Analysis of Secondary School Enrollment Rate and Teen Fertility Rate: Econometrics
Charlie Zheng
4/20/2020
Executive Summary
Does improving a country’s secondary school enrollment rate lower its teen fertility rate? To answer the question, this econometric study is conducted by using OLS regression and difference-in-difference estimate. The study discovered that the increase of secondary school enrollment rate causes the decrease of teen fertility rate.
Data
wdi <- read.csv("wdi.csv")
df <- na.omit(wdi %>% select(countryname,year,sp_ado_tfrt,se_sec_nenr))
df <- rename(df,fertility=sp_ado_tfrt,enrollment=se_sec_nenr)
countries <- unique(df$countryname)
for (i in countries){
dfsubset <- df %>% filter(countryname==i)
#remove countries with fewer than 5 entries
if (nrow(dfsubset)<5){
countries = countries[countries!=i]
}
}
df <- subset(df,countryname %in% countries)OLS regression data
In order to study the correlation between secondary school enrollment rate and teen fertility rate, the data were retrieved from the World Bank’s World Development Indicators (WDI). Entries with missing data and countries with 5 or fewer entries were removed. After the data cleaning, there are 185 countries left in the dataset. The variables are “secondary school enrollment rate (% net)”, represent the percentage of secondary-school-age teenagers who participated the secondary schools in their country; and “teen fertility rate (births per 1,000 women ages 15-19)”. From this dataset, I will randomly choose 40 countries, exclude the regions, and remain only the countries. There are 31 countries left in this randomly chosen sample.
set.seed(65)
sample.countries<- sample(countries,40)
#excluding regions, only include countries
sample.countries = sample.countries[-c(5,6,14,17,22,23,32,33,38)]
df2 <- subset(df,countryname %in% sample.countries)Here is the descriptive statistics about these countries:
description <- data.frame(country=character(),start_year=integer(),end_year=integer(),average_secondary_school_enrollment=double(),average_teen_fertility_rate=double())
for (i in sample.countries){
descrdf <- df2 %>% filter(countryname==i)
descr <- data.frame(country=i,start_year=min(descrdf$year),end_year=max(descrdf$year),average_secondary_school_enrollment=mean(descrdf$enrollment),average_teen_fertility_rate=mean(descrdf$fertility))
description <- rbind(description,descr)
}
description## country start_year end_year
## 1 Brazil 2007 2013
## 2 Nicaragua 1971 2010
## 3 Colombia 2005 2014
## 4 Antigua and Barbuda 2000 2014
## 5 Burkina Faso 1983 2013
## 6 Lebanon 2006 2012
## 7 Portugal 1973 2014
## 8 Sao Tome and Principe 1988 2011
## 9 Swaziland 1970 2013
## 10 Samoa 1995 2014
## 11 Ghana 1999 2015
## 12 Belarus 2010 2014
## 13 United Kingdom 1971 2014
## 14 Cuba 1972 2013
## 15 Bolivia 2001 2013
## 16 Cambodia 1998 2008
## 17 Latvia 1994 2014
## 18 Malaysia 1970 2014
## 19 Macao SAR, China 1990 2014
## 20 Burundi 1976 2014
## 21 Argentina 1974 2013
## 22 Lao PDR 1992 2014
## 23 Grenada 1972 2014
## 24 Iran, Islamic Rep. 2009 2014
## 25 Poland 1999 2013
## 26 Japan 1978 2013
## 27 Bulgaria 1996 2014
## 28 Angola 1972 2010
## 29 Afghanistan 1974 2014
## 30 Cabo Verde 1987 2014
## 31 Myanmar 1999 2014
## average_secondary_school_enrollment average_teen_fertility_rate
## 1 78.070459 69.208520
## 2 30.096843 134.782067
## 3 75.351264 61.131560
## 4 82.360324 52.968600
## 5 10.739043 135.300060
## 6 68.938279 13.153114
## 7 65.482198 23.652247
## 8 32.995250 96.646444
## 9 26.691730 112.456127
## 10 71.040775 34.742380
## 11 42.582463 73.770629
## 12 96.382066 20.723440
## 13 86.328528 28.880275
## 14 72.072438 70.170933
## 15 72.991392 80.168418
## 16 24.577289 48.477960
## 17 87.454518 18.240200
## 18 62.408566 18.939070
## 19 74.227745 4.221700
## 20 8.455610 42.302262
## 21 76.343168 65.304644
## 22 31.730650 78.158010
## 23 71.688490 52.409200
## 24 80.111640 28.727100
## 25 90.724343 15.683787
## 26 98.500041 4.873889
## 27 85.871675 43.216926
## 28 8.625692 203.226000
## 29 29.932566 117.535520
## 30 54.954892 87.452523
## 31 39.970080 21.764154Difference in Difference Data
In 1996, the government of Peru passed education reforms that extended free and compulsory school education to all students aged between 5 and 16 (Clark).This reform significantly improved the secondary school enrollment rate in Peru after 1998. Therefore, I choose to compare the data of Peru and Colombia, another South American country which did not implement such an education reform, from 1993 to 2002. The variables are “secondary school enrollment rate (% gross)”, represent the percentage of gross population who participated the secondary schools in their country; and “teen fertility rate (births per 1,000 women ages 15-19)”.
Peru <- wdi %>% filter(countryname=="Peru",year>1992,year<2003) %>% select(year,sp_ado_tfrt,se_sec_enrr)
Peru <- rename(Peru,fertility=sp_ado_tfrt,enrollment.gross=se_sec_enrr)
Colombia <- wdi %>% filter(countryname=="Colombia",year>1992,year<2003) %>% select(year,sp_ado_tfrt,se_sec_enrr)
Colombia <- rename(Colombia,fertility=sp_ado_tfrt,enrollment.gross=se_sec_enrr)There are no missing data in Peru’s dataset. The only missing data are found in Colombia’s secondary school enrollment rate. Because there are no significant change in Columbia’s secondary school enrollment rate, I imputed the missing data with the mean of last year’s data and next year’s data.
for (i in 1:length(Colombia$enrollment.gross)){
if (is.na(Colombia$enrollment.gross[i])){
Colombia$enrollment.gross[i]<-(Colombia$enrollment.gross[i-1]+Colombia$enrollment.gross[i+1])/2
}
}Here are the illustrations of the data:
p1 <- ggplot(Peru,aes(x=year))+
geom_line(aes(y=fertility,color="teen fertility rate"))+
geom_line(aes(y=enrollment.gross,color="secondary school enrollment rate"))+
ggtitle("Peru")+
xlab("Year")+
ylab("Percentage")+
ylim(50,90)+
scale_x_continuous("year", labels = as.character(Peru$year), breaks = Peru$year)+
geom_vline(xintercept = 1997)
dfperu <- data.frame(country="Peru",start_year=min(Peru$year),end_year=max(Peru$year),average_secondary_school_enrollment=mean(Peru$enrollment.gross),average_teen_fertility_rate=mean(Peru$fertility))
p2 <- ggplot(Colombia,aes(x=year))+
geom_line(aes(y=Colombia$fertility,color="teen fertility rate"))+
geom_line(aes(y=Colombia$enrollment.gross,color="secondary school enrollment rate"))+
ggtitle("Colombia")+
xlab("Year")+
ylab("Percentage")+
ylim(50,90)+
xlim(1993,2002)+
scale_x_continuous("year", labels = as.character(Colombia$year), breaks = Colombia$year)+
geom_vline(xintercept = 1997)## Scale for 'x' is already present. Adding another scale for 'x', which
## will replace the existing scale.dfcolombia <- data.frame(country="Colombia",start_year=min(Colombia$year),end_year=max(Colombia$year),average_secondary_school_enrollment=mean(Colombia$enrollment.gross),average_teen_fertility_rate=mean(Colombia$fertility))
p1
p2
rbind(dfperu,dfcolombia)## country start_year end_year average_secondary_school_enrollment
## 1 Peru 1993 2002 77.20592
## 2 Colombia 1993 2002 66.79231
## average_teen_fertility_rate
## 1 67.7003
## 2 84.0806From the graphs, we can clearly see that before 1997, both Peru and Colombia have no significant fluctuation in secondary school enrollment rate and teen fertility rate. After 1998, Peru’s secondary school enrollment rate drastically increased and its teen fertility rate also decreased significantly. Whereas in Colombia, the secondary school enrollment rate do not have a significant change before or after 1995, and the teen fertility rate decreases year-by-year moderately.
Method
Method 1: OLS Regression
The first method is OLS regression for each country throughout each year. The formula is: fertility_hat = ß0 + ß1enrollment By randomly selecting these countries, I mitigated some omitted variable bias, such as difference of countries between economics, sexual culture, education; because these countries are located all over the 6 continents, consists of countries with most stages of economic and education development. However, there is still omitted variable bias, such as whether the secondary school in this country offer sex education. Because the original dataset does not measure this variable, this omitted variable bias cannot be eliminated. There is also another omitted variable bias, the time gap between each measurements. Because there are too much missing data, each country’s data is from significantly different time period. This omitted variable bias cannot be eliminated either.
#countries whose enrollment is statistically significant
olsresult <- data.frame(country=character(),intercept=double(),coef_enrollment=double(),p_value_enrollment=double())
#OLS regression for each country
for (i in sample.countries){
reg1 <- lm(fertility~enrollment,df2 %>% filter(countryname==i))
ttest1 <- coeftest(reg1, vcov=vcovHC(reg1, type = "HC1"))
if (ttest1["enrollment","Estimate"]<0 & ttest1["enrollment","Pr(>|t|)"]<0.05){
olsresult <- rbind(olsresult,data.frame(country=i,intercept=ttest1["(Intercept)","Estimate"],coef_enrollment=ttest1["enrollment","Estimate"],p_value_enrollment=ttest1["enrollment","Pr(>|t|)"]))
}
}Method 2:Difference in Difference
The treatment “group” is Argentina. The control “group” is Ecuador. The formula is: fertility_hat = 0 + ß1Argentina_enrollment + ß2After + ß3Argentina_enrollment*After
Although this comparison eliminites the omitted variable bias such as difference in culture, economics and education policy; this data set still suffers from the omitted variable bias that these two countries have different secondary school enrollment rate and teen fertility rate at the first place. There is also a threat to the external validity, because the evidence found in Peru may not be able to be applied to other countries in the world.
Results
Result of OLS regression
olsresult## country intercept coef_enrollment p_value_enrollment
## 1 Brazil 95.22160 -0.33319998 1.083821e-03
## 2 Nicaragua 188.17574 -1.77406238 8.327197e-11
## 3 Colombia 137.53101 -1.01391061 4.466536e-05
## 4 Burkina Faso 159.95346 -2.29567947 1.805537e-16
## 5 Lebanon 19.97232 -0.09891757 2.576087e-02
## 6 Portugal 45.77557 -0.33785246 6.934623e-08
## 7 Sao Tome and Principe 116.02514 -0.58731769 2.641541e-02
## 8 Swaziland 193.53959 -3.03777486 2.630048e-09
## 9 Samoa 61.77512 -0.38052424 3.516566e-02
## 10 Ghana 98.77823 -0.58727461 1.220721e-06
## 11 Belarus 66.50266 -0.47497651 1.111921e-02
## 12 United Kingdom 71.71547 -0.49618821 8.277607e-06
## 13 Cuba 168.89714 -1.36981919 4.674622e-24
## 14 Bolivia 186.75786 -1.46030150 2.353980e-02
## 15 Cambodia 51.77444 -0.13412692 7.987789e-04
## 16 Malaysia 90.45142 -1.14587390 3.714588e-18
## 17 Macao SAR, China 11.91991 -0.10371072 8.074978e-08
## 18 Burundi 51.95990 -1.14215726 3.658933e-08
## 19 Argentina 88.37273 -0.30216312 1.844482e-07
## 20 Lao PDR 112.56644 -1.08439098 1.571686e-08
## 21 Grenada 133.10079 -1.12558637 3.613241e-05
## 22 Bulgaria 165.14832 -1.41992568 8.800732e-03
## 23 Angola 269.28477 -7.65837340 4.689551e-03
## 24 Afghanistan 176.79097 -1.97963163 1.217755e-02
## 25 Cabo Verde 120.28281 -0.59740422 1.497068e-05
## 26 Myanmar 40.93080 -0.47952477 1.118741e-06After running the OLS regression for every countries in the sample. There are 26 countries’ enrollment coefficients negative and statistically significant at 90% confidence level. There are statistically siginificant evidence showing that the increase of secondary school enrollment rate is associated with the decrease of teen fertility rate. For example, in Brazil, on average, a unit increase of secondary school enrollment rate is associated with 0.33 unit decrease of teen fertility rate. Compared with the sample size of 31, these 26 countries provide abundant evidence of this association, but does not entail the causal impact.
Result of Difference in Difference
summary(did)## Warning in summary.lm(did): essentially perfect fit: summary may be
## unreliable##
## Call:
## lm(formula = fertility ~ Peru + After + PeruAfter, data = Colombia)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.358e-14 -1.332e-14 3.246e-15 1.078e-14 3.779e-14
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.023e+00 5.887e-12 -8.532e+11 <2e-16 ***
## Peru -6.906e+00 4.616e-13 -1.496e+13 <2e-16 ***
## After 8.509e+01 5.888e-12 1.445e+13 <2e-16 ***
## PeruAfter 6.654e+00 4.616e-13 1.441e+13 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.482e-14 on 6 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: 1
## F-statistic: 7.765e+27 on 3 and 6 DF, p-value: < 2.2e-16PeruAfter is statistically significant at 90% confidence level. On average, the decrease of Peru’s teen fertility rate is 6.654 units higher than the change of Colombia’s teen fertility rate. therefore, Peru’s improvement of its secondary school enrollment rate caused the decrease of its teen fertility rate.