Introduction to Econometrics

# Introduction to Econometrics
### AECN 896-004

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# Outline

1. [Ligistics](#logistics)
2. [What is econometrics about?](#econometrics)
3. [Causality and Association](#causality)
4. [Endogeneity](#endogeneity)

---

# Logistics

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# Instructors

+ <span style = "color: red;"> Instructor </span>: Taro Mieno (Office: 209, E-mail: tmieno2@unl.edu)
+ <span style = "color: red;"> Teaching Assistant </span>: 
  - TBD

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# Goals of the course
+ Learn modern introductory econometric theory
+ Apply econometric theories to real economic problems
+ Learn how to use statistical software (R) so you can conduct research independently (without technical help from your advisor)
  - manage data
  - visualize data
  - run regressions
  - interpret results

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# Text Books

## Recommended:
Wooldridge, Jeffrey M. 2006. "Introductory Econometrics: A Modern Approach (<span style = "color: red;">5</span>th edition)." Mason, OH: Thomson/South-Western.

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# Course Schedule

+ Lectures (MW): 3:00-4:30pm
+ Lab sessions (F): 1:00-2:30pm

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# Course Website

[Course Website](https://github.com/tmieno2/MS-Applied-Econometrics)
+ Lecture Slides 
+ Assignments and submission links
+ Final paper samples and submission link

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# Grading

+ Problem sets (4 assignments): 40% 
+ Small-size midterms  (2): 20% 
+ Paper: 40%

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# Assignments
  
## Problem sets
+ Most questions are from the required text book
+ Some questions come from what we cover in lab sessions

## Rmarkdown to do and submit your problem sets
+ You are required to present your R codes
+ You learn how to compile your assignment with your R code written in a document using <span style = "color: red;"> Rmarkdown </span>, which will be covered in the second lab session

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# Assignments

.content-box-red[**Caution**]  
+ 2nd year students have answers to all the questions I will assign (I will use exactly the same problems because they are really good to learn econometrics)
+ You are free to copy and paste (or rephrase) the answers for your assignment. I won't bother to try to tell if you have copied and pasted answers.
+ However, you are simply doing dis-service to yourself by depriving yourself of learning opportunities
+ Moreover, your lack of understanding of the material will be clearly manifested on your performance at midterms and final paper

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# Midterms

In-class open-book midterms

+ Midterm 1: Oct, 9 (M)
+ Midterm 2: Nov, 20 (M)

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# Paper

In this assignment,
  + you write a paper with a particular emphasis on econometric analysis using a real world data set
  + you are encouraged to use the data set you are using for your masters thesis (talk with your advisor)
  + you need to ensure that you use a <span style = "color: red;"> panel </span> dataset
  + No presentation of your final paper

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# Paper
Here is the time line of the paper assignment:
  + <span style = "color: red;"> Oct, 16 </span>: identify a research topic and the data set you will be using, and get an approval from the instructor
  + <span style = "color: red;"> Oct, 23 </span>: paper proposal 
  + <span style = "color: red;"> Dec, 15 </span>: final paper

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# Paper Proposal

## Introduction
+ clear identification of what you are trying to find out (research question) 
+ why the research question is worthwhile answering

## Simple Model
+ dependent variable (the variable to be explained)
+ explanatory variable (variables to be explain)

## Data Source
+ where you get data

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# Final Paper

## Introduction
  + clear identification of what you are trying to find out (research question) [1 point]
  + why the research question is worthwhile answering [1 point]

## Data description
  + the nature of the data with summary statistics table [1 point]
  + visualize a few key variables in a meaningful way [3 points]

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# Final Paper

## Econometric Methods:
the <span style = "color: red;"> process </span> of how you end up with the final econometric models and methods. [40 points (<span style = "color: red;"> or more </span>)]
+ justification of your choice of independent variables
+ potential endogeneity problems
+ what did you do to address the endogeneity problems?
+ justification of econometric model(s) and method(s)
+ identify appropriate standard error estimation methods

## Results, Discussions, and Conclusions:
+ interpret and describe the results [2 points]
+ implications of the results [1 point]
+ conclusions [1 point]

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name: econometrics

# What is econometrics about?

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# What econometrics is about

Estimate quantitative relationships between variables

+ the impact of fertilizer on crop yield
+ the impact of political campaign expenditure on voting outcomes
+ the impact of education on wage

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# Steps in Econometric Analysis

+ formulation of the question of interest (what are you trying to find out?)
+ develop an economic model of the phenomenon you are interested in understanding (identify variables that matter)
+ turn the economic model into an econometric model
+ collect data
+ <span style = "color: blue;"> estimate the model using econometrics </span>
+ <span style = "color: blue;"> test hypotheses </span>

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# Step 2: Develop an economic model

`$$wage = f(educ,exper,training)$$`

+ `$wage$`: hourly wage
+ `$educ$`: years of formal education
+ `$exper$`: years of workforce experience
+ `$training$`: weeks spent in job training

.content-box-green[**Note**]: Depending on questions you would like to answer, the economic model can (and should) be much more involved

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# Step 3: Develop an econometric model

`$$wage = f(educ,exper,training)$$`

The form of the function `$f(\cdot)$` must be specified (almost always) before we can undertake an econometric analysis

`$$wage = \beta_0 + \beta_1 educ + \beta_2 exper + \beta_3 training + u$$`

## `$\beta_0,\beta_1,\beta_2,\beta_3$`
+ are the <span style = "color: red;"> parameters </span> of the econometric model.
+ describe the directions and strengths of the relationship between `$wage$` and the factors used to determine `$wage$` in the model

## `$u$`
+ is called error term
+ includes <span style = "color: red;"> ALL </span> the other factors that can affect wage other than the included variables (like innate ability)

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# Step 4: Collect data
+ survey
+ websites
+ experiment

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# Data types

+ a sample of individuals, households, firms, cities, states, countries, or a variety of other units, taken at a given point in time
+ the data on all units do not correspond to precisely the same time period
  - some families surveyed during different weeks within a year

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# Cross-sectional Data

```r
here("Data/wage1.rds") %>%
  readRDS() %>%
  data.table() %>%
  .[, .(wage, educ, exper, female, married)]
```

```
##       wage educ exper female married
##   1:  3.10   11     2      1       0
##   2:  3.24   12    22      1       1
##   3:  3.00   11     2      0       0
##   4:  6.00    8    44      0       1
##   5:  5.30   12     7      0       1
##  ---                                
## 522: 15.00   16    14      1       1
## 523:  2.27   10     2      1       0
## 524:  4.67   15    13      0       1
## 525: 11.56   16     5      0       1
## 526:  3.50   14     5      1       0
```

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# Data types: Time-series Data

.content-box-green[**Time-series Data**]
Observations on a variable or several variables over time
  + corn price
  + oil price

.content-box-red[**Note**]:
  + The econometric frameworks necessary to analyze time series data are quite different from those for cross-sectional data
  + We do <span style = "color: red;"> NOT </span> learn time-series econometric methods

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# Data types: Panel (Longitudinal) Data

.content-box-red[**Panel (Longitudinal) Data**]
time series data for each cross-sectional member in the data set (<span style = "color: red;"> same </span> cross-sectional units are tracked over a given period of time)

.content-box-green[**Example**]
  + wage data for individuals collected every five years over the past 30 years
  + yearly GDP data for 60 countries over the past 10 years

.content-box-red[**Notes**]
  + Panel data are much more common than they used to be
  + Panel data econometric methods take advantage of the panel data structure

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# Data types: Panel (Longitudinal) Data

```r
here("Data/crime4.rds") %>%
  readRDS() %>%
  .[, .(county, year, crmrte, prbarr, prbpris)]
```

```
##      county year    crmrte   prbarr  prbpris
##   1:      1   81 0.0398849 0.289696 0.472222
##   2:      1   82 0.0383449 0.338111 0.506993
##   3:      1   83 0.0303048 0.330449 0.479705
##   4:      1   84 0.0347259 0.362525 0.520104
##   5:      1   85 0.0365730 0.325395 0.497059
##  ---                                        
## 626:    197   83 0.0155747 0.226667 0.428571
## 627:    197   84 0.0136619 0.204188 0.372727
## 628:    197   85 0.0130857 0.180556 0.333333
## 629:    197   86 0.0128740 0.112676 0.244444
## 630:    197   87 0.0141928 0.207595 0.360825
```

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# Steps 5 and 6
This is what you learn for the next few months!!
  + estimate the model using econometrics
  + test hypothesis

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name: causality

# Causality and Association

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# Causality and Association

An association of two variables arise because <span style = "color: red;"> either of or both </span> variables affect the other variable

`\begin{align}
  A \longleftrightarrow B \\
  A \longrightarrow B \\
  A \longleftarrow B 
\end{align}`

Association does <span style = "color: red;"> NOT </span> concern which affects which. Under all the three cases above, A and B are <span style = "color: blue;"> associated</span>. Or, we say there is an association between A and B. This is what <span style = "color: blue;"> correlation coefficient </span> measures.

When A has a causal impact on B,

`\begin{align}
  A \longrightarrow B 
\end{align}`

Here, changes in `$A$` cause changes in `$B$`, not the other way around

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Let's watch this [interesting CM](https://www.youtube.com/watch?v=KSHMgoUWBmY).

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People who wear glasses are

+ much smarter than those who don't
+ more likely to pursue higher education
+ 200% more likely to graduate college

For you to be convinced to buy glasses, these claims needs to be causal, not association:
+ Does wearing glasses make you much smarter?
+ Does wearing glasses make it more likely for you to pursue higher education?
+ Does wearing glasses make it 200% more likely for you to graduate college?

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However, this seems to be a more likely explanation of the association:

+ One spends more time studying academic subjects
  - smarter (or knowledgeable) `$\rightarrow$` pursue higher education and graduate college 
  - worsened eyesight `$\Rightarrow$` wear glasses

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.content-box-green[**Important**]:
+ We care about isolating causal effects, but not association
+ Identifying association is super easy
+ Identifying causal effects is extremely hard (this is what we tackle)

---
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name: endogeneity

# Endogeneity: Your Nemesis

---
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# Causality and Association

It is super easy to find an association of multiple variables, but it is incredibly hard to find a causal effect (at least in Economics)!!

---
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# Endogeneity

You are interested in the causal impact of fire fighters on the number of death tolls in fire events

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+ How are they associated?
+ Can you say anything about the causal effect of fire fighters deployment on the number of death tolls?

---
class: middle

# What happened?

You ignored an important variable!!

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style="overflow-wrap:break-word;"><td class="cl-c98b7910"><p class="cl-c98b4e5c"><span class="cl-c98b41c8">2</span></p></td><td class="cl-c98b7905"><p class="cl-c98b4e5c"><span class="cl-c98b41c8">0</span></p></td><td class="cl-c98b790e"><p class="cl-c98b4e5c"><span class="cl-c98b41c8">3</span></p></td><td class="cl-c98b790f"><p class="cl-c98b4e5c"><span class="cl-c98b41c8">5</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-c98b78fb"><p class="cl-c98b4e5c"><span class="cl-c98b41c8">3</span></p></td><td class="cl-c98b78fa"><p class="cl-c98b4e5c"><span class="cl-c98b41c8">5</span></p></td><td class="cl-c98b78e6"><p class="cl-c98b4e5c"><span class="cl-c98b41c8">10</span></p></td><td class="cl-c98b7904"><p class="cl-c98b4e5c"><span class="cl-c98b41c8">20</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-c98b7910"><p class="cl-c98b4e5c"><span class="cl-c98b41c8">4</span></p></td><td class="cl-c98b7905"><p class="cl-c98b4e5c"><span 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---
class: middle

# Endogeneity Problem

+ Variables of interest are correlated with some <span style = "color: blue;"> unobservables </span> (variables that cannot be observed or are missing) that have non-zero impacts on the variable that you want to explain

+ The unobserved variables are also called <span style = "color: blue;"> confounder/confounding factor </span>.

<span style = "color: blue;"> Confound </span>: mix up (something) with something else so that the individual elements become difficult to distinguish (Oxford dictionary).

---
class: middle

In the above example,

+ <span style = "color: red;"> variable of interest </span>: the number of firefighters
+ <span style = "color: red;"> unobservables/confounder </span>: the scale of fire events (and other factors)
+ <span style = "color: red;"> variable to explain </span>: death toll

.content-box-green[**The model**]:
`\begin{align}
  \mbox{death toll} & = \alpha + \beta\; \mbox{# of fire fighters} + \mu\\
  ,\mbox{where } \mu & = (\gamma\; \mbox{scale} + v) \mbox{ is the error term (collection of unobservables)}
\end{align}`

\# of fire fighters is correlated with scale, which we ignored

---
class: middle

.content-box-green[**Another example: education on wage**]
`$$wage = \beta_0 + \beta_1 educ + \beta_2 exper + \beta_3 training + u$$`
    
What are unobservables in `$u$` that are likely to be correlated with `$educ$`?

.content-box-red[**An important unobservable**]      
+ innate ability `$\rightarrow$` wage
+ innate ability `$\rightarrow$` education

---
class: middle

Most of the time, you will be faced with endogeneity problems caused by at least one of the followings,

+ omitted variables (the scale of fire events, innate ability)
+ self-selection
+ simultaneity
+ measurement error

How can we avoid or solve endogeneity problems?

---
class: middle

# How to deal with endogeneity?
+ You have two opportunities to deal with endogeneity problems
  - at the design (design to collect data) stage
  - at the regression stage (what you will learn in this course)
+ Econometrics has evolved mostly to address endogeneity problems at the <span style = "color: blue;"> regression stage </span> because randomized experiments are infeasible most of the time
+ How about econometrics and other fields of statistics: Statistics, Psychometrics, and Biometrics?

---
class: middle

# How to deal with endogeneity?

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---
class: middle

# Deal with endogneity at the design stage

.content-box-red[**Randomized Experiments**]
+ you have a liberty to determine the level of the variable of interest
+ by randomizing the value of the variable of interest, you can effectively break the link (association) with whatever is included in the error term

---
class: middle

# The impact of fertilizer on corn yield (Non-Randomized)

Yield and nitrogen rate data obtained from a field that is managed by a farmer

---
class: middle

# The impact of fertilizer on corn yield (Non-Randomized)

+ decide nitrogen rate based on soil/field characteristics (some of them we researchers do not get to observe)

+ soil characteristics is not observable, so it is in the error term

`$$yield = \beta_0 + \beta_1 N + (\gamma SC + \mu)$$`

+ N (nitrogen rate) and SC (soil characteristics) are correlated

---
class: middle

# The impact of fertilizer on corn yield (Non-Randomized)

Suppose the farmer applied more nitrogen to the area where its soil characteristics lead to higher corn yield

.content-box-green[**Question**]
If the researcher estimate the model (which ignores soil characteristics), do you over- or under-estimate the impact of nitrogen rate on corn yield?

---
class: middle

# Randomized Experiments

---
class: middle

# Randomized Experiments on Education?

Researchers determine randomly how much education subjects (people) can get?

---
class: middle

# Endogeneity Problem in Economics

+ Economics is about understanding human behavior

+ Almost always, you need to deal with endogeneity problem because people are `smart`: we make decisions based on available information (not just randomly) so that our decisions lead to good outcomes (<span style = "color: blue;">whether our decisions turn out to be good or not is irrelevant</span>)
  - how much education one get is determined based on their judgment of their own ability (not by rolling a dice)
  - how many fire fighters to be deployed was determined based on the scale of fire (not by rolling a dice)
  - how much nitrogen to apply based on soil characteristics (not by rolling a dice)

+ If people are not smart and just roll a dice for their decision making, we would have much easier time identifying causal effects