US MSA PCPI Trends: Evidence on Convergence and Divergence

Recent literature suggests that whether you observe state level convergence or divergence in PCPI depends largely on whether period beginning or ending quintile income groupings are used. The prior literature demonstrates that state income distributions based upon 1969 quintiles indicate PCPI convergence, while 2012 quintiles generate the opposite result. Evidence presented in this paper confirms similar patterns through 2017 confirming that previous results are more than recession driven anomalies. We also find considerable variability within MSA rankings over the 1969-2017 time period, a finding which suggests that MSA income performance is considerably more complex than superstar city paradigms would predict.

growing, the analysis presented in this paper will provide additional insight into understanding how changes in PCPI and PCPI rankings over time are influenced.
The Bureau of Economic Analysis (BEA) maintains regional economic data for MSAs dating to 1969.Annual Income, earnings, and employment by Industry are available on an annual basis by MSA from 1969 to 2017 (Tables CA1-3, CA04, CA25, and CA25N). These series provide a wealth of information for comparing economic activity across MSAs and examining changes in MSA data over time. This paper will focus on MSA per Capita Personal Income (PCPI) over the 44 year period and identify trends in MSA PCPI over time and changes in PCPI rank and position among MSAs.

Literature Review
There is a rich and growing body of research testing the conclusions of growth theory's forecast of income convergence. Previous research defines convergence in alternative ways, ranging from β-convergence and σ-convergence to measures such as Gini coefficients and ratios of mean or median income at specific benchmark points in the distribution. Techniques are similarly wide-ranging including OLS, 2-and 3-stage least squares, transition matrices, spatial clustering, unit root tests, and more.
The essential finding is that there are periods of income convergence interrupted by periods of mixed results and general divergence. The earliest work by Barro and Sala-i-Martin (1992) and Mankiw et al. (1992) found evidence of convergence. Research by Levernier, Partridge, and Rickman (1995), and Bernat (2001) established the convergence of PCPI among the states through 1990.Convergence evidence is sufficiently well established that Sala-i-Martin (1996) concluded "we can use a mnemonic rule:economies converge at a speed of two percent per year".
Slowing convergence and divergence in income are generally found in the late 1970s and 1980s and again more recently. Yamamoto (2003) identified several stylized facts concerning income disparity by using a multi-channel analysis, including non-parametric, σ-convergence, mobility tests, and spatial clustering analysis. The paper shows higher mobility in the 1970s and 1980s, with lower, but stable, mobility levels throughout the 1990s. Furthermore, spatial clustering techniques indicate that, at smaller scales, the regional income distribution has increasingly become more fragmented. Ganong and Shoad (2014) attribute the slowing of regional income convergence since 1980 to a reduction in labor mobility. They trace the decline in labor mobility to land use regulations and high housing prices in wealthier areas. Rey and Montouri (1999) use spatial econometric methods to examine US regional economic income convergence from 1929-1994. They find strong geographic characteristics of convergence that further complicate the dynamics of income convergence across states and within state clusters. Bauer et al. (2012)  While convergence is often considered across states or within regions, an examination of a smaller unit (Metropolitan Statistical Areas (MSAs), cities, or counties) is valuable because these units more closely approximate an integrated economic zone. Drennan et al. (1996) examine divergence of median family incomes in the 1980s for the 51 largest US cities and find that cities with a high share of earnings from producer services have higher economic growth rates than cities that began the decade with a higher concentration of earnings from manufacturing. Drennan (2005) looked at changes in wage levels in metropolitan areas for 1969-1979 and for 1979-1999. He finds that large metropolitan areas had stronger wage growth in the later period. The ratio of earnings from producer services to earnings from production and distribution also supported higher wage growth in the later years. Higgins et al. (2006) use county-level data to study convergence rates. They find that public sector employment at any level has a negative effect on economic growth. Education contributes to growth with the largest contributions coming from completed high school and completed college or higher.
Employment in the finance, insurance, and real estate and entertainment industries add to economic growth while employment in education exerts a negative impact. Hammond and Thompson (2006) examine both convergence to the trend (modality) and mobility within groups in their study of metropolitan and nonmetropolitan regions from 1969 to 1999.Their analysis of sub-state units produces higher rates of distributional and rank mobility than state analysis indicated. They find that mobility across income classes is lower in metropolitan areas than for nonmetropolitan zones and that the metropolitan areas have lower mobility across ranks.

Data
This study uses PCPI for each of the 383 Metropolitan Statistical Areas

PCPI and Convergence
MSA PCPI data exhibit substantial variability over the study period as shown by the summary statistics in    The top quintile experiences a small loss in relative income in the early years of the period, but thereafter remains at least 20% above the average for all MSAs. The second and third quintiles experience some loss in relative position and the lowest two quintiles experience gains over the period.

MSA Rank
Given the disparate experiences of MSAs and the seeming lack of consistent income convergence, analysis of the mobility of MSAs is the next logical step. Hammond and Thompson (2006) argue, "… sustained inequality in the income distribution may cause us less concern if we also find a large degree of income class and rank mobility." (p. 36).
The remainder of this paper examines change between the 1969 rank and 2017 rank. These data show some large changes among some MSAs with most MSAs experiencing more moderate changes. Table   4 shows a frequency distribution of both the gains in rank (positive changes) and the loss in rank (negative changes). Three MSAs had no rank change.

Regression Results
To explain the basis for such large changes in MSA rank order over time, a regression model was developed that includes both quantitative variables related to the structure and demographic variability between the MSAs and fixed effects variables that control for regional differences.  The data for all the quantitative variables was from the BEA Regional Economic Accounts. The omitted region for the qualitative variables was for the New England region. Thus, the coefficients on the included regional variables are to be interpreted as the predicted difference in the percentage rank order over the 49 year period for a given MSA in a given region, versus an MSA located in the New England region.
The model was estimated for the 383 MSAs using an OLS regression model and White heteroske dasticity-consistent standard errors and covariance. The regression results are reported in Table 7. This model has an R-squared value of 0.2332 and an F-statistic that tests significant at the 0.01 level.   Private research university: The coefficient for the presences of a private research university ranked in the top 200 by US News and Report in 2012 has a positive sign but does not test significant at 0.10 level.
Regional effects: Three of the coefficients on the regional dummy variables (DGL, DSW, and DFW) have negative signs and test significant at the 0.05 level. MSAs in the Great Lakes region, the Southwest region, and the Far West region all have negative coefficients that indicate that, on average, MSAs within those regions suffered a double digit decline in their rank order compared to MSAs in the control dummy, the New England region. In addition, the regional dummy coefficient for the Mideast region (DME) also has a negative sign but statistically insignificant sign. MSAs within this region suffered a 25.2252 decline in their rank order compared to MSAs in the control dummy, the New England region

Conclusion
The The regression results suggest that changes in MSA PCPI rank over the 49 year period are negatively affected by the size of the service sector, and the MSA's population density. In addition, the regional location of the MSA can also have a negative impact on the change in rank over the 49 year period. Reserve Bank of St Louis study by Charles Gascon and Brian Reinbold portrays the rather stark economic differences between rural and urban areas. For example, Gascon and Reinbold find median growth rates of 1.7% for metro counties as compared to 1.18% for non-metro counties. Our findings regarding divergent PCPI growth across MSAs demonstrates that differences run deeper than urban vs rural distinctions. The widening gap between high and low performing metropolitan areas over time provides particularly strong evidence of performance differences across urban America.

MSAs in the Great
It is also true that differences in economic performance across metro areas are more complex than recent reporting for subgroups of cities suggests. Considerable attention has been directed to the role of so called superstar cities as engines of dynamic innovation and economic growth. The results of this paper provide a caution to all who believe that the disparity in PCPI is either a rural/urban divide, a superstar/all other MSA divide, or a regional divide. The degree to which some