Population Health Eﬀects and Health-Related Costs of Extreme
Temperatures: Comprehensive Evidence from Germany
CINCH, University of Duisburg-Essen††
Nicolas R. Ziebarth
May 14, 2018
This study assesses the short and medium-term impact of extreme temperatures on population
health and health-related costs in Germany. For 1999 to 2008, we link the universe of 170
million hospital admissions and all 8 million deaths with weather and pollution data at the
day-county level. Extreme heat signiﬁcantly and immediately increases hospitalizations and
deaths. This ﬁnding holds irrespective of whether we employ econometric models that are
standard in economics or models that are standard in epidemiology; we compare and discuss
both approaches. We ﬁnd evidence for partial “harvesting.” At the end of a 30-day window,
the immediate health eﬀects are, on average, one quarter lower, but this reduction is primarily
evident for cardiovascular and neoplastic diseases. Moreover, aggregating at the yearly level
reduces the eﬀect size by more than 90 percent. The health-related economic costs accumulate
up to e5 million per 10 million population per hot day with maximum temperatures above
Keywords: population health eﬀects, extreme temperatures, hot day, cold day, weather,
pollution, hospital admissions, mortality, climate change
JEL classiﬁcation: I12, I18, Q54, Q58
‡We thank the German Federal Statistical Office (Statistisches Bundesamt (destatis)), the German Meteorological
Service (Deutscher Wetterdienst (DWD)) and the German Federal Environmental Office (Umweltbundesamt (UBA)) that
provided the data basis for the study as well as Joerg Blankenback for his great support in the interpolation of the geodesic data.
In particular, we thank Evelyn Forget, Silviya Nikolova, Seiro Ito, and Reed Walker for outstanding discussions of this paper.
Moreover, we thank Daniel Baumgarten, Antonio Bento, Damon Clark, John Cawley, Peter Eibich, Maria Fitzpatrick, Rick
Geddes, Albrecht Glitz, Dan Grossman, Don Kenkel, Hyuncheol Kim, Ilyana Kuziemko, Michael Kvasnicka, Dan Lichter, Dean
Lillard, Sean Lyons, Alan Mathios, Jordan Matsudaira, Vincent Pohl, Emily Owens, Sharon Sassler, Steve Stillmann, Hanna
Wielandt, Robert Williams III, Will White, Martina Zweim¨uller and participants at the 2013 meeting of the American Economic
Association (AEA), the 2nd Workshop on Energy Policy and Environmental Economics at Cornell, the 2013 Conference of the
European Society for Population Economics (ESPE) in Aarhus, the 2013 UK Health Economists’ Study Group (HESG) Meeting
at Warwick, the 2013 Canadian Health Economists’ Study Group (CHESG) Meeting in Winnipeg, the Economics of Disease
Conference in Darmstadt 2013 as well as seminar participants of the Population Center (CPC) and the Institute on Health
Economics, Health Behaviors and Disparities (IHEHBD) at Cornell University, the German Institute for Economic Research
(DIW Berlin), and the Berlin Network of Labour Market Researchers (BeNA) for their helpful comments and discussions.
We also thank Maike Schmitt (TU Darmstadt), Felix Heinemann (TU Darmstadt), Peter Eibich (DIW Berlin), Lauren Jones
(former PAM PhD student, now OSU), and Katherine Wen (Cornell University) for excellent research assistance. All remaining
errors or shortcomings of the article are our own. The research reported in this paper is not the result of a for-pay consulting
relationship. Our employers do not have a ﬁnancial interest in the topic of the paper which might constitute a conﬂict of
interest. Funding from the Cornell Institute for Social Science (ISS) Small Grant Program as well as the Cornell
Population Center (CPC) Seed Grant Program are gratefully acknowledged.
∗Corresponding author: Nicolas R. Ziebarth, Cornell University, Department of Policy Analysis and Management
(PAM), 106 Martha Van Rensselaer Hall, Ithaca, NY 14850, USA, phone: +1-(607)255-1180, fax: +1-(607)255-4071,
††University of Duisburg-Essen, Chair of Health Economics, Sch¨utzenbahn 70, 45117 Essen, Germany e-mail:
Climate change is one of the great challenges of modern society. The Stern (2006) report states
that the world’s average temperature has risen by 0.7˚C (1.3˚F) over the past 100 years and
projects that this trend will continue into the future. For the US, the predicted temperature
increase ranges between 2 and 6˚C (4 and 11˚F) by the end of the 21st century (United States
Global Change Research Program,2009). Moreover, climate scientists project a signiﬁcant increase
in inclement weather conditions, such as the number of hot days with temperatures above 30˚C
(86˚F) or the number of heat waves. More precisely, the Intergovernmental Panel on Climate
Change (IPCC) projects: “It is very likely that hot extremes, heat waves and heavy precipitation
events will continue to become more frequent.” (IPCC (2007), p. 46, 53).
Studies in health economics as well as environmental epidemiology and bio-statistics empirically
assess the impact of extreme temperatures on human health. A recent literature review article
in economics summarizes: “[...] with global temperatures expected to rise substantially over the
next century, understanding these relationships [between climatic factors and economically relevant
outcomes] is increasingly important for assessing the “damage function” that is central to estimating
the potential economic implications of future climate change (Dell et al. (2014), p. 2).” Some
economic studies deﬁne a hot day as a day where the daily maximum temperature exceeds 30˚C.1
whereas others use the threshold of 90˚F for the mean daily temperature.
Panel A of Table 1lists and categorizes select economic studies on the impact of extreme
temperatures on human health. Methodologically, these studies typically regress the mortality rate
of (US) counties or states on temporal and spatial ﬁxed eﬀects, e.g., state and month-year ﬁxed
eﬀects. Assuming that the remaining temperature variation is exogenous to humans, this approach
allows one to identify the causal eﬀects of extreme temperatures on mortality.
[Insert Table 1about here]
As Panel B of Table 1shows, the epidemiological and bio-statistical literature on this topic
is older and richer. The majority of studies in this ﬁeld are also based on US data but typically
exploit daily mortality counts of cities over longer time horizons. Instead of employing parametric
OLS ﬁxed eﬀects models using mortality or hospitalization rates as outcomes, these studies mostly
employ log-linear poisson models of death or hospital counts and model seasonal eﬀects as smooth
spline functions. Basu and Samet (2002), ˚
Astr¨om et al. (2011), Deschˆenes (2014) and Hondula
et al. (2015) provide literature reviews on the relationship between heat events and human health.
1This is identical to the oﬃcial deﬁnitions of the public meteorological services in the German speaking countries.
(Deutscher Wetterdienst (DWD),2017).
One unifying theme of both scientiﬁc ﬁelds is the examination of the so called “harvesting
hypothesis.” While it has been clearly documented that deaths and hospital admissions spike in
the short run, there is no conclusive consensus on the medium- to long-run eﬀects of extreme
temperatures on human health. Several studies provide support of the harvesting hypothesis that
mostly older people die during heat waves—that is, people in weak health who would have died
in the near future, regardless of whether there was a heat wave (Braga et al.,2001,2002;Hajat
et al.,2005;Stafoggia et al.,2009;Deschˆenes and Moretti,2009). If extreme temperatures cause
premature death for older people by only a couple of weeks, then the overall population health
eﬀects (and predicted health losses due to climate change) are naturally overestimated in static
Other unifying research questions with inconclusive evidence surround the questions of (i) the
negative impact of cold weather on human health (Braga et al.,2001;Anderson and Bell,2002;
Goldberg et al.,2011;Son et al.,2014;Gasparrini et al.,2015;Chung et al.,2015;Son et al.,
2016;White,2017), and (ii) whether and how fast humans are able to adapt to changes in extreme
ambient temperatures (Braga et al.,2001;Anderson and Bell,2002;Deschˆenes and Moretti,2009;
Deschˆenes and Greenstone,2011;Bobb et al.,2014;Deschˆenes,2014;Nordio et al.,2015;Barreca
The main objective of this paper is to comprehensively assess the short- and medium-run pop-
ulation health eﬀects of extreme temperatures, particularly heat events, for an entire industrialized
nation over one decade. As illustrated in Table 1, the existing evidence is either based on mortality
or hospital data and typically does not use both data sources jointly. Additionally, due to data lim-
itations, most existing studies cannot exploit complete censuses of either deaths or hospitalizations.
Rather, they typically rely on data from single cities or population sub-groups. This paper uses
the universe of hospital admissions and deaths from 1999 to 2008 for Germany, the most populous
European country and fourth largest industrialized nation in the world. We aggregate these data
to the county level and merge them with 11 weather and 11 pollution measures on the daily county
level. Weather and pollution measures were recorded daily by a network of over 2,300 governmen-
tal ambient monitors, distributed over an area the size of Montana. The comprehensiveness of our
data allow us to draw a very complete picture of all severe health shocks that are triggered by
extreme temperatures. However, we do not observe health shocks that do not lead to deaths or
Second, we see this paper as an attempt to bridge the two diﬀerent literature strands in health
economics and epidemiology, which essentially empirically analyze the same research questions. It
is very diﬃcult, if not impossible, to compare results from studies across disciplines as they are
presented in very diﬀerent ways; the metrics that would be needed to make a comparison with
results from other approaches are typically not provided. In order to ﬁll this gap, we carry out
speciﬁcations that are closest to the standard speciﬁcations in each literature strand and compare
the eﬀects sizes of both modeling approaches. We also compare the eﬀects sizes of our ﬁndings
with those in the two literature strands.
Third, thanks to the richness of our data, we carry out extensive tests to check whether the heat-
health eﬀect size varies when we control for other weather and pollution-related confounding factors
or “eﬀect modiﬁers.” The confounding impact of multiple pollutants is an important question of
inquiry, particularly in the epidemiological literature (Katsouyanni et al.,2001;Dominici et al.,
2010;Bobb et al.,2013;Deryugina et al.,2016).
Another main contribution of this paper is to investigate the harvesting hypothesis in detail.
Whereas several deﬁnitions of the harvesting hypothesis exist, the deﬁnition used in this paper
hypothesizes that a signiﬁcant share of the negative short-term eﬀects of heat events are not present
in the medium-run because many hospitalized or dead people would have been hospitalized or dead
even in the absence of the heat event shortly after. This deﬁnition of “harvesting” would predict
short-term excess mortality and hospitalizations, followed by an under proportional development of
mortality and hospitalizations. In other words, we contrast the short and the medium-run health
eﬀects of heat. To provide evidence for or against the validity of the harvesting hypothesis, we
(a) investigate how mortality develops in the 30 days after a heat event. Because the relevance of
the harvesting hypothesis may depend on the disease type, we (b) investigate these time trends
separately for ﬁve disease categories. In addition, we (c) proﬁle the age structure of those who are
hospitalized or die during heat events, again separately by ﬁve disease categories. Finally, we (d)
aggregate the data up to the monthly and annual level. By aggregating up, we solely exploit the
remaining monthly and annual variation in heat events as a source of exogenous variation.
As a ﬁnal contribution, we provide an assessment to better understand the health-related costs
associated with extreme temperatures. The most concrete climate change prediction of the IPCC
(2007) is an increase in the number of extreme heat events. Thus, we attempt to monetize the
health losses associated with one additional hot day for an entire nation. Two factors drive the
estimates: ﬁrst, the choice to consider other climatic eﬀect modiﬁers like air pollution or not and
second, whether short- or medium-run eﬀects are the basis of the calculation. We also decompose
the total health costs into direct eﬀects due to deaths and hospitalizations as well as indirect eﬀects
for lost labor and a loss of quality of life while being hospitalized. When applying standard values
for a statistical life, the mortality eﬀects are responsible for at least half of the total health costs.
Our ﬁndings show that extreme heat has a highly signiﬁcant and large short-term impact on
both hospitalizations and deaths, whereas the results for extreme cold are less consistent. With
regard to heat events, the standard empirical models in economics and epidemiology provide the
same qualitative ﬁndings and are consistent, though the estimated eﬀect on mortality is larger
when we use standard approaches from economics. We are able to rule out that this diﬀerence is
driven by diﬀerences in the deﬁnition of a hot day. Instead, it appears that the diﬀerence is at-
tributable to unobserved heterogeneity between counties. When comprehensively considering other
contemporaneous weather and pollution conditions—eﬀect modiﬁers—the net impact of extreme
temperature on health shrinks signiﬁcantly in both modeling approaches, but the decrease is larger
in the economic models.
At the population level, there is strong evidence for “harvesting”, but only for heart and respi-
ratory diseases. As expected given their medical peculiarities, infectious or metabolic diseases do
not show the characteristic short-term spike followed by a decrease in hospitalizations or deaths.
We also ﬁnd a clear age gradient in the hospitalization and mortality pattern of extreme heat:
mostly older people are hospitalized or die during heat events. However, maybe surprisingly, we
do not ﬁnd such age gradients when considering relative increases in percent, which tend to be
roughly similar for all age groups.
The last part of the paper estimates that—using the economics deﬁnition—one additional hot
day with temperatures above 30˚C (86˚F) causes monetized health losses of between e750 thou-
sand to e5 million per 10 million residents, depending on the underlying assumptions.
2 Datasets, Main Variables, and Identifying Variation
2.1 Mortality Census:
The Universe of all German Deaths 1999-2008
The ﬁrst dataset is the Mortality Census which is provided by the German Federal Statistical
Office. The Mortality Census includes every death that occurred on German territory. Per year,
one observes approximately 800,000 deaths, i.e, about 8 million deaths from 1999 to 2008. To
obtain the working dataset, we aggregate the individual-level data at the day-county level and
generate the mortality rate per 100,000 population.
Appendix A shows all raw measures included in the Mortality Census. It contains information on
age, gender, day of death, county of residence as well as the primary cause of death in ICD-10 (10th
revision of the International Statistical Classiﬁcation of Diseases and Related Health Problems)
Construction of Main Dependent Variables
Using information on the primary cause of death, we generate a series of dependent variables. To
do so, we extract the letter and digits of the ICD-10 code, e.g., J00-J99 refers to “the respiratory
system.” In some cases, the second and third ICD-10 digits are helpful in identifying more speciﬁc
conditions. In addition to the all-cause mortality rate, which is simply the sum of all deaths, we
examine ﬁve speciﬁc subgroups: the (i) cardiovascular mortality rate, (ii) respiratory mortality
rate, (iii) infectious mortality rate, (iv) metabolic mortality rate, and (v) neoplastic mortality rate.
The total daily mortality rate is 3 deaths per 100,000 population—1.4 or almost 50% of which are
caused by cardiovascular health issues. The summary statistics of the all-cause and cause-speciﬁc
mortality rates are displayed in Appendix A.
2.2 Hospital Admission Census:
The Universe of all German Hospital Admissions 1999-2008
The second dataset is the Hospital Admission Census. Access is again provided by the German
Federal Statistical Office. It contains data on all German hospital admissions from 1999 to
2008. Germany has about 82 million inhabitants and registers about 17 million hospital admissions
per year. We observe every single hospital admission from 1999 to 2008, i.e., a total of more than
170 million hospitalizations.2To obtain our working dataset, we aggregate the individual-level
data at the day-county level and normalize admissions per 100,000 people using oﬃcial population
counts (see Appendix E).
As seen in Appendix B, along with other admission characteristics, the Hospital Admission
Census provides information on the age and gender of the patient, the day of admission, the length
of stay, the county of residence as well as the primary ICD-10 diagnosis.
Construction of Main Dependent Variables
Analogous to the Mortality Census, using information on the primary diagnosis, we generate a se-
ries of dependent variables. Again, the dependent variables indicate diﬀerent diagnoses, generated
by extracting the letter and digits of the ICD-10 code. In addition to the all-cause hospitalization
rate, we examine ﬁve subgroups: (i) cardiovascular hospitalizations (I00-I99), (ii) respiratory hos-
pitalizations (J00-J99), (iii) infectious hospitalizations (A00-B99), (iv) metabolic hospitalizations
2By law, German hospitals are required to submit depersonalized information on every single
hospital admission. This excludes military hospitals and hospitals in prisons. The 16 German states
collect the information and the German Federal Statistical Office (Statistische ¨
Bundes und der L¨ander) provides restricted data access for researchers.
(E00-E89), and (v) neoplastic hospitalizations (C00-D49).
For the last section, to assess total health care costs, we also exploit hospital information on
deaths and the length of stay. For example, cardiovascular death identiﬁes people who died after
they were admitted to a hospital due to a cardiovascular disease. Cardiovascular hospital days
includes the number of nights that a patient spent in a hospital after a cardiovascular admission.
After having summed over county-level daily admissions, as above, we normalize the dependent
variables per 100,000 population using oﬃcial population data at the year-county level (Federal
Institute for Research on Building, Urban Aﬀairs and Spatial Development,2012). Appendix B
displays the summary statistics of all dependent variables.3For example, on a given day, we observe
58 hospital admissions per 100,000 population. On average, a day triggers 489 hospital days, i.e.,
the 58 admissions have an average length of stay of 8.4 days. The largest single group of diseases
is cardiovascular hospitalizations. Nine cardiovascular admissions per 100,000 population make up
16% of all admissions.
2.3 Oﬃcial Daily Weather Data from 1,044 stations 1999-2008
The weather data are provided by the German Meteorological Service (Deutscher Wetter-
dienst (DWD)), a publicly funded federal institution. Weather measures were collected from 1999
to 2008 from up to 1,044 meteorological monitors which were distributed all over Germany. Figure
1shows the distribution of all ambient monitors along with county borders. Figure 2a shows a
boxplot of the mean temperature over the twelve months of the year (averaged over all ten years).
The graph illustrates the large cross-county as well as cross-seasonal variation in temperatures.
One observes a clear increase in average temperatures during the summer months. Figure 2b shows
the daily cross-county temperature variation over all ten years. One observes the typical seasonal
trends along with many spikes in the high-frequency data. The empirical models will exploit the
rich positive and negative weather shocks across space and over time.
[Insert Figure 1and 2about here]
The paper uses oﬃcial data from all existing weather stations in a given year. As described in
Appendix D1, we interpolate the point measures into county space on a daily basis using Inverse
Distance Weighting (IDW).
3Note that the German data protection laws prohibit us from reporting min. and max. values.
Construction of Extreme Temperature Indicators & Identifying Variation
Indicators in Economics. In our main speciﬁcation, we employ semiparametric variants of a
standard “economic model” to net out seasonal and geographic eﬀects and let a series of temperature
regressors ﬂoat ﬂexibly while allowing for precise enough estimates. However, we also employ
threshold models to measure extreme heat and cold for the following reasons:
(i) Although there exist no international deﬁnitions of hot or cold days, our threshold measures
follow the oﬃcial deﬁnitions by the German Meteorological Service. They deﬁne a Hot Day
as a day with a maximum temperature above 30˚C (86˚F).
(ii) The economics literature has employed threshold indicators which facilitates a comparison
of results (cf. Deschˆenes and Moretti,2009;Barreca et al.,2016).4
(iii) Deﬁning a binary indicator to measure Hot and Cold Days simpliﬁes the empirical analysis,
provides the reader with a better intuition, and makes it easier to follow the thought experiment
wherein we ask, “What are the health eﬀects of one additional Hot Day?”
(iv) As we will demonstrate in the Results section, there is empirical evidence that most adverse
health eﬀects kick in when temperatures exceed 30˚C (86˚F). Thus we deﬁne the ﬁrst pair of binary
measures, following the economics literature, as:
•Hot Day = 1 if the max. temperature >30˚C (86˚F), 0 else.
•Cold Day= 1 if the min. temperature <-10˚C (14˚F), 0 else.
Indicators in Epidemiology. The second set of extreme heat and cold indicators follows the
standard deﬁnitions in epidemiology. Here, the binary measure for Hot Day II equals 1 when the
average daily temperature exceeds percentile 97.5 of the county-level temperature distribution over
all years.5The deﬁnition for Cold Day II is analogous but refers to percentile 2.5 of the county-level
Panel B of Table C1 in Appendix C shows the descriptive statistics for the two sets of extreme
temperature indicators. Let us start with heat events and the epidemiological deﬁnition. As
expected, 2.5% of all county-day observations are hot days. The maximum daily temperature
during a Hot Day II is on average 31.2˚C (88.1˚F) but varies between 23 and 39˚C (73˚F and
In contrast, according to the standard deﬁnition in economics, 2% of all days are Hot Days with
maximum temperatures above 30˚C (86˚F). The maximum daily temperature during a Hot Day
4To be precise, the US studies by Deschˆenes and Moretti (2009) and Barreca et al. (2016) deﬁne
aHot Day as a day with the mean temperature >90˚F (32˚C).
5Because no oﬃcial deﬁnition exists, many epidemiological papers provide robustness checks
varying the thresholds between the 95th and 99th percentile.
is on average 31.9˚C (89.4˚F) and varies between 30 and 39˚C (86˚F and 102˚F). This means
that the epidemiological deﬁnition leads to lower average maximum temperatures on hot days, but
also a longer left temperature distribution tail with temperatures below 30˚C (86˚F). The two
indicators are identical in 99.2 percent of all days.
However, the deﬁnition in economics results in a quarter fewer hot days over our sample period.
On average, it translates into seven Hot Days per year but this ﬁgure varies between 4 (1999, 2004,
2007) and 18 (2003) over the years. The variation in Hot Days between counties is even larger
and varies between 0 and 40 per year (Figure 3b). In our empirical harvesting tests, we aggregate
the data at the month-county and year-county level and exploit this variation in the monthly and
annual number of Hot Days.
[Insert Figure 3about here]
Figure 3plots the distributions of (i) the maximum daily county-level temperatures, and (ii) the
annual number of Hot Days per county according to the deﬁnition in economics. The ﬁgure shows
that the annual maximum temperatures follow a normal distribution with the mass point around
14˚C (57˚F). Moreover, the annual number of Hot Days is skewed to the right and exhibits
substantial variation with many counties showing more than 10 Hot Days per year. Figure 3
illustrates that the identifying variation stems from the majority of counties and not just a small
subset of “hot” counties. Thus extrapolation and out-of-sample predictions are largely avoided.
Turning to cold events, the epidemiological Cold Day II deﬁnition is symmetric to the one for
Hot Day II, which is why we observe 2.5% of all county-day observations as cold days (Panel B of
Table C1). The average minimum temperature during a Cold Day II is -10˚C (14˚F) and varies
between -3.5 and -25˚C (25.7˚F and -13˚F).
According to the deﬁnition in economics, slightly over 1% or about 20,000 of all county-day ob-
servations are Cold Days with minimum temperatures below -10˚C (14˚F). Similar to the hot day
case, the average minimum temperature on cold days is lower according to the economics deﬁnition
(-12.5˚C or 9.5˚F); and the economics deﬁnition results in a truncated temperature distribution
with minimum temperatures strictly below the threshold of -10˚C (14˚F). This translates into
about 4.5 Cold Days per year, ranging from an average of 0.4 Cold Day in 2008 to 9 Cold Days in
2003. The annual county-level variation in Cold Days lies between 0 and 41 (see Figure 3b).
2.4 Oﬃcial Daily Pollution Data from 1,314 stations 1999-2008
In extended models, we use daily pollution data from ﬁve diﬀerent pollutants (NO2, SO2, NO10,
O3, CO) to study eﬀect size variation when controlling for pollution. The epidemiological literature
discusses extensively relevant aspects of controlling for multiple pollutants and their roles as eﬀect
modiﬁers (Katsouyanni et al.,2001;Dominici et al.,2010;Bobb et al.,2013). The pollution data
are provided by the German Federal Environmental Office (Umweltbundesamt (UBA)), a
publicly funded federal agency. From 1999 to 2008, pollution measures are collected from up to
1,314 ambient monitors (Figure 1). As with the weather measures and as described in Section F1,
we interpolate the monitor point measures into the county space. Table D1 in Appendix D shows
all raw pollution measures on a daily county-level basis.
Appendix D describes and graphically illustrates the tempo-spatial variation of the pollutants
and their association with weather conditions: All pollutants have in common that they (i) exhibit
some seasonal pattern, (ii) exhibit strong (non-)linear associations with the weather indicators—in
particular the temperature.
3 Empirical Approaches and Identiﬁcation
3.1 Empirical Approach in Health Economics
One standard approach in the economics literature would estimate the following model by OLS:
βhM eanT emph
σmmonthm+θ Xct +
γhi M eanT emph
where, depending on the speciﬁcation, Ycd would either denote the mortality rate or the hospital
admission rate per 100,000 population in county con day d.M eanT emph
cd are a series of tempera-
ture regressors that equal 1 if the average daily temperature in the county falls into a bin of 10˚F
and equal zero otherwise. To make our ﬁndings comparable to existing studies (mostly from the
US), we employ eight temperature dummies (<10, 10-20, 20-30, 30-40, 50-60, 60-70,70-80, above
80˚F) and evaluate their health impact relative to temperatures between 40-50˚F (4.4-10˚C). The
temperature coeﬃcients then semiparametrically describe the temperature-health relationship, net
of seasonal inﬂuences. We call this the “temperature bin model” (as compared to the “threshold
model” which solely uses the Hot Day and Cold Day dummies described in Section 2).
In some speciﬁcations, in order to account for the serial correlation in temperature, we add 30
lags of M eanT emph
cd. Moreover, we routinely net out county ﬁxed eﬀects, P468
j=2 νjcountyj, week
ﬁxed eﬀects, P52
k=2 ζkW eekk, and year-month ﬁxed eﬀects, PDec 2008
m=Feb 1999 σmmonthm, in order to
adjust for trends and permanent diﬀerences in health across counties. In our main speciﬁcation,
we thus assume that regional diﬀerences in seasonality are captured by the county ﬁxed eﬀects (as
well as the county-year controls described below). Given the relatively small variation in climatic
conditions across counties in Germany, this assumption is likely to hold.
We also include a set of county-level covariates, Xct. This vector contains the share of private
hospitals, the bed density and the county-level GDP per capita (see Appendix E). We routinely
cluster standard errors at the county level, but show that clustering at the state level or two-way
clustering at the county and day level does not aﬀect the main results. All econometric models are
weighted by the total county population in a given year.6
Our baseline speciﬁcation does not consider any other contemporaneous weather and pollution
conditions. In addition to the ﬁxed eﬀects, only the eight temperature bins are added to the
model. One can think of this approach as a reduced form “intention-to-treat” approach where the
main regressor of interest absorbs all weather and pollution conditions that are correlated with the
exogenous weather or pollution indicator.
In subsequent speciﬁcations, by contrast, we progressively add more variables that control for
various environmental factors. These models include—in addition to the temperature bins—eight
continuous weather (Wcd ) measures (humidity, precipitation, cloud coverage, wind speed, storm
force, air and vapor pressure, hours of sunshine) as well as ﬁve continuous pollution (Pcd) measures
(NO2, SO2, NO10, O3, CO) in addition to their own and cross interactions (see also Tables C1 and
3.2 Empirical Approach in Environmental Epidemiology
The standard approach in environmental epidemiology would estimate a log-linear hierarchical
random-coeﬃcient poisson model of the form:
log(E[Ycd | ·]) = αc+βcH otDaycd +
ζkDayW eekk+θ Xct +ns(timec)
+ns(weatherc) + ns(pollutionc)
6We weight by total pfor two reasons. First, it makes our estimates representative of the entire
German population. Second, when relying on local averages, weighted least squares are more
eﬃcient than OLS. The second point holds only in the absence of common shocks at the local level;
however, our clustered standard errors consider common group errors (cf. Solon et al.,2015).
where the variable deﬁnitions are similar to above. Importantly, instead of including binary ﬁxed
eﬀects for each county and month-year, this empirical speciﬁcation includes (typically cubic) splines
of the date, ns(timec), to capture long-run trends and seasonal pattern. αcis a set of county-speciﬁc
Analogous to above, the baseline model would not consider other contemporaneous climatic
confounders in addition to the Hot Day II and Cold Day II indicators. An “eﬀect modiﬁer model”,
by contrast, would additionally consider a series of separate cubic splines for weather and pollution
measures ns(weatherc), and ns(pollutionc). Speciﬁcally, these models include separate smooth
functions for eight additional weather and ﬁve pollution measures (Tables C1 and D1).
One main purpose of this paper is to compare and contrast empirical approaches in health economics
and epidemiology. Such a comparison is complicated by the fact that the two literatures (a) tend to
deﬁne the outcome diﬀerently, (b) use diﬀerent speciﬁcations for the main independent variables,
and (c) allow for diﬀerent lag structures in the regressions. Concerning (a), epidemiological models
are often based on count data techniques, whereas contributions in economics tend to use mortality
or hospitalization rates as outcomes. Eﬀect sizes can nevertheless be compared by reporting relative
changes (in percent) of the outcome variables. Concerning (c), we compare diﬀerent speciﬁcations
that include diﬀerent numbers of lags.
Concerning (b), to compare estimates based on binary and more ﬂexible representations of
extreme weather events, we translate estimates from ﬂexible speciﬁcations with temperature bins
into binary impact measures using a linear index of the point estimates and their variances. In
particular, we derive the Hot Day eﬀect from equation (1) as follows:
βHotDay = (ΠHotDay −ΠNonHotD ay)0ˆ
βHotDay= (ΠHotDay −ΠNonHotDay)0d
β(ΠHotDay −ΠNonHotDay) (3)
where ΠHotDay represents the histogram of M eanT empcd on a hot day, and ΠNonH otDay the his-
togram on all other days. Our estimates for ˆ
βColdDay and d
βColdDayare deﬁned analogously.
As such, we can compare the changes in mortality attributed to hot and cold days according to
diﬀerent estimation methods.
One appealing aspect of using extreme temperature variation to estimate its impact on health is that
changes in temperatures are very likely orthogonal to the error term in equations (1) and (2). It is
very plausible that short-term weather variation is exogenous to the outcomes of any one individual
(cf. Angrist et al.,2000). As Dell et al. (2014) put it: “By harnessing exogenous variation over
time within a given spatial unit, these studies [a growing body of research applying panel methods
to examine how climate inﬂuences economic outcomes] help credibly identify (i) the breadth of
channels linking weather and the economy [...] (p. 1).” Remember that the econometric models
net out a rich array of geographic, seasonal, and time eﬀects and rely on high-frequency within
county variation. Positive and negative temperature shocks are then linked to contemporaneous
health eﬀects at the day-county level. As Table 1shows, this econometric approach to identiﬁcation
is carried out by the large majority of the leading and published temperature-health studies.
One could still list the following three identiﬁcation concerns: (i) based on (un)observables,
people may self-select into living in speciﬁc regions and (ii) individual-level exposure to weather
and pollution conditions is unknown and (iii) adaption behavior may bias the “true” causal eﬀect
With respect to (i): One particular strength of our approach is its reliance on the universe of all
deaths and hospital admissions over one decade, from the fourth largest industrialized nation in the
world. To the extent that one is interested in the real-world eﬀects of heat on population health
in a given geographic area, we take the view that one should consider and include sorting into
regions; the identiﬁed parameters then represent the eﬀects on population health once geographic
preferences are accounted for. In the case of Germany, it should be added that (intergenerational)
geographic mobility is historically very low. Using the SOEP we ﬁnd that, in a given year, only
about 1% of all SOEP respondents move, which also includes within-county moving (Wagner et al.,
With respect to (ii) and adaptation behavior: Similar to above, we argue that we intention-
ally want to estimate an “intention-to-treat (ITT)” population health eﬀect, including avoidance
behavior and human adaptation to extreme temperatures. This parameter is arguably a relevant
parameter for policymakers. The relationship that this paper intends to expose is: Given that
humans have the capacity to adjust to extreme temperatures, based on current real-world behav-
ioral data, how would climate change in the form of more heat events most likely aﬀect population
health? Without question, this ITT estimate represents a lower bound estimate as compared to
a “full exposure” estimate keeping adaptation behavior constant. On the other hand, it can be
expected that adaptation behavior will further increase if extreme temperatures become more fre-
quent in the future. To the extent that adaptation increases, our estimates will instead represent
upper bound predictions of the eﬀects of future heat waves. Janke (2014) uses English data and air
pollution alerts to show that avoidance behavior exists for asthma but that the lower bound ITT
estimates do not statistically diﬀer from estimates modeling avoidance behavior.
Please note that it is beyond the scope of this paper to make projections about human behavioral
adaptation and/or technological progress that could facilitate adaption behavior in the future. Such
projections are inherently uncertain and notoriously diﬃcult to make. However, recent empirical
evidence shows that humans can adapt to adverse climatic conditions and that adaptation has
increased over time (cf. Zivin and Neidell,2013;Deschˆenes and Greenstone,2011;Deschˆenes,2014;
Barreca et al.,2016). Given this recent empirical evidence, an approach that assumes no further
adaptation behavior will lead to upper-bound estimates of the potential adverse health eﬀects of
climate change. They can thus be interpreted as “business-as-usual” scenarios which are useful to
assess the willingness to pay to avoid these consequences.
Finally, the setup of the German health care system is particularly well-suited for our research
objective because institutional and geographic access barriers to hospitals are very low. Germany
has one of the highest densities of hospital beds worldwide, universal health care coverage, and
virtually no access barriers for inpatient care (cf. OECD,2017). German counties are comparable
to US counties but less heterogeneous in terms of population density and area size. Germany’s
climatic conditions are ideal to empirically study and identify the instantaneous eﬀects of extreme
temperatures. Like most countries in the North Temperature Zone, Germany has four seasons,
hot summers and cold winters (Figure 2). For example, during the 10 years that we study, daily
maximum temperatures range from -14˚C (7˚F) to 39˚C (102 ˚F). As Figures 3demonstrates,
the identiﬁcation of parameters is based on a broad set of counties and largely avoids out-of-sample
predictions. All German counties experienced rich variation in extreme temperature.
4 Short-Term Eﬀects of Heat and Cold on Population Health
4.1 Population Health Eﬀects of Heat and Cold Events
Economic Models. Table 2shows the results for the standard models in the (health) economics
literature as formalized in equation (1). Panel A displays the eﬀects on mortality and Panel B
displays the eﬀects on hospitalizations. Each column in each panel represents one model, estimated
by OLS. The dependent variable always measures the all-cause mortality or hospitalization rate
and does not distinguish by diagnoses. The models in columns (1) and (2) do not control for any
contemporaneous weather or pollution conditions. In contrast, column (3) considers ﬁve continuous
pollutants at the daily level. Column (4) adds several other (than temperature) weather conditions
such as sunshine or precipitation (the list of variables is in Panel A of Table C1 and Table D1).
Column (5) additionally adds 30 lags of Hot Day and Cold Day. In the lower part of each panel, we
report the estimated overall eﬀect of hot and cold days using the approach of Section 3.3. Whereas
the ﬁrst ﬁve columns present the results of the temperature bin model based on the mean daily
temperature, columns (6) and (7) present the results for the threshold model with Hot Day and
Cold Day as main regressors.
[Insert Table 2about here]
For mortality in Panel A, the impact of the mean temperature is roughly ﬂat over a wide range of
temperature bins: from the lowest measured temperatures up to around 60˚F, the point estimates
vary within a range of only 0.07, which corresponds to 2.5% of the baseline risk. From that point
onward, the impact increases rapidly in each bracket. For the highest mean temperature bracket,
80˚F to 90˚F, the point estimate at 0.96 corresponds to 33% of the baseline risk. Controlling for
pollution levels reduces the temperature gradient somewhat (column (2) vs. column (3), Panel A);
including lags of extreme temperatures further reduces it (column (4) vs. column (5), Panel A).
However, the largest drop in the temperature-health relationship is observed when we add other
contemporaneous weather indicators in column (4).7
For hospitalizations in Panel B, the temperature-health relationship is non-monotonic: very
cold mean temperatures (below 10˚F) are associated an increase in admissions. Moderately cold
weather (10-40˚F), on the other hand, is associated with a decrease in admissions relative to
the reference bin of 40-50˚F. For temperatures of between 50-80˚F, the relationship between
temperature and admissions is positive for the parsimonious model without further weather controls
and lags (columns (1) to (3), Panel B). However, as above, adding contemporaneous weather
controls reduces the coeﬃcient sizes substantially and turn them insigniﬁcant (or even negative for
the 60 to 70˚F bin). For the highest temperature bin (80-90˚F), as above for mortality, we ﬁnd a
robust and highly signiﬁcant positive gradient between temperatures and hospital admissions. It is
noteworthy that adding contemporaneous weather controls (other than temperature) reduces the
size of the health-admissions gradient in this highest temperature bin by about half (columns (4)
and (5), Panel B).
7Because we are conducting multiple tests for multiple endpoints, we checked the robustness of
our signiﬁcance tests by using the procedure suggested by Benjamini and Hochberg (1995). For all
conventional false discovery rates, the conclusions regarding signiﬁcance and insigniﬁcance for all
of the parameters remain the same.
When we use equation (3) to calculate the total impact of extreme temperatures, our estimates
for heat and mortality (Panel A) corresponds to an impact of 0.35 or 12% of the baseline risk; in
our most saturated speciﬁcation, this eﬀect size is reduced to 3.5%. When comparing this eﬀect
size to the eﬀect size for the threshold model using solely a Hot Day dummy (columns (6) and
(7)), the results are very similar. The heat-health estimates for hospital admissions (Panel B) yield
eﬀect sizes between 0.7% (column (5)) and 5.9% (column (1)) for the approach in equation (3).
Again, the results for the threshold model are very similar.
With respect to cold and mortality, the ﬁrst three columns of Table 2suggest that cold is
associated with a signiﬁcant reduction in mortality by around two percent. However, this cold
weather eﬀect is not stable; once we control for other weather variables, cold temperatures are
positively associated with mortality. In particular vapor pressure, wind speed and cloud coverage
seem to be responsible for the association. For hospital admissions, we observe exactly the same
pattern, which has also been reported by other studies (Schwartz et al.,2004). White (2017)
argues that the decrease in admissions on cold days is likely driven by behavioral factors, such as
a decreased willingness to seek treatments on cold days.
Comparison with Literature. As shown in Table 1,Deschˆenes and Moretti (2009) estimate a
similar model at the daily level for the US and the years 1972 to 1988. They ﬁnd that average daily
temperatures of more than 80˚F (26.7˚C) increase the death rate by between 4 and 5%. Thus the
results are broadly consistent despite Germany’s stronger heat-health relationship. Explanations
for the diﬀerent eﬀect sizes could be the diﬀerent time periods or diﬀerences in geography and
climate zones. An alternative explanation could be the much lower diﬀusion of air conditioners in
Germany compared to the US (cf. Barreca et al.,2016).
Epidemiological Models. Table 3shows the results when estimating models that are stan-
dard in Epidemiology, see equation (2). Instead of estimating OLS models with a rich set of
temporal and spatial ﬁxed eﬀects, these are random eﬀect poisson models with cubic splines and
estimate incidence rate ratios. The eﬀect can then be directly interpreted in percentages. Other-
wise, the structures of the tables are similar: Panel A shows the eﬀects on mortality and Panel
B the eﬀects on hospitalizations. Each column in each panel represents one model. The models
in columns (1) to (2) and (5) to (6) do not control for contemporaneous weather and pollution
conditions, whereas columns (3) to (4) and (7) to (8) consider cubic splines of ﬁve pollutants and
other weather conditions, such as the hours of sunshine or the precipitation level. In columns (4)
and (8) we also control for 30 lags of the main independent variables Hot Day (Hot Day II ) and
Cold Day (Cold Day II ).
[Insert Table 3about here]
Starting with the heat-health relationship, the epidemiological models ﬁnd that a hot day
increases deaths by about 7% and admissions between 1.2 and 1.4%. These results hold whether
we deﬁne hot days in terms of temperatures or in terms of percentiles. On the other hand, as
above, controlling for eﬀect modiﬁers such as pollutants reduces the eﬀect sizes. In particular, the
inclusion of lags reduces the estimated impact of a hot day to around 4%.
For the cold-health relationship, the least restrictive speciﬁcations in columns (1) and (5) sug-
gests an increase in mortality by 8 to 9% on cold days. However, most of this eﬀect dissipates
once we control for pollution splines, and vanishes almost completely once we control for lags of
the extreme temperature variables. For hospital admissions, a cold day is associated with a signif-
icant reduction of between 1 and 3%. This eﬀect becomes more pronounced when controlling for
Comparison with Economic Models. Concerning the heat-mortality relationship, the re-
sults are similar to those delivered by economic models, even though the eﬀect is roughly one-third
smaller in the least restrictive model. This diﬀerence is not attributable to diﬀerences in the def-
inition of a hot day, as the comparison in Table 3shows. The main diﬀerence between equations
(1) and (2), apart from functional form assumptions, is the absence of county ﬁxed eﬀects in the
epidemiological speciﬁcation. Hence the (small) diﬀerence in eﬀect sizes could be driven by adap-
tation of the human body or endogenous sorting of frail individuals into counties where heat events
Concerning the cold-mortality relationship, the two approaches are in stark contrast with each
other. According to economic models, a cold day is associated with an average reduction in mortal-
ity by 2%, whereas the epidemiological models suggest an increase in mortality ranging from 0.6%
to 10%. The apparent reason for this discrepancy is that the temperature bin model fails to recover
the eﬀect of extreme cold on health. When we use a dummy for extreme cold in the economic model
(columns (6)-(7) of Table 2), the estimated eﬀect is actually positive, albeit relatively small (0.7 to
0.9% of the baseline risk)—smaller than most of the epidemiological eﬀect sizes—but of the same
magnitude as the most restrictive speciﬁcations in Table 3.
For hospitalizations in Panel B of Tables 2and 3, the baseline models are very consistent for
8Note that clustering standard errors in these models using high frequency data and millions of
observations is computational very challenging. Many studies in epidemiology provide unclustered
standard errors and/or do not discuss clustering. We follow this example for illustrative purposes.
However, we strongly advise to interpret the displayed, non-clustered, standard errors with caution.
Thanks to the rich databases and as shown for the economic models, clustering at the county or
county-day level would inﬂate standard errors substantially but the coeﬃcient estimates very likely
would remain statistically signiﬁcant at conventional levels.
cold, but the heat eﬀects diﬀer. Again, we can rule out that the diﬀerence is driven by the diﬀerent
deﬁnitions of a hot day in economics vs. epidemiology. Besides, given that the estimates from the
threshold models in columns (6) and (7) are very consistent with those from the temperature bin
models in columns (1) to (5) of Table 2, we can also rule out that irregularities in the temperature
gradient are responsible for the diﬀerence. Instead, as for mortality, unobserved heterogeneity
between counties appears to be responsible for the diﬀerences.
Comparison with Literature. Table 1lists several epidemiological studies on the relationship
between heat and mortality; almost all of them exploit data from speciﬁc geographic regions,
mostly cities, but not entire countries. Diﬀerences in eﬀects sizes could be due to (i) diﬀerences
in the underlying population, (ii) diﬀerences in the time periods studied, or (iii) diﬀerences in the
temperature distributions across regions. Nordio et al. (2015), for example, use daily mortality
data for US cities—a total of 211 cities over ﬁve decades. They categorize cities by eight clusters,
depending on geography, and ﬁnd that average daily temperatures above 30˚C increase the relative
death risk by more than 10%, consistent with our ﬁndings. Son et al. (2016) report a 6% higher
mortality risk in S˜ao Paulo (Brazil) for the 99th as compared to the 90th temperature percentile.
Chung et al. (2015) use data from the 1990s and 2000s for three cities in Taiwan and six cities each
in Korea and Japan to identify heat-mortality eﬀects of between 5 and 10%. They also identify
cold-mortality eﬀects which were, however, much smaller in size.
We ﬁnd the following for hospital admissions: Bobb et al. (2014) use admission data of Medicare
enrollees for 1,943 US counties and the years 1999 to 2010. They ﬁnd elevated risks of between
5 and 18% for ﬁve disease groups but non-signiﬁcant eﬀects for the majority of the 214 disease
groups investigated. Son et al. (2014) investigate the relationship between heat and cold events
and hospital admissions in eight cities in South Korea. They show for Seoul that admissions for
heart diseases increase almost linearly from zero to ten percent when temperatures increase from
20 to 30˚C.
4.2 Robustness Checks
Table 4presents a series of robustness checks. The reference speciﬁcation is always the eﬀect of
one Hot Day on the hospital admission rate as in column (6) of Table 2, Panel B. All ﬁndings also
hold when using the mortality rate as the dependent variable (results available upon request).
Column (1) in Panel A reports results with standard errors clustered at the state instead of
the county level; Column (2) applies two-way clustering by county and date (Cameron and Miller,
2011) and column (3) corrects for spatial dependence (Driscoll and Kraay,1998). As compared
to the standard speciﬁcation, standard errors increase, but the coeﬃcient estimates remain highly
signiﬁcant at the one percent level.
The next three columns add nation-level (column (4)), state-level (column (5)) as well as county-
level (column (6)) time trends to the model. The latter two speciﬁcations slightly reduce the
magnitude of the estimated Hot Day coeﬃcients. Column (7) in Panel A adds county-by-year ﬁxed
eﬀects. Again, the coeﬃcients are very robust in size and signiﬁcance.9
[Insert Table 4about here]
Column (1) in Panel B serves as comparison for the fully saturated model and excludes the year
2000 for which no P M10 data are available. Excluding this year does not alter the results. Column
(2) simply takes the logarithm of the dependent variable, which is an alternative way of modeling
the heat-health relationship.
Column (3) in Panel B shows yet another way of modeling the heat-health relationship. Here,
the model includes the maximum daily temperature as a continuous variable, along with the Hot
Day dummy and an interaction between Hot Day and a continuous variable which captures the
diﬀerence between the average maximum temperature that prevails on Hot Days, 32˚C (89˚F),
and the county-speciﬁc maximum temperature on a given Hot Day. In other words: The interaction
term indicates the degree to which hospitalizations increase with every temperature degree increase
above 32˚C (89˚F). An average Hot Day increases admissions by about 1.6 per 100,000 population
or 3%. As shown by the interaction term, the eﬀect of a Hot Day increases by 1 percentage point
for every degree Celsius above 32˚C (89˚F).
Column (6) in Panel B exclude all counties in years when no active weather monitor existed
within 60 km (37.5 miles) of the county centroid. In addition to the extensive discussion in Appendix
F, this serves as an additional robustness check for whether measurement errors could potentially
aﬀect the ﬁndings. As seen, this is not the case.10
4.3 Testing for Adaptation Behavior
Columns (4) and (5) of Panel B interacts Hot Day with a dummy for hot and cold regions. A
similar approach has been used by Deschˆenes and Greenstone (2011) and Barreca et al. (2015)
These speciﬁcations indirectly test adaptation behavior: Namely, whether the human body adapts
to heat and warmer temperatures when humans live in warmer versus colder regions. We deﬁne a
9The standard estimate for the years 2006 to 2008 is 2.18***. We have to restrict these speciﬁ-
cations to three years due to computer memory constraints. The results are robust when restricting
the sample to the years 2003-2005 or 2000-2002.
10 In an additional robustness check, we restricted our sample to 100 counties that contained the
same monitors throughout the period. The results, which are available upon request, are also very
similar to our baseline results.
“warm region” as a region where the mean annual county-level temperature falls into the highest
temperature mean quartile for Germany (>10˚C, 50˚F). A “cold region” is deﬁned as a county
with a mean annual temperature in the lowest temperature quartile (<9˚C, 48˚F). Accordingly,
we deﬁne two dummy variables, Cold and Warm Region, and add them to the models in levels and
in interactions with the Hot Day indicator.
As in Barreca et al. (2015), there is clear evidence in support of the human body adaptation
hypothesis because, in warm regions, the eﬀect of a Hot Day is 20% smaller (corresponding to 0.6
fewer admissions per 100,000) than the average Hot Day eﬀect. Likewise, in cold regions, the eﬀect
of a Hot Day is 15% larger. Note that this ﬁnding would also be in line with heat-(in)sensitive
individuals sorting into colder (warmer) regions; however, geographic mobility in Germany is tra-
ditionally very low. Whatever the exact mechanism, it is unlikely to alter our main ﬁndings; in
warm regions, Hot Days still lead to 4% more hospital admissions and in cold regions, they lead to
6% more admissions.
4.4 Eﬀect Heterogeneity by Age
It is well-known that extreme temperatures particularly aﬀect frail members of society, for example,
older people. This has implications for the relevance of “harvesting”, which we will address in the
following section. To assess the age gradient of the heat-health relationship, this section shows
estimates for age-speciﬁc mortality and hospitalization rates, which we also stratify by diagnoses.
Figure 4shows the results for mortality. Figure 4a displays estimates for all-cause mortality
by age group. The line connecting circles shows the absolute eﬀect sizes per 100,000 population
(with 95 percent conﬁdence intervals) and the triangles show the relative eﬀect sizes in percent for
each of the 17 age groups. The absolute eﬀect is relatively ﬂat for most age groups (even though
sometimes statistically signiﬁcant thanks to the large sample size) and increases progressively from
age 50 onward—from less than 0.2 deaths per 100,000 to almost 3 deaths per 100,000 for people
above 75 years. However, the relative increase in percent for each age group ﬂuctuates around 10%
for all age groups above 30 (and is quite irregular for younger age groups).
Figures 4b to 4f show the corresponding estimates by cause of death. Clearly, cardiovascular
diseases (Figure 4b) are responsible for most of the increase in the oldest age group; and neoplasms
(Figure 4e) contribute a signiﬁcant share to the increased risk for individuals above 50. Interestingly,
for most death causes and most age groups, the relative increase in mortality ﬂuctuates between
10 and 20%.
[Insert Figure 4and 5about here]
Figure 5shows the results for hospital admissions. There are several diﬀerences compared to the
ﬁndings for mortality in Figure 4. First, the eﬀect is less heterogeneous with regard to age: also the
least-aﬀected age group of 10 to 19 year olds experiences a signiﬁcant increase in admissions on hot
days. Second, the relative increase in admissions is more stable across age groups and corresponds
to an increase of between 5-10% for all age groups. Third, the eﬀect is less concentrated in speciﬁc
diagnoses; cardiovascular diseases are largely responsible for the increase in mortality, but they
are only responsible for a small share of the increase in admissions on hot days. Individuals with
respiratory, infectious or metabolic diseases all show increases in admission rates of around 10% on
hot days; for metabolic diseases and people above 75, the increase in admission rates is even close
5 Harvesting and the Monetized Health Costs of a Hot Day
Who dies during extreme heat events? Obviously, the answer to this question has important
implications when quantifying the economic relevance of heat events. The literature discusses a
phenomenon called the “harvesting hypothesis” (cf. Rabl,2005;Fung et al.,2005). According
to the harvesting hypothesis, heat events only temporarily lead to higher mortality rates. The
hypothesis suggests, for example, that people who die during heat events would have otherwise
died a few days later in the counterfactual scenario of the absence of the heat event. If this was
true, then the medium-term population health eﬀect of heat events would be substantially smaller
than the immediate short-term eﬀect. Empirically, an increase in mortality rates of predominately
old people during heat events would support the harvesting hypothesis. Similarly, a decline in
mortality rates in the days following a heat event would also be strongly in line with the harvesting
This paper makes several contributions to the harvesting debate. In the previous section, using
the entire German population over a decade, we have shown how excess mortality varies by age for
diﬀerent diseases and death causes. We now turn to a systematic analysis of dynamic aspects of the
heat-health relationship: First, we analyze the medium-term impact of a hot day on mortality by
summing over and plotting mortality rates up to 30 days after a heat event. We do this separately
for diﬀerent causes of death. Second, we analyze the medium- to long-term impact of a hot day by
aggregating the data at diﬀerent levels in time and exploiting hot day variation at these levels, for
example, the annual county level.
5.1 How Does Mortality Develop After Heat Events?
After having established a clear age gradient for hospital admissions and mortality on hot days,
we examine how mortality rates develop in the days following a heat event. Figure 6plots 30
estimated lags using ﬂexible models like the one in equation (1). Figure 6a shows the coeﬃcients
for individual lags (left-hand side) and cumulative eﬀects (right-hand side) for all-cause mortality.
Apparently, the heat eﬀect spikes on the day after the heat event and then returns to zero during
the following week. The cumulative eﬀect increases from 0.2 on the hot day to 0.7 ten days later,
after which a harvesting eﬀect kicks in and reduces the overall eﬀect size. Mortality rates are thus
repressed between day 10 and day 20 following a hot day. This “harvesting” reduces the cumulative
eﬀect from around 0.7 to around 0.5—after which it remains fairly stable.
As before, a large part of the eﬀect is driven by cardiovascular diseases. Investigating this
death cause separately in Figure 6b also reveals clear evidence of harvesting. Moreover, we ﬁnd
evidence for a harvesting eﬀect in neoplasms (Figure 6e) which appears very plausible from a medical
perspective. Cancer patients get admitted to hospitals and die during heat events but mortality
then develops under proportionally in subsequent days and weeks. In contrast, the eﬀects for
respiratory diseases and infections are more persistent over time (Figures 6c and 6d).
[Insert Figure 6about here]
Summing up, it appears to be the case that the general hypothesis of “harvesting” requires
a more nuanced discussion and analysis. While, for some disease groups (such as cardiovascular
diseases or cancer patients), the data show pattern that are clearly consistent with the harvest-
ing hypothesis—excess mortality during heat events, followed by sharp decreases and an under-
proportional development—no such clear pattern exists for other disease groups (such as respiratory
and infectious diseases).
5.2 Aggregating Up: Exploiting Monthly and Annual Variation
In the next step, Table 5aggregates the daily county-level data at diﬀerent levels to provide
evidence for medium-run eﬀects of heat events. This is an alternative test for the relevance of the
harvesting hypothesis. If it were true that heat events triggered persistent adverse health eﬀects
that would not have occurred in the counterfactual state, then an additional hot day should also
signiﬁcantly elevate the monthly and annual mortality and hospitalization rates—not just the daily
one. However, due to data limitations and power issues, researchers often cannot implement this
test because one obviously needs to observe enough years with enough variation in the annual
number of Hot Days.11 In addition, the number of regional units of observations, in this case
counties, must be suﬃciently large. Our data and setting fulﬁll all of these conditions.
Panel A of Table 5shows the results for deaths and Panel B shows the results for hospital
admissions. All models are similar to equation (1). In the ﬁrst column, we simply aggregate at
the weekly level and diﬀerentiate between the ﬁrst, second, third, and fourth week of and after a
Hot Day. When aggregating at the weekly level, the coeﬃcients remain statistically signiﬁcant and
relatively large. As for deaths in Panel A, the coeﬃcient estimate for the ﬁrst week of the heat event
remains as large as the daily estimate in Table 2and highly signiﬁcant. In contrast, the estimates
for the next two weeks are negative and statistically signiﬁcant. As for hospital admissions in
Panel B, the weekly eﬀect size is only one third of the daily one. Additionally, the three weekly
eﬀects for the three following weeks have negative coeﬃcients (but lack statistical precision). These
ﬁndings suggest that, following spikes during heat events, decreases in admissions kick in earlier
than decreases in deaths. However, the overall patterns are very similar and reinforce the harvesting
[Insert Table 5about here]
Column (2) aggregates the data at the county-month level, and column (3) aggregates the data
at the county-year level, solely exploiting the monthly and annual variation in Hot Days. As for
mortality in Panel A, column (2) yields a highly signiﬁcant estimate of 0.013 and column (4) a
highly signiﬁcant estimate of just 0.0025. The yearly coeﬃcient is more than 100 times smaller
than the daily one. This only translates into minor annual mortality increases of 0.08%, or 2
additional deaths per additional Hot Day in Germany. This ﬁnding is very similar to the one
in Deschˆenes and Greenstone (2011) for the US, who ﬁnd an annual age-adjusted mortality rate
increase of 0.11% per additional hot day. Because the applied value of a statistical life year is not
speciﬁc to this study but derived from a rich literature, the monetized health costs estimates are
This ﬁnding is reinforced for hospital admissions in Panel B: the heat-admission coeﬃcients
decrease substantially to 0.03 in columns (2) and (3). These eﬀect sizes translate into admission in-
creases by about 0.05%—reduced by a factor of 100 as compared to the standard estimate in column
(1) of Table 2. However, the coeﬃcients in columns (2) and (3) remain statistically signiﬁcant.
11 Deschˆenes and Greenstone (2011) are an exception.
5.3 Monetizing the Health Loss of One Additional Hot Day
Finally, we assess and monetize the total health eﬀects caused by extreme temperatures. Such
quantitative measures may be useful to design appropriate public health measures, and they may
eventually tell us something about the societal costs associated with climate change. However, we
are reluctant to embark on a full-scale estimate of the health costs of climate change.
Given the complex nature of climate change, it is not surprising that long-term projections
of its future trajectory are relatively vague. Concrete statements are hard to ﬁnd in the famous
Stern (2006) report. According to the IPCC (2007), it is very likely that hot extremes, heat waves
and heavy precipitation events will continue to become more frequent (p. 46, 53). The underlying
state-of-the art global climate model of the IPCC is the third version of the so-called Hadley Centre
Coupled Model (HadCM3) (Pope et al.,2000). These climate models are very complex and require
many assumptions and scenarios. Deschˆenes and Greenstone (2011) make use of the HadCM3
model and the “business-as-usual” scenario to predict the change in the number of Hot Days from
2070 to 2099 relative to 1968 to 2002 for diﬀerent US regions.12 For the region whose climate comes
closest to Germany’s, New England, Deschˆenes and Greenstone (2011) estimate a 20% increase in
the number of Hot Days.H¨ubler et al. (2008) make use of the Regional Climate Model REMO
and predict “two to ﬁve times as many hot days [for Germany from 2071 to 2100 relative to 1971
to 2000]” (p. 383).
Given the diﬃculty and inherent uncertainty of making such long-term predictions (Heal and
Millner,2014), we focus on the monetized health eﬀects of one additional hot day for the following
reasons: (i) Additional hot days are very plausible climate change predictions and are typically re-
ferred to in climate change models. (ii) One additional hot day is an intuitively plausible concept.
The monetized health eﬀects can be easily scaled up or down to alternative climate change predic-
tions. (iii) One additional hot day represents an increase of about 14% in the total number of hot
day in Germany, which is very much in line with the Deschˆenes and Greenstone (2011) prediction
for New England using HadCM3. (iv) Finally, we abstain from estimating the impact of fewer cold
days because projections concerning cold are not unambiguous. On the one hand, the IPCC (2007)
projects that snow cover will contract (globally) in the future. On the other hand, loss of arctic
sea ice has been linked to extreme cold weather in North America and Europe (Liu et al.,2012).
In fact, climate change could result in both more heat and cold events in the mid-latitudes.
Table 6summarizes the ﬁndings from the empirical models and calculates the total health
costs of one Hot Day under competing assumptions. The basis for these calculations is Table 2and
12 Here Hot Days are days with a mean daily temperature above 90˚F.
equivalent tables that use the dependent variables Hospital Days and Hospital Death, see Appendix
B. In line with the dependent variables (see Tables A1 and B1), the monetized health eﬀects include
(A) total hospital days due to a Hot Day, (B) total deaths after a hospital stay due to a Hot Day,
(C) immediate death due to a Hot Day. Table 6additionally diﬀerentiates by three main models:
the (a) parsimonious model, the (b) model that includes eﬀect modiﬁers at the day-county level,
and the (c) the model outlined in column (4) of Table 5, which aggregates at the year-county level,
thereby completely internalizing the harvesting eﬀects.
The ﬁrst four columns of Table 6monetize the diﬀerent costs of hospital stays. Column (1)
multiplies the total number of hospital days by the average cost of one hospital day in Germany,
which is e500 (German Federal Statistical Oﬃce,2013b). Column (2) shows the loss in labor
productivity by multiplying the approximate share of the working population, 50%, by the number
of heat-related hospital days and the average daily gross wage in 2012, including employer-mandated
beneﬁts: e150 (German Federal Statistical Oﬃce,2013a). This column likely overestimates the
true eﬀects, given that mostly the elderly are hospitalized on hot days, see Figure 5.
Columns (3) and (4) convert the number of hospital days into lost Quality-Adjusted Life Years
(QALYs) by assuming that 365 hospital days equal a loss of one QALY (column (3)) and half a
QALY (column (4)), respectively. We evaluate one QALY with e100,000 ($130,000) (Kniesner
et al.,2010;Robinson et al.,2013).
[Insert Table 6about here]
Column (5) monetizes the total number of deaths, which is the sum of deaths after a hospital stay
and immediate deaths. Again, one QALY is evaluated at a value of e100,000. The ﬁrst two rows
use the data at the day-county level and ignore harvesting; here we assume that people who died
would have lived another calendar year absent the heat event. The third row aggregates at the
year-county level and accounts for harvesting; here we assume that people who died would have
lived another 30 years.13
As seen in the ﬁnal two columns: First, the upper and lower bound QALY assumptions barely
aﬀect the estimates (and neither do varying assumptions about their value). Second, the parsi-
monious county-day model yields the largest monetized health loss estimates. The approach that
aggregates at the year-county level, internalizing harvesting, yields the lowest monetized health
loss. Third, all estimates are relatively close and small in size. The estimated monetized losses
range from e6m to e43m per hot day for an entire nation with a GDP of e2.5 trillion and 82
13 30 years is roughly the diﬀerence between the average current age of Germans and their life
expectancy. Alternative assumptions do not alter the main ﬁndings.
million residents. The equivalent values for the US would lie between $30 million and $212 million
or between e0.07 ($0.10) and e0.52 ($0.68) per resident.14 Fourth, assuming that climate change
permanently induces one additional hot day per year and taking the largest annual loss estimate of
e43 million, the nominal health-related welfare loss over one life cycle of 80 years would accumulate
to e3.4 billion for Germany. Applying a discount rate of 2.5% reduces this sum to e470 million
or about e6 ($8) per resident. The equivalent values for the US would be $16.8 and $2.3 billion,
When comparing these back of the envelope calculations with the economics literature on the
impact of adverse weather and pollution on labor productivity, one ﬁnds that even ozone levels
below the US regulatory thresholds would aﬀect the productivity of agricultural workers (Zivin
and Neidell,2012). Accordingly, a reduction in ozone levels by 10ppb could lead to annual labor
productivity beneﬁts of $700 million. Moretti and Neidell (2011) estimate that the annual costs of
hospital admissions due to respiratory diseases accumulate to $44 million per year for Los Angeles.
Chang et al. (2016) estimate the US-wide labor cost savings as a result of reductions in PM2.5
levels to be about $2 billion per year. Finally, Zivin and Neidell (2014) report that a hot day with
maximum temperatures above 85˚F (29.4˚C) induces a re-allocation of time spent outdoors to
indoor leisure as well as a labor productivity loss in “climate-exposed industries.”
This paper assesses the adverse population health eﬀects of extreme temperatures. At the day-
county level, we link weather and pollution measures from more than 2,300 ambient monitors
obtained over 10 years to two administrative datasets: (i) a mortality census comprising all deaths
on German territory from 1999 to 2008, and (ii) a hospital census of all admissions from 1999 to
2008. These databases together allow us to comprehensively analyze the short-term and longer-term
population health eﬀects of heat and cold events.
First, conﬁrming the ﬁndings of the existing literature, we ﬁnd that extreme heat immediately
aﬀects population health negatively and leads to more hospitalizations and deaths. This ﬁnding
holds irrespective of whether we use ﬂexible temperature bin models or threshold models, rich OLS
ﬁxed eﬀects models (as standard in economics) or random eﬀect poisson models (as standard in
epidemiology). The standard models in economics yield an increase in mortality of about 12% and
an increase in hospital admissions of about 6% during heat events.
14 Assuming an exchange rate of 1.3 and that the US has 311/82=3.8 times as many residents as
Second, comparing the standard modeling approaches in health economics and epidemiology, we
ﬁnd that the qualitative ﬁndings for the heat-mortality relationship are remarkably consistent, but
the economic models yield stronger heat-mortality and heat-hospitalization gradients. Modifying
our modelling approaches stepwise, we can rule out that diﬀerences in the deﬁnition of a hot day
are driving eﬀect size diﬀerences whenever they exist. Instead, hundreds of additional county ﬁxed
eﬀects in the economic models, which net out unobserved time-invariant heterogeneity, appear to
be responsible for the diﬀerences.
Third, the magnitude of the heat-health relationship signiﬁcantly decreases when considering
“eﬀect modiﬁers”, i.e., when controlling for other climatic and pollution conditions. For example, in
the economic models the adverse health eﬀects of a hot day is more than halved when comprehen-
sively controlling for non-temperature related climatic conditions such as sunshine, high ozone, or
particular matter concentrations that typically prevail during heat events. Adding lags of extreme
temperature conditions further decreases eﬀect sizes.
Fourth, in line with the sparse literature on this topic, the ﬁndings for cold are inconclusive. In
these models, controlling for other weather conditions such as precipitation or wind-speed makes
a crucial diﬀerence and negative eﬀect estimates turn positive. This holds both for mortality
and hospital admissions where, as expected, the cold-health gradient becomes larger with falling
temperatures. For example, in our economic ﬁxed eﬀects models, relative to temperatures between
40 and 50˚F, daily mean temperatures of less than 10˚F increase deaths by 4% and admissions
by 22%. By contrast, the epidemiological poisson models yield smaller but still positive cold-
mortality associations. However, the cold-hospitalization gradient turns negative for these models
when adding cubic pollution splines as eﬀect modiﬁers.
Fifth, we apply several methods to test the so-called “harvesting hypothesis.” This hypothesis
implies that heat would only bring forward adverse population health eﬀects by a couple of days
and would not have a substantial long-term impact. In other words: excess mortality or admissions
on hot days would be followed by sharp decreases in deaths or admissions—and the annual eﬀects
would be substantially smaller than the daily eﬀects. We investigate the death rates in the 30 days
following a heat event and diﬀerentiate by disease categories. We also investigate the age structure
of those who were admitted or died on hot days, again by disease categories. Lastly, we exploit
the richness of the data by aggregating them at the month-county and year-county level and solely
using monthly and annual variation in the number of hot days as the identifying variation.
Our results clearly show that a nuanced discussion is important when it comes to harvesting
because the ﬁndings depend on the disease category. We ﬁnd very characteristic sharp increases,
followed by sharp decreases, for cardiovascular and neoplastic mortality. However, we do not ﬁnd
these patterns for disease categories such as infections or metabolic diseases. When diﬀerentiating
by age groups, deaths and admissions sharply increase for people above 50 during heat events.
However, this is only true for absolute eﬀect sizes per 100,000 population—the relative increase in
percent is remarkable consistent at around 10% for all age groups above 30. As for mortality, the
main driver are heart diseases during hot days. In contrast, as for hospital admissions, respiratory
and infectious diseases as well as admissions of cancer patients and patients with metabolic problems
all play an important role.
Finally, we try to monetize the health eﬀects of one additional hot day with temperatures above
30˚C (86˚F). We provide results for diﬀerent approaches using diﬀerent sets of assumptions. The
total estimated health loss of one hot day represents a—highly unequally distributed—monetary
welfare loss of up to e50 million ($65 million) per 100 million residents.
As a last point, we would like to note the limitations of this study. This paper solely studies
the health eﬀects of extreme temperatures. Moreoever, it does not consider health eﬀects that
lead to ambulatory doctor visits or no treatments at all. However, our calculations suggest that
mild health eﬀects do not seem to matter substantially when calculating total monetized health
costs. A very large share of the serious health eﬀects should be captured by this study. One
important exception may be fetal health eﬀects which may have long-lasting impacts (cf. van den
Berg et al.,2006;Wilde et al.,2017). For example, Currie et al. (2015) estimate that the overall
discounted long-term societal costs of being born with low birth weight are at least $100,000. We
also acknowledge that we do not explicitly estimate (potential) adverse health eﬀects triggered by
avoidance behavior. However, this omission should not signiﬁcantly impact the central ﬁndings
of this study, which implicitly consider avoidance behavior in its estimates.15 We also disregard
adverse health eﬀects from weather phenomena such as ﬂoods, tornadoes, and hurricanes. Lastly,
this study abstains from estimating cumulative long-term health eﬀects of ongoing and slowly
evolving temperature changes.
More studies on more regions and outcome measures are instrumental for a better understanding
of how climate and human health interact.
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Figure 1: Distribution of Oﬃcial German Ambient Weather and Pollution Monitors
-10 0 10 20 30
Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec
(a) Mean Temperatures (in˚C) by Months
-20 0 20 40
01jan1999 01jan2001 01jan2003 01jan2005 01jan2007
(b) Mean, Min. and Max. Temperatures (in˚C)
Figure 2: Distribution of Temperatures 1999-2008
0 .1 .2 .3 .4
0 5 10 15 20
Daily Min. (black) and Max. (grey) Temperatures of County-Day Observations
(a) Min. and Max. Temperatures (in˚C)
0 .1 .2 .3 .4
0 10 20 30 40
Number of Cold (black) and Hot (grey) Days per County and Year
(b) Number of Hot and Cold Days
Figure 3: Distribution of Temperatures and Hot + Cold Days
Note: Figure 3a shows the county-day distributions of minimum temperatures (avg. 5.5˚C; 42˚F) and maximum
temperatures (avg. 13.9˚C; 57˚F). Figure 3b shows the distribution of Hot (max. temp>30˚C) and Cold Days
(a) All-Cause (b) Cardiovascular
(c) Respiratory (d) Infectious
(e) Neoplasm (f) Metabolism
Figure 4: Age Structure of Heat-Related Mortality by Disease Type
Note: The ﬁgures plot the coeﬃcient of Hot Day of a model similar to equation (1), estimated for 17 age groups
separately, with the mortality rate as the dependent variable. The left y-axis provides the absolute eﬀect per
100,000 population and the right y-axis provides the relative eﬀect in percent.
(a) All-Cause (b) Cardiovascular
(c) Respiratory (d) Infectious
(e) Neoplasm (f) Metabolism
Figure 5: Age Structure of Heat-Related Hospitalizations by Disease Type
Note: The ﬁgures plot the coeﬃcient of Hot Day of a model similar to equation (1), estimated for 9 age groups
separately, with the hospitalization rate as the dependent variable. The left y-axis provides the absolute eﬀect
per 100,000 population and the right y-axis provides the relative eﬀect in percent.
Table 1: Select Published Empirical Papers on the Health Eﬀects of Extreme Temperatures, Developed Countries
A: Economic Journals Area Period Unit of Obs. Method Outcomes Var. of Interest Climate Controls
Deschˆenes and Moretti (2009), continental US, ’72-’88 county-day county-month-year FE mortality rate hot days, precip.
REStat white deaths (cause, age, gender) cold days
Deschˆenes et al. (2009), continental US ’72-’88 ind.-pregn., county-year FE; birth wgt, LBW # days in N/A
AER: PP during gestation 5 temp. bins N/A
Deschˆenes and Greenstone (2011), continental US ’68-’02 county by year county FE, mortality rate # days in 10 precip.
AEJ: Applied state-year FE temp. bins
Barreca (2012), 373/3,100+ ’73-’02 county-month county-month FE, mortality rate mean temp.& temp.-precip.
JEEM US counties county-month trends precip. interactions
Barreca et al. (2016), US 1900-2004 state-month state-month FE, mortality rate # days in 10 precip.
JPE year-month FE temp. bins
White (2017), CAL/US, 1900-2004 state-month state-month FE, mortality rate # days in 10 precip.
JAERE all hospitalizations 2005-2014 zip-day zip-week, county-year FE hospitalization rate temp. bins precip.
B: Epidemiological & Bio-Stat. Journals
Curriero et al. (2002), 11 US cities ’73-’94 daily log-linear poisson, #deaths avg. temp., smooth. spline
Am J Epidemiology distr. lag models 3 ICD groups 10 lags
Braga et al. (2002), 12 US cities ’86-’93 daily log-linear poisson, #deaths temp., humidity, air press.,
Env Health Persp distr. lag models 4 ICD groups 20 lags smooth. param.
Hajat et al. (2005), Delhi, London, ’91-’94 daily log-linear poisson, #deaths heat/cold day, humidity, precip.
Epidemiology S˜ao Paulo distr.lag models 3 ICD groups 28 lags PM10, cubic splines
Hajat et al. (2006), London, Budapest, ’70-’03 daily, June-Sep log-linear poisson, #deaths, 2 lags heat wave black smoke, O3
Epidemiology Milan AR-structure 3 ICD groups var. def. cubic splines
Anderson and Bell (2002), 107 US commun. ’87-’00 daily log-linear poisson, #deaths heat/cold wave, O3, PM10
Epidemiology 2 ICD groups 25 lags cubic splines
Peng et al. (2011), Chicago, US ’87-’05 daily, log-linear poisson #deaths heat wave, temp., O3
Env Health Persp May-Oct climate scenarios splines
Goldberg et al. (2011), Montreal, CA ’84-’07 daily log-linear poisson #deaths max temp., O3, NO2
Env Research distr. lag models 3 ICD groups hot/cold day cubic splines
Heaton and Peng (2012), 4 metrop. areas, US ’01-’05 daily, April-Sep distributed lag models, #deaths avg temp., cubic splines
J Agric Biol Env S Gaussian procedures 60 lags
Barnett et al. (2012), 99 cities, US ’87-’00 daily log-linear poisson, #deaths heat/cold wave, splines
Env Research Bayesian, lags 3 ICD groups var. def.
Bobb et al. (2014), 1943 US counties ’99-’10 daily log-linear regressions #admissions, heat wave, year FE
JAMA Medicare enrollees matching by county-week 283 disease groups 7 lags
Bobb et al. (2014), 105 US cities ’87-’05 daily, May-Oct log-linear poisson, #deaths avg. temp. age cat.
Env Health Persp hier. Bayes cubic splines
Son et al. (2014), 8 Korean cities ’03-’08 daily, Mar-Aug log-linear poisson, #admissions avg. temp. cubic splines
Int J Biometeorol + Sep-Feb hier. Bayes
Schwartz et al. (2015), 209 US cities ’73-’06 daily log-linear poisson, #deaths avg. temp. temp
Env Health cluster analysis
Nordio et al. (2015), 211 US cities ’62-’06 monthly log-linear poisson, #deaths avg. temp. temp
Env Health (no ’67-‘73) cluster anal. + meta reg. 5 lags
Gasparrini et al. (2015), 384 locations depends, max. daily log-linear poisson, #deaths extreme heat temp
Lancet 13 countries ’85-’12 distr. lag models 21 lags + cold cubic splines
Chung et al. (2015), 3+6+6 cities in depends, max. daily log-linear poisson, #deaths heat/cold humidity, air press.
Epidemiology Taiwan, Korea, Japan ’85-’12 hier. Bayes 30 lags var. def. cubic splines
Table 2: Temperature, Mortality and Hospitalizations: Economic Fixed Eﬀects Models
Temperature Bin Model Threshold Model
(1) (2) (3) (4) (5) (6) (7)
Panel A: Mortality per 100,000 population
<10 ˚F -0.0187 -0.0188 -0.0466 0.1209* 0.1067
(0.048) (0.048) (0.048) (0.049) (0.055)
10-20 ˚F 0.0050 0.0050 -0.0194 0.1138*** 0.0782***
(0.014) (0.014) (0.014) (0.016) (0.017)
20-30 ˚F -0.0332*** -0.0332*** -0.0304*** 0.0683*** 0.0332***
(0.005) (0.005) (0.006) (0.007) (0.008)
30-40 ˚F -0.0229*** -0.0229*** -0.0172*** 0.0361*** 0.0144***
(0.003) (0.003) (0.003) (0.004) (0.004)
40-50 ˚F ref. ref. ref. ref. ref.
50-60 ˚F 0.0408*** 0.0408*** 0.0281*** -0.0206*** 0.0008
(0.004) (0.004) (0.004) (0.005) (0.005)
60-70 ˚F 0.1328*** 0.1328*** 0.0936*** -0.0062 0.0151*
(0.005) (0.005) (0.005) (0.007) (0.007)
70-80 ˚F 0.3544*** 0.3545*** 0.2478*** 0.0965*** 0.0780***
(0.008) (0.008) (0.008) (0.011) (0.011)
80-90 ˚F 0.9559*** 0.9557*** 0.6893*** 0.5065*** 0.2409***
(0.040) (0.040) (0.039) (0.040) (0.033)
Hot Day Eﬀect 0.3475*** 0.3475*** 0.2470*** 0.1123*** 0.0763*** 0.3198*** 0.0948***
s.e. (0.007) (0.007) (0.007) (0.009) (0.009) (0.009) (0.009)
Pct. change 12.177 12.178 8.659 3.938 2.674 11.209 3.324
Cold Day Eﬀect -0.0579*** -0.0579*** -0.0571*** 0.0862*** 0.0499*** 0.0250* 0.0195
s.e. (0.009) (0.009) (0.009) (0.011) (0.013) (0.011) (0.013)
Pct. change -2.029 -2.029 -2.004 3.021 1.750 0.877 0.684
R-squared 0.03 0.03 0.03 0.03 0.03 0.03 0.03
N. of cases 1,590,501 1,590,501 1,429,899 1,429,899 1,429,059 1,590,501 1,429,059
Panel B: Hospital Admissions per 100,000 population
<10 ˚F 2.1188** 2.1244** -0.3325 11.0228*** 13.7168***
(0.745) (0.750) (0.822) (0.822) (1.036)
10-20 ˚F -2.2236*** -2.2201*** -4.6711*** 2.4397*** 4.8323***
(0.213) (0.213) (0.286) (0.297) (0.367)
20-30 ˚F -2.5313*** -2.5329*** -3.4483*** 0.7142*** 2.0300***
(0.096) (0.096) (0.120) (0.132) (0.149)
30-40 ˚F -0.7699*** -0.7694*** -1.5315*** 0.1811 0.9333***
(0.055) (0.055) (0.085) (0.093) (0.088)
40-50 ˚F ref. ref. ref. ref. ref.
50-60 ˚F 1.1232*** 1.1216*** 0.8890*** -0.0963 0.2784***
(0.061) (0.061) (0.092) (0.084) (0.078)
60-70 ˚F 1.7562*** 1.7558*** 0.2636 -0.5795*** -0.6134***
(0.063) (0.063) (0.148) (0.148) (0.149)
70-80 ˚F 3.5465*** 3.5433*** 1.1668*** 0.4125 0.6047
(0.117) (0.117) (0.273) (0.267) (0.262)
80-90 ˚F 8.8118*** 8.8174*** 5.3014*** 2.9667*** 3.480***
(0.329) (0.330) (0.499) (0.445) (0.433)
Hot Day Eﬀect 3.4429*** 3.4409*** 1.6834*** 0.5743** 0.3663 2.9080*** 1.0790***
(0.103) (0.103) (0.241) (0.235) (0.229) (0.225) (0.147)
Change in % 5.937 5.934 2.897 0.988 0.631 5.015 1.860
Cold Day Eﬀect -2.6452*** -2.6430*** -3.8223*** 3.6777*** 2.5616*** -1.2194*** 2.1980***
(0.122) (0.122) (0.166) (0.199) (0.2446) (0.121) (0.212)
Change in % -4.562 -4.558 -6.578 3.737 6.339 -2.103 3.789
R-squared 0.48 0.48 0.52 0.53 0.53 0.48 0.53
N 1,590,454 1,590,454 1,429,928 1,429,928 1,408,356 1,590,454 1,408,356
County, week + month-year ﬁxed eﬀects yes yes yes yes yes yes yes
Age, gender + hospital controls yes yes yes yes yes yes yes
Annual county-level controls no yes yes yes yes no yes
Pollution measures no no yes yes yes no yes
Additional weather controls no no no yes yes no yes
Lags of temperature variables 0 0 0 0 30 0 30
* p<0.1, ** p<0.05, *** p<0.01; standard errors in parentheses are clustered at the county level. Regressions are weighted by the
yearly county population. Data sources are discussed in Section 2. All speciﬁcations estimate the model in equation (1) by OLS, where
the ﬁrst ﬁve columns estimate the temperature bin model and the last two columns estimate the threshold model (see main text). In
columns (1) to (5) the reported “Hot Day Eﬀect” and “Cold Day Eﬀect” are based on the approach described in Section 3.3. In Panel
A, the dependent variable is the daily mortality rate per 100,000 population at the county level (mean: 2.99). In Panel B, the dependent
variable is the daily hospital admission rate per 100,000 population at the county level (mean: 57.99). Columns (3) to (5) and (7) have
fewer observations because PM10 data for 2000 are not available.
Table 3: Extreme Temperatures, Mortality, and Hospitalizations: Epidemiological Poisson Spline Models
Extreme Temperature Absolute (<14˚F and >86˚F) Relative (Percentiles 2.5 and 97.5)
Panel A: Mortality (1) (2) (3) (4) (5) (6) (7) (8)
Hot Day 0.0751*** 0.0754*** 0.0680*** 0.0425***
(0.000) (0.000) (0.000) (0.000)
Cold Day 0.0884*** 0.0876*** 0.0190*** 0.0006***
(0.000) (0.000) (0.000) (0.000)
Hot Day II 0.0699*** 0.0703*** 0.0607*** 0.0391***
(0.000) (0.000) (0.000) (0.000)
Cold Day II 0.0846*** 0.0838*** 0.0327*** 0.0141***
(0.000) (0.000) (0.000) (0.000)
N. of cases 1,590,501 1,590,501 1,429,899 1,429,059 1,590,501 1,590,501 1,429,899 1,429,059
Panel B: Hospital Admissions
Hot Day 0.0138*** 0.0145*** -0.0125*** -0.0077***
(0.000) (0.000) (0.000) (0.000)
Cold Day -0.0105*** -0.0114*** -0.0254*** -0.0284***
(0.000) (0.000) (0.000) (0.000)
Hot Day II 0.0116*** 0.0125*** -0.0144*** -0.0093***
(0.000) (0.000) (0.000) (0.000)
Cold Day II -0.0354*** -0.0366*** -0.0538*** -0.0506***
(0.000) (0.000) (0.000) (0.000)
N. of cases 1,590,454 1,590,454 1,429,928 1,408,356 1,590,454 1,590,454 1,429,928 1,408,356
Cubic date splines and day of week yes yes yes yes yes yes yes yes
Age, gender & hospital controls yes yes yes yes yes yes yes yes
Annual county-level controls no yes yes yes no yes yes yes
Cubic CO, NO2, SO2, PM10, and O3splines no no yes yes no no yes yes
Lags of Hot Day (II) and Cold Day (II) 0 0 0 30 0 0 0 30
* p<0.1, ** p<0.05, *** p<0.01; standard errors are in parentheses. Regressions are weighted by the yearly county population. Data sources are discussed in
Section 2. All speciﬁcations estimate the Poisson model in equation (2) with random eﬀects. Each column in each panel represents one model. Models only
diﬀer by the sets of covariates included as indicated. In Panel A, the dependent variable is the daily mortality rate per 100,000 population at the county level
(mean: 2.99). In Panel B, the dependent variable is the daily hospital admission rate per 100,000 population at the county level (mean: 57.99). All variables
of interest, i.e. Hot Day II, are deﬁned as discussed in Section 2.3 and Appendix C. Hot Day II equals one when the average daily temperature exceeds the
97.5th percentile of the county-level temperature distribution over all years. Cold Day II equals one when the average daily temperature does not exceed
the 2.5nd percentile of the county-level temperature distribution over all years. Columns (3), (4), (7) and (8) have fewer observations because PM10 data for
2000 are not available.
Table 4: The Impact of Extreme Heat on Hospital Admissions: Robustness Checks
linear & quadr.
trends [’06-’08] (6)
Hot Day 2.9083*** 2.9083*** 2.9083*** 2.9083*** 2.6515*** 2.1616*** 2.2053***
(0.2376) (0.2474) (1.0899) (0.1585) (0.1303) (0.2188) (0.2287)
change in % +5.0% +5.0% +5.0% +5.0% +4.6% +3.7% +3.8%
N 1,590,454 1,590,454 1,590,454 1,590,454 1,590,454 467,770 467,770
monitors (6)Panel B
Hot Day×[column header] 0.5751*** -1.0389*** 0.4892**
(0.0603) (0.1911) (0.2459)
Hot Day 3.1113*** 0.0573*** 1.6456*** 3.3788*** 2.8509*** 2.7047***
(0.1741) (0.0042) (0.1598) (0.1684) (0.1685) (0.9136)
max. daily temp. 0.1654***
N 1,429,928 1,590,454 1,590,454 1,590,454 1,590,454 1,274,615
* p<0.1, ** p<0.05, *** p<0.01; standard errors in parentheses are clustered at the county level except for columns (1) of Panel A which clusters at the state,
column (2) of Panel A which clusters at the county and day level (2-way cluster), and column (3) of Panel A which corrects for spatial correlation (Driscoll and
Kraay,1998). Regressions are weighted by the yearly county population. Data sources are discussed in Section 2. Each column in each panel represents a model
that does not control for other weather and pollution conditions. However controlling for them yields similar results (available upon request). The dependent
variable is always the hospitalization rate (mean: 57.99, see Table B1); the reference estimate is the one in Column (1) of Table 2. All speciﬁcations estimate a
model similar to equation (1) by OLS. Column (4) of Panel A adds a nation-wide linear and quadratic time trends. Column (5) adds state-level time trends and
column (6) adds county-level time trends (for 2006-2008 only because of computer memory constraints). Column (7) of Panel A includes county-year FE. The
ﬁrst column in Panel B excludes the year 2000 for which no P M10 data are available and column (2) uses the logarithm of the normalized hospitalization rate
as dependent variable. Column (3) adds a continuous measure for the maximum daily temperature as well as an interaction term between the maximum daily
temperature and the average maximum Hot Day temperature (32˚C, 89˚F). Thus, the interaction term estimates the marginal eﬀect of one temperature degree
above 32˚C. Columns (4) and (5) add a dummy for warm region (mean annual county-level temperature falls into the highest temperature quartile for Germany
(>10˚C, 50˚F)) and cold region (mean annual temperature below the lowest temperature quartile (<9˚C, 48˚F)) as well as their interactions with Hot Day.
Column (6) of Panel B excludes all county observations in years without an active weather monitor within a radius of 60 km (37.5 miles) of the county centroid.
Table 5: Testing the Harvesting Hypothesis
Panel A: Mortality Daily Data
Aggr. at Annual
Hot Day -0.0004 0.0025***
First Week of Hot Day 0.3331***
Second Week after Hot Day -0.1188***
Third Week after Hot Day -0.0860***
Fourth Week after Hot Day 0.1313***
N 1,516,538 52,248 4,354
Panel B: Hospitalizations
Hot Day 0.0288*** 0.0297**
First Week of Hot Day 0.9306*
Second Week after Hot Day -0.2353
Third Week after Hot Day -0.2157
Fourth Week after Hot Day -0.1374
N 1,590,454 52,272 4,356
* p<0.1, ** p<0.05, *** p<0.01; standard errors are in parentheses clustered at the county level.
Each column in each panel represents one model. The models in the ﬁrst two columns are as in
equation (1) with county ﬁxed eﬀects, week ﬁxed eﬀects, and month-year ﬁxed eﬀects (but without
pollution and other weather controls). The models in the last two columns are OLS models with
year ﬁxed eﬀects. The variables of interest in column (1) indicate the ﬁrst, second, third, and fourth
week after a Hot Day, respectively. The variable of interest in columns (2) and (3) is the number of
Hot Days per year. Column (2) aggregates the data at the monthly level and column (3) aggregates
the data at the annual level.
Table 6: The Monetized Health Eﬀects of One Additional Hot Day
Hospitalizations Mortality Total
Fixed Eﬀects Model, 19,000×e500 0.5×19,000×e150 (19,000/365)×e100,000×1.0 (19,000/365)×e100,000×0.5 270×1×e100,000
daily =e9.5m =e1.4m =e5.2m =e2.6m =e27m ∼e43.1m ∼e40.5m
Fixed Eﬀects Model, pollution+ 8,000×e500 0.5×8,000×e150 (8,000/365)×e100,000×1.0 (8,000/365)×e100,000×0.5 78×1×e100,000
weather controls, daily =e4.0m =e0.6m =e2.2m =e1.1m =e7.8m ∼e14.6m ∼e13.5m
Fixed Eﬀects Model, 180×e500 0.5×180×e150 (180/365)×e100,000×1.0 (180/365)×e100,000×0.5 2×30×e100,000
annual =e90,000 =e13,000 =e50,000 = e25,000 =e6m ∼e6.2m ∼e6.1m
The table shows the health-related costs associated with one Hot Day. The ﬁrst row is based on the model in equation (1) that does not consider additional weather or pollution
controls. The models that estimate how many hospital days are triggered by a Hot Day are similar to equation (1) but use Hospital Days as dependent variable (see Appendix
B1). The second row uses the model that considers other weather and pollution controls. These ﬁrst two approaches are based on daily county-level observations and do not
consider potential harvesting eﬀects, i.e., focus on short-term eﬀects. The third row considers harvesting and is based on aggregated annual county-level data (see column (4)
of Table 5). Column (1) considers that an average hospital day in Germany is reimbursed with e500. Column (2) considers that the average daily wage in Germany is e150.
Columns (3) and (4) assume that 365 hospital days equal a loss of 1 and 0.5 QALYs, respectively. One QALY is evaluated with e100,000. Column (5) assumes that the
remaining life expectancy for those who die during heat events is one year for rows one and two (excluding harvesting) and 30 years for row three (including harvesting). We
do not discount the monetized health-related loss in welfare. For the approach in the ﬁrst row, a discount rate of 2.5% would reduce the costs over 80 years from e3.2bn to
e1.4bn or e17 per resident. The table does not consider health issues that lead to outpatient treatments. The table also does not consider health-related avoidance behavior
costs or adverse health eﬀects due to tornadoes, hurricanes, or ﬂoods.
Appendix A: Mortality Census
The ﬁrst administrative dataset is the Mortality Census. It contains the universe of deaths
on German territory from 1999 to 2008. This is a restricted access dataset provided by the
German Federal Statistical Office (Statistische ¨
Amter des Bundes und der L¨ander). We
observe all of the 0.8 million annual deaths. The data contain the following information at the
individual admission level:
•age in years
•gender (binary indicator)
•county of residence [between 442 (1999) and 413 (2008) counties]
•day of death
•primary cause of death (ICD-10, 3 digit)
As described in Section F1, we normalize, aggregate, and merge this dataset with the other
datasets at the day-county level. As such, we obtain the following descriptive statistics.
Table A1: Mortality Census: Dependent Variables per 100,000 pop. (Daily County-Level, 1999-2008)
Variable Mean Std. Dev. N
Mortality rate 2.9897 1.5229 1,518,000
Cardiovascular mortality rate 1.3839 1.0788 1,518,000
Respiratory mortality rate 0.1918 0.4039 1,518,000
Infectious mortality rate 0.0374 0.1749 1,518,000
Metabolic mortality rate 0.0973 0.2889 1,518,000
Neoplasmic mortality rate 0.7676 0.2889 1,518,000
Source: German Federal Statistical Office (Statistische ¨
Amter des Bundes
und der L¨ander). The mortality statistic includes the county of residence and the day
of death. The mortality rate counts the daily mortality rate per 100,000 population
at the county level. German data protection laws prohibit us from reporting min.
and max. values.
Appendix B: Hospital Admission Census
The second administrative dataset is the Hospital Admission Census. It contains the universe
of hospital admissions from 1999 to 2008. This is a restricted access dataset provided by the
German Federal Statistical Office (Statistische ¨
Amter des Bundes und der L¨ander).
We observe more than 17 million annual hospital admissions. The data contain the following
information on the individual admission level:
•age in 18 age groups
(0-2 yrs., 3-5 yrs., 6-9 yrs., 10-14 yrs.,..., 60-64 yrs., 65-75 yrs., >75 yrs.)
•gender (binary indicator)
•county of residence [between 442 (1999) and 413 (2008) counties]
•day of admission
•length of stay (censored at 85 days)
•died in hospital (binary indicator)
•primary diagnosis (ICD-10, 3 digit)
•surgery needed (binary indicator)
•primary hospital department (43 categories)
•#hospital beds (12 categories)
•hospital location (federal state level; 16 states)
•private hospital (binary indicator)
As described in Section F1, we normalize, aggregate, and merge this dataset with the other
datasets at the day-county level. As such, we obtain the following descriptive statistics for the
hospital admission data:
Table B1: Hospital Admission Census: Dependent Variables per 100,000 pop. (Daily County-Level,
Variable Mean Std. Dev. N
All-cause hospitalization rate 57.99 25.71 1,590,454
Hospital days 488.87 267.21 1,590,454
Cardiovascular hospitalization rate 9.1116 4.9216 1,590,454
Cardiovascular hospital days 83.69 55.96 1,590,454
Cardiovascular deaths 0.4532 0.6423 1,590,454
Respiratory hospitalization rate 3.6013 2.5195 1,590,454
Respiratory hospital days 27.93 23.39 1,590,454
Respiratory deaths 0.1557 0.3685 1,590,454
Infectious hospitalization rate 1.3442 1.1759 1,590,454
Infectious hospital days 10.45 13.36 1,590,454
Infectious deaths 0.0509 0.2072 1,590,454
Neoplastic hospitalization rate 6.54 5.1076 1,590,454
Neoplastic hospital days 56.92 49.24 1,590,454
Neoplastic deaths 0.2812 0.5022 1,590,454
Metabolic hospitalization rate 1.6476 1.5454 1,590,454
Metabolic hospital days 15.48 18.39 1,590,454
Metabolic deaths 0.02534 0.1489 1,590,454
Source: German Federal Statistical Office (Statistische ¨
Amter des Bundes
und der L¨ander). The German Hospital Admission Census includes the county of
residence and the day when the patient was hospitalized. The hospitalization rate
counts the daily incidence of hospitalizations per 100,000 population on the county
level. Hospital days is the sum of all hospital days that were triggered on a given
day, i.e., it is the product of the hospitalization rate and the length of stay. Deaths
count the number of hospital deaths per 100,000 population on the county level. The
reference point is always the day when the patient was hospitalized. The patient
died sometime after being admitted, but not necessarily on the day of admission.
German data protection laws prohibit us from reporting min. and max. values.
Appendix C: Oﬃcial Weather Data
The third register dataset contains daily weather measures from up to 1,044 ambient weather
stations. The data are provided by the German Meteorological Service (Deutscher Wet-
terdienst (DWD)). It covers the years from 1999 to 2008.
Table C1: Weather Data (Daily County-Level, 1999-2008)
Variable Mean Std. Dev. Min. Max. N
A. Raw Daily Measures
Average temperature in ˚C 9.5573 7.3047 -19 30.6 1,590,454
(2 m (6’7”) above ground)
Minimum temperature in ˚C 5.4671 6.4965 -25.01 23.8 1,590,454
(2 m (6’7”) above ground)
Maximum temperature in ˚C 13.8912 8.5608 -14.1 39.07 1,590,454
(2 m (6’7”) above ground)
Total hours of sunshine 4.6252 4.2373 0 16.7 1,590,454
Precipitation level in mm 2.2246 4.2154 0 144.98 1,590,454
Average humidity in % 78.3161 11.4307 10 100 1,590,454
Average cloud coverage in % 5.3128 2.1534 0 8.23 1,590,454
Average storm force 3.6065 2.0856 0 26.3 1,590,454
Max. wind speed in km/hr. 10.4964 4.4462 0 54 1,590,454
Vapor pressure in hPA 9.8876 3.9981 0.5 25.9 1,590,454
Min. air pressure in hPA 3.8456 6.5299 -29.01 22 1,590,454
(5 cm (2 inches) above ground)
B. Extreme Temperature Indicators
Hot Day (max temp. >30˚C (86˚F)) 0.0198 0.1392 0 1 1,590,454
Cold Day (min temp. <-10˚C (14˚F)) 0.0124 0.1108 0 1 1,590,454
Hot Day II (mean temp. >percentile 97.5) 0.0249 0.1558 0 1 1,590,454
Cold Day II (mean temp. <percentile 2.5) 0.0249 0.1558 0 1 1,590,454
Source: German Meteorological Service (Deutscher Wetterdienst (DWD)). The information was
recorded on a daily basis by up to 1,044 ambient weather monitors (see Figure 1). The number of weather
stations varies from year to year. The weather indicators displayed cover the years 1999 to 2008. As
described in Section F1, all point measures from the stations are interpolated into the county space
by means of deterministic inverse distance weighting (IDW). Level of analysis is the day×county level.
Hence, with exactly 400 counties in each year, we would obtain 400 ×365 ×10 = 1,460,000 observations.
However, the number of counties varies across years from 442 (1999) to 413 (2008). Vapor and air pressure
are measured in hectopascal (hPa).
As described in Section F1, in a ﬁrst step, we interpolate the point measure into the county
space. Then we merge the weather data with the other data at the day-county level.
Panel A of Table C1 shows the descriptive statistics for the interpolated weather measures
as collected by the DWD. The mean daily air temperature is 10˚C (49˚F), averaged over the
whole time period and over all counties. Note the rich variation in the average daily temperatures
which ranges from -19˚C (-2˚F) to 31˚C (87˚F). Equally rich is the variation of the minimum
and maximum temperatures, hours of sunshine and other weather measures.
The raw weather data that we use for interpolation have missing information on some weather
indicators. Table C2 displays the frequency of missing observations by year (at the monitor-day
level). In general, missing observations are very rare: the overall frequency is 0.78%; the year
2001 shows the highest frequency of missing information with 1.0% of observations missing.
Table C2: Missing Weather Information
Mean SD N
1999 0.009 0.093 201,233
2000 0.018 0.132 202,486
2001 0.010 0.099 203,615
2002 0.008 0.090 196,632
2003 0.007 0.086 188,879
2004 0.007 0.081 181,321
2005 0.007 0.085 187,114
2006 0.004 0.065 188,128
2007 0.004 0.059 184,415
2008 0.003 0.051 185,785
Total 0.008 0.088 1,919,608
Figure C7 displays a scatter matrix which shows, illustratively, the associations between
some raw weather measures. Not surprisingly, one ﬁnds a strong positive association between
the hours of sunshine and the temperature, as well as a strong negative association between the
hours of sunshine and the precipitation level.
Figure C7: Scatter Matrix Illustrating Associations Between Temperature, Sunshine, and
Note: The scales of the x and y-axes correspond to the scales of the plotted variables of interest, i.e., temperature,
precipitation, and hours of sunshine.
Appendix D: Oﬃcial Pollution Data
The fourth register dataset contains daily pollution measures from up to 1,314 ambient monitors.
The data are provided by the German Federal Environmental Office (Umweltbundesamt
(UBA)). It covers the years from 1999 to 2008. As described in Section F1, in a ﬁrst step, we
interpolate the point measure into the county space via IDW. Then we merge the pollution
dataset with the other datasets at the day-county level. We make use of the following pollutants
as additional control variables in extended model speciﬁcations:
Table D1: Pollution Data (Daily County-Level, 1999-2008)
Variable Mean Std. Dev. Min. Max. N
Average CO in ppm 0.4342 0.1794 0.0023 1.3083 1,594,154
Average O3in µg/m345.9786 22.0423 0.8612 135.79 1,594,154
Average NO2in µg/m326.8907 10.6284 0.0278 80.3095 1,594,154
Average SO2in µg/m33.7256 1.6115 0.0654 12.5435 1,594,154
Average P M10 in µg/m324.3097 11.4625 2.0625 64.625 1,432,822
Source: German Federal Environmental Office (Umweltbundesamt (UBA)). The infor-
mation was recorded on a daily basis by up to 1,317 ambient pollution monitors (see Figure 1).
The number of counties and weather stations vary from year to year. The pollution measures
displayed cover the years 1999 to 2008. As described in Section F1, all point measures from
the stations are interpolated into the county space by means of deterministic inverse distance
weighting (IDW). Level of analysis is the day×county level. Hence, with exactly 400 counties in
each year, we would obtain 400 ×365 ×10 = 1,460,000 observations. However, the number of
counties varies across years from 442 (1999) to 413 (2008). CO stands for “carbon monoxide”
and ppm for “parts per million.” N O2stands for “nitrogen dioxide,” O3stands for “ozone,”
SO2stands for “sulphur dioxide,” and P M10 stands for “particular matter.” µg/m3stands
for micrograms per cubic meter of air.
D1 Associations Between All 5 Pollutants
Figure D8 shows the associations between all ﬁve air pollutants discussed above. N O2is posi-
tively correlated with SO2and P M10, but negatively correlated with O3. The same is true for
CO. O3exhibits only very noisy and weak associations with SO2and P M10. However, SO2
and P M10 show a strong and positive association. Several recent papers in environmental epi-
demiology and biostatistics have developed innovative approaches to model the joint and partial
health eﬀects of several pollutants (Katsouyanni et al.,2001;Dominici et al.,2010;Bobb et al.,
2013;Zhang et al.,2017).
Figure D8: Scatter Matrix Illustrating Associations Between Pollutants
Appendix E: Annual Socio-Economic County-Level Data
Finally, this paper makes use of yearly county-level data provided by the Federal Institute
for Research on Building, Urban Affairs and Spatial Development (2012)(Bun-
desinstitut f¨ur Bau-, Stadt- und Raumforschung) in their INKAR (Indicators and Maps on
Spatial Development) database. The data vary by year.16 To normalize the dependent variables
and calculate hospitalization and death rates, we use annual county-level population counts. In
the models, we control for the unemployment rate and GDP per capita. Supply-side constraints
are captured by the # hospitals per county,hospital beds per 10,000 pop. and physicians per
Table E1: Descriptive Statistics Other (County-Level, 1999-2008, Annual)
Variable Mean Std. Dev. Min. Max. N
Unemployment rate 10.47 5.28 1.6 29.3 4,354
GDP per capita 24971 10146 11,282 86,728 4,354
# hospitals per county 4.84 5.49 0 76 4,354
Hospital beds per 10,000 pop. 1211.19 1593.88 0 24,170 4,354
Physicians per 10,000 pop. 152.72 52.59 69 394 4,354
County population 189,450 219,753 34,525 3,431,675 4,354
Source: Federal Institute for Research on Building, Urban Aﬀairs and Spatial Development
(2012). The data vary on the county-year level. In addition, in contrast to the register
databases in Appendices A and B, the INKAR data refers to the county codes and boundaries
as of January 1, 2012. Since various county reforms were implemented between 1999 and
2008, we imputed information for pre-reform counties with post-reform data (if possible). For
example, if counties A and B simply merged to county C and only the GDP per capita for county
C was available, we imputed the GDP per capita for A and B using the population information
on A and B which is available for all years and counties. If, as another example, data was
surveyed in every other year, we took the mean value of t0and t2to impute information for
16 The hospitalization and mortality data contain the county of residence according to the county codes and
boundaries of the speciﬁc year. In contrast, the INKAR database contains all information according to the county
codes and boundaries as of January 1, 2012. From 1999 to 2008, various county reforms, mostly mergers between
two counties, led to changes in the county codes and boundaries. Consequently, the number of counties varies
across years from 442 (1999) to 413 (2008). For counties with county reforms, we imputed pre-reform values using
the post-reform boundary data as of January 1, 2012. In addition to reforms, not all information listed above
have been collected in every single calendar year. We imputed missing values for these cases. See notes to Table
E1 for more details.
Appendix F: Interpolation of Weather and Pollution Measures
F1 Interpolation of Weather and Pollution Measures
To obtain the working datasets, we (i) interpolate the point measures of the weather and pol-
lution monitors into the county space, (ii) aggregate and normalize all information at the daily
county level, and (iii) merge the register datasets with the pollution, weather, and the socioeco-
nomic dataset (see Appendix E) at the day-county level. Assuming that the number of counties
is time-invariant and 400, we would obtain 400 ×365 ×10 = 1,460,000 rows, each representing
one county on a given day.
Hanigan et al. (2006) discuss and compare diﬀerent approaches to calculating estimates of
population exposure to daily weather and pollution conditions from monitors. Here, we rely on
inverse distance weighting (IDW) within a certain radius. We ﬁrst determine the centroid of
each county. Then the distance between each county and each monitor is calculated. In the ﬁnal
step, we calculate the weighted average for each county where weights are based on the inverse
distance to all monitors within a radius of 60 km (37.5 miles) of the county centroid. Thus, by
denoting δij —the distance between a location i(a county centroid) and a monitor j—one can
deﬁne the weighting scheme as:
δij if i6=jand δij <60
1 if δiMid >60 and j=Mid
where Mid denotes the nearest station outside location i. Thus, whenever there are no stations
within a radius of 60 kilometers, the measure from the nearest station outside this radius is used.
Henceforth, we call this interpolation approach simply Inverse Distance Weighting. This section
discusses econometric and methodological issues related to the IDW interpolation method.
Twenty percent of all counties over all years have no weather monitor within a radius of 60
km. In 26% of all observations, there is one monitor, in 27% of all observations two monitors,
and in another 27% more than two monitors. In a robustness check, we omitted all counties in
years when there wasn’t an active weather monitor within a radius of 60 km (37.5 miles); our
results were very robust (Panel B, column (7) of Table 4).
Below we present the results of speciﬁcation tests for measurement errors and concludes that
the IDW method works well for heat events. However, our tests suggest some caution is required
when it comes to pollution, which seems to be measured with more noise. Because we only use
the measures for the ﬁve pollutants to control for contemporaneous pollution conditions in our
conditional models, it is no major methodological threat to our main ﬁndings.
F2 Cross-Validation of Interpolated Measures
When mapping ambient monitor point measures into space, one has to deal with measurement
errors. It is known that classical measurement error attenuates parameter estimates. In case of
non-classical measurement error, the direction of the bias is unclear. Moreover, measurement
error in the dependent variables inﬂates standard errors (Chen et al.,2011).
To assess the measurement error that is introduced via the IDW method, following Currie and
Neidell (2005), we perform the following (indirect) test: For each weather and pollution monitor
(not county centroid), we calculate the IDW value using the weighting scheme in equation (4).
The crucial point is that the weighting scheme attaches weight 0 to the own station.17 Thus,
for each ambient monitor and all weather and pollution measures from that monitor Zd, we
calculate a cross-validated ˜
Zd=ZdΩd; where Ωdis the symmetric matrix of weights for day d
with elements ωijd =wijd /Pkwikd . In other words, we predict the values of each monitor using
all surrounding monitors and the IDW interpolation method. Then, we assess the accuracy of
the IDW interpolation by calculating Pearson’s correlation coeﬃcient for the variables Zand ˜
The results of this exercise are in column (1) of Table F1.
Table F1 illustrates that (a) the IDW method dominates the simpler NN weighting scheme:
The NN method delivers only better accuracy for air pressure. Besides, it becomes clear that (b)
our IDW interpolation algorithm delivers a very acceptable accuracy with correlation coeﬃcients
ranging up to 0.98 for the mean temperatures. Note that this paper particularly relies on mini-
mum, mean, and maximum temperature measurements, all of which deliver excellent accuracy
results with correlation values ranging above 0.95 (column (1) of Table F1). This means that
we are able to predict with 95% accuracy the temperature measured by monitor X using our
IDW method and all surrounding monitors. However, the correlation values for pollution range
between 0.4 and 0.8 suggesting a substantial degree of measurement error. Recall, though, that
we only use the pollution measures as additional controls in some model speciﬁcations.
17When using the county centroid in the IDW interpolation of point measures into county space, the closest
monitor obviously gets the largest weight.
One concern with this interpolation test is that a seemingly high degree of accuracy might
be driven by time trends and seasonal variation in the variables. Thus, we calculate alternative
accuracy correlation measures that are based on transformed versions of Z. These are ﬁrst
nonparametrically adjusted for individual day eﬀects. As seen, the correlation coeﬃcients in
columns (3) and (4) of Table F1 drop somewhat, but still show that there is a considerable
correlation between imputed and actual values. For the temperature measures, the time trend
and season-adjusted correlation values all lie around 0.7. Controlling for 3,650 day ﬁxed eﬀects
is very conservative and likely removes “too much” variation from the data because one cannot
disentangle the “true” correlation between monitors and climatic measures from day ﬁxed eﬀects.
By removing the daily mean, one obviously also removes part the non time-trend correlation.
Note that the results are robust to considering individual years instead of the entire pooled
sample (results available upon request).
Table F1: Cross-Validation of IDW Interpolation
Variable Raw Correlation Time and Season-Adjusted Correlation
IDW Method NN Method IDW Method NN Method
Temperature 0.981 0.972 0.733 0.661
Min Temperature 0.968 0.953 0.713 0.637
Max Temperature 0.977 0.966 0.659 0.587
Precipitation 0.788 0.740 0.688 0.634
Sunshine 0.934 0.922 0.556 0.535
Cloud 0.874 0.821 0.585 0.508
Humidity 0.876 0.826 0.643 0.566
Vapor Pressure 0.979 0.970 0.735 0.678
Air Pressure 0.549 0.579 0.239 0.257
Wind Speed 0.497 0.478 0.219 0.156
CO Mean 0.477 0.363 0.149 0.082
NO2 Mean 0.562 0.450 0.407 0.321
O3 Mean 0.862 0.797 0.435 0.362
SO2 Mean 0.616 0.532 0.306 0.265
PM10 Mean 0.837 0.814 0.239 0.212
Source: German Meteorological Service (Deutscher Wetterdienst (DWD)) and German
Federal Environmental Office (Umweltbundesamt (UBA)). The table shows the cross-
validation of the weather and pollution interpolation as discussed in Section F1. The underlying
data stems from up to 1,044 ambient weather monitors and up to 1,317 ambient pollution
monitors between 1999 and 2008. Columns (1) and (3) display the Pearson’s Correlation
Coeﬃcient between the original values of monitor X and its predicted values solely using all
surrounding monitors and Inverse Distance Weighting (IDW). Columns (2) and (4), in contrast,
simply use the Nearest Neighbor (NN) method and thus predict values of monitor X with the
measurement of its nearest neighbor monitor. Columns (3) and (4) are based on values that
have been non-parametrically adjusted for all 3,650 day eﬀects, i.e., the nationwide daily mean
of a speciﬁc measure was ﬁrst removed from all monitor measurements. This exercise removes
time trends, but also the “true” correlation in measurements between monitors and has to be
regarded as a very conservative test.
Table F2 show results of a similar test for the generated extreme weather indicators and
conﬁrms the results of Table F1. Basically, one ﬁnds that the overall share of correctly predicted
heat and cold indicator values is above 99%, as is the share of correctly predicted zeros. Since
there is only a small percentage of extreme temperature events, “false positives” have a larger
impact on estimates than “false negatives.” Thus, it is reassuring to see that (i) IDW clearly
outperforms NN, and (ii) the share of false positives is low and less than 20% in the case of heat.
Finally, we calculate the Reliability Ratio (RR) αthat indicates the magnitude of measure-
ment errors and thus the attenuation bias (Hyslop and Imbens,2001):
Cov Z, ˜
Table F2: Share of Correctly Predicted Extreme Weather Indicators
Panel A: IDW
Overall Positives Zeros Reliability
Correct Predicted Correct Predicted Correct Predicted Ratio
Hot Day 0.9904 0.8133 0.9939 0.8071
Cold Day 0.9927 0.7680 0.9954 0.7634
Panel B: NN
Overall Positives Zeros Reliability
Correct Predicted Correct Predicted Correct Predicted Ratio
Hot Day 0.9881 0.7286 0.9937 0.72233
Cold Day 0.9908 0.6699 0.9951 0.6651
Source: German Meteorological Service (Deutscher Wetterdienst (DWD)). The underlying data
stems from up to 1,044 ambient weather monitors between 1999 and 2008. Panel A tests the predictive
quality of the Inverse Distance Weighting (IDW) interpolation method into the county space and Panel
B the Nearest Neighbor (NN) method. All numbers are shares of predicted relative to actual values. The
predicted value for monitor X are calculated using solely all surrounding monitors and assuming that
monitor X is non-existent. Column (1) reports the overall share of correctly predicted positive or negative
extreme weather indicator values. Column (2) reports the share χof correctly predicted positives and
column (3) the share δof correctly predicted zero values. Consequently, 1-χrepresent false positives and
1-δfalse negatives. Column (4) shows the Reliability Ratio (RR) αwhich indicates the ratio between
OLS and IV estimates and thus assesses the size of the potential attenuation bias (Hyslop and Imbens,
In a bivariate regression, the RR measures the attenuation bias and can thus be used to adjust
estimates. In a multivariate setting, the issue is less straightforward. Under the assumption that
covariates are uncorrelated with the measurement error, a speciﬁc RR—which is typically lower
than the RR for the bivariate case—can be derived. However, as we include covariates which
are prone to measurement error themselves, it is not possible to draw general conclusions about
the size of the bias (Maddala,1977). Nevertheless, it is reassuring that the RR is relatively
high and lies around 0.8 for the most important indicators. Because the RR assumes classical
measurement error, we follow Knittel et al. (2016) and carry out the following test: First,
we generate an ‘error’ variable for each monitor and weather measure by (i) predicting the
weather measure using all surrounding ambient monitors, similar to above. Then we (ii) take
the diﬀerence between the true ambient monitor measure and the predicted measure and label
it ’error.’ Figure F9 shows the mean measurement error in standard deviations by (a) the
maximum daily temperature recorded, and (b) the distance to the next ambient monitor.
Figure F9: Temperature Measurement Error by (a) Baseline Level and (b) Distance to Next Monitor
Note: Figure F9a shows the average measurement error of the IDW method by baseline temperature level. Figure
F9b shows the average measurement error of the IDW method by the distance to the next ambient monitor.
As seen, both scatterplots provide evidence for a very small degree of average measurement
errors. The dots are tightly lined up around the zero line on the y-axis. Not unexpectedly, in
Figure F9a, the plotted dots slightly deviate from the zero line for very high or low maximum
temperatures but the deviations are very small and below 0.1 of a standard deviation. In Figure
F9b, showing the measurement error as a function of the distance to the next monitor, the
curve is straight ﬂat. Overall, this additional test makes us very conﬁdent that the degree of
measurement error is likely to be small and, if existent, likely to be of classical form.
As a ﬁnal conceptual point, we would like to emphasize that the issue of introducing measure-
ment error when extrapolating point measures into space is methodologically not fundamentally
diﬀerent from the issue of unknown individual exposure to weather and pollution conditions.
We approximate the individual level exposure to weather and pollution on a given day by taking
inverse distance weighted averages of the daily measures of the next monitors. Even if we knew
the exact ambient weather and pollution conditions at the exact locations of residence of all
German residents, we would still (i) have to take daily averages in ambient conditions, (ii) lack
knowledge about the exact length, place, and time of the day spent outdoors by the individuals,
and thus (iii) deal with exposure-related measurement error of unknown form.