Working Paper
Baqaee, David, and Emmanuel Farhi. 2019. “Productivity and Misallocation in General Equilibrium”. Abstract
We provide a general non-parametric formula for aggregating microeconomic shocks in general equilibrium economies with distortions such as  taxes, markups, frictions to resource reallocation, and nominal rigidities. We show that the macroeconomic impact of a shock can be boiled down into two components: its ``pure'' technology effect; and its effect on allocative efficiency arising from the reallocation of resources, which can be measured via changes in factor income shares. We derive a formula showing how these two components are determined by structural microeconomic parameters such as elasticities of substitution, returns to scale, factor mobility, and network linkages. Overall, our results generalize those of Solow (1957) and Hulten (1978) to economies with distortions. As examples, we pursue some applications focusing on markup distortions. We operationalize our non-parametric results and show that improvements in allocative efficiency account for about 50% of measured TFP growth over the period 1997-2015. We implement our structural results and conclude that eliminating markups would raise TFP by about 20%, increasing the economywide cost of monopoly distortions by two orders of magnitude compared to the famous 0.1% estimate by Harberger (1954).
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Revise and resubmit, Quarterly Journal of Economics.
Baqaee, David, and Emmanuel Farhi. 2019. “Networks, Barriers, and Trade”. Abstract
We study a non-parametric class of trade models with global production networks. We characterize their properties in terms of interpretable and measurable sufficient statistics. We provide both reduced-form results for measuring the sources of growth and structural results for conducting counterfactuals. Our main objectives are to show how commonly-used stylized models can give misleading results because of simplifying assumptions regarding intermediate inputs, factors, elasticities, and distortions, and to show how more complex models that do not rest on these assumptions work. As an example, 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. As another example, models with value-added production functions, no matter how well-calibrated, are incapable of simultaneously predicting the costs of tariff and non-tariff barriers to trade. Accounting for intermediates doubles the losses from tariffs, and this magnification is due to the double-marginalization of tariffs caused by global value chains and the fact that intermediates endogenously raise the elasticity of quantities with respect to 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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Baqaee, David, and Emmanuel Farhi. 2019. “A Short Note on Aggregating Productivity”.
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Baqaee, David, and Emmanuel Farhi. 2018. “The Microeconomic Foundations of Aggregate Production Functions”. 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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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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Traditional banking is built on four pillars: SME lending, access to
public liquidity, deposit insurance, and prudential supervision.  This paper unveils the logic of the quadrilogy by putting core services to "special depositors and borrowers" at the heart of the analysis, and makes room for bank and depositor implicit and explicit guarantees. It analyzes how prudential regulation must adjust to the emergence of shadow banking. The model also rationalizes ring fencing between regulated and shadow banking and the sharing of liquidity in centralized platforms to counter syphoning and financial contagion.
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Revise and resubmit, Review of Economic Studies.
Farhi, Emmanuel, and Xavier Gabaix. 2017. “Optimal Taxation with Behavioral Agents”. Abstract

This paper develops a theory of optimal taxation with behavioral agents. We use a general behavioral framework that encompasses a wide range of behavioral biases such as misperceptions, internalities and mental accounting. We revisit the three pillars of optimal taxation: Ramsey (linear commodity taxation to raise revenues and redistribute), Pigou (linear commodity taxation to correct externalities) and Mirrlees (nonlinear income taxation). We show how the canonical optimal tax formulas are modified and lead to a rich set of novel economic insights. We also show how to incorporate nudges in the optimal taxation frameworks, and jointly characterize optimal taxes and nudges. We explore the Diamond-Mirrlees productive efficiency result and the Atkinson-Stiglitz uniform commodity taxation proposition, and find that they are more likely to fail with behavioral agents.

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Revise and resubmit, American Economic Review.

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. “The Macroeconomic Impact of Microeconomic Shocks: Beyond Hulten's Theorem.” Econometrica. Abstract

We provide a nonlinear characterization of the macroeconomic impact of microeconomic productivity shocks in terms of reduced-form non-parametric elasticities for efficient economies. We also show how structural microeconomic parameters are mapped to these reduced-form general equilibrium elasticities. In this sense, we extend the foundational theorem of Hulten (1978) beyond first-order terms to capture nonlinearities. Key features ignored by first-order approximations that play a crucial role are: structural elasticities of substitution, network linkages, structural returns to scale, and the extent of factor reallocation. In a business-cycle calibration with sectoral shocks, nonlinearities magnify negative shocks and attenuate positive shocks, resulting in an aggregate output distribution that is asymmetric (negative skewness), fat-tailed (excess kurtosis), and has a lower mean, even when shocks are symmetric and thin-tailed. Average output losses due to short-run sectoral shocks are an order of magnitude larger than the welfare cost of business cycles calculated by Lucas1(987). Nonlinearities can also cause shocks to critical sectors to have disproportionate macroeconomic effects, almost tripling the estimated impact of the 1970s oil shocks on world aggregate output. Finally, in a long-run growth context, nonlinearities, which underpin Baumol's cost disease, account for a 20 percentage point reduction in aggregate TFP growth over the period 1948-2017 in the US.

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Farhi, Emmanuel, and Matteo Maggiori. Forthcoming. “China vs. U.S.: IMS Meets IPS.” American Economic Review, Papers and Proceedings. Abstract
Currently both the International Monetary System (IMS) and the International Price Systems (IPS) are dominated by the U.S. The emergence of China, both as reserve currency and as a currency of invoicing, is likely to disrupt this status quo. We provide a framework to understand the forces that will shape this transition and identify sources of instability. We highlight the risk of an abrupt shift triggered by a run on the dollar.
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Farhi, Emmanuel, and Francois Gourio. Forthcoming. “Accounting for Macro-Finance Trends: Market Power, Intangibles, and Risk Premia.” Brookings Papers on Economic Activity.
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Barbiero, Omar, Emmanuel Farhi, Gita Gopinath, and Oleg Itskkoki. Forthcoming. “The Macroeconomics of Border Taxes.” NBER Macroeconomics Annual.
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