Knowledge that Transforms

This paper notes a simple connection between synthetic control and online learning. Specifically, we recognize synthetic control as an instance of Follow‐The‐Leader (FTL). Standard results in online convex optimization then imply that, even when outcomes are chosen by an adversary, synthetic control predictions of counterfactual outcomes for the treated unit perform almost as well as an oracle weighted average of control units' outcomes. Synthetic control on differenced data performs almost as well as oracle weighted difference‐in‐differences, potentially making it an attractive choice in practice. We argue that this observation further supports the use of synthetic control estimators in comparative case studies.

Most U.S. government spending on highways and bridges is done through “scaling” procurement auctions, in which private construction firms submit unit price bids for each piece of material required to complete a project. Using data on bridge maintenance projects undertaken by the Massachusetts Department of Transportation (MassDOT), we present evidence that firm bidding behavior in this context is consistent with optimal skewing under risk aversion: firms limit their risk exposure by placing lower unit bids on items with greater uncertainty. We estimate the amount of uncertainty in each auction, and the distribution of bidders' private costs and risk aversion. Simulating equilibrium item‐level bids under counterfactual settings, we estimate the fraction of project spending that is due to risk and evaluate auction mechanisms under consideration by policymakers. We find that scaling auctions provide substantial savings relative to lump sum auctions and show how our framework can be used to evaluate alternative auction designs.

Using an endogenous growth model, Liu, Mian, and Sufi (2022) (LMS) show that a decline in the interest rate can lead to a fall in productivity growth and a rise in leader‐laggard productivity gaps and firm profits. We identify two issues in their quantitative analysis of transition dynamics: a time‐scale error and the omission of composition terms in calculating productivity growth along the transition to a new balanced growth path. Correcting the time‐scale error and including the composition terms, the decline in the interest rate that LMS study leads to a large and protracted productivity boom lasting about 20 years. In addition, the average leader‐laggard gap grows much more slowly than reported in their paper. We also point out an issue in their quantitative analysis of steady‐state profit shares. These issues are related to the quantitative exercises, and do not affect the key theoretical contributions of LMS.

This paper assesses when the validity of difference‐in‐differences depends on functional form. We provide a novel characterization: the parallel trends assumption holds under all strictly monotonic transformations of the outcome if and only if a stronger “parallel trends”‐type condition holds for the cumulative distribution function of untreated potential outcomes. This condition for parallel trends to be insensitive to functional form is satisfied if and essentially only if the population can be partitioned into a subgroup for which treatment is effectively randomly assigned and a remaining subgroup for which the distribution of untreated potential outcomes is stable over time. These conditions have testable implications, and we introduce falsification tests for the null that parallel trends is insensitive to functional form.

We study how discounting and monitoring jointly determine whether cooperation is possible in repeated games with imperfect (public or private) monitoring. Our main result provides a simple bound on the strength of players' incentives as a function of discounting, monitoring precision, and on‐path payoff variance. We show that the bound is tight in the low‐discounting/low‐monitoring double limit, by establishing a public‐monitoring folk theorem where the discount factor and the monitoring structure can vary simultaneously.