In my ECONS101 class this week, among other things we discussed the 'faulty causation fallacy'. That occurs when you observe two variables (A and B) that appear to be moving together (either in the same direction or opposite directions), and you assume that a change in Variable A is causing a change in Variable B. You might even be able to tell a really good story about why it is that changes in Variable A cause changes in Variable B. But that doesn't mean that your observation and story about causality is true.
What we observe when we see two variables moving together is correlation. When the two variables move in the same direction, that is positive correlation. When the two variables move in opposite directions, that is negative correlation. [*] Sometimes, when we observe correlation, there really is a causal relationship between the variables. When I push down on the accelerator in my car, my car goes faster. Pushing the accelerator (Variable A) causes a change in the car's speed (Variable B).
However, not all correlations that we observe arise because a change in Variable A causes a change in Variable B. Sometimes, it is the other way around - a change in Variable B causes a change in Variable A. We call this reverse causation. Sometimes, there is some third variable (Variable C), and it is a change in that variable that causes both a change in Variable A and a change in Variable B. We refer to Variable C as a confounder (or a confounding variable). Alternatively, we can say that Variable C is a common cause for both Variable A and Variable B. Finally, the correlation that we observe might be entirely by random chance. In that case, we would say that we have observed a spurious correlation (as in the excellent Tyler Vigen website spurious correlations, which offers up a new classic in the form of correlation #2,204: The number of global pirate attacks is highly correlated with the number of downloads of the Firefox browser - perhaps pirates use Firefox?).
Anyway, I want to illustrate these with an example related to my own research, on the relationship between alcohol outlets and crime. I've published articles on this here and here, with another report here. That research establishes a generally positive correlation between the number (or density) of alcohol outlets and crime. The strength of the correlation varies depending on context - it is different for different locations, and different for different types of alcohol outlets. However, the correlation suggests that where there are more alcohol outlets, there is more crime.
Is this relationship causal though? My earlier research doesn't establish this. However, we can tell a good story, using what is termed availability theory. Availability theory suggests that alcohol consumption depends on the 'full cost' of alcohol - which is made up of the price of alcohol, plus the travel cost of getting to and from the alcohol (such as driving to the alcohol outlet and home). When there are more alcohol outlets in an area, they may compete more vigorously on price, meaning that the first part of the full cost of alcohol is lower. And, when there are more alcohol outlets in an area, consumers don't have to travel as far to get the alcohol, lowering the second part of the full cost of alcohol as well. When there are more alcohol outlets in an area, the full cost of alcohol is lower. And when the full cost of alcohol is lower, people will drink more. And when people drink more, then the amount of crime increases (either because there are more alcohol-impaired victims, or more alcohol-affected offenders). So, this observed relationship could be causal.
On the other hand, there could be reverse causation here. In areas where there is more crime, commercial property rents are lower, and there may be more vacant storefronts. Retailers (including alcohol retailers) looking to set up a store are looking for a vacant storefront, and they will tend to be attracted to low rents. So, perhaps an increase in crime would cause an increase in alcohol outlets, as the crime forces other businesses out of an area?
On the third hand, there could be confounding here. As I noted here, social disorganisation theory is the idea that differences (or changes) in family structures and community stability are a key contributor to differences (or changes) in crime rates between different places (or times). Areas that are more socially disorganised have more crime. Areas that are more socially disorganised are also less able to act collectively to prevent alcohol outlets from opening (or remaining open) in their area. So, social disorganisation might be a confounding variable in the relationship between alcohol outlets and crime, because social disorganisation causes more outlets and more crime.
Finally, the observed relationship could just be a spurious correlation, but spurious correlations tend to arise when you have two variables that are trending over time. In this case, the number of outlets doesn't have an obvious time trend (in some areas it is increasing, and in others it is decreasing), and similarly for crime. So, it seems like there is something more than random chance that leads alcohol outlets and crime to be correlated.
So, we can tell a good story for a causal relationship. However, we can also tell a good story for reverse causation, and a good story for confounding. It requires some careful statistical analysis to disentangle these potential explanations, and that is something that researchers (including myself) will continue to work on. I had an article published in the journal Addiction last year (open access, and I blogged about it here) that shows that at least one potential confounding variable, retail density, doesn't explain the relationship. I also presented at the NZAE Conference a couple of years ago on some further analysis which tentatively suggests that the causal relationship is statistically insignificant (although that research is somewhat hampered by the low quality of alcohol outlets data in New Zealand). There will be more to come on this topic in the future.
*****
[*] This is just one way of conceptualising a correlation between Variable A and Variable B (and I think it is the easiest way). There are other ways we can conceptualise a correlation. For example, if we ignore changes over time, we can observe correlations by looking at variables across different individuals or different areas. In that case, if individuals (or areas) with higher values of Variable A also have higher values of Variable B, that is a positive correlation. And if individuals (or areas) with higher values of Variable A have lower values of Variable B, that is a negative correlation.
No comments:
Post a Comment