Arrows and instruments

Last time's quick check: blocking handles the differences you know about; randomisation handles the ones you don't. Today, a father and son who each found a new way to think about causes. In 1915 a young geneticist, Sewall Wright, joined the US Department of Agriculture to study inbreeding in guinea pigs.

He wanted to know how much of an animal's coat pattern came from its parents, how much from its surroundings, and how much from chance in development. So he drew it. A box for each influence, an arrow for each effect, and a number on each arrow that could be worked out from the data. He called them path diagrams, and in 1921 he published a paper with a title that still sounds modern: Correlation and Causation.

The statistics establishment was unimpressed. A critic argued that correlation could never reveal causation, so Wright's diagrams were assumptions dressed up as results. Wright's reply was that they were assumptions, stated openly so others could check them. That is exactly what a causal map is for.

The idea went quiet for decades, then came back, as you'll see in Module 2. Sewall's father, Philip Wright, was an economist with a different puzzle. In 1928 he was studying tariffs on butter, flaxseed and other oils. How much less flaxseed would people buy if its price went up?

The obvious move is to plot price against quantity sold, year by year. But each point is where supply met demand that year, and both were shifting. The cloud of points traces neither curve. Wright's solution: find something that pushes supply around but has nothing to do with demand. Growing conditions, such as the yield per acre of flaxseed, change how much reaches the market without changing how much buyers want.

Follow how price and quantity move when that outside push moves, and you can trace the demand curve. That outside push is called an instrument. It must move the treatment, and it must have no other route to the outcome. Instruments turn up wherever something outside the farmer's choice nudges a decision. But the second condition is where they fail.

Suppose you want the effect of sowing date on yield, and you use a wet spring, which delays sowing, as your instrument. A wet spring also affects yield directly, through waterlogging and disease. That's a back route, and the instrument is useless. So the family business left us two ideas: draw causes as arrows, and measure a cause from outside. Both came from farming questions, animal breeding and the market for farm produce, and both sit at the heart of causal inference today. Next: the most famous causal argument of the twentieth century, about cigarettes, and the question that settled it.