Answer the problem set without limitation of page and word.

Temperatures and Test Scores (a) In Figure 3 Panel H, Carleton and Hsiang (2016) present one study that estimates the relationship between temperature and student test scores. There are now a number of these studies. One is Park, et al (2020) "Heat and Learning," don't need to read the whole paper for this problem, but it would be helpful to read the introduction: "Hotter countries tend to be poorer, with each 1F increase in average temperature associated with 4.5 percent lower GDP per capita (Dell, Jones, and Olken 2009). Students in hotter places also tend to exhibit lower levels of standardized achievement for any given age or grade. Across countries, a 1F increase in average annual temperature is associated with 0.02 standard deviation lower math scores 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 the county-level climate distribution score on average 0.12standard deviations worse on third through eighth grade math tests, as seen in the bottom panel of Figure 1. Our primary contributions are to show 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 nontrivial portion of racial achievement gaps in the United States. Why might cumulative heat exposure reduce human capital accumulation? The contemporary US context of this study decreases the relevance of channels often studied in less developed settings such as health and disease burden (Bleakley 2010, Cho 2017), agricultural income and the opportunity costs of schooling (Shah and Steinberg 2017), and institutional norms and political stability more broadly (Acemoglu, Johnson, and Robinson 2001; Dell, Jones, and Olken 2012; Hsiang, Burke, and Miguel 2013). We provide evidence consistent with the possibility that in the United States, heat most likely affects learning directly by altering human physiology 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; Seppnen, Fisk, and Lei 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, we link local daily weather data to the test scores of 10 million American students from high school classes between 2001 and 2014 who took the PSAT (a nationally standardized exam designed to assess students' cumulative learning in high school) at least twice.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 12,000 high schools. Student fixed effects regressions identify the impact of heat exposure during the prior 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 and retaking 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 1F hotter school year in the year prior to the test lowers scores by approximately 0.2 percent of a standard deviation, or slightly less than 1 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 temperatures in the 90s(F) reduces achievement by one-sixth of a percent of 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 predicted by 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 controlling for such exposure does not shrink the magnitude of impact of hot school days. This suggests that heat's disruption of instructional time is responsible for the observed drop in test scores. That our effects are robust to controlling for heat-driven labor market shocks and pollution levels suggests that economic and health-related channels observed in other settings are likely not of first-order importance in this context (Cho 2017; Garg, Jagnani, and Taraz 2016). 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 larger than that of a single school year. This suggests that any compensatory investments made by 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 nontrivial, particularly when considering predicted effects of climate change. For the average student, a sustained increase in temperature of 3.6F (2C) lowers achievement gains by 2 percent of a standard deviation, or approximately 7 percent of an average year's worth of learning. This is despite relatively high average levels of income and air 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 long-standing debate on the relationship between geography and economic development (Acemoglu, Johnson, and Robinson 2001; Rodrik, Subramanian, and Trebbi 2004; Dell, Jones, and Olken 2012). A growing literature shows consistent evidence that the short-term impact of heat on exam days reduces cognitive performance but has not determined whether such effects are transitory or lead to permanent reductions in the stock of human capital (Graff Zivin, Hsiang, and Neidell 2018; Park forthcoming). Studies that provide evidence of medium-term impacts have occurred in contexts where heat's direct physiological effects are hard to distinguish from other channels such as agricultural output or health status (Cho 2017; Garg, Jagnani, and Taraz 2016). The only other paper that precisely identifies the impact of cumulative heat exposure on human capital accumulation is Isen, Rossin-Slater, and Walker (2017), which focuses on in utero exposure and thus identifies a very different channel from the learning channel we study here. Our results are consistent with a long-standing, 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." The dataset BELOW provides the data used in creating Figure 1b. These are average standardized test scores, by county, for 3rd-8th graders in 2009-2013, as well as annual average temperatures in the county. Using Excel (or whatever program you like,) recreate the scatter plot in figure 1b. Note that the paper uses a "bin scatter" where temperatures are organized by bin, and each data point presents the average test score within a bin. This reduces the number of points in the scatter. You can try to make a bin scatter if you like, but a basic scatter using all 3000+ observations is fine.

(b) The figure includes coefficients from a regression of math scores on average temperature. This uses the following model: math_meani = a + b tAvg_Fi + i In this equation, b is the incremental average math score change associated with a 1 degree change in average temperature. Run this regression. You should get the same coefficient that is presented in the figure. Interpret the magnitude of the coefficient. Is it statistically significant? (c) What does the graph tell you about the relationship between temperatures and test scores? Provide one reason why this relationship cannot be interpreted as causal. (d) Park, et al. use student-wise data from PSAT scores. They then restrict their data to students to take the test twice. Their strategy, formally called "student fixed effects," is conceptually similar to one that controls for a student's test score in the prior year. In other words, this holds prior test score fixed when looking at the relationship between temperature and test scores in a given year. Yet another way to think about this is that the relationship between temperature and test scores is examined only among students with similar prior-year test scores. How does this improve the causal interpretation of the effects of temperature relative to the analysis in part (a)? (e) What is the headline finding of the paper? Is it consistent with the correlational analysis form part (a)?

DATA for 2a:

fips	urban	totenrl	state	year	ela_mean	math_mean	tAvg_F
1001	0	769	2	2011	0.25	0.36	64.00
1003	0	2175	2	2011	0.20	0.22	66.79
1005	0	143	2	2011	-0.51	-0.55	64.43
1007	0	279	2	2011	-0.16	-0.26	63.07
1009	0	393	2	2011	0.14	0.00	61.06
1011	0	118	2	2011	-0.52	-0.63	63.69
1013	0	257	2	2011	-0.29	-0.10	64.74
1015	1	293	2	2011	0.02	-0.06	61.08
1017	0	187	2	2011	-0.39	-0.52	62.25
1019	0	325	2	2011	-0.13	-0.09	60.52
1021	0	615	2	2011	-0.10	-0.09	63.01
1023	0	143	2	2011	-0.31	-0.22	64.51
1025	0	186	2	2011	-0.18	-0.28	65.10
1027	0	173	2	2011	-0.23	-0.21	60.78
1029	0	201	2	2011	0.08	0.12	60.18
1031	0	240	2	2011	0.00	0.05	65.40
1033	0	162	2	2011	0.04	0.03	60.66
1035	0	126	2	2011	-0.28	0.08	64.91
1037	0	98	2	2011	-0.25	-0.31	62.33
1039	0	155	2	2011	0.08	0.14	65.12
1041	0	177	2	2011	-0.16	-0.08	64.29
1043	0	498	2	2011	0.47	0.50	60.73
1045	0	172	2	2011	-0.12	-0.11	65.73
1047	0	300	2	2011	-0.44	-0.33	64.31
1049	0	465	2	2011	-0.17	-0.17	58.90
1051	0	494	2	2011	-0.05	-0.15	63.39
1053	0	229	2	2011	0.05	0.09	65.38
1055	0	423	2	2011	-0.07	-0.16	61.03
1057	0	191	2	2011	0.03	0.03	61.37
1059	0	220	2	2011	0.04	0.15	60.56
1061	0	158	2	2011	-0.09	0.00	65.78
1063	0	106	2	2011	-0.47	-0.53	63.74
1065	0	218	2	2011	-0.27	-0.09	64.08
1067	0	220	2	2011	-0.27	-0.29	65.65
1069	1	614	2	2011	0.04	0.12	66.30
1071	0	335	2	2011	0.09	0.05	59.22
1073	0	660	2	2011	0.10	0.10	62.50
1075	0	189	2	2011	-0.15	-0.15	61.36
1077	1	499	2	2011	0.11	0.13	60.32
1079	0	391	2	2011	0.01	-0.06	61.10
1081	1	532	2	2011	0.09	0.09	63.20
1083	0	468	2	2011	0.07	-0.07	60.30
1085	0	143	2	2011	-0.64	-0.54	64.46
1087	0	197	2	2011	-0.43	-0.55	63.68
1089	0	1289	2	2011	0.34	0.26	60.02
1091	0	112	2	2011	-0.33	-0.31	64.36
1093	0	196	2	2011	0.27	0.34	60.63
1095	0	252	2	2011	0.21	0.29	60.71
1097	1	2406	2	2011	0.13	0.20	66.72
1099	0	307	2	2011	-0.29	-0.26	64.98
1101	1	2554	2	2011	-0.32	-0.34	64.50
1103	0	511	2	2011	0.15	0.13	60.68
1105	0	145	2	2011	-0.39	-0.30	63.69
1107	0	229	2	2011	-0.24	-0.26	62.87
1109	0	175	2	2011	-0.07	0.04	64.50
1111	0	151	2	2011	-0.25	-0.31	61.14
1113	0	387	2	2011	-0.24	-0.27	63.82
1115	0	485	2	2011	0.07	-0.05	61.10
1117	0	2209	2	2011	0.20	0.16	62.77
1119	0	154	2	2011	-0.68	-0.64	63.85
1121	0	328	2	2011	-0.16	-0.11	61.84
1123	0	242	2	2011	-0.12	-0.07	62.18
1125	1	1078	2	2011	-0.15	-0.18	63.02
1127	0	428	2	2011	0.13	0.12	61.61
1129	0	263	2	2011	-0.20	-0.28	65.21
1131	0	150	2	2011	-0.50	-0.50	64.34
1133	0	171	2	2011	0.03	-0.06	60.70
4001	0	131	4	2011	-0.42	-0.44	50.75
4003	0	149	4	2011	-0.11	-0.18	61.37
4005	0	247	4	2011	-0.31	-0.35	52.78
4007	0	118	4	2011	-0.42	-0.51	58.89
4009	0	112	4	2011	-0.05	-0.13	59.88
4011	0	63	4	2011	-0.08	-0.07	55.41
4012	0	85	4	2011	-0.33	-0.37	71.61
4013	1	1172	4	2011	-0.09	-0.07	70.99
4015	0	311	4	2011	-0.07	-0.10	61.89
4017	0	133	4	2011	-0.25	-0.24	52.84
4019	0	855	4	2011	0.01	-0.01	68.42
4021	0	275	4	2011	-0.23	-0.26	68.89
4023	0	261	4	2011	0.00	0.00	61.04
4025	0	180	4	2011	-0.02	-0.10	59.01
4027	1	534	4	2011	-0.29	-0.23	72.95
5001	0	124	3	2011	-0.14	-0.16	62.83
5003	0	150	3	2011	-0.13	-0.10	63.50
5005	0	130