Fallacy of composition, W-NOMINATE version

I've been neglecting my blog lately. Much of the reason is that I've been working to understand the political science program NOMINATE, so that I can gather information about the ideological make-up of the New Hampshire legislature.

The data is posted on the W-NOMINATE page of my blog. Here's the cool graph (click to enlarge):

Keith Poole and Howard Rosenthal, the main developers of the program, claim that the program measures economic attitudes on the x-axis, and, in recent years, social attitudes on the y-axis.

At first blush this is what it appeared to be doing for New Hampshire legislators. However, after taking a closer look at the votes, I discovered that it's not doing this. At least, not very well.

The x-axis measures economic issues well, and correlates beautifully with the House Republican Alliance's scorecard ratings. (See this impressive graph, courtesy of Seth Cohn.) The y-axis, on the other hand, has issues. Apparently, because there have been so few votes on social issues this year, there is little basis for the y-values. Mostly they reflect positions on gun rights and criminal justice issues, with pro-gun and tough on crime on the bottom.

This is yet another reminder that politics at the state level does not necessarily imitate politics at the federal level.

Thanks to Rep. Seth Cohn, Scott Pauls at Dartmouth, and professor Jason Sorens for criticism and help. Peer review fixed my mistake.

Fallacy of composition, balanced budget version

Nicholas Johnson at the Center on Budget and Policy Priorities argues that the federal government, unlike states, shouldn't have to balance the budget:

From the economy’s perspective, the fact that states have to balance their budgets even in recessions makes it even more important not to require the federal government to do the same. States’ balanced budget requirements force them to cut spending and/or raise taxes at the worst possible time: when the economy is weak and needs more public and private spending, not less. These measures help keep state budgets in balance, but they can also make downturns longer and deeper — and the current downturn is no exception.

There's more to the story. States balance their budgets for a reason— if states attempt to use fiscal policy (government spending) to stimulate the economy, much of the stimulus leaks into bordering states. A New Hampshire stimulus package would end up stimulating Massachusetts, Maine, Vermont, and Canada. Because of these leaks, fiscal policy is less useful to New Hampshire policymakers. State government may perform better by forsaking weak attempts at fiscal policy and sticking to a balanced budget.

Fiscal policy at the federal level is much more effective because it covers a larger area, and there's less leaking as a proportion of the stimulus. It also solves the coordination problem between states (where New Hampshire policymakers don't account for the stimulus to Massachusetts, and Massachusetts policymakers ignore stimulatory effects on New Hampshire).

The macroeconomic policy lesson that we've learned over the last few years is that fiscal policy can matter a lot. Forsaking it at the federal level, where it works best, would be extremely foolish.

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.

Who gets the gas tax cut?

Bill O'Brien's proposed gas tax holiday has at least one thing going for it-- the tax cut will actually be passed on to consumers.

Some commentators intuitively suspected that gas companies will receive the tax break (including myself, to be honest), probably drawing on the reaction to a very similar proposal from Hillary Clinton and John McCain during the last presidential primaries. (See Megan McArdle's discussion for background.)

But this intuition commits a fallacy of composition. The reaction of markets to a gas tax cut on the state level will not mirror the reaction to a cut on the federal level.

While it's true that the supply of gasoline is inelastic for the country as a whole, the supply of gas to New Hampshire in particular is very elastic, even in the short run. This is because gas can easily be shifted from one state to another. A quick search for empirical evidence bears this out.

So consumers get the tax cut.