Levels vs differences regression - motivation for cointegrated regression

This video explains the difference between levels and first differences regression, and discusses how the level regression motivates the concept of cointegration. I also provide a simulation in Matlab\Octave to demonstrate the difference.
clear; clc; close all;
n=100;
dx=zeros(n,1);
dy=zeros(n,1);
y=zeros(n+1,1);
x=zeros(n+1,1);
x(1)=0;
y(1)=0;
b=2;
e=1;
a=10;
for i = 1:n
dx(i)=randn();
dy(i)=b*dx(i) + e*randn();
x(i+1)=x(i)+dx(i);
y(i+1)=y(i)+dy(i);
end
i =1:n+1;
i=i';
j=i(1:end-1);
zoom=1.0;
FigHandle = figure('Position', [750, 300, 1049*zoom, 895*zoom]);
subplot(2,1,1),plot(j,x(1:end-1),'g',j,y(1:end-1),'b','LineWidth',1.4)
title('Levels', 'FontSize', 20);
legend('X','Y')
subplot(2,1,2),plot(j,dx,'m',j,dy,'r','LineWidth',1.4)
title('Differences', 'FontSize', 20);
legend('DX','DY') Check out ben-lambert.com/econometrics-... for course materials, and information regarding updates on each of the courses. Quite excitingly (for me at least), I am about to publish a whole series of new videos on Bayesian statistics on youtube. See here for information: ben-lambert.com/bayesian/ Accompanying this series, there will be a book: www.amazon.co.uk/gp/product/1...

[@111southeastsam111]

I wish this guy was my Econometrics lecturer at university. My actual lecturer is shit and confuses the subject so much more than it needs to be. This guy explains everything so clearly and simply - very important for such a complex subject.

[@DonPedroTheDude]

Amazing that this is surely one of the most important lessons in econometrics, but also the most easily forgotten.

[@spencerantoniomarlen-starr3069]

This video is a really useful supplement to aid in understanding the 2015 study on Minimum Wage Effects on Labor Dynamics (in the USA) by Meer & West

[@lbarberia]

Very helpful. It would be good to show how to interpret coefficients in first differences.

[@Mpuselicious]

Thank you so much for this :)

[@31896eneri]

THANK YOU VERY MUCH!!

[@ajayalmighty]

Thanks for the video, and series as well. I only wish I had heard about your channel earlier.

[@SpartacanUsuals]

Hi, thanks for your message, and kind words. Glad to hear that it was useful. Best, Ben

[@nahshahehsha6794]

Are models such as those used to compute beta coefficients for stock returns considered “first difference” regressions? Or are they a special case because it’s not only the difference but the difference expressed as a % (the return)?

[@jasonleewkd]

Hi Ben, this video has been great! Do you have any views on whether I should use levels or differences when trying to predict interest rates?

[@enkii82]

Are there instances where the variables are cointegrated in level but not in differences? like one where the gaps in level are small but slopes of lines for both variables are 'kinda randomly up and down'?

[@giovanniberardi4134]

If I have a long-run relationship in levels, that implies that there will be some sort of stable relationship in first differences. Is this the reason why, when two time series are cointegrated, it implies that there must be Granger causality in at least one direction?

[@hounamao7140]

If my coefficients are significant at a level regression and insignificant at the difference regression, what does it mean ?

[@user-pq8jk4yg1z]

Thank you for awesome lectures sir! just clarifying that you said level regression is typically non stationary of variables or both level and difference regressions? thank you so much!

[@lastua8562]

Variables in levels are seldomly stationary if you use economic data. In differences, they often are, but not always.

[@arturogonzalez7416]

Great videos, thanks. I would like to know what software or app do you use to create this amazing class. Thank again!

[@lastua8562]

did you find it out?

[@lastua8562]

The reasoning in the proof does not sound complete. Could someone summarize why this is a proof?

[@jeexz]

Excellent video, Ben. Thank you.
I have a couple of questions regarding levels vs. differences though..
1. For financial data, say you would compare the price of spot vs. the price of a futures contract. Should you then regress the levels or the return series (first difference) of the two variables?
2. Often when you find a unit root (non-stationarity) in levels, you might find the first differences to be stationary. If you find cointegration in the levels (the non-stationary series) it might be recommended to run a VECM, and not a VAR.
Why should you do the VECM on levels if you can just run all your tests with first difference (returns)?
The big question boils down to when you should use levels in financial models and when you should use returns. Say you would like to examine the hedge effectiveness of different models. Levels or differences?

[@enkii82]

at 02:35, it's supposed to be minus - E_t.

[@anastasiiazbandut1646]

- e(t-1) to get the difference in error term

[@mihaililiev5932]

@@anastasiiazbandut1646 Indeed!

[@gvj805]

Im sorry, but what on earth is going on here, what! ;D !!11!!
at 2:35 you write (+epsilon_t-1). should it not be (-epsilon_t-1)?

[@Steblyovful]

you're right, it's just a typo apparently

[@mihaililiev5932]

Indeed, a small typo.