library(tidyverse)
## Loading tidyverse: ggplot2
## Loading tidyverse: tibble
## Loading tidyverse: tidyr
## Loading tidyverse: readr
## Loading tidyverse: purrr
## Loading tidyverse: dplyr
## Conflicts with tidy packages ----------------------------------------------
## filter(): dplyr, stats
## lag():    dplyr, stats
library(stringr)
Nat0306 <- read_delim("~/Dropbox/RProjects/Fertility Study/Nat0306.txt","\t", escape_double = FALSE)
## Warning: 66 parsing failures.
##  row col   expected    actual
## 1637  -- 10 columns 1 columns
## 1638  -- 10 columns 1 columns
## 1639  -- 10 columns 1 columns
## 1640  -- 10 columns 1 columns
## 1641  -- 10 columns 1 columns
## .... ... .......... .........
## .See problems(...) for more details.
Nat0715 <- read_delim("~/Dropbox/RProjects/Fertility Study/Nat0715.txt","\t", escape_double = FALSE)
## Warning: 69 parsing failures.
##  row col   expected    actual
## 3713  -- 10 columns 1 columns
## 3714  -- 10 columns 1 columns
## 3715  -- 10 columns 1 columns
## 3716  -- 10 columns 1 columns
## 3717  -- 10 columns 1 columns
## .... ... .......... .........
## .See problems(...) for more details.

Select the variables we want. Convert the character variable Rate to numeric and eliminate the rows where this variable is na. Then combine the two dataframes using rbind.

We could probably do the rbind first and save a few lines of typing. Per-preocesing the two separate files eliminates the possibility of problems because of differences between these two files, which came from different queries.

Nat0306 %>% 
  select(State,Year,Age,Rate) %>% 
  mutate(Rate = as.numeric(Rate)) %>% 
  filter(!is.na(Rate)) -> Nat0306
## Warning in eval(substitute(expr), envir, enclos): NAs introduced by
## coercion
glimpse(Nat0306)
## Observations: 1,224
## Variables: 4
## $ State <chr> "Alabama", "Alabama", "Alabama", "Alabama", "Alabama", "...
## $ Year  <int> 2003, 2004, 2005, 2006, 2003, 2004, 2005, 2006, 2003, 20...
## $ Age   <chr> "15-19 years", "15-19 years", "15-19 years", "15-19 year...
## $ Rate  <dbl> 51.40, 51.02, 48.06, 51.83, 113.67, 113.48, 116.90, 121....
Nat0715 %>% 
  select(State,Year,Age,Rate) %>% 
  mutate(Rate = as.numeric(Rate)) %>% 
  filter(!is.na(Rate)) -> Nat0715
## Warning in eval(substitute(expr), envir, enclos): NAs introduced by
## coercion
glimpse(Nat0715)
## Observations: 2,754
## Variables: 4
## $ State <chr> "Alabama", "Alabama", "Alabama", "Alabama", "Alabama", "...
## $ Year  <int> 2007, 2007, 2007, 2007, 2007, 2007, 2008, 2008, 2008, 20...
## $ Age   <chr> "15-19 years", "20-24 years", "25-29 years", "30-34 year...
## $ Rate  <dbl> 52.07, 123.78, 117.79, 78.00, 31.43, 5.51, 50.53, 121.63...
both = rbind(Nat0306,Nat0715)
summary(both)
##     State                Year          Age                 Rate       
##  Length:3978        Min.   :2003   Length:3978        Min.   :  3.93  
##  Class :character   1st Qu.:2006   Class :character   1st Qu.: 30.56  
##  Mode  :character   Median :2009   Mode  :character   Median : 60.91  
##                     Mean   :2009                      Mean   : 65.96  
##                     3rd Qu.:2012                      3rd Qu.:102.77  
##                     Max.   :2015                      Max.   :184.05

Now create a new dataframe with one row for each combination of State and Year. Create the variable TFR.

both %>% 
  group_by(State,Year) %>% 
  summarize(TFR = 5*sum(Rate)/1000) %>% 
  ungroup() -> SYTFR
glimpse(SYTFR)
## Observations: 663
## Variables: 3
## $ State <chr> "Alabama", "Alabama", "Alabama", "Alabama", "Alabama", "...
## $ Year  <int> 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 20...
## $ TFR   <dbl> 1.92205, 1.91695, 1.93785, 2.00555, 2.04290, 2.02050, 1....

Let’s look at the results. First try side-by-side boxplots to look at the changes over time. Note that we have to cast Year as a factor to get our boxplots.

SYTFR %>% 
  ggplot(aes(x = factor(Year),y=TFR)) + geom_boxplot()

There are some distinct groups of years. For analysis purposes, I would group them as follows:

Try a scatterplot.

SYTFR %>% ggplot(aes(x= Year, y = TFR)) + geom_point()

The next step in our analysis is to introduce per capita personal income data from the Bureau of Economic Analysis.

CA1 <- read_csv("~/Dropbox/RProjects/Fertility Study/CA1.csv")
## Warning: 4 parsing failures.
##  row     col   expected                                                                                       actual
## 9595 GeoFIPS an integer Note: See the included footnote file.                                                       
## 9596 GeoFIPS an integer CA1: Personal Income Summary: Personal Income, Population, Per Capita Personal Income       
## 9597 GeoFIPS an integer Last updated: November 17, 2016-- new estimates for 2015; revised estimates for 1998-2014.  
## 9598 GeoFIPS an integer Source: U.S. Department of Commerce / Bureau of Economic Analysis / Regional Income Division

Looking at the results of the import process, we can see that there are some invalid records at the bottom of the file. These can be eliminated by requiring that GeoFIPS be numeric. We also want to keep only the rows for statewide values. These can be indentified as having GeoName values containing the string “state”. The income data we want can be identified as having LineCode values of 3. In our output, we want only the name of the state and the income data in columns 8 through 54.

CA2 <- CA1 %>% 
  filter(LineCode == 3, str_detect(GeoName,"state")) %>%
  select(GeoName,8:54) %>%
  rename(State = GeoName)

Now we need to remove the extra text from the variable State. All rows have a string " state total" and some have an asterisk. These are removed in separate steps. The asterisk needs two leading backslashes because it has special significance in regular expressions. This is called “escaping.”

CA3 <- CA2 %>%
  mutate(State = gsub(" state total","",State)) %>% 
  mutate(State = gsub("\\*","",State))

Now we need to use the gather function from tidyr to put the column names indicating years into a column named Year with the income values from those columns in a single column named PCInc. In addition, we need to make Year and PCInc numeric. We only want data for the years 2003 through 2015.

CA4 <- CA3 %>% 
  gather(Year,PCInc,-1) %>% 
  mutate(Year = as.numeric(Year),
         PCInc = as.numeric(PCInc)) %>%   filter(Year >= 2003)
glimpse(CA4)
## Observations: 663
## Variables: 3
## $ State <chr> "Alabama", "Alaska", "Arizona", "Arkansas", "California"...
## $ Year  <dbl> 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003, 20...
## $ PCInc <dbl> 26513, 35591, 28166, 25467, 35234, 35132, 45468, 38187, ...

Now we can join the fertility data with the income data and examine the relationship between the two.

AllData = inner_join(CA4,SYTFR)
## Joining, by = c("State", "Year")
glimpse(AllData)
## Observations: 663
## Variables: 4
## $ State <chr> "Alabama", "Alaska", "Arizona", "Arkansas", "California"...
## $ Year  <dbl> 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003, 20...
## $ PCInc <dbl> 26513, 35591, 28166, 25467, 35234, 35132, 45468, 38187, ...
## $ TFR   <dbl> 1.92205, 2.28325, 2.39805, 2.04710, 2.11665, 2.14480, 1....

We can now look at the relationship between per capita personal income and the TFR.

AllData %>% ggplot(aes(x=PCInc,y=TFR)) + geom_point()

The plot suggests something counterituitive - Higher income leads to reduced fertility. This clashes with our explanation for the decline in fertility beginning with the great recession.

Let’s add time to this graphic by mapping color to Year.

AllData %>% ggplot(aes(x=PCInc,y=TFR,color=Year)) + geom_point()

It seems that there may be some correlation between time and our income variable. Review data on real personal income and the CPI in FRED. https://fred.stlouisfed.org/ is the link.

Let’s import the CPI data downloaded from FRED.

CPIData <- read_csv("~/Dropbox/RProjects/Fertility Study/CPIData.csv")

Now we need to join the CPI Data with AllData and adjust the per capita income data for inflation.

AllData2 = inner_join(AllData,CPIData)
## Joining, by = "Year"
AllData2 %>% mutate(RealPCInc = PCInc/CPI) -> AllData2
glimpse(AllData2)
## Observations: 663
## Variables: 6
## $ State     <chr> "Alabama", "Alaska", "Arizona", "Arkansas", "Califor...
## $ Year      <dbl> 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003...
## $ PCInc     <dbl> 26513, 35591, 28166, 25467, 35234, 35132, 45468, 381...
## $ TFR       <dbl> 1.92205, 2.28325, 2.39805, 2.04710, 2.11665, 2.14480...
## $ CPI       <dbl> 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 18...
## $ RealPCInc <dbl> 144.0924, 193.4293, 153.0761, 138.4076, 191.4891, 19...

Now redo the original scatterplot using the adjusted per capita income data.

AllData2 %>% ggplot(aes(x=RealPCInc,y=TFR,color=Year)) + geom_point()

There is still a counterintuitive relationship. How can we explain this?

Let’s repeat the previous graph with a facet by year.

AllData2 %>% ggplot(aes(x=RealPCInc,y=TFR,color=Year)) + geom_point() + geom_smooth() + facet_wrap(~Year)
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Looking back at the side-by-side boxplot, recall the grouping we saw there.

We can use the case_when statement to develop a variable to capture this grouping.

AllData3 <- AllData2 %>% 
  mutate(Period = case_when(
                   .$Year < 2006 ~ "Early",
                   .$Year < 2009 ~ "Peak",
                   .$Year < 2012 ~ "Decline",
                   TRUE ~ "Late"),
         Period = factor(Period,levels=c("Early","Peak","Decline","Late"))
         )
str(AllData3)
## Classes 'tbl_df', 'tbl' and 'data.frame':    663 obs. of  7 variables:
##  $ State    : chr  "Alabama" "Alaska" "Arizona" "Arkansas" ...
##  $ Year     : num  2003 2003 2003 2003 2003 ...
##  $ PCInc    : num  26513 35591 28166 25467 35234 ...
##  $ TFR      : num  1.92 2.28 2.4 2.05 2.12 ...
##  $ CPI      : num  184 184 184 184 184 184 184 184 184 184 ...
##  $ RealPCInc: num  144 193 153 138 191 ...
##  $ Period   : Factor w/ 4 levels "Early","Peak",..: 1 1 1 1 1 1 1 1 1 1 ...

Now we can repeat the plot above with these groupings. We can also do a simple smoothing plot using the new variable to distinguish among periods.

AllData3 %>% ggplot(aes(x=RealPCInc,y=TFR,color=Period)) + geom_point() + 
  geom_smooth() + facet_wrap(~Period)
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Here is another look at this without a facet or the points.

AllData3 %>% ggplot(aes(x=RealPCInc,y=TFR,color=Period)) +  
  geom_smooth() 
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Turning off the confidence interval shading might be better.

AllData3 %>% ggplot(aes(x=RealPCInc,y=TFR,color=Period)) +  
  geom_smooth(level=0.0) 
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

The impact of the peak years is clear. There is some separation of the curves for lower levels of RealPCInc, but the spearation is weaker at higher levles of RealPCInc.

Let’s try a regression model and include the factor Period. R will create dummy variables automatically to take care of the Period variable.

FertMod = lm(TFR~RealPCInc + Period,data = AllData3)
summary(FertMod)
## 
## Call:
## lm(formula = TFR ~ RealPCInc + Period, data = AllData3)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.39463 -0.10693 -0.02544  0.09289  0.53061 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    2.4110913  0.0401444  60.061  < 2e-16 ***
## RealPCInc     -0.0021371  0.0002127 -10.047  < 2e-16 ***
## PeriodPeak     0.0802308  0.0199591   4.020 6.50e-05 ***
## PeriodDecline -0.0684196  0.0199052  -3.437 0.000625 ***
## PeriodLate    -0.1215957  0.0188969  -6.435 2.38e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1735 on 658 degrees of freedom
## Multiple R-squared:  0.2809, Adjusted R-squared:  0.2765 
## F-statistic: 64.26 on 4 and 658 DF,  p-value: < 2.2e-16