Types of Causality II

By Bradley Wright

This post continues a several-part series on causality. Now, why would I spend so much time writing about causality? Maybe I have too much time on my hands, or maybe I think that the readers of this blog have too much time? Actually, the issue of causality comes up in a lot of social research. When a study presents some findings about the social world, these findings usually make a whole string of assumptions about causality. As such, to understand fully sociological research, we need to have a working knowledge of the basics of causality—hence my addressing the topic in this series.

In this post I continue a discussion of different types or dimensions of causality.

Let’s consider linear vs. non-linear causality. Sociologists like to be boring when we talk about methods, so we usually end up using letters in our examples rather than real things. For example, we talk about “x” being a cause of “y.” Far be it from me to violate this norm, so I will use letters, but I’ll also try to give examples to make the ideas more clear.

Linear causality happens when every increase in “x” prompts a similar change in “y”, regardless of the value of “x.” Every time you change “x”, you get the same change in “y.” For example, my sons like to take allowance money to the store and buy a bag of candy. The candy is about a dollar, so every dollar they spend (and, thankfully, it’s usually only one or two), they get a bag of candy. If they spend one dollar, they get one bag. If they spend $50, they get fifty bags. This is a linear relationship—no matter what the value of “x”, whether $1 or $50, a one-unit change in “x” produces the same change in “y”—one more dollar equals one more bag.

In contrast, non-linear causality happens when the effect of “x” on “y” varies by levels of “x”. There are countless forms of non-linearity, but commonly maybe “x” brings about some change in “y” at low levels of “x”, but it causes much less change in “y” at high levels of “y”. 

Here’s a simple example. I like bicycle riding—and even have one of those fancy recumbent bicycles—but I don’t do much riding during winter because, well, it’s cold and snowy out. So, when I first go out in spring, I average about 12 miles an hour. (The area around here is all hills, so average speeds are lower than if it were a flat part of the country). After a month of riding, however, this increases to 14 miles an hour. So, one month riding = two miles an hour extra. If training and speed were linearly related, every additional month would always produce an extra two-miles-an-hour. Let’s see, after six months of the riding season, I’d be at 26 miles an hour—Tour-De-France speed. If I could ride steadily for another year or two, I could be passing cars on the interstate. Alas, that’s not the way it works, for training is a cause, but a non-linear cause, of riding speed.

Now let’s think about unidirectional vs. reciprocal causation. So far, I’ve discussed one variable as a cause and another as the effect. This is unidirectional causation, that “x” causes “y”, but “y” doesn’t cause “x”. Unidirectional causation is usually what people talk about when they talk about causation. However, there is also reciprocal causation. Here, “x” causes “y”, as in unidirectional causation, but also “y” causes “x” at the same time. They are both causes and both effects—how cool is that!

As I mentioned , New England is all hills. We also have rocks, not just a few—a lot. If you dig a hole to plant some flowers, you probably end up tossing out several rocks. (As an aside, the rocky terrain has shaped New England’s social and economic development in numerous ways, but that’s for another time). What do we do with all these rocks? Well, sometimes we build walls out of them. Pretty much wherever you go around here, you see rock walls. The farmers of previous centuries would drag the rocks out of their fields and put them on the borders of their properties, thus both clearing their fields and marking their territory. Homeowners have kept with that style, and they often put up rock walls as part of the landscaping. For me, building rock walls is a summertime hobby, and I’m on my third one. When I put a rock down as part of a wall, it pretty much stays there and doesn’t do anything back to me. This would be an example unidirectional causation—my efforts change the location of the rock.

But let’s say that I went bad, and instead of building walls, I picked up the rocks and started throwing them at my neighbors. Some of my neighbors are elderly widows, and they don’t put up with any crap (plus I think they have pretty good throwing arms), so they would probably start throwing the rocks back at me. As a result, my throwing would give them bumps on the head, but, in response to me, they would throw the rocks back and give me bumps on the head. This is an example of reciprocal causation—the bumps on their heads are both effects of my throwing and causes of their throwing.

Who would have thought that causation could be so dangerous?