in this video I want to provide a description
of the syllabus which we are going to cover in the undergraduate course.
So at the back of our minds within the undergraduate course,
and actually at the graduate level as well. The idea is that there is some
population and within the population there might be countries, there might be individuals,
there might be firms. And the idea is that
we don't actually have the whole population data set
you only have a sample from that population. So perhaps we have the just the figures
which I'm highlighting
here in purple, and these individuals form
a sample data set. And
the idea with econometrics is that we want to use
some sort of tool, some sort of statistical or mathematical tool
on that sample, to enable us to make some
inference about what's going on in the population or to make some
estimation of some sort of population parameter. So what exactly do I mean by
estimating the population parameter? So there might be a relationship between
the level of wage an individual obtains and
their level of education, which is given by the
relationship here which I've drawn mathematically. And
the idea here is that the coefficient beta might represent the effect of
one-year extra of education on an
individual's average level of wages. And that would be defined within
our population, and that would be the average effect of
one year of education on wages within the population but the idea is that
we don't actually have the whole population's data, we only have a sample from that
data, so we'd like to use our tool on the sample to enable us
to estimate this particular parameter, in this case beta.
When we first start off talking about estimation techniques,
we're gonna first start off discussing cross-sectional data so
that might be when we have the level of wages and the level of education
for a set of individuals one point in time.
And it just so happens that under a certain set of criteria
that a tool which we call 'ordinary least-squares'
happens to be quite a good tool to use on our sample.
So under a certain set of criteria ordinary least-squares
happens to be what we call BLUE, so that means it is the best
linear unbiased estimator possible. Don't worry if you don't understand what
that means, we are going to cover that in
due course. The set of criteria which needs to be
fulfilled are what we call the Gauss-Markov assumptions,
and assuming that each of these is satisfied then ordinary least-squares
are a useful thing to use on our sample.
But how do we actually go ahead and test
the certain criteria? Well we need a set of what we call
diagnostic tests, and
what these tests enable us to do, is they enable us to test as to whether it is
the case that these criteria
are satisfied. And if each of these criteria are satisfied
that's fine we can still use OLS on our sample,
and that will enable us to make some sort of good estimate about population
parameters.
But if these criteria aren't satisfied, so these diagnostic
tests show that they aren't satisfied
then ordinary least-squares is no longer BLUE,
and in this particular circumstance we need to define
a whole set of estimators which
may not be BLUE but may possess some sort of
other good
property which an estimator might have; in particular consistency
and under a set of less restrictive assumptions
they may happen to be blue or consistent.
So some of the estimators we are going to discuss here are instrumental variables
estimation GLS estimators
and maximum likelihood estimators. we may also talk
a little bit about GMM and but we are going to keep that to a
minimum. I should also mention that I'm gonna try and make this course
as non-mathematical as possible. Wherever
I can avoid using maths I'm going to avoid it, and where I do use maths
there is not necessarily the need to follow those videos
if you are just looking for the intuition behind the theory.
Ok, so the second part of the course
is going to be concerned with a second type of data
which we call time series data. So an
example of time series data might be let's say
we have a given company's level of sales
and now we don't just have it at one point in time
we might have it across time. So this might represent the company's sales across
time,
Alternatively you might be looking at the GDP
within the UK, we might be looking at inflation within the UK.
And time series is much more the realm of macroeconometrics
opposed to microeconometrics which is where cross-sectional data
is mostly concerned.
In the time series section, we are going to discuss properties of time series
so we're going to talk about what it means
for a time series to be what we call 'stationary'.
We're also going to discuss two particular examples
of time series which we call autoregressive of order one,
and we're also going to discuss MA of order one,
that means a moving average of order one process.
Again don't worry if you don't know what these mean, we're gonna discuss them
due course. So that's going to compose the second half of
the undergraduate course. The final part
is going to be what we call 'panel data methods'.
So that's going to be concerned with what happens if
we don't just have an individual's level of
data at given point in time, but let's say we have
the same individual's data but across time. So we might have
that individual's level wage in 2010 and then we have
that individual's level of wage in 2011.
And it just so happens that for panel data, as well as for time series data
we need to modify the Gauss-Markov assumptions slightly
to take into account the fact that our data is now
correlated across time - it is no longer independent.
And actually when we amend these Gauss-Markov conditions
we're actually not really going to be talking about a population of data anymore.
We're actually going to be talking about what we call a data generating process,
because the idea is that we can't really think about a sample of data
as taken from an infinite amount of time. You have to think about some sort of data
generating process which is generating samples
at different points in time. So it doesn't really make sense to talk about
populations when we are discussing time series and panel data.
For panel data we are going to discuss the between
estimator, we're also going to discuss the within estimator
and then if we have time we are going to discuss fixed effects,
and random effects as well.