WEBVTT

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In social science research we 
typically want to make causal claims. 

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What makes causal claims challenging is that 
we need to eliminate rival explanations. 

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We can't simply say that because x and y are 
correlated, therefore x must be the cause of y. 

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The gold standard for eliminating rival 
explanations for a correlation between x and y  

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is the experiment.
In an experimental research  

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we randomize our sample into two groups.
The treatment group and the control group. 

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The treatment receives x the 
control does not receive x. 

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Then we observe the outcome y  

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after an appropriate time delay.
That allows us to make clean causal claims. 

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Unfortunately in most of the cases 
we can't study things experimentally. 

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For example if we want to study what is the 
effects of early internationalization and  

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firm survival, we can't just take firms and 
tell them to internalize early, randomly. 

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We would have to buy all the 
firms and that's impractical. 

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In practice most of the time we 
have to work with what we observe. 

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We work with observational data and 
we have to use statistical techniques  

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for controlling for alternate explanations.
One of the most commonly used statistical  

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techniques is the regression analysis.
And different variations of regression analysis  

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are pretty much covering like 90% of what 
is published in social science journals. 

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Let's take a look at how statistical 
controlling for alternate explanations  

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and how regression analysis works.
And what are the key ideas. 

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So the idea of controlling is that when 
we observe a correlation between x and y,  

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let's say we observe a correlation between 
CEO-gender and profitability of a company. 

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We should rule out the potential spuriousness 
of that correlation so correlations can exist  

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for multiple different reasons.
Here in Singelton & Straits  

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they give two examples.
I like the example of firefighters. 

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The number of firefighters in a 
fire scene is highly correlated  

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with the amount of fire damage after the fire. 

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Can we say that increasing the number of 
firefighters in the scene causes more damage? 

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Probably not.
There is a third variable the size of the fire. 

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That is the cause of the firefighters 
and it's also the cause of the damage. 

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If there's a big fire then 
more firefighters are sent in. 

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If there's a big fire then 
there will be more damage. 

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And the size of the fire creates a spurious 
correlation between the number of firefighters  

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and the fire damage.
With statistical controlling  

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we try to eliminate these spurious correlations.
Or we try to get the causal effect from an  

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observed correlation that is 
partly causal partly spurious. 

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How do we do that?
Let's take a look at a Talouselämä 500 example. 

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So this is an interesting finding just the fact 
in 2005 the ROA of many women-led companies in  

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the largest 500 Finnish companies was 4.7 
% points higher than man-led companies. 

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Let's assume that we have already 
ruled out chances and explanations. 

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We want to understand whether it's actually the 
women that cause this profitability difference. 

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How do we deal with that?
We see from our observed data that there  

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is an overlap between CEO-gender and performance.
The variables are correlated if we have a bar  

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chart it shows that female-led companies 
ROA is 18.5 for male-led companies is 14.1. 

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These are just made up numbers but the difference 
is roughly the same ballpark than the 4.7. 

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How do we deal with these 
alternative possible explanations? 

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Well first of all, we need to 
have some kind of theory of why  

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there would be a correlation that is not causal.
We could for example say that there's a third  

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variable company size that 
influences the correlation. 

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We could say that small companies 
are more likely to have women CEOs  

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and small companies are more profitable.
Therefore company size causes a spurious  

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correlation between gender and performance.
Now we want to with statistical adjustments  

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or statistical techniques we want to understand 
how much of this correlation mark here with  

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a1 is due to the spurious part c 
and how much is the causal part a2. 

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Assuming that company size is the only 
factor causing a spurious correlation. 

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The simplest possible strategy for 
eliminating the rival explanation of size  

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is to make the companies 
more comparable by matching. 

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So let's assume that most of the women-led 
companies have less than 250 employees. 

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If men-led companies tend to be larger then 
comparing large men-led companies and small women  

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and companies is not a fair comparison.
We don't know whether it's the  

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gender or the size effect.
What we can do is matching. 

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Or analyzing a subsample.
We could for example analyze  

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a sub sample of companies with just 
250 people or less and a compare. 

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With this subsample we will find that 
main companies are still a bit less  

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profitable than women companies but the 
difference is not as great as before. 

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And based on these kind of analysis we could say 
that yes there's a correlation between CEO-gender  

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and profitability but it is mostly explained 
by size differences with this artificial data. 

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This strategy is very simple to 
understand and it is very simple to  

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apply but it's also fairly limited.
It is limited because if we start  

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matching typically, if we have let's say five 
different explanations for the correlation. 

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We have let's say industry effect, we have 
past performance, we have size effect,  

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we could have other effects as well.
If we try to match on many different variables  

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then the problem is that we don't 
really find any more matches. 

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If we want to find two sets of companies 
that are equal on 5 different characteristics  

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our sample will just run out.
So in practice matching works  

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for simple problems for more complicated 
problems we use statistical modeling. 

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This would be an example of a regression model.
So we would say that return on assets is some  

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function of CEO-gender plus company 
size we would code CEO-gender as  

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1 being female 0 being male and then we tell 
our computer to estimate this model for us. 

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So computer gives us estimates of these 
betas called regression coefficients  

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and then we interpret them.
I'll talk about regression  

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a bit more later in this video.
But these are the two main strategies  

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for statistical controlling. Either we try to 
make the samples more comparable by matching. 

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Or we build some kind of statistical 
model that adjusts the difference. 

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To do so we need to have control variables. 

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Control variables are the alternate 
explanations that for the correlation. 

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If we see a correlation between CEO-gender and 
profitability and we want to make the claim  

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that CEO-gender actually influences profitability.
The difference is in profitability is due to some  

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of those companies have female 
CEOs and some have male CEOs. 

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We need to consider what a skeptic would claim.
So if someone does not buy our claim that naming  

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a woman as a CEO causes profitability to increase 
that skeptic needs to develop a counterargument. 

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For example smaller companies are more 
profitable more likely to have women CEOs. 

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Companies in asset heavy industries are more men 
dominated, they also have less return on assets  

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because returns is divided by larger assets.
And so on. 

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We need to consider what are the alternate 
explanations for those for the correlation. 

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And those alternate explanations 
will be our control variables. 

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Quite often when you see an empirical study 
you see this kind of section about controls. 

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And this paper by Heckmann, 
explains the controls quite well. 

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So they are saying that these are 
alternate explanations for the data 

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And then we rule out those alternate 
explanations using statistical model. 

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Importantly an alternate explanation needs to 
be correlated with the explanatory variable. 

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We say that company size 
correlates with CEO-gender  

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and also company size or a control variable 
needs to be a cause of the dependent variable. 

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We say that it's not the women 
CEO that causes the profitability  

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difference rather it's the company size 
that causes the profitability difference. 

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And company size is correlated with women's 
CEO and that causes experience correlation. 

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Let's take a look at the example how it works.
This is from Heckmann's paper again. 

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We have the correlations and we 
have the regression coefficients. 

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Regression coefficients tell us what is 
the effect after controlling for others. 

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I'll talk a bit more about 
regression a bit later in the video. 

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But let's try to understand the 
idea of statistical controlling. 

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So here we have a correlation between patient 
satisfaction and and age of a physician. 

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That correlation is 0.9.
It's not statistically significant  

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but we don't care about that now.
It's a positive correlation. 

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Then regression analysis tells 
us that there is a negative  

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causal effect of age.
How come? 

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Well the reason for this 
correlation is that there's  

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actually a spurious correlation in the data.
If we look at just tenure and age they are  

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highly correlated at 0.69. So tenure is how long a 
person has been employed at this medical company. 

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And age is the age of the person.
Obviously if you are just  

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30 late 20s you just graduated from medical 
school you can't have much experience. 

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If you are closer to retirement then you typically 
have long tenure in the place where you work. 

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Tenure and age are highly 
correlated for that reason. 

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Older people tend to be more 
experienced than younger people. 

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We can see that tenure or your experience is  

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highly, affects highly the dependent 
variable the customer satisfaction. 

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Now we have a situation where 
there's a spurious correlation. 

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Older people are more experienced, experienced 
causes customer satisfaction scores to be higher. 

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age has a negative causal 
effect on customer satisfaction. 

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How do we interpret that?
We interpreted that if two people  

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have the same amount of experience, then 
the patients prefer the younger one. 

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If two people are of the same age patients 
strongly prefer the one with more experience. 

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We can calculate the value of the 
spurious correlation from this diagram  

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by simply multiplying that regression 
coefficient 0.33 and correlation .69. 

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And we can see that there is 0.23 
spurious correlation between age  

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and customer satisfaction due to tenure.
And we can do this for all other variables. 

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But if we simply compare this 0.23 here the 
spurious part of the correlation between  

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age and customer satisfaction, we 
have the estimated causal effect. 

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We take a sum we get pretty close 
to the opposite correlation of 0.09. 

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Of course there are other variables that 
affect that also can cause a spurious  

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correlation but this is the most important one.
So the idea of statistical controlling is that  

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we try to take the observed correlations and then 
take that observation correlation into two parts. 

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We have the part that is spurious and where 
the part that corresponds to the causal effect. 

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If we can eliminate all spurious estimated 
correlation then we have a clean causal effect. 

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Regression and other techniques 
typically use the term holding constant. 

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Control variables are held constant and 
this is what Singleton & Straits explain. 

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Holding constant can mean two different things.
If we have matching or if we have some kind  

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of experimental study where we 
have some control on our sample. 

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Then holding constant can mean that if we want 
to eliminate for example gender differences from  

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the analysis, we study only men or only women.
Quite often this kind of holding constant by  

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actually making a variable to be the 
same in our sample is not possible. 

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If we want to eliminate the effects of company 
size we cannot sample companies that all have  

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exactly, for example 100 employees.
That would not be possible. 

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Another way to understand holding 
constant is statistical control. 

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So in statistical controlling 
like in regression analysis. 

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The term holding constant means 
that we statistically estimate  

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what would be the difference of one variable 
if all other variables were the same. 

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Other variables are not exactly the same 
actually but by statistical analysis we  

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can answer the question: what would be the 
difference if everything else was the same. 

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So for example what would be the difference 
between women and men led companies in ROA. 

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If the women and men like companies were 
the same size and in the same industry. 

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Statistical controlling allows us to 
answer this kind of questions without  

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actually having to observe companies that are 
all of the same size and in the same industry. 

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And this is why statistical 
controlling is very useful. 

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Linear regression analysis as i mentioned already 
is the basic tool for statistical controlling. 

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Many other tools are variants of this 
technique but a basic understanding of this  

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technique takes you a long way in understanding 
quantitative research and analysis results. 

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The idea of linear regression 
is in a two variable case. 

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If we have x variable here this 
is the explanatory variable. 

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This is the one that we would 
manipulate in an experiment. 

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We have the y variable the outcome.
This is the thing that we would observe  

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after the experiment but these are actually 
observed data so we don't manipulate x. 

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What regression analysis does is that it 
finds the best line that explains the data. 

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so it tries to find a line 
that explains the mean of  

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the y the dependent variable for each value of x.
In math we write the regression equation like that. 

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so if a multiple different explanatory 
variables then the expected value or the  

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mean of the y variable is assumed to be the sum 
of the effects of all these different variables. 

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Of course this is a critical 
assumption for regression analysis  

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if different effects act multiplicatively.
For example then we would  

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need different kinds of model.
But regression analysis is a good starting point. 

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We assume that the CEO 
effect our CEO-gender effect,  

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the industry effect and company size effect, 
they're all added together and that gives us  

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some kind of expected value for the performance.
In our Heckmann's paper example we can for example  

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say that patient satisfaction is a function it's 
a sum or weighted sum of physics and productivity,  

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physician quality physician accessibility.
And the regression analysis tells us what  

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would be the effect of increasing productivity 
if quality and accessibility stayed the same. 

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So regression analysis can be used to 
answer these kind of what if questions. 

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What if one variable changes 
and others stay the same? 

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What if we name a women as a CEO of a company and 
industry and size of the company stay the same? 

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That gives us an estimate of the causality.
Regression analysis is not a magic wand  

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or magical tool that always gives us 
valid estimates of causal relations. 

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If you are study about regression analysis if 
you want to become a professional researcher,  

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then you will need to read up books about 
the econometrics that tell you that these  

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six assumptions are needed for regression.
But there are really two important things that  

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you need to understand if you want to get started 
in understanding what quantitative research  

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using regression is about.
The first assumption is that all  

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relevant controls are included in the model.
If we regress company profitability ROA on  

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CEO-gender and company size a skeptic 
comes and says that: "No the correlation  

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that you have is because of the industry."
If we don't include industry in our analysis  

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but industry is actually 
correlated with the CEO-gender  

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and an important cause in company performance 
then regression analysis is not trustworthy. 

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This applies to all statistical 
analysis or quantitative research. 

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Having the right controls the most 
important alternative explanations  

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included in the model is critically important.
Technically this refers to the mlr4 assumption. 

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Another important assumption is 
that all relationships are linear. 

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So when we have the y variable and we 
increase x by one unit the effect on y  

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variable the dependent variable is always the 
same regardless of the current value of x. 

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That that can be true or 
approximately true for some cases. 

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For example if we consider the size 
of the fire and the amount of damage  

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that the fire makes could be linear.
So if the building is twice as large  

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and the fire is twice as large 
there could be twice as much damage. 

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But it's not always true for example if 
we consider the effects of education. 

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Having elementary school education, 
middle school education, the first 9 years  

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probably does not make as much of a difference  

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than the final years of your university degree 
when you're working toward your master's degree. 

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So in that case the returns on education probably 
follow a more closely an exponential line,  

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than exponential curve than just a line.
So not all years are equal. 

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So the linearity is another important 
assumption on regression analysis. 

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In practice when a professional researcher 
applies these techniques there are  

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diagnostics that allow us to test for linearity.
And there are also some diagnostics that allow for  

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testing if all variables that are 
included in the model and so on. 

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But just to understand what regression 
does when it is useful it is important  

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to understand these two assumptions.
Regression analysis and its different extensions  

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for example nonlinear case, for the case 
where we have observations that are clustered. 

00:20:25.280 --> 00:20:30.880
For example students within classes.
They cover probably at least 90%  

00:20:30.880 --> 00:20:37.040
of the research that is done in social sciences.
If you understand regression analysis then you  

00:20:37.040 --> 00:20:40.400
have a pretty good foundation 
of understanding other things. 

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Because they are simply extensions 
and variants of this simple technique. 

00:20:44.960 --> 00:20:50.160
So the idea of regression is that y one 
dependent variable is a weighted sum of  

00:20:50.160 --> 00:20:55.840
x is the independent variable.
Let's summarize in statistical controlling the  

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important thing is that we have control variables.
Control variables and alternative explanation for  

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a correlation between the x variable 
for example CEO-gender, y variable  

00:21:06.240 --> 00:21:12.080
for example company performance.
And controls are held constant either  

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by choosing our sample in a way that studies 
only for example companies of the same size. 

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Or more typically they are held 
constant using statistical techniques. 

00:21:23.040 --> 00:21:28.160
So we use statistical techniques to answer the 
question of what would be the difference if all  

00:21:28.160 --> 00:21:33.520
the companies were of the same size same industry 
and whatever the control variables we have. 

00:21:34.560 --> 00:21:39.520
Controls are must be justified instead 
of just throwing in a standard set. 

00:21:39.520 --> 00:21:44.080
So you need to think through why is there a 
correlation between my import and x variable  

00:21:44.080 --> 00:21:48.960
and my important y variable and then pick controls 
to rule out those alternative explanations. 

00:21:49.600 --> 00:21:52.080
In practice the tool that we apply  

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to study this kind of x y effects controlling 
for other variables is the regression analysis. 

00:21:59.680 --> 00:22:04.000
This is the work course of causal 
analysis in non-experimental research. 

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Regression analysis makes 
two important assumptions. 

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Effect of x is always constant on y.
So everything is linear. 

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It's not that little x does not make a difference.
When you have a large amount of x then having more  

00:22:19.680 --> 00:22:22.880
of that makes more of a difference.
Or it could work the other way. 

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That initial small increments of x make a big 
difference and then when you get further on x  

00:22:29.920 --> 00:22:34.720
then the increments are going to get smaller.
Regression analysis assumes that the effect of x  

00:22:34.720 --> 00:22:40.560
on y is always constant many commonly used 
analysis techniques are simply variation  

00:22:40.560 --> 00:22:43.120
of regression analysis.
So if you understand  

00:22:43.680 --> 00:22:50.160
the basics of when regression analysis works and 
how regression analysis results are interpreted. 

00:22:50.160 --> 00:22:52.320
Then you have a pretty solid foundations  

00:22:52.320 --> 00:22:55.840
on understanding also other 
more complicated techniques