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1. In his 2002 book, Calculated Risks, Gerd Gigerenzer addresses the muddy headed thinking that results from innumeracy and illustrates with telling anecdotes. This (p. 210) is one of my favorites:

   In the late 1970s, the Mexican government faced the problem of how to increase the capacity of the Viaducto, a four-lane motorway. Rather than building a new highway or extending the existing one, the government implemented a clever, inexpensive solution: It had the lines on the four-lane highway repainted to make it six-lanes wide. Increasing the number of lanes from four to six meant a 50 percent increase in capacity. Unfortunately, the much narrower lanes also resulted in an increase in traffic fatalities, which, after a year, forced the government to turn the highway back into a four-lane road. Reducing the number of lanes from six to four mean a 33 percent decrease in capacity. In an effort at touting its progress in improving the country’s infrastructure, the government subtracted the decrease from the increase and reported that its actions had increased the capacity of the road by 17 percent.

   As amusing as it is to chuckle over the transparent flimflammery of the Mexican government, it is considerably more distressing to see one’s fellow economists taken in by the same fallacy. This is precisely what is happening in John Humphreys’ recent publication in Econ Journal Watch, “Education Premiums in Cambodia: Dummy Variables Revisited and Recent Data.” Suppose for the sake of illustration that male college graduates earn $4000 a year in Cambodia, high school graduates earn $2000 a year, and someone entirely uneducated earns $1000 a year. These numbers, it should be clear, are picked for ease of exposition, not for accuracy. Using the usual formula for percentage changes, one would say that university graduates earn 100% more than high school graduates ((400-200)/200 = 1). It would be fallacious to say that college graduates earn 300% ((400-100)/100 =3) more than the uneducated, and high school graduates earn 100% more than the uneducated ((200-100)/100) = 1), so that college graduates earn 200% (300% – 100%) more than high school graduates, yet this is precisely what Mr. Humphrey’s technique does. He computes a percentage premium of college graduates over the base category, and then subtracts a percentage premium of high school graduates over the same base category.

   References:

   Gigerenzer, Gerd. (2002). Calculated Risks. New York: Simon & Schuster.

   Humphreys, John (2015). “Education Premiums in Cambodia: Dummy Variables Revisited and Recent Data,” Econ Journal Watch, 12 (3), pp. 339-45.

   posted 30 Sep 2015, 10:05 AM by Ronald Michener

2. Thanks for your comment Ronald.

   You give me too much credit. The approach I used was not my technique, but the conventional approach used in the literature.

   As it happens, I agree with you that the conventional approach to reporting education level premiums can be misleading. I’ve made the same point elsewhere. Unfortunately for you and I… if we want to make comparisons with other estimates around the world or through history, then we need to use the same approach as others.

   Perhaps we can help change that convention over time. Good luck to us. But the point of this paper was more modest.

   posted 30 Sep 2015, 10:26 PM by John Humphreys

3. John, I do not believe you understand my point. Computed as discrete changes, which is what you do, the percentage difference of the premia (college versus high school) is not equal to to the difference of the percentage premia (college versus base minus high school versus base). You are implicitly using a false assumption; it is the same false assumption made by the Mexican government in the example I cited: that the difference of the percentage changes (+50 – 33.3) is the percentage change of the difference. It causes you to greatly overestimate the education premium.

   posted 30 Oct 2015, 10:57 AM by Ronald Michener