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 how information about school quality affects families’ choices and how scaling up the intervention changes its impact. In a randomized trial in Chile, we offer families a short video and a personalized school report card before they enroll their children. Treated families choose schools with higher test scores and value added. Among families reached before enrollment, treated children score about 0.2 standard deviations higher in fourth grade, with positive but less precise estimates on later assessments. We embed the experimentally identified demand shift in a structural model of school choice and competition to study equilibrium effects at scale. Capacity constraints and centralized assignment attenuate the demand-side gains, but the same shift in demand strengthens schools’ incentives to improve quality, and the supply response roughly offsets the congestion effect. More generally, equilibrium scaling can alter experimental effects in either direction because congestion and endogenous quality responses work against each other. We use the model to guide the design of a follow-up cluster-randomized experiment, focusing on the tradeoff between precision and contamination from equilibrium spillovers.
Using newly linked administrative and commercial data from Virginia spanning 25 years, we study the consequences of incarceration. We provide new evidence on the effects of incarceration on labor market outcomes and recidivism. We also study two of the primary channels through which low-income households build wealth: asset ownership and human capital formation. In our sample of felony defendants, we find that 16% are ever homeowners, while at least 8% have ever enrolled in college. To identify causal effects, we use a matched difference-in-differences design. We find no evidence of scarring effects on labor market outcomes or changes in recidivism beyond the incapacitation period. However, incarceration leads to a persistent reduction in asset accumulation: seven years after sentencing, homeownership has declined by 1.2 percentage points (13.2%) and a car ownership proxy measure has declined by 2.7 percentage points (18.1%). Incarceration also lowers human capital formation, reducing the likelihood of college enrollment by 1.6 percentage points (17.4%).
Let be independent nonnegative random variables with . We prove that, for every ,
To prove this, we consider a relaxed optimization problem over a set of sequences of ordered, but non-independent random variables. This allows us to reformulate it recursively as a dynamic programming problem. The bound becomes an equality for the binary i.i.d. random variables satisfying and , which remains a maximizer in the relaxed problem.
We link high-frequency geocoded protest data during Bangladesh’s 2024 Monsoon Revolution, Facebook measures of protest activity and social connectivity, university enrollment and demographics to establish: (1) campus protest precedes off-campus mobilization; (2) student concentration predicts both on- and off-campus protest, while non-student youth, educated adults, urbanization, and locations of “placebo” universities authorized but not yet operating do not; and (3) social connectivity to campus protests predicts off-campus diffusion one week later. Universities appear to incubate mass uprising by making dissent visible, coordinated, and capable of spreading beyond campus. Such patterns are also evident in U.S. Vietnam War protests and in global data. These results can rationalize why governments in Hungary, Turkey, Iran, India, Russia, Bangladesh, Israel, and the United States have targeted campuses to suppress dissent.
This paper studies the interaction between the decrease in the gender pay gap and the stagnation in younger workers’ careers, analyzing data from Italy and the United States. The changing mix of cohorts among employed men and women accounts for the entire decline in the aggregate pay gap, holding each cohort’s male and female earnings fixed at their initial observed levels. We highlight younger men’s positional losses within firms’ hierarchies as an important factor driving convergence at labor-market entry. We propose a mechanism by which workforce aging limits career growth for younger workers, disproportionately affecting younger men’s trends. Consistent with this explanation, younger men experience the largest positional losses within the firms that are more exposed to workforce aging. We show that these results are robust when accounting for alternative channels, including changes in participation, education, the child penalty, and deindustrialization. Finally, we document that the retirement of older cohorts can account for all of the gender pay gap decline after the mid-1990s.
Complementarities can have important welfare consequences, but quantifying these effects would seem to require identifying and valuing the underlying mechanisms separately. This paper shows that this need not be the case. I provide necessary and sufficient conditions under which baseline subsidized activity and the direct and total responses to a subsidy determine aggregate willingness to pay. A sufficient condition for valuing the equilibrium adjustment is that it has the same effect on utility as an additional subsidy common to all agents and relevant actions. The formula is easy to apply to existing estimates and guides the design of new experiments.
The neoclassical model of discrimination is reformulated as a behavioral model that replaces the disconnected agencies of the taste model with agents’ decisions to conform or not to a dominant group norm governing intergroup behavior. Decisions depend on beliefs about aggregate actions and the social benefit accruing from the endogenously determined group network approving one’s decision. Multiple equilibria describe intergroup employment patterns more empirically consistent with economies lacking effective government policies prohibiting discrimination (20th Century India and the US). Neoclassical discrimination (taste and statistical) becomes more empirically relevant where government institutions enforce non-discriminatory norms (21st Century India and the US). Unlike the neoclassical prediction of segregation without discrimination, no totally segregated equilibrium exists. Unlike the taste model where segregated groups receive identical marginal product wages, discriminatory job assignments in one norm-based equilibrium allocate high and low-skill M workers marginal productivity wages, while all m workers receive low-skill wages. Typical econometric techniques for estimating discrimination suggest current empirical models based on mean comparisons estimate group stratification, not discrimination, and likely underestimated 20th Century caste discrimination in India and discrimination of higher skilled Black and Asian American men in the US. The model applies to ethnic and sex discrimination.
Whether imposing higher taxes on business owners adversely affects business activity by constraining investment and inducing capitalist flight is a central question in the ongoing debate on how to tax the ultra wealthy. To shed new light, I exploit a series of related Norwegian reforms during 2021–2024 that increased dividend tax rates, removed migration-related capital gains tax loopholes, and nearly doubled the effective marginal tax rate on business wealth. These reforms spurred international debate and, allegedly, an “exodus” of Norwegian billionaires (Financial Times, 2023). While I document clear effects on migration, these responses are concentrated among the top 0.1% of the wealth distribution and mostly confined to 2022 and 2023. My results indicate that at most 100 individuals left due to the reforms. I find no evidence of significant outmigration or reduced inflows of startup founders or inventors. I estimate that absent any outmigration, wealth tax revenues would have increased by 75% from 2021 to 2024. Reform-driven outmigration lowers the revenue gain to 71.5%. My findings further show that outmigrating owners’ firms remain economically active and do not reduce investment. In a broader set of analyses, I examine whether business outcomes are affected, regardless of whether owners outmigrate, since firms may reduce investment both due to liquidity constraints or distortions to owners’ savings decisions. I compare firms owned by Norwegian individuals subject to the wealth tax with firms owned by foreigners and other tax-exempt entities. By merging historical ownership data from Orbis with the Norwegian shareholder register, I perform these analyses on both Norwegian and foreign-domiciled firms. Across settings, I find no evidence that Norwegian-owned firms pay out more dividends or invest less after the reforms, nor is there any evidence that the reform induced more bankruptcies. These findings indicate that the short-run economic costs of wealth taxation, in terms of migration and firm investment, are more limited than the public debate implies.
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.
Work experience has been found to be a key determinant of work and wages for educated women, but it seems to play a smaller role for the less educated. For them, welfare, tax credits and family composition matter more, and increasingly so does participation in disability programmes. Here we document how labor supply, wages, health, and disability claims have evolved in the UK over the last three decades, and examine how reforms to tax credits, disability benefits and other welfare programs have changed work incentives over this period. We then introduce these features into an empirical dynamic structural model of life-cycle labor supply, human capital and disability benefit application, in which human capital combines health capital, experience accumulated in work, and education. Estimating the model on a panel of working-age women in the UK, we examine the interactions between experience capital and health capital in driving life-cycle earnings across different education groups. Our results highlight the importance of interactions in the disability benefit, welfare and tax-credit systems for understanding the life cycle pattern of hours, employment, earnings, and disability claims, and for evaluating policy counterfactuals.
This paper considers the estimation of heterogeneous impacts within a Randomized Controlled Trial (RCT) in a situation where heterogeneous status is endogenous and is not fully observed in the control sample. We show how to use information in the treatment sample and a noisy signal on the heterogeneous status to estimate meaningful impacts under a minimal set of assumptions. We provide an application of this approach to a data set from Ghana, collected around a clustered RCT to evaluate the impacts of an early-years intervention, differentiating the impact between households that participate actively in the program from those who participate only passively, as recipients. We show that, for some outcomes, the properly estimated heterogeneous impacts differ substantially from those computed with a naive estimator.
In the classic oligopoly games a Stackelberg leader often chooses exactly the action of an uncontested monopolist. We show that this is a theorem whenever the firms share an affine best response, characterize the demands that make best responses affine—linear, log-linear, shifted constant elasticity, and power demand, with strategic substitutes and strategic complements alike—and show that with such demand every firm can optimally ignore the future in any finite arrangement of sequential and simultaneous play whose simultaneous stages admit an interior equilibrium.
We develop a unified approach to studying cost-price dynamics in the cross-section of firms in order to jointly explain the time series of aggregate inflation and the frequency of price changes, both during normal times and inflation surges. A key novelty is the use of microdata on firms’ prices and production costs to construct an empirical measure of price gaps—the deviation between a firm’s listed and optimal price. Conditional on the path of aggregate cost shocks extracted from the data, a state-dependent pricing model with strategic complementarities accounts well for both the linear cost-price dynamics of the pre-pandemic period and the nonlinear increase in inflation and frequency of price adjustment that followed.
The Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) provides infant formula to low-income households through state-level exclusive supply contracts that cover roughly half of U.S. infants. Although these contracts directly govern purchases by WIC participants, they also affect households that receive no WIC benefits. We study these spillovers using household-level in-store and online transaction data matched to WIC contract changes across states from 2018 to 2025. When a manufacturer becomes the WIC supplier, its market share among non-WIC households rises by roughly 30 percentage points in the regular-size formula segment. The response is concentrated in physical stores, where the new supplier’s market share rises by roughly 50 percentage points, while we find little systematic response online or for bulk-size products. This contrast points to the physical retail environment as a central mechanism. Additional evidence from WIC-authorized retailers and hospital formula-practice data suggests that direct exposure to WIC labels and hospital-provided samples account for relatively little of the spillover. The results show that public procurement can substantially reshape demand among untreated consumers by changing the retail environments in which choices are made.
Faculty: Learn how to share your research with the Cowles community at the links below.