An Infinite Contradiction
David Card has a new study arguing that immigration has basically no effect on the wages of domestic low-skilled workers. This confirms his earlier results on the famed Mariel boatlift, when Castro freed 125,000 Cubans to flee to Miami.
Is this result theoretically possible? How can the supply of labor increase, but leave wages unchanged? Card has little patience for these questions:
As the evidence has accumulated over the past two decades that local labor market
outcomes are only weakly correlated with immigrant densities, some analysts have argued that the
cross-city research design is inherently compromised by intercity mobility of people, goods, and
services. Underlying this argument is the belief that labor market competition posed by immigration
has to affect native opportunities, so if we don’t find an impact, the research design must be flawed.
A better answer, though, would have been to go to the blackboard. Card’s results are theoretically possible. All that is necessary, as Figure 1 shows, is that labor demand be infinitely elastic, i.e., horizontal.
Figure 1: Infinitely Elastic Labor Demand
Notice: When the Supply curve shifts out, the quantity of labor sold increases, and wages stay the same.
But this gets me thinking. Card is of course the co-author, with Alan Krueger, of the legendary study of the fast food industry in Pennsylvania and New Jersey showing that the minimum wage does not reduce employment. Their book goes further, debunking earlier studies that found the opposite.
Is this result theoretically possible? How can the minimum price of labor increase, but leave employment unchanged? Let’s go back to the blackboard.
In turns out that Card and Krueger’s results are theoretically possible too. All that is necessary, as Figure 2 shows, is that labor demand be infinitely inelastic, i.e., vertical. (The thick horizontal line between S and D at the controlled price is a labor surplus, but note that the quantity of labor purchased remains unchanged).
Figure 2: Infinitely Inelastic Labor Demand
Notice: When the minimum wage goes up, workers want to sell more labor, but employers want to buy just as much as before.
David Card has a higher IQ than me. He taught my graduate micro class, and put me in my place, fair and square. But taken together, I have to conclude that his research on immigration flatly contradicts his research on the minimum wage. His results for immigration imply that labor demand is infinitely responsive to price; his results for the minimum wage imply that labor demand is not responsive to price at all.
You could say that my former teacher has two sets of results for two different kinds of markets. But in both cases, he’s focused on markets for low-skill labor. Lots of immigrants from the Mariel boatlift presumably got jobs at McDonald’s. He’s not looking at two different markets; he’s looking at roughly the same market from two different angles.
What gives? I think Card’s work on immigration is closer to the truth than his work on the minimum wage. But it’s not because the immigration studies are well-done and the minimum wage studies are not. The quality of Card’s empirical work is uniformly high. I simply find his results for immigration more intrinsically plausible.
Why? As a theoretical matter, demand is highly inelastic under two main conditions:
1. Total expenditure on the good is a small fraction of one’s budget.
2. There are no good substitutes for the good.
In the market for low-skilled labor, neither assumption is credible. Labor expenses are usually the main cost of doing business. And you only have to peek over the counter at McDonald’s to see how easily machines can replace men.
These simple observations are the main reason why I think immigration does not reduce domestic wages much, and the minimum wage has a substantial employment cost. It would take pretty strong empirical evidence to change my mind. A bunch of studies finding that labor demand is either infinitely elastic or infinitely inelastic don’t come close.