Fortunes and Misfortunes of the Dragon Sons: Direct and...

Fortunes and Misfortunes of the Dragon Sons: Direct

and Cohort Effects of Superstition on Education

Attainment

Andy L. Chou∗

October 2018

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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 zo-

diac 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, [email protected]

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https://sites.google.com/site/andyliyoungchou/research

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

1Nunn and Sanchez de la Sierra (2017) provides another example where the effect at the individual leveldiffers from the overall effect. Using the example of bulletproof spells in Africa, they argue that even thoughin theory individual belief in bulletproof spells is harmful for individual safety, group beliefs in bulletproofspells may be beneficial due to positive externality of individuals making effort to ensure safety of the group.

2While the lunar calender and the zodiacs has origins from China, fertility spikes, particularly those duringdragon zodiac years, didn’t appear in China until the 2000s . Goodkind (1991) hypothesized the policies ofthe Chinese government prohibiting traditional practices are at play. In Taiwan, fertility policies were fairlyrelaxed. The Taiwanese government made efforts to reduce fertility during the 1960s and 1970s, throughpromoting the use of contraceptives and implementing education programs on family planning rather thanthrough penal actions such as fines or jail sentences (Sun, 1989).

3In Hong Kong, school year goes from September to August of next calendar year. However, Students asyoung as 5 years and 8 months old can entry primary school. In Singapore and Malaysia, school year andcalendar year are the same. These children need to be at least 6 years old to enter primary school.

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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 per-

centage 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,

4See Figure 1 for a graphical representation.

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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 supersti-

tions: 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

5See Guiso et al. (2006) for a review.

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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

6Several holidays in Taiwan, such as the Chinese New Year, Dragon Boat Festival, and Mid-AutumnFestival, are based on dates in the lunar calendar rather than dates in the Gregorian calendar.

7The 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 Gregoriancalendar for each zodiac. In Vietnam, rabbit is replaced by cat. The Western equivalent of zodiacs are thehoroscopes. However, the western horoscopes vary by month and not by year.

8Other known zodiac superstitions include firehorse women in Japan (Yamada, 2013), horse zodiac inSouth Korea (Lee and Paik, 2006), and sheep zodiac in China (Mocan and Yu, 2017). There is no evidence

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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.

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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,

9Liu (2015) and Goodkind (1991) suggest the belief to be that tiger zodiac is specifically brings misfortuneto females, as female born in tiger zodiac years are believed to make them stubborn and unsuitable for wifelyduties.

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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 2016.

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 1988. 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.

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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 1970. 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 com-

pleting.

Zodiac dummies are constructed based on self-reported birth year and month. I ap-

proximate 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.

10Surveys before 2000 sampled those age 20 to 65. Surveys in 2000 and 2001 removed the restrictions onmaximum age. Surveys starting in 2002 lowered the minimum age in the sample to 18 to conform with socialsurveys in other countries.

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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; tech-

nical 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 educa-

tion, 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 1988. There were no spikes or drops in

percentage with high school education, possibly due to the prevalence of people having high

school education.

11This designation applies between 1982 and 2009. Hsinchu city and Chiayi city became a provincial cityin 1982. Redesignation in 2010 changed the status of several cities and counties.

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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, 31.01 percent of people born in dragon years have a college education in the

academic track, slightly lower than 31.44 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.

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6 Regression Model

To account for the heterogeneity across different school years that are time invariant,12I

estimate direct and cohort effect using the following models:

Yi = β0 + β1zZodiaciz + SYi + β3Xi + �i (1)

Yi = β0 + β2zZodiacSYiz + ZYi + β3Xi + �i (2)

where Yi is education attainment for individual i. Zodiaciz is a vector of dummies for

individual i being born under zodiac z. ZodiacSYiz 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. SYi,

ZYi are birth academic year/zodiac year fixed effects. Xi 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 β1z whereas the cohort effects are

estimated as β2z. 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.

12The papers in the dragon superstition effect literature address the issue by limiting the sample to yearsclose to the dragon zodiac years. Another reason to use fixed effects is to make my estimates comparableto the estimates in the cohort size effect literature. While the articles in the cohort size literature use dataaggregated at the county or state level, they all include year fixed effects in their estimation.

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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.

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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 dum-

mies 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 differ-

ences 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

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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 status13 by using the difference between different

13See Goodkind (1995) for discussion of the minority immigrant status hypothesis applied in explainingthe variation of dragon fertility effects in Malaysia.

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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 1970.

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.15

7.1 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.

14There were no separate track for college before 1997 since those in vocational track are not expected toget a higher degree beyond high school for their jobs.

15Another known zodiac superstition with historical evidence is the firehorse superstition in Japan. It isbelieved that women born in firehorse years brings misfortune.

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Selection on Observables Table 13 and 14 present summary statistics for observable

characteristics by different treatment groups. Table 13 presents results for individuals af-

fected 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

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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 16.

8 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 out-

comes 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.

16The delta estimates have very large standard errors and need to be interpreted with caution.

18

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

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22

9 Tables and Figures

Figure 1: Dragon Effect Timeline

Note: Solid lines are the calendar year cutoffs. Dashed lines are the school year cutoffs. Thisis for children born in 2000 entering elementary school.

Figure 2: Live birth by birth year, 1947-2016

Note: Green lines are years associated with the zodiac dragon. Orange linesare years associated with the zodiac tiger. Source: Taiwan Ministry ofInterior.

23

Figure 3: Trends in Education Attainment

Note: Green lines are years associated with the zodiac dragon. Orange linesare years associated with the zodiac tiger.

24

Figure 4: Comparison of Methods

(a) College (Academic) - Dragon

Note: Tiger Zodiac is not included in the analysis.

(b) College (Academic) - Tiger

Note: Dragon Zodiac is not included in the analysis.

(c) College (Any) - Dragon


(d) College (Any) - Tiger


(e) High School - Dragon


(f) High School - Tiger


25

Figure 5: 7 year old in first grade (per 1000 7 year olds)

Note: Years after 2000 are not included due to increased enforcement of school entry laws following theamendment of the school entry laws in 1999.

Table 1: Chinese Zodiacs and the corresponding years

Zodiac Years in Gregorian CalendarRat 1936, 1948, 1960, 1972, 1984, 1996, 2008Ox 1937, 1949, 1961, 1973, 1985, 1997, 2009

Tiger 1938, 1950, 1962, 1974, 1986, 1998, 2010Rabbit 1939, 1951, 1963, 1975, 1987, 1999, 2011

Dragon 1940, 1952, 1964, 1976, 1988, 2000, 2012Snake 1941, 1953, 1965, 1977, 1989, 2001, 2013Horse 1942, 1954, 1966, 1978, 1990, 2002, 2014Sheep 1943, 1955, 1967, 1979, 1991, 2003, 2015

Monkey 1944, 1956, 1968, 1980, 1992, 2004, 2016Chicken 1945, 1957, 1969, 1981, 1993, 2005, 2017

Dog 1946, 1958, 1970, 1982, 1994, 2006, 2018Pig 1947, 1959, 1971, 1983, 1995, 2007, 2019

26

Table 2: Zodiac and Log Annual Live Births, 1947-2016 - Overall

(1) (2)Overall Gender Specific

Male 0.071∗∗∗ 0.071∗∗∗

(0.017) (0.019)

Dragon 0.073∗∗∗ 0.073∗∗∗

(0.020) (0.028)

Tiger −0.080∗∗∗ −0.079∗(0.029) (0.042)

Dragon X Male −0.001(0.039)

Tiger X Male −0.001(0.057)

Observations 140 140Quadratic Trend Yes Yes

Note: Standard errors in parentheses.* p < 0.10, ** p < 0.05, *** p < 0.01.

Table 3: Zodiac and Log Annual Livebirths, 1947-2016 - Individual Years

(1) (2)Tiger Years Dragon Years

1974/1976 −0.079∗∗∗ 0.077∗∗∗(0.010) (0.011)

1986/1988 −0.157∗∗∗ −0.014(0.011) (0.012)

1998/2000 −0.072∗∗∗ 0.115∗∗∗(0.013) (0.016)

2010/2012 −0.232∗∗∗ 0.186∗∗∗(0.026) (0.032)

Observations 140 140Quadratic Trend Yes Yes

Note: Standard errors in parentheses.* p < 0.10, ** p < 0.05, *** p < 0.01.

27

Table 4: Zodiac and Log Annual Livebirths, 1947-2016 - Other Zodiacs

(1) (2) (3) (4) (5) (6) (7)Horse Sheep Monkey Chicken Dog Pig Rat

Male 0.071∗∗∗ 0.071∗∗∗ 0.071∗∗∗ 0.071∗∗∗ 0.071∗∗∗ 0.072∗∗∗ 0.071∗∗∗

(0.019) (0.018) (0.018) (0.018) (0.018) (0.017) (0.018)

Zodiac Dummy 0.043 0.030 0.043 −0.004 0.007 −0.046 −0.044(0.032) (0.049) (0.050) (0.042) (0.041) (0.057) (0.047)

Zodiac Dummy X Male 0.003 0.008 0.004 −0.001 0.002 −0.003 −0.001(0.042) (0.067) (0.068) (0.058) (0.055) (0.082) (0.068)

Observations 140 140 140 140 140 140 140Quadratic Trend Yes Yes Yes Yes Yes Yes Yes

Note: Standard errors in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.

28

Table 5: Descriptive Statistics - TSCS

count mean sd min max

Dependent VariablesCollege and above(Academic) 15461 .3076127 .4615202 0 1College and above 15778 .6141463 .4868117 0 1High School and above 15778 .9210293 .2697016 0 1Independent VariableDragon Direct Effect 15778 .095386 .2937566 0 1Dragon Cohort Effect 15778 .1806313 .3847246 0 1Tiger Direct Effect 15778 .0939283 .2917381 0 1Tiger Cohort Effect 15778 .1895044 .3919212 0 1Control VariablesSurvey Year 15778 2009.751 4.73301 1996 2016Birth School Cohort 15778 1977.369 4.962798 1970 1991Birth Lunar Year 15778 1977.929 4.953068 1971 1991Birth Month 15778 6.715807 3.442201 1 12Male 15778 .5176195 .4997053 0 1Born in City 7403 .3807916 .4856143 0 1Father Bachelor’s Education 12156 .069513 .2543349 0 1Father Associate’s Education 12156 .0826752 .275402 0 1Mother Bachelor’s Education 12000 .0320833 .1762288 0 1Mother Associate’s Education 12000 .0394167 .1945923 0 1Father Chinese Nationalist 15384 .0937337 .2914674 0 1Mother Chinese Nationalist 14870 .0412912 .1989696 0 1Father Folk Religion 1585 .4378549 .4962795 0 1Mother Folk Religion 942 .4023355 .4906294 0 1Father Occupation Rank 4174 2.448011 1.263339 0 5Mother Occupation Rank 1690 1.713018 1.237803 0 5Sibling Rank(1=Oldest) 4191 2.201145 1.331591 1 11Family Size 4191 3.301837 1.290055 1 11Oldest Sibling 4191 .3724648 .4835189 0 1

Note: The 2003 survey did not distinguish the education track of the individuals.

29

Table 6: Role of Controls

Dependent Variable: College Education(Academic)

(1) (2) (3)

Dragon Direct Effect 0.004 0.020(0.007) (0.015)

Tiger Direct Effect −0.021∗∗∗ −0.024(0.006) (0.015)

Dragon Cohort Effect −0.046∗(0.025)

Tiger Cohort Effect −0.018(0.018)

Observations 15461 15461 12547Ymean .308 .308 .311Year Fixed Effects No Academic Zodiac

* p < 0.1, ** p < 0.05, *** p < 0.01. Standard errors clustered at birthyear level.

Note: All regressions include survey year, birth month fixed effects,and birth year in controls.

Table 7: Different Education Attainment

CollegeAcademic

CollegeAny

High SchoolAny

Dragon Direct Effect 0.020 0.015 0.007(0.015) (0.010) (0.005)

Tiger Direct Effect −0.024 −0.012 −0.001(0.015) (0.009) (0.006)

Dragon Cohort Effect −0.046∗ −0.041∗ −0.010(0.025) (0.022) (0.018)

Tiger Cohort Effect −0.018 −0.024∗ −0.013(0.018) (0.013) (0.012)

Observations 15461 12547 15778 12791 15749 12791Ymean .308 .311 .614 .615 .921 .922Year Fixed Effects Academic Zodiac Academic Zodiac Academic Zodiac

* p < 0.1, ** p < 0.05, *** p < 0.01. Standard errors clustered at birth year level.

Note: All regressions include survey year, birth month fixed effects, and birth year incontrols.

30

Table 8: Heterogeneity - Gender

CollegeAcademic

CollegeAny

High SchoolAny

Male Female Male Female Male Female

Dragon Direct Effect 0.038 −0.000 0.023 0.008 0.018∗∗∗ −0.004(0.027) (0.007) (0.019) (0.012) (0.007) (0.005)

Tiger Direct Effect −0.039∗∗∗ −0.006 −0.046∗∗∗ 0.025 −0.016∗∗ 0.015∗∗(0.010) (0.024) (0.003) (0.020) (0.007) (0.006)

Observations 7991 7470 8167 7611 7974 7598Ymean .306 .31 .601 .628 .914 .927Year Fixed Effects Academic Academic Academic Academic Academic Academic

Dragon Cohort Effect −0.055 −0.040∗∗ −0.038 −0.047∗∗∗ −0.020 0.003(0.045) (0.017) (0.044) (0.012) (0.023) (0.013)

Tiger Cohort Effect −0.001 −0.040 0.019 −0.071∗∗∗ −0.002 −0.019∗(0.029) (0.032) (0.028) (0.014) (0.015) (0.011)

Observations 6519 6028 6660 6131 6622 6131Ymean .308 .314 .605 .627 .916 .927Year Fixed Effects Zodiac Zodiac Zodiac Zodiac Zodiac Zodiac


Note: All regressions include survey year, birth month fixed effects, and birth year in controls.

Table 9: Heterogeneity - Different dragon/tiger years

CollegeAcademic

CollegeAny

High SchoolAny

1976 Dragon Direct Effect 0.011 0.022∗ 0.009(0.017) (0.011) (0.006)

1988 Dragon Direct Effect 0.053∗∗∗ −0.020∗∗ −0.013(0.013) (0.009) (0.013)

1974 Tiger Direct Effect −0.002 −0.002 −0.001(0.006) (0.006) (0.007)

1986 Tiger Direct Effect −0.076∗∗∗ −0.049∗∗∗ −0.002(0.013) (0.013) (0.011)

1976 Dragon Cohort Effect −0.062∗∗∗ −0.048∗∗ −0.016(0.019) (0.019) (0.016)

1988 Dragon Cohort Effect 0.003 −0.015 0.025(0.009) (0.055) (0.034)

1974 Tiger Cohort Effect −0.043∗∗ −0.038∗∗ −0.022(0.019) (0.017) (0.014)

1986 Tiger Cohort Effect 0.042∗∗∗ 0.028 0.046∗∗

(0.006) (0.035) (0.019)




31

Table 10: Heterogeneity - Relative Age within School Year

CollegeAcademic

CollegeAny

High SchoolAny

Young Dragon Direct Effect −0.015 −0.012∗∗ −0.007(0.022) (0.006) (0.005)

Old Dragon Direct Effect 0.054∗∗∗ 0.043∗∗∗ 0.020∗∗∗

(0.008) (0.011) (0.007)Young Dragon Cohort Effect −0.008 0.002 0.019∗

(0.016) (0.022) (0.011)Old Dragon Cohort Effect −0.066∗∗∗ −0.060∗∗ −0.028∗

(0.024) (0.025) (0.014)


Young Tiger Direct Effect −0.023 0.012 −0.017∗∗∗(0.031) (0.010) (0.006)

Old Tiger Direct Effect −0.024∗∗∗ −0.036∗∗∗ 0.016∗∗∗(0.009) (0.013) (0.006)

Young Tiger Cohort Effect −0.008 −0.023∗∗ 0.002(0.022) (0.009) (0.009)

Old Tiger Cohort Effect 0.014 0.012 −0.020∗(0.019) (0.023) (0.011)




32

Table 11: Heterogeneity - Father Ethnicity

CollegeAcademic

CollegeAny

High SchoolAny

Taiwanese Chinese Taiwanese Chinese Taiwanese Chinese

Dragon Direct Effect 0.025∗∗ −0.009 0.018∗∗ 0.025 0.007∗∗ 0.007∗∗(0.011) (0.055) (0.008) (0.052) (0.003) (0.003)

Tiger Direct Effect −0.028 0.001 −0.028∗∗∗ 0.086∗∗∗ −0.005 −0.005(0.021) (0.031) (0.010) (0.018) (0.005) (0.005)


Dragon Cohort Effect −0.043∗∗ −0.117 −0.033 −0.163∗∗∗ −0.015 −0.015(0.020) (0.085) (0.021) (0.063) (0.015) (0.015)

Tiger Cohort Effect −0.010 −0.144∗∗∗ −0.005 −0.183∗∗∗ −0.010 −0.010(0.016) (0.045) (0.011) (0.031) (0.010) (0.010)




Table 12: Zodiacs before 1970

CollegeAny

High SchoolAny

Middle SchoolAny

Dragon Direct Effect 0.002 −0.006∗ 0.003(0.004) (0.003) (0.004)

Tiger Direct Effect −0.012∗∗∗ −0.019∗∗∗ −0.007∗∗∗(0.001) (0.003) (0.003)

Dragon Cohort Effect 0.009 0.001 0.008(0.009) (0.010) (0.007)

Tiger Cohort Effect 0.007 0.001 −0.002(0.010) (0.007) (0.006)




33

Table 13: Means of Control Variables by Dragon Zodiac group

Observations(1) (2) (3)

DragonsNon-Dragons

Others(1)-(2) (2)-(3)

in Dragon CohortMale 15778 0.518 0.529 0.519 −0.010 0.010

(0.500) (0.499) (0.500) (0.019) (0.015)Born between September and January 15778 0.453 0.467 0.427 −0.014 0.040∗∗∗

(0.498) (0.499) (0.495) (0.019) (0.014)Born in City 7403 0.369 0.384 0.383 −0.015 0.000

(0.483) (0.487) (0.486) (0.027) (0.020)Father Bachelor’s Education 12156 0.078 0.074 0.067 0.004 0.007

(0.268) (0.262) (0.251) (0.011) (0.008)Father Associate’s Education 12156 0.061 0.079 0.087 −0.018 −0.008

(0.240) (0.270) (0.281) (0.011) (0.009)Mother Bachelor’s Education 12000 0.028 0.040 0.032 −0.012 0.008

(0.166) (0.196) (0.175) (0.008) (0.006)Mother Associate’s Education 12000 0.028 0.033 0.042 −0.005 −0.009

(0.166) (0.179) (0.200) (0.007) (0.007)Father Chinese 15384 0.093 0.082 0.095 0.012 −0.014

(0.291) (0.274) (0.294) (0.011) (0.009)Mother Chinese 14870 0.040 0.041 0.043 −0.001 −0.002

(0.196) (0.198) (0.202) (0.008) (0.006)Father Folk Religion 1585 0.480 0.489 0.430 −0.009 0.059

(0.502) (0.502) (0.495) (0.062) (0.045)Mother Folk Religion 942 0.458 0.438 0.397 0.020 0.041

(0.502) (0.500) (0.490) (0.090) (0.064)Father Occupation Rank 4174 2.438 2.444 2.456 −0.006 −0.011

(1.209) (1.298) (1.259) (0.092) (0.073)Mother Occupation Rank 1690 1.623 1.664 1.711 −0.042 −0.047

(1.204) (1.199) (1.243) (0.144) (0.116)Sibling Rank(1=Oldest) 4191 2.210 2.100 2.212 0.110 −0.112

(1.339) (1.275) (1.323) (0.091) (0.071)Family Size 4191 3.422 3.201 3.275 0.221∗∗∗ −0.074

(1.222) (1.174) (1.299) (0.083) (0.069)Oldest Sibling 4191 0.387 0.415 0.362 −0.029 0.054∗∗

(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 15.

34

Table 14: Means of Control Variables by Tiger Zodiac group

Observations(1) (2) (3)

TigersNon-Tigers

Others(1)-(2) (2)-(3)

in Tiger CohortMale 15778 0.491 0.527 0.519 −0.036∗∗ 0.008

(0.500) (0.499) (0.500) (0.018) (0.014)Born between September and January 15778 0.464 0.467 0.427 −0.003 0.039∗∗∗

(0.499) (0.499) (0.495) (0.018) (0.014)Born in City 7403 0.396 0.359 0.383 0.038 −0.025

(0.489) (0.480) (0.486) (0.025) (0.019)Father Bachelor’s Education 12156 0.072 0.068 0.067 0.004 0.001

(0.259) (0.253) (0.251) (0.010) (0.008)Father Associate’s Education 12156 0.089 0.075 0.087 0.014 −0.012

(0.285) (0.264) (0.281) (0.011) (0.009)Mother Bachelor’s Education 12000 0.031 0.031 0.032 0.000 −0.000

(0.175) (0.175) (0.175) (0.007) (0.006)Mother Associate’s Education 12000 0.043 0.038 0.042 0.004 −0.003

(0.202) (0.192) (0.200) (0.008) (0.006)Father Chinese 15384 0.092 0.095 0.095 −0.002 −0.001

(0.290) (0.293) (0.294) (0.011) (0.008)Mother Chinese 14870 0.041 0.034 0.043 0.006 −0.009

(0.197) (0.182) (0.202) (0.007) (0.006)Father Folk Religion 1585 0.421 0.426 0.430 −0.004 −0.005

(0.495) (0.496) (0.495) (0.057) (0.045)Mother Folk Religion 942 0.365 0.423 0.397 −0.058 0.026

(0.484) (0.497) (0.490) (0.075) (0.059)Father Occupation Rank 4174 2.405 2.457 2.456 −0.052 0.001

(1.266) (1.314) (1.259) (0.089) (0.067)Mother Occupation Rank 1690 1.857 1.712 1.711 0.145 0.001

(1.280) (1.228) (1.243) (0.143) (0.107)Sibling Rank(1=Oldest) 4191 2.155 2.275 2.212 −0.120 0.063

(1.328) (1.439) (1.323) (0.100) (0.074)Family Size 4191 3.359 3.400 3.275 −0.041 0.125∗

(1.338) (1.358) (1.299) (0.098) (0.072)Oldest Sibling 4191 0.403 0.355 0.362 0.048 −0.007

(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 15.

35

Table 15: Robustness Check: Accounting for short-term switch in fertility

CollegeAcademic

CollegeVocational

High SchoolAny

Dragon Direct Effect 0.017 0.013 0.006(0.012) (0.013) (0.005)

Tiger Direct Effect −0.022 −0.019∗ 0.000(0.016) (0.011) (0.005)

Dragon Cohort Effect −0.043∗∗ −0.044∗∗ −0.008(0.020) (0.017) (0.017)

Tiger Cohort Effect −0.017 −0.024∗∗ −0.012(0.013) (0.009) (0.011)




Table 16: Selection on Unobservables: DD Model - LPM

Dependent Variable: College Education (Academic)

(1) (2) (3) (4) δ

Dragon Direct Effect 0.012 0.020 −0.260(0.016) (0.015)

Tiger Direct Effect −0.017 −0.023 −0.432(0.013) (0.016)

Dragon Cohort Effect −0.045∗ −0.046∗−3.834(0.025) (0.024)

Tiger Cohort Effect −0.019 −0.018 2.161(0.019) (0.017)

Observations 15461 15461 12547 12547Ymean .31 .31 .31 .31Adjusted R-squared .0299 .118 .0289 .116Controls No Yes No YesYear Fixed Effects Academic Academic Zodiac Zodiac


Note: All regressions include survey year, birth month fixed effects, and birth yearin controls. Columns 1 and 2 present regression coefficients while column 3 presentestimated delta from Oster (2017). Standard errors for estimates of delta parame-ter are not presented due to their magnitude.

36

Appendix A Extra Tables

Figure B1: Comparison of Methods

(a) College (Academic) - Dragon


(b) College (Academic) - Tiger


(c) College (Vocational) - Dragon


(d) College (Vocational) - Tiger


(e) High School - Dragon


(f) High School - Tiger


37

Table B1: Role of Controls

Dependent Variable: College Degree(Academic)

(1) (2) (3) (4) (5) (6) (7)

Dragon Direct Effect −0.005 0.015 0.015 0.022∗∗ 0.024∗∗ 0.024∗∗(0.009) (0.013) (0.013) (0.011) (0.012) (0.012)

Tiger Direct Effect −0.010 −0.017 −0.017 −0.023 −0.024 −0.020(0.008) (0.024) (0.023) (0.025) (0.025) (0.016)

Dragon Cohort Effect −0.021∗−0.021∗−0.025∗∗∗−0.026∗∗∗ −0.051∗∗∗(0.011) (0.011) (0.010) (0.010) (0.011)

Tiger Cohort Effect 0.005 0.006 0.003 0.003 −0.016(0.021) (0.020) (0.022) (0.022) (0.014)

Observations 10400 10400 10400 10400 10400 10400 8489Ymean .273 .273 .273 .273 .273 .273 .276Year Fixed Effects No No No No No Academic Zodiac




Dependent Variable: College Degree(Any Track)

(1) (2) (3) (4) (5) (6) (7)

Dragon Direct Effect −0.002 0.001 0.001 0.006 0.008 0.007(0.009) (0.011) (0.011) (0.012) (0.011) (0.010)

Tiger Direct Effect −0.000 −0.000 −0.001 −0.008 −0.007 −0.005(0.008) (0.017) (0.016) (0.019) (0.019) (0.014)

Dragon Cohort Effect −0.004 −0.004 −0.006 −0.006 −0.048∗∗(0.010) (0.010) (0.009) (0.009) (0.020)

Tiger Cohort Effect −0.001 −0.001 −0.003 −0.003 −0.031∗∗(0.016) (0.015) (0.018) (0.018) (0.013)




38


Dependent Variable: High School Degree (Any Track)

(1) (2) (3) (4) (5) (6) (7)

Dragon Direct Effect −0.014∗∗∗−0.009 −0.009 −0.004 −0.004 −0.007∗(0.003) (0.010) (0.010) (0.011) (0.010) (0.004)

Tiger Direct Effect 0.001 0.001 0.000 −0.004 −0.004 −0.002(0.007) (0.008) (0.008) (0.008) (0.008) (0.005)

Dragon Cohort Effect −0.006 −0.006 −0.008 −0.008 −0.028∗(0.010) (0.011) (0.011) (0.011) (0.016)

Tiger Cohort Effect −0.002 −0.001 −0.001 −0.002 −0.022(0.007) (0.007) (0.008) (0.008) (0.014)




Table B4: Different Education Attainment

CollegeAny

High SchoolAny

Middle SchoolAny

Dragon Direct Effect 0.024∗∗ 0.007 −0.007∗(0.012) (0.010) (0.004)

Tiger Direct Effect −0.020 −0.005 −0.002(0.016) (0.014) (0.005)

Dragon Cohort Effect −0.051∗∗∗ −0.048∗∗ −0.028∗(0.011) (0.020) (0.016)

Tiger Cohort Effect −0.016 −0.031∗∗ −0.022(0.014) (0.013) (0.014)




39

Table B5: Heterogeneity - Gender

CollegeAcademic

CollegeAny

High SchoolAny

Male Female Male Female Male Female

Dragon Direct Effect 0.033∗ 0.015∗∗∗ 0.022∗ −0.003 0.010 −0.026∗(0.018) (0.004) (0.012) (0.008) (0.007) (0.015)

Tiger Direct Effect −0.035∗∗ −0.003 −0.051∗∗∗ 0.043∗ −0.019 0.015∗∗∗(0.017) (0.018) (0.006) (0.026) (0.012) (0.006)


Dragon Cohort Effect −0.056∗∗ −0.050∗∗∗ −0.032 −0.072∗∗∗ −0.034∗ −0.012(0.023) (0.009) (0.032) (0.010) (0.020) (0.019)

Tiger Cohort Effect 0.000 −0.034∗∗∗ 0.044∗∗ −0.107∗∗∗ 0.026 −0.070∗∗∗(0.022) (0.013) (0.020) (0.009) (0.017) (0.016)




40

Table B6: Heterogeneity - different dragon/tiger years

CollegeAcademic

CollegeAny

High SchoolAny

1976 Dragon Direct Effect 0.010 0.008 −0.009∗∗(0.008) (0.011) (0.004)

1988 Dragon Direct Effect 0.082∗∗∗ 0.005 0.006(0.006) (0.016) (0.007)

1974 Tiger Direct Effect 0.002 0.011 0.003(0.009) (0.012) (0.004)

1986 Tiger Direct Effect −0.073∗∗∗ −0.062∗∗∗ −0.040∗∗∗(0.017) (0.003) (0.004)

1976 Dragon cohort Effect −0.064∗∗∗ −0.060∗∗∗ −0.028∗(0.002) (0.011) (0.015)

1988 Dragon cohort Effect −0.008 0.000 −0.031∗∗∗(0.005) (0.048) (0.005)

1974 Tiger cohort Effect −0.034∗∗∗ −0.050∗∗∗ −0.037∗∗∗(0.002) (0.010) (0.014)

1986 Tiger cohort Effect 0.025∗∗∗ 0.032 0.061∗∗∗

(0.004) (0.035) (0.004)




Table B7: Zodiacs before 1970

CollegeAny

High SchoolAny

Middle SchoolAny

Dragon Direct Effect 0.013∗∗ −0.025∗∗∗ −0.002(0.006) (0.006) (0.010)

Tiger Direct Effect 0.006 0.011 0.005(0.008) (0.015) (0.005)

Dragon Cohort Effect −0.007 −0.010 −0.008(0.011) (0.011) (0.013)

Tiger Cohort Effect −0.028∗∗ −0.032∗∗ −0.025(0.013) (0.015) (0.018)




41

Table B8: Heterogeneity - relative age within school year

CollegeAcademic

CollegeAny

High SchoolAny

Young Dragon Direct Effect 0.008 −0.014 −0.015∗∗(0.020) (0.012) (0.006)

Old Dragon Direct Effect 0.039∗∗∗ 0.028∗∗∗ 0.000(0.009) (0.010) (0.004)

Young Dragon Cohort Effect −0.035∗∗∗ −0.010 0.013(0.009) (0.021) (0.021)

Old Dragon Cohort Effect −0.047∗∗∗ −0.053∗ −0.048∗∗∗(0.016) (0.028) (0.008)


Young Tiger Direct Effect −0.017 0.025 −0.014∗∗∗(0.035) (0.022) (0.005)

Old Tiger Direct Effect −0.023∗∗∗ −0.035∗∗∗ 0.010∗(0.007) (0.010) (0.006)

Young Tiger Cohort Effect −0.026 −0.039∗∗∗ −0.007(0.021) (0.014) (0.017)

Old Tiger Cohort Effect 0.044∗∗∗ 0.023 −0.012(0.011) (0.022) (0.022)




42

Table B9: Heterogeneity - Father Ethnicity

CollegeAcademic

CollegeAny

High SchoolAny

Taiwanese Chinese Taiwanese Chinese Taiwanese Chinese

Dragon Direct Effect 0.028∗∗∗ 0.011 0.012∗ 0.034 −0.008∗∗∗ −0.008∗∗∗(0.007) (0.062) (0.007) (0.046) (0.003) (0.003)

Tiger Direct Effect −0.021 −0.037 −0.009 0.004 −0.014∗∗∗ −0.014∗∗∗(0.019) (0.033) (0.015) (0.034) (0.004) (0.004)


Dragon Cohort Effect −0.044∗∗∗ −0.147∗∗ −0.038 −0.160∗∗∗ −0.034∗∗ −0.034∗∗(0.009) (0.070) (0.025) (0.049) (0.015) (0.015)

Tiger Cohort Effect 0.003 −0.170∗∗∗ −0.015 −0.135∗∗∗ −0.022∗ −0.022∗(0.013) (0.037) (0.015) (0.031) (0.012) (0.012)




Table B10: Robustness Check: Accounting for short-term switch in fertility

CollegeAcademic

CollegeAny

High SchoolAny

Dragon Direct Effect 0.026∗∗∗ −0.001 −0.012∗∗(0.008) (0.010) (0.005)

Tiger Direct Effect −0.014 −0.022 0.000(0.016) (0.015) (0.004)

Dragon Cohort Effect −0.044∗∗∗ −0.047∗∗∗ −0.025∗(0.010) (0.012) (0.014)

Tiger Cohort Effect −0.011 −0.028∗∗∗ −0.026∗∗(0.017) (0.007) (0.011)




43

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 agricul-

tural zones calls for the adoption of more efficient irrigation technologies to alleviate the

problem. This paper studies farmers adoption behavior with a structural economet-

rics that explicitly takes profit gain of adoption, its uncertainty and individual-specific

adoption cost into consideration. Using a panel data on Low Energy Precision Applica-

tion (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, poli-

cies 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 in-

terventions.

Keywords: Technology Adoption, Real Option, Uncertainty, Adoption Cost, Dy-

namic Discrete Choice

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 efficiency1 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

1efficiency =amount of water utilized by crop

total water extraction(Pfeiffer and Lin, 2014). Efficiency level is always less

than 1 because part of irrigation water is lost due to evaporation, soil water percolation and wind.

1

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% cost-

share 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

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 dis-

crete 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 technol-

ogy 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 com-

plete 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

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 In-

formation 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 to-

tal. The data also spans a long time period – from 1997 to 2010. 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 Wa-

ter Office. WIMAS data also contains information on water rights2 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 addi-

tion, 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

2A 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

by inconsistent definition of LEPA before and after 19973. 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 1996-1997. 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 20144. 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 substitu

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