Working Papers

A Deep Learning Algorithm for High-Dimensional Dynamic Programming Problems (With Jesús Fernández-Villaverde, Galo Nuño and George Sorg-Langhans) [Preliminary Draft]

To answer a wide range of important economic questions, researchers must solve high-dimensional dynamic programming problems. This is particularly true in models designed to account for granular data. To break the ``curse of dimensionality'' associated with these high-dimensional dynamic programming problems, we propose a deep-learning algorithm that efficiently computes a global solution to this class of problems. Importantly, our method does not rely on integral approximation, instead efficiently calculating exact derivatives. We evaluate our methodology in a standard neoclassical growth model and then demonstrate its power in two applications: a multi-location model featuring 50 continuous state variables and a migration model with 75 continuous state variables.

What Are You Talking About Mr. President? - Topic Modeling for the Economic Reports of the President (With George Sorg-Langhans)

Despite their power, modern natural language processing techniques have not found widespread use in the economic literature. In this paper we demonstrate their potential in the context of a specific economic application, namely the analysis of the Economic Reports of the President. Specifically, we use both Non-Negative Matrix Factorization and Latent Dirichlet Allocation to extract and study the main topics of each presidential report. Whilst both approaches broadly agree on the topics, the NMF proves more versatile. Overall, the topics we identify are well-defined and display remarkable time series patterns, documenting both long-run economic trends and highlighting specific policy events. Based on these findings, the Economic Reports in combination with natural language processing techniques thus present a fertile ground for future research.

Government Policies in a Granular Global Economy (With Cecile Gaubert and Oleg Itshkoki) [Preliminary Draft]

Large firms play a pivotal role in the global economy, shaping the production and export of countries. We use the international granular model developed and quantified in Gaubert and Itskhoki (2020) to study the rationale and implications of three types of government interventions in this context: antitrust, trade and industrial policies. We find that governments face an incentive to use overly lenient antitrust regulation of large domestic firms. It substitutes for beggar-thy-neighbor trade policy, in particular in the most granular sectors with strong comparative advantage. Second, we study the optimal industrial policy of subsidizing national champions. We show it is generally suboptimal in closed economies as it leads to an excessive build-up of market power, but it becomes unilaterally welfare improving in open economies. Finally, we also find that governments face strong incentives to target trade policy at large individual foreign exporters rather than entire import sectors. Doing so largely transforms the domestic burden of tariffs into a reduction of foreign producer surplus. In all three cases, we characterize the unilateral optimal policies, the global Nash equilibrium, as well as the coordinated globally optimal policy. We emphasize the need for international policy coordination in these domains.

Inequality at the Top: Down to the Roots (With Riccardo Cioffi and George Sorg-Langhans)

Multiple theories of inequality compete to explain U.S. wealth inequality and the share of wealth held by the top one percent. To what extent does it matter which of these models we rely on? In this paper we analyze the responses of the different theories to a host of policy experiments. To this end, we form a quantitative model that nests the competing channels and assesses the effects of policy experiments by sequentially shutting off all but one of these model mechanisms. Our model is calibrated on the wealth distribution which allows us to starkly contrast the different theories and clearly understand the mechanisms at work. We find that it indeed matters how one models inequality as the individual channels have significantly different predictions, in both sign and magnitude, about the outcomes of the policy experiments.

Work in Progress

The Dual Role of Migration - Insurance and Volatility in the Schengen Area (With Jesús Fernández-Villaverde, Galo Nuño and George Sorg-Langhans)

Changes in net migration are a key, but often overlooked, margin through which economies absorb aggregate shocks. This mechanism is particularly important for countries within free movement zones like the Schengen area in Europe. After a country receives an asymmetric negative aggregate shock, its citizens can easily migrate to other countries in the free movement zone, lowering labor supply locally and increasing it abroad. Recent work has shown that changes in net migration were, in fact, a major adjustment margin during the European Debt Crisis of 2009-2014. In order to understand the implications of these migration patterns, measure their welfare implications, and gauge their consequences for optimal policy design, we build a large-scale business cycle model of the Schengen Area that incorporates migration decisions across different countries. This naturally gives rise to a high-dimensional problem, which the previous migration literature was not able to solve due to the “curse of dimensionality.” By applying the deep-learning algorithm developed in Fernández-Villaverde, Nuño, Sorg-Langhans, and Vogler (2020), we overcome this “curse of dimensionality.” We investigate the propagation of economic shocks in this model. A vital aspect of our investigation is taking into account the effect of the composition and size of the union. Interestingly, through its membership in such a zone, a country can import or export a substantial amount of unemployment, even in the absence of domestic shocks. This implies that the composition of the migration zone matters, as countries with volatile business cycles receive insurance from the membership while those with more stable business cycles can import volatility.

The Causal Effect of Taxation on Growth - A Machine-Learning Approach (With George Sorg-Langhans)

The impact of taxation on economic growth has been one of the predominant economic questions and has given rise to entire ideologies and fierce political fights. Given the importance of this question, it might seem surprising that there is still little agreement in the economic literature about the size of this causal effect. This is mainly due to the rampant endogeneity problems plaguing any empirical study in this field. In this paper, we contribute to the rich empirical literature by utilizing recent advances in machine-learning approaches to natural language processing. In particular, we analyze the Economic Reports of the President using Non-Negative Matrix Factorization to identify exogenous policy shocks in the spirit of Romer and Romer (2010). In contrast to previous studies, our approach is fully objective, easily replicable and can incorporate new data without complications.