and Cohort Effects of Superstition on Education Attainment

Transcription

1 Fortunes and Misfortunes of the Dragon Sons: Direct and Cohort Effects of Superstition on Education Attainment Andy L. Chou October 2018 Click for latest draft Abstract In many parts of East Asia, the fertility rate spikes every 12 years, starting in the 1970s. Researchers have linked this phenomenon to the belief that being born in years associated with the dragon zodiac leads to better outcomes in life; yet the research linking birth years and education outcomes have found mixed results. One potential explanation for the mixed results is opposing mechanisms: being born in dragon zodiac years, the direct effect, may be positive while being in a larger cohort during dragon years, the cohort effect, may be negative. I use the difference between cutoff for determining school cohort and zodiac cohort to estimate the separate effects from each mechanism. Using the Taiwan Social Change Survey, I find evidence of a positive direct effect and a negative cohort effect for those born during dragon zodiac years. Subsample analysis suggests selective investment after birth is a possible mechanism for the direct effect while changes in cohort size contribute to the cohort effect. Department of Economics, Michigan State University, chouandy@msu.edu 1

2 1 Introduction There is a common belief among people from East Asian countries that being born in certain years, under specific zodiac signs in the lunar calendar, determines a person s fortunes in life. Previous researchers have noted increases in fertility rate during years associated with the dragon zodiac, a symbol of good fortune, as evidence of zodiac superstition. (Goodkind, 1991; Yip et al., 2002). However, the research on effect of zodiac superstition on education outcomes produced mixed findings. Previous researchers noted that those born in years associated with the fortunate zodiac experience both positive effects of beliefs coming from parental expectation, self-confidence, or expectation from others and the negative effects of increased cohort size. On the other hand, people born in a zodiac considered to be unfortunate are faced with a negative effect from beliefs and a positive effect from decreased cohort size. The opposing nature of the two mechanisms results in an ambiguous overall effect from the zodiac superstition (Agarwal et al., 2017; Do and Phung, 2010; Johnson and Nye, 2011; Mocan and Yu, 2017; Senbet and Huang, 2012; Wong and Yung, 2005). 1 I focus on the region of Taiwan. 2 Children in Taiwan are required to be age 6 on September 1st to enter elementary school. 3 Those born between the months of September and December are required to enter school a year later with those born between the months of January and August of the next calendar year. This means that the school cohorts containing 1 Nunn and Sanchez de la Sierra (2017) provides another example where the effect at the individual level differs from the overall effect. Using the example of bulletproof spells in Africa, they argue that even though in theory individual belief in bulletproof spells is harmful for individual safety, group beliefs in bulletproof spells may be beneficial due to positive externality of individuals making effort to ensure safety of the group. 2 While the lunar calender and the zodiacs has origins from China, fertility spikes, particularly those during dragon zodiac years, didn t appear in China until the 2000s. Goodkind (1991) hypothesized the policies of the Chinese government prohibiting traditional practices are at play. In Taiwan, fertility policies were fairly relaxed. The Taiwanese government made efforts to reduce fertility during the 1960s and 1970s, through promoting the use of contraceptives and implementing education programs on family planning rather than through penal actions such as fines or jail sentences (Sun, 1989). 3 In Hong Kong, school year goes from September to August of next calendar year. However, Students as young as 5 years and 8 months old can entry primary school. In Singapore and Malaysia, school year and calendar year are the same. These children need to be at least 6 years old to enter primary school. 2

3 those born in dragon zodiac years also have those born in other zodiac years. I thus estimate the effect of being born in the dragon zodiac year, the dragon direct effect, by comparing the education attainment among those born in these years and those who are not, within the same academic cohort. While the effect of being in a larger cohort due to increased fertility during dragon zodiac years, the dragon cohort effect, is estimated by comparing those in the same academic cohort as those born in the dragon zodiac years and those who are not. 4 I document changes in cohort size during years associated with different zodiac signs using birth data at the national level from the Taiwan Ministry of Interior. Similar to previous research (Goodkind, 1993), I find that birth cohort size is 7 percent larger on average during years associated with the dragon(fortunate) zodiac, while birth cohort size is 8 percent smaller on average during years associated with the tiger(unfortunate) zodiac. These fertility effects do not vary by gender but vary across different years. I find no evidence of changes in birth cohort size during years associated with other zodiacs. There is some evidence these results are related to the limited availability of spots in the academic track in college. I use the Taiwan Social Change Survey from 1996 to 2016 to analyze the effects of different mechanisms. Overall I find evidence of a similar sized direct effect, about 2 percentage points, on probability of having a college education in the academic track for those born in dragon and tiger years. The size of the cohort effect is stronger for those exposed to people born in the dragon years, at around 4 percentage points, than in tiger years. The effects are weaker on less selective measures of academic achievement, suggesting academic competition may play a role. The importance of separately identifying the two effects is highlighted by differing effects across different years. Looking across time, the cohort effect for dragons and tigers roughly follows the relative magnitude of the fertility spike at the national level. However, 4 See Figure 1 for a graphical representation. 3

4 there is little evidence of direct effect in the 1970s when the fertility effects are first observed. In addition, the dragon direct effect is stronger when there is no fertility effect. I examine several possible mechanisms driving the direct and cohort effects through subsample analysis. While there is no fertility effect by gender or relative age within school year, I find direct effects largely concentrated on males and those who are older within a school cohort. The results are consistent with the direct effect driven by selective investment and the cohort effect being driven by both changes in cohort size and composition. I do not find support for the direct effect driven by minority immigrants. This paper contributes to the literature on the effect of culture on economic outcomes. 5 There are many theories trying to explain the persistence of cultural beliefs in cases with a single mechanism (Bénabou and Tirole, 2016; Foster and Kokko, 2009; Fudenberg and Levine, 2006; Guiso et al., 2016). The results from this paper show there may be spillover effect as large as, or even larger than the effects operating through individual beliefs. The indefinite sign of the overall effect suggests a possible reason for the persistence of superstitions: multiple counteracting mechanisms may make evaluating the superstitions difficult or misleading. In addition, even if the individuals are correctly evaluating the outcomes, the superstition may be sustained by groups that benefit from group effects within the academic cohort, namely, the dragons in academic cohorts with dragons or the non-tigers in academic cohorts with tigers. This paper also contributes to the literature on the effect of cohort size. Many articles document a negative relationship of cohort size on education and labor market outcomes (Bound and Turner, 2007; Connelly and Gottschalk, 1995; Welch, 1979). However, articles finding positive relationship between cohort size and education attainment suggest other mechanisms such as increased public spending or scale economies are also at play (Do and Phung, 2010; Reiling, 2016). This paper uses a source of variation that is exogenous from 5 See Guiso et al. (2006) for a review. 4

5 decisions of previous generations and overcomes the problem of distinguishing between cohort and age effects. The evidence from people born in years associated with the dragon zodiac supports the idea of cohort crowding. However, I did not find robust evidence of positive effect on education attainment when cohort size is smaller for people born during years associated with the zodiac tiger. The difference between dragon and tiger cohort effects may imply the negative effects of cohort size scales up at a different pace than that of the positive effects. The rest of the paper is organized as follows: Section 2 reviews the literature. Section 3 discusses impact of zodiac years on cohort sizes. Section 4 describes the data. Section 5 discusses summary statistics on education attainment by different zodiac group. Section 6 presents the regression model. Section 7 presents estimation results. Section 8 discusses the relevant issues and concludes. All the tables and figures are in the back of the paper, in section 9. 2 Literature Review In East Asia, the Chinese lunar calendar (or an adaptation of it) is commonly used in conjunction with the Gregorian calendar. 6 In the Chinese lunar calendar, each year is represented by a creature. 7 The collection of creatures, called zodiacs, follows through a twelve-year cycle. There is a common belief that people born in certain years share the characteristics of the zodiac they were born under. An often studied zodiac is the zodiac dragon. 8 Dragon, the only zodiac with no real life counterpart, is a symbol for mystical power 6 Several holidays in Taiwan, such as the Chinese New Year, Dragon Boat Festival, and Mid-Autumn Festival, are based on dates in the lunar calendar rather than dates in the Gregorian calendar. 7 The twelve creatures, listed sequentially, in the Chinese zodiac are: Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Sheep, Monkey, Chicken, Dog, Pig. Table 1 lists the corresponding years in the Gregorian calendar for each zodiac. In Vietnam, rabbit is replaced by cat. The Western equivalent of zodiacs are the horoscopes. However, the western horoscopes vary by month and not by year. 8 Other known zodiac superstitions include firehorse women in Japan (Yamada, 2013), horse zodiac in South Korea (Lee and Paik, 2006), and sheep zodiac in China (Mocan and Yu, 2017). There is no evidence 5

6 coming from the heavens. Several papers have found that during dragon zodiac years, fertility rates have spiked consistently (Goodkind, 1991). These papers linked this phenomenon to the belief that being born in years associated with the zodiac dragon can bring a person good fortune and power in life. Several previous studies have looked at the effect of being born in dragon zodiac years on education and labor market outcomes, but the results have been mixed. Mocan and Yu (2017) found positive evidence on education attainment and test scores using data in China. Liu (2015) used Taiwanese data and found positive evidence on education attainment, but no effect on wages. However, several studies found no evidence and sometimes even a negative impact of being born in dragon years. Wong and Yung (2005) found no evidence on wages using the Hong Kong Census. Sim (2015) used Singapore data and found a negative effect of being born in dragon zodiac years on the probability of having a college degree. Agarwal et al. (2017) used a difference in differences design to compare Chinese and non-chinese and found a negative effect on income in Singapore. One reason for the mixed findings is due to the multiple mechanisms triggered by the zodiac superstition. For those born in dragon years, the positive effects from beliefs may be weakened by the negative effects from larger cohort sizes. Several studies tried to get around the effect of larger cohort sizes by studying Asian immigrants in countries where Asians are minorities. Johnson and Nye (2011) used US Census and Current Population Survey data and found being born in dragon years is associated with increase in years of education attained. Senbet and Huang (2012) used US Panel Study of Income Dynamics and found no dragon year effect on wages. However, there are concerns about external validity due to differences between native and immigrant population. Among the studies that look at countries where Chinese immigrants represent a significant portion, only Do and Phung (2010) tried to account for cohort size effect by controlling for cohort size in the of superstition on the dragon zodiac for Japan and Korea. 6

7 regression. Yet cohort size may just be an indicator for local economic development. In addition, increases in overall cohort size may not capture the sudden increase in cohort size during fortunate zodiac years. Most of the studies treat individuals within a zodiac year as homogeneous and did not explore differences within zodiac group. Notable exceptions include Do and Phung (2010) and Agarwal et al. (2017). Do and Phung (2010) used gender specific zodiac superstition in Vietnam to explore the timing of the mechanism. Since gender cannot be observed before birth, they argued that the zodiac superstitions were a result of pre-birth planning due to lack of differences between siblings within households. However, most individuals in their sample, between ages 2 and 23, haven t completed their education. It is unclear whether the null result in their study is due to sample selection or zodiac superstition effects. Agarwal et al. (2017) looked at overall effects by gender and time. They found the negative on only the younger cohort but no differing effects by gender. Yet, the authors were unable to distinguish whether these differences or lack of differences are determined by mechanisms in effect before entering the labor market or mechanisms occurring during the labor market process. In my paper, I look at Taiwan where there is a belief that dragon zodiac brings fortune while the tiger zodiac brings misfortune. 9 My paper differs from the literature in the following ways. I estimate the effect of being born in a certain zodiac, named direct effect, and the effect of being in a cohort with different cohort size, named cohort effect, separately. The separation is necessary as it is believed that the direct and cohort effects are driven by different mechanisms. I further explore the possible mechanisms by looking at different subsamples. In addition to variation by gender and time, I also explored variations in relative age within school year and wave of immigration. In terms of outcomes of interest, 9 Liu (2015) and Goodkind (1991) suggest the belief to be that tiger zodiac is specifically brings misfortune to females, as female born in tiger zodiac years are believed to make them stubborn and unsuitable for wifely duties. 7

8 I look at education attainment with varying levels of selectivity. This allows me to explore whether academic competition plays a role in realizing superstitions. 3 Zodiac Years and Cohort Sizes Figure 2 presents the total number of live births in each year between 1947 and There was a sharp rise in birth number in the end of the 1940s possibly due to the influx of Chinese immigrants during the Chinese Civil War (Francis, 2011). The total number of births hovered around four hundred thousand until the early 1980s. Since then, number of births has been declining, reaching a plateau in the last couple of years. There was a spike in cohort size during dragon years since the 1976 dragon year. Before the 1970s, the cohort size stays flat (in 1952) or decreases (in 1964) during dragon years. For the tiger years, birth numbers stay flat for 1962 and 1974 but decrease consistently during tigers years since the 1980s. Goodkind (1991) hypothesize the lack of fertility effect is due to changes in demographics, economic environment, or availability of modern birth controls. Table 2 presents OLS results of log annual births on dummies for dragon and tiger years at the national level. The regression results suggesting a 7.3 percent increase in number of live births during dragon years and 7.9 percent decrease in number of live births during tiger years relative to other years while accounting for a quadratic time trend overall. The interaction terms between zodiac dummies and gender indicates that the changes during dragon or tiger years does not vary by gender. Table 3 present OLS results of log annual births on dummies for each individual dragon or tiger years. The results suggest some variation in change in cohort size during dragon years. Most notable is the statistically insignificant decrease during dragon year of This is possibly due to the response by the Taiwanese government to discourage birth in dragon year(goodkind, 1991). I do not find evidence of fertility spikes or drops in other zodiacs years, as shown in Table 4. 8

9 4 Data I look at the impact of zodiac superstition on education attainment using the Taiwan Social Change Survey (TSCS). TSCS is a biannual survey conducted by researchers in the Academia Sinica. TSCS is nationally representative sample of adults, with sample size of around 2000 per survey. 10 I merged surveys collected between 1990 and 2016 that recorded the birth month of the respondent. The resulting dataset includes 41 surveys spanning over 24 years. To look at completed education, I only include those age 25 or above in the sample. Because the fertility effects are only observed after 1970s, I focus my analysis to those born after TSCS consists of basic characteristics such as gender and education attainment and additional themed questions that rotates every five years. Table 5 presents summary statistics of the variables I used in my regression analysis. Education level is coded into five categories: elementary school degree or below, middle school degree, high school degree, associates degree, and bachelor s degree or above. Other than the survey in 2003, all the other surveys distinguish between vocational and academic track in high school and post-secondary education. Unless otherwise asked in the survey, education level includes those who completed education and those dropped out before completing. Zodiac dummies are constructed based on self-reported birth year and month. I approximate the lunar calendar based on birth month. I coded each lunar year to start in February and end in January of the next calendar year. The control variables are mostly selected to be characteristics determined before birth. The exception is parental occupation, which is during age 15 or 18 of the respondent. 10 Surveys before 2000 sampled those age 20 to 65. Surveys in 2000 and 2001 removed the restrictions on maximum age. Surveys starting in 2002 lowered the minimum age in the sample to 18 to conform with social surveys in other countries. 9

10 Parental ethnicity is coded into three categories: Taiwanese (Fukien and Hakka Taiwanese), Mainlander, and Aborigine. Birth place is defined as being born in the two municipal cities and the five provincial cities: Taipei, Kaohsiung, Keelung, Hsinchu, Taichung, Chiayi, and Tainan. 11 Religion is coded into five categories: No religion, Folk religion, Buddhist, Daoist, and other religions(christianity and Islam). Occupations are coded into five levels according to Hwang (2003): managers and professionals; technician and professional assistants; technical workers; machine operators and assemblers, sales and service personnel; non-technical, labor, and agricultural workers. 5 Zodiac Years and Education Attainment Overall Trend Figure 3 presents percentage of individuals with different levels of education, including high school, college or college in academic track, by birth lunar year. Overall the individuals in later generations are more likely to have a high school, college, or college degree at academic track. Percentage of individuals with high school degree rose from about 60 percent for those born in 1960 to over 90 percent for those born after 1970s. Percentage of individuals with college degrees saw the most dramatic rise, with only 30 percent for those born in 1960 and 80 percent for those born in the 1980s. Percentage of individuals with college degree at the academic track also saw some significant rise, with 10 percent for those born in 1960 and about 40 percent for those born after late 1980s. There is some evidence of spikes in dragon years and drops in tiger years but only during 1986 tiger year and 1988 dragon year for those in the college academic track. There is a drop in percentage of people having college degree for those born in There were no spikes or drops in percentage with high school education, possibly due to the prevalence of people having high school education. 11 This designation applies between 1982 and Hsinchu city and Chiayi city became a provincial city in Redesignation in 2010 changed the status of several cities and counties. 10

11 By Treated Group Figure 4 presents differences in percentage of persons having different education attainment for different zodiac groups: dragons, non-dragons in dragon cohort, tigers, non-tigers in tiger cohort, and others. Dragons and tigers refer to those born in the dragon and tiger zodiac years. Non-dragons in dragon cohort and non-tigers in tiger cohort refers to those born between September and January of the year before a dragon or tiger zodiac year and those born between January and September of the year after a dragon or tiger zodiac year. Because of the school year cutoff in Taiwan, these groups enter school along with those born in dragon or tiger zodiac years. The others group refers to those not in the aforementioned groups. The three figures on the left focus on outcomes during dragon years while the three figures on the right focus on outcomes during tiger years. According to TCSC, percent of people born in dragon years have a college education in the academic track, slightly lower than percent for people born in other years (excluding tiger years). The higher education attainment of people born in dragon years, compared to those who are supposed to be in the same school years, suggests the direct effect is positive. In addition, the lower prevalence of people with college education in the academic track, between non-dragons in dragon cohort and those who are not in the dragon cohort, suggests the cohort effect is negative. Furthermore, people born in tiger years exhibit the opposite pattern as people born in dragon years. However, those who are supposed to be in the same academic cohort as people born in tiger years have a lower probability of having college education compared to those not in the same school years as tigers. This suggests the cohort effect is negative or statistically insignificant for people born in tiger years. Differences in means for having college education in vocational track and high school education do not show particular differences among zodiac groups. 11

12 6 Regression Model To account for the heterogeneity across different school years that are time invariant, 12 I estimate direct and cohort effect using the following models: Y i = β 0 + β 1z Zodiac iz + SY i + β 3 X i + ɛ i (1) Y i = β 0 + β 2z ZodiacSY iz + ZY i + β 3 X i + ɛ i (2) where Y i is education attainment for individual i. Zodiac iz is a vector of dummies for individual i being born under zodiac z. ZodiacSY iz is a vector of dummies for being in the same school year as people born in the zodiac years z. In my case, z = dragon, tiger. SY i, ZY i are birth academic year/zodiac year fixed effects. X i is a vector of control variables. These include parental education, parental ethnicity, parental religion, place of birth, birth year, survey year, birth month fixed effects, and birth order. I estimated both equations using probit and clustered my standard errors at the birth lunar year level. The direct effects are estimated as β 1z whereas the cohort effects are estimated as β 2z. When estimating the cohort effects, I dropped the individuals born in tiger or dragon zodiac years to avoid confounding with the direct effects. To account for the missing data in the TSCS, I added a category for missing variables and included a dummy that equals one if the control variable is missing. 12 The papers in the dragon superstition effect literature address the issue by limiting the sample to years close to the dragon zodiac years. Another reason to use fixed effects is to make my estimates comparable to the estimates in the cohort size effect literature. While the articles in the cohort size literature use data aggregated at the county or state level, they all include year fixed effects in their estimation. 12

13 7 Regression Results Overall Results Table 6 presents probit marginal effects of dragon and tiger dummies on a dummy for having college education in the academic track when all the controls are added. Column 1 only includes dragon and tiger dummies. Column 2 adds school year fixed effects and estimates equation 1. Column 3 estimates equation 2, on dragon and tiger school cohort dummies and zodiac year fixed effects, while those born in dragon and tiger zodiac years are dropped. For the dragon direct effect on having college education in the academic track, the results go from 0.4 to 2.0 percentage points when adding school year fixed effects. For the tiger direct effect on having college education in academic track, the results stayed similar in size, going from -2.1 to -2.4 percentage points but with larger standard errors. The dragon cohort effect is much larger, at -4.6 percentage points, than the tiger cohort effect, at -1.8 percentage points. The relative size of cohort effects explains the difference between the movement in coefficients of dragon and tiger direct effects after accounting for cohort effects. On Different Education Attainment Table 7 presents probit marginal effects of dragon and tiger dummies on different levels of education attainment. Columns 1 and 2 are on college education at the academic track. Columns 3 and 4 are on college education at any track. Columns 5 and 6 are on high school education at any track. The direct effects weakens as the education level becomes less competitive. The cohort effects are similar between college education at academic track or college education in general but is much weaker for having high school education. These results suggest academic competition plays a role in direct and cohort effects. 13

14 By Gender Previous research found male bias exhibited in within household resource distribution in Taiwan (Parish and Willis, 1993). While I find no male bias in terms of fertility change during dragon and tigers years, the male bias can still exhibit in education attainment. Table 8 presents probit marginal effects allowing for heterogeneous male and female effects on various outcomes. While there is no difference in fertility spikes by gender, the results suggest males and females are affected differently during dragon and tiger years. Dragon and tiger direct effects apply mostly to males, with dragon direct effects estimated at 3.8 percentage points and tiger direct effect estimated at -3.9 percentage points on having college education at academic track. There is no dragon or tiger direct effect on females despite the groups having similar education attainment. A similar trend is observed for having high school education. There is also some evidence of resources shifting to women during tigers years with a tiger direct effect of 3.3 percentage points for university degree in vocational track and tiger direct effect of 1.5 percentage points for high school degree on women. The effects on having college education at vocational track are mostly small. The results are consistent with the hypothesis that superstition effects are driven by selective investment. If we assume the same gender bias is driving both fertility and education investment, then the results suggest the timing of the investment to happen after birth. The dragon cohort effects are similar in magnitude for males and females. However, the tiger cohort effect is mostly on the females and in the opposite direction than previous literature would suggest. Across Time Table 9 presents probit marginal effects from equations 1 and 2 when dummies for each individual dragon or tiger years are included. The results suggest that the effects on fertility is related to cohort effect but not the direct effect. Exploiting the differences in size of fertility effects, I find little evidence of direct effect for the 1976 dragons and 1974 tigers, even though there was an effect on fertility for both years. I also find strong evidence of direct effect for the 1988 dragons and 1986 tigers, even though there was no effect on fertility for the 1988 dragons. This suggests the effect of fertility has more to do with the 14

15 cohort effect. Overall the relative size of the cohort effect goes the same direction as the size of the fertility effect. I find negative and significant cohort effect for the 1976 dragons but no cohort effect for the 1988 dragons. I also find a negative cohort effect for the 1974 tigers and a positive cohort effect for the 1986 tigers. By Relative Age within Academic Cohort I investigate variations created by the timing of the school year cutoff. Individuals born between February and August are placed in an earlier school year while individuals born between September and January have to wait and enroll in the next school year. Those born between September and January are thus older within their respective academic cohort. Table 10 presents probit marginal effects allowing estimates to vary by relative age within school year. I run the regressions only on the dragon zodiac or the tiger zodiac due to the sample for estimating young tiger cohort effect and old dragon cohort effect overlaps when using zodiac year fixed effects. I find that the positive dragon direct effect applies only to the dragons relatively older within school cohort. Combined with the findings from different gender, the results support the timing of the dragon effect being after birth and on selective subpopulations. Among those affected by the tiger superstition, the direct effect is similar in magnitude among them. However, the estimates on the effects for the young tigers are noisier. I find a strong negative cohort effect for the older dragons while the cohort effect for the young tigers is statistically indistinguishable from zero. I cannot separately estimate the young dragon and old tiger cohorts effects and thus cannot infer whether cohort composition plays a role in determining cohort effects. Minority Status as a possible mechanism I explore whether the dragon and tiger effects are driven by minority immigrant status 13 by using the difference between different 13 See Goodkind (1995) for discussion of the minority immigrant status hypothesis applied in explaining the variation of dragon fertility effects in Malaysia. 15

16 waves of Chinese immigrants in Taiwan. If the dragon and tiger effects are driven by minority immigrant status, then we should expect people with parents who are more recent Chinese immigrants to have stronger effects. Table 11 presents probit marginal effects for equation 2 and 3 separately by the ethnic group of the father. The Taiwanese groups refers to parents who were born in Taiwan at the time of the Chinese Civil War in early 1950s. The Chinese group refers to people who immigrated to Taiwan during the Chinese Civil War. I find a weaker dragon direct effect for those with Chinese parents. This suggests the effects are not driven by minority immigrant status. Dragon and Tiger effects before 1970s While there is no observed fertility effect before the 1970s, it is possible the zodiac superstition exhibits itself in direct effects on individuals born before the 1970s. Table 12 presents probit marginal effects on those born before Columns 1 and 2 present results for having a college education. Columns 3 and 4 present results for having a high school education. Columns 5 and 6 present results for having a middle school education. 14 I find no evidence of a positive dragon effect on any of the education outcomes, but there is some evidence of tiger direct effect. One explanation for existence of tiger effect but no dragon effect, is that it is more costly to increase education than to decrease it Robustness Checks In this section, I consider four different types of selection issues, selection on observables, selection on unobservables, short-term switching, and delayed school entry, that could bias the estimates for direct and cohort effects. The results suggest selection is not a big concern. 14 There were no separate track for college before 1997 since those in vocational track are not expected to get a higher degree beyond high school for their jobs. 15 Another known zodiac superstition with historical evidence is the firehorse superstition in Japan. It is believed that women born in firehorse years brings misfortune. 16

17 Selection on Observables Table 13 and 14 present summary statistics for observable characteristics by different treatment groups. Table 13 presents results for individuals affected by the belief in dragon zodiac while Table 14 presents results for those affected by the belief in tiger zodiac. Columns 2 to 4 are means for the different groups while columns 5 and 6 are differences in means and significance star from t-tests. Overall the differences are mostly statistically insignificant across groups except a few significant differences across the groups. For those affected by the belief in dragon zodiac, they have a larger family size comparing within school years with dragons, more likely to be older and less likely to have a Chinese Nationalist father comparing across school years without dragons. For those affected by the belief in tiger zodiac, they are less likely to be male within school year and more likely to be older across school years. Short term Switching Modern birth technology such as Caesarean section allows for parents to choose the hour or date of the their children in a limited window. I account for the short-term switching by estimating the DD model without individuals born in the beginning and end of the lunar year (January and February in the Gregorian calendar). Table 15 presents these results. The results are similar in magnitude compared to the DD estimates. Delayed School Entry One possible way parents can avoid the dragon cohort effect related to increases in cohort size is to delay the entry of their children. If a substantial number of parents do this compared to other years, then we should see a spike in 7 year olds in 1st grade one school year after they were supposed to enter. From Figure 5, I do not find evidence of increased delayed entry related to people born in dragon years. Selection on Unobservables I follow the set up in Altonji et al. (2005) test whether these selection issues affect my results. Using the Stata commands from Oster (2017), the results 17

18 suggest selection on unobservables is not an issue. Selection on unobservables needs to go a different direction than selection on observables to explain away the dragon direct effect, tiger direct effect, and dragon cohort effect, while they need to be about 2.1 times as strong as selection on observables to explain away the tiger cohort effect. 16 The corresponding LPM regressions estimates and delta estimates are presented in Table Discussion and Conclusion Informal institutions, such as culture, play a role in determining economic outcomes. These institutions affect economic outcomes directly through changes in beliefs or through selection. However, individuals may react to the superstition and create spillover or cohort effects. Evaluating the impact of culture becomes harder when different mechanisms go in opposite directions. In this paper, I study the effects of zodiac superstition on education outcomes in Taiwan. I develop a new method using institutional details to separately estimate the effects coming from different mechanisms. I find evidence of both direct and cohort effects even though estimates using methods from other papers suggest no statistically significant effect overall. I find some parallels between the dragon(fortunate) zodiac and the tiger(unfortunate) zodiac but not on all effects. The direct effects for dragons and tigers are very similar in magnitude overall and in many of the subsamples for those born after 1970s. However, the dragon cohort effect is larger in magnitude compared to the tiger cohort effect even though the fertility effects are similar in magnitude. Historically, there is some evidence of a tiger direct effect but not a dragon direct effect. I argue that the direct effects are driven by selective investment while the cohort effects are driven by changes in cohort size. I do not find evidence of the direct effect related to fertility or driven by ethnic minority status. 16 The delta estimates have very large standard errors and need to be interpreted with caution. 18

19 These differences may reflect variations in beliefs or economic environment, through which the beliefs operate. Further research is needed to distinguish between the two possibilities. The findings from this paper present challenges to both theoretical and empirical work on superstition. It is possible that superstitions persist because the individuals are making wrong conclusions on the effect of superstition and fail to update their actions. Moreover, the existence of spillover effects by superstition highlight the importance of having larger scale field studies in addition to small scale randomized controlled trials in evaluating psychological effects at scale. The evidence from subsample analysis questions the exogeneity assumption other papers applied to use zodiac superstition as an instrumental variable. The existence of zodiac effects also have implications for evaluating other policies. One particular example is related to the interpretation of the effect of entrance exam change during the year 2000 in Taiwan. The datasets used to evaluate the reform contain a groups with people born in dragon years and a group who were not. A direct comparison between the two groups is thus aggregating both the effect of the reform and the dragon effects. Further studies should try to account for the dragon effect or use different comparison groups. 19

20 References Agarwal, S., Qian, W., Sing, T. F., and Tan, P. L. (2017). Dragon babies. Georgetown McDonough School of Business Research Paper No Available at SSRN: Altonji, J. G., Elder, T. E., and Taber, C. R. (2005). Selection on observed and unobserved variables: Assessing the effectiveness of catholic schools. Journal of Political Economy, 113(1): Bound, J. and Turner, S. (2007). Cohort crowding: How resources affect collegiate attainment. Journal of Public Economics, 91(5): Bnabou, R. and Tirole, J. (2016). Mindful economics: The production, consumption, and value of beliefs. Journal of Economic Perspectives, 30(3): Connelly, R. and Gottschalk, P. (1995). The effect of cohort composition on human capital accumulation across generations. Journal of Labor Economics, 13(1): Do, Q.-T. and Phung, T. D. (2010). The importance of being wanted. American Economic Journal: Applied Economics, 2(4): Foster, K. R. and Kokko, H. (2009). The evolution of superstitious and superstition-like behaviour. Proceedings of the Royal Society of London B: Biological Sciences, 276(1654): Francis, A. M. (2011). Sex ratios and the red dragon: using the chinese communist revolution to explore the effect of the sex ratio on women and children in taiwan. Journal of Population Economics, 24(3): Fudenberg, D. and Levine, D. K. (2006). Superstition and rational learning. The American Economic Review, 96(3):

21 Goodkind, D. M. (1991). Creating new traditions in modern chinese populations: Aiming for birth in the year of the dragon. Population and Development Review, 17(4): Goodkind, D. M. (1993). New zodiacal influences on chinese family formation: Taiwan, Demography, 30(2): Goodkind, D. M. (1995). The significance of demographic triviality: Minority status and zodiacal fertility timing among chinese malaysians. Population Studies, 49(1): Guiso, L., Sapienza, P., and Zingales, L. (2006). Does culture affect economic outcomes? Journal of Economic Perspectives, 20(2): Guiso, L., Sapienza, P., and Zingales, L. (2016). Long-term persistence. Journal of the European Economic Association, 14(6): Hwang, Y.-J. (2003). The construction and assessment of the "new occupational prestige and socioeconomic scores for taiwan": The indigenization of the social science and sociology of education research. Bulletin of Educational Research, (49:4):1 31. Johnson, N. D. and Nye, J. V. (2011). Does fortune favor dragons? Journal of Economic Behavior & Organization, 78(1): Lee, J. and Paik, M. (2006). Sex preferences and fertility in south korea during the year of the horse. Demography, 43(2): Liu, Y.-C. (2015). The years of dragon and tiger and human capital. Master s thesis, National Chi Nan University. Mocan, N. H. and Yu, H. (2017). Can superstition create a self-fulfilling prophecy? school outcomes of dragon children of china. Working Paper 23709, National Bureau of Economic Research. 21

22 Nunn, N. and Sanchez de la Sierra, R. (2017). Why being wrong can be right: Magical warfare technologies and the persistence of false beliefs. American Economic Review, 107(5): Oster, E. (2017). Unobservable selection and coefficient stability: Theory and evidence. Journal of Business & Economic Statistics, pages Parish, W. L. and Willis, R. J. (1993). Daughters, education, and family budgets taiwan experiences. The Journal of Human Resources, 28(4): Reiling, R. B. (2016). Does size matter? educational attainment and cohort size. Journal of Urban Economics, 94: Senbet, D. and Huang, W.-C. (2012). Do dragons have better fate? revisited using the us data. International Journal of Economics and Research, 3(5): Sim, N. (2015). Astronomics in action: The graduate earnings premium and the dragon effect in singapore. Economic Inquiry, 53(2): Sun, T.-h. (1989). A review of Fertility Control Policies in Taiwan Area, ROC, volume Social Phenomena in Taiwan - An Analysis, pages p Sun Yat-Sen Institute for Social Sciences and Philosophy, Academia Sinica. In Chinese. Welch, F. (1979). Effects of cohort size on earnings: The baby boom babies financial bust. Journal of Political Economy, 87(5):S65 S97. Wong, K.-F. and Yung, L. (2005). Do dragons have better fate? Economic Inquiry, 43(3): Yamada, H. (2013). Superstition effects versus cohort effects: is it bad luck to be born in the year of the fire horse in japan? Review of Economics of the Household, 11(2): Yip, P. S., Lee, J., and Cheung, Y. (2002). The influence of the chinese zodiac on fertility in hong kong {SAR}. Social Science & Medicine, 55(10):

23 9 Tables and Figures Figure 1: Dragon Effect Timeline Note: Solid lines are the calendar year cutoffs. Dashed lines are the school year cutoffs. This is for children born in 2000 entering elementary school. Figure 2: Live birth by birth year, Note: Green lines are years associated with the zodiac dragon. Orange lines are years associated with the zodiac tiger. Source: Taiwan Ministry of Interior. 23

24 Figure 3: Trends in Education Attainment Note: Green lines are years associated with the zodiac dragon. Orange lines are years associated with the zodiac tiger. 24

25 Figure 4: Comparison of Methods (a) College (Academic) - Dragon (b) College (Academic) - Tiger Note: Tiger Zodiac is not included in the analysis. (c) College (Any) - Dragon Note: Dragon Zodiac is not included in the analysis. (d) College (Any) - Tiger Note: Tiger Zodiac is not included in the analysis. (e) High School - Dragon Note: Dragon Zodiac is not included in the analysis. (f) High School - Tiger Note: Tiger Zodiac is not included in the analysis. Note: Dragon Zodiac is not included in the analysis. 25

26 Figure 5: 7 year old in first grade (per year olds) Note: Years after 2000 are not included due to increased enforcement of school entry laws following the amendment of the school entry laws in Table 1: Chinese Zodiacs and the corresponding years Zodiac Years in Gregorian Calendar Rat 1936, 1948, 1960, 1972, 1984, 1996, 2008 Ox 1937, 1949, 1961, 1973, 1985, 1997, 2009 Tiger 1938, 1950, 1962, 1974, 1986, 1998, 2010 Rabbit 1939, 1951, 1963, 1975, 1987, 1999, 2011 Dragon 1940, 1952, 1964, 1976, 1988, 2000, 2012 Snake 1941, 1953, 1965, 1977, 1989, 2001, 2013 Horse 1942, 1954, 1966, 1978, 1990, 2002, 2014 Sheep 1943, 1955, 1967, 1979, 1991, 2003, 2015 Monkey 1944, 1956, 1968, 1980, 1992, 2004, 2016 Chicken 1945, 1957, 1969, 1981, 1993, 2005, 2017 Dog 1946, 1958, 1970, 1982, 1994, 2006, 2018 Pig 1947, 1959, 1971, 1983, 1995, 2007,

27 Table 2: Zodiac and Log Annual Live Births, Overall (1) (2) Overall Gender Specific Male (0.017) (0.019) Dragon (0.020) (0.028) Tiger (0.029) (0.042) Dragon X Male (0.039) Tiger X Male (0.057) Observations Quadratic Trend Yes Yes Note: Standard errors in parentheses. * p < 0.10, ** p < 0.05, *** p < Table 3: Zodiac and Log Annual Livebirths, Individual Years (1) (2) Tiger Years Dragon Years 1974/ (0.010) (0.011) 1986/ (0.011) (0.012) 1998/ (0.013) (0.016) 2010/ (0.026) (0.032) Observations Quadratic Trend Yes Yes Note: Standard errors in parentheses. * p < 0.10, ** p < 0.05, *** p <

28 Table 4: Zodiac and Log Annual Livebirths, Other Zodiacs (1) (2) (3) (4) (5) (6) (7) Horse Sheep Monkey Chicken Dog Pig Rat Male (0.019) (0.018) (0.018) (0.018) (0.018) (0.017) (0.018) Zodiac Dummy (0.032) (0.049) (0.050) (0.042) (0.041) (0.057) (0.047) Zodiac Dummy X Male (0.042) (0.067) (0.068) (0.058) (0.055) (0.082) (0.068) Observations Quadratic Trend Yes Yes Yes Yes Yes Yes Yes Note: Standard errors in parentheses. * p < 0.10, ** p < 0.05, *** p <

29 Table 5: Descriptive Statistics - TSCS count mean sd min max Dependent Variables College and above(academic) College and above High School and above Independent Variable Dragon Direct Effect Dragon Cohort Effect Tiger Direct Effect Tiger Cohort Effect Control Variables Survey Year Birth School Cohort Birth Lunar Year Birth Month Male Born in City Father Bachelor s Education Father Associate s Education Mother Bachelor s Education Mother Associate s Education Father Chinese Nationalist Mother Chinese Nationalist Father Folk Religion Mother Folk Religion Father Occupation Rank Mother Occupation Rank Sibling Rank(1=Oldest) Family Size Oldest Sibling Note: The 2003 survey did not distinguish the education track of the individuals. 29

30 Table 6: Role of Controls Dependent Variable: College Education(Academic) (1) (2) (3) Dragon Direct Effect (0.007) (0.015) Tiger Direct Effect (0.006) (0.015) Dragon Cohort Effect (0.025) Tiger Cohort Effect (0.018) Observations Ymean Year Fixed Effects No Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. Table 7: Different Education Attainment College Academic College Any High School Any Dragon Direct Effect (0.015) (0.010) (0.005) Tiger Direct Effect (0.015) (0.009) (0.006) Dragon Cohort Effect (0.025) (0.022) (0.018) Tiger Cohort Effect (0.018) (0.013) (0.012) Observations Ymean Year Fixed Effects Academic Zodiac Academic Zodiac Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. 30

31 Table 8: Heterogeneity - Gender College Academic College Any High School Any Male Female Male Female Male Female Dragon Direct Effect (0.027) (0.007) (0.019) (0.012) (0.007) (0.005) Tiger Direct Effect (0.010) (0.024) (0.003) (0.020) (0.007) (0.006) Observations Ymean Year Fixed Effects Academic Academic Academic Academic Academic Academic Dragon Cohort Effect (0.045) (0.017) (0.044) (0.012) (0.023) (0.013) Tiger Cohort Effect (0.029) (0.032) (0.028) (0.014) (0.015) (0.011) Observations Ymean Year Fixed Effects Zodiac Zodiac Zodiac Zodiac Zodiac Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. Table 9: Heterogeneity - Different dragon/tiger years College Academic College Any High School Any 1976 Dragon Direct Effect (0.017) (0.011) (0.006) 1988 Dragon Direct Effect (0.013) (0.009) (0.013) 1974 Tiger Direct Effect (0.006) (0.006) (0.007) 1986 Tiger Direct Effect (0.013) (0.013) (0.011) 1976 Dragon Cohort Effect (0.019) (0.019) (0.016) 1988 Dragon Cohort Effect (0.009) (0.055) (0.034) 1974 Tiger Cohort Effect (0.019) (0.017) (0.014) 1986 Tiger Cohort Effect (0.006) (0.035) (0.019) Observations Ymean Year Fixed Effects Academic Zodiac Academic Zodiac Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. 31

32 Table 10: Heterogeneity - Relative Age within School Year College Academic College Any High School Any Young Dragon Direct Effect (0.022) (0.006) (0.005) Old Dragon Direct Effect (0.008) (0.011) (0.007) Young Dragon Cohort Effect (0.016) (0.022) (0.011) Old Dragon Cohort Effect (0.024) (0.025) (0.014) Observations Ymean Year Fixed Effects Academic Zodiac Academic Zodiac Academic Zodiac Young Tiger Direct Effect (0.031) (0.010) (0.006) Old Tiger Direct Effect (0.009) (0.013) (0.006) Young Tiger Cohort Effect (0.022) (0.009) (0.009) Old Tiger Cohort Effect (0.019) (0.023) (0.011) Observations Ymean Year Fixed Effects Academic Zodiac Academic Zodiac Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. 32

33 Table 11: Heterogeneity - Father Ethnicity College Academic College Any High School Any Taiwanese Chinese Taiwanese Chinese Taiwanese Chinese Dragon Direct Effect (0.011) (0.055) (0.008) (0.052) (0.003) (0.003) Tiger Direct Effect (0.021) (0.031) (0.010) (0.018) (0.005) (0.005) Observations Ymean Year Fixed Effects Academic Academic Academic Academic Academic Academic Dragon Cohort Effect (0.020) (0.085) (0.021) (0.063) (0.015) (0.015) Tiger Cohort Effect (0.016) (0.045) (0.011) (0.031) (0.010) (0.010) Observations Ymean Year Fixed Effects Zodiac Zodiac Zodiac Zodiac Zodiac Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. Table 12: Zodiacs before 1970 College Any High School Any Middle School Any Dragon Direct Effect (0.004) (0.003) (0.004) Tiger Direct Effect (0.001) (0.003) (0.003) Dragon Cohort Effect (0.009) (0.010) (0.007) Tiger Cohort Effect (0.010) (0.007) (0.006) Observations Ymean Year Fixed Effects Academic Zodiac Academic Zodiac Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. 33

34 Table 13: Means of Control Variables by Dragon Zodiac group (1) (2) (3) Observations Non-Dragons (1)-(2) (2)-(3) Dragons Others in Dragon Cohort Male (0.500) (0.499) (0.500) (0.019) (0.015) Born between September and January (0.498) (0.499) (0.495) (0.019) (0.014) Born in City (0.483) (0.487) (0.486) (0.027) (0.020) Father Bachelor s Education (0.268) (0.262) (0.251) (0.011) (0.008) Father Associate s Education (0.240) (0.270) (0.281) (0.011) (0.009) Mother Bachelor s Education (0.166) (0.196) (0.175) (0.008) (0.006) Mother Associate s Education (0.166) (0.179) (0.200) (0.007) (0.007) Father Chinese (0.291) (0.274) (0.294) (0.011) (0.009) Mother Chinese (0.196) (0.198) (0.202) (0.008) (0.006) Father Folk Religion (0.502) (0.502) (0.495) (0.062) (0.045) Mother Folk Religion (0.502) (0.500) (0.490) (0.090) (0.064) Father Occupation Rank (1.209) (1.298) (1.259) (0.092) (0.073) Mother Occupation Rank (1.204) (1.199) (1.243) (0.144) (0.116) Sibling Rank(1=Oldest) (1.339) (1.275) (1.323) (0.091) (0.071) Family Size (1.222) (1.174) (1.299) (0.083) (0.069) Oldest Sibling (0.488) (0.493) (0.481) (0.034) (0.026) Standard errors in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01 for t-tests in the last two columns. The 2001 surveys ask parents occupations when the respondent is 18 while all other surveys asks when respondent is age

35 Table 14: Means of Control Variables by Tiger Zodiac group (1) (2) (3) Observations Non-Tigers (1)-(2) (2)-(3) Tigers Others in Tiger Cohort Male (0.500) (0.499) (0.500) (0.018) (0.014) Born between September and January (0.499) (0.499) (0.495) (0.018) (0.014) Born in City (0.489) (0.480) (0.486) (0.025) (0.019) Father Bachelor s Education (0.259) (0.253) (0.251) (0.010) (0.008) Father Associate s Education (0.285) (0.264) (0.281) (0.011) (0.009) Mother Bachelor s Education (0.175) (0.175) (0.175) (0.007) (0.006) Mother Associate s Education (0.202) (0.192) (0.200) (0.008) (0.006) Father Chinese (0.290) (0.293) (0.294) (0.011) (0.008) Mother Chinese (0.197) (0.182) (0.202) (0.007) (0.006) Father Folk Religion (0.495) (0.496) (0.495) (0.057) (0.045) Mother Folk Religion (0.484) (0.497) (0.490) (0.075) (0.059) Father Occupation Rank (1.266) (1.314) (1.259) (0.089) (0.067) Mother Occupation Rank (1.280) (1.228) (1.243) (0.143) (0.107) Sibling Rank(1=Oldest) (1.328) (1.439) (1.323) (0.100) (0.074) Family Size (1.338) (1.358) (1.299) (0.098) (0.072) Oldest Sibling (0.491) (0.479) (0.481) (0.035) (0.027) Standard errors in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01 for t-tests in the last two columns. The 2001 surveys ask parents occupations when the respondent is 18 while all other surveys asks when respondent is age

36 Table 15: Robustness Check: Accounting for short-term switch in fertility College Academic College Vocational High School Any Dragon Direct Effect (0.012) (0.013) (0.005) Tiger Direct Effect (0.016) (0.011) (0.005) Dragon Cohort Effect (0.020) (0.017) (0.017) Tiger Cohort Effect (0.013) (0.009) (0.011) Observations Ymean Year Fixed Effects Academic Zodiac Academic Zodiac Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. Table 16: Selection on Unobservables: DD Model - LPM Dependent Variable: College Education (Academic) (1) (2) (3) (4) δ Dragon Direct Effect (0.016) (0.015) Tiger Direct Effect (0.013) (0.016) Dragon Cohort Effect (0.025) (0.024) Tiger Cohort Effect (0.019) (0.017) Observations Ymean Adjusted R-squared Controls No Yes No Yes Year Fixed Effects Academic Academic Zodiac Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. Columns 1 and 2 present regression coefficients while column 3 present estimated delta from Oster (2017). Standard errors for estimates of delta parameter are not presented due to their magnitude. 36

37 Appendix A Extra Tables Figure B1: Comparison of Methods (a) College (Academic) - Dragon (b) College (Academic) - Tiger Note: Tiger Zodiac is not included in the analysis. (c) College (Vocational) - Dragon Note: Dragon Zodiac is not included in the analysis. (d) College (Vocational) - Tiger Note: Tiger Zodiac is not included in the analysis. (e) High School - Dragon Note: Dragon Zodiac is not included in the analysis. (f) High School - Tiger Note: Tiger Zodiac is not included in the analysis. Note: Dragon Zodiac is not included in the analysis. 37

38 Table B1: Role of Controls Dependent Variable: College Degree(Academic) (1) (2) (3) (4) (5) (6) (7) Dragon Direct Effect (0.009) (0.013) (0.013) (0.011) (0.012) (0.012) Tiger Direct Effect (0.008) (0.024) (0.023) (0.025) (0.025) (0.016) Dragon Cohort Effect (0.011) (0.011) (0.010) (0.010) (0.011) Tiger Cohort Effect (0.021) (0.020) (0.022) (0.022) (0.014) Observations Ymean Year Fixed Effects No No No No No Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. Table B2: Role of Controls Dependent Variable: College Degree(Any Track) (1) (2) (3) (4) (5) (6) (7) Dragon Direct Effect (0.009) (0.011) (0.011) (0.012) (0.011) (0.010) Tiger Direct Effect (0.008) (0.017) (0.016) (0.019) (0.019) (0.014) Dragon Cohort Effect (0.010) (0.010) (0.009) (0.009) (0.020) Tiger Cohort Effect (0.016) (0.015) (0.018) (0.018) (0.013) Observations Ymean Year Fixed Effects No No No No No Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. 38

39 Table B3: Role of Controls Dependent Variable: High School Degree (Any Track) (1) (2) (3) (4) (5) (6) (7) Dragon Direct Effect (0.003) (0.010) (0.010) (0.011) (0.010) (0.004) Tiger Direct Effect (0.007) (0.008) (0.008) (0.008) (0.008) (0.005) Dragon Cohort Effect (0.010) (0.011) (0.011) (0.011) (0.016) Tiger Cohort Effect (0.007) (0.007) (0.008) (0.008) (0.014) Observations Ymean Year Fixed Effects No No No No No Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. Table B4: Different Education Attainment College Any High School Any Middle School Any Dragon Direct Effect (0.012) (0.010) (0.004) Tiger Direct Effect (0.016) (0.014) (0.005) Dragon Cohort Effect (0.011) (0.020) (0.016) Tiger Cohort Effect (0.014) (0.013) (0.014) Observations Ymean Year Fixed Effects Academic Zodiac Academic Zodiac Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. 39

40 Table B5: Heterogeneity - Gender College Academic College Any High School Any Male Female Male Female Male Female Dragon Direct Effect (0.018) (0.004) (0.012) (0.008) (0.007) (0.015) Tiger Direct Effect (0.017) (0.018) (0.006) (0.026) (0.012) (0.006) Observations Ymean Year Fixed Effects Academic Academic Academic Academic Academic Academic Dragon Cohort Effect (0.023) (0.009) (0.032) (0.010) (0.020) (0.019) Tiger Cohort Effect (0.022) (0.013) (0.020) (0.009) (0.017) (0.016) Observations Ymean Year Fixed Effects Zodiac Zodiac Zodiac Zodiac Zodiac Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. 40

41 Table B6: Heterogeneity - different dragon/tiger years College Academic College Any High School Any 1976 Dragon Direct Effect (0.008) (0.011) (0.004) 1988 Dragon Direct Effect (0.006) (0.016) (0.007) 1974 Tiger Direct Effect (0.009) (0.012) (0.004) 1986 Tiger Direct Effect (0.017) (0.003) (0.004) 1976 Dragon cohort Effect (0.002) (0.011) (0.015) 1988 Dragon cohort Effect (0.005) (0.048) (0.005) 1974 Tiger cohort Effect (0.002) (0.010) (0.014) 1986 Tiger cohort Effect (0.004) (0.035) (0.004) Observations Ymean Year Fixed Effects Academic Zodiac Academic Zodiac Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. Table B7: Zodiacs before 1970 College Any High School Any Middle School Any Dragon Direct Effect (0.006) (0.006) (0.010) Tiger Direct Effect (0.008) (0.015) (0.005) Dragon Cohort Effect (0.011) (0.011) (0.013) Tiger Cohort Effect (0.013) (0.015) (0.018) Observations Ymean Year Fixed Effects Academic Zodiac Academic Zodiac Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. 41

42 Table B8: Heterogeneity - relative age within school year College Academic College Any High School Any Young Dragon Direct Effect (0.020) (0.012) (0.006) Old Dragon Direct Effect (0.009) (0.010) (0.004) Young Dragon Cohort Effect (0.009) (0.021) (0.021) Old Dragon Cohort Effect (0.016) (0.028) (0.008) Observations Ymean Year Fixed Effects Academic Zodiac Academic Zodiac Academic Zodiac Young Tiger Direct Effect (0.035) (0.022) (0.005) Old Tiger Direct Effect (0.007) (0.010) (0.006) Young Tiger Cohort Effect (0.021) (0.014) (0.017) Old Tiger Cohort Effect (0.011) (0.022) (0.022) Observations Ymean Year Fixed Effects Academic Zodiac Academic Zodiac Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. 42

43 Table B9: Heterogeneity - Father Ethnicity College Academic College Any High School Any Taiwanese Chinese Taiwanese Chinese Taiwanese Chinese Dragon Direct Effect (0.007) (0.062) (0.007) (0.046) (0.003) (0.003) Tiger Direct Effect (0.019) (0.033) (0.015) (0.034) (0.004) (0.004) Observations Ymean Year Fixed Effects Academic Academic Academic Academic Academic Academic Dragon Cohort Effect (0.009) (0.070) (0.025) (0.049) (0.015) (0.015) Tiger Cohort Effect (0.013) (0.037) (0.015) (0.031) (0.012) (0.012) Observations Ymean Year Fixed Effects Zodiac Zodiac Zodiac Zodiac Zodiac Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. Table B10: Robustness Check: Accounting for short-term switch in fertility College Academic College Any High School Any Dragon Direct Effect (0.008) (0.010) (0.005) Tiger Direct Effect (0.016) (0.015) (0.004) Dragon Cohort Effect (0.010) (0.012) (0.014) Tiger Cohort Effect (0.017) (0.007) (0.011) Observations Ymean Year Fixed Effects Academic Zodiac Academic Zodiac Academic Zodiac * p < 0.1, ** p < 0.05, *** p < Standard errors clustered at birth year level. Note: All regressions include survey year, birth month fixed effects, and birth year in controls. 43

44 What Drives (No) Adoption of New Irrigation Technologies: A Structural Dynamic Estimation Approach Haoyang Li Jinhua Zhao November 5, 2018 Abstract Climate change and continuing groundwater level decline in many important agricultural zones calls for the adoption of more efficient irrigation technologies to alleviate the problem. This paper studies farmers adoption behavior with a structural econometrics that explicitly takes profit gain of adoption, its uncertainty and individual-specific adoption cost into consideration. Using a panel data on Low Energy Precision Application (LEPA) adoption in the Kansas part of High plain Aquifer, we find strong evidence that farmers are forward-looking when they make adoption decisions. If farmers are myopic, average LEPA adoption probability would increase by 42% percent during the sample period. LEPA profit gain uncertainty and irreversible adoption cost together create incentives for a forward-looking farmer to delay adoption. Consequently, policies that reduce downward risk (e.g. crop insurance) and reduce adoption cost (e.g. cost-share payments) could effectively promote LEPA adoption. In particular, a 75% cost-share payment to LEPA adopters (i.e. adoption cost rebate) increases the average adoption probability of LEPA by 10%. The results could provide insights to other regions that are considering to promote efficient irrigation adoption through policy interventions. Keywords: Technology Adoption, Real Option, Uncertainty, Adoption Cost, Dynamic Discrete Choice

45 1 Introduction Agriculture is among the most fragile sectors facing climate change. Due to greater variability in rainfall and higher frequency of serious droughts, irrigation is becoming an importation climate change adaptation strategy (Zilberman et al., 2012). Consequently, over-drafting of irrigation water becomes a common practice, especially in most semi-arid agricultural zones such as California and the High Plain Aquifer (HPA) area in the US. Indeed, half of the groundwater storage in south Ogallala aquifer underlying the HPA has been depleted in the recent eighty years and agriculture profits are threatened(haacker et al., 2015). As a result, multiple local level solutions have been proposed to preserve water resource and increase agriculture profits. One of the solutions is to increase water use efficiency 1 through adopting more efficient irrigation technologies such as Low Energy Precision Application (LEPA) irrigation equipment. In practice, however, LEPA was not adopted immediately when they became available in most US agriculture zones. For example, the LEPA diffusion process lasts around ten years in the Kansas part of HPA. The diffusion rate of new technologies can be affected by two major factors. The first factor is adoption cost, which includes the upfront purchasing and installing cost of the technology. Second, farmers face uncertainty regarding the new technology s profitability. A forward-looking farmer will make sure that profit gain from LEPA adoption is high enough when he adopts such that it would not drop to a fairly low level in the future due to possible profit fluctuations (i.e. uncertainty) such that the ex-post sum of discounted profits do not justify adoption cost(carey and Zilberman, 2002). This effect of current period profit on farmers expectations on future profit represents a form of learning according to real option theory (Dixit and Pindyck, 1994). This paper studies the forces that drive LEPA diffusion in the Kansas part of HPA through a structural econometrics approach in which both adoption cost and profit gain 1 amount of water utilized by crop efficiency = (Pfeiffer and Lin, 2014). Efficiency level is always less total water extraction than 1 because part of irrigation water is lost due to evaporation, soil water percolation and wind. 1

46 uncertainty are explicitly considered. We find strong evidence that farmers are forward looking. If farmers are myopic (i.e. behaves according to simple Net Present Value Rule), average LEPA adoption probability would increase by 42% percent during the sample period. A rejection of the NPV rule lends supports to real option theory that uncertainty in profit gain from LEPA adoption creates incentive for farmers to delay adoption even if farmers are risk neutral. An increase in LEPA profit gain uncertainty tends to decrease adoption rate under the current uncertainty level, although the magnitude of the effect is small. Finally, policies that reduce downward risk (e.g. crop insurance) and reduce adoption cost (e.g. cost-share payments) could effectively promote LEPA adoption. In particular, a 75% costshare payment to LEPA adopters (i.e. adoption cost rebate) increases the average adoption probability of LEPA by 10%. To our knowledge, this is the first paper that uses structural dynamic estimation to study irrigation technology adoption. Many reduced form empirical studies (e.g. Probit/Logit model and duration model) of irrigation technology adoption exist in the literature (Caswell and Zilberman, 1986; Dinar and Yaron, 1992; Shrestha and Gopalakrishnan, 1993; Foltz, 2003; Kulecho and Weatherhead, 2006; Alcon et al., 2011). Factors such as crop price, energy price and weather conditions that represents profit gain from adoption are used to explain irrigation technology adoption. While reduced-form studies excel in obtaining the overall effect of those factors on adoption decision, the pathways through which the causality relationships are established remain unclear. For example, how important is profit gain uncertainty on top of the level of profit gain? What is the effect of cost-share rebates in promoting technology adoption? In a reduced form estimation where uncertainty is difficult to measure and cost-share payments are not provided, such questions are impossible to answer because the underlying economics structure has been changed. Based on a structural model that captures all such factors explicitly, we are able to conduct counterfactual policy simulations to answer such questions. Methodologically, this paper is also among one of the first applications to deal with un- 2

47 observed individual heterogeneity in a structural dynamic discrete choice model using the methodology proposed by Arcidiacono and Miller (2011). The importance of accounting for individual heterogeneity in technology adoption studies has been well documented by Suri (2011). The difficulty of incorporating individual heterogeneity in structural dynamic discrete choice model is mainly due to computational burden, which is alleviated in Arcidiacono and Miller (2011) by combining reduced form techniques and structural estimation in a novel fashion. However, the method is not widely utilized in the literature, with an exception of Chung et al. (2013), which studies sale force response to a bonus-based compensation plan. Moreover, we construct a large and long farmer level panel dataset in the estimation. Traditionally, cross sectional (Caswell and Zilberman, 1986; Foltz, 2003; Koundouri et al., 2006) and aggregate time-series dataset (Alcon et al., 2011) are used in irrigation technology adoption. Cross sectional data is just a snapshot of the diffusion process and therefore provides little information on the process. Time series data, on the other hand, represents the aggregate diffusion process, but ignores individual heterogeneity, which can be a fairly important driver of the diffusion pattern (Suri, 2011). The use of a panel dataset combines the merits of cross-sectional and time-series dataset and is expected to provide a more complete view of the adoption process. Only a few studies use panel dataset (Shrestha and Gopalakrishnan, 1993; Genius et al., 2014). However, their dataset contains either too few study periods or too few cross-sectional observations (i.e. farmers). The remainder of the paper proceeds as follows. Section 2 introduce the dataset used in the paper. Section 3 specifies the dynamic LEPA adoption model that forms the backbone of empirical estimation. Section 4 explains the estimation method. Section 5 presents estimation results and discusses evidence of forward looking on adoption decision. Section 6 discusses the counter-factual simulation results and section 7 concludes. 3

48 2 Study Region and Data Our study region is the Kansas part of HPA, which spans more than 30,000 square miles across western Kansas. Irrigation agriculture accounts for more than 90 percent of total agricultural production in this area and groundwater is almost the pure irrigation source. Information about well locations and irrigation technologies is drawn from the Water Information Management and Analysis System (WIMAS) maintained by the Kansas Water Office. Our sample contains a large number of irrigation wells in this area 7251 in total. The data also spans a long time period from 1997 to Information about well locations, irrigation water extractions and irrigation technologies is drawn from the Water Information Management and Analysis System (WIMAS) maintained by the Kansas Water Office. WIMAS data also contains information on water rights 2 associated with each irrigation well. Spatially explicit data on depth to groundwater is obtained from the output files of Haacker et al. (2015). Geo-referenced precipitation and temperature data is obtained from the North America Land Data Assimilation System (NLDAS) maintained by NASA. We match the well level data with the spatially explicit data in ArcGIS according to each well s geographical coordinates. Finally, information on crop price comes from NASS quick stats and information on natural gas price is obtained from EIA. Table 1 presents the summary statistics of the variables used in our study. In addition, figure 1 depicts LEPA s diffusion path. Prior to the introduction of LEPA in 1991, Center Pivot (CP) was the dominant irrigation technology in the study region. Compared to CP, LEPA is more efficient and is therefore more profitable and more likely to preserve groundwater in the aquifer. A sudden jump in total number of adopters is observed in 1997, which is mainly caused 2 A water right specifies the annual maximum amount of groundwater an irrigation well could extract. Although farmers are allowed to require modification to this annual upper limit, they seldom do so in practice. Therefore, water right level is time-invariant. 4

49 by inconsistent definition of LEPA before and after Therefore, we only use data from 1997 onwards in our analysis to avoid potential problems caused by inconsistent variable definition. On average, farmers adopted LEPA around 2000, three years after the start of our sample period. The state of Kansas started to provide cost shares that cover up to 75% of equipment cost to some LEPA adopters since financial year Although we do not observe who benefited from the cost share program, only around 10% of farmers in Kansas received the funding from 1996 to Therefore, the actual cost share payment to an average farmer in the region could be treated as zero. 3 The Dynamic Technology Adoption Model This section outlines a model of irrigation technology adoption, where the economic agents are individual farmers who decide when to replace their current irrigation system with a more efficient substitute. The two irrigation technologies being considered are LEPA (L) and CP (P). LEPA is more efficient than CP such that it withdraws less water to achieve the same level of crop yield. LEPA requires less energy to operate as well the required water pressure to operate the system reduces from around 75 PSI for CP to 18 PSI for LEPA (DeLano et al., 1997). 3.1 Model Setup The time-line of the model is as follows. At the beginning of each year (t), a farmer (i) who has not adopted LEPA yet decides whether to adopt it now. If he decides not to adopt in the current year, the adoption decision is passed to the next year. If he instead decides to adopt, 3 Before 1997, only Center Pivot with LEPA nozzle is called LEPA in the dataset. However, all Center Pivot systems that are equipped with dropped nozzle are called LEPA after Albeit the different name of nozzles, their water application efficiency are similar. The most significant difference between nozzle types are the ability to be adapted to local farming conditions. 4 We thank Lisa Pfeiffer and Cynthia Lin to provide us the data on county-level cost-share subsidy amount 5

50 he pays the adoption cost immediately (C i ) and starts to use LEPA in year t. Converting from CP irrigation system to LEPA requires not only purchasing additional equipments but also changing farming practices 5. Equipment cost could be pretty similar for every farmer, but the cost of changing farming practices are potentially heterogeneous across farmers due to the difference in their current practices. Unfortunately, although farmers know exactly the magnitude of their own adoption cost, we do not observe that information. Therefore, we assume there are two levels of adoption cost, one being high (C H ) and one being low (C L ), and each farmer has non-negative probabilities of belonging to each of the cost groups (τi H and τi L ) 6. LEPA adoption is assumed to be irreversible he never switches back to CP once LEPA has been adopted 7. Therefore, farmers who adopted LEPA in the previous years would not make adoption decisions again. Finally, every farmer, regardless of his LEPA adoption status, makes water use decision in year t conditional on his irrigation system and receives the corresponding farming profits. Let πit P (x it, ε P it) and πit(x L it, ε L it) be the per-period per-acre profit of irrigation using CP and LEPA, respectively. Although state variables (x it ) such as precipitation, crop price and energy price that affect the per-period profit functions could be directly observed by both farmers and econometricians, others could only be observed by the farmers, but are unobserved by econometricians. We group all such unobserved variables to ε it = {ε P it, ε L it}. Therefore, the per-period profit functions could be decomposed into a deterministic part and a random part (random from the perspective of econometricians): π j it (x it, ε j it ) = πj (x it ) + ε j it, for j {P, L} (1) 5 For example, it requires a switch from tillage to No-till management. It also requires construction of water ditches across farmlands. 6 Assuming discrete supports for unobserved heterogeneities (a.k.a finite mixture ) is a common practice in dynamic discrete choice estimation literatures and could provide a good approximation to the true distributions, seemroz and Guilkey (1999), Arcidiacono and Miller (2011) and Chung et al. (2013) for references. 7 This assumption is realistic. In our sample, there are seldom any farmers who switched back from LEPA to CP. This is because LEPA is almost always more profitable than CP due to the increased efficiency and reduced energy requirement. 6

51 While farmers know the realizations of x it and ε it in year t, they could not predict their realizations in the future perfectly. Following Murphy (2017), Group all the observable state variables that help predict x ijt+1 in year t into a vector Γ 8 it, the uncertainty inherent in these state variables are captured by f(γ it+1, ε it+1 Γ it, ε it, C i ), the joint transition probabilities of the state variables above. Following the convention in dynamic discrete choice model literatures, we make the conditional independence assumption: Assumption 1 -Conditional Independence: f(γ it+1, ε it+1 Γ it, ε it, C i ) = f(γ it+1 Γ it )f(ε it+1 ) Finally, we assume that ε it conforms to i.i.d Type 1 Extreme Value Distribution with scale parameter σ ε. To wrap up, the primitives of the model are given by {π, f, τ, β}, where β is the discount factor farmers used to depreciate cash flows in the future. When all the four sets of model primitives are known, farmers adoption behaviors could be inferred. 3.2 Per-Period Profit The first step in defining the per-period profit functions above is to specify a crop-water production function. In order to maintain flexibility, we specify a concave per-acre cropwater production function, following agronomic studies (Martin et al., 1984; Tong and Guo, 2013): q ij (w ijt ) = α 0it + α 1it (θ j w ijt + r it ) + α 2 (θ j w ijt + r it ) 2 for j {P, L} (2) where w ijt is annual water extraction, r it is annual rainfall, and θ j is the efficiency level of CP and LEPA, which denotes the percentage of total water extracted that is utilized by the crop. We set θ P = 0.75 and θ L = 0.9 following Amosson et al. (2002) and Irmak et al. 8 For example, if x ijt+1 follows an AR(1) process, Γ it includes only x ijt. On the contrary, if it follows an AR(2) process, x ijt 1 is also included in Γ it 7

52 (2011). Therefore, θ j w ijt + r it is the total effective water from irrigation and rainfall that is utilized by the crop. We allow production function parameters (i.e. α 0it, α 1it and α 2i ) to be heterogeneous across farmers or years to capture the effect of unobservables on crop yield 9. We believe this heterogeneity concave production function imposes just enough structure while reserving adequate flexibility. Although farmers do plant different crops in Kansas HPA region, corn is most prevalent. It ranks top 2 agricultural crops each year during based on USDA NASS statistics. On the other hand, although we have data on self-reported crop code in WIMAS database, the information is noisy. Reported crop type is often a combination of multiple crops (e.g. corn, wheat and barley), but the areas planted to different crops in the combination are not reported, making it difficult to utilize this information. Therefore, the production function in equation (4) does not distinguish among different crops. This simplification would not cause serious problems due to the dominance of corn in the region. Further, heterogeneity of α 1it across farmers and years could also capture some effects of crop choice. The second step is to specify production cost. Following Rogers and Alam (2006) and Pfeiffer and Lin (2014), variable cost to pump one acre-foot groundwater is specified as a linear function of total groundwater extraction: c j (w ijt ) = p e it w ijt = η p gas t (dtw i P SI j ) w ijt (3) with p e t being energy cost to lift 1 acre-feet of groundwater for farmer i in year t. This energy cost could be calculated from the engineering relationship between amount of natural gas to lift 1 acre-feet groundwater up for 1 foot (η = 0.022), natural gas price (p gas t ), irrigation well s depth to groundwater (dtw i ) and water pressure required to operate irrigation system j {P, L} (P SI j ). We set P SI P = 18 and P SI L = 75 following DeLano et al. (1997). Given the settings above, the cost of water pumping is known to econometricians. 9 α 0it will finally be canceled out when calculating profit difference between LEPA and CP. 8

53 Consequently, farmer i s true per-acre profits from using irrigation system j could be expressed as: π j i (w ijt) = p t q it (w ijt ) c j (w ijt ) (4) where p t is crop price in year t. In the context of irrigation technology adoption, only profit difference between CP and LEPA matters. We omit other variable costs and fixed cost in equation (4) due to data limitation, assuming they are the same for both irrigation systems and are independent of marginal product and marginal cost of water resource. During the study period, the average depth to groundwater level across the study region only increased by 5 feet, compared to the average depth to groundwater level of 108 feet. Therefore, we assume that water use does not influence depth to groundwater level in the model and water extraction decision is static. Maximize equation (4) with respect to w it, the first order condition (FOC) gives the optimal water extraction per acre for farmer i in year t with irrigation technology j: w ijt = α 1it 2α 2 θ j + 1 2α 2 p e it θ 2 j p t r it θ j (5) Plug w ijt into equation (4) gives the optimal deterministic part of the per-period profit function π j (x it ). 3.3 The Adoption Decision Optimal Discrete Choice Farmers are assumed to maximize their sum of discounted lifetime profits by determining the optimal time to adopt LEPA. His life time expected profits could be represented recursively by a Bellman Equation that decomposes the lifetime value function into period t s per-period profit and the expected sum of per-period profits from year t+1 onwards. With this recursive representation, the choice-specific value functions associated with 9

54 adopting and not adopting LEPA in the current year 10 are expressed as: v L (Γ it ) = π L (x it ) + βe [ ] v L (Γ it+1 ) + ε L it+1 Γ it, ε L it = π L (x it ) + β v L (Γ it+1 )f(γ it+1 Γ it )d(γ it+1 ) (6) and v P (Γ it, C i ) = π P (x it ) + βe { max[v P (Γ it+1, C i ) + ε P it+1, v L (Γ it+1 ) C i + ε L it+1] Γ it, ε it } = π P (x it ) + βσ ε { ln exp ( vl (Γ it+1 ) C i σ ε ) + exp ( vp (Γ it+1, C i ) σ ε )} f(γ it+1 Γ it )dγ it+1 (7) where the second equality follows from the i.i.d type I extreme value distribution assumption of ε it. Finally, the farmer will choose to adopt LEPA in year t if the value of choosing LEPA is higher than the value of choosing CP. Otherwise, he will keep using CP for the current year. Let d ijt {0, 1} denote the whether farmer i uses technology j in year t: v L (Γ it ) C i + ε L it > v P (Γ it, C i ) + ε P it d ilt = 1 & d ip t = 0 v L (Γ it ) C i + ε L it < v P (Γ it, C i ) + ε P it d ilt = 0 & d ip t = 1 (8) 4 Estimation There are three set of parameters in the model specified in 3. Let Ω 1 = {α 1it, α 2i } denote parameters in production function, Ω 2 denote parameters in state variable transition function f(γ it+1 Γ it ). Finally, let Ω 3 = {C H, C L, τ H i, λ it, σ ε } denote the collection of adoption cost distribution parameters and the standard deviation of per-period profit shocks. In this 10 Following Rust (1987), the choice-specific value functions are the lifetime expected profit gains (compared to using CP forever) a farmer would receive from using LEPA and CP this year, without considering ε it ) 10

55 section, we discuss the estimation of these three sets of parameters in steps. 4.1 Production Function Estimation Unlike most production function estimation literatures, we do not have access to individual farmer level crop yield data. Therefore, we could not estimate the relationship between water use and crop yield directly. Instead, we rely on equation (5), the optimality condition associated with annual water extraction, to identify parameters in production function (i.e. α 1it and α 2 ). Rearranging equation (5), we have: θ j wijt + r it = α 1it + 1 p e it + µ it (9) 2α 2 2α 2 θ j p t We parameterize α 1it as follows: α 1it = α i + α 1gt D t g i + α 1temp temp it + µ it (10) where α i is an farmer level fixed effect, D t is a series of year dummies, g t is a series of Groundwater Management District (GMD) dummies 11, temp it is a vector of monthly average temperatures in the growing season, and µ it is an idiosyncratic unobserved term. This derived estimation equation is broadly consistent with reduced-form water use estimation equations in Hendricks and Peterson (2012),Pfeiffer and Lin (2014) and Li and Zhao (2018). Ideally, equation (9) could be estimated with a fixed effects model. However, crop price is only available at state level, rather than individual farmer level. It is reasonable to suspect that there is a measurement error associated with crop price in equation (9), leading to biased estimate of α 2. To solve this potential endogeneity problem, we use instrumental variables (IV) to aid the estimation. As corn is the dominant crop in the study area and prices of different crops are often heavily correlated, we use corn price to represent crop 11 The Kansas HPA is divided into five GMDs for groundwater monitoring and regulation purpose. Areas within the same GMD share similar hydrological and climatically conditions 11

56 price. In U.S, corn is used primarily to feed livestocks and to produce ethanol. Therefore, we use annual cattle price and ethanol demand in Kansas as IVs for crop price. The output of this estimation step is ˆΩ 1 = {ˆα 1it, ˆα 2i }. 4.2 Dynamic Discrete Choice Estimation The remaining set of parameters Ω 3 = {C H, C L, τ H i, τ L i, σ ε } has to be estimated in the context of a dynamic LEPA adoption model. Traditionally, Nested Fixed Point Algorithm (NFXP) proposed by Rust (1987) could be utilized to estimate the dynamic discrete choice model. For each iteration of model parameter guess, the NFXP solves the dynamic programming problem defined by equations (6)-(8) and computes choice specific value functions. However, the computational burden of NFXP is relatively high due to this repeated solution of dynamic programming problems. Most Importantly, unobserved heterogeneity, which appears in our model through individual-specific adoption costs, could make NFXP easily become computationally infeasible (Arcidiacono and Miller, 2011). Therefore, we follow the insights from Hotz and Miller (1993), Bajari et al. (2007) and Arcidiacono and Miller (2011) to estimate the model without solving explicitly the dynamic programming model. To proceed, we rearrange equation (7) as 12 : v P (Γ it, C i ) = π P (x it ) + β [v L (Γ it+1 ) C i σ ε lnp r L (Γ it+1, C i )]f(γ it+1 Γ it )dγ it+1 (11) where P r L (Γ it+1, C i ) is the probability of choosing LEPA in year t + 1 given Γ it+1 : P r L (Γ it+1, C i ) = exp[ v L(Γ it ) C i σ ε ] exp[ v P (Γ it,c i ) σ ε ] + exp[ v L(Γ it ) C i σ ε ] = exp[ v P t (v Lt C i ) σ ε ] (12) Subtract equation (11) from sum of equation (6) and adoption cost: v L C i v P = π L it π P it + βσ ε lnp r L (Γ it+1, C i )f(γ it+1 Γ it )dγ it+1 (1 β)c i (13) 12 The details of the derivation is contained in Appendix A1. 12

57 which is a function of per-period profit difference between LEPA and CP (πit D = πit L πit P ) and the next period s probability of adopting LEPA. According to equation (8), the likelihood of observing farmer i whose adoption cost is C i {C H, C L } choosing irrigation technology j {P, L} in year t is: P r[v L (Γ it ) C i + ε L it > v P (Γ it, C i ) + ε P it], l ijt (Γ it ; C i, σ ε ) P r j (Γ it ; C i, σ ε ) = P r[v L (Γ it ) C i + ε L it < v P (Γ it, C i ) + ε P it], j = L j = P (14) Therefore, the likelihood contribution of this farmer in year t is: l it (d it, Γ it+1 Γ it, C i ; σ ε ) = [l ijt (Γ it, C i ; σ ε )] d ijt f(γ it+1 Γ it ) (15) j {P,L} Integrating C i out from equation (15), the full likelihood contribution of farmer i is: l i (d i, Γ i Γ i1, σ ε ) = τ H it T i l it (d it, Γ it+1 Γ it, C H, σ ε ) + τ L it T i t=1 t=1 l it (d it, Γ it+1 Γ it, C L, σ ε ) (16) where T i is the number of years that farmer i waited until he adopted LEPA. In addition, d i = {d i1, d i2... d iti } and π D i = {π D i1, π D i2... π D it i }. To complete the model, parameterize the probability of farmers falling into the two adoption class as: τ H i = τ H (Γ i1 ; δ) = exp(δ 0 + δ 1 Γ i1 ) 1 + exp(δ 0 + δ 1 Γ i1 ) (17) The estimation then follows the E-M CCP algorithm in Arcidiacono and Miller (2011), the details of which could be found at Appendix A2-A3. 13

58 5 Empirical Results In this section, We present estimation results of production function parameters (ˆΩ 1 ) and dynamic parameters (ˆΩ 3 ). Parameters in state variable transition function (ˆΩ 2 ) is reported in Appendix A Production Function Estimation Results Production function estimation results are reported in table 2. Results shown in column (1) and (3) are obtained by applying farm-level fixed effects model to the first order condition of profit maximization (9). The intercept of water s marginal product (α 1it ) depends only on farmer fixed effect and year-by-gmd fixed effect, while it depends also on monthly temperature in the growing season in specification (3). The slope of water s marginal product (α 2 ) is around-33 in both specifications, which is negative and statistically significant, confirming the concave curvature of production function. The pattern of temperature s effect on marginal product of water in specification (3) in is somewhat out of expectation. In general, we expect the effect to be positive during colder months (Sep-Nov) and negative during hotter months (May-Aug), which is not the pattern displayed in column (3). However, the expected α 1it across farmers and years are very close in both specifications (around 143). Therefore, it is possible that monthly temperature in a particular year are pretty homogeneous for farmers in a same GMD and the effect of temperature is largely subsumed in year-by-gmd dummies. Our production function estimation strategy described above estimates production function parameters indirectly by leveraging farmer s profit maximization problem. As a robustness check, we also provide a direct production function estimation using county-level crop yield data. Specifically, we estimate: q ct (w ct ) = α 0ct + α 1ct Wit e + α 2ct Wit e2 + µ ct 14

59 where subscript c indexes county in the study region and W e is effective water calculated from individual farmer-level water use averaged to county level 13. This county level production function is a close approximation of farmer level production function in equation 2. County level fixed effects model is applied to estimate this function and the results are shown in column (2) and (4) in table 2. Similarly, monthly temperature s effects on marginal product of water and is excluded in specification (2) but included in specification (4). The estimated slope of marginal product (α 2 ) and the average of the intercept of marginal product (α 1 ) across farmers and time are pretty similar to each other across specifications (1)-(4). Therefore, we believe our identification strategy based on water use FOC does a good job in identifying production function parameters. We rely on the results of specification (1) in subsequent estimations. We do not use the direct yield function estimation results in specification (2) and (4) because farmer-level fixed effects estimation allows us to estimate farmer-specific marginal product intercept of water resource (i.e. α 1i ). The importance of accounting for individual level heterogeneity has been well documented by Suri (2011). One such farmer-level heterogeneities comes from heterogeneity in farmers per-acre profit difference between LEPA and CP, which in turn comes from farmers heterogeneous production functions. Indeed, the histogram of estimated ˆα 1it across farmers and years in the upper panel of figure 2 exhibits strong heterogeneity in α 1, which is passed into the heterogeneity of per-period profit difference in the lower panel of figure 2, which has an average of $24.07 per acre and a standard deviation of $14.25 per acre. As a final robustness check, the average elasticity of water extraction per acre with respect to energy price calculated from our estimation results is for farmers who uses CP and for those using LEPA. Using a similar dataset in the same study region, Hendricks and Peterson (2012) estimates the elasticity to be However, they do not take into account energy requirement to start the irrigation equipment (i.e. P SI j in equation 3) into consideration when calculating energy cost. After such factor is incorporated in to energy 13 Specifically, we calculate annual effective water for farmer i, θ it w it + r it, for each farmer in our dataset and obtain effective water in county c in year t by averaging effective water for farmers in that county. 15

60 cost calculation, the estimated elasticity for CP obtained by Hendricks and Peterson (2012) increases to (Pfeiffer and Lin, 2014), which is about the same as our estimates of Dynamic Parameter Estimates and Discussion Parameter Estimates and Model Validity Table 3 reports the estimates of adoption cost class and per-period profit shock scale parameter. Adoption cost for farmers with low adoption cost is $59.78 per acre, while that for farmers with high adoption cost class is $ per acre 14. LEPA adoption cost has been estimated to fall in the range of $56-$120 per acre depending on different packages bought and farm conditions according to agronomic and agricultural engineering literatures (DeLano et al., 1997; Hutton et al., 1989). Our cost estimates are broadly consistent with this range. On average, 66% of farmers fall in the low adoption cost class and 34% of farmers fall into the high cost class, which shows the importance of accounting for individual level heterogeneity in the model. Finally, as the deterministic part of the per-period profit difference is known (estimated), per-period profit shock scale parameter σ ε is identified. The estimates of the scale parameter turns out to be $30.94 per acre, slightly higher than the mean of per-period per-acre profit difference between LEPA and CP ($24.07 per acre). To test model validity, we compare the observed adoption path to that predicted by the model. In practice, we parameterize the model defined by equation (6) to (8) with the estimated model parameters and solve explicitly the dynamic programming model faced by each farmer in each year with collocation method described by Miranda and Fackler (2004). In a nutshell, the simulation follows a four-step procedure: Randomly draw each farmer s adoption cost (high or low) according to estimated in- 14 We also tried to increase the number of class to three, and the estimated population level probability of the third class turns out to be very small. Therefore, we stick to our two-class specification. 16

61 dividual farmer s probability of belonging to each adoption cost class (the individualspecific probability expression is shown in Appendix A) Randomly draw per-period profit shock for each farmer in each year according to the estimated shock distribution Calculate the deterministic part of per-period profit difference based on variables such as crop price, energy price and precipitation Solve v P and v L defined in equations (6) and (7) by collocation method Decide whether to adopt LEPA for each farmer in each year according to equation (8). If adopt, record adoption year. If not, continue to the next year Iterate the procedure above over different draws of farmers adoption costs and perperiod profit shock Average over each farmer s adoption year over all the draws and get the average new and cumulative adopters in year year Figure 3 presents the comparison between simulated and observed number of total adopters (upper panel) and number of new adopters (lower panel) in each year. The solid lines represent simulated paths and the dashed lines represent observed paths. For cumulative number of adopters, the simulated path predicts the shape of the observed path well, albeit the number of cumulative adopters in the simulated path is about 500 more than that in the observed path in each year. This is mainly because the simulated number of new adopters in 1998 is around 500 more than that of the observed one. The simulated number of new adopters are pretty close to the observed numbers in all subsequent years. Figure 4 plots each irrigation well s simulated LEPA adoption year versus its observed adoption year. A linear regression line is also fitted in the figure. If the model does perfectly, then all the points will stay on the 45 line. A clear upward sloping trend is observed in the figure, meaning that late adopters are also predicted as late adopters on average by the 17

62 model. The combined evidence from figure 3 and figure 4 therefore implies that the model does a relatively good job in terms of prediction power Forward Looking and Adoption Rate By traditional Net Present Value (NPV) rule, farmers should adopt LEPA as long as the expected sum of discounted future profit gain from LEPA adoption is higher than LEPA adoption cost. However, according to real option theory, this may not be the case if the adoption cost is high and/or profit gain uncertainty is high. Specifically, even though the current profit gain realization is high such that farmers should adopt by NPV rule, there is still chance that the profit gain falls to a fairly low level in the future due to uncertainty. Therefore, a rational (or fully forward looking) farmer tends to wait until the profit gain realization in the current year is high enough such that the probability that it drops to a very low level later is also low. In other words, if he does not adopt this year, he still has the option to make LEPA adoption decision in the next year. But if he adopts now, he would not have the chance to switch back in the future. This option value creates incentive for forward looking farmers to delay adoption. If a farmer s behavior is consistent with real option theory, we say this farmer is forward-looking. On the contrary, we say he is myopic if he behaves according to NPV rule 15. Formally, the myopic behavior decision rule is to adopt LEPA as long as: { } E β τ [π L (x τ ) π P (x τ )] C > 0 (18) τ=t On the other hand, the forward-looking behavior decision rule is to adopt if: v L (x t ) v P (x t, C) C > 0 (19) 15 Our definition of myopic behavior here is different from the traditional definition where farmers do not consider future profit gains. Farmers still consider future gains if he follows NPV rule, but he totally ignores the uncertainty of those gains. 18

63 Figure 5 plots E { τ=t βτ [π L (x τ ) π P (x τ )] } and the average (over farmers and years) value of v L (x t ) v P (x t, C) in two axises, one for low adoption cost farmers and the other for high adoption cost farmers. It is obvious that E { τ=t βτ [π L (x τ ) π P (x τ )] } is always greater than v L (x t ) v P (x t, C) because v P (x t, C) contains an additional option value, which is lost once LEPA is adopted. For both cases, the adoption cost falls in between the two values, which means that farmers should adopt LEPA if they follow the myopic NPV rule, but should not adopt if they follow the forward-looking real option rule. As a consequence, if farmers are myopic instead of forward-looking, average adoption probability over farmers and years will increase by 42%, which is obviously too high to be justified by the data. Therefore, we find strong evidence in support of forward-looking adoption behavior. 6 Counter-Factual Policy Simulations 6.1 Effect of Uncertainty on Adoption In this section, we consider the effect of profit gain uncertainty on adoption rate. Specifically, we double the size of standard deviation (σ η ) in the profit gain transition equation (equation (21)). Figure 6 presents the simulated path with double profit gain uncertainty versus the simulated path without any policy intervention. Note that the latter path is exactly the solid line in the upper panel of figure 3. The results show that increasing profit gain uncertainty decreases adoption rate on average. As uncertainty increases, the probability that profit gain drop to a very low level in the future also increases, raising the profit gain threshold above which farmers adopt LEPA, enhancing farmers incentives to delay adoption 16. However, the effects of uncertainty on adoption rate is small. Translating the figure into 16 However, on the other hand, the probability that profit gain realization path that threshold might also increase due to the increase in its uncertainty. The net effect of uncertainty on adoption rate could be positive, which has been well documented in Sarkar (2000). It is just the case that under current uncertainty level, an increase in uncertainty in our setting decreases adoption rate. 19

64 number, a 1 unit increase in σ η decreases average adoption probability by about 0.33%. (Next simulation: Instead of the uncertainty in overall profit gain, try uncertainty in crop price, energy price, etc that determines profit gain). 6.2 Effect of Cost-Share Programs on Adoption On commonly adopted approach to promote technology adoption is to provide cost-share payments to adopters. The state of Kansas started to provide such payments starting in financial year that pays up to 75% of the adoption cost for LEPA adopters. However, as mentioned earlier, only around 10% of farmers received cost share payments to convert their Center Pivot system to LEPA system during Therefore, the effective average cost share payments could be treated as 0 during this period. Therefore, we simulate the effect of a cost-share program that pay every adopter 75% of their adoption cost in this policy simulation. Figure 7 shows the results of this policy experiment. Again, the solid line represents the adoption path without cost-share program and the dash dotted line represents that with cost-share payments. The effect of cost-share payments on LEPA adoption is significant a 75% cost-share rate increases average LEPA adoption probability by around 10%. 7 Conclusion Climate change and continuing groundwater level decline in many important agricultural zones calls for the adoption of more efficient irrigation technologies to alleviate the problem. The effectiveness of various policies that can help promote efficient technology adoption depends on the underlying decision problem faced by potential adopters. For example, whether farmers are forward looking, how does profit gain affect adoption, and how large is farmer-specific adoption cost. Such factors are difficult to measure with reduced-form estimation technologies. 20

65 This paper builds and estimates a structural dynamic discrete choice model that explicitly take LEPA profit gain, its uncertainty and individual-specific adoption cost into consideration. Estimation results confirm that farmers are forward-looking when they make adoption decisions. LEPA profit gain uncertainty and adoption cost together create incentives for a forward-looking farmer to delay adoption. Counterfactual policy simulation show that policies targeted to reduce LEPA profit gain uncertainty (e.g. crop insurance) and reduce adoption cost (e.g. cost-share programs) help promote LEPA adoption, though cost-share program seems to be a more effective policy vehicle. 21

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70 Tables Table 1: Summary Statistics ( ) N Mean Std. Dev. Min. Max. Variables Water Use (feet/acre) 35, LEPA 6, CP 28, Real Corn Price ($/Bu) 35, Real Gas Price ($/Mcf) 35, Depth to Water (ft) 35, Effective Precipitation (feet/year) 35, Monthly Average Temperature ( C) May 35, Jun 35, Jul 35, Aug 35, Sep 35, Oct 35, Nov 35, # Wells 7,251 # Wells that Adopted LEPA 6,533 LEPA Adoption Year Full Sample 6, Post-1997 Adopters 4,

71 Table 2: Production Function Estimation Results Without Temperature With Temperature Identification Water Use County-Level Water Use County-Level Strategy FOC Yield FOC Yield (1) (2) (3) (4) α *** -29.9* *** * (0.87) (17.81) (0.88) (22.07) α 1it α 1temp5 2.37*** (0.49) (2.38) α 1temp6 1.83*** (0.45) (2.48) α 1temp7-2.95*** (0.42) (2.09) α 1temp8-0.91* (0.51) (2.31) α 1temp9-1.76*** 2.02 (0.48) (1.97) α 1temp *** 9.32*** (0.59) (2.53) α 1temp *** (0.41) (1.84) Farmer FE Y Y County FE Y Y Year-by-GMD FE Y Y Y Y α oit County FE Y Y Year FE Y Y E(α 1it ) R Obs

72 Table 3: Dynamic Parameter Estimation Results Estimates Adoption Cost ($/acre) C L 59.78*** (10.51) C H *** (14.46) Adoption Cost Class Probability C = C L 66% C = C H 34% Per-period Profit Shock Scale Parameter σ ε 30.94*** (3.12) Obs Notes: Bootstrapped Standard Errors are reported in Parenthesis 28

73 Figures Figure 1: LEPA Diffusion Path in Kansas HPA 29

74 Figure 2: Histogram of ˆα 1it in Production Function (upper) and Per-period Profit Difference of LEPA and CP across Farmers and Years (lower) 30

75 Figure 3: Simulated v.s. Observed Number of Cumulative Adopters (upper) and New Adopters (lower) 31

76 Figure 4: Simulated Average Adoption Year v.s. Observed Adoption Year 32

77 Figure 5: NPV and Real Option Decision Rule Critical Values 33