Summary Notes for "Econometrics for ECO "(Tilburg University) - Grade Achieved 9.5/10
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Course
30L203-B-6 (30L203B6)
Institution
Tilburg University (UVT)
Book
Introductory Econometrics
This document is the long summary for the course "Econometrics for ECO" at Tilburg University. The summary is based on both the slides and the book, all in one place. With this document you have enough information to study and easily pass the exam of this course - personally based my studying off t...
Test Bank For introductory econometrics: a modern approach 7th edition by jeffrey m. wooldridge
TEST BANK FOR Introductory Econometrics: A Modern Approach 7th Edition by Jeffrey M. Wooldridge
TEST BANK FOR Introductory Econometrics: A Modern Approach 7th Edition by Jeffrey M. Wooldridge
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Tilburg University (UVT)
Economics
30L203-B-6 (30L203B6)
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Chapter 1:
Chapter 1 focuses on teaching you the general idea of econometrics. It is used in all forms of
applied economics, to test theories, inform governments or policy makers (public or private) and
predict (economic) time series. As economists, we naturally love models. Sometimes
econometric models can be derived from formal economic models but also from informal
reasoning and intuition. As young econometricians we will aim to estimate the parameters in a
model and test different hypotheses on these parameters. We can use these values and signs
to figure out how valid an economic theory is and the effects of specific policies. Econometrics is
the unification of statistics, economic theory and mathematics. Ofcourse, we will be dealing with
heaps of data, and this data will come in different forms. Here are some of the main ones:
Data Types:
Data Type Name Description
Cross-sectional The basic idea is that it is data which is carried out at a single point/
period in time on (a) variable(s). We can also often assume that it is
obtained by random sampling from the underlying population, but not
always! This could not be true if sampling occurs when we sample from
units that are large relative to the population, or if specific groups of
people are less likely to disclose information. Here each observation is
just given a number, many programs do this for you. Ordering doesn’t
matter for analysis.
Time Series Includes obs (observations) on a variable or several variables over time,
examples are stock prices, money supply, consumer price index, etc.
Chronologically ordering these with time could bring forth useful
conclusions/information (notice how ordering in cross-sectional did not
really make a difference…) . Important things like data frequency must
be kept in mind, perhaps a lot of the data is from time a, which is when
the economy was in a low point… Main issue is that obs are rarely
independent, as today’s stock price depends on yesterday’s stock price.
Pooled Cross- This is for data sets which include cross-sectional AND time series.
sectional Here they often take the cross-sectional of year a, then add cross-
sectional of year b and so forth. See page 8 for a representation. We
can often analyze them in the same way as cross-sectional, just need to
keep in mind that some data differs by time, so perhaps certain
economic constants/givens have changed. The point is often to see how
a key relationship has changed over time. The key is that here you
random sample in year 1, then random sample again in year 2, so you
are not certain if the obs are the same people/units.
Panel Data Panel data is a time series for each cross-sectional member. So let's
say we want to look at how much money persons a-z have earned each
year for 10 years. Once we have all this data we can organize it by first
giving the time series for person a, then b, and so forth. It is kind of like
a Pooled Cross-sectional but now the time series is embedded in the
cross-sectional and not just continued with different obsno. So here we
follow the same people/units over time! Like seeing how gdp has
changed in 5 different countries over 10 years.
,The five steps to empirical economic analysis:
1) Careful formulation of question of interests.
a) Mathematical reasoning but also intuitive reasoning can be used to find possible
causal relationships.
2) Formulation of econometric models, sometimes a formal economic theory.
a) You will have β!"#$#%&'&$(!)*+,*!)+--!(*.)!'*&!/+$&,'+.0!#0/!%#10+'2/&!
(.%&'*+01!#33&,'(!'*&!%#+0!42&('+.05!*.)&6&$!7.2!#-(.!*#6&!2!8!&$$.$!'&$%9
/+('2$:#0,&!'&$%;!<*+(!+(!3.$!#07'*+01!)&!*#6&!0.'!#,,.20'&/!3.$=
3) Formulate hypothesis in terms of unknown model parameters.
a) Quite straightforward, just make hypotheses!
4) Data collection & use of econometric methods to estimate parameters in econometric
models and formally test hypotheses of interest.
a) A lot of data is available online! He mentions a few websites in the video.
Econometrics can also be used to estimate the model’s parameters, in many
cases we do this!
5) Carefully interpret the results! Are they economically meaningful?
a) Do the results make sense? What do the magnitudes mean? Often a good
interpretation is to look at confidence intervals.
An economist’s goal is to infer the causal effect of one variable on another, an association may
suggest, but does not establish, a causal effect.
Lastly; Ceteris Paribus and causal inference. Most hypotheses in social sciences are ceteris
paribus in nature, other factors must be fixed when studying the relationship between two
variables. However, because of the non experimental nature of most data collected in the social
sciences, finding causal relationships may be very challenging. The book talks a lot about why,
examples include: ethical issues, economic costs, etc. These reasons are to explain why we
sometimes can't collect data, or keep certain things constant. Ceteris paribus thus plays a key
role, can you fix all else/account for it not being fixed? With econometric methods we can
emulate a case where enough factors are fixed to draw conclusions. With experimental data you
control everything, sometimes you can do a social experiment, but then you need to make sure
it is independent, e.g. don’t give person ‘a’ more education because he is more gifted. The key
is to assign things independently, and never forget about the practical problems. Possible
problems with education’s effect on wages are:
1) People with more education typically have less experience.
2) People with more innate ability often choose more education.
First one is a bit easier to deal with (still hard), but the second one is more difficult.
Chapter 2:
What is a simple regression model?
For two variables y & x that represent some population, explains how y varies
with changes in x.
, y = β0 + β1x + u
Where:
y Dependent variable (or explained variable, regressant)
x Independent variable (or explanatory variable, regressor)
u Error term (disturbance), captures unobserved factors affecting y
β0 Intercept parameter (or constant term)
β1 Slope parameter
If Δu = 0 we can capture the ceteris paribus because Δy = β0 + β1 Δx!
Deriving our OLS estimator as a method of moments;
We want to estimate βo β1 using a random sample. We always need to start with assumptions;
, KLM!#((2%"'+.0!8!E[u] = 0 and that cov(x, u) = E[xu] = 0
Since u = y − β0 − β1 x we can see that;
E[y − β0 − β1x] = 0 & E[x(y − β0 − β1x)] =0
So:
n n
n −1 (yi − β^0 − β^1 xi ) = 0 & n −1 xi(yi − β^0 − β^1 xi ) = 0
∑ ∑
n i=1 i=1
−1
y = β^0 + β^1 xi!8!β^0 = _y − β^1 _x. Now remember… β^0 and β^1are
∑ i
y
Since _ =n
i=1
estimates!
If we simplify this, see the picture on phone, we see that if we are ok with B1 estimate we will
be ok with B0 too….
^ ^
Now that we have a method to find β0 in terms of β1, we are able to combine this equation,
and the second moments equation to make;
n
[n −1 xi(yi − β^0 − β^1 xi ) = 0] + [β^0 = _y − β^1 _x] =
∑
i=1 n
−1
xi(yi − (y_ − β^1 _x ) − β^1 xi ) = 0]
∑
[n
i=1
We can ofcourse simplify this… by taking on one side y and on the other side x to get;
n n
xi(yi + _y) = β^1
∑ ∑
xi(xi − _x )
n i=1 n i=1
(xi − _x )2. If this is bigger than 0, we get;
∑ ∑
In statistics we saw that; xi(xi − _x ) =
n i=1 i=1
∑i=1 xi(yi − _y)
β^1 = n =
∑i=1 xi(xi − _x )
n n n n
∑i=1 (xi − _x )(yi − _y) ∑i=1 (xi − _x )yi ∑i=1 (xi − _x )(β0 + β1xi + ui ) ∑i=1 (xi − _x )ui 1
SSTx ∑ i i
n = n = n = β1 + n = β1 + ( du)
∑i=1 (xi − _x )2 ∑i=1 (xi − _x )2 ∑i=1 (xi − _x )2 ∑i=1 (xi − _x )2
with di = xi − _x
∑
Recall that 1) (xi − _x )β0 = 0 and 2)
∑ ∑ ∑
(xi − _x )β1x1 = β1 (xi − _x )xi = β1 (xi − _x )(xi − _x )
We used that for the equations above ^^^^
If we were to add 1/n to the numerator and denominator (of the second equation), we would
get that β1
^ = cov(x, y) .
var (x)
(isn't sum of d_i also 0? Bcz x_i-xbar?)
OLS as estimates of sum of squared residuals;
β^0 and β^1 minimize the sum of squared residuals (SSR)
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