Suburban Legend: School Cutoff Dates and the Timing of Births Stacy Dickert-Conlin* Michigan State University 110 Marshall Adams Hall East Lansing, MI 48824 517-353-7275 [email protected]

Todd Elder Michigan State University 110 Marshall Adams Hall East Lansing, MI 48824 517-355-0353 [email protected] January 30, 2009 Abstract

Many states require children to reach five years of age by a specified calendar date in order to begin kindergarten. We use birth certificate records from 1999 to 2004 to assess whether parents systematically time childbirth before school cutoff dates to capture the option value of sending their child to school at a relatively young age, thereby avoiding a year of child care costs. Testing for discontinuities in the distribution of births around cutoff dates, we find no evidence that the financial benefits influence the timing of birth. Similarly, we find no systematic discontinuities in average mothers’ characteristics or babies’ health outcomes around cutoff dates. Timing in the neighborhood of school cutoffs occurs only when the cutoffs coincide with weekends or holidays, which may have implications for recent research that assumes birth dates in the neighborhood of cutoffs are essentially randomly assigned.

Key words: Kindergarten cutoff, regression discontinuity, birth timing

* Corresponding Author

“Pregnant with her first child, Isabel Arango wanted a C-section delivery. The doctor said no: Arango had no risk factors warranting a surgical birth. Then, during labor, the umbilical cord wrapped around her daughter's neck and Arango was rushed to an emergency Caesarean section. When Arango was pregnant with daughter No. 2, she again asked for a C-section. This time there was no debate. And the delivery date was picked by Arango to beat the birthday cutoff for kindergarten.” From “Born of convenience?” by Susan Aschoff, Times Staff Writer, St. Petersburg Times, August 19, 2003 http://www.sptimes.com/2003/08/19/news_pf/Floridian/Born_of_convenience.shtml accessed 6/16/08 “Suburban legend: ‘I don't know if the myth of women getting C-Sections for convenience is true or not (but I do know one woman who did it to ensure her child was born before September 1st and thereby would be able to go to Kindergarten before her town's cut off. I kid you not. She's an idiot). … While I'm willing to believe that the media creates myths such as women getting C's for convenience, there still is something going on there.’” http://letters.salon.com/mwt/broadsheet/2006/09/05/c_sections/view/index2.html?order= asc accessed 6/31/08 1. Introduction In 2005, daily birth rates in the U.S. were roughly 60 percent higher on weekdays than on weekends (Martin et al. (2007)). Much of this pattern is due to the widespread use of technologies such as induction of labor and scheduled cesarean sections, which allow for increased ability to manipulate birth timing. The motivation for timing a birth relies on a costbenefit analysis involving possible impacts on the health of the mother and baby, scheduling preferences of the mother and physician, and incentives provided by tax structures and medical institutions. In this paper, we attempt to establish whether the timing of childbirth depends on financial incentives provided by another institution: public education age eligibility requirements. Forty-three states in the U.S. impose statewide cutoff rules that require children to have reached their fifth birthday before a specific day to be eligible to begin public kindergarten each fall. For example, in California a child must turn five on or before December 2, 2009 to be

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eligible to enroll in the fall of 2009. The benefit to the parents of a birth before the cutoff date is the option of sending their children to kindergarten five years in the future, instead of being forced to wait a sixth year. If exercised, this option results in one fewer year of child care costs in the form of money and/or time. These incentives can be large, as estimates suggest that the out of pocket child care expenses among parents with children under age five who use child care are at least seven percent of income.1 The option bears no obligation because parents can always decide to “redshirt” a child by not sending her to kindergarten when first age-eligible. The potential costs of childbirth timing include medical uncertainties for mothers and babies associated with the methods of timing childbirth and the insurance costs of receiving a medical treatment that might otherwise be unnecessary. Although anecdotal evidence suggests that parents respond to these incentives, no previous studies quantify this response or assess whether it is related to factors that might influence the costs and benefits of birth timing. However, previous research shows that parents time birth in response to a variety of other financial incentives. For example, parents in the United States (Dickert-Conlin and Chandra, 1999) and Japan (Wataru and Wakabayashi, 2008) facing high tax benefits of an additional child are more likely to have children at the end of the calendar year rather than the beginning. A $3000 payment by the Australian government for all children born on or after July 1, 2004 resulted in “…more Australian children [born on July 1] than on any other single date in the past thirty years.” (Gans and Leigh, 2009) As these cases illustrate, parents and medical professionals are clearly willing to manipulate the timing of birth in response to non-medical incentives. 1

See the U.S. Census http://www.census.gov/population/www/socdemo/childcare.html for annual estimates from the Survey of Income and Program Participation and Giannarelli and Barsimantov (2000) for comparable estimates from the National Survey of American Families. In the Early Childhood Longitudinal Study (ECLS), 55 percent of families pay for child care outside the home, at an average annual cost of roughly $2500 in 1998 dollars (Datar, 2006b).

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Birth timing behavior around school cutoff dates also plays a crucial role in the rapidly expanding literature that uses a child’s birth date as a potentially exogenous source of variation in her age relative to her grade level. A number of recent studies (for example, Bedard and Dhuey (2006), Black et al. (2008), http://www.ifs.org.uk/docs/born_matters_report.pdf (Black cites this as a paper that Datar (2006a), Elder and Lubotsky (2009), McCrary and Royer (2008), McEwan and Shapiro (2008), and Stipek (2002)) argue that the timing of births around state cutoff dates is essentially random. Some of these papers test this assumption by checking for smoothness in the average values of observable covariates (such as parental education and race) at the cutoff dates; a discontinuity would indicate that births are not randomly distributed in the neighborhood of cutoffs. None directly test for discontinuities in the number of births themselves, and with the exception of McCrary and Royer’s (2008) and Black and McEwan? analysis of the universe of birth certificates from California and Texas, all use relatively small panel datasets that do not have sufficient power to carry out such a test. We analyze the population of births in the United States from 1999 through 2004, comprising roughly twenty million births, in order to shed new light on the validity of the identification strategies used in these studies. Before proceeding to our more formal statistical analysis, we first consider graphical evidence of whether disproportionately large numbers of babies are born on or just before the cutoff dates. We use restricted-use versions of the population of birth certificates from the National Center for Health Statistics (NCHS) that include information on exact date of birth.2 Figure 1A displays counts of births in fifteen-day windows centered around September 1 among the 18 states with September 1 school cutoff dates for the years 1999 to 2004. Specifically, the

2

The public-use data include month and year of birth, as well as day of the week, but not exact birthday. See http://www.cdc.gov/nchs/r&d/rdc.htm for more details on accessing these data.

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vertical axis measures the number of births on a particular day divided by the daily average number of births for a given year. For example, the first date shown is August 25, 1999, and roughly 16 percent more births fell on that day than on an “average” day in 1999. Each vertical bar represents one date, with black bars representing days in the August 25 though August 31 window, white bars representing the September 2 through September 8 window, a gray bar representing September 1 itself, and a “hatched” bar representing Labor Day, a federal holiday on the first Monday of September that fell on September 6 in 1999. Note that in 2003, Labor Day fell on September 1, so the corresponding bar is both hatched and gray. Consider the pattern of births in 2000 in Figure 1A. Many more births occurred on or before September 1st than immediately afterwards, with roughly 20 percent more births occurring on September 1 than on a “typical” day and nearly 20 percent fewer births occurring on September 2 than on a typical day. At first glance, this large discontinuity suggests that cutoffbased birth timing is widespread, but this is actually a result of a much more empirically relevant pattern – in every year, there are large declines in births on weekends and Labor Day. September 1 was a Friday in 2000, so it was followed by large declines in birth rates for three days, the first two being the weekend and the third being Labor Day. This three-day dip recurs annually, in addition to a two-day dip that corresponds to the other weekend in this 15-day window. In 2003, a naïve look at the Figure would suggest that parents time births so that they occur after September 1, given that there is roughly a 42 percentage point increase in births between the first and second of the month, but this again reflects a weekly pattern of increases in births from Sunday to Monday. Figure 1B shows the distribution of births in the neighborhood of September 1 for states that do not have a school cutoff in the August 25 through September 8 window. This figure

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clearly shows the same striking pattern, with a large negative discontinuity in 2000 and a large positive one in 2003. We assume below that differences in the discontinuities in the two figures capture the true effect of the school cutoff laws on birth timing. For example, there is a positive discontinuity of roughly 42 percent in both Figures 1A and 1B in 2003, so that the implied effect of the cutoff laws is approximately zero. A visual comparison of Figures 1A and 1B provides the intuition behind the “difference in discontinuities” empirical approach that we present below. The strict nature of school cutoff dates lends itself to a regression discontinuity design, which we use to contrast birth patterns surrounding school cutoff dates in states where the cutoffs bind versus states where the cutoffs do not apply.3 Consistent with the patterns of Figures 1A and 1B, our estimates indicate that birth timing responses to school entrance eligibility are not empirically relevant – if timing exists, it is sufficiently uncommon that it is statistically unnoticeable in an analysis of over 20 million births. Moreover, characteristics of mothers, such as their education and race; characteristics of births themselves, such as whether they occurred via cesarean section or inducement of labor; and infants’ birth outcomes, such as birthweight and APGAR scores, do not vary discontinuously in the neighborhood of cutoff dates. After an extensive set of comparisons among states and over time, we conclude that while the timing of birth may be associated with school cutoff dates in some years, this pattern exists merely because of the day of the week on which cutoffs fall. The conclusiveness of our results relies on the high-quality data that we introduce in the next section. In Section 3, we use the data to show the dramatic incidence of birth timing in

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Bedard and Dhuey (2006) and Elder and Lubotsky (2009) both find a very high compliance rate with school entry laws, with fewer than 2 percent of children entering school before they are legally eligible to do so. The primary way in which laws can be circumvented is by enrolling in a private kindergarten because private schools are not bound by state cutoff laws.

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general. After establishing that births are increasingly timed for apparently non-medical reasons, we proceed to Section 4 for our analysis of whether births are timed in response to school cutoff dates. We conclude in Section 5 with a discussion of our findings and their implications.

2. Data Since 1985, the U.S. Vital Statistics Natality Detail Files contain a complete record of all live births that reported a Standard Live Birth Certificate, accounting for an estimated 99 percent of all live births in the United States (U.S. Department of Heath and Human Services, 2006). An agreement with NCHS allows us to access the confidential data on exact date of birth, which is essential for identifying timing within small windows around school cutoff dates. The Standard Live Birth Certificate also includes data on medical procedures, method of delivery, birth outcomes, parental demographics, birth order, and prenatal care.4 For our primary analysis we use the most recently available data, 2004, and the five previous years, focusing on this timeframe because data collection was relatively standardized from 1999 to 2004.5 We merge these individual data with information on school cutoff laws as described in Elder and Lubotsky (2009). Between 1999 and 2004, 42 states and the District of Columbia have an explicit statewide cutoff, representing approximately 80 percent of all births. The remaining eight states do not have uniform state cutoffs, so we exclude children living in those states from our analysis. Because our empirical strategy compares the timing of birth around explicit cutoff dates, we further restrict our data in much of the analyses and indicate when we do so. 4 See http://www.cdc.gov/nchs/data/dvs/birth11-03final-ACC.pdf for the 2003 version of the Standard Live Birth Certificate that applies from 2003 to the present. 5 The standard birth certificate was revised in 2003, and the standard birth certificate for 1989 through 2002 is available in the appendices of the Technical Appendix from the Vital Statistics of the United States during that time (for example, see Figure 4-A on page 30 of the 2002 Appendix: http://www.cdc.gov/nchs/data/techap02.pdf).

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3. Timing of Births Given the uncertainties in timing conception nine months in advance and in a baby’s natural arrival conditional on that conception, our discussion of birth timing primarily refers to medically manipulating the timing of birth through cesarean section deliveries and inducement of labor.6 A cesarean section requires a surgical incision through the mother’s abdomen and uterus to retrieve the baby. This procedure may be scheduled in advance when conditions of the baby or mother make vaginal deliveries less desirable, although they are sometimes performed in emergency situations when a birth is not proceeding normally. The induction of labor is the process of using hormones to stimulate uterine contractions before the spontaneous onset of labor. While a set of medical conditions justify timing birth, there is also discretion in using these methods for other nonmedical purposes, such as convenience. For example, the American College of Obstetricians and Gynecologists (ACOG) lists medical conditions such as maternal hypertension as an indication for inducing labor, but they also suggest that “logistic factors” such as distance from a hospital and psychosocial conditions are indications for inducing labor (ACOG (1995)). In a patient pamphlet on cesarean births, the ACOG writes, “sometimes a woman requests a cesarean delivery. This is a complex decision that should be carefully considered and discussed with the doctor.”7 Generally, timing is more precise with a scheduled cesarean section than with an induced labor because of uncertainty in the length of time between the onset of induction and birth, although this is almost never more than 48 hours.

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While the standard definition of a “full term” baby refers to 40 weeks of gestation (based on time since the mother’s last normal menstrual period), the distribution of birth dates is roughly uniform between 38 and 41 weeks of gestation. This implies that attempts to precisely time births by timing conception will largely be unsuccessful. 7 See http://www.acog.org/publications/patient_education/bp006.cfm, accessed 12/15/2007.

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Table 1 shows clear evidence that the timing of births is not random, with this nonrandomness increasing over time. If births were distributed uniformly across days of the week, roughly 14.3 percent of all births would occur on each day. Instead, many fewer births fall on weekends relative to weekdays, with Tuesday through Thursday being the peak days.8 The top three rows of the table display the distribution in births in 1968, 1978, and 1988 in order to put more recent trends into context. In 1968 and 1978, 12.6 percent of all births occurred on Sundays and 15.3 percent occurred on Tuesdays, a 21 percent difference. That differential remained roughly constant through 1978 and increased to 34 percent in 1988. By 1999 the relative discrepancy had grown dramatically to 64 percent, with 10.0 percent and 16.4 percent of births falling on Sundays and Tuesdays, respectively. In 2004, the last year in which data are available, the Sunday versus Tuesday differential increased to 75 percent. Birth timing is not only prevalent, but it is also correlated with maternal demographics and babies’ outcomes.9 To illustrate which groups appear likely to time births, Table 2 presents summary statistics by day of the week for 2002.10 Weekday births, which are more likely to be the result of selective timing, are more common among older, more highly educated, married mothers who are not African-American. Babies born on weekdays are healthier on a variety of dimensions: they receive earlier prenatal care, they are older in gestational weeks, they are heavier, and they receive higher APGAR scores, which are ten-point summary measures of health at birth. Perhaps most striking, mothers’ first deliveries, measured with the binary

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The day of week measures are apparently coded inaccurately in some years of the data, since they conflict with the reported birth date. For example, among births occurring on Sunday, September 3, 2000, nearly 6 percent have “Monday” as the listed day of the week. We treat the reported date as the “truth” and generate a day of the week variable based on this measure in our analyses. 9 These correlations between weekday births and birth outcomes are well documented. See, for example Chandra et al. (2004), Dowding et al. (1987), Gans and Leigh (2009), Gould et al. (2003), Hendry (1981), Luo et al. (2004), MacFarlane (1978), Mangold (1981), and Mathers (1983). In related work, Buckles and Hungerman (2008) document differential patterns in demographic characteristics of the parents over the calendar year. 10 Results for all years, which are quantitatively similar, are available from the authors upon request.

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variable first born, are much less likely to be born on weekdays relative to higher order births, with 43 percent of all weekend deliveries being first births relative to only 37 percent of Monday births. Subsequent births are more likely to have medical conditions revealed in the first birth that warrant timing and experienced parents may be more willing to proactively time birth relative to first time parents. The gender of the baby is uncorrelated with the day of the week, but all other weekend-weekday differentials in the table are statistically significant at conventional levels; for example, the t-statistic associated with the hypothesis of no differences in average maternal age between weekends and weekdays is 83.3. As support for the notion that medical interventions are the principal mechanisms driving birth timing, Table 3 shows the probability of medical interventions by day of the week. In 1999, 10.4 percent of all births on Sundays involved induction of labor, compared to 23.0 percent of Tuesday births. Overall, the incidence of induction increases slightly over these six years. Cesarean sections are also relatively more likely to occur during weekdays, and the trend over time is particularly dramatic – the proportion of births via cesarean section increased from 21.6 percent of all births in 1999 to 28.8 percent in 2004, a 33.3 percent increase in only five years. Finally, the births most likely to be scheduled in advance are repeat cesarean sections, because a primary cesarean section often leads to a scheduled cesarean delivery for subsequent births. Table 3 shows that the rate of repeat cesarean sections increased by nearly 40 percent from 1999 to 2004, and the weekday rate of repeat cesarean deliveries was nearly 2.5 times the weekend rate by 2004. Finally, the last row of the table shows that by 2004 more than 35 percent of mid-week births were either repeat cesareans or involved inductions.11

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Induction and cesarean sections are not mutually exclusive because in some cases in which labor is induced, an emergency cesarean section is ultimately performed when labor does not progress sufficiently.

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Tables 1 through 3 present compelling evidence that births can be precisely timed within short windows and that this timing is related to observable characteristics of mothers and babies. We turn next to direct evidence on whether the incentives created by school cutoff laws influence the timing of births.

4. Do School Cutoff Dates Affect the Timing of Birth? Our empirical strategy involves a comparison of patterns in births and characteristics of mothers and babies in states where a cutoff is in place (treatment) with states where there is no cutoff in place (control). Within the 43 states with explicit state-level cutoffs, we consider five separate cutoff dates which are spaced at least two weeks apart. These cutoffs are September 1, September 30, October 15, December 2, and December 31, each of which is relevant for over five percent of all children born in the U.S. and together apply to 29 states (Appendix Table 1 lists these states). To see the need for dropping some states from the analysis, note that Michigan, which has a December 1 cutoff, would not be a sensible control group for the timing of births around December 2, which is the cutoff in California. Similarly, states with cutoffs within two weeks of September 1 will not be valid control cases for the timing of births around September 1. While dropping these states limits our sample to 75 to 77 percent of all births in states with cutoff laws in place, depending on the year, it permits the cleanest identification strategy by yielding control cases whose distributions of births and characteristics are unlikely to be affected. For example, the timing of births in the neighborhood of September 1 in California should be unaffected by its own December 2 cutoff.12

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All of the results shown hereafter are insensitive to treating September 1 cutoff states as the treatment group and all states with statewide cutoffs earlier than August 15 or later than September 15 as the control group. This sample design leads to fewer individuals in the treatment group and slightly less precise estimates, but no substantive change in point estimates.

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Tests of continuity in the density of births around school cutoff dates We begin our analysis by asking whether the incentives to meet school cutoff deadlines alter the broad pattern of birth counts. Our variable of interest is the share of births in a given year in state s that occurs on calendar date d: share sd =

(1)

births sd 1 365 ∑ births sδ 365 δ =1

,

where birthssd is the number of births in state s on date d. The denominator is the average daily number of births in that state (assuming a 365-day year), so if sharesd equals 1.10, for example, the number of births on day d is 10 percent higher than the average daily number of births for that state and year.13 If women time births to occur before school entrance cutoff dates, the average of sharesd will drop discontinuously after the cutoff date, ceteris paribus. We adopt McCrary’s (2007) twostage procedure to test for discontinuities of the density of a variable. The first stage involves the creation of a histogram of the variable of interest. We use bin sizes of one day, so that the firststage histogram is simply a plot of daily values of the variable sharesd.14 In the second stage, we smooth the first-stage histogram with local linear regressions on either side of the entrance cutoff c, which is the potential point of discontinuity.15 This amounts to estimating linear regression

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In leap years, the denominator of sharesd is the average based on a 366-day year. The empirical results below are nearly identical if, instead of analyzing sharesd, we use the logarithm of the number of births as the dependent variable and include state fixed effects. 14 McCrary (2006) finds that the choice of bin size in this first stage matters little in most applications, and our results are insensitive to aggregating to two-day bins. 15 One could also estimate global polynomial models in order to smooth the estimated histogram of sharesd, but local linear models are asymptotically more efficient and focus attention on behavior near the cutoffs, which is intuitively appealing. Fan and Gibjels (1996) provide a general discussion of local linear regression and its advantages relative to other parametric and nonparametric approaches.

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functions on observations within a pre-specified bandwidth of the point c, fitting separate local linear functions in windows before and after the cutoff: (2)

share sd = α + τ (d sd − c) + γAsd + β ((d sd − c) × Asd ) + ε .

In (2), dsd is a cardinal measure of calendar time, so that in a state with a cutoff of September 1, on September 3 the value of (dsd – c) is 2, and births on that day would contribute to estimation of the density of births after the cutoff but not on or before it. Asd is a binary indicator of whether the date in question falls after the cutoff (that is, Asd = 1 if (dsd – c)>0, and zero otherwise), so γ is the parameter of interest – an estimate of the discontinuity in the histogram of sharesd at the cutoff. Although an estimate of model (2) would measure a discontinuity in the density of births at a school entrance cutoff, the patterns in Figures 1A and 1B above suggest that the findings from such a model may merely stem from the effects of day of the week, holidays, or other unmeasured factors that influence birth timing. A cleaner strategy involves the comparison of behavior around a cutoff between states that actually use that cutoff and states that do not. Intuitively, we would like to measure the difference in discontinuities between Figures 1A and 1B, so we estimate the following model: (3)

sharesd = β 0 + β1 (d sd − c) + β 2 Asd + β 3 ((d sd − c) × Asd ) + β 4 Rsd ' + β 5 ( Rsd × (d sd − c)) + β 6 ( Rsd × Asd ) + β 7 ( Rsd × (d sd − c) × Asd ) + X sd Γ + ε sd

where Rsd is a binary indicator of whether the date d lies in the neighborhood of the cutoff for state s. β6 is the key parameter in this model, in that it measures the difference in the discontinuity in birth shares at a particular cutoff for states in which the cutoff is binding versus states in which it is not. Note that data from two states with different cutoffs is sufficient to identify β6. For example, with birth counts in California (which has a December 2 cutoff) and

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Illinois (September 1 cutoff) from August 15 to September 15, the California data identifies the β0 through β3 parameters, while Illinois births identify the remaining β parameters. β6 measures the magnitude of the discontinuity in the density of births in Illinois around September 1 relative to the same discontinuity in California. Finally, the model includes indicators for individual days of the week, with Tuesday through Thursday aggregated as a single category, and indicators for holidays such as New Year’s Day and Labor Day as additional controls Xsd. Estimates of the parameters of equation (3) will typically be sensitive to the choice of bandwidth, in contrast to the insensitivity to the choice of bin size in the first stage. In general, smaller bandwidths reduce bias but decrease precision. Although one may apply formal crossvalidation methods to select the bandwidth, we adopt Fan and Gijbels’s (1996) rule-of-thumb selector and also estimate models with a variety of bandwidths in order to assess sensitivity of the estimates to the choice of bandwidth. This is equivalent to varying the width of windows that define our estimation sample, and below we report results based on windows of 29 days (that is, including observations within 14 days of the cutoff on both sides), 15 days, and in the Appendix, 9 days. In addition to estimating model (3) on all the births in 29 states, we use the patterns in Table 3 to choose subsamples of births where timing is most prevalent. We select higher order births that are repeat cesarean sections, repeat cesareans or inductions, and repeat cesareans or inductions for college educated women. Selecting on women with a college education deserves more explanation in this context. Table 3 shows that education is positively correlated with weekday births, perhaps because more highly educated mothers have better access to physicians who manage their care more closely than those with lower education. We also expect more highly educated parents to be more well-informed about school age eligibility laws. However,

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the option to send a child to school may be less valuable for more highly educated parents if they prefer to have their child be one of the oldest in the classroom rather than the youngest or if the benefits of one fewer year of paid child care are lower for parents with higher education.16 Table 4 shows estimates of equation (3), with the columns showing estimates of β6 separately by year and the first column aggregating 1999-2004 together. The first row includes all births occurring in a 29 day window centered at the cutoff date. The coefficient estimate in the model that includes all six years is -0.010, indistinguishable from zero at conventional significance levels. To get a sense of the magnitude of this coefficient, recall that the variable sharesd measures daily birth rates relative to a “typical” day, so an estimate of -0.010 implies a discontinuity of 1 percent of the daily average number of births. Assume that this discontinuity results from 0.5 percent of the births that would normally occur the day after a cutoff being moved one day earlier. In 2004, roughly 10,000 births occurred daily in states with cutoff laws in place; therefore, if we ignore sampling variation and interpret the point estimate literally, it implies that 50 births in the United States (out of 4.3 million annual deliveries) are moved annually in response to school eligibility requirements. From another perspective, the data are inconsistent with even modest amounts of birth timing – at the 5 percent significance level we can reject that β6 ≤ -0.035, which would correspond to roughly 175 births being moved annually. As a final way to gauge the magnitude of the estimate, consider the raw day-of-week birth patterns in Table 1 and the estimated coefficients on day-of-week indicators in equation (3), which are shown in Appendix Table 3. In 2004, 20.0 percent of all births occurred on either Saturday or Sunday, which is 30 percent lower than the 28.6 percent (= 2/7) that would be implied by random assignment of births. If manipulation of birth timing is the sole cause of this 16

Elizabeth Graue (in Simms and Erikson, 2002) goes as far as proposing that “some families, mostly well-off and white, plan conception of their children to give them ‘better’ birthdays – birthdays in the fall and winter – so they are among the oldest in their class.”

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discrepancy, then 30 percent of all births that should have fallen on a weekend, or roughly 8.6 percent of all births, involve some timing manipulation. In other words, roughly 370,000 out of 4.3 million births in 2004 may have been moved due to a desire to avoid weekend deliveries, while fewer than 175 births were moved in response to school cutoff laws. To address the possibility that aggregating years masks informative patterns within years, Table 4 also shows the estimates from equation (3) for each of the six years separately. The point estimates are negative in three of the six years we consider (2000, 2003 and 2004), positive in the other three, and none are statistically significant at the five percent level. The pattern across years might be explained by the day of the week that school cutoff dates fall. For example, if a cutoff falls on a weekend or immediately following a weekend, the costs of timing the birth to occur before the cutoff are higher because of lower hospital staffs on weekends, compared to when the cutoff day is a weekday or is preceded by weekdays. Appendix Table 2 shows that 1999 and 2004 have the fewest weekend or holiday constraints near the cutoffs, yet evidence of birth timing is no stronger in these years than in other years. Clearly, these patterns provide no compelling evidence that the timing of births is manipulated. Limiting the sample to births that are most likely to be timed also shows no evidence of systematic timing among states with binding cutoffs. For example, in the second row of Table 4, we show that among all repeat cesarean births, the share occurring after the cutoff is lower in three of the six years and higher in the other three years. None of these coefficients are statistically significant at any standard levels. Similarly, no estimates are statistically significant in the specifications among higher order births that were either repeat cesarean sections or induced labor, regardless of whether the samples are limited to college-educated mothers.

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In order to investigate whether the local linear estimates of model (3) fail to reveal interesting patterns in the data, we also estimate complementary models that include separate indicators for seven days before and after all included cutoffs: (4)

share sd = α +

⎛ 7 D β δ R R + + × ∑ sdj j sd sd ⎜⎜ ∑ Dsdj γ j = −7 ⎝ j = −7 7

⎞ ' ⎟ j ⎟ + X sd Γ + ε sd ⎠

For example, the indicator Dsd3 equals one on dates three days after any of the five cutoffs, for all states. That is, Dsd3 equals one for September 4th in all states and all years because September 1st is a cutoff in our sample. Dsd3 also equals one for October 3, October 18, December 5, and January 3, and is zero for all other days of the year for all states. Rsd is again equal to one in the neighborhood of the actual cutoff for state s, and zero otherwise. The coefficients of interest are the γj terms, which measure whether the share of births on a day near a cutoff are different for states with the cutoff compared to states where the cutoff does not apply. Xsd again includes indicators for day of the week and holidays. For the full sample of births, Figure 2 presents these results graphically together with our local linear estimates. In the figure, the cutoffs are denoted by “Day 0”. Each data point represents an estimate of γj in a particular year, with j ranging from -7 to 7. The local linear estimates from the “all births” sample of Table 4 overlay these points. Apart from 2000, the daily variation in birth rates around entrance cutoffs appears to be the product of noise. While the data points in 2000 suggest systematic birth timing, this pattern is apparently an anomaly because it does not arise in any other years. Tests of continuity in the average of birth-level observable covariates The results from the preceding subsection imply that the timing of, at most, very few births are manipulated in order to “beat” the school cutoff dates; however, it is still possible that

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the incentives to meet the deadline alter the type of births that occur before and after the deadline. To consider this question, we take advantage of the large amount of maternal and infant information in the individual level vital statistics. Our estimation strategy is similar to that used in the estimation of the density of births, except that here we analyze discontinuities in average outcomes. The outcomes Yisd broadly fall into three categories: birth procedures, maternal characteristics, and infant characteristics. Again we fit locally linear regression functions: (5)

Yisd = β 0 + β1 (d sd − c) + β 2 Asd + β 3 ((d sd − c) × Asd ) + β 4 Rsd + β 5 ( Rsd × (d sd − c)) ' + β 6 ( Rsd × Asd ) + β 7 ( Rsd × (d sd − c) × Asd ) + X sd Γ + ε isd .

Table 5 displays estimates of β 6 for a variety of outcomes Yisd, with Panel A displaying the relationships among all births. The rows labeled “Birth Procedures” correspond to estimates of discontinuities in the probability of birth procedures such as inductions, cesarean sections, and repeat cesarean sections. Note that these estimates are closely related to the previous section’s birth count specifications in which the counts were limited to those that involved specific obstetrical procedures. The estimates show negative discontinuities in the probability of inductions in all years except 2004. In 2001 and 2002 the effects are relatively large and statistically significant, suggesting that the probability of an induction is approximately 1.14 to 1.28 percent higher on or before a cutoff date than immediately after. These results are consistent with the notion that mothers time births via inducement of labor to beat school entrance cutoffs. In contrast, the results for cesarean sections and repeat cesareans show no clear pattern. If anything, cesareans appear more common just after cutoff dates than before, with a significantly positive estimate of 0.0097 (0.0046) in 2002 and five of the six estimates for repeat cesareans being positive.

17

Among the other characteristics listed in the table, there are no consistent patterns other than the fact that most estimates are precisely estimated zeros. For example, among “Mother’s characteristics”, the coefficients suggest that mothers of babies born just after the cutoff have somewhere between 0.0298 fewer and 0.0530 more years of education than mothers of babies born just before the cutoff. The standard deviation of mothers’ education across years is roughly 2.85, so the largest coefficient of 0.0530 in 2002, which is marginally statistically significant, corresponds to only a 0.02 standard deviation effect. Similarly, there are statistically significant discontinuities in childrens’ health outcomes such as birthweight, but the signs of the coefficients are inconsistent across years and the magnitudes suggest small effects. For example, the relatively large point estimate of -16.3512 on the discontinuity for birthweight in 1999 corresponds to roughly half of an ounce. Note that the expected signs on the infant health measures are not obvious ex ante. One might expect that only healthy babies’ births are moved forward for nonmedical reasons, implying a negative sign on birthweight. On the other hand, all else equal, babies whose birth dates are manipulated to be earlier are mechanically of lower gestational age, so we might expect a positive sign because age and birthweight are positively correlated. Although the results are far from indisputable, there is no evidence that babies’ health is jeopardized by birth timing around school cutoffs. Panel B of Table 5 presents results based only on higher order births. Although we would expect evidence of birth timing to be strongest among this subsample, again no clear patterns exist. As in Panel A, the results based on inductions suggest that births are timed to beat school cutoffs in 2000-2002, but the estimates for cesarean sections are of opposite sign in these years. The 2001 and 2002 results for inductions are also inconsistent with the discontinuities for the density of births in these years shown in Table 4, which implied that births are moved after

18

cutoff dates, if at all. In spite of this inconsistency, the results of Table 5 suggest that manipulation of birth timing via inductions may be empirically relevant, so we pursue an additional analysis of induction rates. Specifically, we estimate models of induction rates for states with and without cutoffs in the seven days before and after cutoff dates: (6)

Yisd = α +

⎛ 7 D β δ R R + + × ∑ sdj j sd sd ⎜⎜ ∑ Dsdj γ j = −7 ⎝ j = −7 7

⎞ ' ⎟ , j ⎟ + X sd Γ + ε isd ⎠

where Yisd represents an indicator of whether a birth involved an induction and all other parameters are defined as they were in expression (4). Figure 3 combines estimates of γj from equation (6) with the local linear results from Table 5 for all births. For example, in 1999, the estimate of γ0 is 0.012, indicating that roughly 1.2 percent more inductions occurred exactly on a cutoff date in states where that cutoff applied than in states were the cutoff did not apply, and the estimate of γ1 is roughly zero. More importantly, while the local linear estimates for 2001 and 2002 yielded statistically significant negative discontinuities, the plot for 2002 shows that γ0 is negative and over two percentage points lower than γ-1. This decline in induction rates before the cutoff is inconsistent with inductions being used to time births. The estimates for 2001 are consistent with the manipulation of birth timing via inductions, but this pattern appears unique – the only other year that exhibits such a striking pattern is 2004, but in this year the discontinuity is of the opposite sign. On the whole, the evidence from six years of data based on the population of births in 29 states provides no evidence that births are systematically timed to occur before state-level kindergarten entrance cutoff dates. We find no clear patterns based on either the number of births or characteristics of those births, including obstetric procedures, demographics of mothers, or infant health outcomes.

19

5. Discussion and Conclusions

Using the population of births in the U.S. from 1999 to 2004, we estimate flexible models intended to identify the extent to which parents and physicians manipulate the timing of births in the neighborhood of state-level school entrance cutoff dates. The evidence suggests that no such manipulation takes place, even among births and obstetric procedures that are likely to be most susceptible to timing. For example, repeat cesarean sections, which are frequently scheduled in advance and are four times as likely to occur on a typical weekday as on a typical weekend day, are no more likely to be performed on or before school cutoff days than immediately afterward. Two distinct but related empirical strategies, one based on the identification of discontinuities of the density of births and the other based on discontinuities in the average value of observable characteristics of births and mothers, fail to find evidence of birth timing. Our central estimate implies that roughly 50 of the nearly 4.5 million births per year are moved forward in response to school cutoffs. This estimate is insignificantly different from zero but is estimated precisely enough to lead us to reject that more than 175 births are moved each year. The lack of a discernible effect is puzzling, particularly given the findings of two separate literatures. The first, illustrated by Gelbach (2002) and Cascio (2009), shows that a child’s eligibility for public school results in positive maternal labor supply responses, presumably because mothers no longer need to stay at home to care for children. This measureable response to the large implicit child-care subsidy provided by public schooling suggests that families would value taking advantage of this subsidy as soon as possible, or at least the option to do so. The second literature, illustrated by the work of Dickert-Conlin and Chandra (1999) and Gans and Leigh (2009), shows that parents and doctors are willing to manipulate the timing of birth in response to financial incentives.

20

Why is the response to the incentive provided by school cutoff laws so much smaller than the response to the tax- and transfer-based incentives? First, the financial impacts of school entry are deferred until five years after a child’s birth, and a $2500 reduction in child care costs in five years (using calculations from Datar (2006b)) may be discounted substantially, particularly because the probability of relocation to a state with a different entrance cutoff further increases the relevant discount rate. A lack of information may also be important – unlike the transfer analyzed by Gans and Leigh (2009), which was essentially common knowledge among expectant parents, knowledge of school age eligibility requirements is likely much less widespread. Perhaps most importantly, knowledge of school entry laws is likely to be most prevalent among highly-educated parents, and those parents are increasingly choosing to increase the age at which their children begin kindergarten. Figure 4 shows patterns of “academic redshirting”, which refers to parents voluntarily delaying a child’s entrance into schooling until the year after they are first eligible, in the fall 1998 survey of the Early Childhood Longitudinal StudyKindergarten Cohort (ECLS-K). Approximately 15 percent of children born in the month before their state’s kindergarten cutoff date are redshirted, and this number correlates strongly with parental education – it increases to 23 percent among children born to mothers who are college graduates and to nearly 30 percent for offspring of mothers with postgraduate education. Deming and Dynarski (2008) show that the prevalence of redshirting dramatically increased in the past 20 years, based in part on parents’ beliefs that children who are relatively old when they enter school will perform better.17 The prevalence of redshirting among high-SES families implies that the value of the option to send a child to school at a young age may be near zero 17

Several studies have established that the oldest students in a grade perform relatively well early in their schooling careers. However, Black et al. (2008) and Elder and Lubotsky (2009) provide strong evidence that these effects do not persist into secondary schooling and adulthood.

21

because it will not be exercised. Therefore, the benefit of manipulating the timing of birth may be substantially smaller in this context than in those that involve a pure cash transfer. Finally, the findings of this paper suggest that studies relying on the timing of births as an exogenous source of variation of a treatment of interest, such as school entrance age or grade level at a particular age, are likely based on a sound identification strategy. Specifications using the universe of births from 1999 to 2004 reveal no evidence of precise sorting around school cutoff dates or of discontinuities in parental characteristics that are likely to influence child outcomes. This finding must be interpreted with a strong caveat for researchers in this area: when school cutoffs fall adjacent to a weekend – as was the case in 2000, when roughly 75 percent of children lived in states with cutoffs that occurred on a Friday, Saturday, or Sunday – students born on or just before cutoffs may be systematically different from those born immediately afterward because of the variation of the composition of births by day of the week.

22

Acknowledgements:

We thank Mike Conlin, Steven Haider, Gary Solon and seminar participants at Michigan State University, Syracuse University, and the University of Michigan for helpful discussions about this topic. In addition, we are grateful to Negasi Beyene, Santosh Gambhir, and Vijay Gambhir at the NCHS Research Data Center for tireless assistance with remote access to the Natality Detail Files. Brian Moore provided valuable research assistance. The content, including all errors, is solely the responsibility of the authors.

23

References:

ACOG, 1996. “Induction of Labor.” International Journal of Gynecology and Obstetrics 53:6572. Bedard, Kelly and Elizabeth Dhuey. 2006. “The Persistence of Early Childhood Maturity: International Evidence of Long-Run Age Effects.” Quarterly Journal of Economics, 121(4): 1437-72. Black, Sandra, Paul Devereux, and Kjell Salvanes. 2008. “Too Young to Leave the Nest? The Effects of School Starting Age.” NBER Working paper #13969. Buckles, Kasey and Daniel Hungerman. 2008. “Season of Birth and Later Outcomes: Old Questions, New Answers.” NBER Working Paper 14573. Cascio, Elizabeth. 2009 “Maternal Labor Supply and the Introduction of Kindergartens into American Public Schools.” Journal of Human Resources, 44(1), Winter 2009. Chandra, A., L. Baker, S. Dickert-Conlin, and D.C. Goodman 2004. “Holidays and the Timing of Births in the United States,” mimeo., Harvard University. Clark, Laura. 2007. Monday “Mothers Time Their Caesarean to Get Baby into School” Daily Mail (London) February 19, 2007 ED 1ST; Pg. 29. Datar, Ashlesha. 2006a. “Does Delaying Kindergarten Entrance Give Children a Head Start?” Economics of Education Review, 25(1): 43-62. Datar, Ashlesha. 2006b. “The Impact of Kindergarten Entrance Age Policies on the Childcare Needs of Families.” Journal of Policy Analysis and Management: 25(1): 129-53. Deming, David James and Susan Dynarski. 2008. “The Lengthening of Childhood.” Journal of Economic Perspectives 22(3): 71-92. Dickert-Conlin, Stacy and Amitabh Chandra. 1999. “Taxes and the Timing of Births,” Journal of Political Economy, 107(1): 161-177, February. Dowding, V.M, N.M. Duignan, G.R. Henry, D.W. MacDonald. (1987). “Induction of Labour, Birthweight and Perinatal Mortality by Day of the Week,” BJOG: An International Journal of Obstetrics and Gynaecology 94: 413–19. Elder, Todd and Darren Lubotsky. 2009. “Kindergarten Entrance Age and Children’s Achievement: Impacts of State Policies, Family Background, and Peers.” Forthcoming. Journal of Human Resources. Fan J., and I. Gibjels, 1996. Local Polynomial Modeling and Its Applications. Chapman and Hall, London.

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Gans, Joshua and Andrew Leigh. 2009. “Born on the First of July: An (Un)natural Experiment in Birth Timing, Journal of Public Economics, 93(1-2): 246-263. Gelbach, Jonah. 2002. “Public Schooling for Young Children and Maternal Labor Supply”, American Economic Review, 92(1): 307-22, March. Giannarelli, Linda and James Barsimantov. 2000. “Child Care Expenses of America’s Families.” Urban Institute Occasional Paper Number 40. http://www.urban.org/url.cfm?ID=310028 Gould, J.B., C. Qin, A.R. Marks, G. Chavez. 2003. “Neonatal Mortality in Weekend vs. Weekday Births,” Journal of the American Medical Association 289: 2958–62. Hendry, R.A. 1981. “The Weekend-A Dangerous Time to be Born?” British Journal of Obstetrics and Gynaecology 88: 1200–3. Luo, Z.-C., S. Liu, R. Wilkins, and M. S. Kramer. 2004. “Risks of Stillbirth and Early Neonatal Death by Day of Week,” Canadian Medical Association Journal, 170(3): 337-341. MacFarlane A. (1978). “Variations in Number of Births and Perinatal Mortality by Day of Week in England and Wales,” British Medical Journal 2(6153): 1670–3. Mangold, W.D. 1981. “Neonatal Mortality by the Day of the Week in the 1974-75 Arkansas Live Birth Cohort,” American Journal of Public Health 71: 601–5. Martin, Joyce A. Bradey E. Hamilton, Paul D. Sutton, Stephanie J. Ventura, Fay Menacker, Sharon Kirmeyer, Martha L. Munson. 2007. “Births: Final Data for 2005,” December 5, 2007, National Vital Statistics Report. 56(6). http://www.cdc.gov/nchs/data/nvsr/nvsr56/nvsr56_06.pdf Mathers, C.D. 1983. “Births and Perinatal Deaths in Australia: Variations by Day of Week,” Journal of Epidemiology and Community Health 37:57–62. McEwan, Patrick J., and Joseph S. Shapiro. 2008. “The Benefits of Delayed Primary School Enrollment: Discontinuity Estimates Using Exact Birth Dates.” Journal of Human Resources 43(1): 1–29. McCrary, Justin, and Heather Royer, 2006. “The Effect of Maternal Education on Fertility and Infant Health: Evidence from School Entry Policies Using Exact Date of Birth,” Mimeo, University of Michigan. McCrary, Justin, 2007. “Testing for Manipulation of the Running Variable in the Regression Discontinuity Design,” Journal of Econometrics 142 (2): 698-714. National Center for Health Statistics. 1968, 1978 and 1988. Natality Data. Public-use data file and documentation.

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National Center for Health Statistics. 1999-2004. Natality Data. Restricted Use data file and documentation. Simms, Patricia and Doug Erickson. 2002. “’The Greying of Kindergarten’: Couples Plan Births So That Their Child Will Be Older than Classmates.” Wisconsin State Journal (Madison, WI). (Dec 15): A1 Stipek, Deborah, 2002. “At What Age Should Children Enter Kindergarten? A Question for Policy Makers and Parents,” Social Policy Report: Giving Child and Youth Development Knowledge Away, 16 (2): 3-16. United States Department of Health and Human Services, Centers for Disease Control and Prevention, National Center for Health Statistics. 2006. “Technical Appendix from the Vital Statistics of the United States: 2004 Natality. September 12. Wataru, Kureishi and Modori Wakabayashi, 2008. “Taxing the Stork.” National Tax Journal 61: 167-87.

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Figure 1A proportion of births relative to overall average

S tates with S eptember 1st Cutoff 0.35 0.25 0.15 0.05 -0.05 -0.15 -0.25 -0.35 1999

2000

2001

2002

2003

2004

Year Notes: Hatched columns are Labor Day. Solid bars are August 25th-31st. White bars are September 2nd-8th. Grey bars are September 1st, the school cutoff.

Figure 1B

proportion of births relative to overall average

S tates without S eptember 1st Cutoff 0.35 0.25 0.15 0.05 -0.05 -0.15 -0.25 -0.35 1999

2000

2001

2002

2003

2004

Year Notes: Hatched columns are Labor Day. Solid bars are August 25th-31st. White bars are September 2nd-8th. Grey bars are September 1st, the school cutoff.

Source: Authors’ calculations from U.S. Vital Statistics, 1999-2004

27

Figure 2

Source: Authors’ calculations from U.S. Vital Statistics, 1999-2004. 28

Figure 3

Source: Authors’ calculations from U.S. Vital Statistics, 1999-2004.

29

Figure 4

Source: Authors’ calculations from Fall 1998 survey assessment of ECLS-K.

30

Table 1 Share of All Births by Day of Week and Year, 1968-2004 1968 1978 1988 1999 2000 2001 2002 2003 2004

Sunday 0.126 0.126 0.116 0.100 0.102 0.098 0.096 0.095 0.094

Monday 0.146 0.146 0.146 0.145 0.145 0.148 0.149 0.150 0.149

Tuesday 0.153 0.151 0.156 0.164 0.162 0.162 0.167 0.166 0.166

Wednesday 0.150 0.148 0.152 0.161 0.160 0.160 0.159 0.163 0.163

Thursday 0.144 0.148 0.152 0.159 0.160 0.161 0.160 0.160 0.163

Friday 0.148 0.150 0.154 0.157 0.157 0.159 0.159 0.157 0.159

Saturday 0.134 0.130 0.124 0.113 0.115 0.112 0.110 0.108 0.106

N 1,799,289 2,865,627 3,094,342 3,287,206 3,376,503 3,349,877 3,349,205 3,409,378 3,440,552

Source: Authors’ Calculations from Vital Statistics (NCHS, various years). The samples for each year include the 43 states with explicit statewide school cutoff dates.

31

Table 2 Descriptive Statistics by Day of Week, 2002 Sun

Mon

Tues

Wed

Thurs

Fri

Sat

Age in years

26.7 (6.2)

27.2 (6.1)

27.1 (6.2)

27.1 (6.1)

27.1 (6.1)

27.2 (6.2)

26.7 (6.2)

African American

0.16 (0.37)

0.14 (0.36)

0.15 (0.36)

0.15 (0.36)

0.14 (0.36)

0.14 (0.36)

0.16 (0.37)

Married

0.63 (0.48)

0.66 (0.47)

0.66 (0.47)

0.66 (0.47)

0.66 (0.47)

0.67 (0.47)

0.63 (0.48)

Years of education

12.6 (2.9)

12.8 (2.9)

12.8 (2.8)

12.8 (2.8)

12.8 (2.8)

12.8 (2.8)

12.7 (2.9)

College educated

0.23 (0.41)

0.25 (0.42)

0.24 (0.42)

0.24 (0.42)

0.25 (0.42)

0.25 (0.42)

0.23 (0.41)

0.43 (0.50)

0.37 (0.49)

0.39 (0.49)

0.39 (0.49)

0.39 (0.49)

0.38 (0.49)

0.43 (0.50)

0.51 (0.50)

0.51 (0.50)

0.51 (0.50)

0.51 (0.50)

0.51 (0.50)

0.51 (0.50)

0.51 (0.50)

2.45 (1.47)

2.39 (1.42)

2.39 (1.42)

2.39 (1.42)

2.39 (1.42)

2.40 (1.43)

2.44 (1.47)

3254 (619)

3310 (605)

3315 (599)

3310 (603)

3306 (603)

3300 (608)

3266 (620)

8.86 (0.82)

8.90 (0.76)

8.90 (0.75)

8.90 (0.76)

8.90 (0.76)

8.89 (0.76)

8.87 (0.82)

38.5 (2.8)

38.7 (2.6)

38.7 (2.5)

38.7 (2.5)

38.7 (2.5)

38.7 (2.6)

38.6 (2.7)

Mother’s Characteristics

Child’s Characteristics First Born Gender=Boy

First month of prenatal care Birthweight in grams 5-minute APGAR score (/10) Gestational age in weeks

Source: Authors’ calculations from Vital Statistics, 2002. The sample includes the 43 states with explicit statewide school cutoff dates. California and Texas do not report APGAR scores and Michigan infers marital status (National Center for Health Statistics. 1999-2004).

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Table 3 Probability of Medical Interventions by Day of Week and Year, 1999-2004 Year 1999 2000 2001 2002 2003 2004

Sun 0.104 0.107 0.113 0.112 0.112 0.116

Mon 0.181 0.182 0.189 0.195 0.196 0.202

Tues 0.230 0.226 0.232 0.236 0.236 0.244

Wed 0.227 0.227 0.231 0.233 0.233 0.244

Thurs 0.225 0.227 0.232 0.232 0.230 0.240

Fri 0.209 0.212 0.218 0.218 0.215 0.222

Sat 0.156 0.159 0.167 0.168 0.166 0.170

Total 0.197 0.198 0.204 0.207 0.206 0.214

Cesarean Section

1999 2000 2001 2002 2003 2004

0.159 0.166 0.177 0.189 0.198 0.210

0.227 0.237 0.255 0.274 0.292 0.306

0.232 0.240 0.256 0.275 0.289 0.308

0.229 0.238 0.255 0.269 0.285 0.304

0.226 0.237 0.253 0.270 0.284 0.299

0.235 0.251 0.267 0.286 0.298 0.312

0.170 0.178 0.188 0.200 0.210 0.220

0.216 0.226 0.242 0.258 0.272 0.288

Repeat Cesarean Section

1999 2000 2001 2002 2003 2004

0.041 0.044 0.047 0.051 0.052 0.055

0.096 0.101 0.112 0.124 0.132 0.135

0.091 0.095 0.103 0.112 0.118 0.125

0.088 0.093 0.102 0.109 0.115 0.121

0.087 0.093 0.102 0.110 0.115 0.118

0.094 0.103 0.113 0.123 0.127 0.130

0.044 0.045 0.049 0.052 0.054 0.056

0.081 0.086 0.094 0.102 0.107 0.112

Induction or Repeat Cesarean Section

1999 2000 2001 2002 2003 2004

0.142 0.148 0.157 0.161 0.163 0.169

0.271 0.277 0.297 0.315 0.325 0.335

0.313 0.314 0.330 0.344 0.351 0.366

0.308 0.314 0.328 0.338 0.344 0.362

0.304 0.314 0.329 0.337 0.341 0.355

0.297 0.308 0.326 0.338 0.339 0.348

0.195 0.200 0.212 0.218 0.218 0.224

0.271 0.278 0.294 0.305 0.310 0.323

Induction

Source: Authors’ Calculations from Vital Statistics (NCHS, various years). The samples for each year include the 43 states with explicit statewide school cutoff dates.

33

Table 4 Estimates of Discontinuities in Birth Shares in Vital Statistics Data, 1999-2004

All births Higher order births: Repeat c-section births Repeat c-section and/or induced births College educated repeat csection and/or induced births All births Higher order births: Repeat c-section births Repeat c-section and/or induced births College educated repeat csection and/or induced births

All Years Appended

1999

-0.010 (0.016)

0.027 (0.032)

-0.023 (0.052) -0.030 (0.036) -0.066 (0.062)

0.016 (0.098) 0.062 (0.070) 0.069 (0.131)

2000 2001 2002 29 Day Window -0.057 0.013 0.006 (0.030) (0.030) (0.030)

2003

2004

-0.041 (0.031)

-0.043 (0.032)

-0.028 (0.094) -0.025 (0.063) 0.020 (0.116)

0.007 (0.086) -0.039 (0.059) -0.041 (0.107)

-0.041 (0.087) -0.090 (0.062) -0.188 (0.300)

0.022 (0.044)

-0.080 -0.122 (0.105) (0.096) -0.115 -0.102 (0.069) (0.062) -0.032 -0.111 (0.134) (0.115) 15 day window -0.073 0.016 (0.042) (0.041)

0.002 (0.041)

-0.058 (0.043)

-0.063 (0.044)

-0.060 (0.135) -0.003 (0.098) -0.012 (0.166)

0.002 (0.146) -0.076 (0.096) -0.079 (0.170)

0.046 (0.127) -0.037 (0.083) -0.024 (0.159)

0.035 (0.114) -0.090 (0.078) -0.073 (0.143)

-0.035 (0.115) -0.123 (0.082) -0.084 (0.163)

-0.139 (0.135) -0.089 (0.084) -0.092 (0.148)

Note: Each cell represents a separate estimate of β6 from equation (3) in the text, with standard errors in parentheses. Other covariates are described in the text. Results showing coefficients from all regressors are in Appendix Table 3 for “All births”, and the full set of results for “Higher order births” are available upon request. Source: Authors Calculations from Vital Statistics (NCHS, various years). The samples for each year include the 29 states with explicit statewide school cutoff dates listed in Appendix Table 1.

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Table 5 Estimates of the Discontinuity of Observable Covariates in Vital Statistics Data, 1999-2004 DEPENDENT VARIABLES Birth Procedures Induced Labor C-section births Repeat C-section births C-section and/or induced births Repeat c-section and/or induced births Mother's Characteristics Years of education College educated African American Child's Characteristics First Born Gender (1=Boy) First month of prenatal care Birthweight in grams 5-minute APGAR score (/10) Gestational age in weeks

1999

2000

2001 2002 Panel A: All Births

2003

2004

-0.0060 (0.0041) -0.0026 (0.0043) -0.0039 (0.0029) -0.0098 (0.0050) -0.0106 (0.0046)

-0.0093 (0.0041) 0.0071 (0.0044) 0.0016 (0.0030) -0.0019 (0.0051) -0.0076 (0.0046)

-0.0128 (0.0042) -0.0006 (0.0045) 0.0015 (0.0031) -0.0120 (0.0051) -0.0114 (0.0047)

-0.0114 (0.0042) 0.0097 (0.0046) 0.0049 (0.0032) -0.0033 (0.0051) -0.0056 (0.0048)

-0.0053 (0.0041) -0.0003 (0.0046) 0.0030 (0.0032) -0.0047 (0.0051) -0.0021 (0.0047)

0.0024 (0.0043) -0.0016 (0.0049) 0.0029 (0.0035) 0.0048 (0.0054) 0.0055 (0.0050)

-0.0033 (0.0299) -0.0007 (0.0043) 0.0044 (0.0039)

-0.0238 (0.0304) -0.0090 (0.0044) -0.0047 (0.0039)

-0.0289 (0.0308) -0.0053 (0.0044) -0.0027 (0.0039)

0.0530 (0.0308) 0.0052 (0.0045) -0.0070 (0.0038)

-0.0003 (0.0302) -0.0002 (0.0044) -0.0097 (0.0037)

-0.0298 (0.0326) -0.0097 (0.0047) -0.0069 (0.0039)

0.0039 (0.0051) 0.0000 (0.0052) -0.0136 (0.0050) -16.3512 (7.8161) -0.0020 (0.0096) -0.0517 (0.0336)

0.0077 (0.0051) -0.0002 (0.0052) 0.0057 (0.0050) -7.0323 (7.9606) -0.0050 (0.0098) 0.0408 (0.0339)

0.0077 (0.0052) 0.0060 (0.0053) 0.0007 (0.0051) -4.9137 (7.9424) -0.0179 (0.0096) 0.0308 (0.0339)

0.0083 (0.0051) -0.0009 (0.0052) 0.0079 (0.0050) 5.7059 (7.9472) -0.0072 (0.0096) 0.0068 (0.0341)

0.0051 (0.0050) -0.0010 (0.0051) -0.0093 (0.0049) 10.6864 (7.7045) 0.0059 (0.0093) 0.0505 (0.0331)

-0.0067 (0.0053) -0.0012 (0.0055) -0.0084 (0.0052) -7.0941 (7.6036) -0.0111 (0.0096) -0.0234 (0.0327)

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Table 5 (continued) Estimates of the Discontinuity of Observable Covariates in Vital Statistics Data, 1999-2004 DEPENDENT VARIABLES Birth Procedures Induced Labor C-section births Repeat C-section births C-section and/or induced births Repeat c-section and/or induced births Mother's Characteristics Years of education College educated African American Child's Characteristics Gender (1=Boy) First month of prenatal care Birthweight in grams 5-minute APGAR score (/10) Gestational age in weeks

1999

2000

2001 2002 2003 Panel B: Higher Order Births

2004

-0.0131 (0.0051) -0.0054 (0.0055) -0.0059 (0.0047) -0.0184 (0.0065) -0.0202 (0.0062)

-0.0090 (0.0051) 0.0076 (0.0056) 0.0047 (0.0048) -0.0007 (0.0065) -0.0044 (0.0062)

-0.0199 (0.0052) 0.0035 (0.0058) 0.0048 (0.0050) -0.0151 (0.0066) -0.0152 (0.0063)

-0.0175 (0.0052) 0.0142 (0.0059) 0.0110 (0.0051) 0.0008 (0.0066) -0.0050 (0.0064)

-0.0049 (0.0050) -0.0034 (0.0059) 0.0072 (0.0051) -0.0060 (0.0065) 0.0024 (0.0063)

0.0035 (0.0053) 0.0046 (0.0063) 0.0031 (0.0055) 0.0080 (0.0069) 0.0069 (0.0067)

-0.0368 (0.0395) -0.0049 (0.0054) 0.0045 (0.0051)

-0.0727 (0.0401) -0.0136 (0.0055) -0.0089 (0.0051)

-0.0457 (0.0406) -0.0067 (0.0055) -0.0065 (0.0050)

-0.0104 (0.0407) 0.0029 (0.0056) -0.0027 (0.0050)

0.0082 (0.0401) 0.0009 (0.0055) -0.0136 (0.0049)

-0.0225 (0.0431) -0.0094 (0.0058) -0.0092 (0.0050)

-0.0008 (0.0067) -0.0129 (0.0065) -14.4574 (10.2132) 0.0034 (0.0121) 0.0053 (0.0430)

-0.0023 (0.0068) 0.0018 (0.0066) -10.0667 (10.4324) -0.0020 (0.0121) 0.0473 (0.0435)

0.0005 (0.0068) 0.0068 (0.0066) -3.6975 (10.3413) -0.0076 (0.0119) 0.0529 (0.0433)

-0.0002 (0.0068) 0.0080 (0.0065) 0.1539 (10.3418) -0.0089 (0.0118) -0.0221 (0.0434)

-0.0076 (0.0066) -0.0110 (0.0064) 22.8833 (10.0076) 0.0090 (0.0114) 0.0222 (0.0421)

-0.0085 (0.0070) -0.0020 (0.0067) -4.9986 (9.8599) -0.0185 (0.0117) -0.0516 (0.0415)

Note: Each of the cells represents an estimate of β6 from equation (5) in the text, with standard errors in parentheses. All estimates are based on local linear regressions with 29 day bandwidths. The dependent variable relevant to each cell is the variable listed in the first column. Other covariates are described in the text. Shaded cells indicate coefficients which are statistically different from zero at the 5 percent significance level. The samples for each year include the 29 states with explicit statewide school cutoff dates listed in Appendix Table 1.

36

Appendix Table 1 States with Cutoffs in Analysis 1-Sep AL, AZ, FL, GA, ID, IL, MN, MS, NM, ND, OK, OR, RI, SC, SD, TX, WV, WI (18)

30-Sep LA, NV, OH, TN, VA

15-Oct ME, NE

2-Dec CA

31-Dec DC, HI, RI*

(5)

(2)

(1)

(3)

Source: Elder and Lubotsky (2009) * RI changed to September 1 in 2004.

Appendix Table 2 Cutoff Calendar Days and Days of the Week

1999 2000 2001 2002 2003 2004

1-Sep W F Sa Su M W

30-Sep Th Sa Su M Tu Th

15-Oct F Su M Tu W F

2-Dec Th Sa Su M Tu Th

31-Dec* F Su M Tu W F

Labor Day September 6 4 3 2 1 6

Notes: No shade: Weekday not bordered by a weekend. Italics: Bordered by a weekend or holiday on previous day. Bold: Bordered by a weekend or holiday on subsequent day. Shade: Weekend or holiday. * December 31st is New Years Eve on all years.

37

Appendix Table 3 Full Regression Results Based on 29 Day Window Dependent Variable: Share of All Births

Intercept dsd-c Asd (dsd-c) × Asd Rsd (dsd-c) × Rsd Rsd × Asd Rsd × (dsd-c) × Asd Sunday Monday Tuesday-Thursday Friday Labor Day

1999 0.831 (0.018) 0.000 (0.002) 0.023 (0.023) 0.001 (0.002) -0.017 (0.021) -0.002 (0.002) 0.027 (0.032) -0.001 (0.004) -0.087 (0.016) 0.214 (0.017) 0.351 (0.013) 0.338 (0.016) -0.321 (0.027)

2000 0.832 (0.016) 0.000 (0.002) -0.001 (0.021) 0.002 (0.002) 0.008 (0.020) 0.002 (0.002) -0.057 (0.030) 0.002 (0.003) -0.098 (0.014) 0.222 (0.015) 0.336 (0.011) 0.334 (0.013) -0.318 (0.025)

2001 0.829 (0.016) 0.002 (0.002) 0.000 (0.021) -0.001 (0.002) -0.004 (0.020) -0.002 (0.002) 0.013 (0.030) 0.000 (0.003) -0.117 (0.013) 0.261 (0.015) 0.380 (0.011) 0.354 (0.013) -0.353 (0.026)

2002 0.820 (0.017) 0.002 (0.002) 0.009 (0.023) -0.003 (0.003) -0.052 (0.020) -0.003 (0.002) 0.006 (0.030) 0.007 (0.003) -0.079 (0.013) 0.325 (0.014) 0.410 (0.011) 0.386 (0.014) -0.432 (0.027)

2003 0.803 (0.018) 0.001 (0.002) -0.010 (0.023) 0.001 (0.003) 0.017 (0.021) 0.001 (0.002) -0.041 (0.031) 0.002 (0.003) -0.093 (0.015) 0.315 (0.016) 0.420 (0.013) 0.393 (0.015) -0.422 (0.027)

2004 0.759 (0.019) 0.001 (0.002) 0.058 (0.024) -0.004 (0.003) -0.026 (0.021) -0.002 (0.002) -0.043 (0.032) 0.007 (0.004) -0.078 (0.016) 0.345 (0.017) 0.427 (0.013) 0.397 (0.016) -0.406 (0.027)

Note: These are the full set of coefficients from Equation (3) in the text for all births, with standard errors in parentheses. Saturday is the omitted day of the week. The samples for each year include the 29 states with explicit statewide school cutoff dates listed in Appendix Table 1.

38

Appendix Table 4 Estimates of the Discontinuity of Observable Covariates in Vital Statistics Data, 1999-2004 Conditioned on Type of Birth DEPENDENT VARIABLES Birth Procedures Induced Labor C-section births Repeat c-section births C-section and/or induced births Repeat c-section and/or induced births Mother's Characteristics Years of education African American Child's Characteristics Gender (1=Boy) First month of prenatal care Birthweight in grams 5-minute APGAR score (/10) Gestational age in weeks

1999 2000 2001 2002 2003 2004 Panel A: Higher Order Births, Mothers with College Education

-0.0100 (0.0122) -0.0149 (0.0125) -0.0038 (0.0106) -0.0201 (0.0147) -0.0143 (0.0142)

0.0011 (0.0121) 0.0125 (0.0127) 0.0080 (0.0108) 0.0186 (0.0146) 0.0101 (0.0141)

-0.0122 (0.0120) 0.0172 (0.0129) 0.0262 (0.0112) 0.0071 (0.0146) 0.0108 (0.0142)

-0.0036 (0.0117) 0.0154 (0.0130) 0.0188 (0.0113) 0.0148 (0.0144) 0.0179 (0.0141)

0.0057 (0.0113) -0.0204 (0.0128) 0.0001 (0.0112) -0.0109 (0.0140) 0.0069 (0.0137)

-0.0037 (0.0117) -0.0038 (0.0135) 0.0005 (0.0118) -0.0034 (0.0145) -0.0013 (0.0142)

-0.0066 (0.0145) -0.0053 (0.0085)

-0.0028 (0.0144) -0.0061 (0.0085)

0.0288 (0.0144) -0.0152 (0.0084)

-0.0106 (0.0142) -0.0026 (0.0083)

0.0103 (0.0138) -0.0119 (0.0080)

-0.0181 (0.0144) 0.0016 (0.0081)

0.0032 (0.0150) -0.0037 (0.0125) 16.9972 (21.2094) -0.0032 (0.0236) 0.0890 (0.0809)

0.0150 (0.0150) -0.0037 (0.0125) -3.2413 (21.4375) -0.0154 (0.0229) 0.0878 (0.0805)

0.0066 (0.0148) 0.0023 (0.0124) 6.3784 (21.1128) 0.0035 (0.0223) 0.0980 (0.0804)

0.0171 (0.0146) 0.0089 (0.0121) 8.0943 (20.8722) 0.0288 (0.0217) -0.0629 (0.0793)

0.0064 (0.0141) -0.0320 (0.0118) 14.3322 (20.0520) -0.0177 (0.0209) -0.0701 (0.0772)

0.0053 (0.0147) -0.0189 (0.0123) -13.8127 (21.5810) -0.0401 (0.0223) -0.1345 (0.0823)

Continued…

39

Appendix Table 4 (continued) Estimates of the Discontinuity of Observable Covariates in Vital Statistics Data, 1999-2004 Conditioned on Type of Birth DEPENDENT VARIABLES Birth Procedures Induced Labor C-section births Repeat c-section births C-section and/or induced births Repeat c-section and/or induced births Mother's Characteristics Years of education

African American Child's Characteristics Gender (1=Boy) First month of prenatal care Birthweight in grams 5-minute APGAR score (/10) Gestational age in weeks

1999 2000 2001 2002 2003 2004 Panel B: Higher Order Births, Mothers without College Education -0.0110 (0.0063) -0.0060 (0.0071) -0.0074 (0.0060) -0.0178 (0.0083) -0.0197 (0.0079)

-0.0115 (0.0064) 0.0039 (0.0073) 0.0054 (0.0061) -0.0063 (0.0084) -0.0059 (0.0080)

-0.0272 (0.0064) 0.0053 (0.0075) 0.0066 (0.0064) -0.0206 (0.0085) -0.0197 (0.0081)

-0.0248 (0.0065) 0.0157 (0.0077) 0.0116 (0.0066) -0.0030 (0.0086) -0.0114 (0.0082)

-0.0061 (0.0064) -0.0026 (0.0077) 0.0023 (0.0067) -0.0077 (0.0085) -0.0037 (0.0082)

0.0000 (0.0067) 0.0076 (0.0083) 0.0025 (0.0072) 0.0061 (0.0091) 0.0023 (0.0087)

-0.0526 (0.0397) 0.0063 (0.0070)

-0.0209 (0.0404) -0.0082 (0.0070)

-0.0164 (0.0409) 0.0002 (0.0069)

-0.0361 (0.0410) -0.0070 (0.0069)

-0.0469 (0.0405) -0.0112 (0.0068)

0.0182 (0.0436) -0.0150 (0.0069)

-0.0070 (0.0088) -0.0157 (0.0088) -19.9645 (13.7608) 0.0032 (0.0170) -0.0380 (0.0609)

-0.0054 (0.0089) 0.0033 (0.0088) -8.1070 (14.1245) 0.0007 (0.0171) 0.0633 (0.0619)

-0.0040 (0.0089) 0.0145 (0.0089) -0.8580 (14.0205) -0.0005 (0.0169) 0.0616 (0.0618)

-0.0021 (0.0089) 0.0095 (0.0089) -6.7173 (14.1277) -0.0327 (0.0170) -0.0189 (0.0626)

-0.0071 (0.0088) -0.0013 (0.0087) 17.8101 (13.7004) 0.0213 (0.0164) 0.0398 (0.0607)

-0.0052 (0.0093) 0.0031 (0.0092) -1.6483 (12.4701) -0.0177 (0.0156) -0.0740 (0.0545)

Note: Each of the cells represents an estimate of β6 from equation (5) in the text, with standard errors in parentheses. All estimates are based on local linear regressions with 29 day bandwidths. The dependent variable relevant to each cell is the variable listed in the first column. Other covariates are described in the text. Shaded cells indicate coefficients which are statistically different from zero at the 5 percent significance level. The samples for each year include the 29 states with explicit statewide school cutoff dates listed in Appendix Table 1.

40

Appendix Table 5 Estimates of the Discontinuity of Observable Covariates in Vital Statistics Data, 1999-2004 Alternative Bandwidths Induced Labor C-section births Repeat c-section births C-section and/or induced births Repeat c-section and/or induced births Years of education African American First Born Gender (1=Boy) Birthweight in grams 5-minute APGAR score (/10) Gestational age in weeks

1999 0.010 (0.005) 0.001 (0.006) -0.002 (0.004) 0.007 (0.007) 0.007 (0.006) -0.008 (0.039) 0.004 (0.005) 0.001 (0.007) -0.003 (0.007) -19.931 (10.247)

2000 -0.004 (0.006) 0.005 (0.006) -0.002 (0.004) 0.002 (0.007) -0.006 (0.006) -0.018 (0.042) -0.006 (0.005) 0.004 (0.007) -0.006 (0.007) 4.023 (10.925)

15 day window 2001 2002 -0.010 -0.006 (0.006) (0.006) 0.002 0.024 (0.006) (0.006) 0.004 0.012 (0.004) (0.004) -0.005 0.015 (0.007) (0.007) -0.007 0.007 (0.006) (0.006) -0.036 0.055 (0.042) (0.041) -0.006 -0.009 (0.005) (0.005) -0.006 0.006 (0.007) (0.007) 0.001 0.003 (0.007) (0.007) -8.104 12.678 (10.871) (10.789)

2003 0.001 (0.005) 0.007 (0.006) 0.008 (0.004) 0.008 (0.007) 0.009 (0.006) 0.032 (0.040) -0.010 (0.005) 0.004 (0.007) -0.005 (0.007) 25.284 (10.323)

2004 0.022 (0.006) 0.005 (0.006) 0.003 (0.005) 0.028 (0.007) 0.025 (0.007) 0.013 (0.043) -0.002 (0.005) -0.001 (0.007) -0.001 (0.007) 6.920 (9.928)

1999 0.003 (0.008) -0.014 (0.008) -0.022 (0.006) -0.015 (0.010) -0.021 (0.009) -0.070 (0.058) 0.010 (0.007) 0.017 (0.010) -0.006 (0.010) -27.816 (15.313)

2000 0.002 (0.009) 0.000 (0.009) -0.015 (0.006) -0.004 (0.011) -0.012 (0.010) -0.087 (0.064) -0.004 (0.008) 0.023 (0.011) 0.006 (0.011) 12.881 (17.041)

9 day window 2001 2002 -0.050 -0.027 (0.009) (0.008) -0.014 0.015 (0.010) (0.009) -0.007 0.002 (0.007) (0.007) -0.053 -0.007 (0.011) (0.010) -0.057 -0.023 (0.010) (0.010) -0.011 -0.014 (0.064) (0.062) -0.007 -0.006 (0.008) (0.008) -0.013 0.003 (0.011) (0.010) 0.001 -0.002 (0.011) (0.011) -17.791 3.562 (16.879) (16.684)

2003 0.006 (0.008) 0.001 (0.009) 0.011 (0.006) 0.009 (0.010) 0.017 (0.009) 0.064 (0.059) -0.013 (0.007) 0.011 (0.010) -0.001 (0.010) 27.224 (15.451)

2004 0.041 (0.008) -0.026 (0.009) -0.017 (0.007) 0.013 (0.010) 0.022 (0.010) -0.023 (0.063) 0.005 (0.007) 0.007 (0.010) 0.013 (0.011) -33.924 (14.836)

-0.004 (0.013) -0.071 (0.044)

-0.005 (0.014) 0.082 (0.047)

-0.017 (0.013) 0.005 (0.047)

0.013 (0.012) 0.035 (0.045)

-0.008 (0.012) 0.006 (0.043)

-0.027 (0.019) -0.093 (0.067)

-0.015 (0.021) 0.096 (0.073)

-0.034 (0.020) -0.008 (0.072)

-0.014 (0.019) 0.020 (0.067)

-0.010 (0.019) -0.098 (0.064)

-0.027 (0.013) 0.097 (0.046)

-0.024 (0.020) 0.132 (0.072)

Note: Each of the cells represents an estimate of β6 from equation (5) in the text, with standard errors in parentheses. All estimates are based on models including 9 or 15 day bandwidths. See notes to Table 5 for more details. The samples for each year include the 29 states with explicit statewide school cutoff dates listed in Appendix Table 1.

41