med.Rmd

---
title: "Medicare and Medicaid Expenditure"
author: "Alex Perrone"
date: "May 2, 2016"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

```{r lib, include=FALSE}
library(data.table)
library(lubridate)
library(magrittr)
library(ggplot2)
```

## Read in data

Inflation data obtained [here](http://usinflation.org/us-inflation-rate/). 

The total healthcare spending was obtained by manual look-up for 2005 to 2015 by 
loading the PDFs online which are numbered by year. For example, here is the 
page for 2005:

[https://www.fiscal.treasury.gov/fsreports/rpt/mthTreasStmt/mts0905.pdf](https://www.fiscal.treasury.gov/fsreports/rpt/mthTreasStmt/mts0905.pdf)

and here is the page for 2015 (it differs only in final two digits): 

[https://www.fiscal.treasury.gov/fsreports/rpt/mthTreasStmt/mts0915.pdf](https://www.fiscal.treasury.gov/fsreports/rpt/mthTreasStmt/mts0915.pdf)

```{r read}
dat <- fread("med-data.csv")
print(dat)
```

## Clean

```{r clean}
dat$year <- paste0(dat$year, "-01-01") %>% ymd()
```

## Some analysis 

Based on [this formula](https://en.wikipedia.org/wiki/Rule_of_72), 
doubling over 10 years is $\exp{\left(\frac{\log{2}}{10}\right)} - 1$, 
which evaluates to `r exp(log(2)/10) - 1` interest rate. 

The sum of inflation from 2005 to 2015. I'm not sure we should actually include
the year 2005 though. 

```{r analysis}
sum(dat$avg_inflation)  # with 2005 included
sum(dat$avg_inflation[1:length(dat$avg_inflation)-1])  # with 2005 excluded
dat[ , mean(avg_inflation)]  # average rate of inflation
```


## Plot 

```{r plot}
ggplot(dat, aes(year, avg_inflation)) + 
  geom_point() + 
  geom_line() + 
  scale_x_date(date_breaks = "1 year", date_labels = "%Y") +
  labs(title="Average Inflation from 2005-2015")
ggplot(dat, aes(year, total_medicare_medicaid_billions)) + 
  geom_point() + 
  geom_line() + 
  scale_x_date(date_breaks = "1 year", date_labels = "%Y") +
  labs(title="Total Medicare and Medicaid Spending 2005-2015 (Billions)")
```

## Compute rates of increase for total medicare and medicaid spending

```{r}
dat <- dat[order(year)]
cum_rate <- function(vec){
  c(0, diff(vec)) / c(vec[1], vec[1], vec[2:(length(vec) - 1)])
}
dat[ , total_med_rate := cum_rate(total_medicare_medicaid_billions)]
dat[ , mean(total_med_rate[2:nrow(dat)])]  # exclude first year, no rate there
```