Do Immigrants Lower Productivity?

I have two kids; they are the sweetest—I say as I clean spit-up off my shirt for the tenth time today. However, finding childcare has been a constant headache. We have daycare, but if we want to switch providers, there is a year-long waiting period for the newborn. Or if we want to find an in-home nanny for a few hours a week, good luck! That’s not easy, even when you pay well above market rates. The problem is that there are lots of frictions in the market beyond finding an agreeable price.

But this newsletter isn’t about my woes as a parent; it’s about immigration and productivity. The connection is that my woes would be improved with more immigration, especially low-skilled immigration, which would help me be more productive. I’m not alone, and so this effect would benefit lots of other people in an economy, making the overall economy more productive.

Alan Manning disagrees. In an interview in the Financial Times (gated) about immigration and productivity within the UK, Manning claims,

lower-skilled migration tends to be in lower-wage, lower-productivity jobs, so it tends to be a drag on the productivity level in the UK. Not a very big effect, but we know the UK’s got a very big problem with that.

The first part is absolutely true. Lower-skilled immigrants do have lower wages, given the link between skills and wages. The final part is true. The UK has a huge productivity problem, as Sam Bowman and others have written a ton about.

It’s that middle claim that’s the problem. Lower-productivity workers do not lower the overall productivity for any measure we care about. Instead, the claim elides the difference between an accounting statement and an economic statement. The economics is what matters.

We can quickly see the fallacy if we think in terms of an individual firm with one worker. The owner starts out making $25/hour. That’s her average and marginal productivity by assumption. Then she decides to hire another employee as an assistant who “enters the firm” in a similar way to immigrants who enter a country. For standard gains from trade reasons (whether comparative advantage or learning by doing), the existence of the assistant means the owner is now more productive and makes $30/hour. However, the assistant only produces $10/hour. If we go and measure the firm’s output Y, it is now $40/hour. Average labor output (Y/L) drops to $20/hour, compared to $25/hour before the assistant.

“Productivity” has dropped in the sense that average labor productivity has dropped. And average labor productivity is a common measure! But the original population (the owner) is actually more productive. The drop is a statistical artifact of calculating an average. Add short people to a group of tall people, and the average height drops, even though no one’s individual height drops. Presumably, the incoming population (the assistant) is also more productive, or she wouldn’t have accepted the new job.

This simple example highlights the difference between different measures of productivity. The easiest measure is average labor productivity. You take total output, like GDP, and divide it by some unit of labor, like hours worked.

We can also talk about marginal productivity. Marginal productivity is notoriously difficult to measure, but in a competitive economy, workers are paid the value of their marginal product, and so wages can serve as a proxy. In my owner-assistant example, the wage was both the value of average and marginal product.

There is a further complication in measuring productivity for the firm. What if the goods the firm sells become cheaper? Revenue equals price multiplied by output, and revenue may drop when prices drop, and so will the workers’ wages. However, in an important sense, the firm is just as productive in a “physical” sense, while the value they’re producing drops.

But even the one firm example doesn’t fully make the case. It may be that the productivity gains show up for a firm that doesn’t hire the worker.

Let’s consider a related example that has nothing to do with immigration: robots. A new robot arrives on the market that helps me clean my house. That robot may lower the price I’m willing to pay for someone else to clean my house, which in turn lowers the market price and revenue for house cleaners. From a distribution perspective, we may be worried about falling wages for cleaners.

But would we ever say robots lower aggregate productivity? It seems like a silly use of the word productivity if so. This is why we can’t confuse an accounting statement about productivity (output per hour worked) with an economic statement about productivity (which is about producing more value with fewer inputs).

So how does the robot affect productivity? While the robot may lower the value of the marginal product for cleaners since they lower wages, it clearly won’t lower “physical” output and productivity in general. The robot simply allows fewer inputs to produce more outputs that consumers value. In other words, it raises productivity even if some measures of productivity show a decline, such as wages as a measure of the marginal productivity for workers dropping.

But the lower price for cleaning services is a transfer that hurts sellers of cleaning services and helps buyers of cleaning services. Higher or lower prices are neither good nor bad in general. Again, it may be something we worry about in terms of redistribution, but it’s not a drain on productivity. The robot clearly helps productivity by allowing me to spend less time cleaning and more time writing newsletters.

Okay. That’s a bad example. Imagine I spent that free time productively. I become more productive, and so does the US, which produces more stuff with the introduction of the robot. In the same way, the introduction of new workers through immigration to clean houses will show up in my productivity.

And we can expect the gains from immigration to help in two dimensions. First, it allows for the standard gains from trade reasons above. But it also reduces transaction costs. Returning to the nanny example that I opened with, it’s not simply enough to raise the wage to find a nanny. Yes, there is a sufficiently high price where we could find a qualified nanny. That may be more than we are willing to pay. At the same time, there are people in the world willing to work for less than we are willing to pay. Gains from trade exist.

From people in my life, this is the type of help that professionals could especially harness to increase their productivity. Yes, virtual assistants help. But virtual assistants can’t watch the kids for a few hours when school is closed or clean my house. What I really need is a lot of people living near me that are able to do these jobs and willing to at a wage that makes it a mutually beneficial exchange.

The real gain from immigrants is in the form of lower transaction costs by having more trading partners in the areas. That’s true for me when finding a nanny. More importantly, it is true for firms looking for workers in traditional roles. For every “Help Wanted” sign at a McDonald’s, there are thousands of workers in the world willing to work at that job for the going pay.

In between a nanny and the McDonald’s with a worker shortage are jobs like UberEats. More workers mean people can afford more delivered food, which raises productivity or equivalently means more time with friends and family. The main benefit is that not the measured output increases. Part of that is just an artifact of the activity going from within the home to a market transaction that is measured. The real benefit is that people are able to execute trades that they couldn’t before since costs are lower. In a world of positive transaction costs, lowering these costs further increases the gain from trade, and the government saying people can’t move is a high transaction cost. With fewer governmental restrictions, people can help where they are wanted.

However, as soon as we start thinking about these spillovers between firms, we need to be careful about measurement. It gets tricky really quickly. Enough spillovers and anything can happen.

Luckily, a few papers explicitly study the productivity of firms in regions with more immigrants in the region, not just within the firm. For example, Mitaritonnaa, Oreficea, and Peri (2017) look at French firms by geographic region and find that an “increase in the share of foreign-born workers in a French département (a small geographic area) increased the total factor productivity of firms in that département.” Akgündüz and Torun (2020) look at Syrian refugees in Turkey. They find “the inflow of refugees increased natives' task complexity, reducing the intensity of manual tasks, and raising the intensity of abstract tasks.” This is the firm parallel of me being able to spend my time writing instead of cleaning the house. Comparative advantage is a hell of a drug. I should note that not everyone finds a positive effect. Brunello, Lodigiani, and Rocco (2020) find no effect of TFP from more immigration in Italy.

This is not meant to be a comprehensive literature review. Nor am I not saying it is theoretically impossible for more immigrants to lower the productivity (properly measured) of the incumbent workers. Garett Jones argues immigrants generate spillovers for native populations. This post won’t settle that debate.

Instead, I’m saying the line from Prof. Manning is misleading. In standard economic models, more low-skilled workers do not lower the productivity measures we care about. To be fair to him, it was one line in a long interview. I’m sure he has proper rebuttals to my statement.

Instead, now Economic Forces readers will be sure to differentiate an economic argument from an economic-sounding argument about averages, which is actually an accounting or statistical artifact argument. Adding a 5-foot-tall athletic trainer courtside for a basketball team does lower the average height of the “basketball firm,” but that doesn’t harm the team's height where we actually care about the team’s height. The trainer certainly doesn’t hurt the ability of the team to win games unless the trainer actively hurts players. In the same way, to argue immigrants hurt productivity, you need to provide mechanisms and evidence that people can no longer produce as much stuff as they could before. That’s a taller task.