ScPoEconometrics

Florian Oswald
2018-09-14

Welcome to ScPoEconometrics!

scpo

  • This is not a course about R!
  • We want to teach you basic Econometrics, with R.
  • We don't rely on maths, but pratical experience.

Who Are *We*?

floswald JMR vviers

This Course is ...

But:

Exams and Grades

  • There will be quizzes on Moodle roughly every two weeks.
  • There will be a final exam on paper.
  • We will do online quizzes on kahoot.com
    • On your smartphones!
    • Really fun.
    • but those will not be part of your grade.

Today

  1. Logistics
  2. Communication - Slack
  3. R and RStudio

But Right Now:

Slack:

  • Let me tell you a bit about Slack first.
  • Now let's all open Slack on our computers!

R Glossary Number 1

  • 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.

Warning

  • Those slides are a subset of chapter 1
  • You must read the entire chapter.

R as a Calculator

  • Let's do some basic arithmetic first:
4 + 1

[1] 5

8 / 2

[1] 4
  • Great! What about this?
log(exp(1))

[1] 1

# by the way: this is a comment! (R disregards it)

R as a 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.
  • … 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

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.
    1. Provide the entire error message.
  4. Provide enough code to reproduce your error.
    1. You can post post code snippets on slack and SO

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)

The 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] '0.1.3'

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

Your Turn!

Task 1

  • Create a vector of five ones, i.e.
[1] 1 1 1 1 1
  • Notice that the colon operator a:b is just short for construct a sequence from a to b. Create a vector the counts down from 10 to 0, i.e. it looks like
 [1] 10  9  8  7  6  5  4  3  2  1  0
  • Use rep to create a vector that looks like this:
 [1] 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3
  • Find out (using help(), google or whatever) how to get the length of a vector in R!

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

Task 2!

  • From the runif function get 10 numbers drawn from the uniform distribution and store in x.

  • get all the elements of x larger than 0.3, and store them in y.

  • using the function which, store the indices of all of those elements in iy.

[1]  1  2  3  4  9 10
  • Check that y and x[iy] are identical.
[1] TRUE TRUE TRUE TRUE TRUE TRUE

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?

Task 3

  • Create a vector containing 1,2,3,4,5 called v.

  • Create the (2,5) matrix m:

     [,1] [,2] [,3] [,4] [,5]
[1,]    1    2    3    4    5
[2,]    6    7    8    9   10
  • Perform matrix multiplication of m with v. Use the command %*%. What dimension does the output have?
[1] 2 1
  • Why does the command v %*% m not work?

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

Task 4

  1. Copy and paste the above code for ex_list into your R session. Remember that list can hold any kind of R object. Like…another list! So, create a new list new_list that has two fields: a first field called “this” with string content "is awesome", and a second field called “ex_list” that contains ex_list.
  2. Accessing members is like in a plain list, just with several layers now. Get the element c from ex_list in new_list!
  3. Compose a new string out of the first element in new_list, the element under label this. Use the function paste to print the string R is awesome to your screen.
names(new_list)

[1] "this"    "ex_list"

paste("R",new_list$this)

[1] "R is awesome"

DataFrames

  • DataFrames 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 FALSE
2 3   Hello FALSE
3 5   Hello  TRUE
4 7 Goodbye FALSE

DataFrames

  • 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")]

Task 4

  1. How many observations are there in mtcars?
  2. How many variables?
  3. What is the average value of mpg?
  4. What is the average value of mpg for cars with more than 4 cylinders, i.e. with cyl>4?

Basic Programming

  • It's useful for us to review some basics for programming.
  • We won't be going very deep here, but it's good for you to know some of this.

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

  • We can influence which branch our code executes based on
  • Whether we follow one branch or another depends on a condition.
if (condition = TRUE) {
  some R code
} else {
  some other R code
}

Example if-else

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")
}
z

Loops

  • This is an example for a loop:
for (i in 1:5){  # does not have to be 1:5!
  print(i) # loop body: gets executed each time
  # the value of i changes with each iteration
}

[1] 1
[1] 2
[1] 3
[1] 4
[1] 5
  • We can iterate over things other than numbers:
for (i in c("mangos","bananas","apples")){
  print(paste("I love",i))  # the paste function pastes together strings
}

[1] "I love mangos"
[1] "I love bananas"
[1] "I love apples"

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!

Task 5

  1. Write a for loop that counts down from 10 to 1, printing the value of the iterator to the screen.
  2. Modify that loop to write “i iterations to go” where i is the iterator
  3. Modify that loop so that each iteration takes roughly one second. You can achieve that by adding the command Sys.sleep(1) below the line that prints “i iterations to go”.
  4. Finally, let's create a function called ticking_bomb. it takes no arguments, it's body is the loop you wrote in the preceding question. The only think you should add to the body is a line after the loop finishes, printing “BOOOOM!” with print("BOOOOM!"). You can repeatedly redefine the function in the console, and try it out with ticking_bomb().