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I'm curious to hear an explanation of the difference between an endogenous and an exogenous process, preferably with specific examples? My background is a BS in math which included just one econ course, and I wasn't very interested in econ at the time, but if I recall right they never discussed it. Of course, they might have and I simply forgot since it's been 30 years since I graduated. The dictionary definitions I've looked at so far aren't terribly enlightening. Feel free to use advanced math if you need to since that part isn't a problem, I just don't understand much of the economists' jargon and concepts at this point, thank you.

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The terms 'exogenous' and 'endogenous' have to be understood relative to the scope of a model or a theory. Endogenous variables are those explained within the theory, while exogenous variables are not explained by any process within the theory, but rather taken as external (endogenous) inputs. Take the Solow Model of Economic Growth. The aggregate savings rate $s$ is key to long-term economic growth. The model however does not explain the size of $s$. The output growth rate is hence endogenous to the Solow Model, while the savings rate is exogenous.

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In an economic model, an exogenous variable is one whose value is collected from outside the model and is used as input for the model.

On the other hand, the value of an endogenous variable is determined within the model; it is the output that results from using the exogenous variable as input.

In other words, exogenous variables are independent while endogenous variables are dependent.

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In Economics, exogenous variables come from outside the model, while endogenous ones are from within the model. In any given model, exogenous variables try to explain the endogenous ones.

For example, in the LM model of interest rate, supply and demand for money determine the interest rate depending on the level of the money supply, so money supply would be an exogenous variable which is trying to explain the endogenous variable interest rate.

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The other answers for this question answer it quite well, but they provide higher level examples that are more easily understood by someone who already has a grasp of micro- or macroeconomics, rather than a layman. So here is a more layman-friendly example:

Imagine you are a firm selling apples. The apples are purchased by consumers who want to eat them. As a firm, you have to contend with the cost of acquiring the apples you sell, how many apples you have available to sell, how many apples consumers want to purchase, how much you are willing to sell the apples for, and how much they are willing to pay for those apples. These variables tell you the following information: equilibrium price and quantity, marginal costs, and marginal revenue. Each of these things would be represented on a model of your firm and the Apple market, which we will assume is perfectly competitive (the apples sold by different firms are essentially the same and therefore have similar values/cannot be differentiated) and closed (apples are not being imported to or exported from another market/country at a different/world price). This information is dependent on exogenous factors (the cost of acquiring apples is determined by the method or source of the acquisition, and the demand for apples is determined by things like consumer preferences). The equilibrium price and quantity are determined by the information in the model (the intersection of supply and demand), so they are endogenous to the model.

Exogenous variables are things that are independent from the model, and they would likely exist without the existence of your own firm. For example, a substitute good is one that a consumer would purchase instead of purchasing your product. So if you sell apples, a substitute good might be oranges. A consumer will choose one or the other. Let's assume the oranges and apples are currently the same price and are equally easy to access. In this case, each consumer will purchase whichever one they prefer according to taste. Oranges will still be grown and exist even if your apple firm/market doesn't exist, so this is a completely independent variable.

If there is a sudden tropical storm in Florida, a region where many oranges are grown in North America, then the supply of oranges will decrease. Since there will be fewer oranges, the concept of scarcity will result in an increase in the price of oranges. The equilibrium price and quantity for oranges are not represented on a model of your firm and and the Apple market, so those are exogenous variables. They are outside of your market/firm, but they still influence your market/firm in this way: Now that oranges are more expensive, some consumers who like the taste of oranges more than apples will switch from buying oranges to buying apples because the apples are now comparatively cheaper. On your model for your apple firm and the Apple Market, this looks like an increase in demand, and therefore a change in the equilibirum price and quantity, but the increase in demand is caused by an exogenous variable - the price of a substitute good (oranges), which is not represented on your graph. Likewise, the tropical storm itself is exogenous to the Orange market's model, because it is an independent variable that impacted the dependent variable of the supply of oranges.

Endogenous variables are dependent variables and are represented on a model of your market/firm. Exogenous variables are independent and need not be present on your model in order to influence your model. Endogenous variables, however, do not change exogenous ones. A rise in the price of apples does not change the demand curve for apples - rather, it causes the quantity demanded to move along the existent demand curve.

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I will be as simple as possible. Exogenous variables are variables not explained in the model. Take for example law of demand. The higher the price, the lower the quantity demanded i.e qd=f(p). Price is explained in this model, so it's endogenous. However we do know that there are other things that determine qd such as taste, income and so. These are exogenous.

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