Now even though X crosses Y, the mechanisms to which this happens may be,

be through several or one of, of the variables.

The figure indicates this.

In this figure we have introduced a third variable z.

The variable X affects Y both directly and indirectly through Z.

The direct effect is b and the indirect affect is beta.

However, in order for the indirect effect to reach Y, it has to travel through Z.

So first X affect, affects Z.

Theta and then Z affects Y, gamma.

Therefore when you get higher GPA two thing happens.

You get more years of education Z, and you get higher earnings.

However, in addition to the direct effect on your earnings for

higher GPA, beta, you also get even higher earnings.

Because the years of education increases theta, which, again,

increases your earnings, gamma.

So when we manipulate x, this causes a direct change it z and

y, and indirect change in y through z.

The duality between the figure and the mathematical notation of the regress model

is shown in the figure by the two equations.

Variables that mediate causal effects, are called mediators.

So Z is a mediator in the figure,

therefore the total causal effect of X and Y is B.

The direct effect controlling for or holding the Z constant is beta.

In addition, the indirect effect is theta multiplied by gamma.

However, the total effect is the indirect effect plus the direct effect.

The direct effect of GPA and earnings, are the effect of having different GPA for

two individuals with the same years of education.

Therefore, if there's a direct effect of GPA on earnings

this implies that for two university graduates,

the one with the highest GPA also has the highest earnings.