_{1}

^{*}

This paper investigates the inter-county variation of per capita personal income within US states from 1969 to 2006. It is a test of the growth pole cycles theory of spatial-temporal economic development that combines the theory of growth poles with the theory of long wave cycles. Standard OLS regression analysis is performed using data from the Bureau of Economic. Results indicate that regional income variation increased for the majority of states with no indication of a decrease or convergence of regional incomes.

Income inequality is a dynamic that has long been used as an indicator of economic development and overall societal well-being. A working presumption in most analyses and policy considerations is that a more equal dis- tribution of income is beneficial; a goal worth pursuing. Economic literature is replete with studies into the causes and consequences of rising and falling income inequality; that is, income divergence and convergence.

Of particular interest to the study of regional economics and economic development is spatial inequality of income, or the variation of regional incomes. Perhaps the seminal study in this area, laying the foundation for decades of research that followed, is Williamson [

A subsequent investigation into regional income inequality to the early 1980s using Williamson’s methodol- ogy, is undertaken by Amos [

Others investigating the question of regional income inequality and regional convergence have come up with mixed results and differing explanations. Bishop, Formby and Thistle [

Amos [

The objective of this current research is to extend the limited time period of analysis of regional income in- equality in Amos [

The theory of spatial-temporal social-economic development guiding this research is presented in Amos [

This theory of growth pole cycles synthesizes two extensive bodies of research, one on growth poles empha- sizing the spatial dimension of economic growth (Perroux [

The conventional view of income inequality (both regional and individual) that emerged in the middle of the 20th century was that the progress of economic development traversed the noted Kuznets [

By way of contrast, the theory of growth pole cycles implies that Kuznets invert-U is recurring. Rather than one-time inverted-U pattern, the theory suggests that income divergence is followed by convergence, which is then followed by divergence, then convergence, in a continuing process.

Moreover, the theory indicates that sequential repetition of divergence and convergence fundamentally re- structures the economy and society. Fueled by technological innovations that improve transportation efficiency, the realm of influence and the spatial degree of economic integration, expands with each inverted-U traversed. While one particular growth pole centered in the economic “capitol” of a nation might achieve dominance (such as New York in the 20th century, London in the 19th century, and Paris in the 18th century), the global economy invariably contains a multitude of growth poles with differing degrees of spatial influence, each traversing its own series of recurring inverted-U patterns of divergence and convergence. At any given time, the global economy is likely to see a dominant pole; two or more older, secondary growth poles that had previously domi- nated the global scene; and one or more newer growth poles, but still of secondary influence, that are candidates for eventually coming to dominate the global economy.

These assorted growth pole influences are coordinated to the extent that the dominant growth pole exerts in- fluence over, and is integrated with, other lesser growth poles. However, the influences are disjointed and con- flicting to the extent that spatial interaction with outlying, peripheral areas is temporally lagged. That is, the par- ticular position of a given locale in the inverted-U might be predominately influenced by the dominated growth pole, but also influenced by one or more secondary growth poles. The degree of divergence or convergence induced by the dominant growth pole might be partially countered by secondary growth poles.

This study employs standard OLS regression techniques to analyze the variation of regional income estimated using data obtained from the Bureau of Economic Analysis (BEA) [

The BEA regularly tabulates and reports total personal income for each of the 3068 counties in the United States. Population estimates are also obtained using decennial Bureau of Census data that are then extrapolated for each year within corresponding decades. Total personal income and population data are then used to estimate per ca- pita income for each county. State data are generated using a similar methodology. These data are obtained for his study through download from the BEA website [

The measure of regional income variation is that initially specified in Williamson [

where V_{w} = the weighted variation of regional income, Y_{i} = per capita personal income in region (county) i of state s, Y_{s} = per capita personal income in state s, p_{i} = population in region (county) i of state s, p_{s} = total popula- tion in state s.

Standard regression analysis is then performed using V_{w} as the dependent variable and assorted independent variables, most notably state per capital income. Time series regression equations are estimated separately for each of the 50 states as well as comprehensive equations for pooled cross-section, time series for all 50 states combined.

Three alternative regression models are estimated:

where: V_{w} is the variation of per capita personal income among the counties in each state weighted by popula- tion of the county, Y = state per capital personal income or year, and CN = the number of counties in the state. Equation (3) is estimated only for pool cross-section time-series data.

Convergence is indicated if b in Equation (1) is negative and significant and/or g in Equations (2) or (3) is negative and significant. Divergence is then indicated if b in Equation (1) is positive and significant and/or g in Equations (2) or (3) is positive and significant. The conventional Kuznets inverted-U is indicated if b is positive and g is negative in Equations (2) and (3). The onset of a “new” inverted-U, with the transition from conver- gence to divergence, is then indicated if b is negative and g is positive in Equations (2) and (3).

Four segments of this curve are highlighted. Segment I, from a to b, is a regional income convergence (b < 0, or b = 0 and g < 0). Segment II, from b to c, captures the minimum and exhibits neither convergence nor diver- gence (b = 0 and g = 0, or b < 0 and g > 0). Segment III, from points c to d, is a regional income divergence (b > 0, or b = 0 and g > 0). And segment IV, from points d to e, captures the peak and also exhibits neither diver- gence nor convergence (b = 0 and g = 0, or b > 0 and g < 0).

This study hypothesizes that the United States, during the time period of analysis, completed the convergence phase exhibited by segment I, crossed over most of segment II, and largely occupied segment III. It is expected that most states operated in segment III, but given that states likely develop at different rates and influenced by alternative growth poles, some states might be, at least partially, in segments I, II, or IV during the study period, as well.

The first analysis is performed on pooled cross-section, time series data using all three regression models. Re- sults of OLS regression estimates of Equations (1), (2), and (3) using state per capital personal income as the primary independent variable are presented in ^{2}s for Equations (1) and (2) are relatively low, but statistically significant, falling in the range of 0.13 to 0.14. Including the county number variable, CN, in Equation (3) increases the adjusted R^{2} to 0.30. The b coefficient for Equation (1) and the g coefficient for Equations (2) and (3) provide support for the hypothesis that regional income variation is positively correlated with income. In that per capital personal income is increasing during the study period of 1969 to 2006, these results indicate that regional income inequality is increasing and diverging, moving up the first leg (or more likely third leg) of a Kuznets inverted-U, presumably in segment III of

The b coefficient for Equation (1) is highly significant. Including the squared value of per capital personal income in Equation (2) reduces the level of significance of the b coefficient well below acceptable criteria, with the primary explanatory power assumed by the g coefficient. These results are echoed with the inclusion of the CN variable in Equation (3). While the b coefficient remains well below accepted significance level, the t-sta- tistic and significance of level of the g coefficient for the squared value of per capital personal income increases notably as does the adjusted R^{2}.

Similar results are obtained using year as the key independent variable, intended to capture a continuing tem- poral trend of development. ^{2}s for Equations (1) and (2) are relatively low, in the range of 0.10 to 0.11, but statistically significant, and the adjusted R^{2} increases in Equ- ation (3) with the inclusion of the CN to 0.25.

The signs and significance levels also provide similar results to

Pooled data are then separated into states, with individual time analyses performed on each to ascertain the pat- tern exhibited for each. Equations (1) and (2) are estimated for each of the 50 states. Results of these estimates provide further support for the conclusion of income divergence and increased regional income inequality. To ascertain the existence of a general positive trend between regional income variation and per capital personal income,

The adjusted R^{2}s of the 43 states demonstrating statistically significant values of b > 0 range from a low or 0.15 for Virginia to a high of 0.97 for Michigan. Over half of these states, 23, reveal adjusted R^{2}s of over 0.70.

Equation | Intercept | Per capita personal income(t-statistic) | Per capita personal income squared^{ }(t-statistic) | Number of counties (t-statistic) | Adjusted R^{2} (F-statistic) |
---|---|---|---|---|---|

(1) | 0.1338 (56.575)^{*} | 0.0021 (17.201)^{*} | 0.134 (295.876)^{*} | ||

(2) | 0.1443 (37.349)^{*} | 0.0006 (1.231) | 0.0000401 (3.476)^{*} | 0.139 (154.845)^{*} | |

(3) | 0.115 (30.854)^{*} | 0.00011 (0.257) | 0.0000564 (5.409)^{*} | 0.000509 (20.902)^{*} | 0.300 (272.589)^{*} |

^{*}Significant at the 0.01 level. Source: Bureau of Economic Analysis, http://www.bea.gov/regional/reis/default.cfm?catable=CA1-3§ion=2 [

Equation | Intercept | Per capita personal income (t-statistic) | Per capita personal income squared (t-statistic) | Number of counties (t-statistic) | Adjusted R^{2} (F-statistic) |
---|---|---|---|---|---|

(1) | −3.206 (−14.597)^{*} | 1.698 (15.366)^{*} | 0.110 (236.125)^{*} | ||

(2) | 113.238 (2.546)^{*} | −115.482 (−2.580)^{*} | 29.479 (2.618)^{*} | 0.113 (121.853)^{*} | |

(3) | 113.644 (2.822)^{*} | −117.928 (−2.859)^{*} | 30.094 (2.901)^{*} | 0.000455 (18.410)^{*} | 0.247 (208.682)^{*} |

^{*}Significant at the 0.01 level. Source: Bureau of Economic Analysis, http://www.bea.gov/regional/reis/default.cfm?catable=CA1-3§ion=2 [

State | Intercept (t-statistic) | Per capita personal income-PCPI (t-statistic) | Adjusted R^{2} (F-statistic) |
---|---|---|---|

Alabama | 0.151 (45.212)^{*} | 0.00010 (4.922)^{*} | 0.386 (24.229)^{*} |

Alaska | 0.160 (19.520)^{*} | 0.00024 (0.648) | −0.016 (0.420) |

Arizona | 0.121 (25.834)^{*} | 0.00157 (5.881)^{*} | 0.476 (34.586)^{*} |

Arkansas | 0.157 (45.375)^{*} | 0.00105 (4.648)^{*} | 0.358 (21.600)^{*} |

California | 0.073 (13.543)^{*} | 0.00532 (21.569)^{*} | 0.926 (465.218)^{*} |

Colorado | 0.160 (69.403)^{*} | 0.00192 (17.826)^{*} | 0.895 (317.779)^{*} |

Connecticut | 0.098 (26.645)^{*} | 0.00346 (25.586)^{*} | 0.946 (654.619)^{*} |

Delaware | 0.128 (33.729)^{*} | 0.00112 (6.336)^{*} | 0.514 (40.141)^{*} |

Florida | 0.148 (47.958)^{*} | 0.00240 (15.341)^{*} | 0.864 (235.353)^{*} |

Georgia | 0.200 (60.726)^{*} | 0.00218 (12.091)^{*} | 0.797 (146.203)^{*} |

Hawaii | 0.071 (11.237)^{*} | 0.00159 (5.204)^{*} | 0.413 (27.078)^{*} |

Idaho | 0.113 (35.680)^{*} | 0.00525 (27.144)^{*} | 0.952 (736.796)^{* } |

Illinois | 0.111 (25.511)^{*} | 0.00272 (13.517)^{*} | 0.831 (182.722)^{*} |

Indiana | 0.092 (44.994)^{*} | 0.00227 (20.301)^{*} | 0.917 (412.150)^{*} |

Iowa | 0.093 (26.778)^{*} | 0.00121 (6.930)^{*} | 0.518 (40.838)^{*} |

Kansas | 0.156 (34.888)^{*} | 0.00364 (15.521)^{*} | 0.866 (240.911)^{*} |

Kentucky | 0.207 (47.265)^{*} | 0.00093 (3.455)^{*} | 0.228 (11.936)^{*} |

Louisiana | 0.169 (20.581)^{*} | 0.00018 (0.347) | −0.024 (0.120) |

Maine | 0.095 (24.008)^{*} | 0.00197 (8.850)^{*} | 0.676 (78.327)^{*} |

Maryland | 0.176 (89.126)^{*} | 0.00130 (15.488)^{*} | 0.866 (239.878)^{*} |

Massachusetts | 0.089 (33.625)^{*} | 0.00214 (19.817)^{*} | 0.914 (392.696)^{*} |

Michigan | 0.132 (58.864)^{*} | 0.00370 (32.439)^{*} | 0.966 (1052.297)^{*} |

Minnesota | 0.186 (61.091)^{*} | 0.00127 (8.878)^{*} | 0.678 (78.815)^{*} |

Mississippi | 0.169 (41.971)^{*} | −0.00019 (−0.691) | −0.014 (0.478) |

Missouri | 0.212 (54.479)^{*} | 0.00161 (7.640)^{*} | 0.608 (58.371)^{*} |

Montana | 0.133 (25.516)^{*} | −0.00050 (−1.570) | 0.038 (2.466) |

Nebraska | 0.103 (18.531)^{*} | 0.00233 (7.969)^{*} | 0.628 (63.511)^{*} |

Nevada | 0.086 (28.179)^{*} | 0.00059 (4.102)^{*} | 0.300 (16.828)^{*} |

New Hampshire | 0.071 (20.201)^{*} | 0.00116 (7.202)^{*} | 0.579 (51.864)^{*} |

New Jersey | 0.110 (37.632)^{*} | 0.00288 (24.860)^{*} | 0.943 (618.031)^{*} |

New Mexico | 0.165 (31.800)^{*} | 0.00273 (8.361)^{*} | 0.651 (69.903)^{*} |

New York | 0.228 (30.140)^{*} | 0.00712 (22.139)^{*} | 0.930 (490.134)^{*} |

North Carolina | 0.168 (57.459)^{*} | 0.00087 (5.300)^{*} | 0.423 (28.091)^{*} |

North Dakota | 0.139 (14.478)^{*} | −0.00047 (−0.850) | −0.008 (0.722) |

Ohio | 0.113 (56.590)^{*} | 0.00136 (13.025)^{*} | 0.820 (169.654)^{*} |

Oklahoma | 0.209 (50.758)^{*} | 0.00003 (0.136) | −0.027 (0.018) |
---|---|---|---|

Oregon | 0.111 (35.999)^{*} | 0.00151 (9.237)^{*} | 0.695 (85.313)^{*} |

Pennsylvania | 0.128 (42.962)^{*} | 0.00353 (23.996)^{*} | 0.940 (575.784)^{*} |

Rhode Island | 0.016 (4.414)^{*} | 0.00300 (17.366)^{*} | 0.890 (301.578)^{*} |

South Carolina | 0.126 (51.171)^{*} | 0.00103 (6.845)^{*} | 0.553 (46.852)^{*} |

South Dakota | 0.151 (36.339)^{*} | 0.00079 (3.318)^{*} | 0.213 (11.009)^{*} |

Tennessee | 0.167 (68.484)^{*} | 0.00115 (8.368)^{*} | 0.651 (70.023)^{*} |

Texas | 0.194 (68.638)^{*} | 0.00168 (11.140)^{*} | 0.769 (124.099)^{*} |

Utah | 0.114 (38.084)^{*} | 0.00312 (16.729)^{*} | 0.883 (279.874)^{*} |

Vermont | 0.075 (29.836)^{*} | 0.00159 (10.642)^{*} | 0.752 (113.254)^{*} |

Virginia | 0.174 (65.562)^{*} | −0.00034 (−2.745)^{*} | 0.150 (7.533)^{*} |

Washington | 0.101 (23.787)^{*} | 0.00460 (22.822)^{*} | 0.934 (520.825)^{*} |

West Virginia | 0.169 (65.618)^{*} | −0.00000 (−0.058) | −0.028 (0.003) |

Wisconsin | 0.126 (51.845)^{*} | 0.00152 (11.950)^{*} | 0.793 (142.804)^{*} |

Wyoming | 0.110 (16.461)^{*} | 0.00534 (15.909)^{*} | 0.872 (253.084)^{*} |

^{*}Significant at the 0.01 level. Data source: Bureau of Economic Analysis, http://www.bea.gov/regional/reis/default.cfm?catable=CA1-3§ion=2 [

Those states with a combination of convergence and divergence are expected to demonstrate little or no cor- relation between per capita personal income and regional income variation (b = 0) or even a negative correlation (b < 0), but with relatively low adjusted R^{2}s. Alternatively, those states with almost exclusive divergence not only demonstrate a positive correlation between per capita personal income and regional income variation (b > 0), but relatively large R^{2} values. The implied hypothesis can be tested with a meta OLS analysis of the statistic- al results obtained from the 50 individual state equations. This analysis demonstrates a direct correlation with state per capita personal income. Three equations are estimated, each regressing one of three statistical values from the 50 individual state equations (adjusted R^{2}, b coefficient, and t-statistic for b) on a simple average of per capita personal income for each state over the 36-year time period. The results are expected to be consistent across all three equations.

In all three meta equations a positive and statistically significant correlation between average state per capita personal income and the dependent variable (adjusted R^{2}, b coefficient, and t-statistic for b) is observed. Ad- justed R^{2}s range from 0.12 and 0.23. All three the meta coefficients are statistically significant at the 0.01 level.

These results confirm the hypothesis that while the level of development in each state might vary, overall the states are moving through a similar pattern of convergence then divergence, albeit at different times. A small number of the states appear to contain a significant degree of convergence at the beginning of the analysis pe- riod, but most have traversed well into divergence. A number of the states reveal virtually no indication of di- vergence in the study period.

Further evidence of the pattern of convergence/divergence is obtained with OLS regression of Equation (2) for each of the 50 states. These results are presented in

The alternative set of signs with b > 0 and g < 0 for divergence turning to convergence is exhibited in 24 of the 50 states. Of these 24 states, 11 exhibit statistically significant values for both b and c, indicating a pattern of divergence that is lessening and may eventually make the transition back to convergence. Another 11 states ex- hibit statistical significance only for the positive b coefficient, indicating minimal if any convergence at work.

Dependent variable | Intercept | Per capita personal income (t-statistic) | Adjusted R^{2} (F-statistic) |
---|---|---|---|

Adjusted R^{2} | −0.475 (−1.776) | 0.06387 (3.593)^{*} | 0.196 (12.910)^{*} |

b coefficient | −0.00249 (−1.581) | 0.000262 (2.823)^{*} | 0.124 (7.968)^{*} |

t-statistic | −18.717 (−2.439) | 1.76487 (3.900)^{*} | 0.225 (15.211)^{*} |

^{*}Significant at the 0.01 level. Data source: Bureau of Economic Analysis, http://www.bea.gov/regional/reis/default.cfm?catable=CA1-3§ion=2 [

And while the remaining 2 states exhibit b > 0 and g < 0, neither coefficient is statistically significant.

Positive values for both coefficients, b > 0 and g > 0, is exhibited in 14 of the 50 states suggesting not only divergence, but divergence at an increasing rate. However, in only one state, Connecticut, are both coefficients statistically significant. In 5 of the 14 states only the positive b coefficient is statistically significant. In 4 states only the positive g coefficient is statistically significant. And in the remaining 4 states, neither coefficient is sta- tistically significant.

Of some importance, none of the 50 states exhibit a set signs with b < 0 and g < 0, negative values for both coefficients, a result that might be expected with any degree of regional income convergence.

Results of the OLS regression estimate of Equation (2) for the 50 states overwhelmingly supports the hypo- thesis that regional income inequality increases within states over the time period of analysis. While a few of the states might be completing the transition from convergence to divergence in the period of study, most of the states exhibit strong evidence of divergence.

Further insight into the patter of convergence or divergence can be achieved by estimating turning points for each state in which Equation (2) has a sign reversal. This indicates which segment of the curve in

Of the 12 states exhibiting a U-shaped set of coefficients (b < 0 and g > 0), 9 have an estimated minimum within the period of study, but only 5 of those have statistical significance for both signs. These 5 states (Ala- bama, Louisiana, Mississippi, Oklahoma, and Virginia) appear to be in segment II of

State | Intercept (t-statistic) | Per capita personal income-PCPI (t-statistic) | Per capita personal income squared-PCPI^{2} (t-statistic) | Adjusted R^{2} (F-statistic) |
---|---|---|---|---|

Alabama | 0.170 (41.433)^{*} | −0.00251 (−4.000)^{*} | 0.000114 (5.748)^{*} | 0.625 (39.416)^{*} |

Alaska | 0.132 (9.546)^{*} | 0.00367 (2.485)^{*} | −0.000085 (−2.390)^{**} | 0.102 (3.093)^{**} |

Arizona | 0.094 (14.895)^{*} | 0.00606 (6.907)^{*} | −0.000137 (−5.262)^{*} | 0.699 (43.959)^{*} |

Arkansas | 0.171 (32.380)^{*} | −0.00168 (−1.953) | 0.000095 (3.259)^{*} | 0.493 (18.996)^{*} |

California | 0.086 (9.273)^{*} | 0.00356 (3.417)^{*} | 0.000043 (1.744) | 0.930 (247.320)^{*} |

Colorado | 0.174 (60.444)^{*} | −0.00002 (−0.071) | 0.000048 (5.946)^{*} | 0.946 (328.183)^{*} |

Connecticut | 0.111 (19.423)^{*} | 0.00204 (3.802)^{*} | 0.000028 (2.715)^{**} | 0.954 (388.945)^{*} |

Delaware | 0.130 (19.060)^{*} | 0.00088 (1.117) | −0.000006 (−0.308) | 0.431 (19.613)^{*} |

Florida | 0.138 (27.776)^{*} | 0.00381 (6.075)^{*} | −0.000038 (−2.314)^{**} | 0.878 (134.585)^{*} |

Georgia | 0.213 (41.066)^{*} | −0.00052 (−0.069) | 0.000664 (3.055)^{*} | 0.835 (94.687)^{*} |

Hawaii | 0.052 (4.580)^{*} | 0.00431 (2.158)^{*} | −0.000072 (−2.041)^{**} | 0.461 (16.811)^{*} |

Idaho | 0.122 (21.342)^{*} | 0.00376 (4.367)^{*} | 0.000048 (1.762) | 0.955 (391.485)^{*} |

Illinois | 0.095 (12.823)^{*} | 0.00488 (7.224)^{*} | −0.000054 (−2.587)^{**} | 0.853 (242.006)^{*} |

Indiana | 0.084 (24.174)^{*} | 0.00348 (5.851)^{*} | −0.000036 (−1.421) | 0.929 (221.416)^{*} |

Iowa | 0.089 (13.997)^{*} | 0.00184 (2.153)^{**} | −0.000018 (−0.755) | 0.213 (20.459)^{*} |

Kansas | 0.141 (19.041)^{*} | 0.00591 (6.151)^{*} | −0.000064 (−2.425)^{**} | 0.882 (139.727)^{*} |

Kentucky | 0.216 (28.545)^{*} | −0.00077 (−0.658) | 0.000055 (1.488) | 0.253 (7.277)^{*} |

Louisiana | 0.201 (16.399)^{*} | −0.00567 (−3.088)^{*} | 0.000191 (3.282)^{*} | 0.194 (5.463)^{*} |

Maine | 0.085 (12.998)^{*} | 0.00366 (3.908)^{*} | −0.000051 (−1.856) | 0.697 (43.543)^{*} |

Maryland | 0.176 (52.080)^{*} | 0.00121 (3.383)^{*} | 0.000002 (0.256) | 0.862 (116.859)^{*} |

Massachusetts | 0.085 (19.403)^{*} | 0.00263 (5.756)^{*} | 0.000010 (−1.093) | 0.914 (198.007)^{*} |

Michigan | 0.133 (31.093)^{*} | 0.00361 (6.504)^{*} | 0.000003 (0.176) | 0.965 (512.003)^{*} |

Minnesota | 0.184 (34.349)^{*} | 0.00155 (2.439)^{**} | −0.000007 (−0.448) | 0.670 (38.633)^{*} |

Mississippi | 0.194 (38.662)^{*} | −0.00523 (−5.990)^{*} | 0.000185 (5.927)^{*} | 0.479 (18.030)^{*} |

Missouri | 0.213 (30.221)^{*} | 0.00140 (1.449) | 0.000006 (0.219) | 0.597 (28.437)^{*} |

Montana | 0.151 (17.399)^{*} | −0.00366 (−2.927)^{*} | 0.000010 (2.602)^{**} | 0.171 (4.817)^{**} |

Nebraska | 0.116 (12.036)^{*} | 0.00024 (0.190) | 0.000058 (1.686) | 0.646 (34.803)^{*} |

Nevada | 0.087 (15.772)^{*} | 0.00023 (0.362) | 0.000009 (0.570) | 0.286 (8.418)^{*} |

New Hampshire | 0.061 (11.064)^{*} | 0.00262 (4.029)^{*} | −0.000036 (−2.311)^{**} | 0.624 (31.732)^{*} |

New Jersey | 0.094 (25.135)^{*} | 0.00489 (12.931)^{*} | −0.000043 (−5.455)^{*} | 0.969 (570.704)^{*} |

New Mexico | 0.144 (18.136)^{*} | 0.00658 (5.423)^{*} | −0.000128 (−3.262)^{*} | 0.724 (49.631)^{*} |

New York | 0.234 (17.725)^{*} | 0.00636 (4.483)^{*} | 0.000174 (0.551) | 0.928 (240.482)^{*} |

North Carolina | 0.164 (32.456)^{*} | 0.00161 (2.1789)^{**} | −0.000023 (−1.035) | 0.424 (14.609)^{*} |

North Dakota | 0.131 (7.541)^{*} | 0.00083 (0.348) | −0.000038 (−0.563) | −0.027 (0.512) |

Ohio | 0.108 (30.202)^{*} | 0.00216 (4.534)^{*} | −0.000023 (−1.714) | 0.829 (90.861)^{*} |

Oklahoma | 0.228 (38.328)^{*} | −0.00314 (−3.775)^{*} | 0.000097 (3.936)^{*} | 0.268 (7.757)^{*} |
---|---|---|---|---|

Oregon | 0.116 (20.278)^{*} | 0.00079 (1.029) | 0.000021 (0.974) | 0.695 (43.069)^{*} |

Pennsylvania | 0.121 (23.610)^{*} | 0.00443 (6.913)^{*} | −0.000024 (−1.445) | 0.941 (297.632)^{*} |

Rhode Island | 0.027 (4.925)^{*} | 0.00126 (1.833) | 0.000046 (2.631)^{**} | 0.906 (179.045)^{*} |

South Carolina | 0.124 (28.881)^{*} | 0.00143 (2.124)^{**} | −0.000013 (−0.610) | 0.545 (23.203)^{*} |

South Dakota | 0.135 (20.066)^{*} | 0.00342 (3.601)^{*} | −0.000078 (−2.849)^{*} | 0.343 (10.651)^{*} |

Tennessee | 0.178 (52.556)^{*} | −0.00098 (−1.978) | 0.000065 (4.406)^{*} | 0.769 (62.629)^{*} |

Texas | 0.191 (39.000)^{*} | 0.00220 (3.459)^{*} | −0.000015 (−0.853) | 0.767 (61.944)^{*} |

Utah | 0.132 (31.019)^{*} | 0.00004 (0.058) | 0.000101 (4.877)^{*} | 0.928 (240.419)^{*} |

Vermont | 0.055 (22.313)^{*} | 0.00481 (14.456)^{*} | −0.000091 (−9.940)^{*} | 0.933 (259.858)^{*} |

Virginia | 0.189 (62.327)^{*} | −0.00256 (−7.146)^{*} | 0.000056 (6.377)^{*} | 0.596 (28.253)^{*} |

Washington | 0.091 (12.306)^{*} | 0.00598 (6.788)^{*} | −0.000035 (−1.608) | 0.936 (273.167)^{*} |

West Virginia | 0.174 (38.927)^{*} | −0.00112 (−1.552) | 0.000039 (1.501) | 0.013 (1.250) |

Wisconsin | 0.134 (31.609)^{*} | 0.00040 (0.717) | 0.000031 (2.081)^{**} | 0.811 (90.170)^{*} |

Wyoming | 0.146 (15.602)^{*} | 0.00062 (0.589) | 0.000112 (4.606)^{*} | 0.918 (208.214)^{*} |

^{**}Significant at the 0.05 level. ^{*}Significant at the 0.01 level. Data Source: Bureau of Economic Analysis, http://www.bea.gov/regional/reis/default.cfm?catable=CA1-3§ion=2 [

Contrary to conventional wisdom and expectations of neoclassical economic theory, the equilibrium conver- gence of regional incomes is not a foregone conclusion. The convergence of regional income is only part of a more complex process of unbalanced regional or spatial growth, a process that provides the engine for national and global economic growth and development.

The pattern of increasing regional income equality identified here is consistent with other evidence of in- creasing income inequality. The inequality of personal income has been increasing in recent decades. The ratio of income received by the wealthiest 1% compared to the bottom 25% is increasing. The ratio of CEO salaries relative to workers wages is increasing.

Kuznets postulated the inverted-U hypothesis of divergence, then convergence as a pattern traversed over the course of economic development. Evidence from this analysis indicates that this pattern is largely incomplete. The development process appears to be one of divergence, convergence, then divergence once again. While what might transpire beyond the current pattern of divergence is clearly speculative, there is reason to think that divergence will once again give way to convergence, traversing a second Kuznets inverted-U. Several of the states appear to be on the verge of convergence once again. And in the same why that short-run economic insta- bility is characterized by business cycle expansion, contraction, expansion, and contraction, in repetitive fashion, long-run growth and development may very well be characterized by a repetitive pattern of divergence and con- vergence. The difficulty, of course, is that documenting such a pattern requires not merely years of date, but centuries of data, data that are unlikely to exist for some time to come.

However, to the degree that the pattern of regional income variation supports the underlying process of unba- lanced growth as outlined by the growth pole cycles theory, then other implications are worth noting. One is the relative importance of alternative political ideologies, with conservative views tending to dominate during pe- riods of increasing regional income inequality. A second is the structural transition of socio-economic institu- tions associated with an economic and financial depression that transpires as society and the economy reorients from divergence and increasing inequality to convergence and decreasing inequality. The theoretical timing would place this near the end of the third decade of 21^{st} century.

State | Estimated minimum/maximum per capita personal income | Estimated minimum/ maximum year | Segment in |
---|---|---|---|

Alabama | 11,009 | 1971/2 | II |

Alaska | 21,588 | 1989 | IV |

Arizona | 22,117 | 1997/8 | IV |

Arkansas | 8842 | 1982 | II |

California | - | - | III |

Colorado | 200 | <1969 | III |

Connecticut | - | - | III |

Delaware | 73,333 | >2006 | III |

Florida | 50,132 | >2006 | III |

Georgia | 392 | 1973 | III |

Hawaii | 29,931 | >2006 | IV |

Idaho | - | <1969 | III |

Illinois | 45,185 | >2006 | III |

Indiana | 48,333 | >2006 | III |

Iowa | 51,111 | >2006 | III |

Kansas | 46,172 | >2006 | III |

Kentucky | 7000 | 1982 | III |

Louisiana | 14,843 | 1987 | II |

Maine | 35,882 | >2006 | III |

Maryland | - | - | III |

Massachusetts | 23,744 | 1991 | III |

Michigan | - | - | III |

Minnesota | 110,714 | >2006 | III |

Mississippi | 14,135 | 1992 | II |

Missouri | - | - | III |

Montana | 183,000 | >2006 | II |

Nebraska | - | - | III |

Nevada | - | - | III |

New Hampshire | 36,389 | 2004 | III |

New Jersey | 56,860 | >2006 | III |

New Mexico | 25,703 | 2004 | III |

New York | - | - | III |

North Carolina | 35,000 | >2006 | III |

North Dakota | 10,921 | 1982 | II |

Ohio | 46.957 | >2006 | III |

Oklahoma | 16,186 | 1990 | II |
---|---|---|---|

Oregon | - | <1969 | III |

Pennsylvania | 92,292 | >2006 | III |

Rhode Island | - | - | III |

South Carolina | 55,000 | >2006 | III |

South Dakota | 21,923 | 1997 | III |

Tennessee | 7538 | 1979 | II |

Texas | 73,333 | >2006 | III |

Utah | - | >2006 | III |

Vermont | 26,429 | 1998/9 | IV |

Virginia | 22,857 | 1993 | II |

Washington | 85,429 | >2006 | III |

West Virginia | 14,359 | 1990 | II |

Wisconsin | - | - | III |

Wyoming | - | - | III |

A positive correlation between per capita personal income and regional income variation is clearly indicated by the results. Similar results are obtained using time as a dependent variable. Evidence strongly supports the hy- pothesis of increasing regional income inequality or the divergence leg of Kuznets inverted-U.

Comparable results are obtained with OLS regression estimates for each of the 50 states. With both linear and quadratic equations estimated using per capita personal income as the dependent variable, the vast majority of states (36) exhibit clear divergence of regional incomes, falling in segment III of

A meta analysis of the state coefficients generated with the simple linear model regressed against average per capital personal income provides greater insight into the underlying process. The meta analysis indicates that the statistically significant degree of divergence is itself dependent on the average per capita personal income in a state. That is, more prosperous, higher income states also exhibit a more distinct connection and correlation be- tween per capita personal income and regional income inequality. The implication is that some states lag behind other states in the transition from convergence to divergence and onto full blow divergence.

Clearly convergence, divergence, and transition from one to the other are not a ubiquitous process expe- rienced equally and simultaneously by all states or all regions within the United States. In the same way that the shockwaves of an earthquake diffuse outward from the epicenter affecting different points at different times, so too the process underlying the convergence and divergence of incomes affects some regions and states sooner than others.

Most pointedly, the spatial dimension of economic development and unbalanced growth is still not fully un- derstood. It remains murky in most theoretical analysis and marginally incorporated in most empirical studies. However, as suggested by the results of this analysis, the spatial dimension is critical to the process.