Research

Working Paper
Adrien Auclert, Matthew Rognlie, Martin Souchier, and Ludwig Straub. Working Paper. “Exchange Rates and Monetary Policy with Heterogeneous Agents: Sizing up the Real Income Channel”.Abstract
Introducing heterogeneous households to a New Keynesian small open economy model amplifies the real income channel of exchange rates: the rise in import prices from a depreciation lowers households’ real incomes, and leads them to cut back on spending. When the sum of import and export elasticities is one, this channel is offset by a larger Keynesian multiplier, heterogeneity is irrelevant, and expenditure switching drives the output response. With plausibly lower short-term elasticities, however, the real income channel dominates, and depreciation can be contractionary for output. This weakens monetary transmission and creates a dilemma for policymakers facing capital outflows. Delayed import price pass-through weakens the real income channel, while heterogeneous consumption baskets can strengthen it.
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Atif Mian, Ludwig Straub, and Amir Sufi. Working Paper. “A Goldilocks Theory of Fiscal Deficits”.Abstract

This paper proposes a tractable framework to analyze fiscal space and the dynamics of government debt, with a possibly binding zero lower bound (ZLB) constraint. Without the ZLB, a greater primary deficit unambiguously raises debt. However, debt need not explode: When R < G − φ, where φ is the sensitivity of R − G to debt, a modest permanent increase in the deficit can be sustained forever, a policy we call “free lunch”. With the ZLB, the relationship between deficit and debt can become non-monotone. Both high and low deficits can increase debt, as the latter weaken demand and reduce nominal growth at the ZLB. A rise in income inequality expands fiscal space outside the ZLB, but contracts it at the ZLB. Calibrating the model, we find little space for “free lunch” policies for the United States in 2019, but ample space for Japan.

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(New Jan 2022 version!)
Atif Mian, Ludwig Straub, and Amir Sufi. 2021. “The Saving Glut of the Rich”.Abstract
There has been a large rise in savings by Americans in the top 1% of the income or wealth distribution over the past 35 years, which we call the saving glut of the rich. The saving glut of the rich has been almost as large as the global saving glut, and it has not been associated with an increase in investment. Instead, this rise in savings has been associated with substantial dissaving by the non-rich and dissaving by the government. A process by which the financial sector is unveiled reveals that rich households have accumulated substantial financial assets that are direct claims on household and government debt. Analysis using variation across states shows that the rise in top income shares has been important in generating the saving glut of the rich.
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Michael Fishman, Jonathan Parker, and Ludwig Straub. 2021. “A Dynamic Theory of Lending Standards”.Abstract
We propose a dynamic model of credit markets, in which there is a novel two-way interaction between lending standards and the quality composition of the borrower pool. Borrowers can be of high or low types, and each lender privately decides on its lending standard, modeled as the option to screen out low types with some probability. Lending standards are dynamic strategic complements: Screening worsens the borrower pool, increasing the incentive to screen going forward. Despite the complementarity, the equilibrium is unique, but may exhibit two stable steady states, one with normal lending standards and one with tight lending standards. Thus, even temporary adverse shocks can have amplified and long-lasting effects on the health of credit markets. According to the model’s normative predictions, lending standards are inefficiently tight during such episodes, since screening banks do not internalize their effect on the quality of the borrower pool. We discuss several policies such as government support for lending that can help ameliorate this inefficiency, along with several pitfalls to avoid.
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Revise and Resubmit at Review of Financial Studies
Ludwig Straub and Robert Ulbricht. 2021. “Endogenous Uncertainty and Credit Crunches”.Abstract

We develop a theory of endogenous uncertainty where the ability of investors to learn about firm-level fundamentals declines during financial crises. At the same time, higher uncertainty reinforces financial distress, causing a persistent cycle of uncertainty, pessimistic expectations, and financial constraints. Through this channel, a temporary shortage of funds can develop into a long-lasting funding problem for firms. Financial crises are characterized by increased credit misallocation, volatile asset prices, high risk premia, an increased cross-sectional dispersion of returns, and high levels of disagreement among forecasters. A numerical example suggests that the proposed channel may significantly delay recovery from financial shocks.

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Revise and resubmit at Review of Economic Studies
Adrien Auclert, Matthew Rognlie, and Ludwig Straub. 2020. “Micro Jumps, Macro Humps: Monetary Policy and Business Cycles in an Estimated HANK Model”.Abstract
We estimate a Heterogeneous-Agent New Keynesian model with sticky household expectations that matches existing microeconomic evidence on marginal propensities to consume and macroeconomic evidence on the impulse response to a monetary policy shock. Our estimated model uncovers a central role for investment in the transmission mechanism of monetary policy, as high MPCs amplify the investment response in the data. This force also generates a procyclical response of consumption to investment shocks, leading our model to infer a central role for these shocks as a source of business cycles.
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Revise and resubmit at American Economic Review
Ludwig Straub. 2019. “Consumption, Savings, and the Distribution of Permanent Income”.Abstract

Rising inequality in the permanent component of labor income, henceforth permanent income, has been a major force behind the secular increase in US labor income inequality. This paper explores the macroeconomic consequences of this rise. First, I show that in many common macroeconomic models—including models with precautionary savings motives—consumption is a linear function of permanent income. This implies that macroeconomic aggregates are neutral with respect to shifts in the distribution of permanent income. Motivated by this neutrality result, I develop novel approaches to test for linearity in US household panel data, which consistently estimate the elasticity of consumption to permanent income in common precautionary savings models. The estimates suggest an elasticity of 0.7, soundly rejecting linearity. To quantify the effects of this deviation from neutrality, I extend a canonical precautionary savings model to include non-homothetic preferences across periods, capturing the idea that permanent-income rich households save disproportionately more than their poor counterparts. The model suggests that the US economy is far from neutral. In the model, the rise in US permanent labor income inequality since the 1970s caused: (a) a decline in real interest rates of around 1%; (b) an increase in the wealth-to-GDP ratio of around 30%; (c) wealth inequality to rise almost as rapidly as it did in the data.

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Revise and resubmit at Econometrica
Adrien Auclert, Matthew Rognlie, and Ludwig Straub. 2018. “The Intertemporal Keynesian Cross”. Download Paper Old 2017 version
Revise and resubmit at Journal of Political Economy
Journal Article
Veronica Guerrieri, Guido Lorenzoni, Ludwig Straub, and Ivan Werning. Forthcoming. “Monetary Policy in Times of Structural Reallocation.” Proceedings of the 2021 Jackson Hole Symposium.Abstract
We characterize optimal monetary policy in response to asymmetric shocks that shift demand from one sector to another, a condition arguably faced by many economies emerging from the Covid-19 crisis and its aftermath. We show that the asymmetry naturally manifests itself as an endogenous cost-push shock, breaking divine coincidence, and resulting in inflation optimally exceeding its target despite elevated unemployment. In fact, there is no simple, possibly re-weighted, inflation index that is optimally targeted. When labor is mobile between sectors, the benefits of monetary easing can be even higher, if it translates into wage increases in the expanding sector.
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Atif Mian, Ludwig Straub, and Amir Sufi. Forthcoming. “What explains the decline in r*? Rising income inequality versus demographic shifts.” Proceedings of the 2021 Jackson Hole Symposium.Abstract
Downward pressure on the natural rate of interest (r*) is often attributed to an increase in saving. This study uses microeconomic data from the SCF+ to explore the relative importance of demographic shifts versus rising income inequality on the evolution of saving behavior in the United States from 1950 to 2019. The evidence suggests that rising income inequality is the more important factor explaining the decline in r*. Saving rates are significantly higher for high income households within a given birth cohort relative to middle and low income households in the same birth cohort, and there has been a large rise in income shares for high income households since the 1980s. The result has been a large rise in saving by high income earners since the 1980s, which is the exact same time period during which r* has fallen. Differences in saving rates across the working age distribution are smaller, and there has not been a consistent monotonic shift in income toward any given age group. Both findings challenge the view that demographic shifts due to the aging of the baby boom generation explain the decline in r*.
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Veronica Guerrieri, Guido Lorenzoni, Ludwig Straub, and Ivan Werning. Forthcoming. “Macroeconomic Implications of COVID-19: Can Negative Supply Shocks Cause Demand Shortages.” American Economic Review. Publisher's VersionAbstract

Motivated by the effects of the Covid-19 pandemic, we present a theory of Keynesian supply shocks: shocks that reduce potential output in a sector of the economy, but that, by reducing demand in other sectors, ultimately push aggregate activity below potential. A Keynesian supply shock is more likely when the elasticity of substitution between sectors is relatively low, the intertemporal elasticity of substitution is relatively high, and markets are incomplete. Fiscal policy can display a smaller multiplier, but the insurance benefit of fiscal transfers can be enhanced. Firm exits and job destruction can amplify and propagate the shock.

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Sebastián Fanelli and Ludwig Straub. Forthcoming. “A Theory of Foreign Exchange Interventions.” Review of Economic Studies. Publisher's VersionAbstract
We study a real small open economy with two key ingredients: (i) partial segmentation of home and foreign bond markets and (ii) a pecuniary externality that makes the real exchange rate excessively volatile in response to capital flows. Partial segmentation implies that, by intervening in the bond markets, the central bank can affect the exchange rate and the spread between home- and foreign-bond yields. Such interventions allow the central bank to address the pecuniary externality, but they are also costly, as foreigners make carry-trade profits. We analytically characterize the optimal intervention policy that solves this trade-off: (a) the optimal policy leans against the wind, stabilizing the exchange rate; (b) it involves smooth spreads but allows exchange rates to jump; (c) it partly relies on “forward guidance”, with non-zero interventions even after the shock has subsided; (d) it requires credibility, in that central banks do not intervene without commitment. Finally, we shed light on the global consequences of widespread interventions, using a multi-country extension of our model. We find that, left to themselves, countries over-accumulate reserves, reducing welfare and leading to inefficiently low world interest rates.
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Atif Mian, Ludwig Straub, and Amir Sufi. 11/2021. “Indebted Demand.” Quarterly Journal of Economics, 136, 4, Pp. 2243–2307. Publisher's VersionAbstract
We propose a theory of indebted demand, capturing the idea that large debt burdens lower aggregate demand, and thus the natural rate of interest. At the core of the theory is the simple yet underappreciated observation that borrowers and savers differ in their marginal propensities to save out of permanent income. Embedding this insight in a two-agent perpetual-youth model, we find that recent trends in income inequality and financial deregulation lead to indebted household demand, pushing down the natural rate of interest. Moreover, popular expansionary policies—such as accommodative monetary policy—generate a debt-financed short-run boom at the expense of indebted demand in the future. When demand is sufficiently indebted, the economy gets stuck in a debt-driven liquidity trap, or debt trap. Escaping a debt trap requires consideration of less conventional macroeconomic policies, such as those focused on redistribution or those reducing the structural sources of high inequality.
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Adrien Auclert, Bence Bardóczy, Matthew Rognlie, and Ludwig Straub. 9/2021. “Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models.” Econometrica, 89, 5, Pp. 2375–2408. Publisher's VersionAbstract
We propose a general and highly efficient method for solving and estimating general equilibrium heterogeneous‐agent models with aggregate shocks in discrete time. Our approach relies on the rapid computation of sequence‐space Jacobians—the derivatives of perfect‐foresight equilibrium mappings between aggregate sequences around the steady state. Our main contribution is a fast algorithm for calculating Jacobians for a large class of heterogeneous‐agent problems. We combine this algorithm with a systematic approach to composing and inverting Jacobians to solve for general equilibrium impulse responses. We obtain a rapid procedure for likelihood‐based estimation and computation of nonlinear perfect‐foresight transitions. We apply our methods to three canonical heterogeneous‐agent models: a neoclassical model, a New Keynesian model with one asset, and a New Keynesian model with two assets.
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Ludwig Straub and Iván Werning. 1/2020. “Positive Long-Run Capital Taxation: Chamley-Judd Revisited.” American Economic Review, 110, 1, Pp. 86-119. Publisher's VersionAbstract
According to the Chamley-Judd result, capital should not be taxed in the long run. In this paper, we overturn this conclusion, showing that it does not follow from the very models used to derive it. For the main model in Judd (1985), we prove that the long-run tax on capital is positive and significant, whenever the intertemporal elasticity of substitution is below one. For higher elasticities, the tax converges to zero but may do so at a slow rate, after centuries of high tax rates. The main model in Chamley (1986) imposes an upper bound on capital taxes. We provide conditions under which these constraints bind forever, implying positive long-run taxes. When this is not the case, the long-run tax may be zero. However, if preferences are recursive and discounting is locally nonconstant (e.g., not additively separable over time), a zero long-run capital tax limit must be accompanied by zero private wealth (zero tax base) or by zero labor taxes (first-best). Finally, we explain why the equivalence of a positive capital tax with ever-increasing consumption taxes does not provide a firm rationale against capital taxation.
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Ludwig Straub and Robert Ulbricht. 9/2019. “Endogenous Second Moments: A Unified Approach to Fluctuations in Risk, Dispersion and Uncertainty.” Journal of Economic Theory, 183, Pp. 625-660. Publisher's VersionAbstract

Many important statistics in macroeconomics and finance—such as cross-sectional dispersions, risk, volatility, or uncertainty—are second moments. In this paper, we explore a mechanism by which second moments naturally and endogenously fluctuate over time as nonlinear transformations of fundamentals. Specifically, we provide general results that characterize second moments of transformed random variables when the underlying fundamentals are subject to distributional shifts that affect their means, but not their variances. We illustrate the usefulness of our results with a series of applications to (1) the cyclicality of the cross-sectional dispersions of macroeconomic variables, (2) the dispersion of MRPKs, (3) security pricing, and (4) endogenous uncertainty in Bayesian inference problems.

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Vivek Bhattacharya, Lucas Manuelli, and Ludwig Straub. 5/2018. “Imperfect Public Monitoring with a Fear of Signal Distortion.” Journal of Economic Theory, 175, Pp. 1-37. Publisher's VersionAbstract

This paper proposes a model of signal distortion in a two-player game with imperfect public monitoring. We construct a tractable theoretical framework where each player has the opportunity to distort the true public signal and each player is uncertain about the distortion technologies available to the other player. We show that when players evaluate strategies according to their worst-case guarantees—i.e., are ambiguity averse over certain distributions in the environment—perceived continuation payoffs endogenously lie on a positively sloped line. We then provide examples showing that, counterintuitively, identifying deviators can be harmful in enforcing a strategy profile; moreover, we illustrate how the presence of such signal distortion can sustain cooperation when it is impossible in standard settings. We show that the main result and examples are robust to a number of natural modifications to our setting. Finally, we extend our model to a repeated game where our concept is a natural generalization of strongly symmetric equilibria. In this setting, we prove an anti-folk theorem, showing that payoffs under our equilibrium concept are under general conditions bounded away from efficiency.

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