A growing number of authorities use mechanisms to allocate students to schools in a way that reflects student preferences and school priorities. However, most real-world mechanisms incentivize students to strategically misreport their preferences. Misreporting complicates the identification of causal parameters that depend on true preferences, which are necessary inputs for a broad class of counterfactual analyses. We provide an identification approach robust to misreporting and derive sharp bounds on causal effects of school assignment. Our approach applies to allocation rules characterized by placement scores and cutoffs. We use data from a deferred acceptance mechanism that assigns students to university programs in Chile. Matching theory predicts and empirical evidence shows that students behave strategically in Chile because they face constraints on preference submission and have good prior information about school accessibility. Our bounds are informative enough to reveal significant heterogeneity in graduation success with respect to preferences and school assignment.

This paper studies the long-run effects of high-skill return migration on scientific productivity and the direction of research, using U.S.-trained Chinese scientists during the 1950s Great Return Wave. Exploiting quasi-random variation in return opportunities from Cold War U.S. exit restrictions, we compare scholars who returned to China with observably similar scholars who stayed. Combining newly digitized historical archives with multilingual bibliometric data, we follow individual output and research agendas across the international and Chinese-domestic literatures over four decades. We find that return redirected output rather than reducing it: returnees published less internationally and more domestically, at no quality loss, and shifted toward applied, mission-oriented work. In the fields they entered, other domestic scientists' frontier-quality output rose over two decades. Our welfare analysis, priced through a cross-field citation network, shows the U.S. lost more than China gained, a gap driven by scientists' position in the knowledge network rather than their number.

Employer-side wage subsidies are widely used to promote employment among disadvantaged workers. We study how such subsidies translate into firm hiring behavior using the federal Work Opportunity Tax Credit, which subsidizes up to 40% of first-year wages and covers over two million hires annually. Using linked administrative data from Wisconsin and multiple quasiexperimental designs, we find consistent and precise null effects on hiring, earnings, retention, and related outcomes across designs and firm types. Original data on firm hiring practices suggest two mechanisms that can limit employer-side subsidy efficacy: perceived legal risks discourage eligibility screening, and organizational frictions attenuate decision makers’ responsiveness.

Parents make fertility decisions sequentially, updating plans as they learn about each child. This paper examines how a child's endowment at birth affects subsequent fertility. We present a model that combines classical models of 1) the tradeoffs between quantity and quality investments in children and 2) parents' allocation decisions across siblings, namely, whether to reinforce or compensate their children's initial endowments. We then estimate the relationship between initial endowments and subsequent fertility decisions using Demographic and Health Surveys from West Africa. The region offers high fertility, near-zero sex selection before birth, and the presence of exogenous variation in initial endowments from idiosyncratic exposure to Harmattan dust. We find that subsequent fertility falls following larger births. The pattern holds for boys and girls, first and later births, and mothers with different education levels and persists after restricting to surviving children. This is corroborated using exogenous variation in birthweight from idiosyncratic in utero exposure to Harmattan dust. Our results are also consistent with parents' stated preferences for fertility following larger and smaller births. Consistent with previous findings on greater reinforcing behavior in lower-resourced settings, we find greater reductions in fertility from larger births in areas with lower socioeconomic status.

We develop standard errors for estimates of causal effects in settings where the distribution of treatment exposures is known but potentially exhibits complicated dependence patterns across units. Such dependence arises, for example, in settings with spillovers/interference across units or when the treatment assignment is spatially correlated. Our variance estimator generalizes several properties of the Neyman variance estimator for completely randomized experiments to general designs: it is unbiased for an upper bound on the variance from the design-based perspective; the conservativeness of this upper bound depends on the heterogeneity of treatment effects; and it is also valid under certain forms of superpopulation sampling of the potential outcomes. Our estimator reduces to standard approaches in simple designs, such as the Neyman variance estimator in completely randomized experiments and the cluster–robust variance estimator in cluster-randomized experiments. We show that the proposed estimator is admissible among the class of quadratic-form variance estimators and derive asymptotic conditions under which it is consistent for an upper bound on the asymptotic variance of the treatment effect estimator. In simulations and applications based on two empirical studies, one with peer effects and another with a spatially correlated treatment, we find that the proposed variance estimator performs well, and in some cases yields standard errors that are two to three times shorter than those of existing alternatives.

A central question in immigration policy is how mobility restrictions affect the wages of temporary foreign workers (TFWs). We study the labor market return to TFWs gaining permanent residency (PR), which loosens mobility restrictions. Using administrative data linking matched employer–employee data in Canada to temporary and permanent visa records from 2004–2014 along with an event-study design, we find that gaining PR leads to a sharp, immediate, and persistent increase in the job switching rate of 21.7 percentage points and an increase in earnings of 3.2 percent three years after PR. These gains are driven primarily by reallocation across firms: workers move to higher-paying firms, and our estimates are consistent with no within-firm effects. To guide and interpret our reduced- form results, we develop a search-and-matching model featuring heterogeneous workers and firms. Permanent residents and native-born workers search for jobs in the same labor market and engage in on-the-job search, while TFWs search separately within a segmented labor market and do not receive outside wage offers. We calibrate the model to match our reduced-form results, and we use it to simulate the long-run effects of PR and consider two counterfactual policies: (1) increasing the cost to firms of posting a TFW vacancy and (2) allowing TFWs to switch employers freely under “open” visas. We evaluate how these policies affect output, wages, profits, and overall social welfare.

We introduce lwdid, a Stata command that implements the rolling difference-in-differences (DiD) estimator proposed by Lee and Wooldridge (2026a). The rolling approach transforms a panel-data DiD problem into a sequence of cross-sectional estimation problems, allowing flexible analysis of staggered adoption designs with heterogeneous treatment effects. The command accommodates both large- and small-sample panels. In settings with a limited number of treated or control units, it implements the extension developed in Lee and Wooldridge (2026b), where conventional large-sample asymptotic inference may be unreliable. For large panels, lwdid provides computationally efficient inference via a multiplier bootstrap based on exact influence functions. By avoiding repeated model estimation, this approach substantially reduces computation time. For settings with few treated or control units, the command supports several inference methods, including exact inference using the t distribution under normality, HC3-based heteroskedasticity-robust inference, and randomization inference. Overall, lwdid makes the rolling DiD framework readily accessible to applied researchers across a wide range of empirical settings.