# Two variables that can cause each other

Economic deprivation can lead to disability, e.g. if you can not afford a balanced diet and this leads to severely stunted growth.

At the same time disability can lead to economic deprivation, e.g. you get injured at work and then can no longer earn a living.

The two variables 'Deprivation' and 'Disability' have a correlated relationship with each other but given it can go either way is there a statistical term to describe this relationship.

• If the question is set up as wanting to know whether $X$ affects $Y$ but it could also be that $Y$ affects $X$, you typically see that referred to as "reverse causality", at least in economics papers. For this particular case I would however use "vicious circle".. Commented Sep 20, 2019 at 14:32
• To add, reverse causality can be modelled econometrically by using a method called Simultaneous Equations Model or SEM. You can read more about it on the web. Commented Sep 20, 2019 at 14:43

The feedback relationships (aka 'reciprocal determinism', 'co-determination', 'simultaneity') you are describing form a dynamic system. In the statistical and the counterfactual formal causal reasoning world you actually have many variables: Deprivation at time 1 causes Disability at time 2, while Disability at time time 1 causes Deprivation at time 2, generalized as Disability at time $$t$$ causes Deprivation at time $$t+1$$, and vice versa.

Causal systems in which every variable is either directly or indirectly a cause of every variable in the system at some point in time are frequently described as complex causal systems. Note that a variable at some point in time may be a cause of itself at some future point in time.

Counterfactual formal causal reasoning kinda breaks for these kinds of models, since one can always argue that unmeasured prior values of observed variables and times are acting as confounders (see Spirtes). However, there are many analytic approaches to representing complex causal relationships, and inquiring about the behavior of complex causal systems, and these analyses attempt to answer different kinds of questions than one typically sees in, for example, statistical counterfactual formal causal models (see Levins, and Taylor).

References

Spirtes, P. (1995). Directed Cyclic Graphical Representations of Feedback. In P. Besnard & S. Hanks (Eds.), Eleventh Conference on Uncertainty in Artificial Intelligence.

Levins, R. (1974). The Qualitative Analysis of Partially Specified Systems. Annals of the New York Academy of Sciences, 231, 123–138.

Levins, R. (1998). (Dialectics and Systems Theory](https://surplusvalue.org.au/Marxism/levins%2098.pdf). Science & Society, 62(3), 375–399.

Taylor, P. (2005) Unruly Complexity. Chicago, IL: University of Chicago Press.

In econometrics this situation is called endogeneity, particularly, simultaneity. Price in supply and demand equation is a conventional example.

• I think endogeneity is a more general concept: An outcome can be endogenous (autocorrelated), while at the same time exogenous predictors contribute to it's behavior over time without those predictors being themselves caused by the outcome. Right? Commented Sep 20, 2019 at 20:34