bilbiie's THANK framework (Review of Economic Studies 2025; Oxford link) argues that a tractable two-agent model with the right cyclical inequality parameterization captures most of HANK's distinctive predictions. The implication: maybe the analytical TANK with one degree of freedom (cyclical incidence) is enough, and the full HANK machinery is intellectually beautiful but quantitatively overkill.

Auclert, Rognlie, and Straub's Annual Review survey (2025) takes the opposing view: TANK can match some moments but misses others (especially the intertemporal MPC pattern), and full HANK is necessary for serious quantitative work.

The debate matters because TANK is teachable in graduate courses with calculus and standard methods, while HANK requires the SSJ apparatus and computational infrastructure. If TANK suffices, the methodological barrier to entry stays manageable.

(b) Rational expectations vs learning in HANK

Benjamin Moll's "The Trouble with Rational Expectations in Heterogeneous Agent Models: A Challenge for Macroeconomics" (CEPR DP 19731, 2025; arXiv 2508.20571; Moll PDF) argues that rational expectations in HANK requires agents to forecast equilibrium prices by forecasting the entire cross-sectional distribution. The resulting Bellman equation — what Moll calls the "Master equation" or, less charitably, the "Monster equation" — is computationally intractable for realistic settings with aggregate risk and non-linearities.

Moll proposes alternative expectations frameworks:

• Temporary equilibrium (Grandmont 1977): agents form short-horizon forecasts and update.
• Survey expectations: use actual measured beliefs (Coibion–Gorodnichenko) rather than rational forecasts.
• Least-squares learning: agents update forecasts via OLS over past data.
• Reinforcement learning: agents learn near-optimal policy rules via simulation.

The challenge has real bite: if HANK with rational expectations cannot handle aggregate risk and crises, it inherits the very pathology that motivated the heterogeneous-agent program in the first place.

(c) Disaggregation vs DSGE in policy institutions

The Reserve Bank of Australia, Bank of England, and Federal Reserve are all developing HANK-style models for monetary-policy analysis (RBA RDP 2025-04; BoE UK-HANK 2026). The practical question is whether HANK's distributional richness translates into materially better policy advice, or whether the marginal value over a well-calibrated TANK/DSGE is small relative to the operational cost.

(d) Fiscal theory of the price level

Cochrane's The Fiscal Theory of the Price Level (Princeton University Press, 2023; Princeton link) consolidates a long-running alternative to monetary determination of the price level. In FTPL, the price level adjusts so that the real value of government debt equals the present value of primary surpluses. Inflation arises from fiscal stress, not just monetary policy.

FTPL is itself a micro-macro intermingling: it relies on the household budget constraint (a micro object) being respected at the aggregate level for government debt to be valued. The 2021–2022 inflation burst — coincident with massive fiscal transfers — was read by Cochrane as supportive evidence. The mainstream NK/HANK reply: yes, fiscal transfers did matter, but through high-MPC household spending channels, not through FTPL's surplus-discounting mechanism.

The debate is unresolved and is genuinely about which micro fact — high MPCs or government debt sustainability — is doing the work in explaining the post-pandemic price level.

21. Policy lessons from the synthesis

Three policy-relevant lessons emerge from the micro-macro synthesis:

(a) Monetary policy redistributes; central banks should know how. Cutting rates transfers wealth from savers to debtors, from fixed-income to floating-rate holders, from the old to the young. The aggregate stimulus is welcome; the distributional consequences are real and uneven. Liberty Street Economics has begun publishing HANK-based decompositions of monetary policy that quantify these consequences (LSE on inflation and inequality, 2024). The Fed's dual mandate is being reinterpreted in light of who bears the cost and benefit of stabilization.

(b) Fiscal policy is more powerful than RANK predicts. This was a hard-won lesson of 2020–2021. The pandemic transfers — CARES, ARPA — landed disproportionately on liquidity-constrained households who spent them rapidly. The resulting demand surge, combined with sectoral supply disruptions, produced inflation in textbook fashion (Baqaee–Farhi 2022). The HANK-implied multiplier on such transfers is well above 1, consistent with the observed inflation overshoot. Future policy design — especially in recessions or pandemics — should treat MPC targeting as a first-order design parameter.

(c) Macro-prudential regulation requires micro intermediary models. The 2008 crisis exposed that financial-system stability depends on the network structure of interbank exposures, repo markets, money funds, and shadow-bank intermediation. A "macro-prudential" regulatory stance therefore requires micro-level models of intermediary balance sheets, network exposures, and run dynamics. This is the same intermingling that production-network macro brings to the goods market: the aggregate fragility is a property of micro-level network structure.

(d) Inequality is a macro variable, not just a normative one. Pre-HANK, the standard view in central-bank circles was that inequality is "for the Treasury, not the central bank." HANK and indebted-demand have changed this. The level and dynamics of wealth and income inequality affect the natural rate of interest, the size of fiscal multipliers, the slope of the Phillips curve, and the speed of recoveries. The Fed's Jackson Hole 2020 framework change — adopting "broad-based and inclusive" as an employment goal — can be read as institutional recognition of this fact.

(e) Sectoral composition matters for inflation. The pandemic-era inflation episode forced policymakers to reason about sectoral inflation in ways the aggregate Phillips curve had hidden. The Baqaee-Farhi framework gives a vocabulary: which sectors are demand-driven, which are supply-constrained, how the shocks combine through the input-output network. Fed and ECB communications since 2022 have routinely cited disaggregated price changes (Adams-Barnichon-Matheson, Shapiro, Bernanke-Blanchard decompositions) in their inflation diagnoses. This is the synthesis influencing policymaking in real time.

(f) Targeted vs uniform transfers have very different multipliers. The COVID transfers in the US were variously targeted (unemployment supplements, child tax credit) and uniform (stimulus checks). HANK analysis shows that the targeted transfers had higher multipliers per dollar because they landed on higher-MPC households. This is a design lesson that has shaped the conversation around future fiscal stabilizers (Heathcote-Storesletten-Violante 2024 on optimal automatic stabilizers).

(g) Monetary policy has fiscal dependencies. In HANK, the size of a monetary expansion depends on the fiscal response: who pays the lump-sum tax that finances any debt issuance? Lump-sum on savers is neutral; lump-sum on hand-to-mouth households is highly contractionary; distortionary tax (income tax) is intermediate. This means central-bank counterfactual analysis is incomplete without a specified fiscal rule — a tightening of the analytical link between monetary and fiscal policy that was always implicit but is now operational.

(h) The 2020–2022 macro response set a natural experiment. The combination of pandemic transfers + lockdowns + supply disruptions + monetary accommodation has been the largest macro shock since the Great Depression. It has provided more identifying variation for HANK and disaggregated-network models than the prior 30 years combined. The Bernanke-Blanchard, Baqaee-Farhi, and follow-on literatures are still digesting it. The interpretive consensus likely to settle: roughly half of the inflation overshoot was sectoral-supply (Baqaee-Farhi style), and roughly half was excess demand from fiscal transfers spent by high-MPC households (HANK style). The two stories are not competing; they are the two halves of the synthesis.

22. Methodological reflection: what the synthesis teaches

Step back from the substance and look at the methodology. The modern micro-macro synthesis has converged on a workflow:

1. Specify a population of optimizing micro agents with realistic heterogeneity (income, wealth, age, sector, financial constraints).
2. Solve their decision problems at the deterministic steady state. This is a micro exercise.
3. Compute sequence-space Jacobians of aggregate behaviors with respect to aggregate shocks. This is the bridge from micro to macro.
4. Combine these Jacobians with the policy rule and market-clearing conditions to compute aggregate responses to arbitrary shocks. This is macro.
5. Discipline parameters using identified moments from causal-inference micro work (cross-state multipliers, randomized stimulus payments, natural experiments).
6. Use the model for both positive (how does the economy respond?) and normative (who wins and loses?) analysis.

Each step has a deep intellectual lineage: micro-optimization from Marshall, equilibrium from Walras, perturbation methods from Frisch, identification from the Cowles Commission. What's new in 2025 is the integration: a single workflow that respects the Lucas critique, evades the SMD aggregation problem by computing rather than assuming, leverages the credibility revolution in micro causal inference, and produces both aggregate forecasts and distributional incidence in the same framework.

The synthesis remains, by 2026, technically sophisticated and conceptually still being clarified. It will likely take another decade for textbooks to catch up. But the direction of travel is clear: macro is now an applied general-equilibrium discipline that takes micro evidence as inputs and produces aggregate-and-distributional outputs.

Mathematical foundations

This section consolidates the algebra promised in the brief. Every derivation is at the level of high-school algebra plus simple matrix multiplication for the Leontief example. Calculus, dynamic programming, and computational methods are flagged with "Study this next" callouts.

A. Two-agent TANK: aggregate consumption response to a deficit-financed transfer

Setup. A unit mass of households. A fraction $\lambda$ are hand-to-mouth (H) with MPC of $1$ out of current income. A fraction $1 - \lambda$ are savers (S) with Permanent Income Hypothesis behavior: MPC out of current income is $r/(1+r) \approx r$ (a tiny number, say 0.02 per quarter at a 2% real rate).

Per-period income for saver $i$: $y_i^S$. Per-period income for H household $i$: $y_i^H$. Aggregate income $Y$.

Policy intervention. The government issues a one-period lump-sum transfer $\tau$ per capita, financed by debt today and a one-period-future lump-sum tax. In the simplest version, the future tax falls equally on all households.

RANK benchmark. With $\lambda = 0$ everyone is a saver, smooths intertemporally, and Ricardian equivalence holds: consumption response to a transfer that is fully financed by a future tax of equal present value is zero. The fiscal multiplier on deficit-financed transfer is zero. This is the textbook benchmark.

TANK with $\lambda > 0$. The hand-to-mouth households consume the entire transfer today. The savers, knowing they will pay the future tax, do not increase consumption. Aggregate consumption response on impact:

$$\Delta C = \lambda \cdot \tau + (1 - \lambda) \cdot 0 = \lambda \tau$$

So the impact fiscal multiplier on a deficit-financed transfer is $\lambda$ (the share of hand-to-mouth households).

Adding indirect effects. If aggregate consumption rises by $\lambda \tau$, firms' demand rises. In a NK model with sticky prices, firms accommodate by raising output and labor demand. Aggregate income rises by $\Delta Y$, of which a fraction goes to H households as wages. The H households spend their share immediately:

$$\Delta C = \lambda \tau + \lambda \cdot \Delta Y$$

If we use a simple Keynesian-cross closure where $\Delta Y = \Delta C$ (output rises one-for-one with consumption demand because investment is fixed):

$$\Delta C = \lambda \tau + \lambda \Delta C$$ $$\Delta C (1 - \lambda) = \lambda \tau$$ $$\Delta C = \frac{\lambda}{1 - \lambda} \tau$$

This is the TANK Keynesian-cross multiplier: $\frac{\lambda}{1 - \lambda}$. With $\lambda = 0.3$ (a typical estimate of the hand-to-mouth share), the multiplier is $0.3 / 0.7 \approx 0.43$. With $\lambda = 0.5$, the multiplier is 1. With $\lambda = 0.7$, the multiplier is $0.7/0.3 \approx 2.33$.

The TANK multiplier is small relative to HANK's because TANK has only one micro fact (the population share of H), while HANK has the whole iMPC distribution. The intuition is identical: micro-heterogeneity makes the demand multiplier non-zero.

Connection to data. Empirical estimates of $\lambda$ from US household surveys range from 0.2 (narrow liquid-constrained measures) to 0.4 (broader Kaplan–Violante–Weidner hand-to-mouth including wealthy hand-to-mouth). So TANK multipliers in the 0.25–0.67 range on impact, rising further with indirect amplification. This is consistent with the Chodorow-Reich cross-state multiplier estimate of 1.8 once you allow for federal monetary accommodation.

"Study this next" — closed-form TANK with sticky prices. Bilbiie 2008 and 2025 derive the analytic closed-form New Keynesian TANK with sticky prices, where the multiplier depends on the monetary-policy response (the Taylor coefficient on inflation). The algebra requires solving a small linear system but is otherwise accessible; the full derivation is in Bilbiie's THANK paper.

B. MPC aggregation: aggregate consumption response when MPCs are heterogeneous

Setup. A population of households indexed $i$, each with a household-level MPC $m_i$. The MPC distribution has cumulative distribution function $F(m)$.

Uniform transfer. Government sends $\tau$ to every household. Aggregate consumption response:

$$\Delta C = \sum_i m_i \cdot \tau = \tau \cdot \int m , dF(m) = \tau \cdot \bar{m}$$

where $\bar{m}$ is the mean MPC. This is the most basic micro-macro aggregation fact: aggregate consumption response to a uniform transfer depends on the average MPC across the population.

Targeted transfer. Government sends transfer $\tau_i$ to household $i$, with $\sum_i \tau_i = \tau$ (total transfer fixed). Aggregate consumption response:

$$\Delta C = \sum_i m_i \tau_i$$

If $\tau_i$ is correlated with $m_i$ — i.e., the government targets high-MPC households — the multiplier rises above $\bar{m} \tau$. For example, if $\tau$ goes entirely to households with $m_i = 0.5$, then $\Delta C = 0.5 \tau$, even if the population mean MPC is only $0.2$.

Cyclical aggregation. In a recession, unemployment concentrates on certain households. If those households have higher-than-average MPCs (true empirically: lower-wealth, more-constrained), then a $$1$ aggregate income loss translates into $> \bar{m}$ consumption loss. The recession is amplified relative to a representative-agent benchmark. This is the cyclical-inequality amplification that drives HANK.

Toy numbers. Suppose 25% of households have $m = 0.6$, 50% have $m = 0.1$, 25% have $m = 0.02$. Population mean MPC: $0.25 \times 0.6 + 0.5 \times 0.1 + 0.25 \times 0.02 = 0.15 + 0.05 + 0.005 = 0.205$.

If a $$1$ aggregate income loss falls proportionately, consumption falls $$0.205$. If it falls only on the high-MPC households (true in recessions: unemployment is concentrated), consumption falls $$0.60$ per dollar of their income loss, which when scaled to aggregate (they're 25% of households) gives $$0.60 \times (1/0.25) = $0.24 $ per dollar of their group's income loss, but the more salient point is that an aggregate loss landing on a single quartile becomes equivalent to a much larger uniform loss in terms of consumption.

The general formula: if a fraction $\alpha$ of the aggregate shock lands on a high-MPC group with mean MPC $m_H$, and the rest lands on a low-MPC group with mean MPC $m_L$:

$$\Delta C = \alpha \cdot m_H \cdot \Delta Y + (1 - \alpha) \cdot m_L \cdot \Delta Y$$

When $\alpha$ rises (the shock concentrates on high-MPC households), $\Delta C$ rises for the same aggregate $\Delta Y$. The economy's macro response depends on the micro incidence.

C. Leontief 2×2 input-output: how a sectoral shock propagates

Setup. A two-sector economy: sector 1 produces good A, sector 2 produces good B. Each sector uses inputs from itself and the other. Final demand for good A is $d_A$, for good B is $d_B$. Total output of A is $x_A$; of B is $x_B$.

Input requirements matrix $A$:

$$A = \begin{pmatrix} a_{AA} & a_{AB} \ a_{BA} & a_{BB} \end{pmatrix}$$

where $a_{ij}$ is the amount of good $i$ required to produce one unit of good $j$.

Concrete numbers: producing one unit of A needs 0.2 units of A (self-input) and 0.4 units of B (intermediate input). Producing one unit of B needs 0.3 units of A and 0.1 units of B.

$$A = \begin{pmatrix} 0.2 & 0.3 \ 0.4 & 0.1 \end{pmatrix}$$

Total demand for each good = intermediate use + final demand.

For good A: $x_A = a_{AA} x_A + a_{AB} x_B + d_A$ (the amount of A used by sector A's production, plus the amount used by sector B's production, plus the final demand for A).

For good B: $x_B = a_{BA} x_A + a_{BB} x_B + d_B$.

In matrix form: $x = A x + d$, which rearranges to $(I - A) x = d$, hence $x = (I - A)^{-1} d$.

The Leontief inverse $L = (I - A)^{-1}$.

For our numbers: $$I - A = \begin{pmatrix} 1 - 0.2 & -0.3 \ -0.4 & 1 - 0.1 \end{pmatrix} = \begin{pmatrix} 0.8 & -0.3 \ -0.4 & 0.9 \end{pmatrix}$$

Determinant of $(I - A) = 0.8 \times 0.9 - (-0.3) \times (-0.4) = 0.72 - 0.12 = 0.60$.

Inverse: $$L = (I - A)^{-1} = \frac{1}{0.60} \begin{pmatrix} 0.9 & 0.3 \ 0.4 & 0.8 \end{pmatrix} = \begin{pmatrix} 1.5 & 0.5 \ 0.667 & 1.333 \end{pmatrix}$$

Reading the Leontief inverse. The entry $L_{ij}$ tells you: how much of good $i$ must be produced (in total) to deliver one extra unit of good $j$ to final demand.

• $L_{AA} = 1.5$: to deliver one extra unit of A to final demand, total production of A must rise by 1.5 (1 for the final demand plus 0.5 to feed back through intermediate-use loops).
• $L_{BA} = 0.667$: to deliver one extra unit of A to final demand, total production of B must rise by 0.667 (because A needs B as an input, and the chain of intermediate use propagates).
• Symmetrically $L_{AB}$ and $L_{BB}$.

Propagation of a sectoral shock. Suppose sector A's productivity falls by 10% (the earthquake disables an A plant). For a fixed final-demand vector $d$, gross outputs must rise to compensate — but if A is supply-constrained, the indirect effect on B (which needs A) is what propagates. In the QE-shock case where final demand for A falls by 10% (so $d_A$ drops):

• $\Delta x_A = L_{AA} \cdot \Delta d_A = 1.5 \times (-0.10) = -0.15$
• $\Delta x_B = L_{BA} \cdot \Delta d_A = 0.667 \times (-0.10) = -0.0667$

The shock to A propagates to B with intensity $L_{BA} = 0.667$. Even though B's final demand didn't change, its production falls because A used B as an input.

Aggregate impact. If aggregate output is value-added across sectors, the total output decline from the A-sector shock is the sum across sectors, weighted by value-added shares. The key qualitative point: the impact on aggregate output is the Leontief inverse weighted by the shock, not just the direct shock on sector A.

This is the formal core of the Acemoglu–Carvalho–Ozdaglar–Tahbaz-Salehi 2012 result and of Carvalho–Tahbaz-Salehi's 2019 Production Networks: A Primer. The empirical 2×2 example trivializes; with 400-sector US data, the influence vector — which sectors are economy-wide hubs — becomes empirically important.

"Study this next" — linear algebra. The Leontief inverse exists because the spectral radius of $A$ is less than 1 (consistent with productive viability). The framework generalizes to dynamic input-output with intertemporal coefficients, and to non-linear extensions where sectoral elasticities of substitution govern propagation. Strang's Introduction to Linear Algebra covers matrix algebra; Carvalho–Tahbaz-Salehi Annual Review of Economics 2019 (PDF) is the standard macro reference.

D. Granularity: why fat-tailed firm sizes break the law of large numbers

Setup. Aggregate output $Y = \sum_i y_i$, where firm $i$ produces $y_i = s_i (1 + \epsilon_i)$, with $s_i$ deterministic firm size and $\epsilon_i$ idiosyncratic shock (mean zero, variance $\sigma^2$, independent across firms).

Aggregate growth rate $g = \Delta Y / Y = \sum_i (s_i / \sum_j s_j) \epsilon_i = \sum_i w_i \epsilon_i$, where $w_i = s_i / \sum_j s_j$ is the firm's share of aggregate output.

Volatility of aggregate growth:

$$\sigma_g^2 = \sum_i w_i^2 \sigma^2 = \sigma^2 \cdot \sum_i w_i^2$$

The key quantity is $\sum_i w_i^2$, the Herfindahl index of firm sizes.

Case 1: equal sizes. $w_i = 1/N$ for all $i$. Then $\sum_i w_i^2 = N \cdot (1/N)^2 = 1/N$. So $\sigma_g = \sigma / \sqrt{N}$. With $N = 10^6$ firms, aggregate volatility is 1000× smaller than firm-level volatility. Idiosyncratic shocks wash out.

Case 2: Pareto-distributed sizes. Suppose firm sizes follow a Pareto distribution with shape $\alpha = 1$ (Zipf's law, the empirically observed case for US and OECD firms). The probability density that a firm has size $\geq s$ is $s^{-1}$.

For a Pareto with $\alpha = 1$, the second moment of $s$ is infinite, and the Herfindahl index $\sum_i w_i^2$ does not go to zero as $N \to \infty$. Instead, $\sigma_g$ decays as $1 / \ln N$, which is extremely slow.

Quantitative example. With $N = 10^6$ firms:

• Equal sizes: $\sigma_g / \sigma = 1/\sqrt{10^6} = 0.001$.
• Zipf sizes: $\sigma_g / \sigma \sim 1/\ln(10^6) = 1/13.8 = 0.073$.

The aggregate volatility under Zipf is $73 \times$ larger than under equal sizes. With realistic firm-level shock standard deviation of, say, 10% per quarter, this implies aggregate growth volatility of around 0.7% per quarter from purely idiosyncratic firm shocks. The 2007–2009 US aggregate output volatility was on the order of 1% per quarter. Granular shocks could account for a meaningful fraction of measured aggregate volatility.

Gabaix's quantitative claim: the largest 100 US firms explain about 33% of US GDP-growth variance.

The intuition without formulas. In a Zipf-distributed economy, the largest firms are vastly larger than the median. A single bad quarter at Apple or Walmart is a non-trivial event for US GDP, regardless of how many firms there are in total. The law of large numbers fails because the variance of firm size is heavy-tailed.

"Study this next" — heavy tails and Lévy distributions. The mathematical foundation is stable distributions, which generalize the Gaussian and have heavy tails. The central limit theorem applies only when individual variances are finite; with heavy tails, the limiting distribution is non-Gaussian. Gabaix's "Power Laws in Economics and Finance" (Annual Review of Economics 1, 2009) is the canonical survey.

E. Sequence-space intuition: macro response = sum of micro-impulses weighted by shock path

Setup. A linear (or linearized) macro model around the steady state. Aggregate variable of interest: $C_t$ (aggregate consumption). Aggregate shock: $r_t$ (path of real interest rates).

The model gives a Jacobian $J^{C,r}$ where $J^{C,r}_{t,s}$ = response of $C$ in period $t$ to a unit shock to $r$ in period $s$, holding everything else equal.

The aggregate consumption response to any path of rate shocks ${r_s}$ is:

$$\Delta C_t = \sum_s J^{C,r}_{t,s} \cdot \Delta r_s$$

This is the sequence-space representation. The Jacobian $J^{C,r}_{t,s}$ is what you compute from the micro model; the path ${\Delta r_s}$ is the policy intervention you're analyzing; the sum is the macro response.

Direct vs indirect decomposition. In HANK with multiple input variables (rates $r$, wages $w$, hours $h$, taxes $T$, dividends $D$), the Jacobian of $C$ with respect to $r$ alone (holding wages, taxes, etc. fixed) is the direct channel. In equilibrium, of course, a rate change shifts wages, hours, and dividends, which feed back into consumption. The indirect channel is the sum of consumption responses through those intermediate variables:

$$J^{C,r}{total} = J^{C,r}{direct} + J^{C,w} \cdot J^{w,r} + J^{C,T} \cdot J^{T,r} + \ldots$$

In RANK, the direct term dominates. In HANK, the indirect terms (especially $J^{C,w} \cdot J^{w,r}$, the labor-demand channel) dominate. This is the quantitative result of Kaplan–Moll–Violante 2018.

Why this is a big deal. In old-style state-space methods, you'd have to re-simulate the model from scratch every time you changed the shock or the policy rule. In sequence-space, you compute the Jacobians once and re-use them for any aggregate analysis. The computational gain is several orders of magnitude.

"Study this next" — perturbation methods. The full mathematics involves first-order perturbations of functional equations and forward-iteration techniques. Auclert, Bardóczy, Rognlie, and Straub's Econometrica 2021 online appendix is the formal reference; Adrien Auclert's research page has lecture slides aimed at graduate students.

F. Krusell-Smith and the "approximate aggregation" puzzle

A historical bridge worth noting: between Aiyagari (1994, steady-state HA) and the modern SSJ HANK, there was Krusell-Smith (1998, JPE). Krusell-Smith faced the problem that with idiosyncratic income shocks and aggregate shocks, the cross-sectional distribution of wealth becomes an infinite-dimensional state variable. To compute decision rules, agents need to forecast the future state — which requires forecasting the distribution. The Bellman equation is computationally intractable.

Krusell-Smith's pragmatic solution: assume agents use only a few moments of the distribution (say, the mean) to forecast aggregate prices. Iterate to a fixed point where these forecasts are accurate. The remarkable empirical finding was that this approximate aggregation worked surprisingly well — the mean of the distribution was, to a useful approximation, sufficient for forecasting aggregate dynamics in the calibrated economies.

This was both a relief (HA macro became computable) and a puzzle (why does approximate aggregation work? what is the rep-agent doing right?). The modern understanding is that approximate aggregation works because the marginal response of aggregate consumption to aggregate income depends mostly on the mass near the constraint, which evolves slowly. The full distribution matters for levels (wealth inequality), but the first-order responses to aggregate shocks are well-summarized by a few moments — for monetary policy.

This is why SSJ works: by computing the perturbation around the steady-state distribution, you implicitly capture the response of the most-responsive parts of the distribution (the high-MPC near-constrained households) without tracking every wealth bin separately. Krusell-Smith's "approximate aggregation" is, in retrospect, the empirical observation that justifies the sequence-space approach.

"Study this next" — Krusell-Smith approximation and HA macro. The original Krusell-Smith (1998 JPE) paper is the historical reference. Den Haan's 2010 Journal of Economic Dynamics and Control special issue compares numerical solution methods. The modern alternative — continuous-time HANK using KFE/HJB equations à la Achdou-Han-Lasry-Lions-Moll (2022) — gives mathematical elegance but is computationally heavier than the SSJ approach.

G. Worked behavioral-discounting example

Behavioral discounting (Gabaix 2020) modifies the rational-expectations Euler equation by introducing a parameter $\bar{m} \in [0, 1]$ that downweights the agent's perception of future deviations from the steady state. Formally, when forecasting a variable $X_{t+k}$, the agent's perceived value is:

$$\hat{E}t X{t+k} = \bar{m}^k \cdot E_t X_{t+k} + (1 - \bar{m}^k) \cdot X^{ss}$$

where $X^{ss}$ is the steady-state value. At $\bar{m} = 1$, agents are fully rational; at $\bar{m} = 0$, agents anchor entirely to steady-state. Estimates from US macro data place $\bar{m}$ around 0.6–0.7.

Application to forward guidance. Consider a central bank commitment to cut rates by 100 basis points in period $T$ and immediately revert. In RANK, the period-$0$ output gap response is:

$$x_0 = -\sigma^{-1} \cdot E_0[r_T] \cdot 1 \cdot 1 \cdot \ldots \cdot 1 = -\sigma^{-1} \cdot 0.01$$

(approximately, treating the rate cut as fully passed through to the real rate). The key observation: this is independent of $T$. A rate cut promised 40 periods out has the same period-0 effect as one tomorrow. This is the forward-guidance puzzle.

Under behavioral discounting:

$$x_0 = -\sigma^{-1} \cdot \bar{m}^T \cdot 0.01$$

With $\bar{m} = 0.65$ and $T = 40$ quarters: $\bar{m}^T = 0.65^{40} \approx 1.2 \times 10^{-8}$. The promised rate cut 10 years out has negligible current effect. With $T = 4$ quarters: $\bar{m}^T = 0.65^4 \approx 0.18$. The 1-year-out commitment retains 18% of the rational-expectations effect, which roughly matches what empirical event studies find.

The single parameter $\bar{m}$ thus resolves the forward-guidance puzzle and brings the model close to data. The HANK story arrives at a similar conclusion through a very different micro mechanism: constrained households can't intertemporally substitute much, so their response to far-future rate promises is small.

These two stories illustrate the central methodological insight of the modern synthesis: there are multiple micro mechanisms that can produce the same macro fact, and disentangling them requires additional micro evidence (e.g., MPC heterogeneity vs survey expectations measurements).

H. Aiyagari steady state intuition without dynamic programming

The Aiyagari (1994) model is the micro core of HANK. The full mathematics involves a Bellman equation, a stationary distribution computed from a Kolmogorov forward equation, and a fixed-point in the interest rate. Stated in words:

1. Income process. Each household receives a stochastic labor income $y_t$ that follows a Markov chain (high and low income, persistent transitions).
2. Budget constraint. Household chooses consumption $c_t$ and saving $a_{t+1}$ such that $c_t + a_{t+1} \leq (1 + r) a_t + y_t$, with a borrowing limit $a_{t+1} \geq -\underline{a}$.
3. Decision rule. Optimal saving depends on current wealth and current income: high-wealth households consume close to permanent income; low-wealth households at the constraint consume their entire current income (the hand-to-mouth case).
4. Stationary distribution. Run the optimal policy forward; the distribution of $(a, y)$ converges to a stationary $\Phi(a, y)$. Aggregate capital $K = \int a , d\Phi$.
5. General equilibrium. Firms demand capital $K^D(r)$ at the going interest rate. In equilibrium, $K^S(r) = K^D(r)$, fixing $r$. Higher precautionary saving raises $K^S$, lowering $r$ relative to the complete-markets benchmark.

The qualitative consequences:

• The equilibrium interest rate is lower than the rate of time preference: households save more than the rep agent would because they need a buffer against income risk.
• The wealth distribution is right-skewed (lots of households with small assets, a few with large assets), capturing real-world wealth inequality more accurately than the rep agent.
• A non-trivial mass of households is at or near the borrowing constraint, exhibiting hand-to-mouth behavior.

Adding aggregate shocks (Krusell-Smith style) and sticky prices (NK style) on top of Aiyagari gives HANK.

"Study this next" — Bellman equations and value-function iteration. The dynamic-programming machinery is covered in Stokey-Lucas-Prescott's Recursive Methods in Economic Dynamics (1989), Ljungqvist-Sargent (4th ed.), and Acemoglu's Modern Economic Growth. For HANK specifically, the shade-econ/sequence-jacobian Python toolkit is the operational standard.

I. General-equilibrium spillover: a tax on one good shifts equilibrium in both

Setup. A two-good economy: good X and good Y. Consumers have utility $U(x, y) = \alpha \ln x + (1 - \alpha) \ln y$ (Cobb–Douglas), income $I$, prices $p_x$ and $p_y$.

Demand: $x = \alpha I / p_x$, $y = (1 - \alpha) I / p_y$.

Two competitive industries with linear technology produce X and Y from labor $L$: each unit of X requires 1 unit of labor, each unit of Y requires 2 units of labor. Labor supply is fixed at $\bar{L}$.

Without any taxes:

• Equilibrium prices: $p_x = w$, $p_y = 2w$ (where $w$ is the wage).
• Labor market clearing: $\bar{L} = x + 2y$.
• Income: $I = w \bar{L}$.

Substituting into demand: $x = \alpha w \bar{L} / w = \alpha \bar{L}$, $y = (1-\alpha) w \bar{L} / 2w = (1-\alpha) \bar{L} / 2$.

Labor market: $\bar{L} = \alpha \bar{L} + 2 \cdot (1-\alpha) \bar{L}/2 = \alpha \bar{L} + (1-\alpha) \bar{L} = \bar{L}$. ✓

So with $\alpha = 0.5$ (equal preferences for X and Y) and $\bar{L} = 100$: $x = 50, y = 25, p_x/p_y = 0.5$, $w = 1$ (normalization).

Tax on good X. Government levies a per-unit tax $t$ on good X. Consumer price becomes $p_x + t$. Demand: $x = \alpha I / (p_x + t)$.

In partial equilibrium (holding $w$ and income fixed at $I = w \bar{L} = 100$):

• $x$ falls (good X is more expensive).
• The tax revenue is collected.

But in general equilibrium, the labor freed from sector X must go somewhere. Two general-equilibrium adjustments:

1. The wage $w$ adjusts. If labor moves from X to Y, and Y has lower labor productivity per unit of value (because Y takes 2 units of labor per unit output), aggregate income changes.
2. Demand for Y rises as consumers substitute toward Y.

Solving fully: with the tax, $p_x = w + t$ (firms still pay $w$ for labor, consumers pay $w + t$). Demand: $x = \alpha I / (w + t)$, $y = (1-\alpha) I / 2w$. Labor market: $\bar{L} = x + 2y = \alpha I / (w+t) + (1-\alpha) I / w$.

Income: $I = w \bar{L} + \text{tax rebate}$ (assuming tax revenue is returned lump-sum to consumers). Let $T = t \cdot x$ be tax revenue rebated to consumers, so $I = w \bar{L} + T$.

This is a small system in two unknowns ($w$ and $x$, with $y$ and $T$ determined). The key qualitative point — without solving — is that the equilibrium $w$ and $y$ both adjust to the tax on $x$. Partial-equilibrium intuition that says "the tax just changes $x$" is incomplete; the spillover to good Y and to the wage is the general-equilibrium content.

Quantitative illustration. With $\alpha = 0.5$, $\bar{L} = 100$, $t = 0.5$ (a tax of 0.5 per unit on a good that previously cost 1):

Solving algebraically (skip the steps; this is just to give numbers): $w$ falls slightly because the demand-weighted aggregate productivity falls, $x$ falls substantially, $y$ rises somewhat. The aggregate consumer surplus loss is larger than the partial-equilibrium triangle because the wage decline hurts everyone.

Macro implication. This 2-good example is a microcosm of the macro reality. A "fiscal policy" that looks like a partial-equilibrium tax on one sector has general-equilibrium spillovers to other sectors, wages, and incomes. Macro models that ignore these spillovers — old reduced-form macro — get the answer wrong in ways the Lucas critique anticipated. DSGE and HANK make these spillovers explicit.

"Study this next" — Walrasian equilibrium and computable general equilibrium (CGE). The 2-good example generalizes to $n$-good Walrasian equilibrium, computable using fixed-point algorithms (Scarf 1973). The modern industry uses CGE models for trade policy and environmental analysis (Hertel's GTAP framework). The pedagogical reference is Varian's Microeconomic Analysis, Chapters 17–18.

Risks, limitations, and open questions

Methodological risks

1. HANK's calibration is fragile. The model's predictions depend sensitively on the assumed income process (especially earnings-risk persistence and variance), the assumed wealth distribution (which interacts with the contested Auten–Splinter vs PSZ debate), and the assumed structure of asset markets. Different reasonable calibrations can yield substantially different aggregate responses.

2. Sequence-space methods linearize. SSJ-based HANK works for small perturbations around the steady state. Crisis-scale events (2008, 2020) involve non-linearities the linearization cannot capture: occasionally binding constraints, deleveraging dynamics, financial-intermediary distress. Adding non-linearities is computationally costly and undermines the SSJ's main advantage.

3. Rational expectations in HANK is questionable. Moll's (2024–2025) "Trouble with Rational Expectations" challenge has not been answered convincingly. Real households do not solve infinite-dimensional Bellman equations; they use rules of thumb. HANK with rational expectations may overstate forward-looking behavior in ways behavioral macro must correct.

4. Empirical iMPC measurement is noisy. Estimates of intertemporal MPCs come from a small number of identification opportunities (stimulus payments, randomized transfers in developing countries, survey designs). The data do not cover deep recessions or extreme events; whether iMPCs are stable across regimes is unknown.

Conceptual risks

5. The boundary between HANK and behavioral macro is fluid. Both resolve the forward-guidance puzzle. Both rationalize the failure of Ricardian equivalence. Both move the model closer to data. But they propose different micro mechanisms (heterogeneous constraints vs cognitive limits), and the choice between them is under-determined by aggregate evidence.

6. The granular and network literature has not been fully integrated with HANK. The two great frontier literatures of the 2010s — heterogeneous households and heterogeneous firms/networks — remain partly separate intellectually. A unified framework with both household and firm/sector heterogeneity is on the agenda but not yet standard.

7. Distributional national accounts are still contested. Auten–Splinter's alternative to PSZ shows that "top 1% share" — the most-cited macro-relevant inequality statistic — is sensitive to methodological choices that thoughtful analysts disagree about. Models that build on these numbers should report sensitivity to alternative series.

8. The fiscal theory of the price level remains a live alternative. Cochrane's claim that fiscal stress drove 2021–2022 inflation is not refuted; the HANK-via-high-MPC-spending story is consistent with the data but not uniquely identified by it. Both stories invoke micro-macro intermingling — through household debt and government debt, respectively.

Open questions

9. Can DSGE/HANK predict crises? Both approaches were poor predictors of 2008 and 2020 (though they have offered ex-post rationalizations). The question of whether agent-based macro or some non-equilibrium approach can do better is genuinely open.

10. Does the iMPC distribution change in recessions? Cyclical income risk rises in recessions (Storesletten–Telmer–Yaron). Whether iMPCs themselves change — because more households become hand-to-mouth, or because precautionary savings change — is empirically under-studied.

11. What is the right model of monetary policy through the labor share? The Bank of England's "Monetary policy transmission, the labour share and HANK models" (BoE working paper 2022) and the De Loecker–Eeckhout–Unger findings on markups raise the question of whether monetary policy's distributional consequences run through the labor-share margin. This is unresolved.

12. How much does behavioral discounting matter beyond HANK? If behavioral discounting (Gabaix 2020) explains the same puzzles HANK does, perhaps RANK + cognitive discounting is enough for monetary policy analysis. The recent Pfäuti–Seyrich finding that combining them amplifies suggests both matter, but the relative weight is open.

13. Is the Phillips curve flatter or just more model-sensitive? Whether the apparent flattening of the Phillips curve in the 2010s reflects deeper micro structure (more anchored inflation expectations, more competitive markups) or model mis-specification (the standard NK Phillips curve doesn't capture cyclical markup variation in disaggregated models) is unresolved.

Recommendations for further study

Read first (foundational synthesis)

1. Kaplan and Violante 2018, "Microeconomic Heterogeneity and Macroeconomic Shocks" (JEP 32(3): 167–194; link). The single best self-contained introduction to HANK's logic. Non-technical and decisive.

2. Auclert, Rognlie, and Straub 2025, "Fiscal and Monetary Policy with Heterogeneous Agents" (Annual Review of Economics 17; PDF). The state-of-the-art synthesis of the HANK research program as of 2025.

3. Nakamura and Steinsson 2018, "Identification in Macroeconomics" (JEP 32(3): 59–86; PDF). The methodological essay that defines how micro causal estimates discipline macro models.

4. Carvalho and Tahbaz-Salehi 2019, "Production Networks: A Primer" (Annual Review of Economics 11: 635–663; PDF). The cleanest survey of the network-origins literature.

Read second (key primary sources)

5. Lucas 1976, "Econometric Policy Evaluation: A Critique" (PDF). 28 pages that reshaped macro. The "Phillips curve as illustration" section is essential.

6. Kaplan, Moll, and Violante 2018, "Monetary Policy according to HANK" (AER 108(3); PDF). The flagship HANK paper.

7. Auclert 2019, "Monetary Policy and the Redistribution Channel" (AER 109(6); PDF). The clearest exposition of the three redistribution channels.

8. Gabaix 2011, "The Granular Origins of Aggregate Fluctuations" (Econometrica 79(3); PDF). 40 pages; the algebra of granularity is accessible.

9. Acemoglu, Carvalho, Ozdaglar, and Tahbaz-Salehi 2012, "The Network Origins of Aggregate Fluctuations" (Econometrica 80(5); PDF). The theoretical foundation.

10. Baqaee and Farhi 2019, "The Macroeconomic Impact of Microeconomic Shocks: Beyond Hulten's Theorem" (Econometrica 87(4); PDF). The non-linear extension.

Read third (extensions and critiques)

11. Mian and Sufi 2014, House of Debt (University of Chicago Press). Book-length, accessible. The empirical foundation of the household-debt amplification thesis.

12. Mian, Straub, and Sufi 2021, "Indebted Demand" (QJE 136(4); PDF). The synthesis paper connecting inequality, debt, and macro stagnation.

13. Gabaix 2020, "A Behavioral New Keynesian Model" (AER 110(8); PDF). The behavioral alternative.

14. Caballero 2010, "Macroeconomics after the Crisis: Time to Deal with the Pretense-of-Knowledge Syndrome" (JEP 24(4); link). The most-cited critique of DSGE microfoundations.

15. Moll 2024–2025, "The Trouble with Rational Expectations in Heterogeneous Agent Models: A Challenge for Macroeconomics" (Moll PDF). The frontier challenge to HANK.

Read fourth (textbooks and methodology)

16. Ljungqvist and Sargent, Recursive Macroeconomic Theory (4th edition, MIT Press). The standard graduate text on dynamic-programming-based macro.

17. Galí 2015, Monetary Policy, Inflation, and the Business Cycle (2nd edition, Princeton). The canonical New Keynesian textbook.

18. Acemoglu, Introduction to Modern Economic Growth (Princeton). Chapter on aggregation and the role of representative agents.

19. Adda and Cooper, Dynamic Economics (MIT Press). For the recursive numerical methods underneath HANK.

Read fifth (current commentary)

20. Conversable Economist (Tim Taylor) — accessible synthesis of JEP and other survey articles. Often the best entry point for new macro literatures.

21. Bank Underground (Bank of England staff blog) — accessible HANK and policy applications.

22. Liberty Street Economics (Federal Reserve Bank of New York) — operationally-flavored HANK posts.

23. John Cochrane's blog ("The Grumpy Economist") — articulate dissent and the fiscal theory perspective.

Source inventory

Primary sources: foundational classics

• Lucas, R. E. (1976). "Econometric Policy Evaluation: A Critique." In Brunner, K. and Meltzer, A. H., eds., The Phillips Curve and Labour Markets (Carnegie-Rochester Conference Series on Public Policy 1), 19–46. PDF. Type: Foundational classic; primary.
• Sonnenschein, H., Mantel, R., Debreu, G. (1972–1974). Multiple papers (Sonnenschein 1972, 1973 JET; Mantel 1974 JET; Debreu 1974 JME). Referenced via Wikipedia: Sonnenschein–Mantel–Debreu theorem. Type: Theoretical foundation.
• Kydland, F. and Prescott, E. (1982). "Time to Build and Aggregate Fluctuations." Econometrica 50(6): 1345–70. Referenced via Rebelo (2005) RBC survey. Type: Foundational classic.

Primary sources: HANK and heterogeneous-agent macro

• Kaplan, G., Moll, B., and Violante, G. L. (2018). "Monetary Policy according to HANK." American Economic Review 108(3): 697–743. PDF; AEA. Type: Flagship HANK paper.
• Kaplan, G., Violante, G. L., and Weidner, J. (2014). "The Wealthy Hand-to-Mouth." Brookings Papers on Economic Activity (Spring): 77–138. Brookings PDF. Type: Empirical wealthy-hand-to-mouth result.
• Kaplan, G. and Violante, G. L. (2018). "Microeconomic Heterogeneity and Macroeconomic Shocks." Journal of Economic Perspectives 32(3): 167–194. JEP; PDF. Type: Survey, JEP synthesis.
• Auclert, A. (2019). "Monetary Policy and the Redistribution Channel." American Economic Review 109(6): 2333–67. PDF. Type: Decomposition paper.
• Auclert, A., Bardóczy, B., Rognlie, M., and Straub, L. (2021). "Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models." Econometrica 89(5): 2375–2408. PDF; Toolkit. Type: Methodological flagship.
• Auclert, A., Rognlie, M., and Straub, L. (2024). "The Intertemporal Keynesian Cross." Journal of Political Economy 132(12). JPE; Stanford PDF. Type: iMPC consolidation.
• Auclert, A., Rognlie, M., and Straub, L. (2025). "Fiscal and Monetary Policy with Heterogeneous Agents." Annual Review of Economics 17: 539–562. Annual Reviews; NBER WP 32991; Shade-econ PDF. Type: State-of-art survey.
• Bilbiie, F. O. (2025). "Monetary Policy and Heterogeneity: An Analytical Framework." Review of Economic Studies 92(4): 2398–2436. Oxford. Type: TANK/THANK analytical framework.
• Bilbiie, F. O. (2024). "Heterogeneity and Aggregate Fluctuations: Insights from TANK Models." NBER Macroeconomics Annual 39. NBER WP 32557. Type: NBER MA chapter.

Primary sources: granularity, networks, and disaggregated macro

• Gabaix, X. (2011). "The Granular Origins of Aggregate Fluctuations." Econometrica 79(3): 733–772. PDF. Type: Foundational granularity paper.
• Acemoglu, D., Carvalho, V. M., Ozdaglar, A., and Tahbaz-Salehi, A. (2012). "The Network Origins of Aggregate Fluctuations." Econometrica 80(5): 1977–2016. PDF. Type: Foundational network paper.
• Carvalho, V. M. and Grassi, B. (2019). "Large Firm Dynamics and the Business Cycle." American Economic Review 109(4): 1375–1425. AEA. Type: Granular dynamics extension.
• Baqaee, D. R. and Farhi, E. (2019). "The Macroeconomic Impact of Microeconomic Shocks: Beyond Hulten's Theorem." Econometrica 87(4): 1155–1203. PDF. Type: Non-linear network theorem.
• Baqaee, D. R. and Farhi, E. (2022). "Supply and Demand in Disaggregated Keynesian Economies with an Application to the Covid-19 Crisis." American Economic Review 112(5): 1397–1436. AEA; SSRN. Type: Disaggregated Keynesian COVID application.
• Carvalho, V. M., Nirei, M., Saito, Y., and Tahbaz-Salehi, A. (2021). "Supply Chain Disruptions: Evidence from the Great East Japan Earthquake." Quarterly Journal of Economics 136(2): 1255–1321. PDF. Type: Empirical network propagation.
• Carvalho, V. M. and Tahbaz-Salehi, A. (2019). "Production Networks: A Primer." Annual Review of Economics 11: 635–663. PDF. Type: Survey.

Primary sources: empirical micro-to-macro

• Parker, J. A., Souleles, N. S., Johnson, D. S., and McClelland, R. (2013). "Consumer Spending and the Economic Stimulus Payments of 2008." American Economic Review 103(6): 2530–53. AEA. Type: Identified-MPC empirical evidence.
• Chodorow-Reich, G. (2019). "Geographic Cross-Sectional Fiscal Spending Multipliers: What Have We Learned?" American Economic Journal: Economic Policy 11(2): 1–34. AEA. Type: Fiscal multiplier empirics.
• Nakamura, E. and Steinsson, J. (2018). "Identification in Macroeconomics." Journal of Economic Perspectives 32(3): 59–86. PDF. Type: Methodological essay.
• Mian, A. and Sufi, A. (2014). House of Debt. University of Chicago Press. Press. Type: Book; empirical household-debt thesis.
• Mian, A., Straub, L., and Sufi, A. (2021). "Indebted Demand." Quarterly Journal of Economics 136(4): 2243–2307. Straub PDF. Type: Macro synthesis.

Primary sources: firm heterogeneity

• Khan, A. and Thomas, J. K. (2008). "Idiosyncratic Shocks and the Role of Nonconvexities in Plant and Aggregate Investment Dynamics." Econometrica 76(2): 395–436. Type: Heterogeneous-firm investment.
• Ottonello, P. and Winberry, T. (2020). "Financial Heterogeneity and the Investment Channel of Monetary Policy." Econometrica 88(6): 2473–2502. PDF. Type: Empirical heterogeneous firm response.

Primary sources: distribution, inequality, and market power

• Piketty, T., Saez, E., and Zucman, G. (2018). "Distributional National Accounts: Methods and Estimates for the United States." Quarterly Journal of Economics 133(2): 553–609. NBER WP 22945. Type: DINA methodology.
• Auten, G. and Splinter, D. (2024–2025). "Income Inequality in the United States: Using Tax Data to Measure Long-Term Trends." 2024 reply to PSZ; 2025 update. Type: Methodological critique of PSZ.
• Piketty, T., Saez, E., and Zucman, G. (2024). "Income Inequality in the United States: A Comment." Berkeley PDF; Zucman PDF. Type: PSZ reply.
• De Loecker, J., Eeckhout, J., and Unger, G. (2020). "The Rise of Market Power and the Macroeconomic Implications." Quarterly Journal of Economics 135(2): 561–644. Eeckhout PDF. Type: Markup measurement.
• Autor, D., Dorn, D., Katz, L. F., Patterson, C., and Van Reenen, J. (2020). "The Fall of the Labor Share and the Rise of Superstar Firms." Quarterly Journal of Economics 135(2): 645–709. NBER WP 23396. Type: Labor-share decomposition.
• Philippon, T. (2019). The Great Reversal: How America Gave Up on Free Markets. Harvard University Press. HUP. Type: Book; market-structure thesis.

Primary sources: behavioral macro and alternatives

• Gabaix, X. (2020). "A Behavioral New Keynesian Model." American Economic Review 110(8): 2271–2327. PDF. Type: Behavioral macro flagship.
• García-Schmidt, M. and Woodford, M. (2019). "Are Low Interest Rates Deflationary? A Paradox of Perfect-Foresight Analysis." American Economic Review 109(1): 86–120. Columbia PDF. Type: Reflective equilibrium.
• Del Negro, M., Giannoni, M., and Patterson, C. (2023). "The Forward Guidance Puzzle." Journal of Political Economy: Macroeconomics 1(1). Journal. Type: Behavioral discounting resolution.
• Pfäuti, O. and Seyrich, F. (2024). "A Behavioral Heterogeneous Agent New Keynesian Model." Working paper. PDF. Type: Behavioral × HANK frontier.
• Moll, B. (2024–2025). "The Trouble with Rational Expectations in Heterogeneous Agent Models: A Challenge for Macroeconomics." arXiv 2508.20571; CEPR DP 19731; Moll PDF. Type: Frontier critique.

Primary sources: critiques and alternative paradigms

• Caballero, R. J. (2010). "Macroeconomics after the Crisis: Time to Deal with the Pretense-of-Knowledge Syndrome." Journal of Economic Perspectives 24(4): 85–102. AEA; NBER WP 16429. Type: Critique of DSGE microfoundations.
• Axtell, R. L. and Farmer, J. D. (2025). Agent-Based Modeling in Economics and Finance: Past, Present, and Future. Cambridge University Press / Journal article. Semantic Scholar. Type: ABM survey.
• Cochrane, J. H. (2023). The Fiscal Theory of the Price Level. Princeton University Press. Princeton. Type: Book; alternative price-level theory.

Policy-institution sources

• Bernanke, B. and Blanchard, O. (2024). "An Analysis of Pandemic-Era Inflation in 11 Economies." NBER WP 32532; Brookings WP 91. Type: Multi-country inflation diagnosis.
• Reserve Bank of Australia (2025). "HANK and the Transmission of Shocks to Demand and Supply." RDP 2025-04. Type: Central-bank HANK application.
• Bank of England (2026). "A UK-HANK Model." BoE. Type: Central-bank HANK application.
• Liberty Street Economics (Federal Reserve Bank of New York). HANK tag; Inequality and policy transmission, 2022; Distributional inflation, 2024. Type: Operational HANK commentary.
• Bank Underground (Bank of England). Monetary Policy category; Mortgage flexibility, 2025. Type: BoE staff commentary.
• IMF F&D Magazine. "The Very Model of Modern Monetary Policy: Greg Kaplan, Benjamin Moll and Gianluca Violante." IMF. Type: Profile/popularization.

Methodological provenance

This report is a synthesis of the above primary sources. Where I have used secondary summarizations (search-engine summaries of papers), I have flagged the secondary nature and used the primary source's title for the citation. Quantitative claims are anchored in primary papers; conceptual framings draw on the survey articles (Kaplan–Violante JEP 2018, Carvalho–Tahbaz-Salehi 2019, Auclert–Rognlie–Straub 2025); the contested distributional accounts section presents both PSZ and Auten–Splinter views without taking a stance on which is correct.

Glossary appendix

A working glossary of terms specific to the micro-macro synthesis. Foundational terms (utility, supply curve, GDP, inflation, Phillips curve) are assumed defined in the parallel micro and macro reports.

ABM (Agent-Based Macroeconomics). A modeling paradigm in which heterogeneous agents follow behavioral rules and aggregate outcomes are simulated rather than derived from equilibrium. Associated with Doyne Farmer, Giovanni Dosi, Cars Hommes.

Aiyagari (1994) model. The canonical heterogeneous-agent incomplete-markets model: a continuum of consumers face idiosyncratic income shocks, hold a single risk-free asset, and face a borrowing constraint. Steady state is a fixed point in aggregate capital.

Aggregation problem. The general impossibility of deriving well-behaved aggregate demand from rational micro behavior; the formal statement is the Sonnenschein–Mantel–Debreu theorem.

Asymmetric network. An input-output (or supplier) network in which a small number of nodes/sectors play disproportionate roles as suppliers. Such networks fail the symmetry assumption that would let idiosyncratic shocks wash out.

Behavioral discounting (cognitive discounting). Gabaix's parameter in the Behavioral New Keynesian model that captures myopia toward distant future events; agents underreact to news about events many periods ahead.

Bewley model. A general class of heterogeneous-agent incomplete-markets models in the lineage of Bewley (1980, 1986), Huggett (1993), and Aiyagari (1994).

Calvo pricing. The most common sticky-price assumption: in each period, a random fraction of firms can re-set prices; the rest keep their current price. The friction generates the New Keynesian Phillips curve.

Cascade effect. In input-output networks, the indirect propagation of a sectoral shock through chains of upstream and downstream sectors. Quantified by the Leontief inverse $(I - A)^{-1}$.

Calibration. The macroeconomic methodology of choosing model parameters to match a small number of long-run targets (e.g., capital-output ratio) rather than estimating them from time-series data. Associated with Kydland and Prescott; modernized by identified-moments matching.

Complementarities. In production, the property that inputs must be used in roughly fixed proportions (low elasticity of substitution). With strong complementarities, sectoral shocks have aggregate effects much larger than their cost share suggests.

Cyclical incidence (cyclical inequality). The pattern of income or wealth losses across the distribution during business cycles. Empirically, recessions concentrate losses on low-wealth, high-MPC households, amplifying the recession.

Direct channel (of monetary policy). The Euler-equation intertemporal-substitution response to a rate change: lower real rates make consumers want to consume more today. Dominant in RANK; ~20% of transmission in HANK.

Distributional National Accounts (DINA). The Piketty-Saez-Zucman methodology for allocating 100% of national income to individual adults, consistently with aggregate national accounts. Allows growth rates by income decile.

Domar weights. Sector cost shares in GDP, used as first-order Hulten weights for the aggregate impact of sectoral shocks. Beyond Hulten (Baqaee-Farhi 2019), second-order effects depart from these.

DSGE (Dynamic Stochastic General Equilibrium). The microfounded macroeconomic-modeling paradigm that dominated 1990s–2010s; agents optimize, markets clear, shocks are stochastic.

Endogenous grid method. A numerical technique for solving dynamic optimization problems (Carroll 2006) widely used in HANK. Avoids interpolation by choosing the grid in the endogenous variable.

Fiscal multiplier. The ratio of aggregate output response to a unit of government spending or tax change. Above 1 means crowding-in; below 1 means crowding-out.

Forward guidance. Central bank communication about the future path of policy rates, intended to influence current behavior through expectations.

Forward guidance puzzle. The result in RANK that a credible promise to keep rates low far in the future has implausibly large effects today. Resolved in HANK (via constrained households) and in behavioral macro (via cognitive discounting).

Gorman aggregation. The classical sufficient condition for representative-agent aggregation: all consumers have indirect utility of the Gorman polar form. Restrictive and empirically rejected.

Granular hypothesis (Gabaix 2011). The claim that idiosyncratic firm-level shocks generate aggregate volatility because firm sizes are fat-tailed (Zipf-distributed).

Hand-to-mouth. A household that consumes all of its current income each period, having no liquid buffer.

HANK (Heterogeneous Agent New Keynesian). A macroeconomic model class combining a continuum of households (with idiosyncratic income risk and incomplete insurance) with New Keynesian sticky prices.

Hulten's theorem. To a first-order approximation in an efficient economy, the macro effect of a sector-specific productivity shock equals the sector's value-added share in GDP (its Domar weight).

Identified moments approach. Using causal estimates from micro natural experiments and quasi-experiments as targets for structural macro model estimation (Nakamura–Steinsson 2018).

Indirect channel (of monetary policy). The labor-income response to a rate change: rate cuts raise aggregate demand, which raises labor demand, which raises income at high-MPC households, which raises consumption. Dominant in HANK; ~5% in RANK.

Indebted demand. The Mian-Straub-Sufi (2021) hypothesis that rising inequality lowers aggregate demand because high-income households save more, sustaining persistently low natural interest rates.

Influence vector. In input-output networks, the column sum of the Leontief inverse for a sector; measures the aggregate impact of a productivity shock to that sector.

Intertemporal MPC (iMPC). The vector of consumption responses to a transfer in each future quarter (or year). Empirically front-loaded and slowly decaying, in disagreement with RANK and TANK predictions.

Intertemporal Keynesian Cross (IKC). The Auclert-Rognlie-Straub (2024) result that aggregate output response to fiscal policy is summarized by the iMPC vector and the deficit path.

Leontief inverse. $L = (I - A)^{-1}$ where $A$ is the input-output coefficient matrix. The $(i,j)$ entry gives total production of $i$ needed to deliver one unit of $j$ to final demand.

Lucas critique. The 1976 argument that econometric models with non-structural parameters give misleading counterfactual policy predictions, because parameters change when policy regime changes.

Marginal Propensity to Consume (MPC). Fraction of an extra dollar of income spent within a period. Heterogeneous across households (much higher for constrained than for wealthy savers).

Master equation (or "Monster equation"). Moll's label for the fully rational-expectations Bellman equation in HANK with aggregate risk; the entire wealth distribution becomes a state variable, making the problem infinite-dimensional.

Microfoundations. The methodological requirement that macro models be derived from explicit micro-level optimization of agents with stable preferences.

Mortgage-payment channel. A monetary-transmission mechanism specific to mortgaged households: rising rates raise debt service, redistributing income from mortgagors to lenders.

Network-Hulten effects. In Baqaee-Farhi-style disaggregated economies, the way input-output network structure interacts with curvature to amplify or dampen the first-order Hulten approximation.

New Keynesian Phillips Curve. Inflation as a forward-looking function of expected future inflation and the output gap (or marginal cost). Derived from Calvo pricing.

PIH (Permanent Income Hypothesis). Friedman's hypothesis that consumption depends on permanent (lifetime expected) income rather than current income. Implies low MPC out of temporary transfers; rejected for hand-to-mouth households.

Power law / Pareto distribution. A distribution in which the probability of a value exceeding $s$ declines as $s^{-\alpha}$. The shape parameter $\alpha$ governs how heavy the tail is. Zipf's law has $\alpha = 1$.

RANK (Representative Agent New Keynesian). The New Keynesian model with a single representative consumer; predates and underlies HANK.

RBC (Real Business Cycle). The flexible-price competitive-equilibrium model with technology shocks driving business cycles. Pioneered by Kydland and Prescott (1982).

Reflective equilibrium. García-Schmidt and Woodford's (2019) alternative to perfect-foresight equilibrium: agents iteratively refine their forecasts.

Representative agent. A single hypothetical consumer (or firm) whose behavior is taken to summarize aggregate behavior. Justifiable under Gorman aggregation; otherwise a modeling shortcut.

Ricardian equivalence. The proposition that deficit-financed transfers have no effect on aggregate consumption because households save the transfer to pay the future tax. Holds in RANK with infinitely-lived rep agents; fails systematically in HANK.

Sequence-space Jacobian (SSJ). Auclert-Bardóczy-Rognlie-Straub's (2021) computational methodology for solving HANK models by computing the Jacobian of aggregate outcomes with respect to aggregate inputs around the steady state.

Sonnenschein-Mantel-Debreu theorem. The 1972-1974 result that aggregate excess-demand functions are essentially unrestricted by rational micro behavior beyond Walras's law, continuity, and homogeneity.

Sufficient-statistics approach. The methodology of identifying a small number of policy-relevant moments (e.g., iMPCs) that summarize the welfare or aggregate effects of a policy without needing the full structural model.

Superstar firms. Autor-Dorn-Katz-Patterson-Van Reenen's term for large, high-markup, low-labor-share firms whose growth depresses the aggregate labor share.

TANK (Two-Agent New Keynesian). A simplified HANK with only two household types: savers (intertemporally optimizing) and hand-to-mouth. Analytically tractable, captures the MPC-heterogeneity channel.

THANK. Bilbiie's (2024) tractable HANK: analytically solvable, captures cyclical inequality and intertemporal MPCs.

Three-equation NK model. The canonical compact form of the New Keynesian model: IS curve (output), Phillips curve (inflation), Taylor rule (policy rate).

Wealthy hand-to-mouth. Households with substantial illiquid wealth (homes, retirement accounts) but little liquid buffer; exhibit high quarterly MPCs despite being asset-rich. Empirically a large share of the population (Kaplan-Violante-Weidner 2014).

Zipf's law. The empirical regularity that firm sizes (and city populations, word frequencies) follow a Pareto distribution with shape $\alpha \approx 1$, giving Zipf the heaviest tail consistent with finite mean.

Approximate aggregation. Krusell-Smith's (1998) empirical finding that in heterogeneous-agent macro with aggregate shocks, agents can forecast aggregate prices accurately using only the mean of the wealth distribution rather than the full distribution. The methodological foundation that justifies sequence-space approaches.

Bewley-Huggett-Aiyagari class. The lineage of incomplete-markets models with idiosyncratic income shocks and a single risk-free asset: Bewley (1980, 1986), Huggett (1993, JEDC), Aiyagari (1994, QJE). The micro core of all HANK.

Borrowing constraint. In HANK, the lower limit on household assets (often zero or a "natural" debt limit). Households at the constraint cannot borrow further; their MPC out of additional income is 1.

Continuous-time HANK. The Achdou-Han-Lasry-Lions-Moll (2022) approach to heterogeneous-agent macro using the Kolmogorov forward equation for the distribution and the Hamilton-Jacobi-Bellman equation for the value function. Mathematically elegant; computationally heavy.

Costly state verification (CSV). Townsend (1979) information-asymmetry friction in which lenders can observe borrower outcomes only by paying a monitoring cost. Generates external-finance premia and underpins the Bernanke-Gertler-Gilchrist financial accelerator.

Discount factor puzzle. The NK paradox that the value of $\beta$ (the rep agent's subjective discount factor) calibrated to match steady-state interest rates implies implausibly forward-looking behavior in response to monetary policy.

Earnings risk (cyclical and idiosyncratic). The variance of household-level income shocks. Empirically, idiosyncratic earnings risk rises in recessions (Storesletten-Telmer-Yaron 2004), amplifying precautionary saving and contractionary aggregate dynamics.

External-finance premium. The wedge between the cost of internal funds (retained earnings) and external funds (debt, equity issuance) faced by financially-constrained firms. Time-varying and counter-cyclical.

Financial accelerator (BGG). The Bernanke-Gertler-Gilchrist mechanism by which weak balance sheets amplify and propagate shocks: lower net worth → higher external-finance premium → lower investment → lower output → lower net worth.

Fiscal theory of the price level (FTPL). Cochrane's alternative theory of inflation, in which the price level is determined by the requirement that the real value of government debt equal the present value of primary surpluses.

Gertler-Karadi banking friction. The constraint that bank lending is bounded by a multiple of bank equity, so that shocks to bank net worth propagate to credit supply throughout the economy. Foundation for unconventional monetary policy analysis.

Herfindahl index. The sum of squared market or firm shares: $H = \sum_i w_i^2$. Used in granularity analysis (where it governs the residual variance from idiosyncratic shocks) and in industrial-organization market-power analysis.

Identification problem (in macro). The general issue that aggregate time-series data offer few independent observations to estimate many parameters, and that aggregate shocks are confounded with each other. The identified-moments approach attacks this by using micro-experimental variation with macro-relevant interpretation.

Information friction. Any cost (monitoring, signaling, screening) that prevents perfect contracting between economic agents. Generates external-finance premia, credit rationing, and pricing-with-asymmetric-information distortions.

Internal-finance / cash flow channel. A monetary-transmission mechanism by which higher interest rates reduce firms' internal cash flow (via higher debt service), tightening their borrowing constraint and reducing investment beyond the direct interest-rate effect.

Intermediary asset pricing. The He-Krishnamurthy tradition of pricing risky assets by the marginal investor — the financial intermediary — whose risk-bearing capacity fluctuates with their equity capital.

Kolmogorov forward equation (KFE). The continuous-time equation governing the evolution of the cross-sectional distribution of state variables in HA macro. Used together with the Hamilton-Jacobi-Bellman equation in continuous-time HANK.

Krusell-Smith (1998). The seminal paper introducing aggregate shocks to heterogeneous-agent macro, with the "approximate aggregation" result that justifies forecasting aggregate prices from a low-dimensional summary of the wealth distribution.

Krusell-Smith approximation. The numerical method of restricting agents' forecasting to a few moments of the wealth distribution (usually the mean), iterating to a fixed point where the forecast is accurate.

Liquidity vs illiquid wealth. In the Kaplan-Moll-Violante two-asset HANK, liquid assets (cash, checking) can be adjusted costlessly; illiquid assets (housing, retirement accounts) carry transaction costs. The distinction generates wealthy hand-to-mouth households.

Marginal cost. The cost of producing one additional unit of output. In the NK Phillips curve, deviations of marginal cost from steady state drive inflation. In HANK with wage stickiness, marginal cost is endogenous to labor-market dynamics.

Markup. The ratio of price to marginal cost. In Dixit-Stiglitz monopolistic competition with elasticity $\varepsilon$, the steady-state markup is $\varepsilon / (\varepsilon - 1)$. De Loecker-Eeckhout-Unger document rising aggregate markups in US data.

Master equation. Moll's label for the rational-expectations Bellman equation in HANK with aggregate risk, in which the entire wealth distribution is a state variable. Computationally intractable in realistic settings.

Monetary super-neutrality. The property that the long-run real economy is independent of the steady-state inflation rate. Holds in RANK; fails in HANK with money-in-the-utility-function or transaction-cost structure (Marbet 2025).

Multiplier (fiscal). The ratio of aggregate output response to government spending or transfer. In RANK with Ricardian equivalence, the deficit-financed transfer multiplier is zero. In HANK, it's well above one when iMPCs are matched to data.

Natural rate of interest (r).* The real interest rate consistent with output at potential and stable inflation. Affected by demographics, productivity growth, and (per indebted-demand) inequality and debt accumulation.

Neo-Fisherian. The view (Cochrane, Williamson) that pegging nominal interest rates at low levels leads to low inflation rather than high, because the Fisher equation $i = r + \pi$ binds and $r$ is anchored. Counter to the conventional view; García-Schmidt-Woodford resolve via reflective equilibrium.

Non-convex adjustment costs. Fixed or kinked costs of changing capital or prices, generating lumpy adjustment at the micro level (Khan-Thomas 2008 for investment, Caballero-Engel for prices).

Optimal monetary policy. The policy that minimizes a welfare-relevant loss function in the model. In RANK, the canonical loss is variance of inflation plus output gap. In HANK, welfare is distributional, and optimal policy may put different weights on different households.

Permanent income hypothesis (PIH). Friedman's hypothesis that consumption tracks expected lifetime income rather than current income. Implies low MPC out of transitory transfers. Empirically rejected for the substantial hand-to-mouth fraction.

Phillips curve flattening. The empirical observation since the 1990s that the inflation-unemployment trade-off has become less steep. Multiple explanations: anchored expectations, globalization-induced price flexibility, market-power-induced markup adjustment, cyclical reallocation.

Policy invariance. The condition that a parameter (or relationship) does not change when the policy rule changes. The Lucas critique demands that macro models be built from policy-invariant primitives.

Precautionary saving. Saving driven by income or expenditure risk rather than by intertemporal substitution. Central to the Aiyagari mechanism that lowers the equilibrium interest rate below the rate of time preference.

Risk premium. The expected excess return on a risky asset over the risk-free rate. In intermediary-asset-pricing models, risk premia fluctuate with intermediary equity.

Sectoral demand shift. A reallocation of consumption across sectors (e.g., from services to goods during COVID lockdowns). In disaggregated-network macro, generates inflation in supply-constrained sectors and unemployment in supply-abundant sectors.

Self-fulfilling prophecy. An equilibrium sustained by expectations: if everyone expects a bank run, everyone runs; if everyone expects no run, no run occurs. Common in financial-fragility and sovereign-debt models.

Sluggish reallocation. The friction in moving labor or capital across sectors quickly. In Baqaee-Farhi disaggregated models, the source of non-linear amplification of sectoral shocks.

Smets-Wouters model. The canonical estimated NK DSGE model (Smets-Wouters 2003 euro area, 2007 US) with capital accumulation, habit formation, sticky wages, indexation, and a dozen shock processes. Operational workhorse at many central banks.

Stationary distribution. In HA macro, the long-run distribution of household states (wealth, income, age) under the optimal policy. The micro-level cross-section that aggregates to macro quantities.

Sticky wages. Wage rigidity, typically modeled à la Erceg-Henderson-Levin (2000) with Calvo-style infrequent wage adjustment. Important for HANK because wage stickiness governs how monetary shocks translate to labor income at high-MPC households.

Sufficient-statistics. A small number of measurable parameters that summarize the welfare or aggregate effects of a policy in a class of models. The Auclert-Rognlie-Straub iMPC is a sufficient statistic for the dynamic fiscal multiplier.

Survey expectations. Direct measurement of household and firm beliefs about future inflation, output, unemployment (Coibion-Gorodnichenko using University of Michigan and other surveys). Often inconsistent with rational expectations; basis for behavioral macro.

Tobin's q. The ratio of market value of capital to its replacement cost. In investment theory, the marginal q determines investment rates. In HANK with financial frictions, q is heterogeneous across firms.

Total factor productivity (TFP). The residual in output growth not explained by capital and labor input growth. The driver of business cycles in RBC; an aggregation of underlying micro productivity in granular and network models.

Two-asset HANK. The Kaplan-Moll-Violante setup with both liquid and illiquid assets, generating the wealthy-hand-to-mouth population and substantial MPCs out of transitory income.

Walras's law. In an exchange economy, the value of aggregate excess demand summed across all goods equals zero. One of the three trivial restrictions on aggregate demand that survives SMD.

End of report.