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Notes part 2 EMF
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This are the notes that I have taken for the second part of the course, since this was the most difficult part.
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Block 1: Introduction event studies and construction of abnormal returnsConceptual framework:
- The effect of the event is just going to be the return if it happens minus the return if
it didn’t happen. This is like the treated minus the counterfactual
Problem: the same firm cannot be treated and control
- If a firm is subject to the event, we observe the realized return if the event happens
but we don’t observe what would have happened if the event didn’t happen
- If the firm is not subject to the event at that point in time we observe the return if
there is no event, but we don’t observe the return if the event would have happened
Solution:
- For the same firm that had the event, we know the returns before the
announcement of the event (which are actually the returns when the event didn’t
happen). At and after the announcement of the event, we know the realized return
(the return that already includes the announcement).
- What event studies is going to do is take the data before the announcement, it’s
going to transform it in a clever way to construct our right counterfactual with which
we can actually measure the expected effect of the event/announcement
conditional on having an event/announcement
- So here we are only going use firms that had an announcement/event
- Announcement and event will be used interchangeable
- This is called ATT
Example to see the difference between ATE and ATT
- Firm C and F can buy firm T. Firm C discovers that if they buy firm T, they going to
increase their value by 10%. Firm F discovers that it is going to lose 10% of its value if
they buy firm T.
- The ATE is 0%
- ATT is 10%, because firm F will never buy firm T
When ATT useful?
- Evaluating a policy to foster acquisitions→ so we want p firms that were not
acquiring, to acquire more. Bad thing to use an event study, because we didn’t have
those in the sample. We can never say anything about those we were not buying
- Assessing if horizontal or vertical mergers provide higher synergies→ in this case we
have both of them, we observe both of them and have the effect of both of them.
So, ATT seems good
- Quantifying the transaction profits of corporate insiders→ so we know that
managers and directors buy and sell their own shares and they are making more
money and we want to quantify how much money they are making and know how
much money and know how much money they would make if something else
happened. ATT is useful
- Assessing the effect of CEO dismissal→ the fact that we see that the CEO dismissal is
already happening, already tells us that there is something going on, so this is not
purely random. ATT is not useful
, - Assessing the effect of CEO death→ it’s true that we only observe the firms where
the CEO dies and we only have those in our study. But this is random→ when the
treatment/event is random (so it happens across all the firm equally) there is
nothing that affects the returns on the probability of actually being treated/having
an event, then the ATT coincides with ATE→ so here, event studies is as good as
difference-in-differences
- Analyzing the consequences of sport results on their teams→ if ajax wins or loses,
this is purely random conditional on ajax quality, but there is nothing that affects
returns. There is not selection bias here. So, ATT can be used here.
In general, we can always use ATT if:
- The treatment/event/announcement is random
- The aim of our research project is going to be something that we observe
4 models:
- Mean adjusted→ the expected return of firm j at time t is going to be equal to a
constant. The constant has a i, because every parameter that will be discussed in
blue color, depend on the event
- Market adjusted→ expect my firm j to move the way the market moves
- Market model→ assumes some generalized version of the CAPM. The expected
return is an intercept plus some risk premium. Difference with market adjusted
model is that here every event is going to have a different exposure to the market
- FF factors→ same as the market model but we extend the terms and add factors. f is
a vector of different factors and lambda is the exposure to those factors
Joint test problem: Either you assume the market is efficient and then you learn something
about the event. Or you assume the event has an effect and then you test if the market is
efficient. You can never test both the things at the same time.
Block 2: Event studies inference
Data hypothesis estimator
Data we have:
- Every abnormal return for each event and each time in the event window
- Cumulative abnormal return for each event, because we actually summed up
everything that was in the event window
The cumulative average treatment of the treated (CATT)= sum of the deltas (𝛿𝑖,𝜏 is the effect
of the event i at event time 𝜏.
Hypothesis we want to test: if the average CATT is actually 0. We name this term eta.
We
Statistics 101 proposed a t-test→ t statistic is eta divided by its standard error.
Regression approach:
- The error in the second equation is the 𝐶𝐴𝑅𝑖 − 𝜂
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