Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
A Study on Convergence/Divergence of Metropolitan Areas in the
United States
Rita Ray*
This paper investigates the convergence of real GDP per-capita of fifty five largest
metropolitan areas in the United States for the period 2001 and 2012. Additionally, this
paper examines the convergence of real GDP per-capita for eighty nine metropolitan areas
in the Mid-West, forty eight metropolitan areas in the North-East, one hundred and forty
four metropolitan areas in the South and eighty metropolitan areas in the West. This paper
finds that the real GDP per-capita of fifty five largest metropolitan areas in the United
States is diverging for the period 2001-2012. This paper also finds that the real GDP percapita of metropolitan areas in the Mid-West and West is diverging and it is converging for
the North-East and South.
Keywords: Convergence, Growth, United States
JEL Classification: O47, O51
1.
Introduction
Metropolitan areas of the United States produce ninety percent of US real GDP and are
home for eighty percent of US population. However, very little work has been done on the level
and growth of income in the metropolis. This paper fills this gap by investigating the relationship
between initial income and growth of income for fifty five largest metropolitan areas in the United
States. Using panel data for fifty five metropolitan areas in the United States for the period of
2001 and 2012, this paper examines the convergence of income. Income is measured by the percapita personal income and real GDP per-capita. Additionally, this paper collects the data of real
GDP per-capita for three hundred and sixty one metropolitan areas in the United States and sort
the data based on regions. There are eighty nine metropolitan areas in the Mid-West, North-East
has forty eight, South has one hundred and forty four and West has eighty metropolitan areas.
This paper examines the convergence of metropolitan areas for all four regions.
The organization of this paper is as follows. Section 2 provides a review of literature. Section 3
discusses the data sources and the methodology. Section 4 describes the stylized facts
regarding the growth, unemployment and industrial share of GDP. Section5 discusses the
results. Section 6 concludes.
2. Literature Review
Convergence or divergence of income is a widely studied area of research. The
assumption of law of diminishing returns to capital of neoclassical growth model provides the
background of convergence. Barro and Sala-i-Martin (1991, 1992) work extensively on the
empirical evidence of convergence of income among counties and regions.
_______________________
* Dr. Rita Ray, Assistant Professor, Department of Economics and Management, Gustavus Adolphus College, St Peter, MN.
Email: rray@gustavus.edu.
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Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
Barro and Sala-i-Martin (1991) examine the association between per-capita personal income and
its annual growth between 1880 and 1988 for forty eight American states. They also investigate the
connection between per-capita Gross State Product and its annual growth between 1963 and 1986 for
forty eight American states. They extend their analysis on Gross Domestic Product and its annual growth
rate for seventy three regions of Western Europe between 1950 and 1985. They find the evidence of
convergence among American states and the regions of Western Europe. Barro and Sala-i-Martin’s 1992
(I) paper describe the convergence of per-capita personal income and per-capita Gross State Product of
forty eight American states between 1880 – 1988 and 1963 – 1986 respectively. The paper additionally
examines the relationship between per-capita GDP and its annual growth for ninety eight countries
between 1960 and 1985. They find the evidence of divergence across countries. However, when they hold
primary and secondary school enrollment rates and the average ratio of government consumption
expenditure to GDP as constants, they find the evidence of convergence. Barro and Sala-i-Martin (1992,
II) find the evidence of convergence of per-capita income for forty seven Japanese prefectures between
the period 1930 and 1990. Convergence of income is investigated and evident for Australasia (Cashin,
1995), Bangladesh (Hossain, 2000), Greece (Petrakos and Saratsis, 2000), Sweden (Persson, 1997).
Cashin and Sahay (1995) find the evidence of regional convergence of per-capita net state domestic
product among Indian states. However, Marjit and Mitra (1996) and Ghosh, Margit and Neogi (1998) find
the evidence of divergence of per-capita net state domestic product among Indian states. Yao and Weeks
(2000) examine the income convergence in China between the time period 1953 and 1997. They find the
evidence of divergence of income between coastal provinces and interior provinces of China between
1978 and 1997 due to the technological growth rate disparity.
3. Data and Methodology
3.1 Data Sources
I collect the data on real GDP per-capita for metropolitan areas for all metropolitan areas in the United
Sates and industry share of real GDP for fifty five largest metropolitan areas in the United States from the
Bureau of Economic Analysis. I collect the data on unemployment rate from the Bureau of Labor Statistics.
3.2 Methodology
To investigate the convergence of real GDP per-capita of metropolitan areas in the United States, I
use the following model:
I subtract
and,
from equation (1) and get equation (2).
is the real GDP per-capita in metropolitan area i at year t.
) and
are
independent of each other and among themselves.
is the annual growth rate of real GDP per-capita
and annual in metropolitan area i at year t respectively.
represents convergence.
I use the GMM estimator for dynamic panel data model proposed by Holtz-Eakin, Newey and
Rosen (1988) and Arellano and Bond (1991) to estimate equation (1). The lagged dependent variable on
the right hand side makes the regressors endogenous (since
is a function of
so
is also
correlated with ). Metropolis-specific omitted variables also make the regressors endogenous. The GMM
estimator takes the regressors as endogenous and generates additional instruments by utilizing the
orthogonality condition between the lagged values of the regressors and the disturbance term
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Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
4. Stylized Facts
Table 1 provides some facts regarding the rank and change of rank of real GDP per-capita and
unemployment rates for the fifty five largest metropolitan areas in the United States between the period
2001-2007 and 2008-2012. Eight metropolitan areas are able to keep their rank within top ten with respect
to real GDP per-capita between 2001-2007 and 2008-2012. This number is same for bottom ten
metropolitan areas. Twenty two metropolitan areas are able to improve their rank, for seven metropolitan
areas it is same and the rank deteriorates for twenty six metropolitan areas between 2001-2007 and 20082012. For unemployment rates only four metropolitan areas are in bottom ten between 2001-2007 and
2008-2012. This number is two for top ten. Twenty nine metropolitan areas are able to improve their rank,
for only one metropolitan area it is same and the rank deteriorates for twenty five metropolitan areas
between 2001-2007 and 2008-2012.
Number of
Number of
Number of
Number of
Number of
Metropolitan
Metropolitan
Metropolitan
Metropolitan
Metropolitan
Areas
Areas
Areas whose
Areas whose
Areas whose
belongs to
belongs to
Rank
Rank remains Rank
Variable
Top Ten
Bottom Ten
Improves
Same
Deteriorates
between
between
between
between
between
2001-2007
2001-2007
2001-2007
2001-2007
2001-2007
and 2008and 2008and 2008and 2008and 20082012
2012
2012
2012
2012
Real GDP
8
8
22
7
26
Per-Capita
Unemployment
2
4
29
1
25
Rate
Table 1
Table 2 compares the growth rate of metropolitan area with the regional growth rate for the fifty five largest
metropolitan areas between the period 2001-2007 and 2008-2012. There are fourteen metropolitan areas
in the Mid-West region. Two metropolitan areas have higher growth rate compare to the growth rate of
Mid-West in the period 2001-2007. However, none of the metropolitan area has higher growth rate
compare to the Mid-Western growth rate in 2008-2012. There are nine metropolitan areas in the NorthEast region. Five metropolitan areas have higher growth rate compare to the growth rate of North-East in
the period 2001-2007 and this number is four for the period 2008-2012. There are twenty two metropolitan
areas in the South. Nine metropolitan areas have higher growth rate compare to the growth rate of South
for both the period of 2001-2007 and 2008-2012. There are en metropolitan areas in the West. Eight
metropolitan areas have higher growth rate compare to the growth rate of West in the period 2001-2007
and this number is five for the period 2008-2012.
Number of Metropolitan Number of Metropolitan
Areas
with
Higher Areas
with
Higher
Total Number of
Areas
Growth Rate Compare to Growth Rate Compare to
Metropolitan Areas
the Region between 2001 the Region between 2008
- 2007
- 2012
14
2
0
Mid-West
9
5
4
North-East
22
9
9
South
10
8
5
West
Table 2
5 Results
First, I examine the relationship between real GDP per-capita at 2001 and the average of annual
growth rate of real GDP per-capita for the fifty five largest metropolitan areas in the United States between
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Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
2001 and 2012. Next, I investigate the same relationship for eighty nine metropolitan areas in the MidWest, forty eight metropolitan areas in the North-East, one hundred and forty four metropolitan areas in
the South and eighty metropolitan areas in the West.
Divergence of Real GDP Per-Capita
Annual Growth Rate of Real
GDP Per-Capita, 2001-2012
0.05
y = 0.0017x - 0.0139
Divergence of Real
GDP Per-Capita
0.025
Linear (Divergence of
Real GDP Per-Capita)
0
10.34
10.58
-0.025
10.82
11.06
Real GDP Per-Capita, 2001
Diagram 1: Divergence of Real GDP Per-Capita of the Metropolitan Areas in the US
Diagram 1 shows the relationship between log of real GDP per-capita at 2001 and the annual
growth rate of real GDP per-capita between the period 2001 and 2012 for the fifty five largest metropolitan
areas in the United Sates. Positive slope (0.0017) of the fitted line verifies the divergence of real GDP percapita between the period 2001 and 2012.
Growth rate of Real GDP Per-Capita,
2001-2012
Divergence of Real GDP Per-Capita, Mid-West
-0.4
y = 0.0034x + 3E-07
Divergence of Real
GDP Per-Capita, MidWest
-0.2
0
0.2
0.4
Linear (Divergence of
Real GDP Per-Capita,
Mid-West)
Real GDP Per-Capita, 2001
Diagram 2: Divergence of Real GDP Per-Capita of the Metropolitan Areas in the Mid-West
Diagram 2 depicts the relationship between log of real GDP per-capita at 2001 and the annual
growth rate of real GDP per-capita between the period 2001 and 2012 for the eighty nine metropolitan
areas in the Mid-West. Positive slope (0.0034) of the fitted line verifies the divergence of real GDP percapita between the period 2001 and 2012 for the metropolitan areas in the Mid-West.
Diagram 3 represents the relationship between log of real GDP per-capita at 2001 and the annual
growth rate of real GDP per-capita between the period 2001 and 2012 for the forty eight metropolitan
areas in the North-East. Negative slope (-0.0033) of the fitted line verifies the convergence of real GDP
per-capita between the period 2001 and 2012 for the metropolitan areas in the North-East.
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Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
Growth rate of Real GDP Per-Capita,
2001-2012
Convergence of Real GDP Per-Capita, North East
-0.478
y = -0.0033x + 2E-07
Convergence of Real
GDP Per-Capita, North
East
-0.378
-0.278
-0.178
-0.078
Linear (Convergence of
Real GDP Per-Capita,
North East)
Real GDP Per-Capita, 2001
Diagram 3: Convergence of Real GDP Per-Capita of the Metropolitan Areas in the North-East
Diagram 4 shows the relationship between log of real GDP per-capita at 2001 and the annual
growth rate of real GDP per-capita between the period 2001 and 2012 for the one hundred and forty four
metropolitan areas in the South. The fitted line has a negative slope (-0.0034). This indicates the
convergence of real GDP per-capita between the period 2001 and 2012 for the metropolitan areas in the
South.
Growth rate of Real GDP Per-Capita,
2001-2012
Convergence of Real GDP Per-Capita, South
-0.934
y = -0.0034x - 9E-08
Convergence of Real
GDP Per-Capita, South
-0.434
0.066
0.566
Linear (Convergence of
Real GDP Per-Capita,
South)
Real GDP Per-Capita, 2001
Diagram 4: Convergence of Real GDP Per-Capita of the Metropolitan Areas in the South
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Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
Growth rate of Real GDp Per-Capita,
2001-2012
Divergence of Real GDP Per-Capita, West
-0.53
y = 0.005x - 9E-08
Divergence of Real
GDP Per-Capita, West
Linear (Divergence of
Real GDP Per-Capita,
West)
-0.33
-0.13
0.07
0.27
0.47
0.67
Real GDP Per-Capita, 2001
Diagram 5: Divergence of Real GDP Per-Capita of the Metropolitan Areas in the West
Diagram 5 represents s the relationship between log of real GDP per-capita at 2001 and the
annual growth rate of real GDP per-capita between the period 2001 and 2012 for the eighty metropolitan
areas in the West. The fitted line has a positive slope (0.005). This indicates the divergence of real GDP
per-capita between the period 2001 and 2012 for the metropolitan areas in the West.
Table 3 shows the estimation result of equation (2) for real GDP per-capita of the metropolitan
areas for the period 2001 and 2012. The value of ̂ is equal to 0.0005 for fifty five largest metropolitan
areas in the United States between 2001 and 2012 and it is statistically significant. This result signifies
that real GDP per-capita is diverging for the fifty five largest metropolitan areas over the period 2001 and
2012. Next, I divide the three hundred and sixty one metropolitan areas in the United States fifty into four
regions. There are eighty nine metropolitan areas in the Mid-West, forty eight metropolitan areas in the
North-East, one hundred and forty four metropolitan areas in the South and eighty metropolitan areas in
the West. The value of ̂ is equal to -0.0396 for the metropolitan areas in the Mid-West and it is
statistically significant. This result signifies the evidence of convergence. This result is not consistent with
Diagram 2. The values of ̂ are equal to -0.0333 and -0.0385 for the metropolitan areas in the North-West
and South respectively and statistically significant. These results are consistent with the results in Diagram
3 and Diagram 4 respectively. The value of ̂ is equal to 0.0008 for the eighty metropolitan areas in the
West and it is statistically significant. This result is consistent with Diagram 4 and indicates the divergence
of metropolitan areas in the West.
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Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
Table 3: Regression on Real GDP Per-Capita
Dependent Variable: Growth of real wage and salary disbursements per job
̂
Variable
Initial real GDP per-capita for fifty five largest metropolitan areas
No of obs.
Initial real GDP per-capita for eighty nine metropolitan areas in the Mid-West
No of obs.
Initial real GDP per-capita for forty eight metropolitan areas in the North-East
No of obs.
Initial real GDP per-capita for one hundred and forty four metropolitan areas in the
South
No of obs.
Initial real GDP per-capita for eighty metropolitan areas in the West
No of obs.
0.0005***
(1.05-08)
660
-0.0396***
(0.0014)
1068
-0.0333***
(0.0070)
576
-0.0385***
(0.0049)
1728
0.0008***
(0.0009)
960
6. Conclusion
Metropolitan areas of the United States produce ninety percent of US real GDP and are home for
eighty percent of US population. However, very little work has been done on the level and growth of
income in the metropolis. I fill this gap by examining the convergence of real GDP per-capita of fifty five
largest metropolitan areas in the United States for the period 2001 and 2012. Additionally, I examine the
convergence of real GDP per-capita for eighty nine metropolitan areas in the Mid-West, forty eight
metropolitan areas in the North-East, one hundred and forty four metropolitan areas in the South and
eighty metropolitan areas in the West.
I find that the real GDP per-capita for fifty five largest metropolitan areas in the United States is
diverging for the period 2001-2012. I find that real GDP per-capita for forty eight metropolitan areas in the
North-East and one hundred and forty four metropolitan areas in the South are converging for the time
period 2001 and 2012. For eighty nine metropolitan areas in the Mid-West the result is not consistent. The
diagram shows the relationship between log of real GDP per-capita at 2001 and the annual growth rate of
real GDP per-capita between the period 2001 and 2012 West has a positive slope (0.0034) of the fitted
line. This result verifies the divergence of real GDP per-capita between the period 2001 and 2012 for the
metropolitan areas in the Mid-West. However, the regression equation shows the value of -0.0396, which
indicates the convergence. I find the evidence of divergence for the eighty metropolitan areas in the West.
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Proceedings of 5th Asia-Pacific Business Research Conference
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