Using the US states over the period 1929-2012, this paper has examined two of Alonso’s five bells with a particular focus on their space-time co-evolution.
Application of exploratory space-time analytics reveals that the patterns of social, or interpersonal, and regional, or interregional, inequality are complex
and display characteristics that were not considered in Alonso’s original stylized model. Interpersonal inequality displayed a U-pattern resulting in levels of inequality at the end of the period actually exceeding the alarmingly high values found in the 1920’s. By contrast, interregional income inequality between the US states has displayed a general decline up until the end of this period where convergence has slowed or even reversed.
In addition to the differences in the overall trends for the two types of inequality, their distributional dynamics are also found to be distinct with social inequality exhibiting greater mobility than interregional inequality, meaning that states move across the quintiles of the social inequality distri-bution more frequently than they do in the per capita income distridistri-bution.
The spatial patterns of these movements are also differentiated as per capita incomes are strongly spatially autocorrelated each year in the sample, while global spatial dependence is never found for social inequality. A local analysis, however, reveals evidence of pockets of hot and cold spots for inter-regional inequality, as well as spatial outliers for social inequality. Finally, spatial Markov tests reveal that the transitional dynamics for both series are not independent of the local context for a state economy as the estimated transition probability matrices for both social and interregional income in-equality are found to be significantly different across regimes defined on the spatial lag of each series.
Alongside the distinct spatial patterns of interregional and interpersonal inequality are pronounced temporal differences in the spatial distribution of interpersonal inequality. The two periods of high interpersonal inequal-ity, the 1920’s and the post 1980 era, have substantially different spatial distributions with the latter distribution characterized by a spatial homog-enization of high personal income inequality, while in the former period high interpersonal income inequality is more spatially concentrated along the northeastern and western states.
This homogenization of interpersonal income inequality has also coin-cided with a reversal of a long running trend towards regional income con-vergence. The causes of this reversal and its association with increasing interpersonal income inequality are poorly understood. Fan and Casetti (1994) argue that the Rustbelt-Sunbelt shift dominated the US economic landscape up until the late 1960s and was a major force in driving regional income convergence. Subsequently, sectoral shifts reflected in the loss of manufacturing jobs and their replacement with lower paying service resulted in a hollowing out of the personal income distribution. They suggest that the spatial impact of this restructuring may have been uneven with new service and financial sector growth being more prevalent in the traditional
core.
In addition to deindustrialization, fiscal policies and political decentral-ization associated with the Reagan administration have been suggested as possible causes for increasing interregional inequality. Coughlin and Man-delbaum (1988) found that defense expenditures during the Reagan admin-istration were spatially biased towards high income states and away from low income states, increasing interstate inequality.
The decentralization associated with Reagan’s New Federalism gave in-dividual states more freedom to shape economic development policies. De-centralization could have led to greater spatial inequalities through a va-riety of mechanisms such as lost economies of scale in addressing concen-trated poverty and differences in institutional capacities and resources across regions, although the relationship between decentralization and spatial in-equality may vary depending on the level of development of a nation (Rodr´ıguez-Pose and Ezcurra, 2010).
At the same time, the trend towards spatially ubiquitous levels of high personal income inequality uncovered in the latter period of this study may suggest that policies at the national level, such as tax reforms (Stiglitz, 2014), and macroeconomic events, including the great recession, financial meltdown and housing market implosion, have had global effects resulting in greater inequality due to declining real incomes at the bottom and middle of the income distribution and the rise of private debt in the form of loans leveraging ephemeral house price increases (Essletzbichler, 2015; Galbraith, 2012).
Although the housing market bubble appeared to have global impacts in terms of increasing interpersonal income inequality, there is some evidence to suggest that it may have also slowed regional convergence. Ganong and Shoag (2015) argue that high housing costs in high income regions worked to dampen migration of low wage workers from poor to richer regions due to the price sensitivity of low income workers. This reduced the labor and human capital reallocation process that historically had been an engine of regional convergence in the US. In short, the returns to residing in productive regions net of housing costs have moved in opposite directions attracting skilled works but diverting in-migration of unskilled workers. The housing bubble and housing regulations are the argued causes of these house price changes.
The joint consideration of interpersonal inequality and interregional in-equality reveals insights that could have implications for regional economic development polices. The greater mobility in interpersonal inequality, rela-tive to average state incomes, suggests that polices may have more impact on reducing (or increasing) inequality within states than they do on relative
state income growth. At the same time, the strong evidence of spatial depen-dence in the dynamics of both inequality series implies that states should not be considered independent actors as policies adopted by one state may have spillover impacts into neighboring states. Taking these policy spillovers into account would argue for a national or regional perspective on state economic development policies.
Application of exploratory space-time methods is a first step towards the call for the “simultaneous consideration” (Alonso, 1980, p 5) of interpersonal and interregional income inequality dynamics, and a more complete under-standing of the dynamics of different types of inequality and their interde-pendencies. The empirical patterns uncovered here need to be considered from the lenses of existing regional inequality theory and personal income inequality theory with an eye towards their integration. Additionally, from a methodological point of view, the role of spatial context in the dynamics of both social and regional inequality need to be taken into account in future econometric work.
References
Alonso, W. (1980). Five bell shapes in development. Papers in Regional Science, 45(1):5–16.
Amos Jr., O. (1983). The relationship betwen personal income inequality, regional income inequality, and development. Regional Science Perspec-tives, 13:3–14.
Amos Jr., O. (1988). Unbalanced regional growth and regional income in-equality in the latter stages of development. Regional Science and Urban Economics, 18:549–566.
Andersson, M., Klaesson, J., and Larsson, J. P. (2014). The sources of the urban wage premium by worker skills: Spatial sorting or agglomeration economies? Papers in Regional Science, 93(4):727–747.
Anselin, L. (1995). Local indicators of spatial association-LISA. Geograph-ical Analysis, 27(2):93–115.
Barro, R. J. and Sala-i Martin, X. (1991). Convergence across states and regions. Brookings Papers on Economic Activity, 1991(1):107–182.
Bernard, A. and Jones, C. (1996). Productivity and convergence across us states and industries. Empirical Economics, 21:113–135.
Bickenbach, F. and Bode, E. (2003). Evaluating the Markov property in studies of economic convergence. International Regional Science Review, 26(3):363–392.
Bowles, S., Durlauf, S. N., and Hoff, K. (2008). Poverty Traps. Princeton University Press, Princeton.
Breau, S. (2007). Income inequality across Canadian provinces in an era of globalization: explaining recent trends. The Canadian Geographer, 51(1):72–90.
Card, D. and DiNardo, J. E. (2002). Skill biased technological change and rising wage inequality: some problems and puzzles. Journal of Labor Economics, 20(4):733–783.
Chakravorty, S. (1996). Urban inequality revisited - The determinants of income distribution in U.S. metropolitan areas. Urban Affaris Review, 31:759–777.
Chatterji, M. and Dewhurst, J. H. L. L. (1996). Convergence clubs and relative economic performance in Great Britan. Regional Studies, 30:31–
40.
Coughlin, C. C. and Mandelbaum, T. B. (1988). Why have state per-capita incomes diverged recently? Review of the Federal Reserve Bank of St.
Louis, 70:24–36.
Easterlin, R. (1960). Regional growth of income. In Kuznets, S., Miller, A., and Easterlin, R., editors, Population redistribution and economic growth in the United States, 1870-1950. American Philosophical Society, Philadelphia.
Essletzbichler, J. (2015). The top 1% in US metropolitan areas. Applied Geography, 61:35–46.
Fan, C. C. and Casetti, E. (1994). The spatial and temporal dynamics of US regional income inequality, 1950–1989. The Annals of Regional Science, 28(2):177–196.
Frank, M. W. (2009). Inequality and growth in the United States: Evidence from a new state-level panel of income inequality measures. Economic Inquiry, 47(1):55–68.
Galbraith, J. K. (2012). Inequality and instability: A study of the world economy just before the great crisis. Oxford University Press.
Ganong, P. and Shoag, D. (2015). Why has regional income convergence in the US declined? Harvard Kennedy School Working Paper.
Gordon, C. (2014). Growing apart: A political history of American inequal-ity. Institute for Policy Studies.
Janikas, M. V. and Rey, S. J. (2005). Spatial clustering, inequality, and income convergence. R´egion et D´eveloppement, 25:41–64.
Janikas, M. V. and Rey, S. J. (2008). On the relationship between spatial clustering, inequality, and economic growth in the United States: 1969-2000. R´egion et D´eveloppement, 27:13–34.
Kristal, T. (2013). The capitalist machine: Computerization, workers’
power, and the decline in labor’s share within US industries. American Sociological Review, 78(3):361–389.
Krugman, P. and Lawrence, R. (1993). Trade, jobs, and wages. Technical report, National Bureau of Economic Research.
Krugman, P. R. (1991). Geography and trade. MIT press.
Kuznets, S. (1955). Economic growth and income equality. American Eco-nomic Review, 45:1–28.
Leamer, E. E. (1994). Trade, wages and revolving door ideas. Technical report, National Bureau of Economic Research.
Levernier, W., Rickman, D. S., and Partridge, M. D. (1995). Variation in US state income inequality: 1960-1990. International Regional Science Review, 18(3):355–378.
Levy, F. and Murnane, R. J. (1992). US earnings levels and earnings in-equality: A review of recent trends and proposed explanations. Journal of Economic Literature, pages 1333–1381.
Madden, J. F. (2000). Changes in income inequality within US metropolitan areas. WE Upjohn Institute.
Metwally, M. M. and Jensen, R. C. (1973). A note on the measurement of regional income dispersion. Economic development and cultural change, 22(1):135–36.
Moretti, E. (2013). Real wage inequality. American Economic Journal, 5(1):65–103.
Myrdal, G. (1957). Rich Lands and Poor. Harper.
Nielsen, F. and Alderson, A. S. (1997). The Kuznets curve and the great U-turn: Income inequality in US counties, 1970 to 1990. American Soci-ological Review, pages 12–33.
Noah, T. (2012). The great divergence: America’s growing inequality crisis and what we can do about it. Bloomsbury Publishing USA.
Odland, J. and Ellis, M. (2001). Changes in the inequality of earnings for young men in metropolitan labor markets, 1979–1989: The effects of declining wages and sectoral shifts within an efficiency wage framework.
Economic Geography, 77(2):148–179.
Panizza, U. (2002). Income inequality and economic growth: evidence from American data. Journal of Economic Growth, 7(1):25–41.
Partridge, J. S., Partridge, M. D., and Rickman, D. S. (1998). State patterns in family income inequality. Contemporary Economic Policy, 16(3):277–
294.
Partridge, M. D. (1997). Is inequality harmful for growth? Comment. The American Economic Review, pages 1019–1032.
Partridge, M. D. (2005). Does income distribution affect U.S. state economic growth? Journal of Regional Science, 45(2):363–394.
Piketty, T. and Saez, E. (2006). The evolution of top incomes: a histori-cal and international perspective. Technihistori-cal report, National Bureau of Economic Research.
Piketty, T. and Saez, E. (2013). Top incomes and the great recession: Recent evolutions and policy implications. IMF Economic review, 61(3):456–478.
Rey, S. J. (2001). Spatial empirics for economic growth and convergence.
Geographical Analysis, 33(3):195–214.
Rey, S. J. (2004). Spatial analysis of regional income inequality. In Good-child, M. and Janelle, D., editors,Spatially Integrated Social Science: Ex-amples in Best Practice, pages 280–299. Oxford University Press, Oxford.
Rey, S. J. (2014). Spatial dynamics and space-time data analysis. In Fischer, M. M. and Nijkamp, P., editors, Handbook of Regional Science, pages 1365–1383. Springer.
Rey, S. J. (2015). Discrete regional distribution dynamics revisited. Journal of Regional and Urban Economics, 1-2:83–104.
Rey, S. J. and Anselin, L. (2010). PySAL: A Python library of spatial analytical methods. In Fischer, M. M. and Getis, A., editors, Handbook of Applied Spatial Analysis, pages 175–193. Springer, Berlin.
Rey, S. J. and Dev, B. (2006). σ-convergence in the presence of spatial effects. Papers in Regional Science, 85(2):217–234.
Rey, S. J. and Janikas, M. V. (2005). Regional convergence, inequality and space. Journal of Economic Geography, 5(2):155–176.
Rey, S. J. and Le Gallo, J. (2009). Spatial analysis of economic convergence.
In Mills, T. C. and Patterson, K., editors, Handbook of Econometrics Volume II: Applied Econometrics, pages 1251–1290. Palgrave Macmillan, New York.
Rey, S. J. and Montouri, B. D. (1999). U.S. regional income convergence:
A spatial econometric perspective. Regional Studies, 33(2):145–156.
Rietveld, P. (1991). A note on interregional versus intraregional inequality.
Regional Science and Urban Economics, 21(4):627–637.
Rigby, D. and Breau, S. (2008). Impacts of trade on wage inequality in Los Angeles: Analysis using matched employer–employee data. Annals of the Association of American Geographers, 98(4):920–940.
Rodr´ıguez-Pose, A. (2012). Trade and regional inequality. Economic Geog-raphy, 88(2):109–136.
Rodr´ıguez-Pose, A. and Ezcurra, R. (2010). Does decentralization matter for regional disparities? A cross-country analysis. Journal of Economic Geography, 10(5):619–644.
Sachs, J. D., Shatz, H. J., Deardorff, A., and Hall, R. E. (1994). Trade and jobs in US manufacturing. Brookings Papers on Economic Activity, pages 1–84.
Shorrocks, A. and Wan, G. (2005). Spatial decomposition of inequality.
Journal of Economic Geography, 5(1):59–81.
Smeeding, T. M. and Thompson, J. P. (2011). Recent trends in income inequality. Research in Labor Economics, 32:1–50.
Stiglitz, J. (2012). The price of inequality. Penguin UK.
Stiglitz, J. E. (2014). Reforming taxation to promote growth and equity.
Roosevelt Institute.
Wilkinson, R. G. and Pickett, K. E. (2006). Income inequality and popula-tion health: a review and explanapopula-tion of the evidence. Social Science &
Medicine, 62(7):1768–1784.
Williamson, J. (1965). Regional inequality and the process of national de-velopment. Economic Development and Cultural Change, 13(4):3–47.
Wood, A. (1994). North-South trade, employment and inequality: changing fortunes in a skill-driven world. Oxford University Press, New York.
Young, A., Higgins, M., and Levy, D. (2008). Sigma convergence versus beta convergence: Evidence from US county-level data. Journal of Money, Credit and Banking, 40(5):1083–1093.
Figure 1: Mean 0.10 and 0.01 income shares for states, 1916-2012
28
29
Figure 3: Global quintile distribution, 0.01 income shares for states, 1916-2012
30
31
Figure 5: Top 0.01 income share by global quintiles selected years. Legend values are upper bound of each quintile.
32
Figure 6: Relative per-capita incomes by global quintiles selected years. Legend values are upper bound of each quintile.
33
Figure 7: Global spatial autocorrelation, S01 and RSPI, z-values Moran’s I, Queen Contiguity
34
35
Markov Homogeneity Test Number of classes: 5
Number of transitions: 9216 Number of regimes: 2 Regime names: S01, S10
Test LR Q
Stat. 28.629 28.449
DOF 20 20
p-value 0.095 0.099
P(H0) Q0 Q1 Q2 Q3 Q4
Q0 0.809 0.155 0.026 0.006 0.004 Q1 0.172 0.552 0.237 0.031 0.008 Q2 0.025 0.210 0.548 0.190 0.027 Q3 0.010 0.036 0.212 0.582 0.159 Q4 0.001 0.006 0.022 0.152 0.819
P(S01) Q0 Q1 Q2 Q3 Q4
Q0 0.790 0.176 0.026 0.004 0.004 Q1 0.192 0.547 0.227 0.027 0.007 Q2 0.027 0.198 0.558 0.191 0.026 Q3 0.010 0.034 0.216 0.567 0.172 Q4 0.001 0.003 0.017 0.171 0.808
P(S10) Q0 Q1 Q2 Q3 Q4
Q0 0.829 0.133 0.026 0.008 0.003 Q1 0.153 0.557 0.248 0.035 0.008 Q2 0.023 0.222 0.537 0.190 0.028 Q3 0.010 0.039 0.207 0.597 0.146 Q4 0.001 0.008 0.027 0.133 0.830
Table 1: Markov homogeneity tests, 0.01 percentile and 0.10 percentile shares, US state incomes
Markov Homogeneity Test Number of classes: 5
Number of transitions: 7968 Number of regimes: 2
Regime names: GQS01, GQRSPI
Test LR Q
Stat. 252.133 243.255
DOF 17 17
p-value 0.000 0.000
P(H0) Q0 Q1 Q2 Q3 Q4
Q0 0.866 0.127 0.006 0.001 0.000 Q1 0.121 0.745 0.128 0.005 0.001 Q2 0.006 0.128 0.727 0.138 0.002 Q3 0.001 0.005 0.134 0.759 0.102 Q4 0.000 0.000 0.002 0.100 0.898
P(GQS01) Q0 Q1 Q2 Q3 Q4
Q0 0.809 0.186 0.005 0.000 0.000 Q1 0.182 0.656 0.160 0.001 0.000 Q2 0.005 0.154 0.675 0.165 0.001 Q3 0.001 0.003 0.151 0.693 0.151 Q4 0.000 0.000 0.003 0.140 0.858
P(GQRSPI) Q0 Q1 Q2 Q3 Q4
Q0 0.924 0.068 0.008 0.001 0.000 Q1 0.059 0.835 0.096 0.009 0.001 Q2 0.006 0.102 0.779 0.110 0.003 Q3 0.000 0.008 0.116 0.825 0.052 Q4 0.000 0.000 0.001 0.061 0.937
Table 2: Markov homogeneity tests, 0.01 percentile shares and per capita incomes, global quintiles, US state incomes
RSPI S01
Table 3: Local Autocorrelation Statistics by Moran Scatter Plot Quadrant, S01 and RSPI.
NS: Not significant; HH: High (own), High (neighbor); LH: Low (own), High (neighbor);
LL: Low (own), Low (neighbor); HL: High (own), Low (neighbor).
Spatial Markov Test S01 Number of classes: 5
Number of transitions: 3984 Number of regimes: 5
Regime names: LAG0, LAG1, LAG2, LAG3, LAG4
Test LR Q
Stat. 194.130 339.776
DOF 60 60
p-value 0.000 0.000
P(H0) C0 C1 C2 C3 C4
C0 0.809 0.186 0.005 0.000 0.000 C1 0.182 0.656 0.160 0.001 0.000 C2 0.005 0.154 0.675 0.165 0.001 C3 0.001 0.003 0.151 0.693 0.151 C4 0.000 0.000 0.003 0.140 0.858
P(LAG0) C0 C1 C2 C3 C4
C0 0.816 0.179 0.004 0.000 0.000 C1 0.211 0.729 0.061 0.000 0.000 C2 0.000 0.262 0.714 0.024 0.000 C3 0.167 0.000 0.167 0.500 0.167 C4 0.000 0.000 0.000 0.200 0.800
P(LAG1) C0 C1 C2 C3 C4
C0 0.833 0.162 0.004 0.000 0.000 C1 0.178 0.639 0.184 0.000 0.000 C2 0.016 0.207 0.717 0.060 0.000 C3 0.000 0.020 0.255 0.667 0.059 C4 0.000 0.000 0.000 0.136 0.864
P(LAG2) C0 C1 C2 C3 C4
C0 0.646 0.354 0.000 0.000 0.000 C1 0.126 0.615 0.259 0.000 0.000 C2 0.000 0.125 0.667 0.208 0.000 C3 0.000 0.000 0.215 0.718 0.068 C4 0.000 0.000 0.000 0.304 0.696
P(LAG3) C0 C1 C2 C3 C4
C0 0.857 0.114 0.029 0.000 0.000 C1 0.204 0.537 0.241 0.019 0.000 C2 0.006 0.110 0.686 0.198 0.000 C3 0.000 0.000 0.139 0.711 0.150 C4 0.000 0.000 0.000 0.153 0.847
P(LAG4) C0 C1 C2 C3 C4
C0 0.800 0.200 0.000 0.000 0.000 C1 0.250 0.375 0.375 0.000 0.000 C2 0.000 0.273 0.424 0.273 0.030 C3 0.000 0.005 0.087 0.647 0.261 C4 0.000 0.000 0.004 0.121 0.875 Table 4: Spatial Markov Test, S01, k=5
Spatial Markov Test RSPI Number of classes: 5
Number of transitions: 3984 Number of regimes: 5
Regime names: LAG0, LAG1, LAG2, LAG3, LAG4
Test LR Q
Stat. 173.190 195.109
DOF 64 64
p-value 0.000 0.000
P(H0) C0 C1 C2 C3 C4
C0 0.924 0.068 0.008 0.001 0.000 C1 0.059 0.835 0.096 0.009 0.001 C2 0.006 0.102 0.779 0.110 0.003 C3 0.000 0.008 0.116 0.825 0.052 C4 0.000 0.000 0.001 0.061 0.937
P(LAG0) C0 C1 C2 C3 C4
C0 0.972 0.026 0.002 0.000 0.000 C1 0.051 0.803 0.139 0.007 0.000 C2 0.009 0.151 0.717 0.123 0.000 C3 0.000 0.024 0.262 0.619 0.095 C4 0.000 0.000 0.000 0.286 0.714
P(LAG1) C0 C1 C2 C3 C4
C0 0.777 0.182 0.033 0.008 0.000 C1 0.074 0.860 0.062 0.004 0.000 C2 0.000 0.103 0.806 0.091 0.000 C3 0.000 0.000 0.072 0.892 0.036 C4 0.000 0.000 0.000 0.195 0.805
P(LAG2) C0 C1 C2 C3 C4
C0 0.844 0.156 0.000 0.000 0.000 C1 0.063 0.844 0.076 0.013 0.004 C2 0.016 0.089 0.801 0.089 0.005 C3 0.000 0.006 0.091 0.835 0.068 C4 0.000 0.000 0.000 0.132 0.868
P(LAG3) C0 C1 C2 C3 C4
C0 0.948 0.039 0.013 0.000 0.000 C1 0.045 0.836 0.109 0.009 0.000 C2 0.000 0.073 0.794 0.129 0.004 C3 0.000 0.018 0.189 0.732 0.061 C4 0.000 0.000 0.005 0.071 0.924
P(LAG4) C0 C1 C2 C3 C4
C0 0.600 0.400 0.000 0.000 0.000 C1 0.030 0.773 0.182 0.015 0.000 C2 0.010 0.136 0.728 0.126 0.000 C3 0.000 0.005 0.094 0.865 0.036 C4 0.000 0.000 0.000 0.023 0.977 Table 5: Spatial Markov Test, RSPI, k=5