Working Paper
Veronica Guerrieri, Guido Lorenzoni, Ludwig Straub, and Ivan Werning. Working Paper. “Monetary Policy in Times of Structural Reallocation”.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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Prepared for the 2021 Jackson Hole Symposium
Atif Mian, Ludwig Straub, and Amir Sufi. Working Paper. “What explains the decline in r*? Rising income inequality versus demographic shifts”.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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Prepared for the 2021 Jackson Hole Symposium.
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 Policy”.Abstract

When an economy is close to the zero lower bound on nominal interest rates, governments face a trade-off: excessively conservative fiscal policy risks persistently low output but aggressive fiscal expansion raises sustainability concerns. This study builds a framework of dynamic fiscal policy, showing that there exists a Goldilocks zone in which deficits are permanent but not too high, the nominal interest rate on government debt (R) is lower than the economy’s growth rate (G), government debt levels can be substantial, and deficits allow the economy to overcome weak demand to achieve potential output. The size of the Goldilocks zone can be estimated using empirically observed moments in the data, which suggest for the United States that government debt to GDP ratios can reach a maximum of about 250% in the Goldilocks zone, but the maximum permanent government deficit is only about 2% of GDP. In the model, R and G are endogenous to fiscal policy, which disciplines the ability of a government to boost deficits even if R < G. The Goldilocks zone is fragile: it can vanish in the face of a decline in potential GDP growth, a rise in aggregate demand, or a decline in income inequality.

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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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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. “Macroeconomic Implications of COVID-19: Can Negative Supply Shocks Cause Demand Shortages.” American Economic Review.Abstract
We present a theory of Keynesian supply shocks: supply shocks that trigger changes in aggregate demand larger than the shocks themselves. We argue that the economic shocks associated to the COVID-19 epidemic—shutdowns, layoffs, and firm exits—may have this feature. In one-sector economies supply shocks are never Keynesian. We show that this is a general result that extend to economies with incomplete markets and liquidity constrained consumers. In economies with multiple sectors Keynesian supply shocks are possible, under some conditions. A 50% shock that hits all sectors is not the same as a 100% shock that hits half the economy. Incomplete markets make the conditions for Keynesian supply shocks more likely to be met. Firm exit and job destruction can amplify the initial effect, aggravating the recession. We discuss the effects of various policies. Standard fiscal stimulus can be less effective than usual because the fact that some sectors are shut down mutes the Keynesian multiplier feedback. Monetary policy, as long as it is unimpeded by the zero lower bound, can have magnified effects, by preventing firm exits. Turning to optimal policy, closing down contact-intensive sectors and providing full insurance payments to affected workers can achieve the first-best allocation, despite the lower per-dollar potency of fiscal policy.
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Atif Mian, Ludwig Straub, and Amir Sufi. Forthcoming. “Indebted Demand.” Quarterly Journal of Economics.Abstract
We propose a theory of indebted demand, capturing the idea that large debt burdens by households and governments lower aggregate demand, and thus natural interest rates. At the core of the theory is the simple yet under-appreciated observation that borrowers and savers differ in their marginal propensities to save out of permanent income. Embedding this insight in a two-agent overlapping-generations model, we find that recent trends in income inequality and financial liberalization lead to indebted household demand, pushing down natural interest rates. Moreover, popular expansionary policies—such as accommodative monetary policy and deficit spending—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. We document that the behavior of our model is in line with several recent empirical facts and discuss policies to reduce demand indebtedness.
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Adrien Auclert, Bence Bardóczy, Matthew Rognlie, and Ludwig Straub. Forthcoming. “Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models.” Econometrica, Forthcoming.Abstract
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 and composition of sequence-space Jacobians—the derivatives of perfect-foresight equilibrium mappings between aggregate sequences around the steady state. We provide a fast algorithm for computing Jacobians for heterogeneous agents, a technique to substantially reduce dimensionality, a rapid procedure for likelihood-based estimation, a determinacy condition for the sequence space, and a method to solve 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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Sebastián Fanelli and Ludwig Straub. Forthcoming. “A Theory of Foreign Exchange Interventions.” Review of Economic Studies.Abstract

This paper develops a theory of foreign exchange interventions in a small open economy with limited capital mobility. Home and foreign bond markets are segmented and intermediaries are limited in their capacity to arbitrage across markets. As a result, the central bank can implement nonzero spreads by managing its portfolio. Crucially, spreads are inherently costly, over and above the standard costs from distorting households' consumption profiles. The extra term is given by the carry-trade profits of foreign intermediaries, is convex in the spread—as more foreign intermediaries become active carry traders—and increasing in the openness of the capital account—as foreign intermediaries find it easier to take larger positions. Optimal interventions balance these costs with terms of trade benefits. We show that they lean against the wind of global capital flows to avoid excessive currency appreciation. Due to the convexity of the costs, interventions should be small and spread out, relying on credible promises (forward guidance) of future interventions. By contrast, excessive smoothing of the exchange rate path may create large spreads, inviting costly speculation. Finally, in a multi-country extension of our model, we find that the decentralized equilibrium features too much reserve accumulation and too low world interest rates, highlighting the importance of policy coordination.

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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.Abstract

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 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 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 non-constant (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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