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

The paper asks how the presence of heterogeneous, credit-constrained households with high marginal propensities to consume (MPCs) changes the way small open economies respond to exchange rate shocks and domestic monetary policy, relative to the standard representative-agent benchmark (Sec. 1, Introduction). It takes as its point of departure the representative-agent, complete-markets (RA-CM) small open economy model of Galí and Monacelli (2005), and builds a Heterogeneous-Agent New Keynesian (“HANK”) version by adding idiosyncratic income risk, borrowing constraints, and sticky wages (rather than sticky prices, following Auclert, Rognlie and Straub 2024a), while allowing households to hold a domestic stock, a domestic bond, and a foreign bond. The paper considers six nested calibrations along two dimensions: the degree of heterogeneity (representative agent “RA”, two agents “TA”, or heterogeneous agents “HA”) and whether markets are complete or incomplete with respect to aggregate risk (“CM” vs. “IM”), and studies two kinds of aggregate shocks – shocks to the foreign interest rate (exchange rate shocks) and shocks to the domestic monetary policy rate.

Linearizing the home goods market-clearing condition decomposes the output response into an expenditure-switching channel, a real income channel, and a Keynesian multiplier (eq. 38, Prop. 3-4). The expenditure-switching channel, present even in the RA-CM model, is the traditional one: a depreciation lowers the relative price of home goods, shifting domestic and foreign demand toward them, with a strength governed by the trade elasticity χ. The real income channel is new to the HA model: because a depreciation lowers PHt/Pt (the price of what the country sells relative to what it buys), it reduces real income and, via the matrix of intertemporal MPCs M, lowers consumption. The multiplier channel captures how any resulting change in output feeds back into real income and hence further into consumption. In the RA-CM benchmark, M = 0, so only expenditure switching operates and consumption is unaffected by any exchange rate shock that does not affect foreign preferences (Prop. 2).

When the trade elasticity χ equals exactly 1 – the Marshall-Lerner threshold – the real income channel and the multiplier cancel exactly, so the response of consumption and output to any exchange rate shock is identical across every market structure and degree of heterogeneity the paper considers (Prop. 5). Intuitively, at χ = 1 the rise in output from expenditure switching is exactly large enough to offset the higher price of imports, leaving each household’s real income, and therefore its consumption, unchanged; the trade balance is likewise unaffected, since higher import prices are exactly offset by lower import volumes. This threshold does not correspond to the Cole-Obstfeld unitary-elasticity parametrization (that turns out to matter for monetary policy shocks instead, Q6); it is a separate benchmark specific to exchange rate shocks.

Contractionary depreciations require both a large one-time consumption response to an income shock and persistence in that response over time, and the paper shows only the heterogeneous-agent, incomplete-markets (HA-IM) model delivers both, because of the shape of its matrix of intertemporal MPCs (Sec. 2.3, Fig. 1, Table 1). Complete-markets models (RA-CM, TA-CM, HA-CM) insure away most of the aggregate income shock internationally, so their iMPCs are small. Among incomplete-markets models, RA-IM households can smooth a temporary income shock through savings, so their impact MPC is small; TA-IM’s constrained “hand-to-mouth” agents have a large impact MPC but no persistence, since they do not anticipate future income changes; only HA-IM combines a large impact MPC with persistence, as constrained households slowly rebuild depleted buffer stocks after a shock. At an illustrative calibration with χ = 0.1, the paper reports the impact consumption decline is essentially zero for RA/TA under complete markets, -0.09 (RA-IM) and -0.15 (TA-IM) under incomplete markets, versus -0.34 for HA-IM (Table 1) – evidence, the authors argue, that “it is the combination of aggregate market incompleteness and heterogeneity that ‘sizes up’ the real income channel” (Sec. 3.3).

There is a threshold trade elasticity χ∗, at least (1−α)M0,0 and generally larger because of multiplier effects, below which output falls on impact following a depreciation (Prop. 7-8); in the paper’s illustrative HA-IM calibration this threshold is χ∗ = 0.26, and whenever χ < 1−α the present value of the entire output response is negative in any incomplete-markets model. This differs from the older open-economy IS-LM tradition (Polak 1947; Harberger 1950; Laursen and Metzler 1950, as summarized in Dornbusch 1980), which predicted output falls with depreciation whenever χ < 1 (the Marshall-Lerner condition), regardless of MPCs. The paper shows this older result is really a statement about real income, not output volume, and that once the depreciation’s effect on relative prices is properly separated from its effect on real income, a micro-founded model needs a lower trade elasticity than the Marshall-Lerner threshold to generate an actual output contraction – the exact threshold rising with the economy’s effective MPC λ (eq. 41-42, Sec. 3.4).

Under log consumption utility (σ=1), there is a second exact neutrality threshold, χ = 2−α, at which all aggregate quantities and prices from a monetary policy shock are identical in the RA-CM and HA-IM models (Prop. 9). This threshold nests the Cole and Obstfeld (1991) parametrization in which both domestic and foreign elasticities of substitution equal 1, and the paper’s result “generalizes Werning (2015)’s seminal neutrality result for closed economies to an open economy setting” and extends Itskhoki (2021)’s representative-agent version of the same equivalence to heterogeneous agents. Away from χ = 2−α, monetary transmission in the HA-IM model is generally weaker than in RA-CM for an accommodative shock whenever χ < 2−α (Prop. 9), because the open economy’s multiplier – weaker than in a closed economy since only a share 1−α of spending falls on home goods – fails to fully offset the weaker interest-rate channel that heterogeneous, partially-constrained households exhibit (a channel documented in closed-economy HANK work, e.g. Auclert 2019).

When χ < 2−α, a monetary easing generates a current account deficit – households borrow from abroad both to fund higher current spending at lower rates and to smooth the real-income loss from pricier imports – and this negative net foreign asset position must later be repaid through reduced future spending, so the stimulus “steals” demand from later periods (Sec. 4.2, Prop. 10). Proposition 10 derives that, holding the long-run exchange rate fixed, the present-value consumption and output adjustment required to close a given net foreign asset gap dnfa is (1/α)·dnfa and ((α−1)/α)·dnfa respectively – so more closed economies (lower α) require a larger future contraction to repay the same foreign debt. The paper notes this is a close cousin of “limited ammunition” effects found in closed-economy models (McKay and Wieland 2021; Mian, Straub and Sufi 2021) but with one crucial difference: because the mechanism operates through the current account rather than durable-goods or debt dynamics, the present value of monetary policy’s output effect can turn strictly negative once χ falls below 1−α (Appendix C.3) – monetary easing can lower cumulative output on net.

The quantitative model adds delayed substitution (a Calvo-style friction generating a time-varying, rising trade elasticity), sticky import and export prices (allowing partial exchange-rate pass-through), non-homothetic consumption baskets, unequal incidence of aggregate income shocks across the income distribution, and a standard inertial Taylor rule, calibrated broadly to Mexico (Sec. 5.1-5.2). The delayed-substitution block is calibrated to match the dynamic response of trade flows to tariff changes documented by Boehm, Levchenko and Pandalai-Nayar (2023), yielding a trade elasticity of about 0.15 on impact, 0.3 after one quarter, 0.7 after a year, and 6 in the long run – consistent with the well-documented empirical “J-curve.” Non-homothetic preferences are calibrated to Cravino and Levchenko (2017)’s finding that poorer Mexican households spend a larger tradable/import share of their budget; unequal incidence of aggregate shocks (parameter ζ = −0.196) is calibrated to Blanco, Drenik and Zaratiegui’s estimates that low-income Argentine workers’ labor income fell more than high-income workers’ after the 2002 devaluation; import price pass-through is calibrated to the 1994 Mexican devaluation data in Burstein and Gopinath (2015), which shows essentially complete pass-through to import prices (θF = 0).

The quantitative model generates a depreciation that is contractionary for output for about one year and expansionary thereafter (Sec. 5.3, Fig. 8), because it behaves like a low-trade-elasticity model in the short run and a high-trade-elasticity model once households have had time to substitute away from imports. This is a direct consequence of the calibrated J-curve: with a short-run trade elasticity well below the χ∗ = 0.26 threshold identified in the analytical model, the real income channel dominates on impact, but as the trade elasticity rises with delayed substitution, expenditure switching eventually takes over and output growth turns positive around the fourth quarter.

The paper shows that a central bank facing a depreciation-driven recession confronts a genuine dilemma – hiking rates to defend the currency worsens the recession by adding a second contractionary force, while the output-stabilizing policy can require either a rate cut or a rate hike depending on the trade elasticity (Sec. 5.4, Fig. 9). At the paper’s baseline calibrated trade elasticity, the unique output-stabilizing policy actually involves cutting the real interest rate and letting the currency depreciate even further, because at that elasticity the real income channel is not strong enough to offset the ordinary expansionary effects of accommodative monetary policy; stabilizing the exchange rate instead (a rate hike) produces an even deeper recession, “replac[ing] one evil (contractionary depreciation) with another (contractionary monetary policy),” consistent with concerns raised by Gourinchas (2018) and Kalemli-Özcan (2019). Under a lower trade elasticity (e.g., with substitution friction θ = 0.99 instead of the baseline 0.976), the paper reports the output-stabilizing policy flips to a rate hike that mitigates the depreciation.

A systematic comparative-statics exercise (Table 3) shows the contraction is larger with higher openness, higher average MPCs, less dollar currency pricing, non-homothetic (import-skewed) consumption among the poor, unequal incidence of aggregate shocks on low-income workers, a lower short-run substitution elasticity, and faster exchange-rate pass-through into import prices, and smaller under the opposite settings (Sec. 5.5). Relative to the baseline quantitative model’s impact/one-year-cumulative output response of -0.12%/-0.24% of steady-state output, doubling the average-MPC calibration target from 20% to 40% widens the impact decline to -0.29% (one-year cumulative -0.19%); halving import openness to 20% shrinks it to -0.06%/-0.13%; and lowering the short-run trade elasticity further (targeting 0.3 instead of 0.7 after a year) widens it to -0.36%/-1.16%, the largest contraction in the table. Removing dollar currency pricing (full pass-through into export prices instead of the baseline’s partial pass-through) sharply widens the contraction, to -0.83%/-0.45%, because with it exporters’ profits no longer rise to offset the real income loss; the text explains that “Dollar Currency Pricing attenuates the contraction in our quantitative model” by stimulating export profits, which households with a high MPC out of capital income then spend. Limiting pass-through of the exchange rate into import prices instead sharply narrows the contraction, to -0.03%/-0.14%, since it directly weakens the real income channel. The paper further calibrates the model to seven countries with historical depreciation episodes and finds that inferred import-price pass-through is the most important single determinant of cross-country variation in the size of the contraction (Sec. 5.5, referencing Appendix D.5).

The paper finds the real income channel alone is larger than a balance-sheet channel calibrated to a typical country’s net foreign-currency exposure, but the two channels reinforce each other, especially when currency losses are financed regressively (Sec. 5.6, Table 4). Adding gross foreign-currency household debt worth 50% of GDP (an upper-bound calibration relative to the historical cross-country data in Bénétrix et al. 2020) deepens the one-year cumulative output decline from -0.24% to -0.55% of steady-state output; routing the same foreign-currency exposure through the government and repaying it via an immediate lump-sum tax produces the largest amplification of all (-0.79%), because lump-sum taxation falls disproportionately, in relative terms, on high-MPC households – echoing findings in de Ferra, Mitman and Romei (2020) and Zhou (2022) that valuation losses bite hardest for output when they land on high-MPC households.

The paper argues that a micro-founded heterogeneous-agent model produces contractionary depreciations under a narrower and more clearly identified set of conditions than either the older IS-LM tradition or prior representative-agent open-economy models, and that it isolates a channel operating even without foreign-currency debt, distinguishing it from the balance-sheet-focused literature it otherwise complements (Sec. 1, “Layout” and literature review). Building on the real-income-channel logic first proposed by Díaz-Alejandro (1963), Cooper (1968) and Krugman and Taylor (1978), and formalized with unitary elasticities by Corsetti and Pesenti (2001) and with variable elasticities by Tille (2001) and Corsetti, Pesenti, Roubini and Tille (2000) – who found the effect was quantitatively small absent high MPCs – the paper’s central contribution relative to recent heterogeneous-agent open-economy papers such as de Ferra, Mitman and Romei (2020) (sudden stops with foreign-currency household debt) and Guo, Ottonello and Perez (2023) (distributional effects of unequal financial-market access) is to isolate and quantify the real income channel on its own terms, showing that “depreciations can be contractionary even if households do not hold foreign currency debt.”