The urban wage premium is disappearing in U.S. micropolitan areas

A key driver of urbanization is the pursuit of economic opportunities in cities. One such opportunity is the promise of higher wages in larger cities, a phenomenon known as the urban wage premium. While an urban wage premium has been well-documented among U.S. metropolitan areas, little is known about its existence in micropolitan areas, which represent an important link between rural and dense urban areas. Here we measure the power law scaling coefficient of annual wages versus employment for both U.S. metropolitan and micropolitan areas over a 37-year period. We take this coefficient to be a quantification of the urban wage premium for each type of urban area and find the relationship is superlinear in all years for both area types. Though both area types once had wage premiums of similar magnitude, the wage premium in micropolitan areas has steadily declined since the late 1980s while in metropolitan areas it has generally increased. This growing gap between micropolitan and metropolitan wage premiums is ongoing in parallel to other diverging characteristics, such as inequality and voting behavior, suggesting that our result is part of a broader social, cultural, and political divergence between small and large cities. Finally, we speculate that if urban residents respond to the COVID-19 crisis by migrating, the trends we describe may change significantly.

. Scaling of wages versus employment using different data sources -by area type Figure S2. Scaling of wages versus employment using different data sources -by data source Figure S3. Scaling coefficients of total wages versus total employment and population, 1990-2020 Figure S4. Changing employment-to-population ratios in Regional Economic Accounts data of the Bureau of Labor Statistics.  Table S1. Scaling results for total wages versus total employment, 1984 -2020 Table S2. Micropolitan and metropolitan wages and employment, 1990 and 2018, for all industry sectors Supplemental References Section S1. Comparison of alternate employment and wage data sources In our study we used county-level employment and wage data published annually by the U.S. Bureau of Labor Statistics in its Census of Employment Wages (CEW) dataset [1]. These same categories of county-level data are also capture annually by the U.S. Census Bureau's County Business Patterns (CBP) dataset [2] and the U.S. Bureau of Economic Analysis' (BEA) Regional Economic Accounts data, specifically its dataset CAINC4-Personal Income and Employment by Major Component [3]. Each dataset has its advantages and drawbacks, primarily related to differences in coverage of government workers, non-profit businesses, and statistical augmentation [4]. We chose the CEW for our study because it is available for more years than the CBP and typically covers a larger number of employees than the other sets. Furthermore, the underlying wage data used by the BEA are based on place of work but the BEA attempts to adjust those values to reflect place of residence, making the wage and employment values published by the BEA inconsistent with regard to geography. We nevertheless take advantage of these alternative datasets to both validate our study's main finding and to present readers with a more comprehensive picture of metropolitan and micropolitan wage scaling.
The County Business Patterns data set is publicly available for download in data-ready format for years 1986 -2019. Earlier years are available for download from the U.S. National Archives [5] but are not in a format that can be easily read by data analysis software. Thus, our analysis is limited to years 1986 and later.
The publicly available BEA Regional Economic Accounts data offers county-level wages, employment, and other measures, such as income, for the years 1969-2019. Thus, the BEA data offers a longer time period for temporal analysis but was not used in the main study for reasons highlighted above. Furthermore, the BEA data reports both total employment and wage and salary employment. Here we use wage and salary employment because it is meant to align with wages and salaries reported by the BEA. On the other hand, one could calculate a scaling coefficient for Total Employment (Wage and salary employment + Proprietors employment) versus (Wages and salaries + Proprietors' income), all of which are part of the BEA's CAINC4 dataset. However, that analysis is not performed here.
Using the methodology described in the main text we performed the same analysis on the CEW, CBP, and BEA datasets, comparing the scaling coefficients of metropolitan and micropolitan areas. Results shown both by area type ( Figure S1) and by data type ( Figure S2) are similar using all data sources. With metropolitan areas, scaling coefficients using BLS and BEA data are nearly identical while coefficients derived with CBP data are slightly higher in all years ( Figure S1). Temporal dynamics with all data sources follow similar dynamics.
Micropolitan areas also show the same coarse trends, generally declining after 1990 with a slower rate of decline after 2010. However, micropolitan scaling coefficients in earlier years are considerably higher using CBP data but converge with CEW data over time. More importantly, all data sources show the same transition in the mid-to-late 1990s in which scaling coefficients in metropolitan areas become greater than those in micropolitan areas, followed by a sustained decline in micropolitan scaling coefficients. Figure S1. Scaling of wages versus employment using different data sources -by area type. Differences in scaling coefficients using different data sources for wages and employment are shown for (right) metropolitan areas and (left) micropolitan areas. CBP data results in higher scaling coefficients for all years in both area types, while scaling coefficients using CEW and BEA data are nearly identical. For all data types, area types, and years R 2 > 0.94. Regardless of data source, a divergence is revealed between metropolitan and micropolitan scaling coefficients, which was preceded by a period in which micropolitan scaling coefficients were higher than those for metropolitan areas.

Section S2. Comparing alternate metrics of city size: total employment vs. population
In our study we use total employment as our measure of a city's size in order to compute a wage scaling coefficient. However, we note that other studies have calculated similar scaling coefficients using population as the measure of city size [e.g. 6]. We chose total employment because the Census of Earning and Wages (CEW) collects both employment and wages from the same business survey program. Thus, when data is suppressed for privacy reasons, both wage and employment data are equally affected, making aggregations more comparable than if one were to use different data sources for wages and employment.
For comparative purposes we include here additional results using population as the metric of city size. We extracted county-level populations from the U.S. Census Bureau's Annual Population Estimates [7] for years 1990 -2020, linking those values by year to the county-level wages from the CEW. We then apply the methodology described in the main text to aggregate county data to core-based statistical areas (CBSAs) and calculate a scaling coefficient for wages versus population.

We further take county-level wages and population from the Bureau of Economic
Analysis' CAINC4 dataset (BEA) described in Section S1 and performed the same analysis.
A comparison of our main results using employment with supplemental results using population is presented in Figure S3. We find that the scaling coefficients for metropolitan areas are higher when using population as the measure of city size, suggesting a change in the employment-to-population ratios across city sizes. On the other hand, scaling coefficients for micropolitan areas are lower when using population versus employment, so much so that scaling of wages versus population has been sublinear (β < 1) since 2005. The lower values also suggest an inconsistent relationship between employment and population across city size.
We speculate that a primary reason for the observed differences is that employment numbers are based on place of employment while population is based on place of residence.
Despite a BEA procedure to adjust its wage data that it represents wages based on place of residence, results using their data is remarkably similar to the BLS data based on place of employment. Thus, commuting patterns will lead to differences in employment-to-population ratios across cities. A decrease in micropolitan scaling coefficient when using population would indicate that larger micropolitan areas have a larger share of residents working outside the micropolitan boundary. This may be a typical economic trend of urban growth, with new businesses emerging more rapidly beyond the border of a core-based statistical area. It may also indicate shortcomings in the way the micropolitan statistical areas are defined. In any regard, the determination of the ideal metric of city size remains an interesting topic for future research. Figure S3. Comparison of scaling coefficients using population with coefficients using employment. Results are shown for both metropolitan (left) and micropolitan (right) areas. Using both BEA (red) and BLS (blue) data sources, scaling coefficients using population (dashed lines) are consistently higher for metropolitan areas and lower for micropolitan areas than coefficients using employment (solid lines). The relatively large gap between metro and micro population-based coefficients suggests that population is a less reliable measure of area size than employment.
Thus, our primary justification for use of employment over population as our measure of city size is that people represented in the employment data most closely match those in the wage data. However, because we did not know in detail the BEA's procedure for restating employment by place of residence, we sought to determine whether the ratio of employment to population is consistent over time. Therefore, we calculated the value of this ratio from 1969 to 2019 using annual population and annual total employment from the BEA Regional Economic Accounts CAINC4 dataset. For each year and each CBSA type, we performed a linear regression of employment versus population generating a slope for each year and area type. We then plotted those slope values versus time to examine the stability of employment-to-population ratios and whether they differ between metropolitan and micropolitan areas.
The result presented in Figure S4 shows surprisingly that the ratio of employment-to-population is not only consistently higher in metropolitan areas, but the ratios of both CBSA types have steadily increased over the 51 years of available data. Neither the difference in CBSA types nor the ratio's systematic increase over time could be explained by periodic variations in unemployment rates. However, we note that the average population size of each category of CBSA also increased steadily over the period of our study and thus city size may influence the employment-to-population ratio. Further investigation into residential housing patterns, commute patterns, labor force participation rates, and data deficiencies related to, for instance, agricultural workers, may offer insights into the causes of this result.
For the purposes of this study, this inconsistency of employment-to-population ratios over time further justifies the use of employment as a measure of city size and not population.

Section S3. Sensitivity analysis of cutoff between metropolitan and micropolitan areas
A critical aspect of this study's design is the parsing of U.S. core-based statistical areas (CBSAs) into two mutual exclusive categories. We adopted the official demarcation used by all U.S. agencies, as designated U.S. Office of Management and Budget, of micropolitan and metropolitan statistical areas.
The determination of category for any particular CBSA is based on a population threshold of 50,000, with CBSAs less than 50,000 designated as micropolitan and CBSAs more than 50,000 as metropolitan. We acknowledge that this threshold is seemingly arbitrary, yet adhere to the standard metro/micro schema for the following reasons:  Any other cutoff used to distinguish larger cities from smaller cities would be equally arbitrary;  The established convention of metropolitan and micropolitan areas has been used consistently across U.S. national agencies for decades and coincides with official government datasets;  An existing body of literature on urban scaling going back at least as far as [6] has studied metropolitan areas as a distinct set of urban systems, and thus provides nearly 15 years of precedent upon which to build;  Because certain government policies, including funding decisions, are based on the micro-metro determination, the very act of applying these labels can lead to qualitative differences between metropolitan and micropolitan areas [8].
Thus, we believe that, while arguably arbitrary, the cutoff adopted in the paper is superior to others.
Still, we feel it is important to explore the sensitivity of this cutoff value. To do so we further analyze 2019 data in the following manner. Instead of using the official government cutoff of 50,000 residents, we let the cutoff between large and small CBSAs vary of the range of 25,000 employees to 500,000 employees, in increments of 5,000 employees, and calculate the scaling coefficient for both large and small CBSA groups at each cutoff. The results in Figure S5, beta versus cutoff. We see almost no change in betas between large and small over this range of cutoffs, meaning that our cutoff falls within a highly stable range of otherwise arbitrary values and offers robust results. Changes also included a switch in designation between micro or metro. Between 2003 and 2018, 28 micropolitan areas were redesignated as metropolitan areas while 2 metropolitan areas redefined a micropolitan areas. This is an average of less than 2 changes in designation per year out of nearly 940 CBSAs. Given all of these small but frequent changes in boundaries over time, the use of a consistent delineation schema for all years of data offers the best method for understanding temporal dynamics.

Section S4. Full table of metropolitan and micropolitan scaling results, 1984-2020
Here we present the full table of data represented graphically in Figure 2

Section S5. Change in industry sector indicators, metropolitan areas, micropolitan areas, and total U.S., 1990 -2018
In the main text we present an in-depth look at the industry sector Information. Here we present the same in-depth analysis of all industry sectors (Table S1), which are defined as the 2digit level of aggregation using the North American Industry Classification System (NAICS).
NAICS codes were first used in the Bureau of Labor Statistics' Census of Earnings and Wages in 1990. Thus, we compare 1990 to the latest year available at the time of this detailed analysis.

Section S6. Scaling coefficients among non-CBSA counties 1984-2020
While our primary goal was to determine the presence of an urban wage premium among micropolitan areas and how that differed over time compared to metropolitan areas, we also considered those counties that do not fall into a metropolitan or micropolitan statistical area.
Because there is considerable variability in these counties, we used a classification schema published by the U.S. Department of Agriculture's Economic Research Service called the Rural Urban Continuum Codes (URCC). The latest version of this system was created in 2013 and is publicly available at [9]. This schema classifies all U.S. counties into one of nine types, four of which deal with counties that are not already part of a core-based statistical area (CBSA).
After removing all counties that are part of a CBSA using the Office of Management and Budget's September 2018 CBSA delineations, we used the URCC to classify remaining U.S. counties as either adjacent to an MSA or not and either less than or greater than 2,500 residents, resulting in four county groups. We then calculated scaling coefficients for total wages versus total employment for each of the four categories for the years 1984 to 2020 using the method described in the main text.
Results shown in Figure S6 indicate that, like both CBSA types, each rural county group exhibits a wage premium (unadjusted for local prices), meaning that workers in larger rural counties earn higher average wages than workers in smaller rural counties. Over time all categories of rural counties have followed a trajectory similar to that of micropolitan statistical areas, having declined since the 1990s, until they have all converged to scaling coefficients nearly equal to that of micropolitan areas.