1 Introduction
2 Theoretical framework
2.1 Interaction potentials and urban rings
2.2 City growth as a response to the city’s potentials
3 Descriptive statistics and data sources
3.1 Data sources
3.2 Model variables
Obs | Mean | Std. dev | Min | Max | |
---|---|---|---|---|---|
All cities | |||||
Population change | 5440 | 1251.897 | 5209.542 | − 93,272 | 141,328 |
Relative population change* | 5440 | .0569486 | .1202431 | − .5401025 | 1.652266 |
City size (internal potential) | 5712 | 20,458.29 | 38,859.88 | 360 | 847,073 |
Ring I potential | 5712 | 18,790.06 | 52,148.88 | 0 | 770,599.4 |
Ring II potential | 5712 | 458.9876 | 451.7954 | 0 | 7294.201 |
Ring III potential | 5712 | 4.267941 | 4.108314 | .0017775 | 46.58308 |
Cities with a large potential | |||||
Population change | 2720 | 1643.615 | 6974.423 | − 93,272 | 141,328 |
Relative population change* | 2720 | .07285 | .1361869 | − .1909954 | 1.652266 |
City size (internal potential) | 2856 | 20,653.33 | 51,123.86 | 360 | 847,073 |
Ring I potential | 2856 | 33,792.74 | 70,487.48 | 214.386 | 770,599.4 |
Ring II potential | 2856 | 575.1186 | 510.5488 | 7.340092 | 7294.201 |
Ring III potential | 2856 | 4.733501 | 4.253734 | .2436342 | 46.58308 |
Cities with a small potential | |||||
Population change | 2720 | 860.179 | 2310.642 | − 16,845 | 25,781 |
Relative population change* | 2720 | .0410471 | .0993445 | − .5401025 | 1.081939 |
City size (internal potential) | 2856 | 20,263.24 | 20,173.85 | 368 | 197,787 |
Ring I potential | 2856 | 3787.379 | 4600.06 | 0 | 46,135.33 |
Ring II potential | 2856 | 342.8567 | 347.372 | 0 | 4433.294 |
Ring III potential | 2856 | 3.802381 | 3.90314 | .0017775 | 45.66363 |
3.3 Rising importance of ring potentials
4 Absolute and relative city growth 1810–2010
4.1 Long-term absolute growth
Variables and statistics | All cities | Cities with a small potential | Cities with a large potential |
---|---|---|---|
Intra-city potential,\(\beta_{1}\) | 0.0151*** | 0.0437*** | 0.0117*** |
(0.00281) | (0.00385) | (0.00398) | |
Potential in Ring I,\(\beta_{21}\) | 0.0204*** | 0.0101 | 0.0179*** |
(0.00202) | (0.0182) | (0.00293) | |
Potential in Ring II,\(\beta_{22}\) | 0.991*** | 1.877*** | 0.196 |
(0.270) | (0.228) | (0.442) | |
Potential in Ring III,\(\beta_{23}\) | − 12.13 | − 7.729 | − 55.69 |
(31.62) | (20.28) | (57.65) | |
Number of observations | 5,440 | 2,720 | 2,720 |
4.2 Comparing long-term absolute and relative growth
Variables and statistics | All cities | Cities with a small potential | Cities with a large potential |
---|---|---|---|
ln Intra-city potential,\(\beta_{1}\) | − 0.0147*** | − 0.0374*** | − 0.0412*** |
(0.00424) | (0.00611) | (0.00607) | |
ln Potential in Ring I,\(\beta_{21}\) | 0.0766*** | − 0.0266*** | 0.140*** |
(0.00556) | (0.00595) | (0.00927) | |
ln Potential in Ring II,\(\beta_{22}\) | − 0.0137* | 0.00414 | − 0.0264** |
(0.00773) | (0.00786) | (0.0133) | |
ln Potential in Ring III,\(\beta_{23}\) | − 0.0255*** | − 0.000898 | − 0.00771 |
(0.00801) | (0.00802) | (0.0167) | |
Number of observations | 5,440 | 2,720 | 2,720 |
5 City growth 1810–1910 and 1910–2010
5.1 Absolute growth in the first and the second period
Variables and statistics | 1810–2010 | 1810–1910 | 1910–2010 |
---|---|---|---|
Intra-city potential,\(\beta_{1}\) | 0.0151*** | 0.233*** | − 0.152*** |
(0.00281) | (0.00491) | (0.00847) | |
Potential in Ring I,\(\beta_{21}\) | 0.0204*** | 0.0448*** | 0.0422*** |
(0.00202) | (0.00500) | (0.00532) | |
Potential in Ring II,\(\beta_{22}\) | 0.991*** | − 2.622*** | 2.832*** |
(0.270) | (0.555) | (0.648) | |
Potential in Ring III,\(\beta_{23}\) | − 12.13 | − 150.4** | − 42.91 |
(31.62) | (63.60) | (76.30) | |
Number of observations | 5,440 | 2,720 | 2,720 |
5.2 Relative growth in the first and the second period
Variables and statistics | 1810–2010 | 1810–1910 | 1910–2010 |
---|---|---|---|
ln Intra-city potential,\(\beta_{1}\) | − 0.0147*** | 0.0453*** | − 0.108*** |
(0.00424) | (0.0134) | (0.00798) | |
ln Potential in Ring I,\(\beta_{21}\) | 0.0766*** | 0.0453*** | 0.143*** |
(0.00556) | (0.0118) | (0.0147) | |
ln Potential in Ring II,\(\beta_{22}\) | − 0.0137* | − 0.0684*** | 0.0446** |
(0.00773) | (0.0160) | (0.0183) | |
ln Potential in Ring III,\(\beta_{23}\) | − 0.0255*** | 0.0454*** | 0.00656 |
(0.00801) | (0.0157) | (0.0196) | |
Number of observations | 5,440 | 2,720 | 2,720 |
6 Development of cities with a small overall potential
6.1 Absolute growth of cities with a small overall potential in two periods
Variables and statistics | 1810–2010 | 1810–1910 | 1910–2010 |
---|---|---|---|
Intra-city potential,\(\beta_{1}\) | 0.0437*** | 0.0901*** | 0.00157 |
(0.00385) | (0.01000) | (0.00801) | |
Potential in Ring I,\(\beta_{21}\) | 0.0101 | − 0.122*** | 0.0904** |
(0.0182) | (0.0464) | (0.0423) | |
Potential in Ring II,\(\beta_{22}\) | 1.877*** | − 3.435*** | 3.276*** |
(0.228) | (0.891) | (0.448) | |
Potential in Ring III,\(\beta_{23}\) | − 7.729 | − 258.2*** | − 17.91 |
(20.28) | (72.51) | (43.75) | |
Number of observations | 2,720 | 1,360 | 1,360 |
6.2 Relative growth of cities with a small overall potential in two periods
Variables and statistics | 1810–2010 | 1810–1910 | 1910–2010 |
---|---|---|---|
ln Intra-city potential,\(\beta_{1}\) | − 0.0374*** | − 0.0256 | − 0.0746*** |
(0.00611) | (0.0170) | (0.0122) | |
ln Potential in Ring I,\(\beta_{21}\) | − 0.0266*** | − 0.0381*** | 0.0347** |
(0.00595) | (0.0124) | (0.0137) | |
ln Potential in Ring II,\(\beta_{22}\) | 0.00414 | 0.0168 | 0.0383** |
(0.00786) | (0.0158) | (0.0165) | |
ln Potential in Ring III,\(\beta_{23}\) | − 0.000898 | 0.0755*** | 0.0192 |
(0.00802) | (0.0153) | (0.0166) | |
Number of observations | 2,720 | 1,360 | 1,360 |
7 Growth of cities with a large overall potential
7.1 Absolute growth in the first and second period for cities with a large potential
Variables and statistics | 1810–2010 | 1810–1910 | 1910–2010 |
---|---|---|---|
Intra-city potential,\(\beta_{1}\) | 0.0117*** | 0.259*** | − 0.183*** |
(0.00398) | (0.00607) | (0.0124) | |
Potential in Ring I,\(\beta_{21}\) | 0.0179*** | 0.0423*** | 0.0436*** |
(0.00293) | (0.00632) | (0.00765) | |
Potential in Ring II,\(\beta_{22}\) | 0.196 | − 1.632** | 0.943 |
(0.442) | (0.780) | (1.091) | |
Potential in Ring III,\(\beta_{23}\) | − 55.69 | 10.63 | − 161.8 |
(57.65) | (102.3) | (138.7) | |
Number of observations | 2,720 | 1,360 | 1,360 |
7.2 Relative growth in the first and second period for cities with a large potential
Variables and statistics | 1810–2010 | 1810–1910 | 1910–2010 |
---|---|---|---|
ln Intra-city potential,\(\beta_{1}\) | − 0.0412*** | 0.0878*** | − 0.141*** |
(0.00607) | (0.0193) | (0.0113) | |
ln Potential in Ring I,\(\beta_{21}\) | 0.140*** | 0.229*** | 0.193*** |
(0.00927) | (0.0233) | (0.0255) | |
ln Potential in Ring II,\(\beta_{22}\) | − 0.0264** | − 0.192*** | 0.0116 |
(0.0133) | (0.0370) | (0.0323) | |
ln Potential in Ring III,\(\beta_{23}\) | − 0.00771 | − 0.106** | − 0.0118 |
(0.0167) | (0.0491) | (0.0397) | |
Number of observations | 2,720 | 1,360 | 1,360 |