Knowledge that Transforms

We provide sufficient conditions for equilibrium existence in first‐price auctions with private values that accommodate non quasi‐linear utilities and value‐distributions that contain atoms and exhibit positive or negative correlation. These conditions show that equilibrium existence often turns on properties of a single statistic of the joint distribution of values, namely, the minimum value in the support of the high‐value distribution (the mHV). We also show that modifying the standard tie‐breaking rule only at the mHV is enough to guarantee equilibrium existence without our sufficient conditions. Our results also apply to Bertrand price competition when each firm's constant marginal cost is private information.

A multi‐product monopolist faces a buyer who is privately informed about his valuations for the goods. As is well known, optimal mechanisms are in general complicated, while simple mechanisms—such as pure bundling or separate sales—can be far from optimal and do not admit clear‐cut comparisons. We show that this changes if the monopolist has sufficiently precise information about the buyer's valuations: Now, pure bundling always outperforms separate sales; moreover, there is a sense in which pure bundling performs essentially as well as the optimal mechanism. To formalize this, we characterize how fast the corresponding revenues converge to the first‐best revenue as the monopolist's information grows precise: Pure bundling achieves the same convergence rate to the first‐best as optimal mechanisms; in contrast, the convergence rate under separate sales is suboptimal.

We study the problem of a partisan gerrymanderer who assigns voters to equipopulous districts to maximize his party's expected seat share. The designer faces both aggregate, district‐level uncertainty (how many votes his party will receive) and idiosyncratic, voter‐level uncertainty (which voters will vote for his party). Segregate‐pair districting , where weaker districts contain one type of voter, while stronger districts contain two, is optimal for the gerrymanderer. The optimal form of segregate‐pair districting depends on the designer's popularity and the relative amounts of aggregate and idiosyncratic uncertainty. When idiosyncratic uncertainty dominates, a designer with majority support pairs all voters, while a designer with minority support segregates opposing voters and pairs more favorable voters; these plans resemble uniform districting and “packing‐and‐cracking,” respectively. When aggregate uncertainty dominates, the designer segregates moderate voters and pairs extreme voters; this “matching slices” plan has received some attention in the literature. Estimating the model using precinct‐level returns from recent U.S. House elections shows that, in practice, idiosyncratic uncertainty dominates. We discuss implications for redistricting reform, political polarization, and detecting gerrymandering. Methodologically, we exploit a formal connection between gerrymandering—partitioning voters into districts—and information design—partitioning states of the world into signals.

Macroeconomic outcomes depend on the distribution of markups across firms and over time, making firm‐level markup estimates key for macroeconomic analysis. Methods to obtain these estimates require data on the prices that firms charge. Firm‐level data with wide coverage, however, primarily come from financial statements, which lack information on prices. We use an analytical framework to show that trends in markups over time or the dispersion of markups across firms can still be well‐measured with such data. Measuring the average level of the markup does require pricing data, and we propose a consistent estimator for such settings. We validate the analytical results using simulations of a quantitative macroeconomic model and offer supporting evidence from firm‐level administrative production and pricing data. Our analysis supports the use of financial data to measure trends in aggregate markups.

Using multiple administrative data sources from Norway, we examine how firm performance changes after entrepreneurs become parents.Female-owned businesses experience a substantial decline in profits, steadily decreasing to 30% below baseline ten years post-childbirth.In contrast, male-owned businesses show no decline, often growing in revenues and costs after childbirth.The profit decline for female-owned firms is most pronounced among highly capable entrepreneurs, women who are majority owners, and those with working spouses.Entrepreneurial effort is key to performance, and our findings suggest that time demands from childbirth and childcare are a significant determinant of the decline in firm profits.

This paper estimates the causal impacts on child skills and the mechanisms producing these impacts using data from a randomized control experiment. We study a widely emulated early-childhood home visiting program and show the feasibility of replicating it at scale. We go beyond reporting treatment effects as unweighted item scores and assess item difficulties. To interpret treatment effects, we estimate individual-level latent skills and compare treatments and controls. The program substantially improves multiple skills. We decompose the source of treatment effects and find that enhancements in latent skills explain most of the conventional treatment effects for language and cognition.

I study the role of social networks in the propagation of economic shocks across space. Combining comprehensive data on US online friendships with extraction activity during the fracking boom, I show that exogenous changes in economic conditions in one area affect outcomes in socially proximate places, regardless of how far apart they are geographically. Social exposure to fracking generates a wage spillover amounting to one-third of every dollar of energy produced in a county’s social network. This spillover decays slowly in space and is associated with a large mobility response. Diffusion mainly stems from the commuting of transient fracking workers.

This paper utilizes wealth shocks from winning lottery prizes to examine the causal effect of financial resources on fertility. We employ extensive panels of administrative data encompassing over 0.4 million lottery winners in Taiwan and implement a triple-differences design. Our analyses reveal that a substantial lottery win can significantly increase fertility, the implied wealth elasticity of which is around 0.06. Moreover, the primary channel through which fertility increases is by prompting first births among previously childless individuals. Finally, our analysis reveals that approximately 25% of the total fertility effect stems from increased marriage rates following a lottery win.

We characterize the joint evolution of cross-sectional inequality in earnings, other sources of income and consumption across generations in the U.S. To account for cross-sectional dispersion, we estimate a model of intergenerational persistence and separately identify the influences of parental factors and of idiosyncratic life-cycle components. We find evidence of family persistence in earnings, consumption and saving behaviours, and marital sorting patterns. However, the quantitative contribution of idiosyncratic heterogeneity to cross-sectional inequality is significantly larger than parental effects. Our estimates imply that intergenerational persistence is not high enough to induce further large increases in inequality over time and across generations.