Heat and Learning∗
Joshua Goodman
Harvard University
Joshua Goodman@hks.harvard.edu
Michael Hurwitz
College Board
mhurwitz@collegeboard.org
R. Jisung Park
University of California, Los Angeles
jisungpark@luskin.ucla.edu
Jonathan Smith
Georgia State University
jsmith500@gsu.edu
April 11, 2019

Abstract
We demonstrate that heat inhibits learning and that school air-conditioning may mitigate
this effect. Student fixed effects models using 10 million PSAT-retakers show hotter school daysin years before the test reduce scores, with extreme heat being particularly damaging. Weekend and summer temperature has little impact, suggesting heat directly disrupts learning time.
New nationwide, school-level measures of air-conditioning penetration suggest patterns consistent with such infrastructure largely offsetting heat’s effects. Without air-conditioning, a 1◦ F
hotter school year reduces that year’s learning by one percent. Hot school days disproportionately impact minority students, accounting for roughly five percent of the racial achievement
gap.
∗
Thanks to Lawrence Katz, Joseph Aldy, Joshua Graff-Zivin, Matt Neidell, Alan Barreca, Lucas Davis, Olivier Deschenes, Matt Kahn, Sarah Reber, Wes Yin, Manisha Shah, Greg Duncan and Patrick Behrer for valuable comments
and feedback. We also thank seminar participants at Harvard, UCLA, UCSB, UCSD, IZA, CESifo, and West Point, as
well as participants at the annual meetings of the AEA, SEA and SREE. Melanie Rucinski provided excellent research
assistance.

1

Introduction

Hotter countries tend to be poorer, with each 1◦ F increase in average temperature associated with
4.5 percent lower GDP per capita (Dell et al., 2009). Students in hotter places also tend to exhibit
lower levels of standardized achievement for any given age or grade. Across countries, a 1◦ F
increase in average annual temperature is associated with 0.02 standard deviation lower mathscores for 15-year-olds taking the 2012 Programme for International Student Assessment (PISA),
as shown in the top panel of Figure 1. Within the United States, students in the hottest decile of thecounty-level climate distribution score on average 0.12 standard deviations worse on 3rd through8th grade math tests, as seen in the bottom panel of that figure. Our primary contributions are toshow that part of the cross-sectional relationship between temperature and academic achievement
is causal, that heat’s cumulative learning impacts may be mitigated by school air-conditioning,
and that differential heat exposure and learning impacts of heat account for a non-trivial portionof racial achievement gaps in the US.
Why might cumulative heat exposure reduce human capital accumulation? The contemporary
US context of this study makes less relevant channels often studied in less developed settings, suchas: health and disease burden (Bleakley, 2010; Cho, 2017); agricultural income and the opportunity
costs of schooling (Shah and Steinberg, 2017); or institutional norms and political stability more
broadly (Acemoglu et al., 2001; Dell et al., 2012; Hsiang et al., 2013). We provide evidence consistent with the possibility that, in the US, heat most likely affects learning directly by altering humanphysiology and cognition. Even moderately elevated temperatures can impair decision-making
and cause substantial discomfort, and short-term impacts of heat on cognition have been extensively documented in laboratory settings (Mackworth, 1946; Seppanen et al., 2006). Hot classrooms may thus reduce the effectiveness of instructional time through physiological impacts on
both students and teachers, making it harder for both to focus and accomplish a given set of learning tasks. In cases of extreme heat, schools may close or dismiss students early, directly reducing
the amount of instructional time.
To estimate the causal impact of cumulative heat exposure on human capital accumulation, welink local daily weather data to test scores of 10 million American students from the high schoolclasses of 2001-14 who took at least twice the PSAT, a nationally standardized exam designed

1

to assess students’ cumulative learning in high school.1 We also construct the first nationwide
measures of school level air-conditioning penetration in the United States by surveying students
and guidance counselors across the country about heat-related conditions in approximately 12,000high schools. Student fixed effects regressions identify the impact of heat exposure during theprior school year by leveraging within-student variation in temperature over multiple test takes.
Our identification strategy relies on the premise that variation in temperature over successive
school years for a given student is uncorrelated with unobserved determinants of learning. We
provide evidence consistent with that assumption, showing that selection into test-taking andretaking is not endogenous to temperature, even when controlling for regional trends in warming
and secular changes in school quality or student composition.
We then generate three primary findings about the impact of heat on human capital accumulation. First, cumulative heat exposure reduces the rate of learning. A 1◦ F hotter school year in
the year prior to the test lowers scores by approximately 0.2 percent of a standard deviation, orslightly less than one percent of an average student’s learning gain over a school year.2 Extreme
heat is particularly damaging. Relative to school days with temperatures in the 60s (◦ F), each additional school day with temperature in the 90s (◦ F) reduces achievement by one-sixth of a percentof year’s worth of learning. A day above 100 (◦ F) has an effect that is up to 50 percent larger. These
effects are precisely estimated, are robust to controlling for test-day weather, and are not predictedby heat exposure in the year following the test. Only school-day exposure to higher temperatures
affects test scores. Hot summers and weekends have little impact on achievement and controllingfor such exposure does not shrink the magnitude of impact of hot school days. This suggests thatheat’s disruption of instructional time is responsible for the observed drop in test scores. That oureffects are robust to controlling for heat-driven labor market shocks and pollution levels suggeststhat economic and health-related channels observed in other settings are likely not of first-orderimportance in this context (Cho, 2017; Garg et al., 2017).
Importantly, these learning effects appear to be cumulative and persistent beyond just the year
prior to the test. Hot school days two, three and four years prior to the test also lower scores,
so that the cumulative effect of elevated temperature over multiple school years is substantially
1

The PSAT is designed to be a test of knowledge and not of general intelligence or IQ.
On average, students score 0.3 standard deviations higher on their second PSAT take than their first PSAT taken
one year prior.
22

larger than that of a single school year. This suggests that any compensatory investments madeby students, parents, or teachers in response to such heat shocks do not fully offset their impacts.
Heat-related disruptions thus appear to reduce the rate of human capital accumulation over time.
The implied magnitudes are non-trivial, particularly when considering predicted effects of climate change. For the average student, a sustained increase in temperature of 3.6◦ F (2◦ C) lowers
achievement gains by two percent of a standard deviation, or approximately seven percent of an
average year’s worth of learning. This is despite relatively high average levels of income andair-conditioning in the United States compared to most other countries.
Our study shows that cumulative heat exposure can reduce the rate of human capital accumulation, and thus speaks to a longstanding debate on the relationship between geography andeconomic development (Acemoglu et al., 2001; Rodrik et al., 2004; Dell et al., 2012). A growing
literature shows consistent evidence that the short-term impact of heat on exam days reducescognitive performance but has not determined whether such effects are transitory or lead to permanent reductions in the stock of human capital (Graff Zivin et al., 2017; Park, 2017). Studies thatprovide evidence of medium-term impacts have occured in contexts where heat’s direct physiological effects are hard to distinguish from other channels such as agricultural output or healthstatus (Cho, 2017; Garg et al., 2017). The only other paper that precisely identifies the impact of
cumulative heat exposure on human capital accumulation is Isen et al. (2017), which focuses onin utero exposure and thus identifies a very different channel from the learning channel we study
here. Our results are consistent with a longstanding lab-based literature documenting adverse
cognitive impacts of hot temperature, the long-run implications of which have not previously
been tested in real-world learning environments.
Our second major finding is evidence consistent with the possibility that school air-conditioning
mitigates the impacts of heat on learning. We generate the first nationwide, school-specific air
conditioning penetration rates, based on survey questions sent to students and high school counselors. We then show that, in the cross section, school air-conditioning penetration reported in2016 is strongly related to heterogeneity in heat’s effects, such that hot school days reduce learning by one-fifth as much in fully air-conditioned schools as in schools with no air conditioning.
To better identify the mitigating effect of school air-conditioning, we use a triple-difference strategy that combines our within-student comparisons with within-school changes over time in re3

ported air-conditioning status. This approach reveals that later cohorts in schools that increased
air-conditioning penetration experienced reduced heat-related learning impacts relative to earlier cohorts in those same schools and relative to cohort differences across schools that did notincrease air-conditioning penetration. Both variation in the cross section and over time are thus
consistent with the hypothesis that school air-conditioning reduces the negative impacts of hot
school days. Our estimates, if taken as causal and combined with estimates of the achievementearnings relationship from Chetty et al. (2011), suggest that in hot areas such as Houston, TX, thepresent value of air-conditioning is approximately $2.1 million per year for each 1,000 student
high school. Global climate change means however that the private return to air-conditioning will
increase by approximately $500,000 per school by 2040-2050 for the median US school, according
to our back-of-the-envelope calculations.3
That school air-conditioning may improve learning speaks directly to a recent literature showing that school resources can have positive impacts on educational achievement (Jackson et al.,2015; Lafortune et al., 2018). Existing studies that focus on school infrastructure funding generally
estimate the impact of broad funding packages and not targeted upgrades to specific school facilities (Cellini et al., 2010).4 Two recent studies finding positive achievement impacts of school infrastructure investment generally are consistent with the positive impacts of school air-conditioning
we document. A comprehensive school construction project in New Haven, CT that included
installation of air-conditioning in schools that lacked it raised reading scores by 15 percent of astandard deviation (Neilson and Zimmerman, 2014). Major school building and renovation efforts in the Los Angeles Unified School District raised reading and math scores between five and10 percent of a standard deviation, most likely due to “reduced distractions from inadequate heating, cooling, or other aspects of the physical environment” (Lafortune and Schonholzer, 2017).
The lack of achievement impact from recent school infrastructure investment in Texas is consistent with our data suggesting most schools in that state were likely air-conditioned to begin
with (Martorell et al., 2016). Our paper is the first to attempt to isolate the impact of school air3
Episodes of acute heat exposure are becoming more frequent in many parts of the world, and are predicted toincrease at an accelerating rate (Stocker, 2014). Importantly, much of this warming will occur in places and during
times of year that do not currently feature such temperature extremes, meaning that many local institutional arrangements – whether in terms of the timing of examinations or policies regarding protective built infrastructure (e.g. airconditioning) – might not be efficiently adapted to new expected climate distributions.
4
A notable exception is (Stafford, 2015), who provides evidence that mold remediation and ventilation improvements had positive impacts on performance in 66 Texas elementary schools.

4conditioning from other aspects of school infrastructure. These results also highlight the fact that
small reduced form impacts of heat in developed countries may mask large biological and welfare
impacts, underscoring the importance of taking adaptations such as air-conditioning into accountwhen studying the relationship between climatic variables and economic outcomes (Graff Zivin
and Neidell, 2014; Deschenes et al., 2017).
Our third and final result is that the temperature environment in which learning occurs appears to be a meaningful contributor to racial and geographic achievement gaps. Black and Hispanic students’ learning is roughly three times as inhibited by the prior school year’s heat compared to the learning of White students. We estimate that between three and seven percent of the
gap in PSAT scores between White students and Black and Hispanic students can be explainedby differences in the temperature environment experienced by students in each group. These disparities appear to be driven both by school-level investments, such as differential air-conditioning
penetration, as well as the geographic distribution of racial minorities whereby Black and Hispanic
students overwhelmingly reside in hotter locations than White students. This is consistent withthe theory of residential sorting, which suggests that lower income individuals are more likely
to sort into areas with lower levels of environmental amenities and local public goods (Tiebout,
1956; Roback, 1982; Banzhaf and Walsh, 2008). We also find that historically cool places experience much larger impacts per unit of warming. This suggests that, without high average levelsof adaptation in the South, the North-South achievement gap would be even larger than it is currently. Minority students appear, however, less likely to have school air-conditioning even in agiven historical climate.
That heat has larger impacts on Black and Hispanic students and accounts for a non-trivial proportion of the racial achievement gap are facts not documented previously in the vast literature on
racial disparities in educational outcomes (Jencks and Phillips, 2011; Duncan and Murnane, 2011;
Fryer Jr, 2011). Most empirical analyses in this literature have focused on social factors such asteacher quality, racial bias, or neighborhood culture, and have more rarely explored disparities in
the physical environment. “Environmental factors” in this literature often explicitly or implicitly
refer to the social environment or use the term to denote non-genetic factors. The few studies
that assess the impact of physical environmental factors on achievement are either non-identified
cross-sectional analyses (Durán-Narucki, 2008) or assess short-run outcomes such as cognitive5

performance during a hot period (Mackworth, 1946; Seppanen et al., 2006; Park, 2017). A substantial proportion of the variation in achievement remains unexplained by traditional socioeconomic
variables (Reardon et al., 2017). Our findings suggest that the physical factors such as temperature and the built environment may play a larger role in explaining disparities in achievement
than previously realized.
Our empirical strategy relies on temperature fluctuations across multiple years as opposed tomultiple decades. Our central estimates of the impact of heat and of air conditioning as a mitigating factor are thus driven by these short to medium term changes in the efficacy of instructional
time. Longer-term exposure to heat may change students’ study and other behaviors in ways we
do not capture. School air conditioning may, for example, be a workplace amenity capable of
attracting higher quality teachers and thus affecting student outcomes over time through an improved teacher workforce. Our estimates will not capture such longer-term impacts of a school’s
physical environment on student outcomes and thus may underestimate the total impacts of suchinvestments.

2

Data and Empirical Strategy

2.1

Data

We combine three primary data sources on test scores, temperature and school air-conditioning.
Test score data come from the College Board, which administers the PSAT exam to millions ofAmerican high school students annually. The PSAT consists primarily of a reading and a mathsection.5 The test is offered once a year roughly during the third week of October and most students first take it in 10th or 11th grade, though some start as early as 9th grade.6 Students take andcan retake the PSAT for a variety of reasons, including preparation for the SAT college entrance
exam, qualification for National Merit Scholarships, and provision of information about their college readiness to them and their schools. The PSAT has multiple advantages over other tests used5

A writing section has been added in more recent years. Basic scientific concepts and history are assessed as part of
the reading comprehension section.
6
We use the PSAT rather than the SAT for two reasons. First, the SAT is offered at seven different times of theyear, making it harder to assign easily comparable measures of long-term heat exposure to a given exam take. Second,
the PSAT is taken by roughly twice as many students as the SAT because the latter is taken in later grades by a morecollege-oriented and thus selected set of takers.

6

to study the impact of heat on cognitive skills, including: the test is given once a year on a fixed
date with advanced registration required, limiting the scope of endogenous taking or timing decisions; proctoring is nationally harmonized and the test is centrally graded, limiting potential for
endogenous score manipulation of any sort (Dee et al., 2016; Park, 2017); and the test is designed
to assess cumulative progress on skills learned during secondary school, rather than generalized
intelligence, making it arguably better-suited for assessing the effects of formal schooling.
We have test scores and dates from all takes for the universe of PSAT-takers from the intended
high school classes of 2001-2014. Our primary outcome is a student’s combined math and reading score, standardized by test administration. The student-level data also contains basic demographic information such as gender, race, parental education, and residential ZIP code, which we
use to assign students ZIP code level mean incomes as reported by the Internal Revenue Service.
High school identifiers allow us to assign students to testing locations and other school-level characteristics. We observe only the most recent high school attended and thus permanently assignthat location to each student across all PSAT takes. Doing so reduces concerns about potentiallyendogenous migration but may generate measurement error in the heat exposure treatment variable. The magnitude of that error is, however, likely quite small. Data from the 2005-12 American
Community Survey show that, among 16-17 year-old high school students, only 2.8 percent lived
in a different Public Use Microdata Area in the year prior and fewer than one percent lived in astate not contiguous with their current one. Very few high school students substantially change
temperature zones in the course of a year.
Daily temperature data come from the National Oceanic and Atmospheric Administration’s
Daily Global Historical Climatology Network, which includes station-level data for thousands ofweather stations across the United States. We focus on the subset of nearly 3,000 weather stations
with daily temperature data available for at least 95 percent of the days from 1996 to 2014, the time
period covering potential test-taking dates of our sample. Doing so allows us to assign each highschool to a single, stable weather station over the entire time period, which avoids endogeneity
concerns driven by the possibility that stations coming online or going offline are somehow correlated with local population growth, economic conditions or temperatures conditions in ways thatmight contaminate our estimates (Auffhammer and Mansur, 2014). We impute the small proportion of missing daily observations with those from the nearest stations with non-missing data. We
7assign each high school to the nearest weather station, resulting in an average distance of 9.7 miles
between a student’s test site and weather station being used to measure temperature at that site.
We construct two primary measures of cumulative heat exposure experienced by a student: theaverage daily maximum temperature and the number of days that temperature exceeded a given
multiple of 10◦ F in the 365 days prior to the test.7 We use daily maximum temperature because
schooling occurs during the daytime when such temperatures usually occur.8 We focus particularly on temperature experienced on school days, treating summer and weekend temperatures as
separate sources of variation.9 We also use the weather stations to construct test date temperature,rain and snowfall, as well as cumulative rain and snowfall exposure over the year prior to the test,
which help account for potential independent effects of such precipitation (Goodman, 2014).
School-level air-conditioning data do not exist at the national level and very rarely exist at thestate and local level. We generate measures of school-level air-conditioning penetration througha survey the College Board regularly administers by e-mail to all SAT takers and to high school
guidance counselors registered to administer PSAT or other exams. In 2016, we added to the survey the statement “On hot days, classrooms get too hot.” Respondents could choose “Never”,“Some of the time”, “Most of the time”, or “All the time”.10 We received valid responses fromstudents in nearly 12,000 schools enrolling 87 percent of our sample’s PSAT-takers. To constructschool-level measures from individual responses, we assign the four possible responses a value of0, 13 , 23 , and 1, then average across all students within a school. We interpret this measure as thefraction of a school’s classrooms with adequately functioning or sufficiently frequently activatedair-conditioning. This measure of school air-conditioning penetration has the advantage of being
reported by the students themselves and of being based on the largest set of responses to our ques7
Focusing on the prior year implies that the measured heat exposure occurred prior to a given PSAT administration
but after the most recent one before that. Because of slight annual variation in the timing of the PSAT, we exclude thethird week of October from these measures to guarantee no overlap between PSAT administrations and the constructedmeasure of heat exposure. The year prior to the test take thus runs from late October of the preceding year to midOctober of the current year.
8
We note that it is possible for nighttime heat to affect learning through disrupted sleep as well. To the extent thatdaytime high and nighttime low temperatures are correlated, it is possible that our estimates may include some impacts
due to disrupted sleep, though the results on weekend days versus weekdays is suggestive of effects driven primarily
by instructional time, as we discuss below.
9
No comprehensive national data set of school calendars covering this time period exists, so we assign to each
student a likely school start and end date based on the calendar of the largest school district in that student’s state, as
seen in Figure A.1. We then divide the year into three periods: school days, the summer, and weekends or national
holidays.
10
Respondents were also allowed to choose “I don’t know.” We coded such answers as missing.

8

tions about air-conditioning. It has the disadvantage of measuring air-conditioning penetration ata single point in time and thus may correlate with other unobserved school-level factors.
A different measure of school air-conditioning penetration comes from our addition to thesurvey of two questions posed to high school guidance counselors: “How many of your school’sclassrooms have air-conditioning?” and “Ten years ago, how many of your school’s classrooms
had air-conditioning?” Guidance counselors could respond with “None”, “Fewer than half”,“About half”, “More than half”, and “All”. To construct school-level measures, we assign these
possible responses a value of 0, 14 , 12 , 43 , and 1, then average across all guidance counselors withina school. This measure has the disadvantage that we received responses from guidance counselors in only about 2,000 high schools. It has the advantage, however, of directly asking about
air-conditioning and of allowing us to measure air-conditioning penetration at two points in time
instead of one. Variation in air-conditioning penetration over time is more plausibly exogenous
than cross-sectional measures, helping us construct stronger causal claims about the impact ofschool air-conditioning in offsetting heat’s impacts. Air conditioning upgrades may nonethelessbe correlated with other school improvements that protect against high temperatures.
Finally, we supplement our three primary data sources with additional data on residential airconditioning, local economic conditions and pollution levels. We construct county-by-year dataon residential air-conditioning penetration by combining county-level residential air-conditioning
penetration estimates from the 1980 decennial census with data on changes in such penetration
over time by census region from the Energy Information Agencies Residential Energy Consumption surveys.11 We estimate county-level economic conditions by constructing the logarithm ofannual payroll per capita from the U.S. Census Bureau’s County Business Patterns, focusing on
sectors that the National Institute of Occupational Safety and Health categorizes as being highly
exposed to weather (namely: construction, mining, transportation, manufacturing, agriculture
and utilities). Based on evidence of the adverse impact of hot days on highly exposed sector payroll, we use this measure to control for local economic shocks driven by annual fluctuations in heat
(Deryugina and Hsiang, 2014; Behrer and Park, 2017). Similarly to our temperature measures, we
11

We use the reported penetration rates in 1980 as a basis and then extrapolate based on the region-level growthrate of total air-conditioning penetration recorded by RECS, which provide penetration rates by region from 1980 to2009 with a two or three-year frequency. We linearly interpolate growth rates for the missing years and assign counties
their corresponding regional growth rate. Using this growth rate and the observed penetration rate in 1980 we create ameasure of penetration in every county in each year from 1980 to 2011. We top-code penetration at 100 percent.

9

construct both cumulative and test date measures of exposure to major air pollutants (ozone, sulfur dioxide, nitrogen dioxide, carbon monoxide, and PM10 particulate matter) using data fromthe Environmental Protection Agency’s Ambient Air Monitoring network. Previous research suggests that such pollutants can affect student absenteeism and performance, at least in the shortrun (Currie et al., 2009; Ebenstein et al., 2016), though there is relatively less evidence regarding
the impact of longer-term exposures.

2.2

Summary Statistics

As shown in Table 1, the starting sample comprises over 38 million test scores from 27 million
students in the high school classes of 2001 to 2014, who took the PSAT as early as October of 1998
and as late as October of 2012.12 Because our primary identification strategy relies on withinstudent variation in heat exposure for identification, we focus on the subset of 21 million scoresfrom the nearly 10 million students who took the PSAT at least twice.13 Those retakers are slightly
more advantaged than the general pool of PSAT takers, living in higher income zip codes, more
likely to have mothers with college degrees, and with first PSAT scores 0.14 standard deviations
about the national average. Importantly, retakers seem geographically similar to the general poolof SAT takers. Both groups experience school days with mean temperature in the mid 60s◦ F in
the year prior to the test, with an average of 12 school days above 90◦ F. Maps of takers and retakers locations also suggest that both groups have similar geographic distributions in line with the
population distribution across the United States.14 On average, PSAT takers and retakers reportthat nearly 60 percent of their classrooms are adequately air-conditioned, with closer to 80 percent
likely to have air-conditioning at home. Dividing the retaking sample by race and by income reveals that black and Hispanic students and lower income students score lower on the PSAT thantheir white and higher income counterparts.
The raw data suggest a strong negative relationship between cumulative heat exposure andacademic achievement. Figure 2 maps average PSAT performance by county. On average, Southern counties have substantially lower test scores than do Northern counties. This tracks closely
12

We exclude a very small number of observations of PSATs taken during October of 12th grade.
In our sample, 85 percent of students take the PSAT twice and 15 percent take it three times, the maximum given
testing opportunities in 9th, 10th and 11th grades.
14
See Figure A.2.
13

10

with differences in heat exposure by geography, as seen in Figure 3. In Florida and southern
Texas, the average school day experienced by a student is above 80◦ F, compared to an averageschool day temperature in the 50s◦ F in much of the Northern U.S. Southern students in many
counties experience 30 or more school days above 90◦ F, compared to fewer than 5 such days innearly all Northern counties. The existence of such a strong North-South temperature gradientand test score gradient could be causal or could be driven by other important regional differences.
Our goal is disentangle the impact of heat from such other factors.

2.3

Empirical Approach

We exploit the fact that for students who take the PSAT multiple times, differences across takes inprior year heat exposure are likely uncorrelated with differences in other factors that might affectacademic achievement. We thus ask whether students score lower immediately following a hotter
year relative to their own score immediately following a cooler school year and, if so, we argue
that heat is the only factor that can explain such a difference in outcomes. We implement thisidentification strategy with student fixed effects regressions of the following form:

Scoreiscyn = βHeatsy + ηi + γcyn + isycn(1)Here, Score denotes the standardized PSAT math and reading score for student i in high schools, high school class c, taking the test in October of year y for the nth time. Inclusion of student
fixed effects η implies that identification comes from within-student comparisons of heat exposureand test score differences over multiple takes.15 We define cumulative heat exposure Heat as theaverage maximum temperature experienced during school days in the year prior to the test, for all
students in high school s taking the test in year y. In that case, the coefficient of interest β can beinterpreted as the standard deviation impact on a student’s test score of experiencing a one degree
F hotter school year on average. High school class by test year by take number fixed effects γ
flexibly control for a variety of potential confounds, including differential selection into test-taking
15
We use student fixed effects rather than high school fixed effects because the latter approach depends on the assumption that selection into PSAT-taking at the school level does not vary over time in ways correlated with heat
exposure. This assumption fails empirically because, over the time period in question, PSAT taking expands to a wider
set of students and moreso in regions of the country that are differentially affected by longer-term warming trends. The
student fixed effects approach avoids this selection margin entirely.

11

across high school classes, differential difficulty of the test across test dates, and differential test
performance based on past number of test takes. We cluster standard errors by weather station,
the level of variation in our treatment variable.
We also use a specification that replaces this single heat exposure measure with a vector ofcounts of the number of school days falling into various temperature bins:
Scoreiscyn = β1 DaysAbove100sy + β2 DaysIn90ssy + β3 DaysIn80ssy + β4 DaysIn70ssy(2)+β5 DaysBelow60sy + ηi + γcyn + isycn
In this specification, the coefficient on days in the 90s can be interpreted as the impact of experiencing one more very hot school day, relative to a school day with temperature in the 60s. This
specification allows us to study non-linearities in the effect of school year temperature.16 Identification therefore relies on both spatial variation in heat exposure, as previously shown in Figure 3,
as well as temporal variation in heat exposure.17 To understand the magnitude of such identifying
variation, we compute the residual from regressing heat exposure on the aforementioned student
and class-year-take fixed effects. The distribution of such residuals suggests that a one standard
deviation increase in mean school day temperature is about 1◦ F, while a one standard deviation
increase in the number of schools day above 90◦ F is about three days.
One potential threat to identification comes from the possibility that cumulative heat exposure
drives selection into taking the PSAT for the first time or choosing to retake it. To test for selection
into taking the PSAT the first time, we collapse the data by high school and regress the numberof first-time test-takers (as well as its logarithm) on high school fixed effects and cohort by test
date fixed effects. We see no evidence that within-school fluctuations in annual heat exposure affects the number of test takers and can rule out economically meaningful effect sizes. We then run
similar student-level regressions using the demographic characteristics of first-time test-takers as
outcomes. The results rule out meaningful impacts of heat exposure on the observable composition of the test-taking population, particularly when controlling for differential heat trends bystate.18 Finally, we ask whether heat in the year prior to the first take or in the year following
16

We do not find strong evidence that cold weather affects learning in our sample, hence our focus on the upper endof the temperature distribution.
17
See Figure A.3 for annual variation in average school day temperatures.
18
See Table A.1 for detailed estimates.

12

the first take affects the probability that a student retakes the PSAT. We again find no evidence ofsuch selection, with point estimates suggesting a 1◦ F hotter school year increases the probabilityof retaking by 0.05 percentage points and confidence intervals that rule out effects larger than 0.15
percentage points.19 In total, these results suggest little evidence of endogenous selection into
test-taking or retaking as a result of cumulative heat exposure.

3

The Impact of Cumulative Heat Exposure

3.1

Prior Year Impacts

On average in the U.S., experiencing a 1◦ F hotter school year lowers academic achievement by
0.002 standard deviations, a result that is very precisely estimated and robust to a variety of controls for potential confounding factors. Table 2 shows these results. The first column of panel
A contains the baseline specification described in equation 3, where the test score outcome ismeasured in hundredths of a standard deviation. The coefficient is highly statistically significant
and precise enough to rule out effects smaller than 0.001 standard deviations. The magnitude ofthese impacts is small enough to have been missed by previous studies with less precision but
large enough to imply non-trivial cumulative effects of temperature on learning. For example,
the average gain in PSAT score performance between 10th and 11th grade is about 0.3 standard
deviations, implying that a 1◦ F hotter school year reduces learning by close to one percent of the
expected gains over that year. As we will see below, learning impacts are even larger for certain
demographic subgroups and in the absence of air-conditioning.
That students score lower following hotter years relative to their own scores following cooler
years does not appear to be driven by other channels potentially correlated with heat in the school
year leading up the exam, as seen in the next four columns of Table 2. Controlling for total snowfall and rainfall in the prior year and for temperature and precipitation on the day of the exam
has nearly no effect on the point estimate. This suggests that we are not mistakenly attributing tocumulative heat exposure effects that are actually driven by cumulative precipitation exposure orby contemporaneous heat exposure. Similarly, controlling for both cumulative and contemporaneous pollution exposure leaves our estimate nearly unchanged, implying that we are measuring
19

See Table A.2 for detailed estimates.

13

the direct impact of heat and not of pollutants such as ozone that may be more common on hot
days.
Controlling for county-level payroll in industries highly exposed to weather conditions also
does little to our point estimate, suggesting that cumulative heat exposure is not operating throughthe channel of family income or local economic conditions.20 The robustness of our estimate
to controls for state-specific time trends suggests we are not picking up spurious correlations
driven by subtle geographic differences in warming trends that may be correlated with other local changes in selection into or preparation for PSAT-taking or retaking.21 Regardless of whichof the aforementioned controls are included, the estimated impact of a 1◦ F hotter school year,
which represents a roughly one standard deviation change in cumulative heat exposure, is neversubstantially different from 0.002 standard deviations.
Given that the mean distance between weather stations and high schools in our data is justunder 10 miles, the cumulative heat exposure we assign to each student may be mismeasured,particularly for students farthest away from weather stations. The final column of Table 2 limits the sample to high schools within five miles of a weather station, for which we assume thatmeasurement error is less of an issue. For students whose high schools are particularly close to
weather stations, the impact of cumulative heat exposure on academic achievement is about 25
percent larger than for the sample as a whole. Interacting heat effects with distance from the nearest sensor also suggests students farther from sensors see less measured impact from heat, withthe model predicting that those in the immediate vicinity of a sensor would experience impacts
similar to the estimate in that final column of Table 2.22 This is consistent with the possibility
that measurement error in our treatment variable is generating downward bias in our estimates,
though it is also consistent with the possibility of heterogeneous treatment effects correlated withfactors that make weather stations more likely to be online near schools.
In addition to estimating the impact of generally hotter school years, we also show that very
hot days are particularly damaging to student achievement. Panel B of Table 2 shows the specification in which we measure cumulative heat exposure by counts of school days falling into various
20This is perhaps unsurprising given the developed country context but contrasts with research in developing countries that shows agricultural yield shocks driving schooling outcomes (Garg et al., 2017; Shah and Steinberg, 2017).
21
The estimates are also robust to using quadratic or cubic trends instead of linear trends.
22
See column 1 of Table A.3.

14

temperature bins. Replacing a school day in the 60s with a hotter school day lowers achievement,with the extent of that damage increasing roughly linearly with temperature above 70◦ F. Consistent with our baseline specification, these estimated magnitudes also imply that a one standard
deviation increase in heat exposure, or over three additional days above 90◦ F, lower achievement
by 0.002 standard deviations. Cold days, those below 60◦ F, appear to have little impact on achievement. Figure 4 shows these point estimates with further disaggregation of colder school days and,consistent with laboratory studies on cognition and recent studies on labor supply and mortality, shows damage that increases with temperature starting around 70◦ F. Estimated impact of hotdays are, like those for mean heat, robust to controls for cumulative precipitation and pollution,
test day weather and pollution, local economic conditions and state-specific trends.
Heat’s cumulative impact on academic achievement is not driven by one particular subject, incontrast to findings focusing on short-run cognitive impacts (Graff Zivin et al., 2017; Garg et al.,2017). Both math and reading scores drop by similar magnitudes for a given level of additional
heat exposure.23 The effect is also not driven by one particular test take. Heat prior to a first test
take has relatively similar negative effects on achievement as heat prior to second take, although
there is some evidence that heat’s learning impact, if anything, increases with take number.24 Thiseliminates the possibility that our results are driven by differential selection into retaking basedon correlations between heat exposure, first take performance and students’ belief about whether
their first scores reflect their true abilities. It also makes unlikely the possibility that our results are
driven by subtle warming trends over time. Using future temperature shocks as a placebo test also
yields results consistent with our interpretation of these impacts as causal. Controlling for meanschool day temperatures in the years one, two and three years after the exam does little to change
our estimated impact of cumulative heat exposure and the coefficients on future temperature aremuch closer to zero than our main effect and never statistically significant.25 This makes it lesslikely our results are a statistical artifact driven by spurious correlations between temperature andtest scores.
The statistical significance of our estimates is not particularly sensitive to how we account forpotential spatial correlation in temperature shocks. Our default specification clusters standard
23

See Table A.4 for details.
See Table A.5 for details.
25
See Table A.6 for details.
24

15

errors by weather sensor, following the suggestion by Abadie et al. (2017) to cluster at the levelof treatment variation. Given potential spatial correlation between heat shocks across distinct but
nearby weather sensors, we cluster by state to allow for correlations within much broader geographic areas. This very conservative approach increases our standard errors by at most 30-50
percent, so that our central estimates of the impact of average heat or days above 90◦ F remain
highly statistically significant.26 Following Conley (1999), non-parametrically adjusting our standard errors to account for spatial correlation does not inflate our standard errors significantly,
again leaving our main inferences unchanged.

3.2

Productivity of Instructional TimeOne indication that cumulative heat exposure affects achievement by directly lowering the productivity of instructional time comes from examining the impact of heat on three mutually exclusive sets of days in the year prior to the test: school days, weekends and national holidays
during the school year, and summer days. The first two columns of Table 3 contrast our baseline
specification to one in which we control for heat on summer days. Two important facts emerge.
First, controlling for summer heat has little effect on our estimated impacts of school day heat.
Second, the impact of summer heat on academic achievement is very small and statistically indistinguishable from zero. That summer heat has no impact on academic achievement seems torule out potential channels such as student health or local economic conditions given that suchchannels should be affected by summer heat as well as school day heat.
Controlling for school year weekend and holiday heat somewhat increases the estimated effects of school day heat. We see no evidence that weekend and holiday heat lowers student
achievement. This is again consistent with the possibility that time in school is critical to understanding the relationship between heat exposure and human capital accumulation. One challenge
in interpreting the coefficients in column 3 of Table 3 is that residual variation in weekend heatis highly collinear with variation in school day heat. Summer heat variation, by contrast, is substantially less collinear with school day heat variation. The large, positive coefficients on weekend
heat could represent a real impact of substitution away from leisure time and toward study time.
They may also simply be an artifact of that high degree of collinearity. Regardless, controlling for26

See Table A.7.

16

weekend heat does not affect the conclusion that school day heat affects academic achievement.
One further test yields results consistent with our interpretation that heat exposure interfereswith actual learning. In column 4 of Table 3, we break heat exposure into three time periods
corresponding to distance in time to the test: post-summer school days (the roughly two months
just prior to the PSAT), summer days (roughly three to five months prior to the PSAT), and presummer days (roughly six to twelve months prior to the PSAT). Summer heat again has little clear
impact on achievement while both pre- and post-summer heat have large negative impacts. Thatthe damage from pre-summer heat is as large as or larger than the impact of post-summer heatsuggests that heat operates not just through periods where students might be “cramming” for atest. Instead, heat appears to affect cumulative learning over a longer time frame.

3.3

Persistent and Cumulative Impacts

To provide evidence about the impacts of heat exposure further back in time than the prior school
year, we augment our regression specifications 3 and 2 with temperature measures from schooldays in the years starting two, three, four and five years prior to each exam take. Equation 3
becomes:
Scoreiscyn = β1 Heat1Y earAgosy + β2 Heat2Y earsAgosy + β3 Heat3Y earsAgosy(3)+β4 Heat4Y earsAgosy + β5 Heat5Y earsAgosy + ηi + γcyn + isycn
This accomplishes two things. First, our estimates of prior year heat exposure from Equations 3
and 2 are downward biased if such effects persist beyond one year, and controlling for further
lagged measures of temperature should help eliminate that downward bias. Failing to control
for dynamic effects can cause our student fixed effects approach to understate the impact of heatbecause that approach implicitly assumes complete decay of effects after one year, so that heat
before the first take affects only the first take and not the second take itself. Second, the estimatedimpacts of earlier years’ heat exposure allows us to more accurately estimate longer run impactsof exposure to different temperature environments. For example, the sum of the coefficients β1
through β5 estimates the test score impact of a one degree increase in the average temperature
over a student’s five prior school years.

17

Table 4 shows these estimates, with coefficients for individual years shown in each column andthe sum of those coefficients shown at the bottom of each column. Two important facts emerge.
First, controlling for earlier heat exposure increases our estimates of the impact of prior year heatby 20 to 40 percent, suggesting that such estimates may have been downward biased by our baseline specification’s identifying assumption that prior year heat’s impact fades out entirely afterthat year. Second, we see fairly clear evidence that heat up to four years prior affects test scores.
This evidence is clearer with respect to the impact of hot days than the impact of average temperature but is present in the point estimates of both. We see no evidence that heat five years prior has
impacts on test scores and tests of further lags (not shown here) also show no clear impact. Theseestimates suggest that heat effects are somewhat more persistent than teacher effects, which theliterature estimates fade out substantially within one to two years (Kane and Staiger, 2008; Jacobet al., 2010; Rothstein, 2010).
We take the cumulative impact over the past four years as our favored estimate of cumulative
impacts for two reasons. First, because five year and further lags have little apparent impact on
test scores, cumulative impacts tend to level off after four years. Second, we are estimating lagged
heat exposure based on the high school a student is enrolled in at the time of taking the PSAT.
Because we do not know where a student attended primary school, going back much further
in time likely increases the measurement error of our treatment variable. We therefore take thefour-year cumulative impact as a lower bound on the total impact but one that our best estimatessuggest is likely not far from the truth. The cumulative impact of increased heat exposure overmultiple years is thus three to five times larger than the impact of just the prior year’s heat. Ourestimates suggest that a 1◦ F increase in the average temperature of the past four school years leads
to about a 0.006 standard deviation decrease in test scores, or 2 percent of the typical increase in
PSAT scores over a single school year. Experiencing one additional day above 90◦ F in each of
those four years would reduce scores by beween 0.002 and 0.003 standard deviations, or 1 percent
of a typical school year’s PSAT increase.

18

4School Air-Conditioning as a Defensive Investment

4.1

Descriptive Analysis

Adaptive responses and defensive investments are important for understanding the welfare implications of environmental shocks, particularly in the long run (Graff Zivin and Neidell, 2013;
Kahn, 2016; Deschenes et al., 2017). School air-conditioning represents one potential investment.27
To explore its role in mitigating the effects of heat exposure, we first provide descriptive analysisof the prevalence of school air-conditioning across the U.S.
Figure 5 shows county-level averages of school air-conditioning penetration as measured by
the extent to which students (panel A) and guidance counselors (panel B) report that “On hot days,
classrooms get too hot.” The resulting map is roughly the inverse of an average temperature map.
Students and counselors are much less likely to report hot classrooms in the hotter regions of thecountry and much more likely to report hot classrooms in cooler regions. Students in the Northeast, for example, report that heat interferes with learning on the majority of hot days. Students
in the South report heat interfering with learning on only about one-fourth of hot days.
Because this reporting may partly reflect the extent to which students and counselors are accustomed to heat, rather than actual air-conditioning status, we ask guidance counselors directly
about the fraction of classrooms with air-conditioning. That map, in panel A of Figure 6, looks
quite similar to the map of hot classrooms. According to guidance counselors, nearly all classrooms in the South have air-conditioning while the majority of classrooms in the Northeast lackit. We therefore interpret student reports of hot classrooms as a measure of air-conditioning penetration. That our student-generated measure based on hot classrooms has a nearly 0.7 correlation
with the counselor-generated responses to the direct question about air conditioning suggests theformer is largely measuring actual school air conditioning.28
These various measures are the first we know of to provide national school-level estimates of27
Teachers and parents seem to value school air-conditioning, judging by recent labor disputes and community petitions. During a major teacher strike in Chicago in 2012, “Timetable for air-conditioning” was one of four major contract
demands, with an agreement to provide universal air-conditioning eventually reached in 2016. Parents and teachers ina number of major school districts such as New York City, Los Angeles, and Denver have have recently signed petitions
asking districts to upgrade air-conditioning equipment. See: http://www.denverpost.com/2011/09/08/heat-relatedillnesses-spur-petition-for-sept-school-start-in-denver/.
28
See Figure A.5, which shows a tight relationship between counselor reports of air conditioned classrooms andstudent reports of classrooms too hot for learning.

19

air-conditioning status. We also note, as seen in panel B of Figure 6, that both home and school
AC seem to vary substantially by region, with lower penetration rates particularly in more mountainous regions of the country.

4.2

School Air-Conditioning as Potential Mitigator

We use two approaches to assess whether school air-conditioning can offset heat’s adverse impact
on learning. First, we interact the cross-sectional measure of air-conditioning penetration reported
by students with our heat exposure measure and add it to our baseline specification. This regression has the form:

Scoreiscyn = αHeatsy + βHeatsy ∗ SchoolACs + ηi + γcyn + isycn(4)

The coefficient α now has the interpretation of the impact of heat on a school with no air-conditioning,
while β represents the predicted difference between that impact and the impact on a fully airconditioned school.
This analysis, if taken as causal, suggests that school air-conditioning almost fully offsets theimpacts of cumulative heat exposure. In column 1 of Table 5, the main coefficient implies that,for students in schools with no air-conditioning, a 1◦ F hotter school year lowers achievement
by 0.0032 standard deviations. The interaction coefficient suggests that, in fully air-conditioned
schools, this effect is 0.0025 standard deviations smaller. For the average student, school airconditioning thus appears to offset 73 percent of the learning impact of hot school days. This
interaction coefficient may represent the causal impact of school air-conditioning but it may also
be picking up effects of other factors correlated in the cross-section with a school’s air-conditioning
status.
In particular, school air conditioning may be correlated with other adaptations students havemade to deal with hot environments or with wealth or other resources available to students thatindependently improve their achievement. To account for the possibility that school air conditioning is proxying for other adaptive measures, we add to equation 4 additional terms in which heat
exposure is interacted with county-level home air-conditioning rates and mean school year temperature. To account for school air conditioning as a proxy for other academic resources available
20

to students, we also control for such interactions with ZIP code level income, the racial composition of a school’s PSAT takers, and per-pupil district-level school capital expenditures, the last ofwhich helps account for the possibility that schools with air conditioning have made other capital
investments that boost achievement.29 The results of this augmented specification are shown incolumn 2 of Table 5. The topmost coefficient now suggests that, for a student with neither school
nor home air-conditioning, a 1◦ F hotter school year lowers achievement by 0.0057 standard deviations. School air-conditioning and home air-conditioning respectively offset 41 and 57 percentof this effect, implying that a student with access to both would see little negative impact of heat
exposure. That the magnitude of the school air-conditioning coefficient does not change substantially with the addition of these controls implies that omitted variable bias from such sources isunlikely to explain the observed effect.
We make one further attempt to isolate the impact of school air-conditioning. To do so, we
use the change over time in penetration rates implied by differences in counselors’ reports about
their schools’ air-conditioning status in 2016 versus 10 years before that. We assign to students avariable SchoolACchange, which represents their high school cohort’s change in air-conditioning
penetration rate relative to 2006 implied by the counselors’ answers. Cohorts from 2006 and earlier
are assigned a value of zero and more recent cohorts are assigned a change linearly interpolated
from the counselors two responses. We then run the following specification:

Scoreiscyn = βHeatsy ∗ SchoolACchangesc ∗ HSClassi + δHeatsy ∗ SchoolACchangesc+ µHeatsy ∗ HSClassi + νHeatsy + ηi + γcyn + isycn (5)Here, HSClass is a continuous measure of a student’s cohort. In effect, the coefficient β from this
triple-difference approach estimates whether schools that have installed additional air-conditioning
over time see the impact of heat shrink across cohorts, relative to schools that have not added airconditioning.
The results in column 3 of Table 5 suggest that this is the case. The coefficient on the tripleinteraction term is positive and highly statistically significant, implying that later cohorts do see
29

We use sample-demeaned versions of these control variables so that coefficients can be interpreted as impacts on
students with average school temperatures, income, racial composition and capital expenditures.

21

smaller impacts of heat in schools that improved air-conditioning penetration, relative to schoolsthat did not. This conclusion is unchanged when we control for additional interactions with home
air-conditioning and the other controls described previously. This provides additional evidence
consistent with the possibility that school air-conditioning mitigates the impacts of heat exposure.
The main threat to validity here is that a school’s adoption of air-conditioning correlates withother unobserved changes over time in that school that might also mitigate the impacts of heat (e.g.
more tree cover, improved ventilation). Though possible, it seems likely that changes in school airconditioning penetration are more exogenous than cross-sectional variation in such penetration.
That both approaches yield consistent results suggests school air-conditioning may mitigate asubstantial portion of the learning impacts of heat exposure.
To provide a back-of-the-envelope estimate of the monetized value of school air-conditioning,
we apply previous estimates of the relationship between test scores and later life earnings fromChetty et al. (2011). That paper finds that having a teacher who raises test scores by 0.1 standard
deviations results in a net present value of $8,500 in future increased earnings for current 16 year
olds.30 Our estimates in Table 5 suggest that school air-conditioning offsets about 0.0025 standard
deviations in learning damage for each 1◦ F increase in temperature. This translates into a netpresent value of $212 in recovered future earnings per student, per 1◦ F increase in temperatureduring a given school year. In a city like Houston, where the average school day is approximately
80◦ F and thus 10◦ F above the point where heat’s impact on learning first appears, the present
value of school air-conditioning is approximately $2,120 per year for each student, $53,000 per
year for each 25 student classroom, or $2.1 million per year for each 1,000 student high school. Put
differently, the extent to which school air-conditioning would offset the earnings loss driven by
the 5◦ F increase predicted by climate change models is $1,060 per student, $26,500 per classroom,or just over $1 million per high school.
Although these are rough estimates, benefit values of this order of magnitude imply that school
infrastructure may more than justify their costs. Based on available data, we conservatively esti30
Chetty et al. (2011) compute a $7,000 net present value in increased earnings for the typical 12 year old student intheir sample. We apply their five percent discount rate to generate the $8,500 figure for the typical 16 year old student
taking the PSAT. An important assumption we make by using these estimates is that the achievement gains due to abetter teacher result in later life impacts that are equivalent in magnitude to those associated with having a climatecontrolled learning environment. For instance, if teachers impart valuable non-cognitive skills but air-conditioning
does not, these estimates would be overstated.

22

mate the amortized cost of school air conditioning to be approximately $125,000 per school per
year, or $125 per student per year for a 1,000 person school.31 Given variation in the averageamount of school year heat, we estimate that the cost of improving scores by 1 percent of a standard deviation for the average US school is between $25 and $125 per student per year.32 For
comparison, the average cost associated with the Tennessee STAR experiment – which reduced
class sizes by roughly one-third at a cost of $3,602 per student per year ($2,151 in 1995 dollars) andresulted in test score gains of approximately 0.22 standard deviations Krueger (1999) – is approximately $163 per 1 percent of a standard deviation improvement per student.

5

Heat and Achievement Gaps

5.1

Inequality in School Air-Conditioning

We next document racial and income gaps in school air-conditioning penetration rates. To do so,
we regress the student-generated measure of school air-conditioning penetration on an indicatorfor being black or Hispanic (relative to being white) and separately on an indicator for being in
the lower half of the ZIP code income distribution (within cooler and hotter halves of the country
to account for temperature differences). We also control for a quartic in school-level mean school
year temperature experienced over the sample time period.33 As panel A of Table 6 shows, blackand Hispanic students report 1.7 percentage point (9 percent of a standard deviation) lower rates
of school air-conditioning penetration relative to white students, while lower income students
report 2.8 percentage point (15 percent of a standard deviation) lower rates than higher income31

We note that the average school AC budget allocations from two recent bond initiatives in New York City and
Denver public schools were reported as being $100,000 and $886,000 per school respectively. We therefore conservatively assume that these allocations only represent up-front fixed costs, and that variable costs associated with
operating school air conditioners are an additional 10% of fixed costs each year. Conservatively assuming $886,000
in up-front fixed costs, a 5% discount rate and an average lifetime of 20 years, we estimate total amortized costsof $125,000 per school per year. (For Denver, see: https://www.chalkbeat.org/posts/co/2016/06/09/how-denverpublic-schools-could-spend-70-million-cooling-its-hottest-schools/. For NYC, see: https://www1.nyc.gov/office-ofthe-mayor/news/261-17/mayor-de-blasio-chancellor-fari-a-city-council-every-classroom-will-have-air.)
32
The benefits of installing school air conditioning will likely be proportional to the average school year heat thatis offset. In a place like Houston, which experiences approximately 35 school days above 90 and 48 days in the 80’s,
our estimates (using coefficients from column 1 of table 2) suggest that air conditioning offsets around 5.7 percent ofa standard deviation in learning losses that would occur due to hot temperature. In a cooler place such as New York,
which experiences 2 days above 90◦ F and 14 days in the 80’s, we estimate the present value of air conditioning to beapproximately 1 percent of a standard deviation.
33
In these regressions, we limit the sample to one observation per student and use all PSAT takers to get a more
representative picture of national patterns.

23students. These disparities appear somewhat stronger in cooler areas of the country than in hotter
areas, defined by dividing schools into those below and above the national median school year
temperature.
Panel B of Table 6 also measures gaps in school air-conditioning penetration, instead using asan outcome an indicator having “inadequate” school air-conditioning. We define schools with inadequate air-conditioning as those where the average student responded that classrooms get too
hot on hot days “Most of the time” or “All the time”. Black and Hispanic students are 1.6 percentage points more likely than white students to be in schools with inadequate air-conditioning.
Lower income students are 6.2 percentage points more likely to be in schools with inadequate
air-conditioning than their higher income counterparts. These disparities are again substantiallylarger in cooler areas of the country than in hotter areas. Figure 7 further shows that racial gaps inschool air-conditioning access are not explained purely by ZIP code level income differences.

5.2

Heterogeneous Impacts of Heat

Heat exposure has heterogeneous impacts by race, income, and geography, which we show inTable 7.34 As panel A shows, the impact of prior year heat on black and Hispanic students isthree times larger than the impact on white students. The impact of prior year heat on students
in lower income ZIP codes is twice as large as on those from higher income ZIP codes.35 The lasttwo columns split the sample into high schools with below and above national median school
year temperatures. Even though cooler areas of the country are less likely to experience extreme
heat, students in these areas seem to experience more learning disruption per unit of extreme heat,consistent with lower average levels of defensive investments. Each school day above 90◦ F has
more than three times the negative impact on test scores in cooler areas than in hotter areas.36 We
also see suggestive evidence that heat is more damaging to achievement in more humid areas of34

We find no evidence of heterogeneity by student gender.
Measurement error may imply that these racial and income gaps in heat’s effects are, if anything, somewhat understated. The last four columns of Table A.3 suggest that measurement error may generate more underestimation in heat’s
effects for Black and Hispanic students and low income students than their White and high income counterparts. If
weather sensors were immediately adjacent to high schools, these estimates suggest that heat’s impacts would be about
25 percent larger for minority and low income students but largely unchanged for White and high income students.
36
In cooler areas, the observed impact of heat could be driven partly by higher temperatures generating an increased
number of otherwise scarce pleasant days for students to skip school. That days above 90◦ F show negative impacts
and are too hot to be considered pleasant likely implies that channel is not the only explanation of heat’s effects.
35

24

the country.37
Panel B shows cumulative impacts measured by adding coefficients from the previous four
years of heat exposure. Experiencing 1◦ F hotter school years over the past four years has a nearly
80 percent larger impact on black and Hispanic students than on white students. The impact of
one additional day above 90◦ F in each of the preceding four school years has a 40 percent larger
impact on black and Hispanic students than on white students. Interestingly, four-year cumulative
impacts of heat exposure do not appear to vary by ZIP code income as much as one-year impacts.
The cumulative effects of a 1◦ F increase in school year temperatures is nearly twice as high incooler areas, while the cumulative impact of each year having an additional day above 90◦ F is fivetimes larger in cooler areas.
That the achievement of minority and lower income students suffers more from heat exposure is consistent with minority households and high-minority schools having fewer resources
to make defensive investments, either ex ante or ex post (Graff Zivin and Neidell, 2013; Kahn,
2016). Wealthier students may be able to compensate for lost learning time by getting additional
instruction from their parents or private tutors. Such students may also be more likely to attend
schools where teachers have better capacity to compensate for lost learning time by adjusting
lesson plans or adding more instructional time to the day.38 A simpler explanation for this heterogeneity is that minority and lower income students have less access to school conditioning, as wehave shown, and home air-conditioning, both of which help offset the negative impacts of heat,though it appears that minorities and low income students also tend to live in historically hotter
climates which appear to feature other effective adaptations.39
The estimates in Table 7 allow us to compute the fraction of the racial achievement gap thatis driven by a combination of the heterogeneous impacts of heat by race and racial differences inheat exposure. To do this, we ask how much larger racial achievement gaps are than they would
be if all students always experienced school day temperatures that appear optimal for learning(i.e. those in the 60s). Our estimates suggest that total exposure to days above 90◦ F lowers black37
Though heat indices accounting for humidity are not available from our weather sensor data, Table A.8 estimatesheat effects separately by typical humidity and finds that heat appears more damaging in humid areas than arid areas.
38
Both research and media reports suggest teachers are aware of the adverse impacts of heat on student performanceand make efforts to offset some of those impacts ex post. Park (2017) finds that New York City teachers selectively
boosted grades of students who experienced hot exam sittings and scored just below pass/fail cutoffs.
39
While our residential AC data is not student-specific, we note using RECS microdata that Black and Hispanic
households are 7% and 6% less likely respectively to have residential air conditioning for a given climate.

25

and Hispanic students’ achievement by 0.043 standard deviations (-0.00277 standard deviations
per additional day above 90◦ F * 15.7 days above 90◦ F). For white students, the comparable effectis 0.021 standard deviations (-0.00197 standard deviations per additional day above 90◦ F * 10.06
days above 90◦ F). This means that extremely hot days widen the racial achievement gap by approximately 0.022 standard deviations, or about three percent of the 0.8 standard deviation gap
in PSAT performance between black and Hispanic students and white students. If we also account for the cumulative impacts of school days between 70 and 90◦ F, then excess heat accounts
for about seven percent of the racial achievement gap.40 The physical environment students are
exposed to, as measured by school day temperatures, thus accounts for a small but non-trivial
portion of the racial achievement gap.
Similarly, our analyses suggest that the disruptive influence of heat may play a causal role ingenerating cross-sectional differences in standardized achievement. The North-South gradient in
PSAT performance is 0.023 standard deviations per ◦ F hotter average climate. This presumably
captures many correlated factors, including differences in teacher quality, parental incomes, andrates of air conditioning. Our estimate of the causal (cumulative) impact of a 1◦ F hotter climate on
learning is approximately -0.0056 standard deviations at current average levels of air conditioning(column 4 of Table 4). This suggests that up to 24 percent (-0.0056/0.023) of the North-South
gradient in PSAT scores may be attributable to the causal impact of a hotter climate. This most
likely overstates heat’s contribution to that gradient, given the positive correlation between hotter
climate and levels of air conditioning, but suggests that a non-trivial portion of existing crosssectional differences in learning may be caused by differences in the thermal conditions underwhich learning occurs.

6

Conclusion

We provide the first evidence that cumulative heat exposure inhibits cognitive skill development
and that defensive investments such as school air-conditioning may mitigate this effect. Our findings imply that the physiological impacts of heat directly interfere with learning. This work highThough the estimated impacts of school days between 70 and 90◦ F are smaller and noisier than those from days
above 90◦ F, the cumulative coefficient on such days for black and Hispanic students is -0.0004 standard deviations andthey experience nearly 84 such days a year. The estimated impact of such days on white students is zero (out to fourdecimal places).
40

26

lights the understudied role that students’ and teachers’ physical environments play in generating
educational outcomes. It also highlights the extent to which disparities in such physical environments contribute to inequality in educational outcomes such as the racial achievement gap. The
results allow us to estimate the value of one potential public investment, school air-conditioning,that may help reduce such gaps.
Evidence that heat exposure affects human capital accumulation points to a potential understudied channel through which heat may affect macroeconomic growth. A variety of recent papers
have documented clear connections between country-level temperature fluctuations and growth
but the mechanisms explaining that connection have remained a matter of speculation (Dell et al.,2012; Burke et al., 2015). Hypothesized channels include the negative impacts of heat on physicalhealth and on labor productivity, particularly for physically intensive occupations (Hsiang, 2010;
Heal and Park, 2016). Our evidence suggests that heat not only interferes with the physical capabilities of a nation’s workforce but also with its cognitive capacities, and most crucially the rate at
which valuable skills are accrued by the workforce over time.
Understanding the causal relationship between cumulative heat exposure and learning is ofheightened policy relevance given accelerating warming in most parts of the world, and given thatthe overwhelming majority of the world’s population does not yet have access to air-conditioning(Davis and Gertler, 2015). Based on current estimates of projected warming in the U.S., we engage
in the following thought experiment: By 2050, how much heat-related learning disruption can we
expect for the average high school student, relative to a student attending high school in 2010?
Median climate change scenarios for the contiguous United States predict average warming ofroughly 5◦ F by 2050. To generate a summary measure of the impact of climate change on futurelearning, we take the average treatment effect in degree F terms from above (0.006 standard deviations) and multiply by the extent of predicted mid-century warming (5◦ F), yielding an estimateof 0.03 standard deviation lower achievement, or approximately 10 percent of the average learning achieved in a given school year. Without further investments in school infrastructure, climatechange would likely also result in a further widening of current racial achievement gaps.41
41

These calculations do not account for potential non-linearities in the damage function for temperatures outside
the range of historical experience, such as days above 110◦ F. It is important to note that these back-of-the-envelope
estimates do not account for heterogeneity in warming or air-conditioning penetration patterns across regions, or forthe costs of installing air-conditioning, both of which are likely to be important determinants of net welfare impacts.
They also do not account for potential migration responses.

27

Further questions about the impact of heat on learning remain. The average American student experiences approximately 12 school days above 90◦ F per year, whereas the average Indian
student experiences over 100 such days annually. What portion of the achievement gap between
hot and cool countries is explained by the direct impact of heat exposure on learning documented
here? Do these impacts on cognitive skill and learning have longer-term impacts on students’economic outcomes, affecting rates of economic mobility and convergence? Other than school
air-conditioning, what alternative investments or actions can be taken to mitigate the impacts ofheat on learning? While it is possible that individuals in hotter climates are better acclimatedand thus experience reduced sensitivity per unit of heat exposure, given much lower levels of
air-conditioning and the potential for other correlated health or nutritional impacts, we speculatethat our estimates represent a conservative appraisal of the inhibiting influence of a hotter climate
on human capital development. We hope future work addresses such questions.

28

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31

Figure 1: Climate and Achievement Across Geographies

-1

-.5

0

β = -.0203(.0034)-1.5

Standardized PISA math score.5(A) Across countries

20

30

40

50

60

70

80

90

Average annual temperature (°F)

.05
-.15

-.1

-.05

0

β = -.0036(.0005)-.2Standardized SEDA math score(B) Across U.S. counties

20

30

40

50

60

70

80

90

Average annual temperature (°F)

Notes: The above figure shows a scatterplot of mean 2012 PISA (panel A) or SEDA (panel B) mathscores and average annual temperature by country or U.S. county. Average annual temperatures
are measured over the period 1980-2011. Panel B shows a binned percentile plot of standardized
3rd-8th grade math scores (2009-2013) by percentile of the county-level average temperature distribution, with scores standardized by subject, grade and year as in Fahle et al. (2017). Also shown
is a fitted line and slope coefficient from a bivariate regression of scores on temperatures, using
heteroskedasticity robust standard errors.

32

Figure 2: Spatial Distribution of PSAT Z-Scores

Notes: The above figure shows county-level average standardized PSAT scores from the highschool classes of 2001-14.

33

Figure 3: Spatial Variation in Prior Year Temperature

Notes: The above figure shows the mean daily maximum temperature (panel A) and number ofdays above 90◦ F (panel B) experienced by students on school days in the 365 days prior to taking
the PSAT, by county. The sample consists of all PSAT-takers from the high school classes of 200114, whose PSATs were taken between 1997 and 2012.

34

0
-.05
-.1

PSAT z-score (0.01σ).05

Figure 4: Cumulative Hot Days and Test Performance

<40

40-50

50-60

60-70

70-80

80-90

90-100>100

Days in temperature range (°F)
Notes: Shown above are coefficients from a regression of hundredths of a standard deviation in
PSAT total (math plus reading) scores on the number of school days within a given temperature
range during the 365 days preceding the PSAT take. The regression includes student fixed effects
and fixed effects for each combination of cohort, test date and take number. Heteroskedasticity
robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05 *** p<.01).
The sample comprises all students from the high school classes of 2001-14 who took the PSAT
more than once.

35

Figure 5: Hot Classrooms

Notes: The above figure shows by county the mean fraction of classrooms reported as “too hot”
on hot days by students (panel A) and guidance counselors (panel B). Both measures are derived
from student or counselor responses to a survey administered by the College Board. The sample consists of all PSAT-takers from the high school classes of 2001-14, whose PSATs were taken
between 1997 and 2012.

36

Figure 6: School and Home Air-conditioning

Notes: The above figure shows by county the mean fraction of classrooms (panel A) and homes(panel B) lacking air-conditioning. Classroom measures are derived from guidance counselor responses to a survey administered by the College Board. Home measures are derived from the1980 Census and the 1993-2015 quadrennial Residential Energy Consumption Surveys. The sample consists of all PSAT-takers from the high school classes of 2001-14, whose PSATs were taken
between 1997 and 2012.

37

.62
.6
.58
.56

School air conditioning penetration.64

Figure 7: School Air-conditioning by Percent Black or Hispanic

0

20

40

60

80

100

Percent of high school black or Hispanic
Notes: The above figure is a binned percentile plot of high school air-conditioning penetration
rates as implied by student survey responses, by percentile of the school-level percent black or
Hispanic distribution. It plots residual variation after controlling for average daily maximum
temperature by school and average income by zip code between 1997 and 2012.

38

Table 1: Summary Statistics
PSAT Retakers
Alltakers(1)Allretakers(2)Black or
Hispanic
(3)

White
(4)

Lower
income(5)Higherincome
(6)

0.53
0.58
0.29
0.22
63.2

0.55
0.58
0.28
0.33
69.6

0.56
0.00
1.00
0.18
49.4

0.54
1.00
0.00
0.40
78.3

0.56
0.45
0.43
0.20
38.9

0.53
0.69
0.16
0.44
95.6

0.36
1.42
-0.00

1.00
2.15
0.14

1.00
2.17
-0.49

1.00
2.14
0.40

1.00
2.14
-0.15

1.00
2.15
0.40

65.1
11.9

65.8
12.2

68.8
15.7

64.2
10.6

65.9
12.7

65.6
11.7

0.58
0.77

0.59
0.80

0.60
0.85

0.58
0.79

0.58
0.77

0.60
0.82

38,303,474
27,023,119

21,076,009
9,795,654

6,023,145
2,775,607

12,161,058
5,689,371

9,570,444
4,462,169

11,322,404
5,259,910(A) Demographics
FemaleWhite
Black or Hispanic
Mother has B.A.
ZIP code mean income(B) PSAT scores
Retook PSAT
Total takes
First PSAT z-score(C) Temperature
Mean temperature (◦ F)
Days above 90 ◦ F(D) Air conditioning
Classrooms with ACHomes with AC
N (scores)
N (students)

Notes: Notes: Mean values of key variables are shown. Column 1 includes comprises all students from the highschool classes of 2001-14 who took the PSAT at least once. Column 2 includes only those who took the PSAT morethan once. Columns 3-6 include subgroups of retakers, with columns 5 and 6 respectively including below andabove median ZIP code-level income within below and above median temperature areas.

39

Table 2: Prior Year Temperature and PSAT Scores
(1)

(2)

(3)

(4)

(5)

(6)

-0.181∗∗∗(0.028)-0.211∗∗∗(0.036)-0.185∗∗∗(0.029)-0.182∗∗∗(0.028)-0.176∗∗∗(0.027)-0.230∗∗∗(0.042)-0.067∗∗∗(0.018)-0.053∗∗∗(0.013)-0.035∗∗∗(0.009)-0.024∗∗∗(0.008)0.010(0.009)-0.077∗∗∗(0.020)-0.061∗∗∗(0.014)-0.037∗∗∗(0.010)-0.024∗∗∗(0.008)0.013(0.009)-0.075∗∗∗(0.017)-0.059∗∗∗(0.013)-0.039∗∗∗(0.009)-0.026∗∗∗(0.008)0.008(0.008)-0.065∗∗∗(0.018)-0.053∗∗∗(0.013)-0.035∗∗∗(0.009)-0.024∗∗∗(0.008)0.010(0.009)-0.064∗∗∗(0.016)-0.053∗∗∗(0.012)-0.029∗∗∗(0.009)-0.023∗∗∗(0.008)0.010(0.007)-0.098∗∗∗(0.033)-0.064∗∗∗(0.018)-0.046∗∗∗(0.013)-0.020∗(0.012)0.007(0.011)

21,046,448

21,046,448

21,046,448

21,046,448

21,046,448

5,378,273

No
No
No
No
No
No

Yes
Yes
No
No
No
No

No
No
Yes
No
No
No

No
No
No
Yes
No
No

No
No
No
No
Yes
No

No
No
No
No
No
Yes

(A) Average heat
Mean temperature (◦ F)(B) Hot days
Days above 100 ◦ F
Days in 90s (◦ F)
Days in 80s (◦ F)
Days in 70s (◦ F)
Days below 60 ◦ F

NPrior year snow, rain
Test day weather
Pollution
Economic conditions
State-specific trends
Sensor within 5 miles

Notes: Heteroskedasticity robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05*** p<.01). Coefficients in each column and panel come from a regression of hundredths of a standard deviation in
PSAT total (math plus reading) scores on the weather measure(s) shown. Temperature is measured with the daily
maximum temperature from school days in the 365 days preceding the PSAT take. All regressions include student
fixed effects and fixed effects for each combination of cohort, test date and take number. Column 2 adds controls forprior year rainfall and snowfall, as well as test day temperature, rainfall and snowfall. Column 3 controls for prioryear and test day pollution levels (carbon monoxide, ozone, suflur dioxide, nitrogen dioxide and PM10). Column 4controls for the logarithm of per capita county-level payroll in industries highly exposed to weather. Column 5 adds
state-specific linear time trends. Column 6 limits the sample to high schools within 5 miles of the nearest weather
sensor. The sample comprises all students from the high school classes of 2001-14 who took the PSAT more than once.

40

Table 3: Timing of Temperature Shocks
(1)

(2)

(3)

-0.181∗∗∗(0.028)-0.205∗∗∗(0.030)0.039(0.026)-0.270∗∗∗(0.043)(4)(A) Mean temperature (◦ F)
School days, 1 year prior
Summer days, 1 year prior

0.047∗(0.026)
0.114∗∗∗(0.038)

Weekend days, 1 year prior-0.061∗∗(0.025)-0.160∗∗∗(0.029)School days, post-summer
School days, pre-summer(B) Days above 90 ◦ F
School days, 1 year prior-0.056∗∗∗(0.012)-0.061∗∗∗(0.011)0.016(0.011)

Summer days, 1 year priorWeekend days, 1 year prior-0.073∗∗∗(0.016)0.018(0.011)
0.043(0.028)-0.074∗∗∗(0.019)-0.074∗∗∗(0.016)

School days, post-summer
School days, pre-summerN

21,046,448

21,046,448

21,046,448

21,046,448

Notes: Heteroskedasticity robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05 ***p<.01). Coefficients in each column and panel come from a regression of hundredths of a standard deviation in PSAT
total (math plus reading) scores on the weather measure(s) shown. School day temperature is measured with the daily
maximum temperature from school days in the listed 365 day period relative to the PSAT take. Summer temperatureis measured across all days in the summer break preceding the PSAT take. Weekend temperature is measured acrossall weekends and national holidays in the 365 days preceding the PSAT take. All regressions include student fixed
effects and fixed effects for each combination of cohort, test date and take number. The sample comprises all students
from the high school classes of 2001-14 who took the PSAT more than once.

41

Table 4: Lagged and Cumulative Impacts of Heat Exposure
(1)

(2)

(3)

(4)

(5)

-0.181∗∗∗(0.028)-0.189∗∗∗(0.036)-0.017(0.036)-0.185∗∗∗(0.041)-0.010(0.052)0.012(0.043)-0.213∗∗∗(0.044)-0.096(0.061)-0.088(0.057)-0.168∗∗∗(0.049)-0.215∗∗∗(0.048)-0.099(0.071)-0.093(0.080)-0.173∗∗(0.076)-0.009(0.058)-0.181∗∗∗(0.028)-0.206∗∗∗(0.066)-0.182(0.121)-0.565∗∗∗(0.178)-0.589∗∗(0.296)-0.056∗∗∗(0.012)-0.066∗∗∗(0.013)-0.031∗∗∗(0.010)-0.078∗∗∗(0.014)-0.051∗∗∗(0.013)-0.048∗∗∗(0.014)-0.083∗∗∗(0.015)-0.069∗∗∗(0.018)-0.072∗∗∗(0.021)-0.043∗∗∗(0.017)-0.080∗∗∗(0.016)-0.061∗∗∗(0.021)-0.054∗(0.028)-0.024(0.025)0.031(0.019)Cumulative impact-0.056∗∗∗(0.012)-0.097∗∗∗(0.021)-0.178∗∗∗(0.034)-0.268∗∗∗(0.060)-0.188∗(0.096)

N

21,046,448

21,046,448

21,046,448

21,046,448

21,046,448(A) Mean temperature (◦ F)
1 year prior
2 years prior
3 years prior
4 years prior
5 years prior

Cumulative impact(B) Days above 90 ◦ F
1 year prior
2 years prior
3 years prior
4 years prior
5 years priorNotes: Heteroskedasticity robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05*** p<.01). Each coefficient comes from a separate regression of hundredths of a standard deviation in PSAT total(math plus reading) scores on the weather measure(s) shown. Panel A measures mean temperature using the daily
maximum temperature from school days in the 365 day period starting the given number of years prior to the PSAT
take. Panel B measures the number of such school days above 90 ◦ F and controls for the number of days in othertemperature ranges, so that days in the 60s are the reference category. Beneath each column is the cumulative impactof heat exposure, generated by adding the listed coefficients. All regressions include student fixed effects and fixed
effects for each combination of cohort, test date and take number. The sample comprises all students from the highschool classes of 2001-14 who took the PSAT more than once.

42

43
N

18,665,967

Y

18,665,967

0.324∗∗∗(0.110)-0.569∗∗∗(0.104)0.235∗∗∗(0.070)-0.322∗∗∗(0.067)0.253∗∗(0.099)N

2,935,907

0.117∗∗∗(0.039)-0.011(0.015)-0.218(0.168)-0.229∗∗∗(0.060)(3)

Y2,935,907

0.116∗∗∗(0.038)0.003(0.016)-0.275∗(0.153)0.211(0.185)-0.456∗∗∗(0.169)(4)Notes: Heteroskedasticity robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05 *** p<.01). Coefficients in each column
come from a regression of hundredths of a standard deviation in PSAT total (math plus reading) scores on the heat measure and interaction shown. Mean
temperature is measured by the daily maximum temperature from school days in the 365 days preceding the PSAT take. Columns 1 and 2 interact heatwith school air conditioning penetration rates as reported by students in 2016. Columns 3 and 4 interact heat with high school class, the change in school
air conditioning penetration rates between 2006 and 2016 as reported by guidance counselors, and the interaction of those two variables. Columns 2 and4 also control for interactions between heat and county-level home air conditioning penetration rates, as well as (not shown) sensor-level mean school year
temperature, ZIP code-level income, the school-level fraction of PSAT-takers who are black or Hispanic, and the school district’s average per-pupil capital
expenditures from 1996-2000. All regressions include student fixed effects and fixed effects for each combination of cohort, test date and take number. The
sample comprises all students from the high school classes of 2001-14 who took the PSAT more than once and whose school air conditioning penetration rate(columns 1 and 2) or change in that rate (colunns 3 and 4) are non-missing.

Interactions with ZIP code income, school racial composition,
typical school temperature, and district capital expenditures

N

Mean temp. * Home AC penetration

Mean temp. * School AC penetration change

Mean temp. * HS classMean temp. * HS class * School AC penetration change

Mean temp. * School AC penetration

Mean temp.

(2)

(1)

Table 5: Adaptation through School Air Conditioning

Table 6: Heterogeneity in School Air Conditioning AccessAllschools(1)

Coolerareas(2)

Hotterareas(3)Black or Hispanic-0.017∗∗∗(0.004)-0.020∗∗∗(0.006)-0.016∗∗∗(0.005)Lower income-0.028∗∗∗(0.005)-0.034∗∗∗(0.008)-0.020∗∗∗(0.005)

Black or Hispanic

0.016∗∗∗(0.006)0.022∗(0.012)0.015∗∗(0.006)Lower income

0.062∗∗∗(0.008)0.082∗∗∗(0.016)0.039∗∗∗(0.006)

N

22,347,878

11,176,342

11,171,536(A) School AC(B) Inadequate school AC

Notes: Heteroskedasticity robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05 ***p<.01). Each coefficient comes from a separate regression of school air conditioning penetration rate (panel A) or anindicator for inadequate air conditioning (panel B) on the listed subgroup indicators. Inadequate air conditioning isdefined as the average student’s response that, on hot days, classrooms are too hot to learn “most of the time” or “allof the time.” The reference groups in each panel are white students (top row) and higher income ZIP codes (bottomrow). Lower income refers to students living in below median income ZIP codes within hotter and cooler areas. Eachregression controls for a quartic in school-level mean temperatures over the entire time period. Cooler and hottersareas identify schools whose long-term mean temperatures are below or above the median. The sample comprises
one observation from each PSAT-taker from the high school classes of 2001-14.

44

Table 7: Heterogeneity by Race, Income and Geography
Black or
Hispanic
(1)

White
(2)

Lower
income(3)Higherincome(4)

Coolestareas(5)

Hottestareas(6)

Mean temperature (◦ F)-0.320∗∗∗(0.043)-0.093∗∗∗(0.019)-0.217∗∗∗(0.034)-0.115∗∗∗(0.022)-0.215∗∗∗(0.047)-0.170∗∗∗(0.047)

Days above 90 ◦ F-0.072∗∗∗(0.015)-0.027∗∗∗(0.008)-0.067∗∗∗(0.013)-0.030∗∗∗(0.010)-0.082∗∗∗(0.029)-0.025∗(0.013)

Mean temperature (◦ F)-0.516∗∗∗(0.217)-0.292∗(0.151)-0.348∗∗(0.159)-0.446∗∗(0.180)-1.312∗∗∗(0.358)-0.712∗∗∗(0.236)

Days above 90 ◦ F-0.277∗∗∗(0.070)-0.197∗∗∗(0.054)-0.222∗∗∗(0.050)-0.241∗∗∗(0.063)-0.621∗∗∗(0.168)-0.122∗(0.067)

68.8
15.7

64.2
10.6

65.8
12.5

65.8
11.8

58.1
3.9

73.5
20.5

6,023,145

12,161,058

10,658,547

10,234,301

10,535,013

10,511,435(A) 1 year prior(B) Cumulative impact(C) Average heat
Mean temperature (◦ F)
Days above 90 ◦ F
NNotes: Heteroskedasticity robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05 ***p<.01). Each coefficient comes from a separate regression of hundredths of a standard deviation in PSAT total (mathplus reading) scores on the weather measure(s) shown. The first row in panel A measures mean temperature using
the daily maximum temperature from school days in the 365 days preceding the PSAT take. The second row in panel
A measures the number of such school days above 90 ◦ F and controls for the number of days in other temperature
ranges, so that days in the 60s are the reference category. The first and second rows in panel B measure the cumulative
impact of heat by summing lagged coefficients from each of the four years preceding the PSAT take. All regressions
include student fixed effects and fixed effects for each combination of cohort, test date and take number. The sample comprises all students from the high school classes of 2001-14 who took the PSAT more than once. Columns 3
and 4 contain students living in below and above median ZIP code-level income within below and above mediantemperature areas.

45

Figure A.1: School Year Calendars by State

Notes: The above figure shows state’s approximate school year start and end dates based on thelargest school district in each state and as of 2016.

46

Figure A.2: Spatial Distribution of PSAT Takers

Notes: The above figure shows by county the total number of PSAT takers (panel A) and retakers(panel B) from the high school classes of 2001-14.

47

Figure A.3: Temporal Variation in Prior Year Temperature

63

Degrees Fahrenheit

67(A) Mean temperature

1998

2005

2012

Test year

9

Days

16

(B) Days above 90 °F

1998

2005

2012

Test year

Notes: The above figure shows the mean daily maximum temperature (panel A) and number ofdays above 90◦ F (panel B) experienced by students on school days in the 365 days prior to taking
the PSAT, by test year. The sample consists of all PSAT-takers from the high school classes of 200114, whose PSATs were taken between 1997 and 2012. Dot size is proportional to the number ofstudents in each test year. Test year 1997 is excluded due to the small number of observations.

48

Figure A.4: Residuals of Prior Year Temperature

0.51(A) Mean temperature (°F)-30Residual

3(B) Days above 90 °F

0.15

0.00

Density

SD = 1.05

0.00

Density

SD = 3.17-100Residual

10

Notes: The above figure shows the distribution of residuals resulting from regressions on student
fixed effects of the mean daily maximum temperature (panel A) and number of days above 90◦ F(panel B) experienced by students on school days in the 365 days prior to taking the PSAT. All
regressions include fixed effects for each combination of cohort, test date and take number. The
figure excludes residuals with magnitude above three (panel A) and 10 (panel B). The standard
deviation of the full set of residuals is shown in each panel.

49

80
60
40
20
0

Students (% of time classrooms are too hot)

Figure A.5: Students and Counselors Reports of School Air Conditioning

0

20

40

60

80

100

Counselors (% of classrooms with AC)

Notes: The above figure shows a bin scatter comparing two measures of school air conditioning
penetration rates. The vertical axis shows our preferred measure, constructed from student reportsof the fraction of hot days on which classrooms are too hot for learning. The horizontal axis shows
counselor reports of the fraction of classrooms with air conditioning. The sample includes all PSAT
retakers for whom these two measures are non-missing. The correlation between the measures inthis sample is 0.67.

50

Table A.1: Temperature and PSAT-Taking

Takers(1)

Ln(takers)(2)

Female(3)Black or
Hispanic(4)

Mother
has B.A.
(5)

Father
has B.A(6)-0.0107(0.0902)-0.0021(0.0017)-0.0001(0.0001)

0.0007∗∗∗(0.0002)0.0003(0.0003)0.0003(0.0003)

Mean temperature (◦ F)-0.0924(0.0812)-0.0013(0.0016)0.0001(0.0001)

0.0001(0.0002)-0.0001(0.0002)-0.0001(0.0002)N

686,977

686,977

27,021,552

27,021,552

27,021,552

27,021,552(A) Baseline
Mean temperature (◦ F)(B) State trends

Notes: Heteroskedasticity robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05 ***p<.01). Each coefficient comes from a separate regression of the listed characteristic of PSAT-takers on the average
daily maximum temperature from school days in the 365 days preceding a student’s first PSAT take. All regressions
include fixed effects for each high school and for each combination of cohort and test date. Panel B also includes
state-specific linear time trends. The sample comprises all students from the high school classes of 2001-14 who took
the PSAT at least once.

51

Table A.2: Temperature and Retaking(1)
Prior year temperature (◦ F)

(2)

(3)

(4)

(5)

0.0003(0.0004)

0.0005(0.0005)
0.0003(0.0005)

0.0003(0.0005)
0.0003(0.0005)-0.0001(0.0004)-0.0004(0.0004)

27,021,551

27,021,551

27,021,551

27,021,551

27,021,551

No
No

No
No

No
No

Yes
No

Yes
Yes

0.0005(0.0005)

Following year temperature (◦ F)

N
Test day temperatureState-specific time trends

Notes: Heteroskedasticity robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05*** p<.01). Each coefficient comes from a separate regression of the probability of retaking the PSAT on the weather
measure(s) shown. Yearly temperatures are measured with the daily maximum temperature from school days inthe 365 days preceding and following a student’s first PSAT take. All regressions include fixed effects for each highschool, for each combination of gender, race, income and parental education, and for each combination of cohort andtest date. Columns 4 and 5 control for temperature on the day of the first PSAT take. Column 5 includes state-specificlinear time trends. The sample comprises all students from the high school classes of 2001-14 who took the PSAT atleast once.

52

Table A.3: Measurement Error from Sensor Distance

Mean temp. (◦ F)
Sensor distance * Mean temp. (◦ F)

N

All
students(1)

Black or
Hispanic
(2)

White
(3)

Low
income(4)High
income(5)-0.237∗∗∗(0.045)0.006∗∗(0.003)-0.389∗∗∗(0.061)0.008∗(0.004)-0.085∗∗∗(0.025)-0.001(0.002)-0.279∗∗∗(0.050)0.006∗∗(0.003)-0.091∗∗∗(0.032)-0.002(0.002)

21,046,448

6,023,145

12,161,058

10,658,547

10,234,301

Notes: Heteroskedasticity robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05 ***p<.01). Each coefficient comes from a separate regression of hundredths of a standard deviation in PSAT total (mathplus reading) scores on the weather measure(s) shown. Each regression measures mean temperature using the daily
maximum temperature from school days in the 365 days preceding the PSAT take. Also included is the interaction
between temperature and distance from the nearest weather sensor (in miles). All regressions include student fixed
effects and fixed effects for each combination of cohort, test date and take number. The sample in column 1 comprises
all students from the high school classes of 2001-14 who took the PSAT more than once. Columns 4 and 5 containstudents living in below and above median ZIP code-level income within below and above median temperatureareas.

53

Table A.4: Temperature Effects by Test Subject
Math
(1)

Verbal(2)-0.159∗∗∗(0.034)-0.177∗∗∗(0.023)Days above 90 ◦ F-0.042∗∗∗(0.014)-0.062∗∗∗(0.010)N

21,046,448

21,046,448(A) Average heat
Mean temperature (◦ F)(B) Hot days

Notes: Heteroskedasticity robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05 ***p<.01). Coefficients in each column and panel come from a regression of hundredths of a standard deviation in PSAT
math or reading scores on the weather measure shown. Panel A measures temperature with the daily maximum
temperature from school days in the 365 days preceding the PSAT take. Panel B measures the number of such schooldays above 90 ◦ F. All regressions include student fixed effects and fixed effects for each combination of cohort, test
date and take number. Panel B also controls for the number of days in other temperature ranges, so that days in the
60s are the reference category. The sample comprises all students from the high school classes of 2001-14 who took
the PSAT more than once.

54

Table A.5: Heterogeneity by Take Number(1)
Mean temp. (◦ F)
Mean temp. * 1st take
Mean temp. * 2nd take
Mean temp. * 3rd take

N

(2)

(3)

(4)

-0.152∗∗∗(0.034)-0.200∗∗∗(0.027)0.048∗∗(0.021)-0.269∗∗∗(0.069)0.116(0.079)0.069(0.065)-0.152∗∗∗(0.034)-0.200∗∗∗(0.027)-0.269∗∗∗(0.069)-0.048∗∗(0.021)-0.116(0.079)-0.069(0.065)21,046,448

21,046,448

21,046,448

21,046,448

Notes: Heteroskedasticity robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05 ***p<.01). Coefficients in each column and panel come from a regression of hundredths of a standard deviation in PSAT
total (math plus reading) scores on interactions between take number and the average daily maximum temperaturefrom school days in the 365 days preceding the PSAT take. All regressions include student fixed effects and fixed
effects for each combination of cohort, test date and take number. The sample comprises all students from the highschool classes of 2001-14 who took the PSAT more than once.

55

Table A.6: Future Temperature Shocks

Mean temp., 1 year prior (◦ F)

(1)

(2)

(3)

(4)

(5)

-0.181∗∗∗(0.028)-0.229∗∗∗(0.039)-0.090∗(0.048)-0.182∗∗∗(0.028)-0.178∗∗∗(0.029)-0.037(0.033)-0.228∗∗∗(0.049)-0.092(0.080)-0.006(0.073)-0.037(0.051)

21,046,448

21,046,448

Mean temp., 1 year after (◦ F)
Mean temp., 2 years after (◦ F)

0.053(0.032)

Mean temp., 3 years after (◦ F)

N

21,046,448

21,046,448

21,046,448

Notes: Heteroskedasticity robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05 ***p<.01). Coefficients in each column and panel come from a regression of hundredths of a standard deviation in PSAT
total (math plus reading) scores on the weather measure(s) shown. School day temperature is measured with thedaily maximum temperature from school days in the listed 365 day period relative to the PSAT take. All regressions
include student fixed effects and fixed effects for each combination of cohort, test date and take number. The sample
comprises all students from the high school classes of 2001-14 who took the PSAT more than once.

56

Table A.7: Clustering by weather sensor versus state
(1)

(2)

-0.181∗∗∗(0.028)-0.181∗∗∗(0.041)-0.067∗∗∗(0.018)-0.053∗∗∗(0.013)-0.035∗∗∗(0.009)-0.024∗∗∗(0.008)0.010(0.009)-0.067∗∗∗(0.014)-0.053∗∗∗(0.020)-0.035∗∗(0.014)-0.024∗(0.015)0.010(0.014)

21,046,448

21,046,448

Weather sensor

State(A) Average heat
Mean temperature (◦ F)(B) Hot days
Days above 100 ◦ F
Days in 90s (◦ F)
Days in 80s (◦ F)
Days in 70s (◦ F)
Days below 60 ◦ F

NClustering byNotes: Heteroskedasticity robust standard errors clustered by weather sensor (column 1) or state (column 2) are inparentheses (* p<.10 ** p<.05 *** p<.01). Coefficients in each column and panel come from a regression of hundredthsof a standard deviation in PSAT total (math plus reading) scores on the weather measure(s) shown. Temperature ismeasured with the daily maximum temperature from school days in the 365 days preceding the PSAT take. All
regressions include student fixed effects and fixed effects for each combination of cohort, test date and take number.
The sample comprises all students from the high school classes of 2001-14 who took the PSAT more than once.

57

Table A.8: Heterogeneity in Prior Year Temperature Impacts by Humidity
Humid
areas
(1)

Arid
areas
(2)

Mean temperature (◦ F)-0.186∗∗∗(0.038)-0.111∗∗∗(0.028)Days above 90 ◦ F-0.068∗∗∗(0.014)-0.035∗∗(0.015)

N

14,492,113

6,435,636

Notes: Heteroskedasticity robust standard errors clustered by weather sensor are in parentheses (* p<.10 ** p<.05*** p<.01). Each coefficient comes from a separate regression of hundredths of a standard deviation in PSAT total(math plus reading) scores on the weather measure(s) shown. The first row measures mean temperature using thedaily maximum temperature from school days in the 365 days preceding the PSAT take. The second row measures
the number of such school days above 90 ◦ F and controls for the number of days in other temperature ranges, sothat days in the 60s are the reference category. All regressions include student fixed effects and fixed effects for eachcombination of cohort, test date and take number. The sample comprises all students from the high school classes of
2001-14 who took the PSAT more than once. Columns 1 and 2 contain students living in areas with below and above
the median of the US summer humidity distribution, as characterized by ZIP code level summer dewpoints.

58