My name is Maria Giamouzi and I'm a lecturer in the Department of
Economics since September 2020 at the University of Bath.
We live in the big data era and everything around us is all about
information. Everything is data, right?
Data can come in different forms like transactional data,
interest rates data, stock prices, data from social media.
So we need to find ways to analyse this data given appropriate
tools. In the past, this, the analysis of big sources of data
was a little bit impossible because we didn't have the
technology to store the data, but at the same time to analyse
the data. Nowadays, with different software developments, these
limitations have been overcome.
Therefore, we can analyse these big sources of data in the right
way. Econometrics is the application of statistical methods to
economic data in order to give empirical content to economic
relationships. More precisely, it is the quantitative analysis
of actual economic phenomena based on the concurrent development
of theory and observation, related by appropriate methods of
inference. In order to analyse this data, we need econometric
analysis. This analysis can be applied to a number of fields,
for instance, in strategy to estimate the demand.
In human resources, to understand who we should promote or who we
should not promote, to understand whether incentive or
incentives will probably increase productivity.
In finance, to understand whether it is the right time to buy
into stocks or not.
In marketing, to understand what persuades our customers.
And many more econometric can provide directions or help in the
decision making process.
So let's start now with a description.
Imagine that you want to decide whether you want to do a master's
degree or not.
That decision is obviously associated with a cost.
Right. So it's important to know that you will invest in
education, you will invest in one or two years doing a
postgraduate degree with the purpose of these additional years
of education to provide you some sort of increase in your future
income. We need to make sure that the model that we develop is
adequate to capture whether indeed the years of education do
increase earnings.
How much do they increase earnings?
Is it 1, 5 or 10 percent?
How can we answer that question?
One way to answer it is by introspection.
Or we can use econometric analysis to make our, to make a
decision that will be based on statistical evidence.
What can we do in order to do that?
We can collect a sample of individuals with the year of
education and the earnings and analyse what is the association
between years of education and earnings.
So our dependent variable here is earnings and our explanatory
variable is the years of education.
So what is happening to our dependent variable, earnings, every
time our education is increasing by one year.
That association can be expressed mathematically using that
equation, the expected value of Y given here, where Y is the
earnings, and X is education equals Alpha plus Beta X.
Where X is education and Y, as I said, is the earnings.
However, economic variables cannot be only based on one single
cause, for instance, education cannot only be the only cause
that makes our earnings increase or decrease.
There are additional explanatory variables that can cause a Y
earnings to change.
That can be the years of experience.
That can be the other qualifications that we might have, or it
might be the role in which we're working and so on.
So all these variables, causes, that are not included in the
model, in this model here, are captured by the error term that
is called u in that case, you might also see as epsilon.
OK, so the error term that you hear represents all of the
variables that are not included in my regression model.
So econometrics is all about identifying the value of that Beta.
What is that Beta?
Is it positive?
Is it negative? What is that Beta?
So we need to find a way to estimate the Beta value.
We need to find a method that will estimate Beta, being
unbiased, efficient and consistent, as we say.
And in order to do that, we have to use a linear regression
model. That is the method that is used to estimate the value of
Beta to understand what is happening to Y every time X is
changing. So if we plot the relationship, population
relationship here, Alpha is where the X value is zero, the Y
value is equal to Alpha.
The Y intercept as you say or constant.
As I name it here.
Then we'll have a plus Beta the slope of our regression line that
can be positive, as is indicated here.
It can also be negative.
Plus the error term, OK, the error term summation of the
distance of its actual point of observation, its data in our
sample, the distance from the regression line, and our purpose
is to find the regression line that will minimise the distance
between the data points, imagine here that we have additional
observations, additional dots, the actual observations, for
instance, the years of education of the participants in our
sample. And I'm trying to find the line that will best fit the
dots. So every time how do we interpret Beta, every time that X
is increasing by one unit, then we accept, expect Y to increase
by Beta.
So, in case Beta is positive, of course, right, if Beta is
negative, we expect Y to decrease by Beta.
What does it imply for the problem under investigation?
So every time the years of education are increasing by one year,
I'm expecting the earnings to increase by an amount equal to
Beta. Or if the association is negative, every time the years of
education are increasing by one year, I'm expecting the years of
education to decrease by Beta.
Now, the methodology, what can we do once we have the data?
The first thing is to obtain the data, to have a dataset that
you want to analyse in the example that I've used before.
My intention was to analyse whether the additional years of
education increased my earnings.
You have to collect the data.
As I mentioned before, this data can either be collected via a
survey you have to perform to collect primary data in that case.
Or you might base your analysis on secondary data where you can
download data from a from a dataset.
The second step is to assess a theory or hypothesis.
So the idea is that we have a sample of data, we'll have a
dataset, and we want to assess whether something is true or false
about that dataset.
Right. So we have the null hypothesis that states the status
quo, as we say, the hypothesis that specifies a default course
of action unless contradicted by data and the alternative
hypothesis, which is always the mutually exclusive of the null
hypothesis that contradicts what is the statement of the null
hypothesis. The next step is to perform the preliminary tests
and assess the assumptions.
We have different types of data that can be used for econometric
analysis. We have the cross-sectional data, this data are data
for different individuals at the same point in time.
OK, for instance, monthly visas balances, return on equity or
even the example with the years of education and the salaries
for 100 or 200 individuals, asking them what is their income and
how many years of education do they have today?
And that's it, that's cross-sectional data. Longitudinal data or
panel data that follow the same individual, or the same firm for
a number of years.
OK, and time series data variables that are measured over time.
For instance, interest rates, stock prices.
The type of data determine the mathematical model that can be
used, for instance, with Time series data.
You can use one of these possible alternatives.
A autoregressive model, moving average models, autoregressive
moving average models, a vector error correction model, vector
autoregression moving average models.
Depending on the type of data and what is the purpose or what are
you trying to investigate?
You have to select the ideal model.
With time series data we need to make sure to identify whether
the change in X was temporary or permanent.
And given if the change is temporary or permanent, the Beta
coefficients here have a different meaning.
OK, Beta naught is the impact, the short run or the impact
multiplier, as we call it.
Beta one is the change in Yt one period after the temporal
change, and so on.
In a permanent change when something happened to X and was keep
happening after that change will have the Beta naught plus Beta
one is, they give the change in Yt in the next period following a
permanent change and Beta naught Beta one and Beta two are the
change after two periods or the long run multiplier.
An example with cross-sectional data where I want to identify the
variables that affect the house prices.
OK, I'm using square feet, bedroom and lot size from the
estimate, estimation output, I can see that my regression model
can be written as this one.
How can I interpret the coefficients here?
Each extra square feet will be expected to increase the price by
123 dollars.
Each extra bedroom will expected to increase the house price by
13, approximately 13 thousand dollars, but be very careful.
How is it possible just one extra bedroom only to increase the
price by 13850 dollars?
That doesn't sound very reasonable, but you have to be careful
that every time in a multiple linear regression, every time that
we interpret these coefficients, we assume that the remaining
coefficients are constant.
OK, so I assume that the square feet and the lot size to remain
constant when I interpret the number of bedrooms.
So I mean that for the for this, for some reason houses with the
same square feet, some of them have three bedrooms or some of
them have two bedrooms and so on.
So in that case, for the same square feet and for the same lot
size, if the number of bedrooms is increasing from two to three,
that will increase the price by 13 thousand dollars.
OK, how we can estimate all these coefficients.
You can use econometric software.
There are a number of them.
There is Stata. There is EViews.
And there is also RStudio.
Once I've estimated my model, given the, I determine the model
based on the type of data, we need to assess whether the
hypothesis, I have to accept or reject my null hypothesis in the
beginning. In order to do that, we have to look at the P values
here. You can see that every coefficient is associated with a P
value every time that that P value is greater than this, any
significance level or the significance level that you are using,
that means that you have to accept the null hypothesis.
If the P value is less than Alpha, then we can reject the null
hypothesis. In that case here, assessing the null hypothesis
that these coefficients are statistically different from zero.
You can also look at the R-squared value that indicates how much
of the variability in the Y can be explained by these
explanatory variables in your models.
That's how we assess the statistical significance.
And of course, there are additional steps that need to be
followed. We'll have to assess whether nonlinear terms should be
added in a regression model.
We'll have to assess whether there are important omitted
variables that should be included in the analysis.
We have to assess whether our residuals are heteros-, homos
cedastic and normally distributed.
If this is not the case, then there are a number of ways that
can be followed. These ways are listed here.
In order to make the residuals being homoscedastic and also being
normally distributed, the previous process needs to be repeated
over and over again.
Until you identify the statistic, that the model is statistically
significant and robust.
All of the models have limitations.
It's impossible to identify a model that will best capture
reality. We try just to approach reality in the best possible
way. As long as you've done the econometric analysis, you can
move on to forecast or prediction.
If your econometric analysis is robust, statistically
significant and accurate.
If your data was cross-sectional data, then you can conclude
whether this data, this explanatory variables are the factors
affecting, for instance, the house prices.
Or you can might be able to conclude cause and effect
relationship that every time that education is increasing,
earnings are increasing.
However, it's a very strong argument to be made, the cause and
effect associations are very strong arguments to be made,
therefore, we will have to be very careful when we conclude that
indeed X causes Y to change.
We have to be very careful and make sure that indeed that is the
case, before we draw that conclusion.
If you have panel data, usually with panel data, it's easier,
it's the nature of the data that allow us better to assess the
cause and effect associations.
And of course, if your data are time series data, the main
purpose is forecasting or again, prediction to identify the
factors that might affect stock prices, interest prices, GDP
levels and so on. Thank you very much for watching.
I hope you liked my presentation.
Thank you.