The long-run effects of fetal PM2.5 exposure on mental health: evidence from China

This paper investigates the long-run effects of PM2.5 exposure in utero on the mental health of adolescents. Using nationally representative survey data from China, we instrument the PM2.5 exposure with wind speed to tackle the possible endogeneity problem. Our results show that mothers’ PM2.5 exposure during their pregnancy negatively affects the mental health of their children aged between 10 and 15 years. A 1 µg/m3 increase in PM2.5 exposure in utero increases the probability of having a severe mental illness for adolescents by 0.6%. Our evidence supports the “fetal origins” hypothesis. We also find that fetal PM2.5 exposure leads adolescents to be more likely to be absent from school and quarrel with their parents, implying that fetal PM2.5 exposure may affect individuals’ behavior when they grow up.


Introduction
Air pollution, particularly fine particulate matter (PM 2.5 ), poses a severe threat to health, resulting in economic and social costs. Figure 1 presents a positive relationship between PM 2.5 concentrations and medical care expenses paid by urban households in China. However, the ambient air quality report (Bluetech Clean Air Alliance 2017) shows that the average concentration of PM 2.5 in the 74 largest cities in China is 50 µg/m 3 , and only 14 cities satisfy the Chinese national standard (less than 75 µg/m 3 ). Moreover, the World Health Organization (WHO) considers that PM 2.5 concentrations exceeding 35 µg/m 3 pose a threat to human health (WHO 2006). Thus, air pollution is a severe problem in China.
A growing body of literature has examined the short-term impact of air pollution on physical and mental health outcomes: obesity (Deschenes et al. 2020), student illnesses (Chen et al. 2018a, b), life expectancy (Chen et al. 2013), infant and adult mortality (Chay and Greenstone 2003a;He et al. 2020), subjective well-being (Zhang et al. 2017), and depression symptoms (Szyszkowicz 2007;Xue et al. 2019). However, there are few studies on the long-term influence of prenatal exposure to air pollution on adolescent mental health in developing countries. Prenatal exposure to air pollution can affect adolescent mental health through biological channels. This finding is consistent with the "fetal origins" hypothesis. Exposure to external stimuli (e.g., air pollution) during pregnancy may affect fetal development and genetic expression, resulting in permanent changes in adult health outcomes (Bharadwaj et al. 2016).
The mental health conditions of adolescents are merely effectively treated in developing countries because of the little knowledge about the prevention of mental disorders and the lack of professional health care. Our focus on China provides a unique opportunity to study the link between air pollution exposure during pregnancy and adolescent mental Responsible Editor: Lotfi Aleya Hongshan Ai, Jia Wu, Zhihan Zhou contributed equally to this work, and they are listed in alphabetical order.
health. Depression has become the second leading cause of adolescent death in China. According to the Chinese National Mental Health Development report in 2021 (Institute of Psychology, Chinese Academy of Sciences 2021), 24.6% of Chinese adolescents suffered from depression, of which 17.2% had mild depression and 7.4% had severe depression.
This study provides the first trial to study the causal relationship between air pollution exposure in utero and adolescent mental health. Measurement errors in the air pollution variable and the omitted variables may bias our estimated results. On the basis of the evidence that wind speed may help pollutants spread, we construct an instrumental variable (IV) for air pollution to correct the biases from measurement errors and omitted variables by using the average 2-min wind speed of 10 m above the ground. We combine the individual mental health and socioeconomic information from the China Family Panel Studies (CFPS) with the air pollution information from the National Aeronautics and Space Administration (NASA) Socioeconomic Data and Applications Center (SEDAC) and wind speed information from the National Meteorological Information Center (NMIC).
The present study contributes to the existing literature in three ways. First, to the best of our knowledge, this study is the first to explore the long-term effects of fetal air pollution exposure on adolescent mental health in a highly polluted developing country context, namely, China. Although a large body of literature has investigated the causal impact of air pollution on adult mental health in China, whether the effect also exists for adolescents remains an important and unanswered question. Zhang et al. (2017) and Chen et al. (2018a, b) study the contemporaneous effect of the air pollution index (API) and PM 2.5 on adult mental health and subjective well-being. Zhang et al. (2017) use the Center for Epidemiological Studies-Depression (CES-D) score data from the CFPS 2010 and 2014 to define a binary variable for depressive symptoms with a cutoff of four. The OLS estimate shows that a day-to-day 10-unit increase in API increases the possibility of depressive symptoms by 3.3%. Chen et al. (2018a, b) also define a dummy variable for several mental illnesses when the CES-D score is equal to and above 13. They also focus on urban residents from 2014 to 2015 covered by the CFPS. The main results instrumented by thermal inversions show that the 1 µg/m 3 increase in the average PM 2.5 in the past month increases the probability of having mental illness by 0.37%, which is smaller than our main IV estimation (0.6%). Our finding is the closest to that of Chen et al. (2018a, b), but we focus on the effects of different levels (during pregnancy versus during the month before the date of the interview) of air pollution exposure on the mental health of different age groups of residents (adolescent versus adult) by using different IVs (wind speed versus thermal inversion). However, the biological and behavioral channels through which air pollution affects adolescent and adult mental health in the short and long run may differ. The findings from Chen et al. (2018a, b) may not be simply extrapolated to the present study.
Second, this study contributes to the literature in terms of the effects of fetal exposure to air pollution on shortterm and long-term economic and health outcomes, such as infant health (Chay and Greenstone 2003a, b;Currie et al. 2009;Sanders and Stoecker 2015), human capital formation (Bharadwaj et al. 2017), and educational outcomes (Sanders 2012). We identify a new health cost of fetal exposure to air pollution and find that the increase in PM 2.5 concentration from 2002 to 2007 (compared with the previous year) induced nearly 964.4 thousand children aged 10 to 15 years to have severe mental illness in 2018, thereby causing an economic loss of approximately 23.94 billion yuan.
Third, this study contributes to a growing body of literature investigating the relationship between early-life conditions and later-life mental health. The negative impact of the early critical development period of life may be highly detrimental to human capital accumulation; thus, it cannot be easily compensated in the later stage (Cunha and Heckman 2007;Cunha et al. 2010;Heckman 2006). Many researchers have found that early life circumstances, including cocoa price shocks (Adhvaryu et al. 2019), prenatal exposure to Ramadan (Almond and Mazumder 2011), and prenatal exposure to family ruptures (Persson and Rossin-Slater 2018), can affect adult mental health. We aim to complement this strand of literature by studying the effects of fetal air pollution exposure as an environmental factor in early life on adolescent mental health. On the basis of these factors, the impact of PM 2.5 concentration in utero on the mental health of adolescents is investigated in the present study by focusing on the causal effects. Moreover, the present study supplements the literature on "fetal origins." The rest of this paper is organized as follows. The "Material and method" section is material and method, which offers our data and statistical strategy for the empirical analysis. The "Results" section reports our main results. The "Discussion" section presents a discussion of the mechanism and consistency. Finally, the "Conclusion" section concludes.

Air pollution
We obtain the city-by-year level of PM 2.5 concentrations from 1998 to 2016 from NASA SEDAC. On the basis of the year of birth, we define the year prior to birth year as the prenatal period. The birth city recorded by CFPS can be used to identify the city where the adolescent's prenatal mother is located. 1 Therefore, we can match the individual information and city-level air pollution based on year and place of birth.

Mental health
The data on mental health and individual characteristics are from the CFPS. The CFPS is a nationally representative survey carried out by Peking University with funding from the Chinese government. The CFPS was launched in 2010, and follow-up surveys were conducted in 2012, 2014, 2016, and 2018. The stratified three-stage probability proportional size sampling method was used to select respondents in the sample area. 2 The CFPS includes more than 16,000 households comprising approximately 42,500 individuals in 25 provinces. It also collects detailed demographic information of respondents and their children, such as gender, age, education level, and birth information (e.g., birth date, birth place, birth order, and birth weight). The CFPS also includes two sets of questionnaires to measure respondents' mental health.
The mental health conditions of adolescents aged 10 to 15 years are the key outcome of this study. 3 The CFPS includes the Kessler Psychological Distress Scale to illicit the anxiety-depression spectrum mental distress of respondents. The Kessler Psychological Distress Scale, developed by Ron Kessler and Dan Mroczek in 1992, is a widely used self-report measure of psychological distress (Adhvaryu et al. 2019;Andrews and Slade 2001;Mitchell and Beals 2011). In the 2010 and 2014 waves of the CFPS, the 6-question Kessler Psychological Distress Scale (K6) was used to assess the anxiety and depression of respondents. The K6 is an abbreviated version of the 10-question Kessler Psychological Distress Scale (K10). Weiss and Lunsky (2011) and Easton et al. (2017) show that K6 and K10 are consistent. Thus, K6 performs as well as K10 does. The reliability of the K6 has been established in various contexts, including China (Chan and Fung 2014). The K6 comprises six questions about the respondents' emotional status in the last month. In particular, respondents are asked (1) "How often did you feel depressed and you could not be cheered up no matter what you were doing," (2) "How often did you feel nervous," (3) "How often did you feel upset and you could not remain calm," (4) "How often did you feel hopeless about the future," (5) "How often did you feel that everything was difficult," and (6) "How often did you feel that life was meaningless." Each question is rated on the 5-point Likert scale, including 0 (not at all), 1 (a little of the time), 2 (half of the time), 3 (most of the time), and 4 (all the time). We follow Kessler et al. (2003) to add up the scores of the six questions and define a dummy variable, "severe mental illness," which takes a value of 1 if the sum of the K6 test passes 12 and 0 if otherwise.
In the 2012 and 2016 waves of the CFPS, the CES-D was used to measure the depression of respondents. The CES-D was developed by Radloff (1977). Studies have demonstrated the validity and reliability of the CES-D for depressive symptoms (Radloff 1977(Radloff , 1991Crawford et al. 2011). The CES-D is applicable for adolescents up to the elderly and for the Chinese (Cheng and Chan 2005). The CES-D comprises 20 questions inquiring about the respondents' emotional states in the past week. Table 8 in the Appendix lists these questions. Each question is rated on a 5-point Likert scale ranging from 0 (not at all or less than 1 day) to 5 (nearly every day). We follow Radloff (1991) to add the scores of 20 questions and define a dummy variable, "severe mental illness," which takes a value of 1 if the sum of the K20 test passes 27 and 0 if otherwise.
The performance of the K6 is comparable with that of the CES-D (Sakurai et al. 2011). For most of our analysis, we pool 4 years of data together. The underlying assumption is that the "severe mental illness" measures are consistent when measured by the K6 and CES-D. We use the inverse of the number of times an individual is observed in the sample as the sample weight because some individuals are observed multiple times.

Demographic and survey data
We also obtain birth outcomes, mental health conditions of mothers, parenting styles, and other mechanism variables from the CFPS. In the 2010, 2012, 2014, and 2016 waves of the CFPS, five questions are selected to measure the authoritarian parenting style of parents, including "the parents/guardians would tell you the reasons when they asked you to do something," "the parents/guardians liked to talk with you," "the parents/guardians told stories to you," "the parents/guardians praised you," and "the parents attended parent-teacher meetings at school." Each question has five options, including 1 (never), 2 (rarely), 3 (sometimes), 4 (often), and 5 (always). If the adolescents were asked about their parents' parenting style in a wave, they would not be asked the same question in the next waves. We add all scores of the five questions and define a dummy variable to measure whether parents adopt the authoritarian parenting style. The authoritarian parenting style means that parents take their ideas as the center, do not communicate with their children emotionally, and conduct controlled education to children through punishment and forcing children to be obedient. If the total score of parenting style is less than 22, we believe that parents adopt the authoritarian parenting style to educate their children, and the dummy variable is equal to 1; otherwise, it is equal to 0.

Meteorological conditions
The weather data comes from the NMIC, which records annual surface climate data from 1951 to 2019, including wind speed, rainfall, temperature, and humidity. According to the location information of the meteorological stations, we match the stationlevel weather data with the individual-level data in the following steps. First, we collect all station-level weather data in one city and calculate the annual average city-level weather data. Second, if a city has no weather station, we collect the station-level weather data from the stations in the same province and calculate the annual average city-level weather data. We test the correlation of IV with other explanatory variables in Appendix Table 9. Table 1 provides the summary statistics of the main variables. Panel A reports the individual characteristics of adolescents. The average concentration of PM 2.5 is 27.6 µg/m 3 , which is higher than 10 µg/m 3 , the annual average guideline value for PM 2.5 by the WHO air quality guidelines (WHO 2006). Moreover, 2.5% of adolescents have a severe mental illness. The average birth year of adolescents is 2002. The proportion of males is approximately 53%, with an average of one sibling. Only 0.4% of adolescents have migrated between cities.

Summary statistics
Panel B reports the parental and household characteristics. The average age of fathers and mothers is 41 and 39 years old, respectively. The average age at which fathers and mothers have a child is 29 and 27 years old, respectively. The education years of fathers and mothers are 7.5 and 6.4 years, respectively, which are lower than the 9 years of compulsory education. The probable reason for this scenario among parents is that China's compulsory education law has not yet been formally implemented 4 when they reached school age. The average household income, adjusted for the 2010 price index, is 41,239 yuan.
Panel C reports the mechanism variables. The mean birth weight of adolescents is 3.2 kg, and 6.9% of the adolescents' birth weights are less than 2.5 kg. Approximately 87% of adolescents achieved the standard breastfeeding duration when they were born, and 3.3% were born prematurely. The average number of quarrels with their mothers in the last month is 1. Moreover, 97.9% of mothers adopt the authoritarian parenting style for their children.
Panel D shows the city-level weather conditions. The average annual wind speed is 2.17 m/s, the average total annual rainfall is 921.95 mm, the average temperature is 14.54 °C, and the average annual humidity is 69.38%.

Statistical method
The immense challenge of our identification is the endogeneity of PM 2.5 exposure because individuals may take measures to avoid PM 2.5 exposure. For example, families may reduce the frequency of outdoor activities to reduce respiratory particle uptake when air pollution is severe. If their residential areas suffer from longstanding air pollution, families may move to other cities to keep their children safe. If these cautious parents contribute considerably to children's development, the estimate of interest is biased downward. Our solution is to find an IV that is orthogonal to individual mental health conditions but can affect PM 2.5 concentration.

IV estimation
Following Cai et al. (2016), Hering and Poncet (2014), and Shi and Xu (2018), we use the average 2-min wind speed of 10 m above ground as the IV. First, high wind speed leads to a favorable dispersion condition of pollutants in the air. This finding has been indicated in astrological studies. Second, the children's performance does not respond directly to wind speed. No evidence shows that wind adversely affects human health and even those living near wind turbines (Knopper et al. 2014). One may worry that parents' location choice may also depend on wind speed. This scenario occurs at slight odds. However, our IV remains valid as long as the parents' location choices concerning the wind are not due to their consideration of children.
The two-stage least square (2SLS) estimation includes the following: where i represents the individual, c indicates the city, t indicates the year of childbearing age of i's mother, and r indicates the survey year. wind ic,t−1,r is the average wind speed of city c where adolescent i is located in the fetal period t − 1 , and PM 2.5ic,t−1,r is the fitting value of the first-stage regression, which denotes the concentration of PM 2.5 in city c where adolescent i is located during the fetal period (t-1) in survey wave r. Y ictr is a dummy variable of the mental health status of adolescents aged 10 to 15 years. A value of 1 means that individual i suffers from a severe mental illness, whereas a value of 0 means that he or she does not have a severe mental illness. X ictr is a variety of individual and household control variables, including age, gender, number , 6 φ c is the city fixed effect, γ t is the birth year fixed effect, and δ r is the survey year fixed effect. μ ictr is the random error term. The estimated coefficient β of P M 2.5ic,t−1,r represents the longterm effect of a 1 µg/m 3 increase in the concentration of PM 2.5 during the fetal period on the probability of suffering from severe mental illness.
Because the children's psychological status may be correlated at the city level, all standard errors are clustered at the city level. Given that some individuals may be observed several times, the inverse of the observed times of individuals in the data is used as the weight in the regression in the present study.
Hence, the estimation is a linear probability model. Angrist (2001) finds that the linear probability model is effective in the second stage. Moreover, the estimation coefficient is easy to explain when the result variable is binary and 2SLS estimation is used. In this study, the probit model and IV-probit model with IVs are also used for estimation in robustness checks, and the results are consistent with the main findings (Table 10). 7

Main results
As mentioned above, endogenous issues can lead to estimation bias. People may move to other cities or reduce outdoor activities when air pollution is severe, thereby leading to a self-selection problem. Therefore, the city-level average 2-min wind speed of 10 m above the ground is used in the present study as the IV of PM 2.5 during the fetal period for 2SLS estimation. The IV estimated effects of air pollution exposure are reported in Table 2. Panel A reports the firststage estimation results. Columns (1) and (2) show that wind speed significantly reduces PM 2.5 concentration whether we control individual and household characteristics. In particular, a 1 m/s increase in the average wind speed decreases the PM 2.5 concentration by 5 µg/m 3 . The estimated coefficient is significant at the 1% level, indicating that the IV is highly correlated with the endogenous variable. The F value of the first stage is 21, which is greater than 10, reassuring the validity of the IV (Stock and Yogo 2005).
Panel B reports the results of the second-stage IV estimation. Column (3) shows that a 1 µg/m 3 increase in fetal PM 2.5 concentration significantly increases the probability of suffering severe mental illness for adolescents by 0.6%, after the birth year fixed effect, survey year fixed effect, and city fixed effect are added. We further control for individual and household characteristics in column (4). The value of the coefficient in column (4) is the same as that in column (3). The table presents the 2SLS estimates from Eq. (1). The IV is the average wind speed of 2 min at 10 m above the ground. All regressions use the reciprocal of the number of times an individual appears in the sample as the regression weight. Adolescents' individual characteristics include sex, age, and the number of brothers and sisters. Family characteristics include parents' childbearing age, years of education, and family income. Weather conditions include rainfall, temperature, and humidity. Standard errors are in parentheses, clustered at the city level. *, **, and *** represent significant at the levels of 10%, 5%, and 1%, respectively

Nonlinear effects of air pollution
We further explore the nonlinear effects of fetal exposure to air pollution on adolescent mental health using OLS because the IV estimation of the nonlinear effects of air pollution requires more than one IV. We construct three bins of air pollution concentration (0-25, 25-50, and above 50 µg/m 3 ) 8 and generate three dummy variables. The bin of 0-25 µg/m 3 is the reference bin. Table 3 provides the nonlinear effects of air pollution exposure. Compared with the fetal exposure to air pollution in the omitted bin, the fetal exposure to air pollution in the bins of 25-50 and above 50 µg/m 3 increases the probability of having severe mental illness by 0.9% and 3%, respectively. However, the estimated coefficient of the bin of 25-50 µg/m 3 is not significant. The nonlinear effect suggests that mental illness follows a nonlinear dose-response pattern with the increase in PM 2.5 . The higher the PM 2.5 concentration is, the larger the effect is. Our finding is consistent with the impact of pollution on children's lives (Grönqvist et al. 2020).

Heterogeneity analysis
In this section, we explore the heterogeneous effects of air pollution exposure during pregnancy across gender, mother's education level, and household income. We include an interaction between a dummy variable of individual and household characteristics and air pollution exposure.
First, Sanders and Stoecker (2015) find that male fetuses are more vulnerable to air pollution than female fetuses. We define a dummy variable of gender, which is equal to one if one adolescent is male; otherwise, it is equal to zero. Column (1) of Table 4 shows the homogeneous effect of air pollution exposure in utero across genders. Second, Bharadwaj et al. (2017) find that mothers with low education levels may be more vulnerable to air pollution exposure because of their poor self-protection awareness. We construct an indicator variable of low education attainment based on the number of years of education. The results are presented in column (2) of Table 4. The heterogeneous effect of fetal exposure to air  pollution is absent across years of education. Finally, more affluent households may have better home environments or equipment to withstand the effects of PM 2.5 air pollution. Column (3) of Table 4 examines the effect of fetal PM 2.5 exposure on the probability of having a severe mental illness for adolescents from high-and low-income households. The coefficient of "fetal exposure to PM 2.5 × high family income" is − 0.003 and not significant, indicating that household income does not mitigate the negative effects of fetal air pollution exposure on adolescent mental health.  (Xu et al. 2016). Therefore, the treatment cost caused by the additional 964,400 adolescents with severe mental illness is $3.535 billion, which translates to 23.943 billion RMB in 2018, based on the exchange rate and the consumer price index (CPI). 10

Biological channel
Previous studies have found that air pollution exposure during pregnancy increases the possibility of neuroinflammation and leads to cerebrovascular damage or oxidative stress (Sass et al. 2017), which may affect fetal development. Fetal development is crucial for future health. Shonkoff (2011) shows that some components of mental health are coded during fetal development. If fetal exposure to PM 2.5 disrupts this coding process, adolescent mental health would be affected by longlasting negative impacts. This finding is consistent with the "fetal origins" hypothesis. See Table 2 for more information on the controls. The dependent variables of columns 1-3 are the proxy measures of children's physical health at birth, column 4 is the proxy measure of maternal health during pregnancy, column 5 is the mother's mental health, and column 6 is the adolescent's mental health. Standard errors are in parentheses, clustered at the city level. *, **, and *** represent significant at the levels of 10%, 5%, and 1%, respectively Considering data availability constraints, we can only use breastfeeding duration as a proxy indicator to reflect the mother's physical condition at that time. Given that mothers who are unhealthy during pregnancy may give birth to unhealthy children (Aizer and Currie 2014), we use birth weight and the details indicating whether the baby was born prematurely to measure the health status of fetuses in the womb (Black et al. 2007;Currie and Moretti 2007;Currie 2009). We also provide suggestive evidence of biological mechanisms. Columns (1) to (2) of Table 5 report the estimated results of fetal PM 2.5 exposure on birth outcomes. We find that a 1 µg/m 3 increase in fetal PM 2.5 exposure reduces the adolescent birth weight by 28 g and increases the probability of low birth weight (less than 2.5 kg) by 1.3%. These findings suggest that fetal exposure to PM 2.5 can significantly reduce the birth weight of newborns. Column (3) shows that exposure to air pollution during pregnancy increases the probability of preterm birth, defined as fewer than 32 weeks of gestation. In addition, breastfeeding is good for children's health, and its health benefits can extend into adulthood. Breastfeeding is recommended for no less than 6 months. As we can see in column (4), the probability of breastfeeding duration reaching the standard value decreases significantly for every extra unit of PM 2.5 . A plausible reason for this scenario is that breastfeeding mothers are affected by the negative impact of air pollution on their bodies, thereby reducing breastfeeding duration.
Our findings suggest that fetal exposure to PM 2.5 affects mental health through biological mechanisms. This negative effect on the innate endowment is reflected in the short term and continues to the future human capital accumulation, such as mental health. The results of the present study are consistent with the findings of Persson and Rossin-Slater (2018). The authors find that a child has a high risk of developing mental health problems in childhood and adulthood if his or her mother has experienced a demise of a family member during pregnancy. Thus, fetal PM 2.5 contamination is transmitted directly from mother to infant. Shonkoff (2011) points out that the fetal period is critical for an individual's mental health.

Other channels
Pregnancy is also a critical period for maternal mental health development (Sandman et al. 2012). Air pollution exposure during pregnancy may lead to maternal mental disorders in the future, 11 a problem that can affect children's mental health conditions. Several studies have found evidence of an intergenerational correlation between maternal and children's psychological status (Hammen et al. 1991;Luoma et al. 2001;Pilowsky et al. 2006). We find from column (5) of Table 5 that fetal exposure to air pollution does not have a significant negative effect on maternal mental health. We further control maternal mental health conditions and re-estimate Eq. (1). The result is shown in column (6). The core independent variable remains significantly positive, suggesting that the transmission of maternal mental disorders is not the main channel through which fetal air pollution exposure affects adolescent mental health.

Further discussion
Furthermore, we explore the effects of fetal exposure to air pollution on adolescent behaviors to provide an intuitive result. In particular, we focus on the aspects of air pollution's impact on children's mental health and use the detailed access information from the Children's Questionnaire in CFPS, including bad behaviors for adolescents, such as smoking, drinking, absenteeism, and quarreling with parents, to profile psychological problems. The regression results are presented in Table 6. We notice that school-aged children are likely to be absent from school (col. 1) and frequently quarrel with their parents (col. 2), despite controlling for family and individual factors. Similarly, PM 2.5 increases adolescent smoking and drinking behaviors (cols. 3 and 4), but the results are not significant.
Does fetal PM 2.5 exposure work through individuals' physiological characteristics? To rule out this possibility, we provide evidence by controlling for some physiological characteristics when studying the effects of fetal PM 2.5 exposure on adolescent behaviors. First, we use body mass index (BMI) to measure health, given that BMI can determine the health risks associated with obesity. To further exclude the possible compounding effects that arise from physiological status, we control for the health condition, which is assessed by whether individuals have been diagnosed with any common disease. 12 We also control for the diagnoses of hearing or vision problems because they are relatively common problems among children, and children with hearing or vision problems may not be able to focus on learning (Currie et al. 2010), increasing bad behaviors. Table 11 in the Appendix shows that the effect of fetal exposure to PM 2.5 on adolescent behaviors remains positive across all columns. In addition, Appendix Table 12 provides evidence that controlling for CO 2 , SO 2 , and other pollutants (PM 10 , NO 2 , CO, and O 3 ) 13 does not change the effects of fetal PM 2.5 exposure on adolescent behaviors.
Parenting style is crucial to the healthy growth of children and can be divided into the following four types: authoritarian, permissive, uninvolved, and authoritative (Doepke and Zilibotti 2017). We explore the effects of air pollution on authoritarian parenting style in columns (5) to (7) of Table 6. The result in column (5) shows that a 1 µg/m 3 increase in PM 2.5 during pregnancy increases parents' probability of adopting the authoritarian parenting style for children by 1.5%. The coefficient is significant at the 10% level. One possible reason is that given the negative impacts of fetal exposure to PM 2.5 on adolescent behaviors, mothers may take measures to correct these bad behaviors and discipline their children. However, columns (6) and (7) show that the pattern does not exist in the first and second years after birth, indicating that fetal exposure to PM 2.5 has a considerable effect on the use of the authoritarian parenting style. See Table 2 for more information on the controls. The dependent variables are adolescent behaviors (cols. 1-4) and authoritarian parenting style (cols. 5-7). Standard errors are in parentheses, clustered at the city level. *, **, and *** represent significant at the levels of 10%, 5%, and 1%, respectively  Table 7 Robust analysis of the impact of fetal exposure to PM 2.5 on adolescent mental health (2SLS) See Table 2 for more information on the controls. The estimation equation of specifications (1) and (3) to (7) is Formula (1), and the estimation equation of specification (2) is Formula (3). The dependent variable is adolescent mental health. Standard errors are in parentheses, clustered at the city level. *, **, and *** represent significant at the levels of 10%, 5%, and 1%, respectively

Robustness test
In this section, we discuss several confounding factors that may alter our main results.

Migration
Wind speed may affect individual migration decisions, thereby preventing the IV from satisfying the exogenous hypothesis. Although the CFPS does not have data on the city where mothers live during pregnancy, we identify migrants by comparing the interview city and birth city. We construct an indicator variable of migration. If two cities are the same, the dummy variable is equal to one; otherwise, it is equal to zero. The cross-city migration rate in the sample is only 0.4%, indicating that cross-city migration is not common in our sample. Then, we estimate the effects of wind speed on this dummy variable and find that wind speed does not affect adolescent migration choices (see Appendix Table 9, cols. 5 and 6). Finally, we exclude all migrants and re-estimate Eq.
(1). The result is presented in column (1) of Table 7. We find that our baseline result remains unchanged.

Time-series correlation of PM 2.5
The concentrations of PM 2.5 may have a time-series correlation in different years, and the effects of fetal PM 2.5 pollution exposure on adolescent mental health may be confounded by the PM 2.5 concentrations in other years. We generate a new model to control the average PM 2.5 exposure from birth year to the interview year and rule out such compounding effects (see Appendix for more details). Column (2) of Table 7 provides the result. We find that fetal exposure to PM 2.5 still increases the probability of suffering from serious mental illness for adolescents by 0.8%. The result is different from 0 at the significance level of 5%. Compared with the main result in Table 2, the result in Table 7 shows that the magnitude is amplified. This finding indicates that after the possible time-series correlation of PM 2.5 pollution is accounted for, the negative impact of PM 2.5 pollution on the mental health of adolescents aged 10 to 15 years still exists. The additional analysis in Appendix Table 13 shows no evidence that exposure to PM 2.5 at an early age is time-serially correlated at the city level. Given that pollution can directly affect children's fetal gene expression through epigenetic channels, fetal exposure to PM 2.5 may be more harmful to adolescent mental health than postnatal exposure.

Alternative fetal period
We define the previous year of the birth year as the fetal period in our main regressions. However, this approach may not be accurate, which may lead to errors in the calculation of PM 2.5 concentration in the fetal period. Thus, we redefine the fetal period. If the birth month is between January and March, the fetal year is 1 year before the birth year. If the birth month is between April and December, the fetal year is the birth year. The estimated result is robust in column (3) of Table 7.

Multiple identical individual problems
In the baseline regression, we combine the four-wave survey data as mixed cross-sectional data. Although we use the inverse of the number of adolescents observed in the sample to adjust the weight of the sample, the correlation between multiple observations of the same individual still leads to the possibility of standard error calculation errors. Next, we only include the first survey data of each adolescent in the fourwave survey to address this issue. We re-estimate Eq. (1) and find from column (4) of Table 7 that a 1 µg/m 3 increase in PM 2.5 during pregnancy increases the probability of having a severe mental illness for adolescents aged 10 to 15 years by 0.7%. This finding is consistent with our baseline result.

Controlling for other types of air pollutants
Other types of pollutants may affect mental health through similar channels (Bharadwaj et al. 2017;Grönqvist et al. 2020). Hence, we present the estimated results of PM 2.5 when further controlling for the concentrations of CO 2 , SO 2 , and other pollutants, including PM 10 , NO 2 , CO, and O 3 . The results are presented in columns (5) to (7) in Table 7. We find that a 1 µg/m3 increase in PM 2.5 during pregnancy increases the probability of having a severe mental illness for adolescents by 0.6% to 0.8%, implying that the estimated effects from the main model do not overestimate the actual effects. Fig. 2 Robustness tests to alternative specifications and samples. Notes: Fig. 2 plots IV estimates and 95% confidence intervals for the robustness tests to alternative specifications and samples, which directly correspond to the results of Table 7. Our preferred specification is in the first row Figure 2 plots the IV estimates and the 95% confidence intervals for the robustness checks.

Conclusion
In this study, we estimate the long-term effects of air pollution exposure during pregnancy on adolescent mental health. Our results indicate that air pollution exposure in early life has persistent health effects in later life. This finding is consistent with the "fetal origins" hypothesis. The IV estimation shows that a 1 µg/m 3 increase in PM 2.5 significantly increases the probability of having severe mental illness by 0.6%. The heterogeneous effects of prenatal air pollution exposure are absent across gender, maternal education years, and household income levels. We also examine the possible mechanisms behind the negative health effects of air pollution during pregnancy. The results indicate that the biological channel is the main channel through which fetal exposure to air pollution impacts adolescent mental health. We also find that fetal exposure to air pollution can increase the probability of being absent from school and frequent quarrels with their parents. Our back-of-the-envelope calculation suggests that the increase in PM 2.5 concentration from 2002 to 2007 led to approximately 964,400 adolescents aged 10 to 15 years with severe mental illness in 2018, thereby resulting in an economic loss of 23.943 billion yuan.
Our findings suggest that reducing air pollution has not only contemporaneous economic and social benefits but also persistent and profound health benefits in later life. Pregnant women should take effective measures to avoid air pollution exposure. This action can protect their children from adverse health consequences. In this study, we cannot examine all physiological and behavioral effects caused by prenatal air pollution exposure and explore all possible channels because of data availability constraints. We leave these topics for future research.  Table 9 The relationship between IV and other disturbance terms See Table 2 for more information on the controls. The dependent variables are medical expense (cols. 1-2), health condition (cols. 3-4), and migration (cols. 5-6). Standard errors are in parentheses, clustered at the city level. *, **, and *** represent significant at the levels of 10%, 5%, and 1%, respectively

Medical expenses Health condition Migration
(1)  See Table 2 for more information on the controls. The dependent variables are adolescent absenteeism (cols. 1-2) and quarrel with parents (cols. 3-4). Standard errors are in parentheses, clustered at the city level. *, **, and *** represent significant at the levels of 10%, 5%, and 1%, respectively  The table presents the probit and IV coefficients on fetal PM 2.5 exposure. Columns 1-2 are estimated by the probit model, and columns 3-4 are estimated by the IV-probit model. See Table 2 for more information on the controls. Standard errors are in parentheses, clustered at the city level. *, **, and *** represent significant at levels of 10%, 5%, and 1%, respectively Presumably, PM 2.5 concentration may change smoothly with time, which generates negative effects on the developing fetus and also harms young children. The effects of PM 2.5 exposure after birth may increase with age as the children spend more time outdoors or decrease with age because the immune system functions better. This proposes a challenge that we need to disentangle the effects of PM 2.5 exposure in utero from those that occurred during other early life stages. To further rule out such compounding effects, we control average PM 2.5 exposure from the time when the outcomes are measured. Specifically, our estimation equation is: where Average PM 2.5 afterbirth ictr is the average concentration of PM 2.5 exposure for individual i after birth (2) Y ictr = + PM 2.5 ic,t−1,r + Average PM 2.5 after birth ictr + X � ictr Γ + c + Y t + r + ictr , Table 12 Effects of fetal exposure to PM 2.5 on adolescent behaviors (accounting for other types of pollutants and the physiological effect) See Table 2 for more information on the controls. The dependent variables are adolescent absenteeism (cols. 1-3) and quarrel with parents (cols. 4-6). Standard errors are in parentheses, clustered at the city level. *, **, and *** represent significant at the levels of 10%, 5%, and 1%, respectively  Table 13 Time-series correlation of PM 2.5 at an early age (0 to 9 years old) See Table 2 for more information on the controls. Standard errors are in parentheses, clustered at the city level. *, **, and *** represent significant at levels of 10%, 5%, and 1%, respectively The estimated model obtained by using the two-stage least square (2SLS) is: Among them, wind ic,t−1,r is the average wind speed of the city c where the adolescent i is located in the fetal period t − 1 , PM 2.5ic,t−1,r is the fitting value of the first stage regression, and the definitions of other variables are the same as that of Formula (1).

Author contribution
The three authors contributed equally to this work, and they are listed in alphabetical order. All authors contributed to the conception, design, data collection, and analysis. The first draft of the manuscript was written by Zhihan Zhou. All authors read and approved the final manuscript.
Funding The funding supports from the National Natural Science Foundation of China (Grant No. 72073051) and Guangdong Natural Science Foundation (Grant No. 2021A1515012304) are gratefully acknowledged.

Data availability
The datasets are available from the corresponding author on reasonable request.

Declarations
Ethics approval and consent to participate Not applicable.

Consent for publication Not applicable.
Competing interests The authors declare no competing interests.