Exogeneous, Endogenous Variables in Structural Causal Model

Question

Exogeneous, Endogenous Variables in Structural Causal Model

Eisen

2021年8月20日 20:36

https://en.wikipedia.org/wiki/Causal_model#Definition

Wikpedia defines causal models as:

an ordered triple $\langle U, V, E\rangle$, where $U$ is a set of exogenous variables whose values are determined by factors outside the model; $V$ is a set of endogenous variables whose values are determined by factors within the model; and $E$ is a set of structural equations that express the value of each endogenous variable as a function of the values of the other variables in $U$ and $V$.

I'm confused what the exogenous variables here in this case. What are some examples of exogenous variables in a real causal example?

Topic inference statistics machine-learning

Category Data Science

Peter · Accepted Answer · 2021年8月20日 20:36

Suppose you want to study the effect of the size of a city's police force on crime. You could claim that "more police" implies "less crime" (see Eide, 1994).

$$ crime = \beta_0 + \beta_1 police + u .$$

However, the marginal effect $\beta_1$ will likely be biased because you could also claim that "more crime" also leads to "more police". This is sometimes called a simultaneity bias.

In order to disentangle the two effects, you could estimate a simultaneous equations model (SEM). In this case you have two equations which you estimate, one determining $crime(police,otherthings)$ and the other $police(crime,otherthings)$.

Problems of endogeneity, meaning situations where $x$ (the independent variables in some model are not really "independent"), are big e.g. in econometrics. There are a number of models, including "instrumental variable" (IV) models, which aim to tackle endogeneity in different settings (often with limited success).

For more details please refer to Wooldridge "Introductory Econometrics" (probably available online), i.e. Ch. 16 "Simultaneous Equations Models".

Exogenous variables are variables (in addition to the endogenous ones) which help to explain either crime or police force in the example above.

Exogeneous, Endogenous Variables in Structural Causal Model

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