What Is Endogeneity? What Is An Exogenous Variable?

In econometrics, endogeneity means an explanatory variable is correlated with the model’s error term, which biases ordinary least squares estimates. An endogenous variable is determined inside the model (it depends on other variables), while an exogenous variable is set outside it and is uncorrelated with the error. The three classic sources are omitted variables, simultaneity, and measurement error.

In econometrics, endogeneity is the headache that shows up when an explanatory variable in your model is tangled up with the model’s error term (the part of the outcome the model can’t explain). A variable is called endogenous when its value is determined inside the system, from the other variables, rather than handed to the model from outside. It’s like a secondary problem that crops up while you’re solving a real one: tug on it and it tugs back, changing the very thing you were trying to measure and spawning fresh problems of its own.

For our convenience, let’s use an example.

Suppose a cotton thread plant produces a certain amount of cotton. The amount of product (cotton thread) is the endogenous variable and is dependent on a number of other variables, which include weather around the cotton fields, price of fuel and other transportation costs of the process, pests and pesticides used to counter them and their cost, etc.

The amount of cotton threads produced is directly proportional to the supply of harvested cotton, which is further dependent on the other factors in the system, as stated above. This dependence makes it an endogenous variable. However, in real life, purely endogenous variables are extremely hard to find.

Why Does Endogeneity Matter In Statistics?

So far this sounds like harmless bookkeeping, but for anyone running a regression, endogeneity is the difference between a trustworthy answer and a misleading one. When you fit a model, you assume your explanatory variables are exogenous, meaning they carry no information about the error term (the leftover bit of the outcome the model doesn’t capture). If an explanatory variable is instead correlated with that error term, ordinary least squares (OLS) pins part of the error’s effect onto that variable, and your estimate of its impact comes out biased and inconsistent. Worse, the bias doesn’t shrink away as you collect more data, so a bigger sample won’t save you.

Econometricians point to three classic ways this correlation sneaks in:

• Omitted variable bias: a relevant factor you left out of the model influences both your explanatory variable and the outcome. In the cotton example, soil quality might drive both how much a farm plants and how much it harvests; ignore it and your “planting” variable secretly carries the soil effect.
• Simultaneity (reverse causality): the explanatory variable and the outcome determine each other at the same time. Price and quantity in a market are the textbook case, since price moves the quantity demanded while the quantity supplied moves price right back.
• Measurement error: when an explanatory variable is recorded imprecisely, the measurement noise lands in the error term and drags the variable along with it, typically pulling the estimated effect toward zero.

The standard fix is an instrumental variable (IV): a third variable that nudges your problem regressor but has no direct line to the error term. Run it through two-stage least squares (2SLS), which first predicts the troublesome variable from the instrument and then uses that cleaned-up prediction in the real regression, and you can recover a consistent estimate that endogeneity would otherwise spoil.

Do Purely Endogenous Variables Even Exist?

It’s more likely that endogenous variables are only partially endogenous and simultaneously determined by exogenous factors. For example, cotton production is affected by pests, and pests are affected by changes in weather. Therefore, pests in this system are partially endogenous and partially exogenous, making cotton production a partially exogenous and endogenous variable at the same time.

What Is An Exogenous Variable?

An exogenous variable is a variable that is not affected by other variables, but will affect other variables of the system. Exogenous comes from the Greek word “exo”, meaning “outside” and “gignomai”, meaning “to produce”.

For example, take a simple system like vegetable farming. Factors like farmer skill, weather, and the availability of seed are all exogenous to crop production. This means that the crop production usually does not result in any change to the weather, or farmer skill. If the farmer is a skilled laborer, then his skill surely makes the process of farming easier, but the skill isn’t affected by the output. If there is a low output for some reason, it does not affect the farmer’s skill. The output is affected by the weather conditions, but the weather conditions aren’t affected by the output. Thus, these factors are exogenous.

However, we are proved wrong again, because with all the transpiration that occurs in most plants, if grown in large quantities, it can make a difference to the climate around the area. Therefore, to see a perfectly endogenous or exogenous variable is a rarity. In contrast, an endogenous variable is one that is influenced by other factors in the system. In this example, crop growth is affected by sunlight and is therefore endogenous.

Unlike independent variables and dependent variables in an experiment, identifying which variables are exogenous, and which are endogenous, can pose a challenge due to their confusing relations with other variables in the system. Using the cotton thread production example again, something might cause the amount of cotton produced to rise.

For example, there may be a new area of fertile land where farmers invest in cotton plants and reap many benefits. This would result in an increase in cotton output due to the sudden supply of raw material. In order to decide if this new variable is exogenous, you would have to decide if the increase in output would cause the new variables to change. A variable like “weather” is definitely exogenous, as a rise in output would have no effect on the weather.

But What About Price?

The price of the threads produced isn’t affected by one small manufacturing plant’s output, but what if this was the biggest manufacturing plant in the world that suddenly increased its production, resulting in a saturated market? In this case, price would be partially an endogenous variable and partially an exogenous one. Hence, every small change in a variable in a system usually changes the output, which in turn changes more variables and so on and so forth. I guess what they say is true, What goes around, comes around!