City Limits Are the Wrong Border for Measuring a Local Economy

Picture a map of one US metro area, drawn at the city-limits level. It is a choropleth: one polygon for the central city, shaded by poverty rate in five fixed classes with one sequential hue (light to dark), year stated in the legend, and the surrounding suburbs left blank because they are "not the city." Now redraw it. Merge the city with every county whose residents mostly work in the same labor market. The blank ring becomes part of the picture. The jobs stay where they were. The people who fill them now sit inside the border.

That redrawing is the question of this post. Do official city limits miss a large part of the local labor market, and does the missing part change city statistics on jobs, income and poverty?

My answer has two parts. For jobs and population present, the direction is clear and the arithmetic is simple. For income and poverty, the direction is plausible, but I did not compute the size, and I will say so plainly. I changed the working thesis because the evidence I read supports the first part and not yet the second.

Data and where it came from

I used four kinds of source.

The border itself. The USDA Economic Research Service (ERS) 2020 commuting zones sort 3,222 counties and county-equivalents into 598 labor markets [1]. The scale is the county. The unit is a cluster of counties. The year is 2020, from decennial census commuting data [2]. A zone is not a city. It is the region that a set of county-to-county commuting flows ties together.

The accounting rule. The Census Bureau defines commuter-adjusted population (often called daytime population) as resident population plus workers working in the area, minus workers living in the area [3]. The source tables are B01003 for residents, B08604 for workers working in the area and B08301 for workers living in the area [3].

One worked case. Wikipedia reports that Washington, D.C. had 689,545 residents in the 2020 census and that commuters raise its weekday population to more than one million, citing Census Bureau research [4]. This is a secondary source for a Census claim. I did not open the Census file behind it, so I treat it as an illustration, not a measurement.

The methods critique. An AEA conference paper replicates the standard Tolbert and Sizer clustering method and reports that results are sensitive to errors in the commuting flow data and to the clustering cutoff [5]. Openshaw's classic MAUP monograph gives the general warning: areal units are arbitrary and modifiable, so a statistic depends on who drew the lines [6].

I did not find, and did not open, a published table of city-limit versus commuting-zone poverty rates for US metros. I also could not read several PDFs I tried (two Census working papers and an IZA discussion paper) because they returned as unreadable binary. I cite none of them.

Method

I used no code and no Lab run. Everything below is hand arithmetic on the figures above, and a reader can repeat it.

Write the Census rule as

$A = R + W_{in} - W_{out}$

where $A$ is commuter-adjusted population, $R$ is residents, $W_{in}$ is workers who work in the area and $W_{out}$ is workers who live in the area. The net commuter flow is $W_{in} - W_{out}$. For a city, $W_{in} - W_{out}$ is positive when more people come in to work than go out.

The key point is what happens to this term when the border moves to a commuting zone. A commuting zone is built so that most commuting stays inside it. So, by design, $W_{in} - W_{out}$ for the whole zone is close to zero, and $A$ is close to $R$. At the city-limits level, the same term can be large. So the daytime gap is a measure of how much the city border cuts through commuting flows.

This is a design property, not a finding. ERS builds zones by hierarchical clustering on a matrix of proportional commuting flows [2], and the clustering stops at a judgment threshold. I did not check, county by county, how closely the final zones reach zero net flow.

Result

Jobs and people present. Take the D.C. figures [4]. If the weekday population is "more than one million" and the 2020 resident count is 689,545, then the net inflow is more than $1{,}000{,}000 - 689{,}545 = 310{,}455$ people. That is more than 45% of the resident count. The source also reports a rise of 79 percent for an earlier, smaller resident base of about 600,000 [4]. I cannot reconcile the two bases exactly, because they come from different years and I did not see the underlying tables. So I give a range: the daytime population is between roughly 1.45 and 1.79 times the resident population in the sources I saw. Treat both ends as rough.

What does this do to a jobs statistic? Any measure that divides jobs by residents inside the border, such as jobs per resident, is inflated for the city and understated for its suburbs. Redraw the border to the zone, and both numbers sit in one pool. The ratio then describes one labor market, not two halves of one.

Income. City-limit median income describes residents of the city. A job located in the city may pay a worker who lives outside. So a "city income" figure answers the question "how much do people who sleep here earn?" and not "how much does this economy pay?" These are different questions. Only a zone-level table with the same year and the same ACS tables would show how far they differ. I did not build it.

Poverty. Poverty rate is a ratio of residents. City limits can include or exclude whole neighborhoods by the history of annexation, not by the economy. That is a zoning effect in the MAUP sense [6]. The zone border reduces that effect for the labor market, but it does not remove it. A zone mixes rich and poor places into one average. If the zone includes a wide suburban ring, its poverty rate can look mild and hide a concentrated city core. This is my reasoning, not a measured result.

Uncertainty, stated as a number where I can. The D.C. range above (1.45 to 1.79) comes from two figures that I could not tie to one table. For poverty and income I have no number and I will not invent one. My confidence that city-limit poverty and income figures differ materially from commuting-zone figures for a typical large US metro is about 0.8, but that is a prior from method, not a measured effect. My confidence in the claim as a general US pattern, for every size of metro, is lower, about 0.6, because small and mid-size cities often have little commuting across their limits.

Sensitivity: which assumption moves the result most

Four assumptions matter. I rank them by how much I think each moves the answer.

1. The clustering threshold. The AEA paper finds that cutoffs are arbitrary and that choices change empirical estimates [5]. A looser cutoff merges zones and puts more people inside one border. A tighter one splits them. If a metro sits at a cutoff, its zone statistics can change a lot. I think this moves the result most, because it decides whether a given suburb counts as "inside."
2. The county as building block. ERS zones are made of whole counties [1]. A county can be bigger than the real commute shed or can cross two. So the zone border is only as fine as the county border. A city that straddles two counties is a hard case. This is the scale effect in MAUP terms [6].
3. The year. The zones use 2020 data [2]. The 2020 census year is also the year many people changed work habits. Commuting flows from that year may not describe an ordinary year. I have no number for how much this matters.
4. Measurement error in flows. The AEA paper reports that clustering is sensitive to errors in the flow data [5]. Survey flows for small county pairs are noisy. This pushes zone borders around at the edges more than in the core.

One more point. A commuting zone is still a border. It does not give the "true" edge of a city. It gives a better-justified one for the question "where do people work and live together?" For a question about housing, schools or city taxes, the city limit may be the right border, because the city government decides those. I do not claim zones win in every case.

My current view

The idea that a city is only what sits inside its limits is a legal fact, not an economic one. The Census accounting rule [3] shows this in one line: if workers cross the border, resident counts and worker counts split apart. The D.C. case shows a gap of at least 45% [4], which no one would call small.

I am less sure about the claim that income and poverty "change meaningfully." They may. I expect they do for big metros. But I have not seen the table, and I will not claim a size without it. If a zone-level versus city-limit comparison for ten large metros shows poverty and median earnings within a few percent of each other, I will drop the strong form of this claim and keep only the jobs result.

My own earlier view, that commuting zones describe local economies better than city limits do, stays at 0.7. This post gave me no new test of it for income. It gave me a clearer reason why jobs figures differ.

Same data, different borders.