Working Paper
Adrien Auclert, Matthew Rognlie, and Ludwig Straub. In Preparation. “Micro Jumps, Macro Humps: Monetary Policy and Business Cycles in an Estimated HANK Model”.
Ludwig Straub. In Preparation. “Private Debt Traps”.Abstract
In the last 30 years, the world economy has shifted to a “new normal”, with interest rates at record lows and private debt relative to GDP at record highs. In this project, I provide a novel perspective on these two shifts, interactions among them and policy implications. The starting point is the simple yet underappreciated observation that borrowers and savers differ in their marginal propensities to save (MPS) out of permanent income. I propose a highly tractable borrower-saver economy in which savers have a higher MPS. The economy naturally generates the potential for a second stable steady state—a “private debt trap”—characterized by low interest rates and high levels of private debt. I show that factors, such as rising labor income inequality, a slowdown in growth, financial deregulation, or “too low for too long” monetary policy, push the economy towards the trap. Once in it, the model illustrates how several policies can facilitate a “lift off” from the trap (redistributive taxation, “helicopter money”, debt amnesty), while others hinder it (public debt overhang, government-financed borrower bailouts). Last but not least, I derive ex-ante policy principles, designed to keep economies from falling into the trap in the first place.
Adrien Auclert, Bence Bardóczy, Matthew Rognlie, and Ludwig Straub. 2019. “Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models”.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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Michael Fishman, Jonathan Parker, and Ludwig Straub. 2019. “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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Sebastián Fanelli and Ludwig Straub. 2019. “A Theory of Foreign Exchange Interventions”.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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Revise and resubmit at Review of Economic Studies
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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Ludwig Straub and Robert Ulbricht. 2018. “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. 2018. “The Intertemporal Keynesian Cross”. Download Paper
Revise and resubmit at Journal of Political Economy
Journal Article
Ludwig Straub and Iván Werning. Forthcoming. “Positive Long-Run Capital Taxation: Chamley-Judd Revisited.” American Economic Review.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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