Normal-form two-player games are categorized by players into K analogy classes so as to minimize the prediction error about the behaviour of the opponent. This results in Clustered Analogy-Based Expectation Equilibria in which strategies are analogy-based expectation equilibria given the analogy partitions and analogy partitions minimize the prediction errors given the strategies. We distinguish between environments with self-repelling analogy partitions in which some mixing over partitions is required and environments with self-attractive partitions in which several analogy partitions can arise, thereby suggesting new channels of belief heterogeneity and equilibrium multiplicity. Various economic applications are discussed.
We examine how shootings at schools—an increasingly common form of gun violence in the States—impact the educational and economic trajectories of students. Using linked schooling and labor market data in Texas from 1992 to 2018, we compare within-student and across-cohort changes in outcomes following a shooting to those experienced by students at matched control schools. We find that school shootings increase absenteeism and grade repetition, reduce high school graduation, college enrollment, and college completion; and reduce employment and earnings at ages 24–26 years. We further find school-level increases in the number of leadership staff and reductions in retention among teachers and teaching support staff in the years following a shooting. The adverse impacts of shootings span student characteristics, suggesting that the economic costs of school shootings are universal.
Economists are often interested in the mechanisms by which a treatment affects an outcome. We develop tests for the “sharp null of full mediation” that a treatment D affects an outcome Y only through a particular mechanism (or set of mechanisms) M. Our approach exploits connections between mediation analysis and the econometric literature on testing instrument validity. We also provide tools for quantifying the magnitude of alternative mechanisms when the sharp null is rejected: we derive sharp lower bounds on the fraction of individuals whose outcome is affected by the treatment despite having the same value of M under both treatments (“always-takers”), as well as sharp bounds on the average effect of the treatment for such always-takers. An advantage of our approach relative to existing tools for mediation analysis is that it does not require stringent assumptions about how M is assigned. We illustrate our methodology in two empirical applications.
We present a method to determine optimal monetary policy in heterogeneous-agent economies with nominal frictions and aggregate shocks, under various assumptions regarding fiscal policy. We analyze models with either sticky prices or sticky wages. In the sticky-price economy, when fiscal policy is optimally set, optimal monetary policy implements price stability. Inflation volatility remains low when fiscal policy follows empirically relevant rules. The inflation response is more pronounced when the Phillips curve is steep and profits are skewed toward highly productive agents. In the sticky-wage economy, optimal price inflation becomes significantly more volatile, while wage inflation remains small. Under both types of nominal rigidity, agents with lower productivity tend to benefit more from optimal monetary policy.
We show how to use randomized participation incentives to test and account for nonresponse bias in surveys. We first use data from a survey about labour market conditions, linked to full-population administrative data, to provide evidence of large differences in labour market outcomes between survey participants and nonparticipants, differences which would not be observable to an analyst who only has access to the survey data. These differences persist even after correcting for observable characteristics. We then use the randomized incentives in our survey to directly test for nonresponse bias and find evidence of substantial bias. Next, we apply a range of existing methods that account for nonresponse bias and find they produce bounds (or point estimates) that are either wide or far from the ground truth. We investigate the failure of these methods by taking a closer look at the determinants of participation, finding that the composition of participants changes in opposite directions in response to incentives and reminder emails. We develop a model of participation that allows for two dimensions of unobserved heterogeneity in the participation decision. Applying the model to our data produces bounds (or point estimates) that are narrower and closer to the ground truth than the other methods. Our results highlight the benefits of including randomized participation incentives in surveys. Both the testing procedure and the methods for bias adjustment may be attractive tools for researchers who are able to embed randomized incentives into their survey.
We evaluate the efficiency of dynamic linked environmental regulation. Linked regulation allows inspectors who uncover violations at one plant to increase future enforcement at other plants that share a common owner. When compliance costs are correlated, regulators can then target scarce enforcement resources towards bad actors without inspecting everyone. We develop an empirical framework of dynamic moral hazard under linked regulation that allows for large portfolios of plants and for choices to be interdependent within the portfolio of plants and across time. Using the framework we evaluate a linked regulation scheme in Texas and find that linked regulation performs substantially better than both unlinked regulation and untargeted regulation. We test two alternative theoretical mechanisms that underpin the benefit—a “firm-wide moral hazard mechanism” and a “correlated targeting mechanism”—and find that a large share of the value of linked regulation is due to the former.
We study sequential experiments where sampling is costly and a decision-maker aims to determine the best treatment for full-scale implementation by (1) adaptively allocating units between two possible treatments, and (2) stopping the experiment when the expected welfare (inclusive of sampling costs) from implementing the chosen treatment is maximised. Working under a continuous time limit, we characterise the optimal policies under the minimax regret criterion. We show that the same policies also remain optimal under both parametric and non-parametric outcome distributions in an asymptotic regime where sampling costs approach zero. The minimax optimal sampling rule is just the Neyman allocation: it is independent of sampling costs and does not adapt to observed outcomes. The decision-maker halts sampling when the product of the average treatment difference and the number of observations surpasses a specific threshold. The results derived also apply to the so-called best-arm identification problem, where the number of observations is exogenously specified.
This paper combines new data and a narrative approach to identify variation in political pressure on the Federal Reserve. From archival records, I build a data set of personal interactions between U.S. Presidents and Fed officials between 1933 and 2016. Since personal interactions do not necessarily reflect political pressure, I develop a narrative identification strategy based on President Nixon’s pressure on Fed Chair Burns. I exploit this narrative through restrictions on a structural vector autoregression that includes the President-Fed interaction data. I find that political pressure to ease monetary policy (i) increases the price level strongly and persistently, (ii) does not lead to positive effects on real economic activity, (iii) contributed to inflationary episodes outside of the Nixon era, and (iv) transmits differently from a typical monetary policy easing, by having a stronger effect on inflation expectations. Quantitatively, increasing political pressure by half as much as Nixon, for six months, raises the price level by about 7% over the following decade.
This article examines the emergence of coercive labour institutions using the case of serfdom in early modern Russia. We argue that serfdom consolidated under the pressure of landholding military elites who gained political influence due to the prolonged struggle with steppe nomads. To contain nomadic raids, the Russian state erected defence lines on the southern frontier, and granted land in the area to soldiers in charge of its defence. The soldiers could not farm while on defence duty, nor could they compete in the market for peasant labour, as the land had been selected for its defensive rather than agricultural value. The system was therefore only sustainable by restricting labour mobility. In response to the volume of landholders’ collective petitions, the Russian state gradually tied peasants to the land and institutionalized serfdom in the written law. Using newly digitized population data from the 17th century, we show a higher prevalence of serfs and military landholders in districts on the defence line. We also find a higher prevalence of small estates—up to 25 serf households—sufficient to support a soldier and his family. Placebo tests show that these patterns do not hold for non-serf peasants, or for merchants and artisans. To ensure causality, we develop a novel algorithm that reconstructs the optimal invasion routes for nomads and pinpoints the optimal location of the defence line using topographic data. Our results highlight the primacy of political economy factors over purely economic ones, such as the land–labour ratio or the grain trade, in the development of serfdom. This sheds new light on the possible mechanisms of institutional divergence between Eastern and Western Europe in the early modern period.
We use variation in state corporate income tax rates to re-examine the relation between taxes and corporate leverage. Contrary to prior research, corporate leverage rises after tax cuts for small private firms. An estimated dynamic equilibrium model shows that tax cuts make capital more productive and spur the use of leverage. Tax cuts also produce more distant default thresholds and lower credit spreads. These effects outweigh the lower interest tax deduction and lead to higher optimal leverage choices, especially for firms with flexible investment policies. The presence of the interest tax deduction raises consumer welfare in equilibrium.