Important: this summary follows the order of the lectures in this specific course, not the chapters of the book. If you want to know what the lecturer discussed during these lectures, this is your perfect summary!
Applied Financial Econometrics
Summary of the Lectures
University of Amsterdam
MSc Finance
2022
,Week 1 - OLS and Experiments
Part B: OLS & Endogeneity
What you should already know: Ordinary Least Squares or “doing a regression”
OLS: Drawing a line through data (Ch4; p146[159])
It is called OLS because Stata draws a line through the points such that the sum of the squares
residuals (difference from predicted line) is minimal.
OLS estimator formulas
● B1 hat is the slope of the line. Sxy is the sample covariance of the dataset. S2x is the sample
variance of x. You should know this formula!
● Second formula is the intercept of the line. You should know this formula!
1
,OLS: testing and interpreting a slope coefficient (Ch7 & 8)
● If schooling goes up with one year, income increases 16.52%.
● T-statistic = coëfficiënt / standard error = 0..0083 = 19.86.
○ 19.86 > 1.96 meaning that there is a relationship.
● P value = 0.000 -> chance that coefficient in another sample is 0.1653 and there is no relation
between schooling and wage.
OLS: Core assumptions
The following 3 core assumptions must hold:
1. X does not move with u. The mean of u will be 0.
2. Sample must be random e.g. not only sampling from high education people.
3. The tales of the variables should go to 0 quickly enough e.g. you can't have negative earnings
(natually bounded) so that is okay.
2
,OLS: Consistency
Consistency: what if we take the entire population, will it still hold?
Covariance rules:
● Because B1 is a constant, you can put it in front.
● Because B0 is a constant, the covariance between X and B0 is 0.
So when you calculate your B1hat you get the B1 + formula and you hope that is as small as possible
and it will be 0 as assumption 1 holds!
What you (hopefully) already know: Ordinary Least Squares Inconsistency
When is OLS consistent?
Endogeneity leads to OLS inconsistency
● Even when you take the whole population as sample, you get B1 + *formula* because X is
correlated with u.
● Positive selection: *formula is positive - > overestimation of B1
● Negative selection: *formula is negative -> underestimation of B1
3
,Observational (just random sample) Data in general
Sources of endogeneity: 4 situations
● Omitted variables: if y1cov(xi,Wi) is not 0, then cov (X,u) is also not 0, meaning that we have
endogeneity by some omitted variable W. Only the W that are related to Y cause problems!
● Reversed causality: X causes Y and Y causes X.
○ To get the the cov formula on the bottom right: plug Xi in with ui. y0 and B0 are
constants. ni has 0 covariance with ui (bottom left).
○ We get reversed causality problems when: the y1 is not 0!
Example: Reversed causality in the knowledge-about and the use-of student loans
Knowledge about student loans and loan take-up
When a students loans more -> students learn more
OR
When a student leans more -> students loan more
4
,Does knowledge increase loan take-up?
Or does loan take-up increase knowledge?
Part C: Potential Outcomes
Causal Effects
● Treatment variable because you “treat” the sample with X.
5
,Potential outcomes
● Example: getting a MSc degree or not for each individual i and then taking the average ->
ATE
Potential outcomes example: loan take-up and knowledge
Person 1 is not borrowing even when given more information -> Treatment effect is 0.
If everybody is given more information 25% will borrow. Same for not giving more information.
The counterfactual problem
What would have happened if Robben scored? -> other state of the world.
6
,● The question marks are the counterfactuals.
● If we used this dataset, we would believe that the ATE would be 0.50.
7
,The counterfactual problem: Solve by OLS?
● Homogeneous treatment effect: effect is the same for everyone
● If X is 0 you observe Y0, if X is 1 you observe Y1.
● You add E(Y(0)) to get a B0. This is the average Y if nobody received the treatment And then
you also subtract it because otherwise you modify the equation.
● B1 measures the improvement if everyone gets the treatment.
● ui measures if the individual is below or above average.
● In this case there is an upward bias as the *formula* next to B1 is positive (0.5) -> exogeneity
does not hold.
The counterfactual problem and endogeneity: in a graph
Identification: Solutions to the counterfactual problem
● Experimental: you manipulate X variable and randomly assign people
● Observational: not changing just observing (from gotten sample) assuming random sample
8
, Part D: Experiments - Design
Identification using experimental data
● Randomized Control Trail (RCT): randomly assign individuals with X=1 or X=0. In this way
you eliminate all endogeneity.
● Spillovers: what happens to someone, happens also to somebody else because of that.
2 ways of achieving exogeneity by construction
Unconditional Random assignment
● Randomly decide if a person receives treatment.
Conditional Random assignment
9
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