This paper investigates the variation of per capita personal income among counties within each state from 1969-2013. Department of Commerce BEA data and Department of Labor BLS data for 1969 to 2013 are analyzed. This study follows up on previous analysis of U.S. regional income variation by adjusting time series estimates for serial correction and using random effects models for panel data analysis. In addition, potential short-run disruption of a longer run trend is investigated by including an unemployment rate variable into the model. Results suggest that a general pattern of per capita income divergence has transpired in recent decades, contrary to conventional expectations of convergence.
The spatial distribution of economic activity is a fundamental concern in the study of regional economic analysis. This study dates back at least to the seminal work of Williamson [
However, during the later quarter of the 20th century, evidence began mounting that regional income variation was diverging (Amos [
One objective of this current study is to update data used to document regional income variation within each of the 50 states in Amos [
As noted, previous analysis of regional income variation in the United States (Amos [
The foundation of this analysis of regional income variation is a measure (Vw) first presented by Williamson [
V w = Σ ( Y i − Y ) 2 p i / p Y
where Vw = the weighted variation of regional income, Yi = per capita personal income in county i, Y = per capita personal income of the state, pi = population in county i, and p = total population in the state. This measure is estimated for each state for the period 1969 to 2013. A higher (or increasing) value for Vw indicates greater income inequality (or divergence) and a lower (or decreasing) value indicates lesser inequality (or convergence). And of course, no change in Vw not only indicates a period of stasis but also might suggest a transition from convergence to divergence or divergence to convergence.
Previous studies (Amos [
V w = α + β Y (1)
V w = α + β Y + γ Y 2 (2)
V w = α + β Y + γ Y 2 + φ C N (3)
where: Vw is the variation of per capita personal income among the counties in each state weighted by population of the county, Y = state per capita personal income, and CN = the number of counties in each state. Convergence is indicated if β < 0 in Equation (1) and/or β < 0, γ < 0 in Equation (2). Convergence is also indicated if in Equation (2) β > 0, γ <0, and β < −2γY or if β < 0, γ > 0, and β < −2γY. Divergence is then indicated if β > 0 in Equation (1) and/or β > 0, γ > 0 in Equation (2). Divergence can also be indicated in Equation (2) if β > 0, γ < 0, and β > −2γY or if β < 0, γ > 0 and β > −2γY. Rather than general statements of divergence/convergence for the entire 1969-2013 time period of analysis, some of these conditions determine divergence/convergence based on specific values of per capital income. The number of counties in each state variable has proven consistently significant in previous panel and cross-section analysis (Amos [
γ < 0, and β > −2γY. Stage III (segment c-d) results if β < 0 and γ < 0, or if β > 0, γ < 0, and β < −2γY. And stage IV (segment d-e) is consistent with β < 0, γ > 0, and β < −2γY. It is possible that a given state might be in one stage at the beginning of the time period of analysis, but then move into a different stage before the end of the time period.
While, standard Ordinary Least Squares (OLS) regression techniques were used in the two previous studies (Amos [
Building on the pilot study analysis of regional income variation within regions in Oklahoma (Amos and Ireland [
V w = α + β Y + δ U (4)
V w = α + β Y + γ Y 2 + δ U (5)
V w = α + β Y + γ Y 2 + δ U + φ C N (6)
where: Vw is again the population-weighted variation of per capita personal income among the counties in each state, Y = state per capita personal income, U = state unemployment rate, and CN = the number of counties in each state. As with the baseline analysis, the Equations are initially estimated using OLS and panel estimators, then re-estimated if necessary with a serial correlation adjustment.
The question is whether shorter-run increases in the unemployment rate will counter or reinforce the longer-run development trend. Preliminary analysis of Oklahoma by Amos and Ireland [
The analysis of regional income variation in the United States from 1969-2013 begins with panel data (pooled cross section-time series) for all 50 states. First, panel data are used to estimate Equations (1), (2), and (3) so as to provide a baseline update of Amos [
The quadratic version of the model, Equation (2), estimated when the squared value of per capita income, is added, supports the previous conclusion. The β coefficient is positive and statistically significant and the γ coefficient is negative and not statistically significant with OLS but statistically significant with the random effects model. Previous analysis using the 1969-2006 data range (Amos [
As expected, the inclusion of the number of counties variable is positive and statistically significant. Moreover, per capita income remains positive and statistically insignificant, while per capita income squared changes from negative to positive, but statistically significant in the OLS model. In the random effects model per capita income is significantly positive and per capita income squared remains negative and statistically significant. All forms support the divergence pattern3.
Durbin-Watson coefficients presented for the three estimated Equations in
Equation | Intercept | Per Capita Personal Income (t-statistic) | Per Capita Personal Income Squared (t-statistic) | Number of Counties (t-statistic) | Adjusted R2 | Durbin-Watson |
---|---|---|---|---|---|---|
OLS | ||||||
(1) | 0.141708 (65.71)* | 0.001374 (15.45)* | 0.0956 | 0.0949 | ||
(2) | 0.139969 (41.30)* | 0.001585 (4.81)* | −0.00004 (−0.66) | 0.0954 | 0.0954 | |
(3) | 0.112588 (33.02)* | 0.001249 (4.10)* | 0.000004 (0.80) | 0.000468 (20.00)* | 0.2319 | 0.1068 |
Random Effects | ||||||
(1) | 0.142310 (20.53)* | 0.001345 (33.65)* | 0.0956 | 0.0495 | ||
(2) | 0.137128 (19.50)* | 0.001986 (13.56)* | −0.000013 (−4.54)* | 0.0946 | 0.0500 | |
(3) | 0.107370 (10.37)* | 0.001972 (13.47)* | −0.000013 (−4.48)* | 0.000487 (3.64)* | 0.2272 | 0.0584 |
+Significant at 0.10 level; ^Significant at 0.05 level; *Significant at 0.01 level.
Equation | Intercept | Per Capita Personal Income (t-statistic) | Per Capita Personal Income Squared (t-statistic) | Number of Counties (t-statistic) | Adjusted R2 | Durbin-Watson |
---|---|---|---|---|---|---|
(1) | 0.154951 (20.30)* | 0.000761 (13.52)* | 0.9201 | 2.1128 | ||
(2) | 0.181857 (21.12)* | −0.002352 (−7.47)* | 0.000062 (10.04)* | 0.9237 | 2.0855 | |
(3) | 0.153383 (18.98)* | −0.002567 (−8.47)* | 0.000066 (11.14)* | 0.000497 (13.71)* | 0.9296 | 2.0883 |
+Significant at 0.10 level; ^Significant at 0.05 level; *Significant at 0.01 level.
Once again, including the number of counties in each state has no significant impact on the results. The county variable is statistically significant, as expected, but the signs of the β and γ coefficients remain negative/positive and statistically significant. These findings still indicate divergence.
This second analysis is undertaken using time series data for each of the 50 states. While results from pooled models are useful, certain tests (not reported here) indicate that more valuable information may be obtained by examining states separately. Equation (5) is estimated first using standard OLS regression techniques and subsequently adjusting for serial correlation where needed5.
Preliminary evidence of possible divergence/convergence can be examined via the signs and significance of the regression coefficients in Equation (5). The coefficients of per capita income (β) and per capita income squared (γ) are positive and negative, respectively, and statistically significant in 35 of the 50 states. Three other states (Alabama, Arkansas, and Nevada) exhibit the same positive/ negative set of signs, but no statistically significant coefficients. Rhode Island and South Dakota also exhibit the positive/negative signs, but only the β coefficient for per capita income is statistically significant in each.
The positive/negative coefficients suggests that regional income variation is most likely increasing over the time period of analysis, but beginning to level off, possibly approaching the peak of an inverted-U. Previous analyses in Amos [
Of the remaining 10 states, only 5 have statistically significant values for both coefficients. Mississippi, Montana, North Dakota, and Virginia exhibit statistically significant negative/positive values for β and γ. Colorado has statistically significant positive values for both coefficients. Whereas the first four states might capture a notable portion of pre-1980 convergence before the onset of divergence during the time period of analysis, Colorado might be relatively farther from the inverted-U peak than those states with a negative γ value.
The final 5 states exhibit a mix of negative and positive values for β and γ, with a mix of statistical significance, as well. Georgia and Utah have statistically significant positive β values, but no significance for the positive γ coefficient. Like Colorado, Tennessee exhibits positive/positive values for the coefficients, but while close, neither achieves the minimum accepted standards for statistical significance. Louisiana and Oklahoma have negative/positive coefficient values, like Mississippi, Montana, North Dakota, and Virginia, but only the β coefficient of per capital income for Oklahoma is statistically significant.
The unemployment rate is also in the OLS regression estimates included in
The vast majority of the states, 36, have statistically significant negative δ coefficients for unemployment. This reinforces preceding panel data analysis that higher unemployment disrupts the longer-run divergence trend. Of the
Equation | Intercept | Per Capita Personal Income (t-statistic) | Per Capita Personal Income Squared (t-statistic) | Unemployment Rate (t-statistic) | Number of Counties (t-statistic) | Adjusted R2 | Durbin-Watson |
---|---|---|---|---|---|---|---|
OLS | |||||||
(4) | 0.147326 (38.43)* | 0.001376 (15.48)* | −0.000962 (−1.77)+ | 0.0965 | 0.0929 | ||
(5) | 0.145674 (31.00)* | 0.001569 (4.76)* | −0.000004 (−0.60) | −0.000952 (−1.75)+ | 0.0962 | 0.0933 | |
(6) | 0.117476 (25.79)* | 0.001236 (4.06)* | 0.000005 (0.85) | −0.000810 (−1.61) | 0.000467 (19.99)* | 0.2324 | 0.1046 |
Random Effects | |||||||
(4) | 0.159801 (22.38)* | 0.001358 (34.92)* | −0.003022 (−11.24)* | 0.0911 | 0.0489 | ||
(5) | 0.155054 (21.39)* | 0.001892 (13.24)* | −0.000011 (−3.88)* | −0.002949 (−10.98)* | 0.0906 | 0.0491 | |
(6) | 0.126891 (12.02)* | 0.001880 (13.16)* | −0.000011 (−3.83)* | −0.002927 (−10.90)* | 0.000458 (3.42)* | 0.2226 | 0.0573 |
Serial Correlation | |||||||
(4) | 0.163627 (21.10)* | 0.000879 (15.01)* | −0.001901 (−6.60)* | 0.9216 | 2.1415 | ||
(5) | 0.185917 (21.71)* | −0.001979 (−6.15)* | 0.000056 (9.03)* | −0.001429 (−4.97)* | 0.9245 | 2.1108 | |
(6) | 0.157345 (19.55)* | −0.002251 (−7.25)* | 0.000061 (10.19)* | −0.001194 (−4.31)* | 0.000487 (13.47)* | 0.9301 | 2.1113 |
+Significant at 0.10 level; ^Significant at 0.05 level; *Significant at 0.01 level.
State | Intercept (t-statistic) | Per Capita Personal Income (t-statistic) | Per Capita Personal Income Squared (t-statistic) | Unemployment Rate (t-statistic) | Adjusted R2 | Durbin-Watson |
---|---|---|---|---|---|---|
Alabama | 0.177422 (30.58)* | 0.000693 (1.25) | −0.000003 (−0.24) | −0.00335 (−5.69)* | 0.5589 | 0.6627 |
Alaska | 0.035933 (0.93) | 0.006568 (5.36)* | −0.000107 (−5.24)* | 0.002376 (0.74) | 0.4145 | 1.3673 |
Arizona | 0.105727 (15.84)* | 0.005981 (9.82)* | −0.000128 (−8.68)* | −0.002184 (−2.85)* | 0.7211 | 0.5599 |
Arkansas | 0.169081 (20.87)* | 0.000874 (1.37) | −0.000012 (−0.77) | −0.001406 (−1.37) | 0.1256 | 1.0907 |
California | 0.091784 (7.92)* | 0.006758 (8.91)* | −0.000049 (−3.37)* | −0.003857 (−3.18)* | 0.9308 | 0.5547 |
Colorado | 0.173971 (54.39)* | 0.001141 (4.54)* | 0.000010 (2.08)^ | −0.001408 (−3.02)* | 0.9508 | 1.4929 |
Connecticut | 0.129428 (8.81)* | 0.003845 (5.60)* | −0.000023 (−2.15)^ | −0.005143 (−3.19)* | 0.8836 | 0.5500 |
Delaware | 0.119873 (12.19)* | 0.002558 (3.83)* | −0.000050 (−3.61)* | 0.000082 (0.07) | 0.2379 | 0.7359 |
Florida | 0.146590 (24.12)* | 0.005101 (9.26)* | −0.000079 (−6.60)* | −0.002941 (−4.11)* | 0.8122 | 0.7275 |
Georgia | 0.237884 (27.80)* | 0.001589 (2.11)^ | 0.000021 (1.18) | −0.006503 (−5.99)* | 0.8280 | 0.8424 |
Hawaii | 0.052149 (3.59)* | 0.003005 (3.26)* | −0.000036 (−1.95)+ | 0.001514 (0.84) | 0.4633 | 1.1239 |
Idaho | 0.140431 (15.56)* | 0.009620 (12.47)* | −0.000175 (−8.74)* | −0.007951 (−6.81)* | 0.9137 | 1.0014 |
Illinois | 0.107333 (15.79)* | 0.007402 (13.80)* | −0.000118 (−11.10)* | −0.004847 (−6.43)* | 0.8723 | 0.8557 |
Indiana | 0.090604 (28.34)* | 0.004208 (14.24)* | −0.000059 (−8.32)* | −0.001743 (−5.71)* | 0.9533 | 1.2914 |
Iowa | 0.085548 (13.26)* | 0.002448 (4.75)* | −0.000040 (−3.65)* | 0.000072 (0.07) | 0.4482 | 1.9602 |
Kansas | 0.161759 (19.39)* | 0.008342 (15.04)* | −0.000140 (−11.83)* | −0.008267 (−4.95)* | 0.8805 | 1.1456 |
Kentucky | 0.219737 (23.99)* | 0.003726 (4.25)* | −0.000109 (−4.80)* | −0.003852 (−3.65)* | 0.4767 | 0.4881 |
Louisiana | 0.185270 (15.70)* | −0.001491 (−1.54) | 0.000026 (1.19) | −0.000460 (−0.34) | 0.0219 | 0.7805 |
Maine | 0.108041 (9.68)* | 0.003501 (5.22)* | −0.000055 (−3.60)* | −0.003271 (−2.67)^ | 0.7302 | 0.8379 |
Maryland | 0.192568 (33.14)* | 0.002811 (9.20)* | −0.000034 (−6.39)* | −0.002861 (−3.46)* | 0.8307 | 0.9233 |
Massachusetts | 0.088486 (12.01)* | 0.003458 (9.61)* | −0.000033 (−5.52)* | −0.001398 (−1.70)+ | 0.9089 | 0.3866 |
Michigan | 0.149406 (22.25)* | 0.007135 (12.47)* | −0.000122 (−9.03)* | −0.004112 (−8.66)* | 0.9224 | 0.6201 |
Minnesota | 0.184067 (21.24)* | 0.003176 (6.06)* | −0.000057 (−5.54)* | −0.001842 (−1.46) | 0.4955 | 0.9940 |
Mississippi | 0.192912 (31.75)* | −0.001708 (−2.55)^ | 0.000047 (2.53)^ | −0.002062 (−3.09)* | 0.2765 | 1.1501 |
Missouri | 0.228659 (27.36)* | 0.003959 (6.10)* | −0.000081 (−5.44)* | −0.005116 (−4.82)* | 0.5893 | 1.1995 |
Montana | 0.160189 (11.04)* | −0.002330 (−2.90)* | 0.000046 (2.47)^ | −0.002373 (−1.27) | 0.1409 | 1.2194 |
Nebraska | 0.101962 (7.33)* | 0.0040186 (4.58)* | −0.000073 (−4.02)* | −0.001609 (−0.52) | 0.3268 | 1.2351 |
Nevada | 0.089984 (14.11)* | 0.000546 (1.01) | −0.000003 (−0.30) | −0.000406 (−0.75) | 0.1766 | 0.6785 |
New Hampshire | 0.073901 (11.51)* | 0.002350 (5.78)* | −0.000027 (−3.46)* | −0.002666 (−2.67)^ | 0.7325 | 0.4095 |
New Jersey | 0.116207 (17.56)* | 0.005313 (16.62)* | −0.000059 (−11.03)* | −0.003578 (−5.35)* | 0.9597 | 0.6276 |
New Mexico | 0.162952 (13.26)* | 0.010421 (11.64)* | −0.000274 (−11.75)* | −0.005329 (−3.39)* | 0.7573 | 0.4595 |
New York | 0.272531 (13.47)* | 0.011008 (11.02)* | −0.000111 (−6.37)* | −0.010541 (−4.43)* | 0.9146 | 0.5252 |
North Carolina | 0.171237 (30.25)* | 0.002546 (4.91)* | −0.000052 (−4.07)* | −0.002406 (−3.41)* | 0.4754 | 0.8457 |
North Dakota | 0.162583 (4.41)* | −0.005003 (−3.62)* | 0.000123 (5.05)* | 0.001341 (0.19) | 0.4621 | 1.2623 |
---|---|---|---|---|---|---|
Ohio | 0.112965 (33.66)* | 0.002378 (7.63)* | −0.000026 (−3.66)* | −0.001057 (−3.01)* | 0.8864 | 0.8486 |
Oklahoma | 0.239868 (28.60)* | −0.001410 (−2.03)* | 0.000009 (0.62) | −0.003759 (−2.77)* | 0.4972 | 0.9007 |
Oregon | 0.121124 (16.57)* | 0.002681 (4.79)* | −0.000041 (−3.15)* | −0.002274 (−3.07)* | 0.6344 | 0.7244 |
Pennsylvania | 0.138445 (27.61)* | 0.006237 (18.07)* | −0.000080 (−11.27)* | −0.004243 (−7.60)* | 0.9623 | 0.7083 |
Rhode Island | 0.040790 (4.98)* | 0.002818 (5.37)* | −0.000004 (−0.41) | −0.003395 (−4.17)* | 0.9192 | 0.5591 |
South Carolina | 0.133546 (25.75)* | 0.002085 (4.38)* | −0.000033 (−2.65)^ | −0.002189 (−3.66)* | 0.5976 | 0.7102 |
South Dakota | 0.125080 (12.02)* | 0.001003 (1.71)+ | −0.000005 (−0.47) | 0.006514 (2.79)* | 0.4306 | 1.7036 |
Tennessee | 0.179807 (39.26)* | 0.000639 (1.55) | 0.000015 (1.50) | −0.001541 (−2.99)* | 0.7922 | 0.7501 |
Texas | 0.198903 (36.58)* | 0.004958 (8.87)* | −0.000093 (−7.93)* | −0.005089 (−5.09)* | 0.6614 | 0.9626 |
Utah | 0.115188 (20.70)* | 0.002398 (5.42)* | 0.000010 (0.96) | 0.000958 (1.37) | 0.9488 | 0.6311 |
Vermont | 0.062206 (11.73)* | 0.004564 (15.35)* | −0.000091 (−14.79)* | −0.000861 (−1.29) | 0.8828 | 1.0817 |
Virginia | 0.193958 (52.29)* | −0.001757 (−6.86)* | −0.000037 (7.58)* | −0.002384 (−3.81)* | 0.6169 | 0.7586 |
Washington | 0.116885 (8.13)* | 0.007892 (10.61)* | −0.000103 (−7.20)* | −0.004484 (−3.47)* | 0.9114 | 0.7774 |
West Virginia | 0.180538 (52.31)* | 0.000768 (2.09)^ | −0.000030 (−3.08)* | −0.001738 (−5.72)* | 0.4627 | 0.9677 |
Wisconsin | 0.141757 (28.28)* | 0.001996 (5.27)* | −0.000022 (−2.73)* | −0.003118 (−5.27)* | 0.7930 | 0.7887 |
Wyoming | 0.163662 (11.31)* | 0.009984 (9.11)* | −0.000119 (−6.07)* | −0.018123 (−7.49)* | 0.8562 | 0.7163 |
+Significant at 0.10 level. ^Significant at 0.05 level. *Significant at 0.01 level.
remaining 14 states without statistically significant negative δ coefficients, only one, South Dakota, has a statistically significant positive δ coefficient value. Arkansas, Minnesota, Montana and Vermont have the expected negative δ coefficient values and are close to statistical significance, but fall short of the accepted threshold. In contrast, Utah is also close to statistical significance, while falling short of the accepted threshold, but like South Dakota has a positive unemployment rate coefficient. The remaining 8 states have either positive or negative coefficient values, but are nowhere close to statistical significance.
Adjusting for serial correlation reduces the total number of states that exhibit statistically significant positive/negative values for both β and γ from 35 to 25. This continues to suggest evidence for the possible divergence of regional incomes during the time period of analysis. A dozen additional states also exhibit
State | Intercept (t-statistic) | Per Capita Personal Income (t-statistic) | Per Capita Personal Income Squared (t-statistic) | Unemployment Rate (t-statistic) | Adjusted R2 | Durbin-Watson |
---|---|---|---|---|---|---|
Alabama | 0.178864 (17.24)* | 0.000289 (0.23) | 0.0000006 (0.02) | −0.002690 (−3.28)* | 0.7178 | 2.2015 |
Alaska | 0.080329 (1.66) | 0.005529 (3.38)* | −0.000093 (3.40)* | −0.001173 (−0.29) | 0.4596 | 2.0058 |
Arizona | 0.111346 (8.62)* | 0.004231 (2.36)* | −0.000084 (−1.91)+ | −0.001202 (−1.69)+ | 0.8708 | 1.6126 |
Arkansas | 0.174505 (15.74)* | 0.000656 (0.70) | −0.000008 (−0.35) | −0.001951 (−1.45) | 0.2749 | 2.0559 |
California | 0.086875 (5.11)* | 0.006254 (4.28)* | −0.000042 (−1.59) | −0.002259 (−1.76)+ | 0.9662 | 1.4796 |
Connecticut | 0.123213 (5.78)* | 0.002747 (1.47) | −0.000005 (−0.20) | −0.002387 (−1.63) | 0.9471 | 1.8740 |
Delaware | 0.128007 (9.51)* | 0.002095 (1.91)+ | −0.000040 (−1.81)+ | −0.000695 (−0.52) | 0.5318 | 1.7738 |
Florida | 0.144608 (3.19)* | 0.000102 (−0.04) | 0.000061 (1.50) | −0.001586 (−2.02)^ | 0.9023 | 1.4540 |
Georgia | 0.217441 (13.99)* | 0.002260 (1.29) | −0.000006 (−0.14) | −0.002930 (−1.97)+ | 0.8922 | 1.8031 |
Hawaii | 0.044553 (2.40)^ | 0.002794 (2.01)+ | −0.000032 (−1.18) | 0.003736 (1.59) | 0.5482 | 2.2550 |
Idaho | 0.129047 (9.62)* | 0.009675 (7.64)* | −0.000177 (−5.50)* | −0.006124 (−3.44)* | 0.9336 | 1.9186 |
Illinois | 0.109519 (10.36)* | 0.006834 (6.87)* | −0.000108 (−5.72)* | −0.004188 (−4.05)* | 0.9097 | 1.8619 |
Indiana | 0.090037 (22.43)* | 0.004161 (10.68)* | −0.000058 (−6.26)* | −0.001576 (−4.06)* | 0.9583 | 1.9888 |
Kansas | 0.161228 (16.64)* | 0.008098 (10.17)* | −0.000136 (−8.22)* | −0.007528 (−4.30)* | 0.8985 | 2.1490 |
Kentucky | 0.240158 (10.27)* | −0.000033 (−0.01) | −0.000026 (−0.38) | −0.002082 (−1.67) | 0.7627 | 1.8986 |
Louisiana | 0.206829 (10.33)* | −0.001770 (−0.98) | 0.000028 (0.71) | −0.003013 (−1.62) | 0.3781 | 1.4699 |
Maine | 0.099483 (7.26)* | 0.003252 (2.63)^ | −0.000052 (−1.88)+ | −0.001227 (−0.88) | 0.8080 | 2.0286 |
Maryland | 0.190364 (25.70)* | 0.002883 (6.09)* | −0.000035 (−4.38)* | −0.002600 (−2.72)* | 0.8742 | 1.7470 |
Massachusetts | 0.083472 (8.84)* | 0.003414 (4.97)* | −0.000032 (−2.95)* | −0.000643 (−0.99) | 0.9679 | 1.4935 |
Michigan | 0.148116 (14.88)* | 0.006902 (6.55)* | −0.000116 (−4.73)* | −0.003849 (−6.80)* | 0.9580 | 1.9893 |
Minnesota | 0.185937 (17.15)* | 0.002802 (3.35)* | −0.000051 (−3.17)* | −0.001395 (−0.95) | 0.6036 | 1.9489 |
Mississippi | 0.193744 (22.69)* | −0.002204 (−2.08)^ | 0.000057 (2.02)^ | −0.001559 (−1.58) | 0.3305 | 1.9595 |
Missouri | 0.230277 (22.07)* | 0.003624 (3.91)* | −0.000075 (−3.59)* | −0.004790 (−3.73)* | 0.6281 | 1.9297 |
Montana | 0.147627 (7.07)* | −0.002076 (−1.89)+ | 0.000043 (1.69)+ | −0.000796 (−0.32) | 0.2408 | 2.0692 |
Nebraska | 0.104663 (6.26)* | 0.003651 (3.08)* | −0.000066 (−2.73)* | −0.001426 (−0.39) | 0.4096 | 1.9343 |
Nevada | 0.095164 (10.01)* | 0.000054 (0.05) | 0.000008 (0.42) | −0.000648 (−1.02) | 0.5258 | 1.4937 |
New Hampshire | 0.0666231 (7.07)* | 0.002461 (3.19)* | −0.000028 (−2.08)^ | −0.001459 (−1.90)+ | 0.9046 | 1.7087 |
New Jersey | 0.116808 (13.20)* | 0.004821 (6.18)* | −0.000050 (−3.71)* | −0.003141 (−4.39)* | 0.9786 | 1.8212 |
New Mexico | 0.160577 (7.14)* | 0.005349 (1.92)+ | −0.000137 (−2.01)+ | −0.000676 (−0.58) | 0.9281 | 1.1618 |
New York | 0.255746 (9.51)* | 0.011075 (5.76)* | −0.000114 (−3.58)* | −0.008054 (−3.44)* | 0.9604 | 1.7906 |
North Carolina | 0.170688 (20.49)* | 0.002124 (2.23)^ | −0.000045 (−2.02)^ | −0.001496 (−1.74)+ | 0.6415 | 2.0013 |
North Dakota | 0.137720 (2.94)* | −0.005176 (−2.85)* | 0.000133 (4.14)* | 0.006905 (0.76) | 0.5089 | 1.8541 |
Ohio | 0.116242 (22.08)* | 0.002076 (3.82)* | −0.000019 (−1.61) | −0.00147 (−2.55)^ | 0.9197 | 2.0354 |
---|---|---|---|---|---|---|
Oklahoma | 0.234242 (4.49)* | −0.005425 (−1.84)+ | 0.000136 (2.83)* | −0.003816 (−2.63)* | 0.6880 | 2.0681 |
Oregon | 0.120405 (12.44)* | 0.002713 (2.88)* | −0.000042 (−1.98)+ | −0.002208 (−2.69)* | 0.7762 | 1.6174 |
Pennsylvania | 0.138254 (13.82)* | 0.005404 (5.23)* | −0.000066 (−3.39)* | −0.002738 (−3.24)* | 0.9756 | 1.9218 |
Rhode Island | 0.029192 (2.60)^ | 0.003257 (3.38)* | −0.000017 (−0.92) | −0.001808 (−2.23)^ | 0.9632 | 1.4764 |
South Carolina | 0.137700 (12.81)* | 0.000728 (0.46) | −0.000003 (−0.08) | −0.001052 (−1.58) | 0.7456 | 1.6017 |
Tennessee | 0.179970 (26.45)* | 0.000391 (0.54) | 0.000019 (1.17) | −0.001210 (−1.85)+ | 0.8693 | 2.0811 |
Texas | 0.213632 (6.80)* | 0.000166 (0.08) | 0.000026 (0.64) | −0.004126 (−3.57)* | 0.7830 | 1.8866 |
Utah | 0.113720 (15.80)* | 0.002828 (3.57)* | −0.0000006 (−0.03) | 0.000605 (0.89) | 0.9715 | 1.7463 |
Vermont | 0.067992 (10.72)* | 0.004168 (9.04)* | −0.000082 (−8.42)* | −0.001400 (−1.93)+ | 0.9053 | 2.0014 |
Virginia | 0.184526 (19.42)* | −0.001315 (−1.62) | −0.000022 (1.51)* | 0.000202 (0.31)* | 0.7981 | 1.4725 |
Washington | 0.113308 (7.13)* | 0.007750 (6.74)* | −0.000101 (−4.56)* | −0.003784 (−2.93)* | 0.9423 | 1.7692 |
West Virginia | 0.184733 (29.93)* | 0.000227 (0.31) | −0.000018 (−0.97)* | −0.001679 (−3.73)* | 0.5135 | 1.8867 |
Wisconsin | 0.138937 (17.74)* | 0.001859 (2.46)^ | −0.000023 (−1.46) | −0.002025 (−2.61)^ | 0.8589 | 1.7162 |
Wyoming | 0.155309 (5.52)* | 0.007356 (2.91)* | −0.000076 (−1.80)+ | −0.011150 (−3.50)* | 0.9186 | 1.4629 |
+Significant at 0.10 level; ^Significant at 0.05 level. *Significant at 0.01 level.
the positive/negative coefficient values but lack statistical significance in one or both. Seven of those 12 states, however, have statistically significant β coefficient values. And in three of those 7 states the coefficient of the quadratic term falls just below the accepted level of statistical significance.
Four other states, Alabama, Nevada, Tennessee and Texas, also have a positive/positive coefficient sequence, but none are statistically significant. The remaining 8 states have negative β coefficient values. For Mississippi Montana, North Dakota, and Oklahoma the β coefficient is statistically significant as is the positive γ coefficient value, suggesting that they exhibit a notable amount of convergence in the time period of analysis before possibly undertaking divergence. For the other four states, Florida, Kentucky, Louisiana, and Virginia, neither β nor γ is statistically significant.
Results presented in
Estimated results of Equation (5) of all 50 states using standard OLS, and then after adjusting for serial correlation where needed, are used to determine which stage each state is in based on a comparison of signs for β, γ and the relationship between β and −2γY. Three separate calculations are made: 1) based on per capita income at the beginning of the time period (1969), 2) using an average per capita income for the all years, and 3) then using per capita income at the end of the time period (2013). These results are presented in
Using per capita income at the beginning of the time period (1969), the vast majority of states, 43, exhibit unquestionable divergence with the new inverted U (Stages I or II) using both OLS and serial correlation estimations. Only six states have evidence of convergence (Stages III or IV) at the beginning of the study period (Louisiana, Mississippi, Montana, North Dakota, Oklahoma, and Virginia). One state, Kentucky, provides mixed results with divergence indicated by OLS and convergence with serial correlation estimates.
Similar results are obtained using average per capita income for the 45 years of data. In this case 42 states exhibit unquestionable divergence into the new inverted U using both OLS and serial correlation estimations. North Dakota has evidence of convergence for OLS and divergence for serial correlation estimates. The remaining 7 states exhibit convergence using both OLS and serial correlation. Kentucky (only in the OLS form) and West Virginia are two states diverging using 1969 per capital income that converge using average per capital income. This provides overwhelming evidence that regional income variation increased for the majority of states during the time period of analysis.
Using per capita income for the final year of the study period (2013) provides interesting and unexpected results. Of the 42 states exhibiting divergence using average per capita income, 26 exhibit convergence using 2013 per capita income, again for both OLS and serial correlation estimates. Five additional states (Arkansas, Florida, South Carolina, Texas, and Wisconsin) show signs of convergence after divergence for at least one of the estimation procedures. These results suggest that several states may have passed through a Stage II and are entering a “new” Stage III, which is surprising because the onset of a new Stage III is not expected until on or around 2030.
The onset of a new Stage III is a tentative conclusion at best. It is possible that the observed convergence is but a short-run “blip” in the long-run divergence trend. Although inclusion of the unemployment rate is intended to capture short-run disruption of the long-run regional income variation trend, other forces might be at play. Given that much of the convergence occurs after the post-2007 housing market collapse, subsequent recession, and historic anemic recovery, the unemployment rate alone may not be sufficient to capture the overwhelming severity of this disruption. More study is clearly needed.
State | 1969 | Average 1969-2013 | 2013 |
---|---|---|---|
Alabama | Diverging | Diverging | Diverging |
Alaska | Diverging | Diverging | Converging |
Arizona | Diverging | Diverging | Converging |
Arkansas | Diverging | Diverging | Diverging |
California | Diverging | Diverging | Diverging |
Colorado | Diverging | Diverging | Diverging |
Connecticut | Diverging | Diverging | Diverging |
Delaware | Diverging | Diverging | Converging |
Florida | Diverging | Diverging | Diverging |
Georgia | Diverging | Diverging | Diverging |
Hawaii | Diverging | Diverging | Converging |
Idaho | Diverging | Diverging | Converging |
Illinois | Diverging | Diverging | Converging |
Indiana | Diverging | Diverging | Converging |
Iowa | Diverging | Diverging | Converging |
Kansas | Diverging | Diverging | Converging |
Kentucky | Converging | Converging | Converging |
Louisiana | Converging | Converging | Diverging |
Maine | Diverging | Diverging | Converging |
Maryland | Diverging | Diverging | Converging |
Massachusetts | Diverging | Diverging | Converging |
Michigan | Diverging | Diverging | Converging |
Minnesota | Diverging | Diverging | Converging |
Mississippi | Converging | Converging | Diverging |
Missouri | Diverging | Diverging | Converging |
Montana | Converging | Converging | Diverging |
Nebraska | Diverging | Diverging | Converging |
Nevada | Diverging | Diverging | Diverging |
New Hampshire | Diverging | Diverging | Converging |
New Jersey | Diverging | Diverging | Converging |
New Mexico | Diverging | Diverging | Converging |
New York | Diverging | Diverging | Converging |
North Carolina | Diverging | Diverging | Converging |
North Dakota | Converging | Diverging | Diverging |
Ohio | Diverging | Diverging | Diverging |
---|---|---|---|
Oklahoma | Converging | Converging | Diverging |
Oregon | Diverging | Diverging | Converging |
Pennsylvania | Diverging | Diverging | Converging |
Rhode Island | Diverging | Diverging | Diverging |
South Carolina | Diverging | Diverging | Diverging |
South Dakota | Diverging | Diverging | Diverging |
Tennessee | Diverging | Diverging | Diverging |
Texas | Diverging | Diverging | Diverging |
Utah | Diverging | Diverging | Diverging |
Vermont | Diverging | Diverging | Converging |
Virginia | Converging | Converging | Diverging |
Washington | Diverging | Diverging | Converging |
West Virginia | Diverging | Converging | Converging |
Wisconsin | Diverging | Diverging | Converging |
Wyoming | Diverging | Diverging | Converging |
aBased on serial correlation adjustment results except for Colorado, Iowa, and South Dakota which do not require it.
This study sought to provide an updated and statistically improved investigation into regional income variation among the 50 states. Previous studies suggest that regional income variation began to increase in the mid-1970s, contrary to conventional wisdom that regional income converged in the latter stages of development.
With data updated from 2006 to 2013 and using improved statistical estimation techniques to adjust for serial correlation, the results are overwhelmingly indicative of regional income divergence over the past several decades. These results are consistent using standard OLS regression analysis and after adjusting for serial correlation and reinforce previous analyses that also indicate regional income divergence.
This study also sought to test for the impact of short-run stability, using the unemployment rate, on the long-run divergence trend. Results from a study of Oklahoma suggest that higher unemployment rates negatively impact regional income variation. This initial expectation is clearly confirmed with this analysis.
An unexpected implication from this study is that several states appear to be entering a new period of convergence after an extended period of divergence. While this pattern is consistent with the Growth Pole Cycle theory, the onset of convergence is at least a decade earlier than expected. The convergence onset is clearly a preliminary conclusion and needs additional years of data to determine if this is a short-run aberration or an actual change in the long-run trend. Suspicions of a short-run aberration are supported given that the new convergence coincided with 2007 housing market collapse, subsequent recession, and prolonged recovery. Including the unemployment rate might not have sufficiently captured the short-run impact caused by this disruption.
Evidence of regional income divergence and subsequently support of the Growth Pole Cycle theory has significant implications for social-economic activity in the coming decades. In particular, the Growth Pole Theory suggests that a significant economic and financial collapse is likely 100 years after, and comparable to, the 1930s Great Depression. It further suggests that a period of structural and institutional change is possible as the economy transitions from increasing income inequality (both regional and individual) that corresponds with the emergence of a technology-based industrial pole that benefits small segments of the economy to decreasing income inequality that results from the dispersion of this technology across the rest of the economy. Evidence of increasing regional income inequality is compelling enough that other implications of the Growth Pole Cycle theory should be carefully considered and evaluated.
Amos Jr., O.M. and Ireland, T.C. (2017) An Analysis of Regional Income Variation in the United States: 1969-2013. Modern Economy, 8, 232-248. https://doi.org/10.4236/me.2017.82016