Heterogeneous Treatment Effects of Safe Water on Infectious Disease: Do Meteorological Factors Matter?

Cliometrica https://doi.org/10.1007/s11698-017-0169-6

ORIGINAL PAPER

Heterogeneous treatment effects of safe water on infectious disease: Do meteorological factors matter?

1 2 Kota Ogasawara • Yukitoshi Matsushita

Received: 2 June 2017 / Accepted: 13 November 2017 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2017

Abstract Mortality from waterborne infectious diseases remains a serious issue globally. Investigating the efficient laying plan of waterworks to mitigate the risk factors for such diseases has been an important research avenue for industrializing countries. While a growing body of the literature has revealed the mitigating effects of water-purification facilities on diseases, the heterogeneous treatment effects of clean water have been understudied. The present study thus focuses on the treatment effect heterogeneity of piped water with respect to the external meteorological environment of cities in industrializing Japan. To estimate the varying effects, we implement fixed-effects semivarying coefficient models to deal with the unob- servable confounding factors, using a nationwide city-level panel dataset between 1922 and 1940. We find evidence that the magnitude of safe water on the reduction in the typhoid death rate is larger in cities with a higher temperature, which is consistent with recent epidemiological evidence. These findings underscore the importance of the variations in the external meteorological conditions of the municipalities that install water-purification facilities in developing countries.

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11698- 017-0169-6) contains supplementary material, which is available to authorized users.

& Kota Ogasawara [email protected] Yukitoshi Matsushita [email protected]

1 Graduate School of Social Sciences, Chiba University, 1-33, Yayoicho, Inage-ku, Chiba 263-8522, Japan 2 Graduate School of Economics, Hitotsubashi University, 2-1, Naka, Kunitachi, Tokyo 186-8601, Japan 123 K. Ogasawara, Y. Matsushita

Keywords Climate Á Heterogeneous treatment effects Á Panel-data analysis Á Public health Á Semi/nonparametric estimation

JEL Classiﬁcation C14 Á I18 Á Q54 Á N55

1 Introduction

The global burden of waterborne infectious diseases remains considerable. Typhoid fever, for instance, caused 11.9 million illnesses and 129 thousand deaths in low- and middle-income countries in 2010 (Mogasale et al. 2014). Launching efficient social programs to reduce the risk factors for typhoid fever is thus an important agenda. Therefore, experience from countries that previously had developing status can offer valuable lessons for present-day industrializing societies. During the nineteenth and early twentieth centuries, typhoid fever was one of the most common waterborne infectious diseases in the world. In the USA, the impact of clean water on waterborne diseases has thus been widely studied. By using data on 13 major US cities in 1900–1936, Cutler and Miller (2005) found that the installation of clean water technologies led to the near-eradication of typhoid fever. Ferrie and Troesken (2008) also argued that the installation of water-purification technology and subsequent eradication of typhoid fever led to 35–56% of the reduction in the crude death rate in Chicago between 1850 and 1925. Moreover, the recent study by Beach et al. (2016) found that eliminating early-life exposure to typhoid fever increases later-life earnings, suggesting the long-run positive impact of safe water. Similar mitigating effects of clean water via water-purification systems are found in current developing countries (Nandi et al. 2017).1 While the growing body of the literature has revealed the mitigating effects of water-supply systems, the heterogeneous treatment effects of clean water have been understudied. Although a few studies investigate the varying effects of clean water on mortality rates across or within municipalities, most previous works have assumed that the effect of water-supply systems does not depend on the physical environment of societies.2 The important fact related to this point is that a growing body of the literature in epidemiology and bacteriology has found a significant association between meteorological conditions and the infection risk of waterborne infectious diseases

1 See also Jalan and Ravallion (2003), Gamper-Rabindran et al. (2010), and Devoto et al. (2012) for the cases of India, Brazil, and Morocco, respectively. Daley et al. (2015) provide an interesting evidence on the importance of residents’ perceptions of the functionality of current water and water sanitation systems in a remote Arctic Aboriginal community. 2 For example, Jalan and Ravallion (2003) found a variation in the effects of piped water on the prevalence and duration of diarrhea across mothers’ education levels. Ogasawara et al. (2016) also found varying effects of piped water with respect to poverty levels in prewar Tokyo. However, neither study directly modeled the nonlinearity of these effects. A few exceptions include Gamper-Rabindran et al. (2010), employed a panel quantile regression approach, and Ogasawara and Matsushita (2017), employed a semiparametric fixed-effects approach. However, we are the first to use the fixed-effects semivarying coefficient panel-data model to bridge the gaps in the body of the literature. 123 Heterogeneous treatment effects of safe water on infectious disease such as typhoid fever, which are directly improved by safe water. Infectious agents such as protozoa, bacteria, and viruses are devoid of thermostatic mechanisms. Thus, their temperature and fluid levels are determined by local meteorological conditions such as temperature and precipitation (Patz et al. 2003). For instance, a higher temperature drives the transmission of pathogens through the contamination of food and/or drinking water, whereas heavy rainfall is associated with outbreaks of enteric pathogens because of the contamination of water supplies, usually river water (Tseng et al. 2009).3 Moreover, a recently growing literature in economics has also demonstrated causal links between these meteorological conditions and human health (Descheˆnes 2014). A more recent study by Barreca et al. (2016) found striking evidence that the temperature-mortality gradient declined over the course of the twentieth century. In other words, the heavy mortality penalty for living in warm climates has slowly diminished. Considering this fact, it is then important to explore the mechanisms that have helped attenuate the temperature–mortality relationship. To bridge this gap in the body of knowledge, therefore, we first investigate the heterogeneous treatment effects of clean water with respect to meteorological factors by implementing a fixed-effects semivarying coefficient panel-data model. To ensure a reliable estimation, we use the nationwide city-level panel dataset with populations of above 20,000 between 1922 and 1940 in Japan, which covers approximately 90% of the total city population at that time.4 We find that the heterogeneity of the impacts of clean water is obvious with respect to temperature. While the estimate from the parametric specification suggests that a 1% increase in the coverage of tap water decreased the typhoid death rate by 0.117, that from the semiparametric specification suggests declines by 0.018, 0.137, and 0.158 per 10,000 people under the condition of the 5th, 50th, and 95th percentiles of temperature, respectively. This result suggests that the increased availability of clean water accounts for approximately 11, 40, and 61% of the improvements in the typhoid death rate from 1922 to 1940 in cities with an average annual temperature of around 8.9, 14.6, and 15:8 C, respectively. A set of robustness checks confirms our results. This article contributes to the literature in three main ways. The first contribution is to implement a semiparametric fixed-effects model to examine nonlinear effects in public health intervention. Heterogeneous treatment effects when evaluating social programs have attracted wide scholarly attention (Imai and Ratkovic 2013). For instance, recent studies have considered both treatment effect heterogeneity and multiple treatments and examined the most appropriate way in which to make statistical inferences (Athey and Imbens 2016; List et al. 2016; Lehrer et al. 2016). In accordance with these studies, we first extend the approaches of Fan et al. (2005) and Lee and Mukherjee (2014) to estimate a fixed-effects semivarying coefficient panel-data model by using a comprehensive city-level dataset than previous studies

3 See also Guzman Herrador et al. (2015), Wang et al. (2012), Dewan et al. (2013), and Listorti and Doumani (2001) for this epidemiological evidence. 4 The total city population is derived from the population in all cities reported in the vital statistics for each year (Appendix B in ESM). While Noheji and Kato¯(1954) and Ogasawara et al. (2016) investigated the impacts of water supply on mortality in Gifu and Tokyo, respectively, the present study aims to offer a more thorough discussion on this topic by using a comprehensive city-level dataset. 123 K. Ogasawara, Y. Matsushita

(Cutler and Miller 2005). A related minor contribution is that we investigate treatment effect heterogeneity in the context of post-reform covariates that are random. Predetermined characteristics such as racial and gender differences are usually used to estimate the heterogeneous effects (Flory et al. 2015a, b). By contrast, the present study uses meteorological factors as an exogenous grouping variable, which means that we do not need principal stratification methods. The second is to provide fundamental evidence on the relationship between the impact of water-supply facilities and the meteorological conditions in industrializing countries. In many developing countries, an efficient laying plan of water- supply facilities is still needed to mitigate the risk of waterborne disease infection, especially in Asia where the incidence rate of typhoid fever is highly concentrated (Banerjee and Duflo 2007; Javaid Siddiqui et al. 2006). Therefore, as a policy consideration, the variations in the effects of water purification on mortality rates that vary with the surrounding environment within a local municipality cannot be ignored. The result obtained in this study suggests that the social rate of return of water-purification facilities should vary across local municipalities, thus helping identify the areas where the intervention is needed to minimize the adverse effects of climate change on people’s health (Ebi et al. 2013; Rodo´ et al. 2013). Finally, this study complements the growing body of the literature focusing on the economic impacts of climate change (Descheˆnes and Greenstone 2007; Descheˆnes and Kolstad 2011). As described earlier, Barreca et al. (2016) found that a large part of the mortality penalty for living in regions that have higher temperatures attenuated over the twentieth century. Our finding highlights that the popularization of safe water among people could be one mechanism that rendered the climatic conditions that promote diseases less relevant. Our analytical results also bolster and support the identification strategy used in the recent study by Antman (2016), who analyzed the impacts of tea consumption on waterborne diseases in eighteenth-century England. The annual mean temperature in the Japanese archipelago is similar to those in Western Europe, the USA, and the southern part of Latin America.5 Therefore, our finding could have external validity for these countries. The rest of the paper is organized as follows. Section 2 briefly overviews the background knowledge on the water-supply systems and typhoid fever in industrializing Japan. Section 3 explains our semiparametric estimation technique. Section 4 describes the data used in the analysis. Section 5 provides the empirical results, and Sect. 6 provides the sensitivity analyses. Section 7 discusses them.

2 Background

2.1 Typhoid mortality

The construction of modern water-supply systems, which have ﬁltration plants and deliver water via steel pipes, gathered pace in Japanese cities from the early 1920s

5 See Appendix B (ESM) for the data source. Annual precipitation in Japan is also similar to those observed in the Southeast Asian countries. 123 Heterogeneous treatment effects of safe water on infectious disease until the weakening of the wartime regime after 1940. As shown by the dotted line in Fig. 1, the coverage of tap water, defined as the number of filtered water taps per 100 citizens, increased during the interwar period, especially in 1920s.6 Throughout the 1920s and 1930s, the majority of cities used slow-speed filtration technology. In the filtration process, water passes through layers of sand, thereby removing impurities and bacteria, including pathogens. The action of a membrane of microorganisms that forms on the surface of the sand layers is used in the purification process. By the early twentieth century, Japanese cities had established an agreed set of testing methods for waterworks and conducted bacteriological testing to ensure that the colonial forming unit (CFU) of bacteria was maintained below 100 CFU/ml of water at the tap point based on knowledge of modern microbiology (Exner et al. 2003, p. 13). Therefore, the water-purification technologies used in cities at that time reached levels that led to a reduction in the risk of waterborne infectious diseases.7 The eradication of representative waterborne infectious diseases such as typhoid fever in Japan was observed throughout the 1920s and 1930s. As shown in Fig. 1, the typhoid death rate, defined as the number of deaths due to typhoid fever per 10,000 people, began to decline continuously from the early 1920s. It improved by 0.93 (50.8%), from 1.83 in 1920 to 0.90 in 1940. In particular, in the major cities, this rate declined by 1.7 (57.6%), from 2.95 in 1920 to 1.25 in 1940. This clear decline in the typhoid death rate implies considerable improvements in the water- related environment in urban areas, because the incidence of typhoid fever is closely related to the availability of clean drinking water. Typhoid fever is indeed caused by the bacterium Salmonella enterica serotype Typhi (S. typhi). Since S. typhi is transmitted through the ingestion of contaminated food or water, people in societies with defective sanitary facilities are more likely to be infected by typhoid fever via fecal-contaminated drinking water or infected food (Crump and Mintz 2010). Thus, the development of clean drinking water facilities can significantly reduce typhoid death rates. S. typhi is an invasive bacterium that rapidly and efficiently passes through the intestinal mucosa of humans to reach the reticuloendothelial system. The onset of symptoms is marked by fever and malaise, including influenza-like symptoms with chills, a dull frontal headache, anorexia, nausea, poorly localized abdominal discomfort, a dry cough, and myalgia, but with few physical signs.8 Although the case-fatality rate of typhoid fever is reported to be approximately 10–20%, typhoid fever causes numerous complications, which can cause crucial damage in the end (see World Health Organization 2011). In fact, Ferrie and Troesken (2008) showed that this feature of typhoid fever causes the Mills–Reincke phenomenon, namely

6 See also Appendix A.1 (ESM) for details of older water-supply systems. Although old waterworks were installed in a few cities in the nineteenth century, those did not introduce any purification technology. Ogasawara et al. (2016) describe finer details of the waterworks in prewar Tokyo city. 7 A recent study by Ogasawara and Matsushita (2017) revealed that filtration technology significantly improved water quality. On average, the number of bacterial colonies decreased from roughly 470 CFU/ ml in source water to 14 CFU/ml in taps in Japanese cities, well below the criterion value of 100 CFU/ml. 8 See World Health Organization (2011) and Parry et al. (2002) for the finer details of the symptoms of typhoid fever. 123 K. Ogasawara, Y. Matsushita

3.25 9.5

3.00 9.0 8.5 2.75 8.0 2.50 7.5 2.25 7.0 2.00 6.5

1.75 6.0 5.5 1.50 5.0 1.25 4.5

1.00 4.0 Number of water taps per 100 people

Number of typhoid deaths per 10,000 people 0.75 3.5

6 19221923192419251926192719281929193019311932193319341935193 1937193819391940 Year Entire Japan Major cities Coverage of tap water

Fig. 1 Typhoid death rate and coverage of tap water. The dashed and solid line show the typhoid death rate in cities with a population above 100,000, and the rate in entire Japan, respectively. The dotted line shows the coverage of tap water per 100 people in our sample cities. These ﬁgures show the ﬁve-year moving average of the typhoid death rate, incidence rate, and coverage of tap water, respectively. Sources: Created by authors from the Bureau of the Home Department (1924–1938); Sanitary Bureau of the Department of Welfare (1939–1940); Population Bureau of the Department of Welfare (1942–1943); Statistics and Information Department, Minister’s Secretariat, Ministry of Health and Welfare (1999, p. 84). The sample cities are the cities that were recorded both in the Sanitary Bureau of the Home Department (1877–1938) and in the Sanitary Bureau of the Department of Welfare (1939–1940) that the declines in the typhoid death rate subsequently led to improvements in non- waterborne mortality such as deaths from respiratory or heart disease. They found that at least three non-waterborne deaths were prevented for every one typhoid death that was prevented by clean water in Chicago. Based on these evidence, a recent study concludes that the decline in typhoid mortality has long-run positive effects on human capital accumulation (Beach et al. 2016).

2.2 Meteorological conditions

The neglected but important epidemiological fact related to our topic of interest is the signiﬁcant link between meteorological conditions and typhoid fever infection.9 Since the bacteria are devoid of thermostatic mechanisms, their temperature and ﬂuid levels are affected by temperature and precipitation (Patz et al. 2003, p. 104) A higher temperature drives the transmission of pathogens through the contamination of food and/or drinking water (see Guzman Herrador et al. 2015). Heavy rainfall is also associated with outbreaks of enteric pathogens because of the contamination of water sources (see Wang et al. 2012; Dewan et al. 2013). In particular, this positive

9 See also an important study by Tseng et al. (2009), which ﬁnds the signiﬁcant relationship between climate change and dengue fever infection. 123 Heterogeneous treatment effects of safe water on infectious disease

1900 9000 35 300 Deaths Temperature

Patients Precipitation 275 1700 8000 30 250 1500 7000 25 225

1300 6000 200 20

1100 5000 175

15 150 900 4000

10 125 700 3000 100 Number of typhoid deaths 5 500 2000 Numbe of patients typhoid fever 75 Average precipitatoin in millimeters Average temperature in degrees Celsius

300 1000 0 50 January March May July September November January March May July September November February April June August October December February April June August October December (a) Monthly typhoid deaths and patients (b) Monthly temperature and precipitation

Fig. 2 Relationship between typhoid fever and the meteorological conditions. a Average monthly deaths and patients from typhoid fever in Japan between 1922 and 1927. b Average monthly temperature and precipitation in our sample cities between 1922 and 1927. Sources: Created by authors from the Sanitary Bureau of the Home Department (1929, pp. 56–57); JMA database (see Appendix B in ESM) association can be observed clearly as the seasonality of both the incidence and the death rate of typhoid fever (Javaid Siddiqui et al. 2006). To confirm these relationships, Fig. 2a illustrates the average monthly deaths and patients of typhoid fever between 1922 and 1927 in Japan.10 Overall, these large seasonal variations in typhoid epidemics are consistent with the findings of Sedgwick (1902) and Whipple (1908). As shown, the number of patients of typhoid fever begins to increase from June and peaks in August and September (i.e., during late summer in Japan). Given typhoid’s long gestation period, this finding suggests that most people contracted typhoid fever during the peak of summer in August. Accordingly, typhoid deaths were noted in September or even in October.11 Correspondingly, Fig. 2b shows the average monthly temperature and precipitation for the same period. As expected, the highest temperature was observed in August. This fact supports the abovementioned epidemiological evidence that a higher temperature in the summer provides a favorable environment for pathogens; thus, temperature is more likely to be positively correlated with the likelihood of infection. Considering this evidence, the improving effects of clean water on the risk of infection for typhoid fever may vary with temperature changes. However, we should be careful when drawing conclusions about the relationship with respect to precipitation. As shown in Fig. 2b, while precipitation increases by July as in the case of temperature because of the rainy season in June and July, it drops in August when typhoid infections become relevant. Therefore, it is unclear whether precipitation is positively correlated with the likelihood of infection. In Sect. 5, we see that the improving effects of safe water with respect to meteorological factors are clear for temperature but unclear for precipitation.

10 Since data on the monthly incidences of typhoid fever are not available after 1928, we present the data between 1922 and 1927. 11 The gestation period of Typhi and onset of symptoms of typhoid fever are usually 7–14 days and more than two weeks, respectively (Parry et al. 2002, p. 1774). Given this relatively long infection period (i.e., roughly one month), the lag between infection and deaths would be valid. 123 K. Ogasawara, Y. Matsushita

2100 10000 Deaths

1900 Patients 9000

1700 8000

1500 7000

1300 6000

1100 5000

900 4000 Number of typhoid deaths

700 3000 Numbe of patients typhoid fever

500 2000

300 1000

May,July, 1922 1922 May,July, 1923 1923 May,July, 1924 1924 May,July, 1925 1925 May,July, 1926 1926 May,July, 1927 1927 March, 1922 March, 1923 March, 1924 March, 1925 March, 1926 March, 1927 January, 1922 January, 1923 January, 1924 January, 1925 January, 1926 January, 1927 September,November, 1922 1922September,November, 1923 1923September,November, 1924 1924September,November, 1925 1925September,November, 1926 1926September,November, 1927 1927

Fig. 3 Monthly typhoid deaths and patients between 1922 and 1927. Source: Created by authors from the Sanitary Bureau of the Home Department (1929, pp. 56–57)

Figure 3 shows the monthly incidences of and deaths from typhoid fever between January 1922 and December 1927 in Japan. An important trend is that the seasonality of typhoid fever seems to be attenuated throughout the period. For instance, the standard deviations of both patients of and deaths from typhoid decline by approximately 40% from 2685 in 1922 to 1626 in 1927 and by 51% from 559 in 1922 to 272 in 1927, respectively. In fact, the correlation coefﬁcients between these standard deviations and the coverage rate of tap water reported in Fig. 1 are À 0:8354 (p value = 0.0384) and À 0:7986 (p value = 0.0568), respectively.12 This result suggests that the popularization of safe water attenuates the seasonality of typhoid fever. Finally, we provide a descriptive analysis of the association between the declines in typhoid mortality and diffusion of safe water. Figure 4 presents this relationship between the 1920s and 1930s in our sample cities (Sect. 4). We again separated the cities into two groups based on their mean temperature. Figure 4a shows the clear negative correlation between improvements in typhoid mortality and greater access to safe water in cities with a warm climate. For example, Akashi and Fukuyama, located in the southwest of the main Japanese island, experienced substantial improvements both in the typhoid death rate and in access to safe water. By contrast, that relationship in cities with cooler weather shown in Fig. 4b is somewhat vague. While Ashikaga, which is adjacent to the northeast region of Japan, experienced large improvements, the majority

12 Therefore, we used six observations between 1922 and 1927 to calculate the coefﬁcient for each typhoid measure. 123 Heterogeneous treatment effects of safe water on infectious disease

0.0 0.0 Oita Osaka NagaokaKiryu Nagasaki Tsu Wakamatsu(Fukusima) OnomichiShizuokaSakai IchinomiyaMiyazakiHamamatsu −0.5 Kobe −0.5 Hakodate Sapporo Aomori Kawasaki Nagoya Nagano Hachioji KofuAkita Toyohashi −1.0 Otsu −1.0 Tobata Otaru Yamagata Wakayama Sendai Hiroshima Koriyama Morioka −1.5 OkayamaSasebo Himeji −1.5 Okazaki UwajimaTokyo Marugame −2.0 Fukuoka TakamatsuMoji −2.0 Kyoto Kure Kochi Akashi Kushiro −2.5 Yokohama −2.5 Ashikaga Yawata −3.0 −3.0

Tottori −3.5 −3.5 Fukuyama Ube −4.0 −4.0 Fukushima

−4.5 −4.5

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 Decline in mean typhoid death rate, per 10,000 people Improvement in coverage of tap water, percentages Decline in mean typhoid death rate, per 10,000 people Improvement in coverage of tap water, percentages (a) Warmer cities (b) Cooler cities

Fig. 4 Improvements in the typhoid death rate and coverage of tap water by temperature class between the 1920s and 1930s. The decline in the mean typhoid death rate is the difference between the mean typhoid death rate in 1922–1929 and that in 1930–1940. The improvement in the mean coverage rate of tap water is the difference between the mean coverage rate in 1922–1929 and that in 1930–1940. Cities that experienced improvements in the typhoid death rate are divided into two groups (cool and warm) based on their mean annual temperature. The reference temperature is the sample mean of 13.85 (see Table 1) of cities with cooler climates did not experience more than a 1.5 decline in the mean typhoid death rate from the 1920s to the 1930s. These relationships suggest that the positive effects of improved access to safe water are stronger in cities that have a warm climate.13 The modern sewage system is also an important public health facility for reducing the risk of infectious diseases (Alsan and Goldin 2015; Kesztenbaum and Rosenthal 2017). Despite the rapid growth of the water-supply system in interwar Japan, the coverage of sewage systems among citizens continued to be very low during that period (Nagashima 2004). In fact, the share of households with ﬂushable toilets in 1935 was only 0.16% (see Appendix B in ESM for the data sources). In addition, a recent study found no signiﬁcant improving effects of these sewage systems on the mortality rate in Tokyo in 1930 (Ogasawara et al. 2016). Considering this evidence, we focus on the impacts of the water-supply systems on mortality rates.14

13 In Appendix A.2 (ESM), we confirm a similar relationship by using maps that illustrate the spatial distribution of the typhoid death rates in the 1920s and 1930s across the Japanese archipelago. We find that the cities in the southwestern part of Japan had relatively high initial typhoid death rates and experienced larger improvements in these rates between the 1920s and 1930s. By contrast, the cities in the northeastern part had relatively low initial rates and experienced smaller improvements. 14 Another possible path for typhoid infection may relate to the fly population, which builds up over several months from the survivors of the winter and early spring. However, the number of flies can be easily reduced during the continuous monsoons in Japan, as they are less likely to carry human fecal particles onto human food during heavy rain. In fact, our analytical result supports the evidence that the improving effects of safe water on typhoid fever are less likely to depend on precipitation (see Sect. 5). 123 K. Ogasawara, Y. Matsushita

3 Econometric framework

To examine the heterogeneous treatment effects of clean water on the typhoid death rate over meteorological factors, we implement a ﬁxed-effects semivarying coefﬁcient panel-data model. The proposed semiparametric model is as follows:

0 yit ¼ XitaðUitÞþZitb þ li þ vit; i ¼ 1; ...; n; t ¼ 1; 2; ...; Ti; ð1Þ where yit is the typhoid death rate, Xit is the coverage of tap water, Uit is the meteorological factors (i.e, temperature or precipitation), the vector Zit are the other control variables, and li are the unobserved individual effects that can be arbitrarily correlated with Xit, Uit and Zit. The marginal effect from Xit, which may depend on Uit in a nonlinear way, is described by aðÁÞ, where the unobserved individual- speciﬁc characteristics on the level of yit are controlled for by li. The nonlinear functional form aðÁÞ is assumed to be common over i and t. For simplicity, we do not explicitly show the year-ﬁxed effects in Eq. (1). Model (1) can be rewritten in matrix form:

Y ¼ MfX; aðUÞg þ Zb þ Dll þ V; ð2Þ where 0 1 0 1 0 1 0 y11 X11aðU11Þ Z11 B C B C B C B . C B . C B . C B . C B . C B . C B . C B . C B C B C B C B Z0 C Y ¼ B y1T1 C; MfX; aðUÞg ¼ B X1T aðU1T Þ C; Z ¼ B 1T C; B C B 1 1 C B 1 C B . C B . C B . C @ . A @ . A @ . A 0 ynT XnT aðUnT Þ Z 0 n 1 n n nTn iT1 0 ÁÁÁ 0 B C B 0 i ÁÁÁ 0 C B T2 C Dl ¼ B . . C; @ . .. A

00ÁÁÁ iTn 0 l ¼ðl1; ...; lnÞ , and iTi denotes a vector of the ones of dimension Ti. Let K denote a kernel function on R and h be a bandwidth. Set KhðuÞ¼

Kðu=hÞ=h and WhðuÞ¼diagðKhðU11 À uÞ; ...; KhðU1T1 À uÞ; ...; KhðUnTn À uÞÞ. We estimate model (1) by extending the methods proposed by Fan et al. (2005) to deal with unbalanced panel data. In particular, we estimate the parametric component, b, by using the proﬁle least-squares estimator proposed by Fan et al. (2005) and the nonparametric component, aðuÞ, by using the local linear estimator. The estimation is composed of the following three steps. aðuÞ 1. Given ðb0; l0Þ, we can estimate by ha_ðuÞ

123 Heterogeneous treatment effects of safe water on infectious disease ÀÁ aðuÞ 0 À1 0 ¼ D WhðuÞDu D WhðuÞðY À Zb À DllÞ; ha_ðuÞ u u where 0 1 U11 À u B X11 X11 C B h C B C B . . C B . . C B C B U1T1 À u C Du ¼ B X X C: B 1T1 h 1T1 C B C B . . C B . . C @ . . A U À u X nTn X nTn h nTn In particular, the estimator for aðuÞ is given by ÀÁ 0 À1 0 aðuÞ¼ð10Þ DuWhðuÞDu DuWhðuÞðY À Zb À DllÞ: 2. Substituting aðuÞ into model (1) yields the proﬁle least-squares estimator of the parameter ðb0; l0Þ: ^ 0 ðb; l^Þ¼arg min½Y À Zb À Dll À SðY À Zb À DllÞ b;l

½Y À Zb À Dll À SðY À Zb À DllÞ; where S is the smoothing operator 0 1 À1 0 0 B ðX11 0Þ D Whðu11ÞDu11 D Whðu11Þ C B u11 u11 C B C B . C B . C B À1 C S B 0 0 C ¼ B ðX1T1 0Þ Du Whðu1T1 ÞDu1T Du Whðu1T1 Þ C B 1T1 1 1T1 C B C B . C B . C @ . A À1 0 0 ðXnT 0Þ D WhðunT ÞDu D WhðunT Þ: n unTn n nTn unTn n

Hence, we obtain

0 0 b^ ¼ðZÃ MÃZÃÞÀ1ZÃ MÃYÃ; ð3Þ and

0 0 l^ ¼ðDÃ DÃÞÀ1DÃ ðYÃ À XÃb^Þ; ð4Þ

Ã Ã Ã Ã Ã where D ¼ðIN À SÞDl, Y ¼ðIN À SÞY, Z ¼ðIN À SÞZ, M ¼PIN À D Ã0 Ã À1 Ã0 n ðD D Þ D , IN denotes an identity matrix with dimension N and N ¼ i¼1 Ti. 3. Finally, aðuÞ is estimated by the local least-squares estimator

123 K. Ogasawara, Y. Matsushita

ÀÁ 0 À1 0 ^ a^ðuÞ¼ð10Þ DuWhðuÞDu DuWhðuÞðY À Zb À Dll^Þ:

Under certain regularity conditions, it can be shown that the estimators a^ðuÞ and b^ are consistent and asymptotically normal following the argument in Fan et al. (2005) and Lee and Mukherjee (2014).15 We use the standard normal kernel 2 1 Àu KðuÞ¼pffiffiffiffi e 2 . The bandwidth used is selected by Silverman’s ‘‘rule of thumb’’: 2p À1=ð5À0:5Þ h ¼ 1:06SUN , where SU denotes the sample standard deviation of Uit and we undersmooth the estimates to reduce the bias. Motivated by the proposed model, the following model was fitted to the data in our empirical analysis:

0 yit ¼ XitaðUitÞþZitb þ li þ kt þ thi þ vit; ð5Þ where li is the unobserved city-specific effects and kt is the unobserved year- specific effects. To relax the common trend assumption, we also added the interaction term between the city-fixed effects and linear time trend, thi. Despite the complexity of the econometric model, we can control for any time-invariant determinants of the city’s regulatory capacity, preference for public health policy, or geographical features as well as macroeconomic shocks by including the city- and year-fixed effects. Note that the standard partial linear approach cannot control for these unobserved factors, causing a certain scale of bias in the estimates. The important historical fact that relates to our identification strategy is that not only the variation in the timing of installation but also the transition of the coverage of water taps per capita was affected by both the geographical factors of cities and unpredictable events. Indeed, the timing of the adoption of clean water technology in US cities was greatly influenced by random components such as political issues (Cutler and Miller 2005). This kind of story is a common issue in laying water- supply systems in industrializing countries. The history of waterworks shows that the development of modern water-supply systems in prewar Japan was also influenced by natural disasters, the outbreak of war, economic fluctuations, and political issues such as water rights, residents’ opposition to laying plans, delayed land acquisition, and conflict between city councils, leading to the rejection of laying plans in the councils (Japan Water Works Association 1967; Ogasawara and Matsushita 2017). Following this historical evidence, we assume that after controlling for the appropriate covariates, city- and year-fixed effects, and city-

15 In particular, we have ffiffiffiffiffiffi 2 p h d Nh a^ðuÞÀaðuÞÀ c a€ðuÞ !Nð0; fðuÞÞ; as n; T !1; 2 2 i

2 2 2 R rv ðc1d0þ2c1c2d1þc2d2Þ 2 2 i where fðuÞ¼ f u E x2 , c1 ¼ c2=ðc2 À c1Þ, c2 ¼Àc1=ðc2 À c1Þ, ci ¼ u KðuÞdu, and R ð Þ ½ it i 2 di ¼ u K ðuÞdu. 2 A consistent estimator of rv is given by 1 r^2 ¼ ðY À MfX; a^ðUÞg À Zb^ À D l^Þ0ðY À MfX; a^ðUÞg À Zb^ À D l^Þ: v N l l

123 Heterogeneous treatment effects of safe water on infectious disease speciﬁc time trend, we can estimate the nonlinear effects of these systems on the typhoid death rate precisely by using our semiparametric panel-data model.

4 Data

We use panel data on 93 Japanese cities with a population above 20,000 between 1922 and 1940. The sample cities used herein are well distributed throughout Japan and cover approximately 90% of the population in all cities. Following previous studies, we use the typhoid death rate as a representative measure of the risk of infectious disease in an industrializing society (Ferrie and Troesken 2008; Beach et al. 2016). The typhoid death rate is defined as the number of deaths due to typhoid fever per 10,000 people. The incidence rate of typhoid fever, defined as the number of patients due to typhoid fever per 10,000 people, is also used as an alternative measure in the sensitivity analysis. The numbers of patients and deaths described above are taken from Japan’s official cause-of-death statistics, which were compiled under a comprehensive registration system (see Johnston 1995; Nagashima 2004; Drixler 2016). The data on typhoid deaths are reliable for the statistical analysis to the extent that they can capture the variations in typhoid fever epidemics. According to an old book written by a well-known Japanese doctor (Nukada 1925, pp. 143–154), at that time, typhoid infection had already been able to be identified by either the small rose spots (called barashin) or the Widal test, an agglutination test. A potential issue with the typhoid death statistics is not the social incentive to misreport like stillbirth (Drixler 2016) but the complications of typhoid fever. Since typhoid fever could subsequently cause deaths from non-waterborne diseases such as respiratory and meningococcal infectious diseases, these complications might have disturbed its diagnosis (Parry et al. 2002). Thus, for the placebo experiments, we use the epidemic cerebrospinal meningitis (CSM) death rate and scarlet fever death rate, defined as the number of either CSM or scarlet fever deaths per 10,000 people, to measure the risk of meningococcal and respiratory infectious diseases.16 As we see in Sect. 5, we found no statistically significantly negative effects on these non-waterborne death rates. Accordingly, we confirm that our typhoid fever statistics provide a reliable conclusion to our estimates. The key measure of the popularization of tap water in each city is the number of filtered water taps per 100 citizens.17 This study uses this measure as the share of a city’s population who received tap water in each year instead of the indicator

16 These experiments could be regarded as falsiﬁcation tests. This means that if these non-waterborne deaths did not include a set of deaths from typhoid fever, the estimated effects of safe water on the CSM death rate and scarlet fever death rate should be negligible. 17 The taps for piped water without ﬁltration technology are not considered here as these waterworks could not provide clean water and were sometimes contaminated (Fukushima et al. 1940). 123 K. Ogasawara, Y. Matsushita

0.6 0.0015

0.4 0.0010 Density Density

0.2 0.0005

0.0 0.0000 6 7 8 9 10 11 12 13 14 15 16 17 18 500 1000 1500 2000 2500 3000 Average temperature in degree Celsius Annual precipitation in millimeters (a) Temperature (b) Precipitation

Fig. 5 Distribution of temperature and precipitation. Temperature is the average annual temperature (Celsius). Precipitation is annual precipitation (millimeters) variable of the installation of clean water technology, which is widely used in previous studies (Cutler and Miller 2005).18 This continuous measure of clean water accessibility enables us to analyze the nonlinear effects of modern water-supply systems by using the proposed semiparametric smooth coefﬁcient estimation technique. Regarding the meteorological variables, we compiled the average annual temperature and annual precipitation from the database of the Japan Meteorological Agency (JMA). Since our sample cities are scattered across the Japanese archipelago, variations in the meteorological conditions are ensured, as shown in Fig. 5. As explained in Introduction, we estimate treatment effect heterogeneity in the context of post-reform covariates that are random. This is somewhat unique since the groups are exogenous, as we use meteorological factors, rather than being based on predetermined characteristics such as racial and gender differences. Thus, we do not need principal stratiﬁcation methods. Using this type of method is an additional contribution of the present study. Regarding the control variables, we use the natural logarithm of the total population, shares of the population aged 0–14, 15–24, 25–59, and 60? years, and the sex ratio of the population aged 0–14, 15–24, 25–59, and 60? years to control for the demographic characteristics of the cities.19 The natural logarithm of total revenue, number of doctors per 1,000 people, and proportion of factory workers per 100 people are used to control for the heterogeneities of socioeconomic status in the cities. We also include average humidity from the JMA database as an additional

18 Since clean water improves overall hygiene levels via clean drinking water itself, handwashing, food washing, bathing, and laundry, the popularization of tap water may decrease the risk of typhoid fever infection (World Health Organization 2011). Therefore, the larger the value of the coverage of tap water, the more citizens are able to access clean water. Note that we cannot use the number of households with water taps or the number of supplied people here; thus, the coverage rate is defined by using the number of water taps. Since the average number of family members in cities at that time was approximately 4.6 people, 10% of the coverage may imply that roughly 40% of households had water taps. 19 Since children above five years would typically be susceptible to typhoid fever, we singled out this age group. We have confirmed that the main results are unchanged if we use the shares of population aged 0–5, 6–14, 15–24, 25–59, and 60?. See Appendix C.2 (ESM) for the results. 123 Heterogeneous treatment effects of safe water on infectious disease

Table 1 Summary statistics Mean SD Min Max

Dependent variables Typhoid death rate 1.93 1.68 0.00 14.32 Incidence rate of typhoid fever 10.27 7.81 0.00 72.27 CSM death rate 0.09 0.23 0.00 2.40 Scarlet fever death rate 0.08 0.12 0.00 0.98 Variables of interest Coverage of tap water (%) 6.63 3.99 0.00 18.05 Temperature (Celsius) 13.85 2.06 6.71 17.45 Precipitation (millimeters) 1485.22 417.38 593.20 2877.80 Additional control variables Population (ln transformation) 11.49 1.00 10.00 15.73 Share of the population aged 0–14 years (%) 33.75 2.60 27.35 43.53 Share of the population aged 15–24 years (%) 22.33 2.83 11.25 33.17 Share of the population aged 25–59 years (%) 38.21 1.97 33.06 43.27 Share of the population aged 60? years (%) 5.70 1.28 3.13 9.56 Sex ratio of the population aged 0–14 years 0.99 0.05 0.52 1.30 Sex ratio of the population aged 15–24 years 1.02 0.22 0.12 1.67 Sex ratio of the population aged 25–59 years 0.95 0.09 0.66 1.18 Sex ratio of the population aged 60? years 1.34 0.12 0.71 1.68 Coverage of doctors (%) 0.78 0.26 0.06 2.15 Proportion of factory workers (%) 3.57 2.47 0.24 12.47 Revenue per capita (yen) (ln transformation) 2.83 0.52 0.48 4.90 Humidity (%) 75.03 2.91 67.50 83.92

The numbers of cities and observations for the typhoid death rate are 93 and 1239, respectively. The numbers of cities and observations for the CSM and scarlet fever death rates are 72 and 990, and 79 and 1060, respectively. The share of the population aged 60? years is used as the reference group. Details of the data sources of each variable used in the regression are provided in Appendix B (ESM) meteorological factor to control for the possibility of a relationship between moisture and the activity of Salmonella (Listorti and Doumani 2001). Table 1 shows the summary statistics of the variables. The ﬁner details of the data sources are described in Appendix B (ESM).

5 Results

We begin our empirical analysis by studying the effects on the typhoid death rate. Figure 6 presents the baseline results. Overall, the estimated effects of clean water are signiﬁcantly negative. The estimate from the parametric speciﬁcation, which is shown as the red line in Fig. 6a, shows that a 1% increase in the coverage of tap water decreased the typhoid death rate by 0.117. By contrast, the marginal effects at the pth quantiles for p ¼

123 K. Ogasawara, Y. Matsushita

0.10 0.10 0.08 0.08 0.05 0.05 0.03 0.03 0.00 0.00 −0.03 −0.03 −0.05 −0.05 −0.07 −0.07 −0.10 −0.10 −0.12 −0.12 −0.15 −0.15 −0.17 −0.17 −0.20 −0.20 Marginal Effects −0.22 Marginal Effects −0.22 −0.25 −0.25 −0.27 −0.27 −0.30 −0.30 −0.33 −0.33 −0.35 −0.35 −0.38 −0.38 −0.40 −0.40 6 7 8 9 10 11 12 13 14 15 16 17 18 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 Average annual temperature in degrees Celsius Annual precipitation in millimeters (a) Temperature (b) Precipitation

Fig. 6 Marginal effects of safe water on the typhoid death rate. The black solid and dotted lines show the marginal effects and their 95% confidence intervals from the fixed-effects semivarying coefficient estimation. The red solid line shows the marginal effects from the parametric specification. All control variables, city- and year-fixed effects, and the city-specific time trend are included in both specifications

0:05; 0:25; 0:5; 0:75; 0:95 from the semiparametric specification are À 0:018, À 0:130, À 0:137, À 0:143, and À 0:158, respectively. This means that the estimated effects in the upper percentile are approximately 7 times greater than those observed in the lower percentile. The same figure also highlights the disparity in the estimates between the parametric and semiparametric specifications. Although the estimates in the parametric specification are close to those in the semiparametric specification around the mean value of temperature, i.e., approximately 14 C, the parametric model fails to capture the nonlinear effects of the systems at both the lower and the higher quantiles, especially less than 12 and more than 15 C. Regarding precipitation, however, Fig. 6b is less likely to support the evidence on the heterogeneity in the effects of clean water, despite the significantly negative effects. The marginal effects at higher ranges of precipitation (more than 2700 millimeters) drop drastically by approximately 0.27 from À 0:12 to À 0:39. Although this result may be consistent with the epidemiological evidence that argues the heavy rainfall is associated with outbreaks of enteric pathogens because of water contamination (Sect. 2), the confidence intervals are large at the right end of precipitation. Thus, we must be careful not to conclude that the impact of water- purification technology is greater in cities with higher precipitation where the source water is frequently contaminated by heavy rain. We next check the sensitivity of the variable definition by using an alternative measure of the virulence of typhoid fever. We define the incidence rate of typhoid fever as the number of patients per 10,000 people. This means that the results for this measure should be similar to those for the typhoid death rate in Fig. 6. Figure 7 presents the results for the incidence rate with the same order of graphs. Figure 7a shows that the marginal effects at the pth quantiles for p ¼ 0:05; 0:25; 0:5; 0:75; 0:95 from the semiparametric specification are 0.043, À 0:502, À 0:529, À 0:544, and À 0:688, respectively. Clearly, the results are similar to our main results obtained by using the typhoid death rate as the dependent variable reported in Fig. 6a. This finding supports the robustness of our main estimates. Figure 7b also illustrates the

123 Heterogeneous treatment effects of safe water on infectious disease

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 −0.2 −0.2 −0.4 −0.4 −0.6 −0.6 −0.8 −0.8 Marginal Effects −1.0 Marginal Effects −1.0 −1.2 −1.2 −1.4 −1.4 −1.6 −1.6 −1.8 −1.8 −2.0 −2.0 6 7 8 9 10 11 12 13 14 15 16 17 18 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 Average annual temperature in degrees Celsius Annual precipitation in millimeters (a)Temperature (b) Precipitation

Fig. 7 Marginal effects of safe water on the incidence rate. The black solid and dotted lines show the marginal effects and their 95% confidence intervals from the fixed-effects semivarying coefficient estimation. The red solid line shows the marginal effects from the parametric specification. All control variables, city- and year-fixed effects, and the city-specific time trend are included in both specifications similar shape of the marginal effects shown in Fig. 6b, confirming fuzzy nonlinearity with respect to precipitation. To further explore the association between precipitation and the impacts of safe water, we limit our sample to the 50 cities that used surface water as their water source. Since heavy rainfall mainly affects surface water sources compared with groundwater sources (Tornevi et al. 2014), limiting the sample to those cities that relied on surface water may elucidate that relationship. Figure 8a, b indicates the results for the typhoid death rate and incidence rate, respectively. The marginal effects are stronger than those for the full sample reported in Figs. 6a and 7b. The effects for the typhoid death rate and incidence rate estimated from the parametric specifications are approximately À 0:2 and À 0:85, respectively, which are roughly twice as great as those for the full sample. This result suggests that these cities benefitted from greater improvements in the infection risk of typhoid fever by the installation of water-supply systems because the initial quality of the water source might have been lower than that in the other cities because of the vulnerability of surface water to the external environment. The nonlinear relationship is vague both in Fig. 8b and in Fig. 8b. The narrow relationship between the marginal effects of safe water and precipitation is consistent with our finding in Fig. 2. While this result partly suggests that water contamination that could increase the risk of typhoid infection was caused regardless of the level of precipitation, the confidence intervals are still large at the right end of precipitation. This finding implies that a small number of observations around these higher ranges of precipitation might have disturbed the estimation. Therefore, further analyses are needed to explore the relationship between the impacts of safe water and precipitation. Finally, to check the validity of our main result for temperature in Figs. 6a and 7a, Fig. 9 presents the results for the falsification tests using the CSM and scarlet fever death rates. As explained in Sect. 4, the infection risks for meningococcal and respiratory infectious diseases are less likely to depend on clean water accessibility as those are not waterborne infectious diseases. This fact suggests linear relationships between the CSM and scarlet fever death rates and 123 K. Ogasawara, Y. Matsushita

0.05 0.03 0.30 0.00 0.15 −0.02 0.00 −0.05 −0.15 −0.07 −0.10 −0.30 −0.12 −0.45 −0.15 −0.60 −0.17 −0.75 −0.20 −0.22 −0.90 −0.25 −1.05 −0.27 −1.20 −0.30 −0.32 −1.35 −0.35 −1.50 Marginal Effects −0.37 Marginal Effects −1.65 −0.40 −1.80 −0.42 −0.45 −1.95 −0.47 −2.10 −0.50 −2.25 −0.52 −0.55 −2.40 −0.57 −2.55 −0.60 −2.70 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 Annual precipitation in millimeters Annual precipitation in millimeters (a)Typhoid death rate (b) Incidence rate

Fig. 8 Marginal effects of safe water with respect to precipitation for the cities using surface water source. The black solid and dotted lines show the marginal effects and their 95% confidence intervals from the fixed-effects semivarying coefficient estimation. The red solid line shows the marginal effects from the parametric specification. All control variables, city- and year-fixed effects, and the city-specific time trend are included in both specifications

0.040 0.040 0.035 0.035 0.030 0.030 0.025 0.025 0.020 0.020 0.015 0.015 0.010 0.010 0.005 0.005 0.000 0.000 −0.005 −0.005 −0.010 −0.010 Marginal Effects Marginal Effects −0.015 −0.015 −0.020 −0.020 −0.025 −0.025 −0.030 −0.030 −0.035 −0.035 −0.040 −0.040 6 7 8 9 10 11 12 13 14 15 16 17 18 6 7 8 9 10 11 12 13 14 15 16 17 Average annual temperature in degrees Celsius Average annual temperature in degrees Celsius (a) CSM death rate (b) Scarlet fever death rate

Fig. 9 Falsification tests for the CSM and scarlet fever death rates. The black solid and dotted lines show the marginal effects and their 95% confidence intervals from the fixed-effects semivarying coefficient estimation. The red solid line shows the marginal effects from the parametric specification. All control variables, city- and year-fixed effects, and the city-specific time trend are included in both specifications waterworks with respect to temperature. Figure 9a, b presents the results for the CSM and scarlet fever death rates, respectively. The estimates are mostly linear and do not show a decreasing trend across regions in contrast to the results for the typhoid death rate in Fig. 6a. The small but significantly negative effects around 10– 15 C, where the density of temperature is relatively high (see Fig. 5a), are not unusual, as improvements in sanitary conditions by providing safe water can reduce the risk of non-waterborne mortality (Ray 2014).20 Overall, however, these negative effects are negligible as the estimates from the parametric specifications for the

20 Another possibility is the Mills–Reincke phenomenon, which emphasizes the case in which improvements in waterworks can also improve deaths from water-related diseases, including respiratory infections. See Ferrie and Troesken (2008). 123 Heterogeneous treatment effects of safe water on infectious disease

Table 2 Magnitudes of the effects of safe water by temperature Temperature Ranges (C) Average marginal Average improvements Magnitudes (%) effects (AME) [AME Â Water/TDR] Water (%) Typhoid death rate (TDR)

Low 8.9 ± 0.5 - 0.028 6.785 1.653 11.29 Middle 14.6 ± 0.5 - 0.133 4.780 1.607 39.54 High 15.8 ± 0.5 - 0.147 4.789 1.153 61.19

Low, middle, and high indicate the temperature at the 5th, 50th, and 95th percentiles, respectively (8.9, 14.6, and 15:8 C). Average marginal effect is the average value of the mean marginal effects of each city. Average improvements in the coverage of tap water (Water) are the average value of the improvement in the coverage of each city. Average improvements in the typhoid death rate (TDR) are the average value of the improvement in the typhoid death rate of each city. Magnitude is deﬁned as the contribution of waterworks (i.e., AME Â Water) divided by the average improvements in the TDR, percentage points. The numbers of cities with low, middle, and high temperatures are 3, 25, and 13, respectively

CSM and scarlet fever death rates are close to zero, i.e., À 0:008 and À 0:003, and statistically insignificant, respectively (see Appendix C.1 in ESM for the results). We turn to illustrate the heterogeneities in the magnitude of the estimated effect of water-supply systems on the typhoid death rate. As discussed, the estimated coefficient of the coverage of tap water in the parametric specification suggests that a 1% increase in the coverage of tap water decreased the typhoid death rate by 0.117 (Appendix C.1 in ESM). The median of the coverage of tap water across our sample cities increased from 3.83% in 1922 to 8% in 1940. Thus, clean water helped improve 0.49 per thousand of the typhoid death rate (i.e., 0:117 Â 4:17). Based on our estimate, therefore, the increased availability of clean water accounts for approximately 25.8% of the total decline in the typhoid death rate from 3.13 to 1.24.21 Table 2 presents the magnitudes of the estimated effects from our main results for the semiparametric specification with respect to temperature (Fig. 6a). Column (3) shows that the average marginal effects for each city suggest that a 1% increase in the coverage of tap water decreased the typhoid death rate by 0.028, 0.133, and 0.147 around the 5th, 50th, and 95th percentiles (8.9, 14.6, 15:8 C) of temperature, respectively. Column (4) shows that the average improvements in the coverage of tap water around these points of temperature are 6.79, 4.78, and 4.79%, respectively, Column (5) shows that the improvements in the typhoid death rate are 1.65, 1.61, and 1.15, respectively. As Column (6) shows, this implies that the increased availability of clean water accounts for approximately 11.3, 39.5, and 61.2% of the improvements in the typhoid death rate, respectively. Overall, we find that heterogeneity in the effects of safe water with respect to the meteorological variables. While the dependency of clean water with respect to precipitation is unclear, the impact of safe water clearly depends on temperature. The improving effects of safe water increase until 12 C and reach À 0:15. These effects stay around À 0:13 between 12 and 15 C, which is close to that estimated in

21 Using the mean value of the coverage of tap water does not change this estimate with approximately 24% of the total decline in the typhoid death rate. 123 K. Ogasawara, Y. Matsushita the parametric speciﬁcation. For the range of temperature above 15þ, however, the improving effects begin to increase again and show a maximum value around À 0:23, which is approximately twice as great as the estimated effect at the mean from the parametric speciﬁcation. Similarly, the magnitudes of clean water are also larger in cities with a higher temperature than cities with a lower temperature. The increased accessibility of clean water at the 5th and 95th percentiles of temperature (approximately 9 and 16 C) accounts for roughly 11 and 61% of the improvements in the typhoid death rate, respectively, suggesting large (i.e., approximately 550%) disparities in the magnitudes of waterworks across cities.

6 Robustness

6.1 Alternative speciﬁcations

Finally, a set of sensitivity checks is conducted to confirm our main results. First, in order to check the robustness of our baseline specification for the typhoid death rate, we also run regressions with alternative specifications. Table 3 presents the results. Column (1) presents the results for the dynamic panel-data model that includes the lagged dependent variable. Column (2) presents our full flexible specification that includes the interaction terms between the control variables and year-fixed effects instead of the control variables. Column (3) presents the results for the dynamic panel-data model with the full flexible specification. Column (4) presents the results for the specification reported in Column (3) but clusters the standard error at the prefecture level to deal with the spatial correlations. As reported in Columns (1), (3), and (4), the estimated coefficient of the lagged dependent variables is small and statistically insignificant. This result supports the validity of our baseline static models used. Moreover, the estimated coefficient of the coverage of tap water is stable across the flexible specifications that allow the effects of all the control variables to vary across years. This result adds strong evidence to our baseline specification, whichassumesthattheeffectsofthecontrols are stable across our sampled periods. The estimates range from À 0:146 to À 0:112, which are close to our baseline estimate of À 0:117 (Appendix C.1 in ESM). Table 4 presents the results for another specification to check for omitted variable bias. Column (1) presents the result for the specification including the typhoid death rate in the nearest neighboring city.22 This specification is considered because the transmission from neighboring areas might have played a role in the number of typhoid deaths in a certain city. As shown in the column, the estimated coefficient of the typhoid death rate in the nearest neighboring city is not statistically significant, whereas the estimate of the water variable shows a similar

22 Note that the number of observations in Columns (1) and (2) is lower because of the unbalanced dataset. 123 Heterogeneous treatment effects of safe water on infectious disease

Table 3 Results for the alternative speciﬁcations: dynamic panel-data models and clustering Typhoid death rate

(1) (2) (3) (4)

Coverage - 0.146*** - 0.112*** - 0.131*** - 0.131*** (0.055) (0.042) (0.046) (0.036) Lagged typhoid death rate 0.061 - 0.029 - 0.029 (0.049) (0.054) (0.052)

Control variables Yes No No No Control variables Â year-fixed No Yes Yes Yes effects City- and year-fixed effects Yes Yes Yes Yes City-specific linear time trend Yes Yes Yes Yes Clustering City City City Prefecture Observations 1080 1239 1080 1080

Coverage of tap water (Coverage) is the number of water taps per 100 total population. Dependent variable is the typhoid death rate ***, **, and * represent statistical signiﬁcance at the 1, 5, and 10% levels, respectively. Cluster-robust standard errors are in parentheses

Table 4 Results for the alternative speciﬁcations: Potential omitted variable bias Typhoid death rate

(1) (2) (3)

Coverage - 0.095** - 0.093** - 0.108** (0.046) (0.046) (0.046) Typhoid death rate in nearest neighboring city 0.031 0.073 (0.063) (0.077) Typhoid death rate in nearest neighboring city Â - 0.002** Elevation (in meters) (0.001) Indicator variable for the Great Kanto¯ Earthquake 1.703 (1.070) Control variables Yes Yes Yes City- and year-ﬁxed effects Yes Yes Yes City-speciﬁc linear time trend Yes Yes Yes Observations 946 946 1239

123 K. Ogasawara, Y. Matsushita magnitude to that of our baseline parametric specification reported in Fig. 6. Column (2) adds the interaction term between the typhoid death rate in the nearest neighboring city and the elevation of the city to address the potential effects of topography.23 The transmission effect from neighboring areas could be attenuated in cities located at higher altitudes because of transport difficulties. Nonetheless, all the sampled cities have railway and/or marine transportation (Ministry of Railways 1930), and thus cities at higher elevation might have been less likely to be contagious. As expected, the estimated coefficient of the interaction term is statistically significantly negative. However, the main effect, captured in the estimated coefficient of the typhoid death rate in the nearest neighboring city, is again statistically insignificant, whereas the estimate of the water variable is largely unchanged. Finally, Column (3) presents the result for the specification that includes the indicator variable for Tokyo, Yokohama, and Kawasaki between 1923 and 1925, which were hardest hit by the Great Kanto¯ Earthquake of 1923.24 Considering the potential persistent effects of the earthquake on the sanitary conditions, we take a relatively long treatment period from 1923 to 1925.25 While the estimated coefficient of this indicator variable is positive but not statistically significant, the estimate of the water variable still shows a similar magnitude to that of our baseline estimate. These results suggest that neither transmission from neighboring areas nor the earthquake that hit a specific region of the Japanese archipelago affected our sampled cities. In addition to the alternative specifications, Appendix C.1 (ESM) also confirms that our main result is largely unchanged if we take the prefecture-level unobserved trend and spatial correlations. These results finally confirm that the spatial correlation from the sorting does not potentially matter in our analysis.

6.2 Falsiﬁcation tests

Second, in order to check the validity of the common trend assumption, we conduct falsiﬁcation tests by including the leads of the coverage of tap water in years t þ 1, t þ 2, t þ 3, and t þ 4 in our baseline parametric speciﬁcation.

23 Distances are measured between the city ofﬁces by using geospatial information. Elevation is measured by using GSI Maps of the Geospatial Information Authority of Japan (see Appendix B in ESM for the data source). The mean distance value between a certain city and its nearest neighboring city is 36 km. The elevation ranges from 1.0 to 457.5 m with a median value of 7.3 m. As shown in Fig. A.1 (ESM), most Japanese cities are coastal cities, whereas several cities are located at higher altitudes. 24 See Nagashima (2004) for a discussion on the potential adverse effects of the Great Kanto¯ earthquake of 1923 on typhoid fever in Tokyo. 25 See also Hunter (2014) and Hunter and Ogasawara (2016) for the detailed discussions on the relatively short-run impacts of the earthquake of 1923. 123 Heterogeneous treatment effects of safe water on infectious disease

Table 5 Falsiﬁcation tests using the lead values of the coverage rate Typhoid death rate

(1) (2) (3) (4)

Coveragetþ4 0.006 (0.052)

Coveragetþ3 - 0.053 - 0.052 (0.051) (0.044)

Coveragetþ2 - 0.027 - 0.042 - 0.078* (0.057) (0.053) (0.044)

Coveragetþ1 0.079 0.068 0.047 0.000 (0.069) (0.060) (0.056) (0.050)

Coveraget - 0.210*** - 0.172*** - 0.141** - 0.126** (0.073) (0.063) (0.057) (0.055) Control variables Yes Yes Yes Yes City- and year-fixed effects Yes Yes Yes Yes City-specific linear time trend Yes Yes Yes Yes F statistics p values for the joint 0.5237 0.2001 0.1845 significance on the lead values Observations 705 815 939 1080

The estimates are shown in Table 5. Overall, the estimated coefficients of the lead variables are considerably weak and statistically insignificant in most specifications. This result supports the evidence that the parallel-trend assumption of our fixed-effects model should hold. In addition, the estimated coefficients of the coverage of tap water at year t remain significantly negative, confirming the robustness of our baseline result.

6.3 Alternative bandwidth values

Third, we estimate our semiparametric specifications under alternative bandwidth À1=ð5À0:1Þ values with c ¼ 0:8 and c ¼ 1:2 for h ¼ c Â 1:06SUN to check the sensitivity to bandwidth selection. Figure 10 shows the results for the typhoid death rate under values for c ¼ 0:8 and c ¼ 1:2. Overall, although the estimates under c ¼ 0:8 show slightly waved surfaces, the results are similar to those of our baseline results reported in Fig. 6a, b. These figures finally confirm the robustness of our main findings from the baseline semiparametric specifications.

123 K. Ogasawara, Y. Matsushita

0.10 0.10 0.08 0.08 0.05 0.05 0.03 0.03 0.00 0.00 −0.03 −0.03 −0.05 −0.05 −0.07 −0.07 −0.10 −0.10 −0.12 −0.12 −0.15 −0.15 −0.17 −0.17 −0.20 −0.20 Marginal Effects Marginal Effects −0.22 −0.22 −0.25 −0.25 −0.27 −0.27 −0.30 −0.30 −0.33 −0.33 −0.35 −0.35 −0.38 −0.38 −0.40 −0.40 6 7 8 9 10 11 12 13 14 15 16 17 18 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 Average annual temperature in degrees Celsius Annual precipitation in millimeters (a) Temperature (c =0.8) (b) Precipitation (c =0.8)

0.10 0.10 0.08 0.08 0.05 0.05 0.03 0.03 0.00 0.00 −0.03 −0.03 −0.05 −0.05 −0.07 −0.07 −0.10 −0.10 −0.12 −0.12 −0.15 −0.15 −0.17 −0.17 −0.20 −0.20

Marginal Effects −0.22 Marginal Effects −0.22 −0.25 −0.25 −0.27 −0.27 −0.30 −0.30 −0.33 −0.33 −0.35 −0.35 −0.38 −0.38 −0.40 −0.40 6 7 8 9 10 11 12 13 14 15 16 17 18 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 Average annual temperature in degrees Celsius Annual precipitation in millimeters (c) Temperature (c =1.2) (d) Precipitation (c =1.2)

Fig. 10 Marginal effects of safe water on the typhoid death rate under alternative bandwidth values. The black solid and dotted lines show the marginal effects and their 95% confidence intervals from the fixed- effects semivarying coefficient estimation. The red solid line shows the marginal effects from the parametric specification. All control variables, city- and year-fixed effects, and the city-specific time trend are included in all specifications

7 Discussion

While most previous works have assumed that the effect of clean water is constant across neighboring environments, this study examined the extent to which the effects of safe water on the typhoid death rate vary with the external meteorological conditions. To estimate the heterogeneous treatment effects of water-supply systems, we first expanded a fixed-effects semiparametric smooth coefficient model. By using a city- level panel dataset of Japanese cities, we found that the impact of clean water depends on temperature. While the estimate from the parametric specification suggests that the contribution of clean water was approximately 26% of the decline in the typhoid death rate from 1922 to 1940, the estimates from our semiparametric fixed-effects model show that the increased availability of clean water accounts for approximately 11, 40, and 61% of the improvements in the typhoid death rate in cities with an average annual temperature around 8.9, 14.6, and 15:8 C, respectively. We also confirm these heterogeneities by using an alternative specification for the incidence rate of typhoid fever.

123 Heterogeneous treatment effects of safe water on infectious disease

These findings are considered to be important contributions to the literature for two reasons. First, our results are highly consistent with the findings from the epidemiological studies discussed in Sect. 2; a higher temperature increases the likelihood of typhoid fever infection. Since filtration technology can provide pure and safe water to citizens regardless of the temperature, cities with a higher temperature might have experienced a greater reduction in the typhoid death rate at that time. By contrast, cities in cold regions and/or periods benefited less from the installation of water-purification facilities because the likelihood of infection might have been low in the cooler areas and/or years. Accordingly, we can conclude that the contribution of clean water depends on the external meteorological conditions of the municipalities that install water-supply systems. This finding suggests that the authorities must take these variations in the external environment into account when estimating the benefit from the installation and popularization of clean water technologies. Second, as the effects of clean water vary across temperature ranges, the parametric specification may be unable to capture all the effects of water-supply systems. The estimated effects at the upper percentile of temperature from the semiparametric specification are approximately 1.4 times greater than the effects from the parametric specification (0.158 / 0.117). Regarding the magnitudes, this disparity becomes 2.4 times (61.2 / 25.8), which is considerably large. Local municipalities may therefore overestimate (underestimate) the effects of water- supply systems relative to the mean effect if a system is installed in an area with a lower temperature (higher temperature). This result suggests that the semiparametric and/or polynomial specification can offer better insights into the impacts of clean water facilities than standard parametric models, especially when the sample has large variations in the external environment. The semiparametric smooth coefficient estimation we propose could thus offer rich information on the varying effects of waterworks to local municipalities. As discussed in Introduction, the global burden of typhoid fever, which causes lasting effects on human capital accumulation, remains considerable. An efficient laying plan of waterworks is thus needed to improve human health in developing countries (Banerjee and Duflo 2007). Our findings can help identify the areas in which the intervention is needed to minimize the adverse effects of climate change on people’s health (Ebi et al. 2013; Rodo´ et al. 2013; Descheˆnes 2014). As for the methodological aspects, we extended the existing semiparametric approach to estimate a more general semiparametric panel-data model that avoids imposing the strong restrictions assumed in parametric panel-data models. We found evidence that misspecified parametric models may provide misleading inferences. Our findings can thus add insights into heterogeneous treatment effects when evaluating social programs (Imai and Ratkovic 2013). Finally, we first to highlight the importance of external climatic conditions in the historical mortality declines (Cutler and Miller 2005; Ferrie and Troesken 2008; Barreca et al. 2016).

Acknowledgements This study was supported by JSPS KAKENHI Grant No. 16K17153. There are no conﬂicts of interest to declare. The authors wish to thank the editor, two anonymous referees, and Badi Baltagi for helpful comments on the paper. We also thank Tatsuki Inoue for excellent research assistance.

123 K. Ogasawara, Y. Matsushita

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