Correlation, Causation and Thinking Things Through

Us teaching type folks love to say that correlation isn’t causation. As with most things in life, the trouble starts when you try to decipher what this means, exactly. Wikipedia has an entire article devoted to the phrase, and it has occupied space in some of the most brilliant minds that have ever been around.

Simply put, here’s a way to think about it: not everything that is correlated is necessarily going to imply causation.

For example, this one chart from this magnificent website (and please, do take a look at all the charts):

But if there is causation involved, there will definitely be correlation. In academic speak, if x and y are correlated, we cannot necessarily say that x causes y. But if x does indeed cause y, x and y will definitely be correlated.

OK, you might be saying right now. So what?

Well, how about using this to figure out what ingredients were being used to make nuclear bombs? Say the government would like to keep the recipe (and the ingredients) for the nuclear bomb a secret. But what if you decide to take a look at the stock market data? What if you try to see if there is an increase in the stock price of firms that make the ingredients likely to be used in a nuclear bomb?

If the stuff that your firm produces (call this x) is in high demand, your firm’s stock price will go up (call this y). If y has gone up, it (almost certainly) will be because of x going up. So if I can check if y has gone up, I can assume that x will be up, and hey, I can figure out the ingredients for a nuclear bomb.

Sounds outlandish? Try this on for size:

Realizing that positive developments in the testing and mass production of the two-stage thermonuclear (hydrogen) bomb would boost future cash flows and thus market capitalizations of the relevant companies, Alchian used stock prices of publicly traded industrial corporations to infer the secret fuel component in the device in a paper titled “The Stock Market Speaks.” Alchian (2000) relates the story in an interview:
We knew they were developing this H-bomb, but we wanted to know, what’s in it? What’s the fissile material? Well there’s thorium, thallium, beryllium, and something else, and we asked Herman Kahn and he said, ‘Can’t tell you’… I said, ‘I’ll find out’, so I went down to the RAND library and had them get for me the US Government’s Dept. of Commerce Yearbook which has items on every industry by product, so I went through and looked up thorium, who makes it, looked up beryllium, who makes it, looked them all up, took me about 10 minutes to do it, and got them. There were about five companies, five of these things, and then I called Dean Witter… they had the names of the companies also making these things, ‘Look up for me the price of these companies…’ and here were these four or five stocks going like this, and then about, I think it was September, this was now around October, one of them started to go like that, from $2 to around $10, the rest were going like this, so I thought ‘Well, that’s interesting’… I wrote it up and distributed it around the social science group the next day. I got a phone call from the head of RAND calling me in, nice guy, knew him well, he said ‘Armen, we’ve got to suppress this’… I said ‘Yes, sir’, and I took it and put it away, and that was the first event study. Anyway, it made my reputation among a lot of the engineers at RAND.

I learnt about this while reading Navin Kabra’s Twitter round-up from yesterday. Navin also mentions the discovery of Neptune using the same underlying principle, and then asks this question:

Do you know other, more recent examples of people deducing important information by guessing from correlated data?

… and I was reminded of this tweet:

Whether it is Neptune, the nuclear bomb or the under-reporting of Covid deaths, the lesson for you as a student of economics is this: when you marry the ability to connect the dots with the ability to understand and apply statistics, truly remarkable things can happen.

Of course, the reverse is equally true, and perhaps even more important. When you marry the ability to connect the dots with a misplaced ability to understand and apply statistics, truly horrific things can happen.

Tread carefully when it comes to statistics!