Welcome to ScPoEconometrics!

• In this course you will learn about the basics of Econometrics.

• You will also learn to use the R software.

What is Econometrics, actually?

• A set of techniques and methods to answer questions with data.

• Econometrics shares many things with Applied Statistics and Machine Learning.

• Some Examples!

Answering Questions with Econometrics

Does inauguration of World Bank-financed projects in Sub-Saharan Africa cause an electoral benefit for the incumbent?

Does a certain concentration of airbnb listings in some urban area cause an increase in long-term rents?

Will increasing the minimum wage cause greater unemployment?

Causality

This Course

• Teach you the basics of Linear Regression

• Introduce you to the R software environment.

• This is not a course about R.

Grades

1. There will be quizzes on Moodle roughly every two weeks.

2. There will be two or three take home exams / case studies.

3. There will be no final exam. Your grade will be 40% of 1 and 60% of 2.

Course Materials

1. The Book.

2. The Slides

3. The code repository for book and R package

4. Quizzes on Moodle

What is R?¹

To quote the R project website:

R is a free software environment for statistical computing and graphics. It compiles and runs on a wide variety of UNIX platforms, Windows and MacOS.

What does that mean?

• R was created for statistical and graphical work.

• R has a vibrant, thriving online community. (stack overflow)

• Plus it's free and open source.

Why are we using R?

1. R is free and open source—saving both you and the university 💰💵💰.

2. Related: Outside of a small group of economists, private- and public-sector employers favor R over Stata and most competing softwares.

3. R is very flexible and powerful—adaptable to nearly any task, e.g., 'metrics, spatial data analysis, machine learning, web scraping, data cleaning, website building, teaching.

4. Related: R imposes no limitations on your amount of observations, variables, memory, or processing power. (I'm looking at you, Stata.)

5. If you put in the work², you will come away with a valuable and marketable tool.

6. I 💖 R

Data Wrangling

library(nycflights13)
 # select 3 cols of interest
fl = flights[ ,c("dest","distance","arr_delay")] 
# show first 4 lines of this dataframe
head(fl,n = 4)

## # A tibble: 4 x 3
##   dest  distance arr_delay
##   <chr>    <dbl>     <dbl>
## 1 IAH       1400        11
## 2 IAH       1416        20
## 3 MIA       1089        33
## 4 BQN       1576       -18

Data Wrangling

• There are always several ways to achieve a goal. (In life 😄)

• Here are the two leading data packages:

delays_dplyr <- fl %>% 
  group_by(dest) %>% 
  summarise(
    count = n(),
    dist = mean(distance, na.rm = TRUE),
    delay = mean(arr_delay, na.rm = TRUE)
  ) %>% 
  filter(count > 20, dest != "HNL")

library(data.table)
dl_dt = data.table(fl)
delays_dt <- 
  dl_dt[, list(count = .N, 
              dist = mean(distance,na.rm=T),
              delay = mean(arr_delay, na.rm=T)),
          by = dest][count > 20 & dest != "HNL"]

Plotting

ggplot(data = delays_dt, 
       mapping = aes(x = dist, y = delay)) +
  geom_point(aes(size = count), alpha = 1/3) +
  geom_smooth(se = FALSE)

Plotting in Base R vs ggplot

• R has very good graphical capabilities outside of contributed packages like ggplot2.

• We will encounter both approaches in this course.

• You will quickly see that some things are easier in base rather than ggplot and vice versa.

Spatial Data

library(sf)
plot(paris_sh[,"n"],
     main = "Number or IRIS by Arrondissement",
     key.pos = 3, 
     axes = FALSE, 
     key.width = lcm(1.3), 
     key.length = 1.0)

Spatial Plotting with ggplot

3D ggplots

Like, real 3D...

Tool Time!

Start your Rstudio!

First Glossary of Terms

• R: a statistical programming language

• RStudio: an integrated development environment (IDE) to work with R

• command: user input (text or numbers) that R understands.

• script: a list of commands collected in a text file, each separated by a new line, to be run one after the other.

R as a Calculator

Calculator 2

• We can also do exponents with ^:

  x = 2
  x^3

  ## [1] 8

• Square roots

  sqrt(2)

  ## [1] 1.414214

• and many logarithmic and trigonometric functions.

• many ... What??

Where to get Help?

• R built-in help:

  ?log
  ?sin
  ?paste
  ?lm
  help(lm)   # help() is equivalent
  ??plot  # get all help on keyword "plot"
  help(ggplot,package="ggplot2")  # show help from a certain package

• Help from Humans!

  • stackoverflow.com [SO]
  • Your classroom channel on Slack
  • rstudio forum

HOW to get Help?

1. Describe what you want to do.

2. Describe what you expect your code to do.

3. Describe what you your code does instead.

   • Provide the entire error message.

4. Provide enough code to reproduce your error.

   • You can post post code snippets on slack and SO

R Packages

• R users contribute add-on data and functions as packages

• Installing packages is easy!

  install.packages("ggplot2")

• To use the contents of a packge, we must load it from our library:

  library(ggplot2)

ScPoEconometrics package

• We wrote an R package for you.

• It's hosted on github.com

• You can install (and frequently update!) from there:

  if (!require("devtools")) install.packages("devtools")
  library(devtools)
  install_github(repo = "ScPoEcon/ScPoEconometrics")

• Did it work?

  library(ScPoEconometrics)
  packageVersion("ScPoEconometrics")

  ## [1] '0.2.2'

Data Types and Data Structures

• Numeric: 1.0, 2.1

• Integer: 1L, 2L, 42L

• Logical: TRUE and FALSE

• Character: "a", "Statistics", "1 plus 2."

• Categorical or factor

• You should read more right here!

Vectors

• What is a vector?

• The c function creates vectors.

  c(1, 3, 5, 7, 8, 9)

  ## [1] 1 3 5 7 8 9

• Coercion to unique types:

  c(42, "Statistics", TRUE)

  ## [1] "42"         "Statistics" "TRUE"

• Creating a Range

  (y = 1:6)

  ## [1] 1 2 3 4 5 6

Vectors from Sequences and Repetitions

• seq creates a sequence from to in steps of by:

  seq(from = 1.5, to = 2.1, by = 0.1)

  ## [1] 1.5 1.6 1.7 1.8 1.9 2.0 2.1

• rep repeats items:

  rep("A", times = 10)

  ##  [1] "A" "A" "A" "A" "A" "A" "A" "A" "A" "A"

• They also work in combination:

  c(x, rep(seq(1, 9, 2), 3), c(1, 2, 3), 42, 2:4)

  ##  [1]  2  1  3  5  7  9  1  3  5  7  9  1  3  5  7  9  1  2  3 42  2  3  4

Indexing or Subsetting a Vector

• R uses 1-based indexing.

• We use [] to get the value at an index

  x = c(1, 3, 5, 7, 8, 9)
  x[2]

  ## [1] 3

• Works with vectors of indices:

  x[c(2,5)]

  ## [1] 3 8

• And can get all but indices:

  x[-4]

  ## [1] 1 3 5 8 9

Logical Subsetting

• One can use a vector of TRUE and FALSE to index:

  x = c(1, 3, 5, 7, 8, 9)
  x[c(TRUE,TRUE,TRUE,FALSE,TRUE,FALSE)]

  ## [1] 1 3 5 8

• Let's create a logical vector for condition x > 3

  x > 3

  ## [1] FALSE FALSE  TRUE  TRUE  TRUE  TRUE

• We can get all values of x where x>3 is TRUE:

  x[ x > 3 ]

  ## [1] 5 7 8 9

Matrix

• A Matrix is a two-dimensional Array

  X = matrix(1:9, nrow = 3, ncol = 3)
  X

  ##      [,1] [,2] [,3]
  ## [1,]    1    4    7
  ## [2,]    2    5    8
  ## [3,]    3    6    9

• Subsetting needs two indices now:

  X[1,2]

  ## [1] 4

  X[3, ]

  ## [1] 3 6 9

Matrix Operations

• Let's create two matrices.

  X = matrix(1:4, 2, 2)
  Y = matrix(4:1, 2, 2)

• Arithmetic!

  X * Y # equally for +, - and /

  ##      [,1] [,2]
  ## [1,]    4    6
  ## [2,]    6    4

• But X * Y is not matrix multiplication. All of above are element by element operations.
• Matrix multiplication uses %*%. What is X %*% Y for you?

Lists

• Up to now, all containers were homogeneous
• lists are more flexible:

# works with and without fieldnames
ex_list = list(
  a = c(1, 2, 3, 4),
  b = TRUE,
  c = "Hello!",
  d = diag(2)
)
ex_list

## $a
## [1] 1 2 3 4
## 
## $b
## [1] TRUE
## 
## $c
## [1] "Hello!"
## 
## $d
##      [,1] [,2]
## [1,]    1    0
## [2,]    0    1

Indexing Lists

• [] gets a sublist
• [[]] gets a list element
• Can index by numerical index or name

ex_list[1]

## $a
## [1] 1 2 3 4

ex_list[[1]]

## [1] 1 2 3 4

ex_list$d

##      [,1] [,2]
## [1,]    1    0
## [2,]    0    1

data.frame's

data.frame's are like spreadsheets.

example_data = data.frame(x = c(1, 3, 5, 7),
                          y = c(rep("Hello", 3), "Goodbye"),
                          z = sample(c(TRUE,FALSE),size=4,replace=TRUE))
example_data

##   x       y     z
## 1 1   Hello  TRUE
## 2 3   Hello FALSE
## 3 5   Hello  TRUE
## 4 7 Goodbye  TRUE

data.frames

• Useful methods for a dataframe:

nrow(example_data)

## [1] 4

ncol(example_data)

## [1] 3

names(example_data)

## [1] "x" "y" "z"

Data on Cars

• The mtcars dataset is built-in to R.

  head(mtcars,n=3)  # show first 3 rows

  ##                mpg cyl disp  hp drat    wt  qsec vs am gear carb
  ## Mazda RX4     21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
  ## Mazda RX4 Wag 21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
  ## Datsun 710    22.8   4  108  93 3.85 2.320 18.61  1  1    4    1

• To access one of the variables as a vector, we use the $ operator as in mtcars$mpg

• Or we use the column name or index: mtcars[,"mpg"] or mtcars[,1]

Subsetting data.frames

• Subsetting is like with matrices, [,]

  # mpg[row condition, col index]
  mtcars[mtcars$mpg > 32, c("cyl", "disp", "wt")]

  ##                cyl disp    wt
  ## Fiat 128         4 78.7 2.200
  ## Toyota Corolla   4 71.1 1.835

• But there is a special function which looks nicer.

  subset(mtcars, subset = mpg > 32, select = c("cyl", "disp", "wt")]

Variables

• A variable refers to an object.

• Another way to say it is that a variable is a name or a label for something:

  x = 1
  y = "roses"
  z = function(x){sqrt(x)}

• local variables are only defined (and hence visible) within a certain area of your code, called a scope

• global variables are defined everywhere.

• Try to avoid global variables.

Control Flow

if (condition == TRUE) {
  some R code
} else {
  some other R code
}

x = 1
y = 3
if (x > y) {  # test if x > y
  # if TRUE
  z = x * y  # assign value to z
  print("x is larger than y")
} else {
  # if FALSE
  z = x + 5 * y  # assign other value to z
  print("x is less than or equal to y")
}

## [1] "x is less than or equal to y"

z

## [1] 16

Nested Loops

We often also see nested loops, which are just what its name suggests:

for (i in 2:3){
  # first nest: for each i
  for (j in c("mangos","bananas","apples")){
    # second nest: for each j
    print(paste("Can I get",i,j,"please?"))
  }
}

## [1] "Can I get 2 mangos please?"
## [1] "Can I get 2 bananas please?"
## [1] "Can I get 2 apples please?"
## [1] "Can I get 3 mangos please?"
## [1] "Can I get 3 bananas please?"
## [1] "Can I get 3 apples please?"

Functions

• Function say_hello tells R what to do when it you tell it say_hello().

say_hello <- function(your_name = "Lord Vader"){
  paste("You R most welcome,",your_name)
}
# we call the function by typing it's name with round brackets
say_hello()

## [1] "You R most welcome, Lord Vader"

• We specified a default argument, but we don't have to.

• Call the function with your name!