The ongoing revolution in deep learning is reshaping research across many fields, including economics. Its effects are especially clear in solving dynamic economic models. These models often lack closed-form solutions, so economists have long relied on numerical methods such as value function iteration, perturbation, and projection techniques. Unfortunately, these approaches suffer from the curse of dimensionality, which makes global solutions computationally infeasible as the number of state variables increases. Deep learning offers a different approach: flexible tools that solve dynamic economic models by minimizing residuals in equilibrium conditions and that can handle high-dimensional problems. This development promises to broaden the scope of quantitative economics. I illustrate the approach using the neoclassical growth model.

Ray Fair's Estimating How the Macroeconomy Works is the latest in a series of books by Fair that build, estimate, and apply his macroeconometric model to study the U.S. economy. In this book, Fair updates the model to incorporate the most recent data and uses it to analyze several important empirical questions, such as whether the U.S. economy moved into a new age of high productivity in the last half of the 1990s and the dynamics of prices, output, and unemployment. This review places his work in the context of the historical evolution of aggregate econometric models, compares it with the current developments in the estimation of dynamic stochastic general equilibrium models, and discusses some salient aspects of Fair's contributions.

What are the effects of fiscal policy in the presence of financial frictions? This question is particularly relevant given the great recession of 2008–2009, how forcefully some governments have resorted to fiscal stimulus over the last two years to fight it, and the widespread view that financial markets have played a decisive role in our current economic problems. To analyze this topic, I build a dynamic stochastic general equilibrium (DSGE) model with financial frictions and fiscal policy, calibrate it to observations of the US economy, and compute the response of output to several fiscal shocks. I. A DSGE Model with Financial Frictions and Fiscal Policy Due to space constraints, I will only briefly describe the main elements of the model that I employ for my investigation. The interested reader can find a more detailed exposition in Fernández-Villaverde (2010). Suffice it to say in terms of motivation that the model is based on the work

This paper shows how particle filtering facilitates likelihood-based inference in dynamic macroeconomic models. The economies can be non-linear and/or non-normal. We describe how to use the output from the particle filter to estimate the structural parameters of the model, those characterizing preferences and technology, and to compare different economies. Both tasks can be implemented from either a classical or a Bayesian perspective. We illustrate the technique by estimating a business cycle model with investment-specific technological change, preference shocks, and stochastic volatility.

We document five novel facts about the role of search effort in forming trading relationships among firms by combining a variety of micro and macro datasets. These facts strongly suggest the presence of search complementarities. To study the implications of these facts for aggregate fluctuations, we build a dynamic general equilibrium model, disciplined by our new firm-level evidence on search effort. The model matches key aspects of the macro and micro data that have remained unaccounted for by standard models, including the time-varying bimodal distribution of output and the strong, nonlinear propagation of shocks. Also, changes to the volatility of shocks have nonlinear effects on macroeconomic fluctuations that advance a novel interpretation of the Great Moderation. Finally, we provide a new account of the state-dependent effects of fiscal policy.

This paper uses Consumer Expenditure Survey data and a seminonparametric statistical model to estimate life-cycle profiles of consumption, controlling for demographics, cohort, and time effects. We construct age profiles for total and nondurable consumption as well as expenditure patterns for consumer durables. Special emphasis is placed on the comparison of different approaches to control for changes in demographics over the life cycle. We find significant humps over the life cycle for total, nondurable, and durable expenditures. Changes in household

We postulate a continuous‐time heterogeneous agent model with a financial sector and households to study the nonlinear linkages between aggregate and financial variables. In our model, the interaction between the supply of bonds by the financial sector and the precautionary demand for bonds by households produces significant endogenous aggregate risk . This risk makes the economy transition between a high‐leverage region and a low‐leverage region, which, in turn, creates state dependence in impulse responses: the same shock starting from the high‐leverage region gets propagated and amplified more than when the shock arrives when leverage is low. State dependence in impulse responses generates a time‐varying aggregate precautionary savings motive that, by moving the risk‐free rate, justifies the leverage level of the financial sector in each region. Finally, we illustrate the usefulness of neutral networks to solve for the nonlinear perceived law of motion of the model, and the importance of household heterogeneity in driving its quantitative properties.

We study how unexpected changes in uncertainty about fiscal policy affect economic activity. First, we estimate tax and spending processes for the United States with time-varying volatility to uncover evidence of time-varying volatility. Second, we estimate a VAR for the US economy using the time-varying volatility found in the previous step. Third, we feed the tax and spending processes into an otherwise standard New Keynesian model. Both in the VAR and in the model, we find that unexpected changes in fiscal volatility shocks can have a sizable adverse effect on economic activity. An endogenous increase in markups is a key mechanism.

We show how changes in the volatility of the real interest rate at which small open emerging economies borrow have an important effect on variables like output, consumption, investment, and hours. We start by documenting the strong evidence of time-varying volatility in the real interest rates faced by four emerging economies: Argentina, Brazil, Ecuador, and Venezuela. We estimate a stochastic volatility process for real interest rates. Then, we feed this process in a standard small open economy business cycle model. We find that an increase in real interest rate volatility triggers a fall in output, consumption, investment, hours, and debt.

This article studies the pruned state-space system for higher-order perturbation approximations to dynamic stochastic general equilibrium (DSGE) models. We show the stability of the pruned approximation up to third order and provide closed-form expressions for first and second unconditional moments and impulse response functions. Our results introduce generalized method of moments (GMM) estimation and impulse-response matching for DSGE models approximated up to third order and provide a foundation for indirect inference and simulated method of moments (SMM). As an application,we consider a New Keynesian model with Epstein–Zin preferences and two novel feedback effects from long-term bonds to the real economy, allowing us to match the level and variability of the 10-year term premium in the U.S. with a low relative risk aversion of 5.