The Complexity of Infinite Computations In Models of Set Theory

We prove the following surprising result: there exist a 1-counter B\"uchi automaton and a 2-tape B\"uchi automaton such that the \omega-language of the first and the infinitary rational relation of the second in one model of ZFC are \pi_2^0-sets, while in a different model of ZFC both are analytic but non Borel sets. This shows that the topological complexity of an \omega-language accepted by a 1-counter B\"uchi automaton or of an infinitary rational relation accepted by a 2-tape B\"uchi automaton is not determined by the axiomatic system ZFC. We show that a similar result holds for the class of languages of infinite pictures which are recognized by B\"uchi tiling systems. We infer from the proof of the above results an improvement of the lower bound of some decision problems recently studied by the author

Improving School Accountability Measures

A growing number of states are using annual school-level test scores as part of their school accountability systems. We highlight an under-appreciated weakness of that approach the imprecision of school-level test score means -- and propose a method for better discerning signal from noise in annual school report cards. For an elementary school of average size in North Carolina, we estimate that 28 percent of the variance in 5th grade reading scores is due to sampling variation and about 10 percent is due to other non-persistent sources. More troubling, we estimate that less than half of the variance in the mean gain in reading performance between 4th and 5th grade is due to persistent differences between schools. We use these estimates of the variance components in an empirical Bayes framework to generate filtered' predictions of school performance, which have much greater predictive value than the mean for a single year. We also identify evidence of within-school heterogeneity in classroom level gains, which suggests the importance of teacher effects.

Estimating Returns to Schooling When Schooling is Misreported

We propose a general method of moments technique to identify measurement error in self-reported and transcript-reported schooling using differences in wages, test scores, and other covariates to discern the relative verity of each measure. We also explore the implications of such reporting errors for both OLS and IV estimates of the returns to schooling. The results cast a new light on two common findings in the extensive literature on the returns to schooling: sheepskin effects' and the recent IV estimates, relying on natural experiments' to identify the payoff to schooling. First, respondents tend to self-report degree attainment much more accurately than they report educational attainment not corresponding with degree attainment. For instance, we estimate that more than 90 percent of those with associate's or bachelor's degrees accurately report degree attainment, while only slightly over half of those with 1 or 2 years of college credits accurately report their educational attainment. As a result, OLS estimates tend to understate returns per year of schooling and overstate degree effects. Second, because the measurement error in educational attainment is non-classical, IV estimates also tend to be biased, although the magnitude of the bias depends upon the nature of the measurement error in the region of educational attainment affected by the instrument.

Preferences and Heterogeneous Treatment Effects in a Public School Choice Lottery

This paper combines a model of parental school choice with randomized school lotteries in order to understand the effects of being assigned to a first-choice school on academic outcomes. We outline a simple framework in which those who place the highest weight on academics when choosing a school benefit the most academically when admitted. Although the average student does not improve academically when winning a school lottery, this average impact conceals a range of impacts for identifiable subgroups of students. Children of parents whose choices revealed a strong preference for academic quality experienced significant gains in test scores as a result of attending their chosen school, while children whose parents weighted academic characteristics less heavily experienced academic losses. This differential effect is largest for children of parents who forfeit the most in terms of utility gains from proximity and racial match to choose a school with stronger academics. Depending on one's own race and neighborhood, a preference for academic quality can either conflict with or be reinforced by other objectives, such as a desire for proximity and same-race peers.

What Does Certification Tell Us About Teacher Effectiveness? Evidence from New York City

We use six years of data on student test performance to evaluate the effectiveness of certified, uncertified, and alternatively certified teachers in the New York City public schools. On average, the certification status of a teacher has at most small impacts on student test performance. However, among those with the same certification status, there are large and persistent differences in teacher effectiveness. This evidence suggests that classroom performance during the first two years, rather than certification status, is a more reliable indicator of a teacher's future effectiveness. We also evaluate turnover among teachers with different certification status, and the impact on student achievement of hiring teachers with predictably high turnover. Given relatively modest estimates of experience differentials, even high turnover groups (such as Teach for America participants) would have to be only slightly more effective in their first year to offset the negative effects of their high exit rates.

Parental Preferences and School Competition: Evidence from a Public School Choice Program

This paper uses data from the implementation of a district-wide public school choice plan in Mecklenburg County, North Carolina to estimate preferences for school characteristics and examine their implications for the local educational market. We use parental rankings of their top three choices of schools matched with student demographic and test score data to estimate a mixed-logit discrete choice demand model for schools. We find that parents value proximity highly and the preference attached to a school's mean test score increases with student's income and own academic ability. We also find considerable heterogeneity in preferences even after controlling for income, academic achievement and race, with strong negative correlations between preferences for academics and school proximity. Simulations of parental responses to test score improvements at a school suggest that the demand response at high-performing schools would be larger than the response at low-performing schools, leading to disparate demand-side pressure to improve performance under school choice.

Roe v. Wade and American Fertility

We consider the effect of abortion legalization on births in the United States. A simple theoretical model demonstrates that the impact of abortion legalization on the birth rate is ambiguous, because both pregnancy and abortion decisions could be affected. We use variation in the timing of legalization across states in the early 1970's to estimate the effect of abortion on birth rates. Our findings indicate that states legalizing abortion experienced a 5% decline in births relative to other states. The decline among teens, women over 35, and nonwhite women was even greater: 13%, 8%, and 12% respectively. Out-of-wedlock births declined by twice as much as births in wedlock. If legalization in some states affected birth rates in neighboring states (through travel to obtain an abortion), comparing births between states will underestimate the actual reduction. Using more distant comparison states increases the estimated impact of abortion legalization on birth rates to about 8%. Applying this estimate to the current level of births, a complete recriminalization of abortion would result in 320,000 additional births per year.

The Effect of Randomized School Admissions on Voter Participation

There is little causal evidence on the effect of economic and policy outcomes on voting behavior. This paper uses randomized outcomes from a school choice lottery to examine if lottery outcomes affect voting behavior in a school board election. We show that losing the lottery has no significant impact on overall voting behavior; however, among white families, those with above median income and prior voting history, lottery losers were significantly more likely to vote than lottery winners. Using propensity score methods, we compare the voting of lottery participants to similar families who did not participate in the lottery. We find that losing the school choice lottery caused an increase in voter turnout among whites, while winning the lottery had no effect relative to non-participants. Overall, our empirical results lend support to models of expressive and retrospective voting, where likely voters are motivated to vote by past negative policy outcomes.

Estimating Teacher Impacts on Student Achievement: An Experimental Evaluation

We used a random-assignment experiment in Los Angeles Unified School District to evaluate various non-experimental methods for estimating teacher effects on student test scores. Having estimated teacher effects during a pre-experimental period, we used these estimates to predict student achievement following random assignment of teachers to classrooms. While all of the teacher effect estimates we considered were significant predictors of student achievement under random assignment, those that controlled for prior student test scores yielded unbiased predictions and those that further controlled for mean classroom characteristics yielded the best prediction accuracy. In both the experimental and non-experimental data, we found that teacher effects faded out by roughly 50 percent per year in the two years following teacher assignment.

Gender and Performance: Evidence from School Assignment by Randomized Lottery

School choice programs are intended to improve student achievmement, by allowing for better matches between students and schools. However, it is not clear that academic achievement will improve if parents make school choice decisions over both academic and non-academic school attributes (Justine Hastings et al., 2005a,b). Indeed, many randomized studies of impacts of school choice find little or no effect of school choice on academic outcomes. For example, initial evaluations of randomized voucher experiments in Milwaukee and New York City found modest academic impacts on eligible students (John F. Witte, et al. 1995; Daniel P. Mayer et al., 2002).1 More recently, evaluations of public school choice lotteries in Chicago and Charlotte have found no difference between the average lottery winner and loser in academic outcomes such as test scores (Julie Cullen et al., 2003; Hastings et al., 2005b). When parents are choosing schools for academic and non-academic reasons, school choice may increase utility but not necessarily improve academic outcomes. There is growing evidence that educational interventions may have heterogeneous treatment effects by gender. Analysis of the Moving To Opportunity demonstration, i