Post hoc, ergo propter hoc

After this, therefore because of this.

One of the common logical fallacies of reasoning is the post hoc fallacy. Post hoc is latin for 'after the event'. The essence of the fallacy is captured in "Post hoc ergo propter hoc". That means "After this therefore BECAUSE of this". It implies causality on the basis of a temporal (i.e. sequential) association. If an event A is preceded by some event B, then the reasoning is that BECAUSE Event B preceded Event A in time, B CAUSED A. So here A is the effect, and B is the Cause. Because B preceded A, the fallacy is to assert that B Caused A.

Let me illustrate this with an recent and topical example. The event or observation of interest is the apparent decline of manufacturing in America. (remember president Trump justifies his mad tariff wars by claiming to want to bring Manufacturing back.) That is the Effect. What could possibly explain it? It's easy to note that Chinese manufacturing has grown dramatically in recent decades. Since the early 1990s in fact, when China formally joined the WTO. That is the Event B, the Cause of the Effect. But is it true? Did China’s WTO entry and the growth of Chinese manufacturing really CAUSE the apparent decline of US manufacturing.

I keep saying apparent decline of US Manufacturing. That is because in absolute terms USmanufacturing, in terms of the value produced has NOT declined. According to the US Bureau of Economic Analysis US manufacturing's contribution to the GDP has steadily grown (barring small dips during periods of recession) in absolute terms. from 1.4 trillion USD in 1997 to 2.9 trillion in 2024.

Of course the nature of jobs has changed. Automation has replaced many jobs and low value manufacturing has given way to higher-value-added work. The garment industry in New York has given way to aircraft manufacturing in Seattle.

But manufacturing GDP has not shrunk. Indeed it has grown; albeit not as much as the total GDP. As other sectors of the economy have grown - finance, retail, healthcare, science and tech, teaching and leisure, it is a fact that the proportion of GDP accounted for by Mnaufacturing has declined. From 15% in 1994 when the North American Free Trade Agreement came in to 12.5% in 2001 when China joined the WTO and became part of the global trading system, to just about 10% in 2024.

It makes it at least plausible, then, that China is the cause of the decline of US manufacturing as a share of the GDP.

Really? Could that be a case of Post hoc ergo propter hoc fallacious reasoning? How can we examine that assertion? This is where the technique of looking at a long run time series comes into its own.

Here I am grateful to @haugejostein for producing this instructive chart looking at the long run time trend in US manufacturing as a share of GDP from 1947 (when China had just about survived the ravages of war) to now. The data come from the same source the FRED database and the US Bureau of Economic Analysis.

Looking at this long run time series data makes it crystal clear that US Manufacturing's contribution (in % terms) to the GDP was declining steadily for a very long time - long before China became a manufacturing power house in the early 2000s. Take care to make the distinction - Manufacturing as a % age of GDP was declining despite the absolute value of manufacturing actually rising over the same time period. That is because the overall GDP was growing faster.

Conclusion: It is all too easy to fall into the logical fallacy trap of "Post hoc ergo propter hoc". But a simple look at a long rime time series that goes back to BEFORE the alleged causal event allows a quick and sobering check on the conclusion of causality.