This paper develops a gradient-based optimization method to estimate stochastic dynamic models in economics and finance and assess identification globally. By extending the state space to include all model parameters and approximating the mapping between parameters and moments, we only need to solve the model once to structurally estimate parameters. We approximate the mapping between parameters and moments by training a neural network on model-simulated data and then use this mapping to find the set of parameters that minimizes a function of the distance between model and data moments. We show how the mapping between parameters and moments can also be used to assess identification globally, detecting issues that a local diagnostic would miss. We illustrate the algorithm by solving and estimating a dynamic corporate finance model with endogenous investment, costly equity issuance, and capital adjustment costs. In this application, our method reduces the estimation time from many hours to a few minutes.

In many areas of economics, relatively simple models developed for insight are used as quantitative guides. We study the accuracy of such simple quantitative guidance in an area where it has been widely adopted — lifecycle portfolio choice among stocks, bonds, and liquid accounts — by developing a machine-learning algorithm to solve for optimal portfolio choice in a calibrated lifecycle model that includes many features of reality modeled only separately in previous work. Both for optimizing households and for households that under-save, the average fully optimal portfolio at each age conforms well to current simple age-dependent prescriptive rules until shortly before retirement, validating existing analyses. We further show that the consumption-equivalent losses from conditioning portfolio shares on age alone are substantial, around 2 to 3 percent of consumption. Fully optimal equity shares have substantial heterogeneity, particularly by wealth level, state of the business cycle, and dividend-price ratio, implying substantial gains to further customization in these dimensions.

Media: Wall Street Journal, Morningstar

U.S. mortgage borrowers are "locked in'': unwilling to sell their house and move, as that would require giving up low fixed mortgage rates for higher current rates. We study the general equilibrium effects of mortgage lock-in on house prices, mobility, and homeownership and evaluate policies aimed at unlocking mortgage lock-in. To do so, we design a spatial housing ladder model that captures moving patterns across different housing market segments. Households can move between locations differing in economic opportunity and cost of living, and within the housing ladder by deciding whether to rent, own a starter home, or own a trade-up home. In equilibrium, house prices and rents are endogenously determined by household mobility within and between locations, and are thus impacted by lock-in. We provide new empirical evidence on moving behavior along the housing ladder and over the life cycle and calibrate the model with rich microdata from 2024. While higher rates reduce the demand of households who would otherwise move up the housing ladder, we show that mortgage lock-in substantially reduces downsizing and exits from homeownership, increasing net demand for housing and resulting in higher house prices. We further evaluate the equilibrium effects of the proposed 2024 Mortgage Relief Credit, which would provide a $10,000 subsidy to sellers of starter homes. We find that the policy modestly increases first-time home buying and has larger effects on upward mobility at the top of the housing ladder. However, upward mobility within the housing ladder comes at the cost of renters and starter homeowners moving from high- to low-opportunity areas, as house prices in higher-priced areas increase.

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Media: NPR Planet Money (The Indicator), NPR Planet Money, NPR Morning Edition