Jordi Galí | Macro Paper Warehouse

Heterogeneity and Aggregate Fluctuations: Insights from TANK Models

By building three nested HANK economies and then constructing a deliberately simple two-agent counterpart for each, this paper argues that what household heterogeneity does to aggregate output can be read off the differential behaviour of just two household types, hand-to-mouth and unconstrained, and that idiosyncratic income risk itself contributes little. The nesting isolates three ingredients in turn: idiosyncratic income risk alone (HANK-I, with a natural debt limit so no constraint binds), an occasionally binding borrowing constraint (HANK-II), and a portfolio choice between liquid bonds and partly illiquid equity subject to an adjustment cost and a short-sale constraint (HANK-III). In HANK-I the whole gap from the representative-agent model runs through a single “risk shifter” term in the aggregate Euler equation, and that term barely moves: output volatility under HANK-I exceeds RANK’s by a factor of only 1.22 with a correlation of 0.97, because the squared elasticity of individual consumption to idiosyncratic income is strongly convex in consumption, so the households whose risk actually responds carry a small weight in the aggregate. The paper is blunt that the standard two-agent model is not a good approximation: in TANK-I the output response to an expansionary monetary shock is “highly amplified… almost trebling the effect on impact,” and the response to a technology shock has the wrong sign, because TANK-I misses the interest rate exposure channel entirely and reverses the sign of the income distribution channel. Three changes repair it — hand-to-mouth households are held permanently against the borrowing limit and so service interest on a constant debt, they are given productivity below the unconstrained (0.56 against a normalized mean of one), and they receive dividends on the same rule as in HANK — and the resulting TANK-II tracks HANK-II closely, with a volatility ratio of 1.10 for monetary shocks and near-unit correlation, while also reproducing the effect of tightening the borrowing limit from 30% to 50% constrained. Adding portfolio choice changes the answer again: because wealthy hand-to-mouth households can smooth cash-on-hand by liquidating equity at a cost, dividends no longer pass one-for-one into their consumption, the income distribution channel weakens, monetary shocks are amplified, and a positive technology shock now lowers output — a prediction the authors immediately flag as contrary to existing evidence and as hinging on their counterfactual constant-real-rate assumption. Splitting the hand-to-mouth into poor (weight 0.05) and wealthy (0.25) restores the approximation in TANK-III. Section 6 relaxes the constant real rate for a Taylor rule with φ_π = 1.5 and φ_y = 0.125, and the models converge dramatically; the mechanism is stated as a proposition, since the natural level of output is invariant to idiosyncratic risk and the shared Phillips curve displays divine coincidence, so under strict inflation targeting every model delivers the identical output path. The caveats are the authors’ own and are load-bearing: the result applies to environments where precautionary saving responds little to aggregate shocks, countercyclical income risk is absent from the analysis, only monetary and technology shocks are studied, heterogeneity is not allowed to touch the supply side, and nothing normative is claimed — the irrelevance proposition concerns output, not the real interest rate, and not welfare.

Labor Markets and Monetary Policy: A New Keynesian Model with Unemployment

Standard New Keynesian models generate no unemployment, only voluntary movements in hours or employment, which the authors call a surprising basis for the workhorse models used by central banks. They extend the framework with a labour market in which hiring is costly and the cost per hire rises with labour market tightness – defined as the ratio of aggregate hires to the pool of jobless individuals available at the start of the period, which is also the job-finding rate facing an unemployed worker – and they proceed in two steps. With flexible prices and their utility specification (log consumption, power disutility of employment), the constrained-efficient allocation has a constant job-finding rate and hence a constant unemployment rate, invariant to productivity shocks, because income and substitution effects on labour supply exactly offset; the same invariance survives under Nash bargaining, though the bargained unemployment rate generally differs from the efficient one unless a Hosios-like condition holds (no effective market power by final goods firms, and worker bargaining power equal to the elasticity of hiring costs with respect to tightness). The authors are careful to distinguish this invariance from the Shimer puzzle: Shimer derived small unemployment responses assuming a constant marginal rate of substitution, whereas here “our neutrality result follows entirely from movements in the marginal rate of substitution,” which moves one-for-one with productivity so that labour market frictions play no role – and they note that under more general assumptions “the Shimer puzzle will be even stronger than in the original Shimer set-up.” Because the one-for-one wage response looks counterfactual, they impose real wage rigidity through a schedule indexed by a parameter running from Nash bargaining at zero to Hall’s fully rigid wage at one, and add Calvo price staggering. Real marginal cost then depends on tightness and on the rigidity index, which yields a Phillips curve linking inflation to expected inflation and to the current, lagged and expected unemployment rate – with the weights on the level versus the change in unemployment determined by how fluid the labour market is. Since constrained-efficient unemployment is constant, both stabilisation goals are desirable, but with partial wage adjustment neither can be achieved alone: there is no divine coincidence. Calibrating quarterly (discount factor 0.99, unit Frisch elasticity, elasticity of substitution 6 implying a gross markup of 1.2, Calvo slope 1/12, rigidity index 0.5, hiring cost elasticity 1) to a fluid U.S. market (5 percent unemployment, job-finding rate 0.7, separation rate 0.12) and a sclerotic European one (10 percent unemployment, job-finding rate 0.25, separation rate 0.04), with hiring costs set at 1 percent of GDP in the U.S. case, they find that after a persistent (AR(1) coefficient 0.9) one percent fall in productivity, stabilising unemployment requires about a 150 basis point rise in inflation on impact under both calibrations, while strict inflation targeting raises unemployment by about 3 percentage points on impact under both and, in Europe, produces a hump-shaped path peaking near 8 percentage points – a response the authors themselves label possibly unrealistic while noting the policy assumed is also unrealistically extreme. Optimal policy sits between: unemployment rises 50 basis points in the U.S. calibration and about half that in Europe, at the price of persistently higher inflation of roughly 1 and 1.4 percentage points, and the welfare losses under strict inflation targeting are 25 times those under optimal policy in the European calibration.

Monetary Policy and Endogenous Financial Crises

This paper asks whether a central bank should deviate from strict inflation targeting (SIT) to promote financial stability, studying the question in a textbook New Keynesian model augmented with capital accumulation and microfounded endogenous credit-market crises. The model embeds two financial frictions — limited contract enforcement and asymmetric information about firm productivity — that together generate fragile credit markets in which, when productive firms’ marginal return on capital falls below a threshold, the credit market collapses (a “financial crisis”). The calibrated model matches the empirical regularity that economies spend roughly 8% of time in financial crises. The central finding is threefold: (1) monetary policy affects crisis probability both in the short run (via output and markups) and in the medium run (via capital accumulation dynamics); (2) a Taylor-type rule that responds to output fluctuations — rather than SIT — reduces crisis incidence and raises welfare, with TR93 (φ_y = 0.125) generating a 0.016% permanent consumption equivalent gain over SIT; (3) prolonged unexpected monetary easing followed by abrupt tightening is itself a mechanism that can trigger financial crises. These findings imply a genuine price-versus-financial-stability tradeoff and challenge the “divine coincidence” view that SIT is sufficient in the presence of financial frictions.

Monetary Policy and Exchange Rate Volatility in a Small Open Economy

This paper builds a tractable, microfounded small open economy version of the Calvo staggered-price New Keynesian model – one economy among a continuum making up the world – and uses it to analyze rule-based monetary policy. Its first main result is that, under complete international asset markets and the paper’s specific preference and technology assumptions, the economy’s log-linearized equilibrium dynamics reduce to exactly the same two-equation “canonical” system used to study closed economies: a New Keynesian Phillips curve linking domestic (producer) inflation to the output gap, and a forward-looking dynamic IS equation, with openness and cross-country substitutability entering only through composite coefficients and world output entering only through the natural rate of interest. Its second main result, obtained for the special case of log utility and unit elasticities of substitution, is that once an appropriately chosen employment subsidy neutralizes both firms’ market power and the small open economy’s incentive to manipulate its terms of trade, the welfare-optimal policy is to fully stabilize domestic prices – strict domestic inflation targeting. The paper then uses a calibrated version of the model to compare this optimal benchmark with two simple, more standard policy rules (a domestic-inflation-based Taylor rule and a CPI-inflation-based Taylor rule) and an exchange rate peg, finding a systematic trade-off: regimes that stabilize domestic inflation and the output gap most successfully necessarily generate substantially more volatile nominal exchange rates and terms of trade, and vice versa, with the exchange rate peg delivering the worst welfare outcome of the three simple rules because its “excess smoothness” of the terms of trade – consistent with the Mussa (1986) puzzle – amplifies domestic inflation and output-gap volatility instead.

Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory*

Estimating a forward-looking Federal Reserve policy rule separately for 1960-79 and 1979-96, this paper finds that the Fed let real short-term rates fall as expected inflation rose before Volcker, but raised real rates more than one-for-one with expected inflation under Volcker and Greenspan. The rule takes the Federal Funds rate target as a linear function of the gap between expected future inflation and a target, plus the expected output gap, nests Taylor’s (1993) backward-looking rule as a special case, and is estimated by GMM on quarterly U.S. data from 1960:1-1996:4. The inflation-response coefficient is estimated at 0.83 (s.e. 0.07) pre-Volcker and 2.15 (s.e. 0.40) under Volcker-Greenspan – a difference the authors show is robust to alternative inflation and output-gap measures, alternative target horizons, subsample splits by Fed chairman, and a backward-looking specification. They argue this shift, not oil shocks alone, is central to the change in macroeconomic behavior: the timing of the 1970s inflation build-up predates the first oil shock, and multivariate evidence suggests oil shocks account for only a modest share of output and inflation variation over the period. Embedding the estimated rules in a standard New Keynesian sticky-price model, the authors show that an inflation-response coefficient below one (as estimated pre-Volcker) admits self-fulfilling, sunspot-driven swings in inflation and output with no fundamental shocks at all, while a coefficient above one (as estimated post-1979) rules this out; even short of formal indeterminacy, a near-unity coefficient substantially amplifies the economy’s response to ordinary supply and demand shocks relative to a coefficient well above one. The paper explicitly leaves open why the Fed followed the inferior pre-Volcker rule for so long, offering only speculative explanations (misperceived potential output, an immature understanding of inflation dynamics).

Monetary Policy with Heterogeneous Agents: Insights from TANK models

This paper asks how much of the HANK literature’s message about aggregate behaviour survives in a far simpler model, and answers by first identifying exactly what heterogeneity does. Building on a framework related to Werning (2015), the authors show that a heterogeneous-agent economy departs from its representative-agent counterpart along precisely two dimensions: the difference in average consumption between constrained and unconstrained households at any point in time, and the dispersion of consumption within the subset of unconstrained households. Both appear as “wedges” in an Euler equation for aggregate consumption, so each can be traced in response to any aggregate shock and its quantitative significance measured rather than asserted. A two-agent (TANK) model, with fixed shares of “Ricardian” households who trade financial markets freely and “Keynesian” households who consume current labour income each period, captures the first wedge and ignores the second entirely. The paper’s central finding is that this omission costs little for aggregates: in a canonical HANK calibration the first form of heterogeneity fluctuates substantially with aggregate shocks and is well captured by TANK, while the second remains roughly constant, because unconstrained agents limit their consumption swings by borrowing and saving. Quantitatively, with constant transfers the real-interest-rate elasticity of output on impact is about 70 percent larger in HANK than in RANK, and 64 percent larger in TANK – close agreement – and the two models track each other across alternative transfer rules and borrowing limits, which the authors read as TANK remaining a “good approximation to the richer HANK model” throughout (the widest gap between them is under the loosest borrowing limit, 1.23 against 1.46). Two analytical payoffs follow. Heterogeneity may amplify or dampen the effects of aggregate shocks, depending on the share of constrained agents and the cyclicality of fiscal transfers, but independently of the degree of nominal rigidity or the conduct of monetary policy. And a benevolent central bank’s welfare criterion acquires a third term penalising fluctuations in consumption heterogeneity, which generally cannot be stabilised alongside inflation and the output gap – so the divine coincidence fails. The authors are careful about the size of that last result: for standard calibrations the optimal policy still implies minimal fluctuations in inflation and the output gap, and is “nearly identical” to the representative-agent optimum. The manuscript is marked Preliminary and Incomplete, and its comparisons are restricted throughout to the responses of aggregate variables to aggregate shocks; it makes no claim that TANK reproduces HANK’s distributional detail.

Real Wage Rigidities and the New Keynesian Model

Most central banks behave as though stabilising inflation and stabilising the gap between output and its desired level are competing goals, yet the standard New Keynesian framework implies no such conflict: because the New Keynesian Phillips curve makes inflation a function of expected inflation and the output gap alone, holding inflation constant delivers a zero output gap, and because the log distance between the efficient (first-best) and natural (second-best) levels of output is a constant in that model, a zero output gap is also a zero welfare-relevant gap. The authors name this property the “divine coincidence” and argue it is an artefact of the absence of non-trivial real imperfections rather than a robust feature. Introducing one such imperfection – real wages that adjust only partially toward the marginal rate of substitution, with the adjustment weight serving as an index of real rigidity – makes the distance between first- and second-best output fluctuate with both supply and preference shocks, so that stabilising inflation, while still equivalent to stabilising the output gap, is no longer equivalent to stabilising the welfare-relevant gap, and the central bank faces a genuine tradeoff. The authors show the tradeoff is quantitatively non-trivial: with a real-rigidity index of 0.9 (a six-quarter half-life for real wage adjustment), an oil share in production of 0.025, an average price duration of six months and the discount factor taken to one, a 10 percent rise in the price of oil requires annualised inflation slightly above 4 percent on impact if the welfare-relevant gap is fully stabilised, or a 1.1 percent first-quarter fall in the welfare-relevant output gap if inflation is fully stabilised – with both magnitudes falling sharply, to roughly 2 percent and 0.5 percent at an index of 0.8 and to below 0.5 percent and 0.1 percent at 0.5, since the expressions are highly non-linear in the rigidity index. The same friction multiplies the short-run output cost of a disinflation by a factor of ten at an index of 0.9, turning a move from 5 percent inflation to zero from a 0.25 percentage point permanent output loss into a 2.5 percentage point short-run loss. On the positive side, real wage rigidities generate inflation inertia – persistence in inflation beyond that inherited from the output gap – and yield an inflation equation in lagged and expected inflation, unemployment and the change in the real price of the non-produced input that is close to traditional Phillips curve specifications; estimated by instrumental variables on annual U.S. data for 1960-2004 (GDP deflator inflation, the civilian unemployment rate, and the PPI raw materials index relative to the GDP deflator, instrumented with four lags of each), all coefficients carry the predicted sign and are statistically significant, and the restriction that the coefficients on lagged and expected inflation sum to one cannot be rejected at the 5 percent level, though the authors note it is not rejected by much.

The Science of Monetary Policy: A New Keynesian Perspective

This widely cited survey derives monetary policy design from a simple forward-looking New Keynesian model built from first principles – a forward-looking IS-type output-gap equation and a forward-looking Phillips curve – and states its conclusions as a numbered sequence of general “Results” meant to be robust across a wide variety of macroeconomic frameworks. Under discretion (no commitment), optimal policy embeds implicit inflation targeting: the central bank should adjust the nominal rate more than one-for-one with expected future inflation (Result 3, later known as the Taylor principle), should perfectly offset demand shocks but let the nominal rate stay put in the face of shocks to potential output (Result 4), and, more generally, should raise real rates whenever inflation is forecast above target and let it return only gradually. Under commitment, the paper derives a genuinely new result: even when the central bank has no temptation to push output above its natural level (ruling out the traditional Kydland-Prescott/Barro-Gordon inflationary-bias motive for commitment), a credible commitment to a rule still improves the current output-inflation trade-off, because current inflation depends on expectations of future policy, and a rational private sector will discount an un-committed promise of future toughness (Result 7). The paper also formalizes Alan Blinder’s “opportunistic” approach to disinflation as optimal when policy-makers weight small output deviations more heavily than small inflation deviations, showing it is equivalent to targeting inflation within a zone rather than at a point (Result 12), and works through practical complications including imperfect information, interest-rate smoothing, and model uncertainty. Turning from theory to practice, the paper applies its “Taylor principle” criterion to U.S. monetary history, arguing pre-Volcker policy “tended to accommodate rather than fight increases in expected inflation” while Volcker-Greenspan policy adopted the kind of implicit inflation targeting the theory recommends, and closes with simple rules (including Taylor’s and the authors’ own forward-looking variant) and open questions for future research, including endogenous inflation persistence, open-economy extensions, and the zero lower bound.