Why do employers offer pensions? We empirically investigate two rationales, namely that they improve worker effort and selectively retain good workers. We test these hypotheses using rich administrative data on effort and output for public school teachers around the pension-eligibility threshold. When teachers cross the threshold, their effective compensation falls by over 50 percent of salary due to sharply reduced pension accruals. Standard economic models predict that this effective pay cut reduces teacher effort and output, but we observe no such decline. This suggests that yearly pension accruals do not meaningfully increase effort. Similarly, if pensions selectively retain better teachers, we would expect average teacher quality to decline when the retentive incentive disappears at the threshold. Instead, we find no change in workforce composition, suggesting pensions do not selectively retain higher-performing teachers around the threshold.

The teacher labor market is a two-sided matching market where the effects of policies depend on the actions of both sides. We specify a matching model of teachers and schools that we estimate with rich data on teachers' applications and principals' ratings. Both teachers' and principals' preferences deviate from those that would maximize the achievement of economically disadvantaged students: teachers prefer schools with fewer disadvantaged students, and principals' ratings are weakly related to teacher effectiveness. In equilibrium, these two deviations combine to produce a surprisingly equitable current allocation where teacher quality is balanced across advantaged and disadvantaged students. To close academic achievement gaps, policies that address deviations on one side alone are ineffective or harmful, while policies that address both deviations could substantially increase disadvantaged students' achievement.

Why do employers offer pensions? We empirically examine two theoretical rationales, namely that pensions improve worker effort and worker selection. We test these hypotheses using rich administrative measures on effort and output for teachers around the pension-eligibility notch. When workers cross the notch, their effective compensation falls by roughly 50 percent of salary, but we observe no reduction in worker effort or output. This implies that pension payments do not increase effort. As for selection, we find that pensions retain low-value-added and high-value-added workers at the same rate, implying similar preferences across teacher quality and no influence on selection.

We present simple procedures for estimating non linear panel data models in the presence of unobserved heterogeneity and possible endogeneity with respect to time-varying unobservables. We combine a correlated random effects approach with a control function approach while accounting for missing time periods for some units. We examine the performance of the approach in comparisons with standard estimators using Monte Carlo simulation. We apply the methods to estimate the effects of school spending on student pass rates on a standardized math exam. We find that a 10% increase in spending leads to an approximately 2 percentage point increase in math pass rates.

Summary We propose a per‐cluster instrumental variable (PCIV) approach for estimating linear correlated random coefficient models in the presence of contemporaneous endogeneity and two‐way fixed effects. This approach estimates heterogeneous effects and aggregates them to population averages. We demonstrate consistency, showing robustness over standard estimators, and provide analytic standard errors for robust inference. In Monte Carlo simulation, PCIV performs relatively well in finite samples in either dimension. We apply PCIV in estimating the price elasticity of gasoline demand using state fuel taxes as instrumental variables. We find significant elasticity heterogeneity and more elastic gasoline demand on average than with standard estimators.

In this paper, we estimate the impact of a learning community on first-year college retention at a four-year public research university using a randomized control trial (RCT) for those students who opt into the experiment. Intent-to-treat and local-average-treatment-effect estimates reveal no discernable programmatic effects. We also generate estimates of program impact using observational techniques and find estimated impacts that are positive, large and statistically significant. We explore a variety of selection processes to better understand the differences between the RCT and observational estimates and to reflect on the generalizability of the RCT results for various other populations of interest. Non-random selection into the experimental sample accounts for the major difference in the two estimates and also cautions against generalizing the RCT result for populations outside the experiment.

Informational asymmetries between employers may inhibit optimal worker mobility. However, researchers rarely observe shocks to employers' information. I exploit two school districts' adoptions of value-added (VA) measures of teacher effectiveness—informational shocks to some, but not all, employers—to provide direct tests of asymmetric employer learning. I develop a learning model and test its predictions for teacher mobility. I find that adopting VA increases within-district mobility of high-VA teachers, while low-VA teachers move out of district to uninformed principals. These patterns are consistent with asymmetric employer learning. This sorting from widespread VA adoption exacerbates inequality in access to effective teaching.

Voluntary selection into experimental samples is ubiquitous and leads researchers to question the external validity of experimental findings. We introduce tests for sample selection on unobserved variables to discern the generalizability of randomized control trials. We estimate the impact of a learning community on first-year college retention using an RCT, and employ our tests in this setting. We compare observational and experimental estimates, considering the internal and external validity of both approaches. Intent-to-treat and local-average-treatment-effect estimates reveal no discernable programmatic effects, whereas observational estimates are significantly positive. The experimental sample is positively selected on unobserved characteristics suggesting limited external validity. Contact: Azzam: Gevirtz Graduate School of Education, University of California, Santa Barbara, Santa Barbara, CA, 93106 (email: tarekazzam@ucsb.edu); Bates: Department of Economics, University of California, Riverside, Riverside, CA 92521 (email: mbates@ucr.edu); Fairris: Department of Economics, University of California, Riverside, Riverside, CA 92521 (email: dfairris@ucr.edu). Acknowledgements: We acknowledge the able research assistance of Melba Castro and Amber Qureshi. David Fairris acknowledges support from the "Fund for the Improvement of Post-Secondary Education" at the U.S. Department of Education, grant number P116B0808112. The contents of this paper do not necessarily represent the policy of the Department of Education. This experiment is registered at the Registry for Randomized Controlled Trials under the number AEARCTR-0003671. The authors are prepared to provide all data and code for purposes of replication. This work was conducted under exempted IRB approval through the University of California, Riverside.

We introduce a classroom simulation to teach core concepts in hedonic price analysis. Students decide where to live in order to maximize utility. Locations differ in two dimensions: school quality and environmental quality. Endogenous housing prices in each location equilibrate the market. The simulation demonstrates the power of hedonic analysis, as well as its limitations and assumptions. It is fun, engaging, and accessible for both undergraduate and graduate students. We provide materials for implementation in an online Appendix.

School choice in the United States has expanded rapidly over the past two decades, but the degree to which parents value this expanded choice is unclear. Using multiple estimation strategies that exploit discontinuities along administrative boundaries, we estimate the degree to which access to inter-district school choice is capitalized into the housing market. Our estimates indicate a positive home-price premium associated with access to higherperforming school districts, and this premium decreases as distance between residence and district of choice grows and charter school access increases. The school choice premium also increases with the differential in school performance between residential districts and districts of choice, though not enough to overcome the residential school quality home price premium.

Like other states, Michigan has implemented a number of policies to change governance and administrative arrangements in local school districts deemed to be in financial emergency. This paper examines two questions: ( 1) Which districts get into financial trouble and why? and ( 2) Among fiscally distressed districts, are there significant differences in the characteristics of districts in which the state does and does not intervene? We analyze factors influencing district fund balances utilizing fixed effect models on a statewide panel dataset of Michigan school districts from 1995 to 2012. We evaluate the impact of state school finance and choice policies, over which local districts have limited control, and local district resource allocation decisions ( e. g., average class size, teacher salaries, and spending devoted to administration, employee health insurance, and contracted services). Our results indicate that 80% of the explained variation in district fiscal stress is due to changes in districts' state funding, to enrollment changes including those associated with school choice policies, and to the enrollment of high-cost, special education students. We also find that the districts in which the state has intervened have significantly higher shares of African-American and low-income students than other financially troubled Michigan districts, and they are in worse financial shape by some measures.

This article discusses estimation of multilevel/hierarchical linear models that include cluster-level random intercepts and random slopes. Viewing the models as structural, the random intercepts and slopes represent the effects of omitted cluster-level covariates that may be correlated with included covariates. The resulting correlations between random effects (intercepts and slopes) and included covariates, which we refer to as cluster-level endogeneity, lead to bias when using standard random effects (RE) estimators such as (restricted) maximum likelihood. While the problem of correlations between unit-level covariates and random intercepts is well known and can be handled by fixed-effects (FE) estimators, the problem of correlations between unit-level covariates and random slopes is rarely considered. When applied to models with random slopes, the standard FE estimator does not rely on standard cluster-level exogeneity assumptions, but requires an uncorrelated variance assumption that the variances of unit-level covariates are uncorrelated with their random slopes. We propose a per-cluster regression (PC) estimator that is straightforward to implement in standard software, and we show analytically that it is unbiased for all regression coefficients under cluster-level endogeneity and violation of the uncorrelated variance assumption. The PC, RE, and an augmented FE estimator are applied to a real data set and evaluated in a simulation study that demonstrates that our PC estimator performs well in practice.