What is the difference between endogenous and exogenous variables, considering the determinates of demand. - FreeEconHelp.com, Learning Economics... Solved!

## 9/10/18

This post was updated in September 2018 with new information and examples.

One of the things to do when analyzing a supply and demand graph is shift the demand curve.  When we consider what factors will shift a demand curve, we need to make a distinction between the endogenous factors (those contained in the model) and exogenous factors (those occurring outside of the model).  The easiest way to tell the difference between endogenous and exogenous factors is to look at the graph.  You can see from the graph to the right that both quantity and price are on the axis, which means they are controlled for within the model, or they are endogenous.  Every other factor that is not controlled for would therefore be exogenous, (which means that it is determined outside of the model and held constant).

Some determinants of demand include income, tastes and preferences, and number of buyers. If one of these exogenous factors change, such as income or preferences, then we would need to shift the demand curve because that factor is not accounted for on the axes of the graph.  In this example, demand shifted right, so we would need to see an increase in income (assuming a normal good/not an inferior good), or a change in preferences towards more positive feelings toward the good or service being studied.

Let’s look at another example using math.
Consider the following demand function, which shows quantity demanded as a function of exogenous variables and price.

Qd=a-bP

Where Qd is quantity demanded, a is the intercept, b is the slope coefficient for P price. When we consider the endogenous factors in this model we only have one variable on the right hand side which has its own coefficient, which is price.  Because the relationship between price and quantity is known (it is the coefficient b) it is considered endogenous to the model. Quantity is on the left hand side so it is considered the dependent variable (but also endogenous).  The exogenous are all considered within the a variable, which gives us the intercept.  They are considered exogenous because they are determined independently from the model... when Q or P changes, we do not expect the variable a to change.

This makes sense both mathematically and intuitively. Mathematically the only variables that are allowed to change (and therefore be graphed) are Q and P. While b and a can be changed by the user, they do not react to changes in quantity or price. Intuitively, this makes sense because changes in income and tastes and preferences are not directly affects by quantity and price. Just because the price of a good changes does not mean that our income changes. Our income is determined by other factors outside of the supply and demand framework and is therefore exogenous.

Let’s consider another example:

Qd=a+bI.

Here everything is the same except for the I variable which represents income.  Because income is on the right hand side with a coefficient (which determines the slope) it is now the endogenous variable in this model.  Now the price variable is exogenous and is considered in the a variable which determines the intercept.  Here is what the graph would look like below for a normal good (as income goes up, quantity demand goes up).

This may seem a bit confusing at first, how can price be exogenous in one model and endogenous in another? The reason is because of the assumptions we are making and the functional forms of the models we choose to use. Sometimes we hold everything else constant (ceteris paribus) when conducting analysis in economics. This allows us to explore the effects that one variable has on another without worrying about the potential cross-impacts that variables can have on each other.

Is this the most accurate--real world way to run predictions? No, but it is one method used by analysts and economists to try to better understand how different variables affect one another.

So this post went over an easy way to remember the difference between exogenous and endogenous variables.  If you have access to the graph, or equations, look at the variables controlled for on the axis, or controlled for on the right hand side with a slope coefficient.