More on the Happy Planet Index

In the comments on my last post, Joel Bernstein and Blar point out a possible justification for the NEF’s Happy Planet Index: that it’s not intended to measure total happiness, but rather happiness per unit of input. Blar quotes a relevant passage from the report:

The HPI is a measure of the ecological efficiency of delivering human well-being. It reflects the average years of happy life produced by a given society, nation or group of nations, per unit of planetary resources consumed. Put another way, it represents the efficiency with which countries convert the earth's finite resources into well-being experienced by their citizens.

So apparently it was the news reports about the NEF study, and not the study itself, that erred in interpreting the results to mean that Vanuatu is the happiest place on earth.

But even with the above justification, the HPI is still hopelessly flawed. Why? Because for any production function that displays diminishing marginal returns, the average productivity per unit of input will be highest for low levels of production, and vice versa. If we assume, as seems likely, that the marginal impact of resources in delivering happiness is positive (more resources lead to more happiness) but decreasing (each additional unit of resources adds less to happiness than the previous one), then the HPI will necessarily give the best scores to those nations with the worst productivity. Hence the remarkable performance of such economic powerhouses as Vanuatu, Cuba, and Vietnam (see JB’s comment).

A simple mathematical example. Suppose a country’s happiness function is y = x^(0.5). That is, happiness output (y) is the square root of resource input (x). Then a country with input of x = 1 will get happiness y = 1; its average happiness per unit input will be 1. A country with input of x = 4 will get happiness y = 2; its average happiness per unit input will be 0.5. A country with input of x = 16 will get happiness y = 4; its average happiness per unit input will be 0.25. So the more inputs a country uses, the higher is its total happiness, and the lower is its average happiness per unit input. The HPI thus gives the highest rating to those countries that use the least inputs and are therefore the least happy.

Anyone with a rudimentary knowledge of business economics can see the flaw here. Say you’re an employer trying to decide how many workers to hire. If you decided to maximize output per worker, you would choose to hire very few workers, because labor exhibits diminishing marginal returns: as you add more workers, the added output from each added worker gets smaller. But an employer who chose that route would not maximize his profits, and would most likely go out of business. A smart employer would continue to hire workers as long as the value of the output added by a new worker exceeded the cost of hiring. Average output per worker would decline, but profits would rise.

The point is that defining “efficiency” in terms of an average, rather than a total, doesn't make sense here. You can plausibly argue that there’s a point where the gain from additional resource usage doesn’t justify the cost, and it would be inefficient to go beyond that point. But you can’t find that point by simply looking at the average happiness per unit of resource input; you need to attach a value to the resources used.

Also, the “Ecological Footprint” method the study used as its measure of resource usage is also terribly flawed.