Econometrics

We prove that the probability that Gaussian elimination with partial pivoting on n × n random matrices has growth ρ is at least inverse quasi-polynomial: Ω(exp(−c log²(ρ) log(n))) for some constant c > 0. This lower bound breaks standard conjectures in the smoothed and average-case analysis of Gaussian elimination. To the best of our knowledge, it is the first non-trivial lower bound on the probability of large growth for Gaussian random matrices.

We study the relation between strategic complementarities and aggregate persistence in linear-quadratic mean field games with interactions in states and actions. The framework provides local approximations to common macroeconomic problems, including capital accumulation and multiproduct pricing. We show that the equilibrium aggregate dynamics coincide with those of a single-agent linear-quadratic control problem in which state and action curvatures are adjusted for strategic interactions. This result gives conditions for equilibrium existence, establishes uniqueness, and links strategic interactions to aggregate adjustment. We establish conditions under which stronger state complementarities increase persistence, while stronger action complementarities reduce it, even in multidimensional problems whose underlying matrices are not simultaneously diagonalizable. Under these conditions, internalizing state complementarities makes the utilitarian planner’s allocation more persistent, while internalizing action complementarities makes it less persistent. With common shocks, we give conditions under which individual and aggregate dynamics can be combined to identify strategic interactions and model parameters. Finally, we extend the analysis to interactions through higher moments of the state distribution.

The enormous gravity-model-of-trade literature has illustrated important advantages of estimation via Poisson Pseudo Maximum Likelihood (PPML). That literature’s prioritization of parameter estimation over hypothesis testing has left questions of testing in the PPML framework underexplored. In this paper we show analytically that scaling the dependent variable can affect the outcome of some joint hypothesis tests, but not others. Likelihood-ratio, model-based Wald, and model-based Lagrange Multiplier test statistics depend on scale, and therefore do not support scale-invariant inference. Wald and Lagrange Multiplier tests constructed with heteroskedasticity-robust sandwich adjustments are invariant to scale. We illustrate these points empirically with an application from the literature on Revealed Comparative Advantage.

This paper develops a framework for fast online inference on semiparametric models with large sample sizes and possibly many covariates. The computational algorithm itself is the object of statistical study: after a globally consistent warm start in the first phase, the path of averaged online iterates generated in the second phase automatically delivers estimators with optimal convergence rates and valid confidence sets. Both phases require only a single pass over the data stream and are well suited to streaming data or to settings with storage/privacy constraints. For semiparametric monotone index models, the averaged trajectory of the second phase lead to estimators that are automatically orthogonalized and satisfy the laws of the iterated logarithms, and policy functionals are updated along the same trajectory at negligible additional cost. The averaged trajectories satisfy functional central limit theorems, which yield fast online inference via random scaling and bypass the explicit variance estimation that complicates inference for semiparametric models. Applied to a fixed large sample, our online algorithm achieves substantial computational gains over corresponding offline procedures without sacrificing statistical performance. Monte Carlo experiments show adequate behavior. Our methods are applied to 19 million traffic-stop online records from the North Carolina State Patrol (Pierson et al. 2020) and to the international trade data of Helpman et al. (2008) with over 300 regressors. We also compare our estimator to its parametric benchmark in both empirical illustrations.

Empirical models of multi-product demand rely on low-dimensional product representations to capture substitution patterns, increasingly using proxies built from unstructured data. When proxies are imperfect, standard workflows yield biased counterfactuals and invalid inference. We develop a practical toolkit to address these issues. Our methods apply to market-level and/or individual data, require minimal additional computation, provide simple standard-error formulas, and accommodate proxies from fine-tuned models. Further, we propose diagnostics to assess proxy quality. Our methods yield meaningful improvements in predicting substitution in empirically calibrated simulations and in an application where we assess counterfactual prediction performance against a ground truth.

The AI boom has driven the Nasdaq and the Magnificent Seven tech stocks to record highs. But how much do these new records reflect underlying value, how much is speculation, and how vulnerable are these stocks and the wider market to a major downturn? Our evidence and analyses show clear signs of bubble exuberance in most of these stocks, concentrated in a few names like Nvidia, leading to latent risks for investors who assume their index funds are safely diversified and supported by wider economic fundamentals.