The New York Times Needs To Learn Algebra

Caption: An F-algebra commutative diagram. Not exactly relevant here, but it's a cool diagram nonetheless.

Image credit: Physis/Wikimedia

If you want proof that journalists need to study mathematics, at least at the level of algebra, consider this bit of nonsense from The New York Times:

A free-trade agreement between South Korea and the European Union goes into force next July, while Seoul is trying to reach a similar agreement with the United States. Staying out of a pan-Asian free-trade bloc would shave at least 1.5 percent, or 10.5 trillion yen ($128 billion), from the Japanese gross domestic product and eliminate eight million jobs, according to a recent estimate by Japan’s trade ministry.

Japan’s Farmers Oppose Pacific Free-Trade Talks

Just about anyone who has worked in the fields of engineering, business, or economics should recognize the problem here. Economics Professor Dean Baker speaks for the latter:

According to the OECD, employment in Japan is just over 62 million. This means that the estimates in the NYT imply that not taking part in this trade agreement would cost Japan a number of jobs approximately equal to 13 percent of its current employment the equivalent of roughly 18 million jobs in the United States.

NYT: Making Up Numbers to Push Trade Agreements

Dr. Baker goes on to mention that these countries do a pretty lively trade already, so nothing about failing to reach agreement is likely to be catastrophic.

What caught my eye was the direct relationship alleged between the $128 billion in GDP lost equating to eight million jobs. It turns out that the principles of idiot savant economics can be applied here, and should have been by the NYT staff. The reason these two numbers are questionable can be worked out by anyone with a rough idea of how budgets and desk calculators work.

A rule of thumb that I use to figure out how many jobs a big pile of money translates into is to divide it by $100,000. That's a rough idea of how much money a job costs per year in the United States. Of course, it could be more or less depending what type of job we're talking about, but if you know that a new plant that will have a budget of $100 million a year opens up in your town, you can guess pretty accurately that it will mean about a thousand new jobs in the area. From the CIA World Factbook page on per capita income (PCI), Japan's PCI is about 69% of ours ($32.6k vs. $46.0k). So, let's use $70k as the cost of a job in Japan. That means that $128B would cost about 1.83 million jobs.

Naturally, we can be a bit more scientific about this. We can take Japan's actual GDP (also from the CIA page), $4.15 trillion, and divide that by the size of Japan's work force (from this CIA page), 65.9 million, and discover that it takes about $63.0k of Japan's GDP to employ one average Japanese worker. Dividing that $128B by $62.9k$63.0k suggests that this much GDP loss translates to roughly 2.03 million jobs lost.

Looking at the relevant numbers, and assuming that the estimate of $128 billion GDP loss isn't fanciful, it would be reasonable to assume that roughly two million jobs would be lost in Japan. Yet the NYT didn't blink at a number four times as large. Just dividing the GDP loss by the estimated job loss would show that this translates to costs of $16k per job, which would be ridiculously low in any developed country.

So, yes, kids, algebra, the branch of mathematics that can be used to explore a relationship between two quantities, really is important. And by "kids", I mean the press.

UPDATE: Initially, I rounded off the GDP per worker figure in Japan to $62.9k, which was wrong. It should have been $63.0k. I didn't make that edit everywhere. I've left the old number in as a strike-through, so anyone who had read the article before would notice the correction.