Research Papers

Abstract: We develop a new method to globally solve and estimate search and matching models with aggregate shocks and heterogeneous agents. We characterize general equilibrium as a high-dimensional partial differential equation with the distribution as a state variable. We then use deep learning to solve the model and estimate economic parameters using the simulated method of moments. This allows us to study a wide class of search markets where the distribution affects agent decisions and compute variables (e.g. wages and prices) that were previously unattainable. In applications to labor search models, we show that distribution feedback plays an important role in amplification and that positive assortative matching weakens in prolonged expansions, disproportionately benefiting low-wage workers.

Presentations: NBER Summer Institute, ASU, Atlanta Fed, Chicago, CKGSB, Copenhagen, EIEF, HEC Lausanne, HKU, Norges Bank, NYU, PKU, PSE, Rice, St. Gallen, Tsinghua, Yale, Zurich; AMLEDS, ASSA, Econometric Society DSE 2023 Conference on "Deep Learning for Solving and Estimating Dynamic Models", EEA-ESEM Invited Session on "Machine Learning and Macroeconomic Analysis", Minnesota Finance Junior Conference, Swiss Winter Conference on Macroeconomics and Finance, T2M, SFI, Zurich Workshop on the Frontier of Quantitative Macro, CEF, CICM, SED, Philly Fed-Chicago Booth Conference on Frontiers in Machine Learning and Economics, Frankfurt Workshop on Numerical Methods in Macroeconomics, DC Search & Matching Workshop.

Abstract: We develop a new method to efficiently solve for optimal lotteries in models with non-convexities. In order to employ a Lagrangian framework, we prove that the value of the saddle point that characterizes the optimal lottery is the same as the value of the dual of the deterministic problem. Our algorithm solves the dual of the deterministic problem via sub-gradient descent. We prove that the optimal lottery can be directly computed from the deterministic optima that occur along the iterations. We analyze the computational complexity of our algorithm and show that the worst case complexity is order of magnitudes better than the one arising from a linear programming approach. We apply the method to two canonical problems with private information. First, we solve a principal-agent moral hazard problem, demonstrating that our approach delivers substantial improvements in speed and scalability over traditional linear programming methods. Second, we study an optimal taxation problem with hidden types, which was previously considered computationally infeasible, and show when the optimal contract will involve lotteries.

Presentations: BSE Summer Forum, ES World Congress, SED, SFI Research Day, Warwick.

Abstract: We propose an efficient, reliable, and interpretable global solution method, the Deep learning-based algorithm for Heterogeneous Agent Models (DeepHAM), for solving high dimensional heterogeneous agent models with aggregate shocks. The state distribution is approximately represented by a set of optimal generalized moments. Deep neural networks are used to approximate the value and policy functions, and the objective is optimized over directly simulated paths. In addition to being an accurate global solver, this method has three additional features. First, it is computationally efficient in solving complex heterogeneous agent models, and it does not suffer from the curse of dimensionality. Second, it provides a general and interpretable representation of the distribution over individual states, which is crucial in addressing the classical question of whether and how heterogeneity matters in macroeconomics. Third, it solves the constrained efficiency problem as easily as it solves the competitive equilibrium, which opens up new possibilities for normative studies. As a new application, we study constrained efficiency in heterogeneous agent models with aggregate shocks. We find that in the presence of aggregate risk, a utilitarian planner would raise aggregate capital for redistribution less than in absence of it because poor households do more precautionary savings and thus rely less on labor income.

Presentations: Stanford SITE, Yale, Federal Reserve Bank of Philadelphia, Princeton, UPenn, Zurich, ETH Zurich, Rutgers, HKU, CUHK, PKU, Tsinghua, Guelph, SDU, T2M (King's College London), 2022 CEA (Carleton), 2022 ES {North America, Asia} Meetings, 2022 CICM, CES Rising star, HKUST-Jinan Workshop, EEA-ESEM, CESifo, FRB Conference on "Nontraditional Data, Machine Learning, and Natural Language Processing in Macroeconomics", BSE Summer Institute.

Abstract: Inflation has heterogeneous impacts on households, which then affects optimal monetary policy design. I study optimal monetary policy rules in a quantitative heterogeneous agent New Keynesian (HANK) model where inflation has redistributive effects on households through their different (1) consumption baskets, (2) nominal wealth positions, and (3) earnings elasticities to business cycles. I parameterize the model based on the empirical analysis of these channels using the most recent data. Unlike in representative agent models, a utilitarian central bank should adopt an asymmetric monetary policy rule that is accommodative towards inflation and aggressive towards deflation. Specifically, by accommodating stronger demand and higher inflation, the central bank benefits low-income and low-wealth households through nominal debt devaluation and higher earnings growth.

Presentations: Princeton, Zurich, UNC Chapel Hill, Bank of Canada, Rice, St Gallen, U Houston, Baruch, NUS, HKU, CUHK {Econ, Finance}, PKU {Guanghua, HSBC, INSE, Econ}, Tsinghua, Sveriges Riksbank, Macro Finance Society Workshop, CEBRA, CICF, CES, AEA 2024.

Abstract: The current knowledge system of macroeconomics is built on interactions among a small number of variables, since traditional macroeconomic models can mostly handle a handful of inputs. Recent work using big data suggests that a much larger number of variables are active in driving the dynamics of the aggregate economy. However, most of such work is model-free and purely data driven. To integrate human knowledge with high dimensional statistical modeling, we build a knowledge graph (KG) that consists of not only linkages between traditional economic variables but also new alternative big data variables. We propose an active learning natural language processing (NLP) algorithm to extract these variables and linkages from the massive textual data of academic literature and research reports. The KG provides a systematic approach to incorporate human knowledge when dealing with a large number of variables in macroeconomic models. For example, in macroeconomic forecasting, we use the KG as the prior knowledge to select variables as model inputs. When applied to inflation and investment forecasts, the KG-based method achieves significantly higher accuracy, especially for long run forecasts, compared to statistical variable selection methods.

Presentations: Banca d'Italia and Federal Reserve Board Conference, Federal Reserve Bank of Philadelphia, Her Majesty's Treasury, Monash-Warwick-Zurich Text-as-Data Workshop, 2021 SoFiE Machine Learning Workshop, 21st IWH-CIREQ-GW Macroeconometric Workshop, RES 2021, 2021 ESCoE, 2021 AMES. 

Abstract: The speed at which the US economy has recovered from recessions ranges from months to years. We propose a model incorporating the innovation network, the production network, and cross-sectional shocks and show that their interactions jointly explain large variations in the recovery speed across recessions in the US. In the model, besides the production linkages, firms learn insights on production from each other through the innovation network. We show when the innovation network takes a low-rank structure, there exists one key direction: the impact a shock becomes persistent only if the shock is parallel to this key direction; in contrast, the impact declines quickly if the shock follows other directions. Empirically, we estimate the model in a state-space form and document a set of new stylized facts of the US economy. First, the innovation network among sectors takes a low-rank structure. Second, the innovation network has non-negligible overlap with the production network. Third, recessions with slow recovery are those witnessing sizable negative shock to sectors in the center of the innovation network. Such network structures and the time-varying sectoral distribution of the shocks can well explain the large variation in the recovery speed across recessions in the US. Finally, to emphasize the prevalence of the channel, we explore the application of the theory in asset pricing.

Presentations: Princeton Macro Workshop, 2021 AMES.