# Are locational wage differentials also productivity differentials?

Suppose that we observe that zip code X has higher average wages for waiters than zip code Y. Can we infer that waiters in X are more productive than waiters in Y? Can we infer that removing barriers to mobility so that waiters can move more easily from Y to X will raise real GDP?

I think that we need to know more about why waiters are paid more in X.

a. It could be that, working with a given level of capital, the same waiter can serve more customers per hour in X than in Y. Maybe restaurants in zip code X are better managed. Or maybe restaurants in zip code Y do not get enough customers.

b. It could be that the cost of living is higher in X than in Y. Waiters serve the same number of customers per hour in each, but if you raised wages in Y all the waiters would move there to get a higher real income. There has to be a wage differential to compensate for the cost of living differential.

If (a) is true, then removing mobility barriers would raise real GDP in the restaurant industry. But if (b) is true, then removing mobility barriers would not raise real GDP in the restaurant industry.

Suppose that the mobility barrier is a housing market restriction in X. Then getting rid of the housing restriction might raise social welfare by making the housing market function more efficiently. But there is no additional benefit from waiter productivity. What would happen if you got rid of the housing market restriction is that the wages of restaurant workers in X and Y would equalize. As waiters move from Y to X, the wage differential would go away. The new wage would be somewhere between the old wage in X and the old wage in Y.

Note that in case (b), restaurants might use more capital in X than in Y, because the cost of labor is higher (because the cost of living is higher). That would enable waiters in X to serve more customers per hour than in Y, but this is not a pure productivity differential. If you remove the mobility restriction, then eventually the capital intensity of restaurants in X and Y will be equalized.

What if the main difference between zip code X and zip code Y is that quality of life is better in zip code X? In that case, other things equal, cash wages ought to be lower in zip code X. Of course, other things are unlikely to be equal. Housing supply is probably not perfectly elastic, so some of the quality-of-life differential should be eaten up by housing costs. And of course, quality of life means different things to people with different tastes, and that accounts for some (much?) of location choice.

If I might try to coin a phrase of opprobrium, I believe that economists who equate locational wage differentials to productivity differentials are guilty of casual neoclassicism. They should be required to read James Buchanan’s Cost and Choice and take an exam afterward.

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### 22 Responses to Are locational wage differentials also productivity differentials?

1. Tyler Cowen says:

Aren’t the waiters more productive *because they are serving wealthier customers*?

• Does it matter if that wealth comes from productivity or economic rents derived from capital repression?

• Slocum says:

But what if the customers are only wealthier for the same reason as the waiters — namely that they have to be paid more to make up for the high cost of living?

Has the SF Bay region raised its productivity by restricting development and thereby driving up living costs and wages of all workers? If development restrictions were loosened, a construction boom commenced, and area housing prices (and, therefore, salaries) began to converge with the rest of the country — would you argue that convergence would mean a loss of productivity (as waiters and many of their customers were no longer so wealthy relative to the rest of the country)?

• Yancey Ward says:

Finally, someone asked the right question.

• MikeP says:

Yes.

To make this clearer, change “waiter” to “maid” and redo.

2. collin says:

I think that we need to know more about why waiters are paid more in X.

Maybe restaurants serve more people per day in restaurant X not just busy hour. Although they probably serve more per hour but isn’t there a difference in the dinner, lunch, and breakfast rush? So a restaurant in San Francisco has dinner run 5 – 9 so they are ‘very’ productive for 4 straight hours versus a small town restaurant of 5:30 – 7:30.

3. GC says:

Maybe waiters in zip code X are more likely to work at restaurants with higher average food check per table than workers in zip code Y.

4. Geoffrey says:

Productivity should not be measured in “meals served per hour” but in “the \$value of meals served per hour”

So yes – waiters in New York City (or Washington DC where I live) are more productive than in Ames Iowa.

• asdf says:

Restaurants in NYC do serve more customers at a higher price. Does that mean that the waiter is more productive?

When I think of a restaurant in NYC it has a very high rent expense. Most of the extra income from extra meals served + higher meal prices goes towards paying the rent on the property along with other expenses (taxes, etc). It seems that the restaurant pays the waiter roughly the same real wage, indicating that the waiter is not the scarce productivity enhancing good in this example.

The land under which the waiter serves patrons is the most productive asset. If the waiter was more productive we would see his real wage, not just his nominal wage, increase.

5. Dagon says:

Tyler responded correctly – the waiters are more productive not because they’re serving more people, but because they’re providing more valuable meals.

There are lots of reasons that the “same” meal is more valuable in San Francisco than in Boise, and if you try to aggregate to “cost of living”, you’ve lost a lot of explanatory power.

• asdf says:

The waiter isn’t providing a more valuable meal. The land on which the waiter serves the meal provides a more valuable meal. Most of that goes to paying rent on the restaurant space and the minimum necessary to pay for the waiters increase living expenses comes through as a higher nominal wage but not a higher real wage.

• Slocum says:

But then, as I said above, the value of meals (and productivity) rises as policies such as development restrictions and rent control drive up housing costs. Do you really want to be in a position of claiming that rent control and heavy development regulations make NYC and SF more ‘productive’?

6. Tom DeMeo says:

If only there was some way to aggregate all these opinions about what value is true and what isn’t and come up with some sort of medium of exchange that accounted for all of it in some subjective way we can all agree to…

• Jeff R. says:

I think there’s a Bitcoin exchange that does that now.

• The problem is that we don’t have such an exchange in the real estate markets of 5 of our most prosperous cities, so the basic foundation for determining the value of that highly paid waiter doesn’t exist. Kind of like if we still had a stock exchange, but basically made it illegal to register a start up venture, do an IPO, or invest venture capital. There would still be a price for various firms, but it wouldn’t be particularly informative as a measure of productivity.

• Dave says:

some sort of medium of exchange that accounted

The dispute here is how to decompose the price into various components, such that intelligent things can be said across a variety of situations. There is no market for San Franscisco-fresh-made espressos in Reno, so we actually don’t know what the disaggregated price would look like.

7. Weir says:

Seems like the workers in Shenzhen are a great deal more productive in Shenzhen than they would be if, hypothetically, Apple elected to have the factory rebuilt in Cupertino.

8. Lord says:

It isn’t that they aren’t more productive but what being more productive means. It doesn’t mean you can employ more to produce more at the same rate. The cost of living is a cost to someone but a benefit to someone else and you can’t lower one without lowering the other, whether preferred or not, without increasing productivity, but changing regulations can’t accomplish this. That can only shift who ends up with it.

9. Handle says:

The conversation in this thread is very confused because people are trying to have one of those philosophical / semantic arguments about what *the* single meaning of a word should be. But that’s not how language works.

There are several ways one can interpret economic “productivity” in this context. Here are three, and there are probably more.

1. Nominal market value (i.e., nominal wage = nominal, marginal labor productivity) at a particular place in a local market equilibrium.
2. Output per Labor Input at a particular ratio of Labor to Capital per some potential production function. (i.e. real labor productivity)
3. Production of total surplus (or perhaps welfare, utility, smiles, etc.) per labor input, again in a particular local market equilibrium.

So we have the difference between someone earning \$10 an hour, producing 20 coffees an hour, and producing some amount of total surplus for themselves and others in an hour.

I am not saying any of these definitions is *right or wrong*. To be clear about my argument, I am objecting only to the rhetorical use of the word in which statements can be justified and validated as technically accurate according to the first definition, but which, when heard by an ordinary member of the educated public, tends to be interpreted and understood with a different meaning, probably along the lines of the second definition.

No one seems to want to address this rhetorical objection. Instead they want to double down on the semantic argument. To address the rhetorical objection, one could argue against my position by saying something along the lines of, “No, most ordinary members of the public think the words ‘productivity’ and ‘higher wages but a higher cost of living’ are basically equivalent concepts they interchange all the time.”

But they’re not. “Productivity” is understood differently and almost always has a positive valence and connotation. Which, duh, is precisely why it’s being abused in this rhetorical fashion, because it’s understood to be a happy-warm-good-feelin’ kind of word. But if one is going to play this bait-and-switch game, then one can produce examples where the term is used in perfectly technically correct senses along the lines of the first definition, but which produces statements which completely rub our linguistic intuitions the wrong way. E.g., If we impose quotas or force lower output that raises prices, we make the workers that remain “more productive”, and so politicians could argue that making building regulations even more restrictive would make workers in those cities “even more productive!” True! At least, for the workers that still have jobs and who can afford the higher rents.

• ColoComment says:

THANK you. I was one of those ordinary people who thought that an employee’s productivity was measured by how many widgets per x an employee produced, not the price of that widget, which is set by other factors.
Trying to figure out how an individual could qualify as “more” productive if he were serving \$25 hamburgers at a rate of 25/hour at Classy Dining Spot in San Francisco than if he were serving \$5 hamburgers at a rate of 25/hour at fast-food emporium in Julesburg, Colorado, was driving me crazy.
If his job is taking orders & serving food, it seemed to me that each would be equally “productive” at his individual job.
…or am I simply *proving* myself a fool by commenting?

• Roger Sweeny says:

No, you’re perfectly sane

One of the things that is supposed to be taught in Introductory Micro is that there is a difference between marginal physical product (which is about how much stuff is produced) and marginal revenue product (which is about how much that stuff sells for). Referring to “productivity” without specifying which kind you mean is an invitation to confusion.

10. Maximum Liberty says:

A high minimum wage cuts off a significant part of a distribution curve for waiter’s wages. That has the effect of eliminating many waiters from working as waiters and raising observable average productivity and wages. This changes the sustainable pattern of work done in the jurisdiction from low-wage to high-wage by dis-employing low-wage workers, most of whom presumably move away.

High housing costs have a similar effect, I think. It similarly changes the pattern of work done in the jurisdiction — you get more investment bankers and fewer baristas, with prices for the barista’s output tending toward a higher price than would be the case elsewhere.

This conflicts with my sense that New York City has lots of great restaurants and bars (I would expect to see a lower quantity supplied) but agrees with my sense that the prices in New York City restaurants and bars are jaw-dropping high (a \$24 mixed drink on my last visit that would have gone for \$8-10 back home). I guess the demand curve is pretty inelastic in New York City.