Working Paper
We study supply and demand shocks in a general disaggregated model with multiple sectors, factors, and input-output linkages, as well as downward nominal wage rigidities and a zero lower bound constraint. We use the model to understand how the Covid-19 crisis, an omnibus of supply and demand shocks, affects output, unemployment, and inflation, and how it leads to the coexistence of tight and slack labor markets. Under some conditions, the details of the production network can be summarized by simple sufficient statistics. We use these sufficient statistics to conduct global comparative statics. Negative sectoral supply shocks and sectoral demand shocks are stagflationary, whereas negative intertemporal demand shocks are deflationary. Complementarities magnify Keynesian spillovers for the former shocks but mitigate them for the latter. We illustrate the intuition using a nonlinear AS-AD representation. In a quantitative model of the US calibrated to current disaggregated data, sectoral supply and demand shocks on their own generate more than 10% inflation, and negative intertemporal demand shocks on their own generate 7% deflation. Both types of shocks are necessary to capture the disaggregated data, each explains about half the reduction in real GDP, and putting both together results in 0.3% inflation and as much as 8.5% Keynesian unemployment in April 2020. Nevertheless, aggregate demand stimulus is only about a third as effective as in a typical recession where all labor markets are slack. More targeted forms of demand stimulus are more effective.
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We study the effects of negative supply shocks and shocks to the composition of final demand on aggregate output in a disaggregated neoclassical model with multiple sectors, factors, and input-output linkages. We show how nonlinearities associated with complementarities in consumption and production amplify the effect of negative supply shocks by creating supply bottlenecks and disrupting supply chain networks. These nonlinearities are particularly potent when the shocks are more heterogeneous as the worst-affected sectors drag down the other sectors. Nonlinearities are strengthened when changes in preferences lead households to tilt the composition of their demand towards the crippled sectors directly and indirectly through their supply chains. And nonlinearities are further intensified
when factors cannot easily be reallocated across sectors to reinforce weak links. A quantitative investigation suggests that nonlinearities may amplify the impact of the Covid-19 shock by between 10%-100%, depending on the horizon of analysis and the exact size of the shocks.
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Baqaee, David, and Emmanuel Farhi. 2020. “The Darwinian Returns to Scale”. Abstract
How does an increase in the size of the market due to fertility, immigration, or trade integration, affect welfare and GDP? We study this question using a model with heterogeneous firms, fixed costs, and monopolistic competition. We show how the shape of residual demand curves endogenously determines the variation of markups with firm size and the inefficiency of the decentralized equilibrium. We decompose changes in welfare from increased scale into changes in technical efficiency and changes in allocative efficiency due to reallocation. We non-parametrically identify residual demand curves with firm-level data and, using these estimates, quantify our theoretical results. We find that somewhere between 70% to 90% of the aggregate returns to scale are due to changes in allocative efficiency. In bigger markets, competition endogenously toughens and triggers Darwinian reallocations: big firms expand, small firms shrink and exit, and new firms enter. However, important as they are, the improvements in allocative efficiency are not primarily driven by oft-emphasized reductions in markups or deaths of unproductive firms. Instead, they are mostly caused by a composition effect that reallocates resources from low-markup to high-markup firms. Our analysis implies that the aggregate return to scale is an endogenous outcome shaped by frictions and market structure and likely varies with time, place, and policy. Furthermore, even mild increasing returns to scale at the micro level can give rise to large increasing returns to scale at the macro level. 
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Baqaee, David, and Emmanuel Farhi. 2020. “Entry vs. Rents”. Abstract
We show that the tension between entry and rents lies at the core of a general theory of aggregation with scale effects. We characterize the responses of macro aggregates to micro shocks in disaggregated economies with general forms of entry, internal or external returns to scale, input-output linkages, and distortions. In particular, we decompose changes in aggregate productivity into changes in technical and allocative efficiency, and show that the latter depend on changes in rents and quasi-rents across markets. In addition, we give formulas for the social costs of distortions. Finally, we prove that while first-best industrial policy is network-independent, second-best policy supports the more ``networked'' parts of the economy by boosting the backward linkages of markets with high forward linkages and returns to scale. As an application, we quantify the misallocation from markups in the U.S.: accounting for entry raises the aggregate efficiency loss from 20% to 40%. This number depends sensitively on how entry is modeled, in ways that we make precise.
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Traditional banking is built on four pillars: SME lending, insured deposit
taking, access to lender of last resort, and
prudential supervision. This paper unveils the logic of the quadrilogy by showing that it emerges naturally as an equilibrium outcome in a game between banks and the government. A key insight is that regulation and public insurance services (LOLR, deposit insurance) are complementary. 
The model also shows how prudential regulation must adjust to the emergence of shadow banking, and rationalizes
structural remedies to counter financial contagion:
ring-fencing between regulated and shadow banking and the sharing
of liquidity in centralized platforms.
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Revise and resubmit, Review of Economic Studies.
Caballero, Ricardo, Emmanuel Farhi, and Pierre-Olivier Gourinchas. 2019. “Global Imbalances and Policy Wars at the Zero Lower Bound”.
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Baqaee, David, and Emmanuel Farhi. 2019. “Networks, Barriers, and Trade”. Abstract
We study a non-parametric class of neoclassical trade models with global production networks. We characterize their properties in terms of sufficient statistics useful for growth and welfare accounting as well as for counterfactuals. We establish a formal duality between open and closed economies and use it to analytically quantify the gains from trade. Accounting for nonlinear (non-Cobb-Douglas) production networks with realistic complementarities in production significantly raises the gains from trade relative to estimates in the literature. We use our general comparative statics results to show how models that abstract away from intermediates, no matter how well calibrated, are incapable of simultaneously predicting the costs of tariff and non-tariff barriers to trade. Given trade volumes and elasticities, accounting for intermediates doubles the losses from tariffs. Better quantitative accuracy demands the use of more complicated, oftentimes computational, models. This paper seeks to help bridge the gap between computation and theory.
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Revise and resubmit, Econometrica.
Baqaee, David, and Emmanuel Farhi. 2019. “A Short Note on Aggregating Productivity”.
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The goal of this paper is to simultaneously unbundle two interacting reduced-form building blocks of traditional macroeconomic models: the representative agent and the aggregate production function. We introduce a broad class of disaggregated general equilibrium models with Heterogeneous Agents and Input-Output networks (HA-IO). We characterize their properties through two sets of results describing the propagation and the aggregation of shocks. Our results shed light on many seemingly disparate applied questions, such as: sectoral comovement in business cycles; factor-biased technical change in task-based models; structural transformation; the effects of corporate taxation; and the dependence of fiscal multipliers on the composition of government spending.

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Caballero, Ricardo J., Emmanuel Farhi, and Pierre-Olivier Gourinchas. 2016. “Global Imbalances and Currency Wars at the ZLB”. Abstract

This paper explores the consequences of extremely low equilibrium real interest rates in a world with integrated but heterogenous capital markets, and nominal rigidities. In this context, we establish six main results: (i) Economies experiencing liquidity traps pull others into a similar situation by running current account surpluses; (ii) Reserve currencies have a tendency to bear a disproportionate share of the global liquidity trap--a phenomenon we dub the \reserve currency paradox;" (iii) Beggar-thy-neighbor exchange rate devaluations stimulate the domestic domestic economy at the expense of other economies; (iv) While more price and wage exibility exacerbates the risk of a
deflationary global liquidity trap, it is the more rigid economies that bear the brunt of the recession; (v) (Safe) Public debt issuances and increases in government spending anywhere are expansionary everywhere, and more so when there is some degree of price or wage exibility. We use our model to shed light on the evolution of global imbalances,interest rates, and exchange rates since the beginning of the global financial crisis.

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Farhi, Emmanuel, Samuel Fraiberger, Xavier Gabaix, Romain Ranciere, and Adrien Verdelhan. 2015. “Crash Risk in Currency Markets”. Abstract

Since the Fall of 2008, out-of-the money puts on high interest rate currencies have become significantly more expensive than out-of-the-money calls, suggesting a large crash risk of those currencies. To evaluate crash risk precisely, we propose a parsimonious structural model that includes both Gaussian and disaster risks and can be estimated even in samples that do not contain disasters. Estimating the model for the 1996 to 2014 sample period using monthly exchange rate spot, forward, and option data, we obtain a real-time index of the compensation for global disaster risk exposure. We find that disaster risk accounts for more than a third of the carry trade risk
premium in advanced countries over the period examined. The measure of disaster risk that we uncover in currencies proves to be an important factor in the cross-sectional and time-series variation of exchange rates, interest rates, and equity tail risk.




































































































































































































































































































































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Revise and resubmit, Review of Financial Studies.

Farhi, Emmanuel, and Ivan Werning. 2014. “Bequest Taxation and R-G”. Abstract
We analyze the role of the gap r-g between the return of return on capital r and the growth of the economy g rate in a political economy model of bequest taxation. Higher values of r-g lead to higher wealth inequality, and higher and more progressive optimal taxes on bequest. These conclusions hold only under certain specific but reasonable assumptions regarding the bequest motive, the relative magnitudes of bequest and labor income inequality, and the nature of the political economy process.
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Farhi, Emmanuel, and Ivan Werning. 2014. “Labor Mobility Within Currency Unions”. Abstract

We study the effects of labor mobility within a currency union suffering from nominal rigidities. When the demand shortfall in depressed region is mostly internal, migration may not help regional macroeconomic adjustment. When external demand is also at the root of the problem, migration out of depressed regions may produce a positive spillover for stayers. We consider a planning problem and compare its solution to the equilibrium. We find that the equilibrium is generally constrained inefficient, although the welfare losses may be small if the economy suffers mainly from internal demand imbalances.

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Revise and resubmit, Journal of Monetary Economics.
Caballero, Ricardo J., and Emmanuel Farhi. 2013. “A Model of the Safe Asset Mechanism (SAM): Safety Traps and Economic Policy”. Abstract

The global economy has a chronic shortage of safe assets which lies behind many recent macroeconomic imbalances. This paper provides a simple model of the Safe Asset Mechanism (SAM), its recessionary safety traps, and its policy antidotes. Public debt plays a central role in SAM as long as the government has spare fiscal capacity to back safe asset production. We show that Quantitative Easing type policies have positive effects on spreads and output. In contrast, Operation Twist type policies, where the duration of public debt held by the public is reduced, can be counterproductive. Monetary policy commitments work if they support future bad states of nature. All these policies depend on fiscal capacity. Once the latter runs out, short term cyclical policy becomes ineffective. In contrast, credible long run fiscal consolidation relaxes the fiscal capacity constraint and enhances the effectiveness of short term policy. An economy that is near its scal limits is susceptible to runs on its public debt and to destabilizing feedback loops.

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We consider a standard macroeconomic model of a small open economy with a fixed exchange rate and study optimal capital controls. We characterize their use in response to a variety of macroeconomic shocks. We show that capital controls are more effective when employed against transitory shocks and when the degree of openness (exports/GDP) is small. They are particularly effective at neutralizing risk-premium shocks that affect the interest rate differential. Although we focus on fixed exchange rates, we show that in some cases capital controls may be optimal even if the exchange rate is flexible. Finally, we compare the single country's optimum to a coordinated world solution. We find a limited need for coordination.
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Farhi, Emmanuel, Mark Aguiar, Manuel Amador, and Gita Gopinath. 2012. “Crisis and Commitment: Inflation Credibility and the Vulnerability to Sovereign Debt Crises”. Abstract
We explore the role of inflation credibility in self-fulfilling debt crises. In particular, We propose a continuous time model of nominal debt with the potential for self- fulfilling debt crises as in Calvo (1988) and Cole and Kehoe (2000). We characterize crisis equilibria conditional on the level of commitment to low inflation. With strong commitment, which can be interpreted as joining a monetary union or issuing foreign currency debt, the environment is a version of the one studied by Cole and Kehoe. The paper contrasts this framework with one in which sovereign debt is nominal and is vulnerable to ex post devaluation. Inflation is costly, but reduces the real value of outstanding debt without the full punishment of default. In a debt crisis, a government may opt to inflate away a fraction of the real debt burden rather than explicitly default. This flexibility potentially reduces the country's exposure to self-fulfilling crises. On the other hand, the government lacks commitment not to inflate in the absence of crisis. This latter channel raises the cost of debt in tranquil periods and makes default more attractive in the event of a crisis, increasing the country's vulnerability. We characterize the interaction of these two forces. We show that there is an intermediate level of commitment that minimizes the country's exposure to rollover risk. On the other hand, low inflation credibility brings the worst of both worlds --high inflation in tranquil periods and increased vulnerability to a crisis. Weak inflationary commitment also reduces the country's equilibrium borrowing limit. These latter results shed light on the notions of original sin and debt intolerance highlighted in the empirical literature; that is, the fact that developing economies issue debt exclusive in foreign currency to international investors as well as encounter solvency issues at relatively low ratios of debt-to-GDP.
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Farhi, Emmanuel, and Ivan Werning. 2008. “The Political Economy of Nonlinear Capital Taxation”. Abstract
We study efficient nonlinear taxation of labor and capital in a dynamic Mirrleesian model incorporating political economy constraints. Policies are chosen sequentially over time, without commitment, as the outcome of democratic elections. We study the best equilibrium for this dynamic game. Our main result is that the marginal tax on capital income is progressive, in the sense that richer agents face higher marginal tax rates.
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In this paper we investigate whether stock market overpricing leads to aggregate (real) inefficiencies. We first investigate a standard dynamic contracting model of investment subject to financing constraints. We show that stock market mispricing will have two robust effects on welfare: on the one hand it will distort investment decisions and lead to inefficiencies. On the other hand it will alleviate underinvestment problems and allow some efficient projects to be undertaken. We then turn to the data and investigate which of the two effects dominates at the aggregate. By using proxies for investor sentiment within a vector autoregression (VAR) we find that positive shocks to sentiment boost (real) investment while reducing aggregate profits over the long run, all else equal. We interpret this as evidence that mispricing causes more inefficiencies than it corrects.
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Journal Article
Baqaee, David, and Emmanuel Farhi. Forthcoming. “Productivity and Misallocation in General Equilibrium.” Quarterly Journal of Economics. Abstract
This paper develops a general theory of aggregation in inefficient economies. We provide non-parametric formulas for aggregating microeconomic shocks in economies with distortions such as taxes, markups, frictions to resource reallocation, financial frictions, and nominal rigidities. We allow for arbitrary elasticities of substitution, returns to scale, factor mobility, and input-output network linkages. We show how to separately measure changes in technical and allocative efficiency. We also show how to compute the social cost of distortions. We pursue applications focusing on firm-level markups in the U.S. We find that improvement in allocative efficiency, due to the reallocation over time of market share to high-markup firms, accounts for about half of aggregate TFP growth over the period 1997-2015. We also find that eliminating the misallocation resulting from the large and dispersed markups estimated in the data would raise aggregate TFP by about 20%, increasing the economy-wide cost of monopoly distortions by two orders of magnitude compared to the famous 0.1% estimate by Harberger (1954). These exact numbers should be interpreted with care since the data is imperfect and requires substantial imputation.
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Baqaee, David, and Emmanuel Farhi. Forthcoming. “The Microeconomic Foundations of Aggregate Production Functions.” Journal of the European Economic Association. Abstract
Aggregate production functions are reduced-form relationships that emerge endogenously from input-output interactions between heterogeneous producers and factors in general equilibrium. We provide a general methodology for analyzing such aggregate production functions by deriving their first- and second-order properties. Our aggregation formulas provide non-parameteric characterizations of the macro elasticities of substitution between factors and of the macro bias of technical change in terms of micro sufficient statistics. They allow us to generalize existing aggregation theorems and to derive new ones. We relate our results to the famous Cambridge-Cambridge controversy.
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Article for the BBVA lecture of the European Economic Association and the BBVA Foundation