 Moderation and mediation are concepts that are associated with the relationship of three variables. These concepts are very common in empirical research and management, and moderation and mediation models are typically estimated using regression analysis. Let's take a look at moderation and mediation. Mediation basically refers to a scenario where the effect of one variable x on another variable y goes through a third variable m. So we are saying that the effect of x is mediated by y, so the causality goes from x to m from m to y. For example, studying causes learning, learning causes increased performance on the final exam. So mediation is about mechanisms, and singleton straights use the term intervening variable, so it's a variable that sits in the middle. If x causes m and m causes y, then if for some reason the level of m would not change, even if it changes x, then y would not occur. For example, if you study but you don't learn, then you can't expect to perform well. So studying must lead to learning, learning leads to a performing well on the exam. Moderation on the other hand refers to a scenario where a third variable determines the strength of association between two variables. For example, if x is the amount of weight training that you do, and y is the amount of gains that you have in muscle mass, then the mediator could be the amount of eating that you do. If you train and you eat a lot, you gain muscle, if you train equally much but you don't eat as much, then your muscle gains will not be as large. So moderation models are useful for studying contexts. So we can do these moderation models to understand under which conditions something happens, and also what determines the strength of effects, are there any contextual factors. Let's take a look at how these are estimated in the context of regression analysis. So our first example is Hekman's paper, and Hekman is studying a moderation model. So moderation model, this is one moderation effect, they are hypothesis 3a, they are saying that because of our customer, racial or gender bias, women or minorities are rewarded less for performance than our white men. So the effect of service provider performance is assumed to be positive on rating of employees, but that positive relationship is assumed to be less for women and minorities compared to white men. So this is moderation, and how do we do moderation in regression analysis? So the idea of moderation was that the regression coefficient of x, beta 1 here, depends on the value of m. So we can say that the regression coefficient beta 1 is actually a function of beta m1, beta m2 multiplied by m, so it depends on m, it's not the constant value that is same for everybody. We can do a little bit of math and we plug in the second equation in place of beta 1, we get that kind of equation and we simplify it a bit by eliminating the parenthesis, and we can see that moderation can be studied by doing these interaction models. So interaction refers to multiplying two things together. So we have x, the main interesting variable, here quality, m, the moderator, here gender or minority race. As the moderator, we multiply them together and then we can see if the race or gender has an effect on how much a person is rewarded for being a high quality doctor. And here are the interaction terms we can see in the model 2 that female are rewarded less for being high quality. So the overall effect of quality is positive, but women are rewarded less than men. So this is how the table would be interpreted. In practice interpreting the magnitude of these effects is difficult because they are interactions, so people will do plotting. In Heckman's paper, they have these four plots, so this is how the recursion lines would go. This is the line for male, this is for female, this is for white, this is for non-whites. And they found something really interesting, they found that actually if you are non-white, then if you get better, you get more productive, then you're actually penalized in the customer satisfaction score. They explained that in the paper and that is an unexpected finding. I'm 100% sure that this is actually just an analysis error. What kind of error it is, it's beyond the scope of this video, but basically the right results would be that all the lines go up, but the slope or how steeply the line goes up for women and minorities is less than it goes up for men. So this is a more race. Let's take a look at media. So now our example article is Baron and Tang. They have a hypothesis, a multiple hypothesis, one of them is hypothesis 3 and then hypothesis 3a is simply a more precise variant of hypothesis 3. So they're basically saying that entrepreneurs with good social skills are better at gathering essential resources. And if you have more essential resources, then that allows your venture to perform better. So there is the mechanism through which social skills allow an entrepreneur venture to perform better is that social skills allow you to get more resources. And those resources are the ones that affect performance, not the social skills per se. How is this kind of a moral tested with recursion analysis? We have these very simple approach consisting of free recursion analysis introduced by Baron and Kenny and this is known as Baron and Kenny method or causal steps method. So the idea first is that we regress Y on X to see if there is a causal effect of X on Y that can be mediated. Then we regress M on X. So we regress the mediator on the first independent variable and then we regress both Y on the mediator and the original variable. If we ideally want to show that X influences M and M influences Y but not necessarily that X influences Y when we control four values of M. We can see these three models, three steps here. So the model number three is the first step. It is sales, which is the Y variable regressed on all the interesting variables and controls except for the mediator variables, which are two in this case. Then we have model two, which is step number two. That is resource acquisition, a mediator variable. And then we have model three, where we regress the final dependent variable on the mediators and the original X variables. And then we simplify, simply multiply the recursion coefficients together to get the mediation effect. So mediation involves testing a series of recursion analysis. There are of course other techniques for testing mediation, but this is the simplest one. Mediation can be of two different kinds if there is mediation. There is full mediation and a partial mediation. Full mediation means that after we control for the mediator, in this case, resource acquisition, there is no effect on expressiveness. So if there is a very expressive entrepreneur, if that expressiveness does not translate into better resource acquisition skills, then there is no effect on the employment. To use another example, if a person studies really, really hard, but does not learn anything, then they will not perform well in an exam. Because learning is a mediator between studying and performing in an exam. If we look at the actual regression results, we can see the full mediation, a partial mediation, if evidence here. So this is partial mediation. We can see that the effect of expressiveness here persists in model five, which contains the original variables and the mediator. I have left out the controls just to simplify the table a bit. And then when we look at this full mediation here, we can see that the effect of expressiveness is non-significant on employment growth rate after we control for the mediator. So the effect, if we hold the mediator in a constant, then our increasing expressiveness does not make it express. Okay, to summarize, mediation and moderation are two ways of analyzing relationships that are about three variables. Mediation is the study of mechanism. Is there a variable that sits in between, that is a step in the causal path from X to Y, and that allows us to study mechanisms. Singleton and straights use the term interviewing variable for this kind of model. Then we have moderation, and moderation means that the effect of X and Y depends on the third variable. This kind of model is useful because it allows us to study context. When does an effect occur? When does it not occur?