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Consumer debt is an important means for consumption smoothing. In the United States, 70% of households own a credit card, and 40% borrow on it. When borrowers cannot (or do not want to) repay their debts, they can declare bankruptcy, which provides additional insurance in tough times. Since the 2000s, up to 1.5% of households declared bankruptcy per year. Clearly, the option to default affects borrowing interest rates in equilibrium. Consequently, when assessing (welfare) consequences of different bankruptcy regimes or providing policy recommendations, structural models with equilibrium default and endogenous interest rates are needed. At the same time, many questions are quantitative in nature: the benefits of a certain bankruptcy regime critically depend on the nature and amount of risk that households bear. Hence, models for normative or positive analysis should quantitatively match some important data moments. Four important empirical patterns are identified: First, since 1950, consumer debt has risen constantly, and it amounted to 25% of disposable income by 2016. Defaults have risen since the 1980s. Interestingly, interest rates remained roughly constant over the same time period. Second, borrowing and default clearly depend on age: both measures exhibit a distinct hump, peaking around 50 years of age. Third, ownership of credit cards and borrowing clearly depend on income: high-income households are more likely to own a credit card and to use it for borrowing. However, this pattern was stronger in the 1980s than in the 2010s. Finally, interest rates became more dispersed over time: the number of observed interest rates more than quadrupled between 1983 and 2016. These data have clear implications for theory: First, considering the importance of age, life cycle models seem most appropriate when modeling consumer debt and default. Second, bankruptcy must be costly to support any debt in equilibrium. While many types of costs are theoretically possible, only partial repayment requirements are able to quantitatively match the data on filings, debt levels, and interest rates simultaneously. Third, to account for the long-run trends in debts, defaults, and interest rates, several quantitative theory models identify a credit expansion along the intensive and extensive margin as the most likely source. This expansion is a consequence of technological advancements. Many of the quantitative macroeconomic models in this literature assess welfare effects of proposed reforms or of granting bankruptcy at all. These welfare consequences critically hinge on the types of risk that households face—because households incur unforeseen expenditures, not-too-stringent bankruptcy laws are typically found to be welfare superior to banning bankruptcy (or making it extremely costly) but also to extremely lax bankruptcy rules. There are very promising opportunities for future research related to consumer debt and default. Newly available data in the United States and internationally, more powerful computational resources allowing for more complex modeling of household balance sheets, and new loan products are just some of many promising avenues.

The effects of news (i.e., information innovations) are studied in dynamic general equilibrium models where liquidity matters. As a leading example, news can be announcements about monetary policy directions. In three standard theoretical environments—an overlapping generations model of fiat currency, a new monetarist model accommodating multiple payment methods, and a model of unsecured credit—transition paths are constructed between an announcement and the date at which events are realized. Although the economics is different, in each case, news about monetary policy can induce volatility in financial and other markets, with transitions displaying booms, crashes, and cycles in prices, quantities, and welfare. This is not the same as volatility based on self-fulfilling prophecies (e.g., cyclic or sunspot equilibria) studied elsewhere. Instead, the focus is on the unique equilibrium that is stationary when parameters are constant but still delivers complicated dynamics in simple environments due to information and liquidity effects. This is true even for classically-neutral policy changes. The induced volatility can be bad or good for welfare, but using policy to exploit this in practice seems difficult because outcomes are very sensitive to timing and parameters. The approach can be extended to include news of real factors, as seen in examples.

Solving dynamic economic models that capture salient real-world heterogeneity and nonlinearity requires the approximation of high-dimensional functions. As their dimensionality increases, compute time and storage requirements grow exponentially. Sparse grids alleviate this curse of dimensionality by substantially reducing the number of interpolation nodes, that is, grid points needed to achieve a desired level of accuracy. The construction principle of sparse grids is to extend univariate interpolation formulae to the multivariate case by choosing linear combinations of tensor products in a way that reduces the number of grid points by orders of magnitude relative to a full tensor-product grid and doing so without substantially increasing interpolation errors. The most popular versions of sparse grids used in economics are (dimension-adaptive) Smolyak sparse grids that use global polynomial basis functions, and (spatially adaptive) sparse grids with local basis functions. The former can economize on the number of interpolation nodes for sufficiently smooth functions, while the latter can also handle non-smooth functions with locally distinct behavior such as kinks. In economics, sparse grids are particularly useful for interpolating the policy and value functions of dynamic models with state spaces between two and several dozen dimensions, depending on the application. In discrete-time models, sparse grid interpolation can be embedded in standard time iteration or value function iteration algorithms. In continuous-time models, sparse grids can be embedded in finite-difference methods for solving partial differential equations like Hamilton-Jacobi-Bellman equations. In both cases, local adaptivity, as well as spatial adaptivity, can add a second layer of sparsity to the fundamental sparse-grid construction. Beyond these salient use-cases in economics, sparse grids can also accelerate other computational tasks that arise in high-dimensional settings, including regression, classification, density estimation, quadrature, and uncertainty quantification.