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The impact of population agglomeration of an area on its neighbors: evidence from the USA

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Abstract

Regions with high population agglomeration have always been important centers of growth throughout history. However, little is known about the economic spillovers an agglomerated region produces on its neighboring areas. In this paper, I look at the effect of growth of an agglomerated county on its surrounding non-agglomerated counties, by using the methods outlined in Qu and Lee (J Econom 184(2):209–232, 2015) and Qu et al. (Econom J 19(3):261–290, 2016). I use the US county as the geographic unit of analysis. The results show that the impact of is inverted U-shaped—at low levels of per capita income of an agglomerated county, growth has a positive impact on the neighboring non-agglomerated counties, relative to non-agglomerated counties that do not have any agglomerated counties nearby. However, as the agglomerated county gets richer, its relationship with the neighboring non-agglomerated county becomes negative, relative to the growth rate of a non-agglomerated county that has no agglomerated county nearby.

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Notes

  1. The numbers are further illustrated in Table 2 of the paper.

  2. I first define a county to be agglomerated if it has more than 1000 people per square mile. In robustness tests, I relax this assumption and define an agglomerated county as one with more than 500, 1500, 2000, and 2500 people per square mile, respectively.

  3. These numbers were obtained from the “American FactFinder” of the Census Bureau. https://factfinder.census.gov/faces/nav/jsf/pages/index.xhtml.

  4. “2017 US Gazetteer Files” US Census Bureau. https://www2.census.gov/geo/docs/maps-data/data/gazetteer/2017_Gazetteer/2017_gaz_place_04.txt.

  5. “Historical Statistical Area Delineations.” The Census Bureau. 2015 http://www.census.gov/population/metro/data/pastmetro.html.

  6. Barrow, Bartow, Butts, Carroll, Cherokee, Clayton, Cobb, Coweta, Dawson, DeKalb, Douglas, Fayette, Forsyth, Fulton, Gwinnett, Haralson, Heard, Henry, Jasper, Lamar, Meriwether, Morgan, Newton, Paulding, Pickens, Pike, Rockdale, Spalding, and Walton Counties constitute the Atlanta Metropolitan Statistical Area (“Metropolitan and Micropolitan Delineation Files”, The Census Bureau, 2015. http://www.census.gov/population/metro/data/def.html).

  7. Data from “American FactFinder” Census Bureau.

  8. The 1970 data are from “Table 1: Place of Work of Workers During the Census Week by Means of Transportation to Work: 1970,” retrieved from the 1970 Decennial Census. The 1990 data are from “Table 1: 1990 County-to-County Commuting Flows for the United States and Puerto Rico”. The 2010 data are from “Table 1: 2009–2013 County-to-County Commuting Flows for the United States and Puerto Rico.” The 1990 and 2009–2013 data are from https://www.census.gov/topics/employment/commuting/guidance/flows.html. The numbers in 1970 only include the number of people traveling for work to metropolitan counties with more than 250,000 people.

  9. A referee pointed out that adding the squared term would not allow for proper identification. This is because in a spatial model of the form: \( Y_{I} = a + bX_{i} + rWY_{i} + \varepsilon_{i} \), where W is a square weight matrix, the identification is dependent upon the invertibility of matrix (\( I - rW \)). Under the current setup, this is not possible. However, in this case, I treat Eq. (2) as already in reduced from, and I model vector y is as different from the vector G (y includes the income per capita of non-agglomerated counties, and G includes the income per capita of agglomerated counties that are near the non-agglomerated counties, similar to what Qu et al. (2016) have done). Additionally, I will be using instrumental variables and a GMM setup to estimate the coefficients, which allows for estimating the coefficients.

  10. Such variables are measuring the role of amenities to attract people to a region (Roback 1982).

  11. \( {\text{Var}}(\varepsilon_{it} |\nu_{it} ) = {\text{Var}}(\phi \nu_{it} + \xi_{it} |\nu_{it} ) \), and since \( \nu_{it} \) is uncorrelated with \( \xi_{it} \), and \( \phi = \chi_{\upsilon }^{ - 1} \sigma_{\varepsilon \nu } , \) then \( {\text{Var}}\left( {\varepsilon_{it} |\nu_{it} } \right) = {\text{Var}}\left( {\chi_{\upsilon }^{ - 1} \sigma_{\varepsilon \nu } \nu_{it} } \right) + {\text{Var}}\left( {\xi_{it} |\nu_{it} } \right) \)

    \( \Rightarrow \sigma_{\varepsilon }^{2} = {\text{Var}}\left( {\chi_{\upsilon }^{ - 1} \sigma_{\varepsilon \nu } \nu_{it} } \right) + \sigma_{\xi }^{2} \)

    \( \Rightarrow \sigma_{\varepsilon }^{2} = \chi_{\upsilon }^{ - 1} \sigma_{\varepsilon \nu } \chi_{\upsilon } \chi_{\upsilon }^{ - 1} \sigma_{\varepsilon \nu } + \sigma_{\xi }^{2} = \sigma_{\varepsilon \nu } \chi_{\upsilon }^{ - 1} \chi_{\upsilon } \chi_{\upsilon }^{ - 1} \sigma_{\varepsilon \nu } + \sigma_{\xi }^{2} \)

    \( \Rightarrow \sigma_{\xi }^{2} = \sigma_{\varepsilon }^{2} - \sigma_{\varepsilon \nu } \chi_{\upsilon }^{ - 1} \sigma_{\varepsilon \nu } \), making \( \sigma_{\xi }^{2} \) a scalar and a constant, which makes the error term \( \xi \) is homoscedastic and uncorrelated with ln(pop) variable.

  12. QWL (2016) suggests using the first and second lags of the first difference of each of the regressors as instruments to estimate the coefficients. Since I added a lagged dependent variable, I am also adding the second and third lags of the first difference of ln(pop) as instruments.

  13. “State Maps with Counties & Climate Divisions” NOAA. 2015 http://www.cpc.ncep.noaa.gov/products/analysis_monitoring/regional_monitoring/CLIM_DIVS/states_counties_climate-divisions.shtml.

  14. In the first-stage regression, the dependent variable is the natural log of population, and the regressors are the 10-year lag of natural log of population, proportion with high school or higher degree, proportion non-white, poverty headcount rate, unemployment rate, average January temperature, and average July temperature. The instrument set is listed in the model section.

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  1. Department of Economics, Elon University, 100 Campus Drive, Elon, NC, 27244, USA

    T. M. Tonmoy Islam

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Appendix

Appendix

See Tables 8 and 9.

Table 8 First-stage regression
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Table 9 Regression results using weighted average of 10-year lagged agglomerated county’s income per person, and a different first-stage regression
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Islam, T.M.T. The impact of population agglomeration of an area on its neighbors: evidence from the USA. Ann Reg Sci 65, 1–26 (2020). https://doi.org/10.1007/s00168-019-00971-6

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