The fallacy of composition, union version

Earlier, I used an equation and some data from Richard Freeman and James Medoff's book What Do Unions Do? to estimate the deadweight losses created by New Hampshire unions.

But I committed a subtle fallacy of composition, which biases my estimate downward. (The fallacy of composition arises when someone assumes that the part -- in this case, New Hampshire -- works the same as the whole -- the United States. It doesn't.)

I also want to clarify what exactly deadweight losses are, because, in retrospect, it seems that my earlier essay could easily be misinterpreted.

This is a diagram of the unionized labor market:



The demand curve slopes downward because, as the wage decreases, employers want to buy more labor. The supply curve slopes upward because, as the wage increases, more people want to work in this sector.

In a perfectly competitive market, the wages offered and the amount of labor hired would be set at the intersection of the supply and demand curves. If the wage were higher, the available workers would outnumber the available jobs, and employers would find that they could lower wages and still get all the labor they need. If the wage were lower, the available jobs would outnumber the available workers, and employers would have to raise wages in order to attract more workers into the market. This feedback effect leads employers to offer the wage where the two lines intersect, where the quantity of labor demanded and the quantity of labor supplied are equal.

But if workers bargain as a union, instead of accepting the competitive market wage, they can set the price-- in effect, choosing any point they'd like on the demand curve. Higher wages, however, come at the expense of fewer jobs, since employers want fewer workers at the higher wage.

This creates the deadweight loss. Some workers would like to work at the competitive market wage but cannot, and the businesses that would be happy to hire them at that wage are unable to. The potential benefits from employment that go unrealized are deadweight losses, and these losses are represented by the red triangle. The area of this triangle is what I was trying to find.

To arrive at the earlier conclusion, I used data from the federal level to estimate the elasticity of demand (a measure of the shape of the demand curve), but this is not similar to the elasticity of demand in the New Hampshire market by itself. The New Hampshire market in isolation has a higher elasticity of demand (that is, a flatter demand curve, meaning employers are more sensitive to changes in wages), because employers have the option of crossing the border into a different state. To do the same thing on the U.S. level would require leaving the country entirely, which is more difficult.

If the earlier graph represents my earlier estimate, the revised estimate should look more like this:



This graph shows that the union wage differential leads some businesses move to different states, so that the demand for New Hampshire union labor is lower. This increases deadweight loss, first because there are more people who would like to work at the market wage, but can't. Second, when businesses leave the state to avoid the higher union wages, the businesses do better, but the costs of moving are pure deadweight losses, as opposed to the higher wages, which redistribute wealth from employer to employee (businesses shift from blue to smaller red losses).

The takeaway from all of this is that my earlier estimate, that the deadweight losses due to unions were .05% of New Hampshire GDP, is probably too low. Watch out for that fallacy of composition.