Cowles Foundation for Research in Economics

We develop a new approach to estimating earnings, job, and employment dynamics using subjective expectations data from the NY Fed Survey of Consumer Expectations. These data provide beliefs about future earnings offers and acceptance probabilities, offering direct information on counterfactual outcomes and enabling identification under weaker assumptions. Our framework avoids biases from selection and unobserved heterogeneity that affect models using realized outcomes. First-step fixed-effects regressions identify risk, persistence, and transition effects; second-step GMM recovers the covariance structure of unobserved heterogeneities such as ability, mobility, and match quality. We find lower risk and persistence of the individual productivity component than in prior work, but greater heterogeneity in ability and match quality. Simulations show that reduced-form estimates overstate persistence and volatility on individual-level productivity due to job transitions and sorting. After accounting for heterogeneity, volatility declines and becomes flat across the earnings distribution. These results underscore the value of expectations data.

In this paper, we propose a triple (or double-debiased) Lasso estimator for inference on a low-dimensional parameter in high-dimensional linear regression models. The estimator is based on a moment function that satisfies not only first- but also second-order Neyman orthogonality conditions, thereby eliminating both the leading bias and the second-order bias induced by regularization. We derive an asymptotic linear representation for the proposed estimator and show that its remainder terms are never larger and are often smaller in order than those in the corresponding asymptotic linear representation for the standard double Lasso estimator. Because of this improvement, the triple Lasso estimator often yields more accurate finite-sample inference and confidence intervals with better coverage. Monte Carlo simulations confirm these gains. In addition, we provide a general recursive formula for constructing higher-order Neyman orthogonal moment functions in Z-estimation problems, which underlies the proposed estimator as a special case.

We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four properties are equivalent for any such order: (i) the test function cone is closed under pointwise minimum, (ii) the value function is affine, (iii) the solution correspondence has a convex graph with decomposable extreme points, and (iv) every ordered pair of measures admits an order-preserving coupling. As corollaries, we derive the extreme and exposed point properties involving integral stochastic orders such as multidimensional mean-preserving spreads and stochastic dominance. Applying these results, we generalize Blackwell's theorem by completely characterizing the comparisons of experiments that admit two equivalent descriptions—through instrumental values and through information technologies. We also show that these results immediately yield new insights into information design, mechanism design, and decision theory.

This paper develops a novel method for identifying observable determinants of latent common trends in nonstationary panel data, which are typically removed or controlled in two-way fixed effects regressions. By examining cross sectional dispersion processes, we assess whether panel series exhibit distributional convergence toward specific observed time series, revealing them as long run determinants of the underlying latent trend. The approach also offers a new perspective on cointegration between time series and panel data, focusing on the relative variation of the panel data with respect to the cointegration error. Applying this method to U.S. state-level crime rates demonstrates that the percentage of young adults is a key determinant of violent crime trends, while the incarceration rate drives property crime trends. These findings, which differ from standard two-way fixed effects analysis results, provide a compelling explanation for the sharp decline in U.S. crime rates since the early 1990s.

This paper shows that the pace of technology creation is a key driver of the skill premium. It develops a model in which skilled workers have a comparative advantage in learning new technologies. As technologies age, they become standardized and accessible to other workers. The skill premium is determined by the interplay between the pace of technology creation and standardization. A rapid pace of technology creation leads to a sustained increase in the skill premium. We calibrate the model using novel text-based data on new technologies and their changing demand for skills as they age. These data show that new technologies are initially skill intensive but become less so as they age. The data also point to an increased pace of new technology creation starting in the 1970s and tapering off in the 2000s. In response to this rapid pace of technology creation, the model generates a 32 percent increase in the college premium, which begins to reverse in the 2010s. Our framework also explains why the college premium is higher in dense cities, why its increase was mainly urban, and why it rose first for young workers and later for older workers.

Modern theories of the business cycle do not allow for the simultaneous rational choice of both prices and quantities, instead assuming that an “invisible hand” determines one of these variables to clear markets. In this paper, we develop a macroeconomic framework in which both prices and quantities are chosen directly by firms, and exchange is both voluntary and efficient. Because of uncertainty about demand and productivity, individual product markets can be in excess supply or rationed. The absence of market-clearing changes pricing and production in qualitatively important ways: markups are no longer determined solely by the elasticity of demand, and higher uncertainty reduces production and increases markups. In equilibrium, production in rationed markets has a negative aggregate demand externality on demand in slack markets. Differently from New Keynesian economies, monetary shocks propagate by reducing economic slack, raising aggregate labor productivity and consumption, while uncertainty shocks act as stagflationary cost-push shocks. We integrate our theory of disequilibrium in a dynamic, rational-expectations “New Old Keynesian Model” and demonstrate its implications for the business cycle.

We develop a framework for the optimal pricing and product design of LLMs in which a provider sells menus of token budgets to users who differ in their valuations across a continuum of tasks. Under a homogeneous production technology, we show that users’ high-dimensional type profiles are summarized by a scalar index, reducing the seller’s problem to one-dimensional screening. The optimal mechanism takes the form of committed-spend contracts: buyers pay for a budget that they allocate across token classes priced at marginal cost. We extend the analysis to environments with multiple differentiated models and to competition between a proprietary leader and an open-source fringe, showing that competitive pressure reshapes both the intensive and extensive margins of compute provision. Each element of our theory (token-budget menus, maximum- and minimum-spend plans, multi-model versioning, and linear API pricing) has a direct counterpart in the observed pricing practices of providers such as Anthropic, OpenAI, and GitHub.

Many economic parameters are identified by “thin sets” (submanifolds with Lebesgue measure zero) and hence difficult to recover from data in an ambient space. This paper provides a unified theory for estimation and inference of such “thin-set” identified functionals. We show that thin sets are not equally thin: their intrinsic dimensionality m matters in a precise manner. For a nonparametric regression h₀ with Hölder smoothness s and d-dimensional covariates in the ambient space, we show that$\mathrm{ n}—\frac{s}{2s\mathrm{+}d\mathrm{-}m}$, where s is the minimax optimal rate of estimating linear and nonlinear (e.g., quadratic, upper contour) integrals of h₀ on an m-dimensional submanifold (0 ≤ m < d), which is the fastest possible attainable rate among all estimators. The minimax lower bound rate result is generalized to estimating submanifold integrals when h₀ is a nonparametric density and a nonparametric instrumental variable function. The asymptotic normality of t statistics is established via sieve Riesz representation, and the corresponding inference is computed using Sobol points.