1、ECONOMIC CONVERGENCE: EVIDENCE FROM COUNTIES IN VIRGINIAC. Barry Pfitzner, Department of Economics and Business, Randolph-Macon CollegeAshland, VA 23005, (804) 752-7307, bpfitznermc.eduSteven D. Lang, Department of Economics and Business, Randolph-Macon CollegeAshland, VA 23005, (804) 752-7356, slan
2、grmc.eduDavid A. Brat, Department of Economics and Business, Randolph-Macon CollegeAshland, VA 23005, (804) 752-7356, dbratrmc.eduEconomics Track2ECONOMIC CONVERGENCE: EVIDENCE FROM COUNTIES IN VIRGINIAEconomics TrackABSTRACTThis paper applies the empirical methodology for testing for convergence of
3、 incomes across the counties and independent cities in Virginia. Decennial data from the Bureau of the Census on real personal income per capita for 124 geographic areas within the Commonwealth are used to test for two types of income convergence over the 1959-1999 time span. The results indicate th
4、at both beta and sigma convergence occurred across the regions for the full period, but there was a ten year sub-period (the 1980s) over which neither measure of convergence was evident. The paper also tests for conditional convergence by controlling for both educational attainment and patent produc
5、tion by division.3INTRODUCTIONIt is an obvious empirical fact that some regions (here measured by counties and cities) in the Commonwealth of Virginia are poorer than others. It is also a fact that counties and cities1 in Virginia experience different rates of economic growth. These facts raise at l
6、east two important questions. First, are counties and cities that are initially poorer than others somehow destined to remain so? Or, are the initially poorer counties likely to catch up to the richer ones? A second related question is whether the degree of income inequality across counties increase
7、s or decreases over time, that is, should we find that the gaps in per capita incomes between the richer and poorer counties diminish or increase (or remain the same) over time? We attempt to provide empirical answers to these questions by applying standard growth analysis focusing on regions in the
8、 Virginia economy.Modern Growth Theory and ConvergenceModern growth theory, based on neoclassical models introduced by Ramsey 6, Solow 9, and Swan 10, has lent itself in recent years to wide application in empirical estimations that often confirm the convergence in per capita incomes predicted by th
9、e models. The type of convergence that is implied by the Solow-Swan neoclassical models is known as conditional convergence. The convergence is conditional because the models assume the same technology, population growth rate, and the same saving rate for all of the economies in the sample. The mode
10、ls then imply convergence in that per capita incomes will converge across nations and regions within nations. The lower the initial 4level of real per capita income relative to the long run or steady state position, the faster will be the growth rate. This result implies that nations or regions with
11、 lower initial starting incomes will eventually close the gap between themselves and those nations or regions with greater initial real incomes per capita. The convergence is ultimately a product of diminishing returns to capital, as economies with less initial capital per worker relative to their s
12、teady state equilibrium will have greater returns and higher growth rates.If in fact, poorer nations (or regions) grow faster than rich nations (or regions), irrespective of technology (patents), human capital (education), population growth rates, and savings, then convergence is absolute.This paper
13、 tests for both absolute and conditional convergence of incomes across counties and independent cities in the Commonwealth of Virginia. The following section describes the methodology for such tests. A description of the data set employed, the results of the convergence tests, some additional experi
14、ments, and our conclusions follow in the subsequent sections.METHODOLOGYThe literature on convergence has generated two tests of convergence that produce implications for convergence in per capita incomes across nations or regions. 5Beta ConvergenceEmpirical testing for what is known as convergence
15、in per capita income across nations or regions often utilizes a form of the neoclassical growth model, popularized by Barro and Sala-i-Martin 1, 2, and 3, that allows the growth rate of per capita income between two points in time to be related to some initial level of income. That form may be repre
16、sented as:(1)tititi yeay ,1,1, )log()()/log( where y represents per capita real GDP, t represents the time (year), i represents the nation or region and is the stochastic error term. The coefficients, a and , are estimated by non-linear least squares techniques.2 Equation 1 is a solution of the neoc
17、lassical model of growth that can be utilized to test empirically the transitional dynamics implied by the model. The left side of the equation simply represents the growth rate of, say, per capita income over the period from t-1 to t. The only variable on the right-hand side is initial level of inc
18、ome in time period t-1 (the earlier time period). Then for a group of counties, a positive statistical estimate of implies that the initially poorer counties grow on average at a faster rate than do the richer ones. A negative implies greater growth for the initially richer counties. Further represe
19、nts the speed of convergence (or divergence) among the counties. Assuming convergence, it will allow us to estimate how long it will take for incomes to close some 6proportion of the gap between the rich and poor counties across Virginia. We will discuss these implications later in the paper.For tim
20、e separated by years, equation (1) is modified as , (2)TitiTTtit yeayT 0, )log(/)1()/log()/1( where T = the length of the interval in years between initial income and its level at the end of the period, so that the left-hand side of (2) becomes an annualized growth rate. The estimate of in this form
21、 is independent of the interval T.Finally, for convergence, the estimate of can be biased if there are shocks that affect certain subgroups within the regions in asymmetric ways. For example, an energy price shock could affect the coal mining regions in a different way than regions in which economic
22、 activity is oriented more toward service or manufacturing.Sigma ConvergenceSigma () convergence is a simpler concept. Data on per capita income (net of transfers, if it is possible to obtain data on transfers3) are collected as a time series for each of the nations or regions under analysis. Then t
23、he standard deviation of the log of per capita income is computed for each year across the regions. This is a simple measure of dispersion, or income inequality for the sample data. If this standard deviation declines 7over time, per capita incomes are less dispersed and convergence is implied. This
24、 concept, sigma-convergence, provides a measure of the extent of income inequality and how such inequality changes over time. Generally convergence implies convergence, but the process may be offset by shocks that increase income dispersion 4. Put differently, convergence is a necessary, but not suf
25、ficient, condition for convergence. It follows that the reverse does not hold; it is possible to have sigma divergence accompanied by beta convergence 8. This could occur if the initially poor regions (counties) grew such that they “passed” those above to such an extent that dispersion () increased.
26、APPLICATION TO VIRGINIA COUNTIESIn order to test for convergence among counties in Virginia, we obtained annual data on per capita personal income from the Bureau of the Census for the 1959 to 1999 period.4 Income data were not available for all of the 134 counties and independent cities in the Comm
27、onwealth. Missing observations limited the number of geographic units to 124. The current dollar per capita income data were converted to constant dollars using the consumer price index, normalized to 1989. Thus all of the data are in 1989 constant dollars.Some Simple Data Summaries8Tables I and II
28、give a summary of some of the relevant characteristics of the ten richest and poorest counties/cities as measured by income per capita in the first census year for which the data are available, 1959.Table I lists the ten poorest counties in term of per capita income for the year 1959. For those ten
29、poorest counties (and they are all counties), per capita income (adjusted to 1989 dollars) ranged from $2,514 for Lee County to $3,226 for Halifax County. Not surprisingly, these ten counties share the characteristic of being generally rural in nature.Table I: Lowest Ten Counties/Cities in 1959 per
30、capita Income (1989 dollars)County/city Income per capita (1959) Annual Growth(1959-1999) Growth Rankof 124Lee County $2,514 3.49% 16Cumberland County $2,598 3.66% 7Highland County $2,857 3.57% 12Buckingham County $2,872 3.16% 35Sussex County $2,880 3.33% 23Greene County $3,080 3.87% 3Surry County $
31、3,096 3.47% 17Amelia County $3,124 3.17% 5Brunswick County $3,124 3.76% 34Halifax County $3,226 3.32% 25Table II: Highest Ten Counties/Cities in 1959 per capita Income (1989 dollars)County/city Income per capita (1959) Annual Growth(1959-1999) Growth Rankof 124Arlington County $12,008 2.12% 98Falls
32、Church City $10,201 2.74% 64Alexandria City $9,823 2.62% 76Fairfax County $9,391 2.68% 72Henrico County $8,798 2.01% 103Waynesboro City $8,629 1.09% 124Colonial Heights City $8,255 1.89% 104Charlottesville City $7,824 1.20% 122Williamsburg City $7,820 1.41% 119Chesterfield County $7,769 2.21% 969The
33、 ten richest county/city entities in Table II are dominated by cities and other densely populated areas (for example, many would consider Arlington County to have “city like” characteristics). Included in each of the tables are the annual growth rates in per capita incomes for the for the year perio
34、d from 1959 to 1999 and the ranks of the growth rates among the 124 county/city areas for which full data were available. Notice that all of the ten poorest counties in 1959 had average annual growth in per capita real incomes that exceeded 3% for the 1959-1999 period, and not one of the ten richest
35、 county/cities in 1959 had an annual growth rate of as much as 3% for that same period. Indeed the average growth rate for the forty-year period was 3.48% for the ten initially poorest areas and only 2.00% for those ten initially richest areas. Clearly, at least for the ten poorest localities versus
36、 the ten richest, the poorer areas grew faster than the initially richer areas. Note further that the ranks of the growth rates (1 = fastest, 124 = slowest) are consistent with the hypothesis that poorer areas grew faster than did richer areas, again at least for the ten poorest versus the ten riche
37、st localities in 1959.In the following section, the data are tested for evidence of sigma convergence over the 1959-1999 period. In addition, convergence is tested via regressions of the type described above and implemented as equation (2). RESULTSIn the following two subsections we present the resu
38、lts of the analysis of sigma convergence for this data set, followed by our findings for beta convergence.10Sigma Convergence for Virginia CountiesFigure 1 presents the results of the sigma computations for the 124 geographic areas for which data are available. Generally, over the sample period, the
39、 data reflect some degree of sigma convergence, with most of the convergence taking place in the 1960s and 1970s. Sigma is estimated at 0.32 in 1959 and declined to 0.23 by 1999. The data also suggest that the dispersion in real per capita incomes increased in the 1980s and then fell slightly again
40、in the 1990s for these regions.It is interesting to note that the pattern in Figure 1 for Virginia counties is very similar to the pattern of income dispersion across states in the U.S. as observed by Sala-i-Martin 8. Further, Sala-i-Martin notes that sigma convergence within nations (and for other
41、nations as well as the US) stopped for about a decade approximating the 1980s. The same phenomenon appears to be present in the data on Virginia regions. 11FIGURE 1: DISPERSION OF PERSONAL PER CAPITA ACROSS VIRGINIA COUNTIESSigma Convergence00.10.20.30.41949 1959 1969 1979 1989 1999 2009YearsSigmaFi
42、gure 1, then confirms sigma convergence for the forty year period, with some increase in income inequality for the decade of the 1980s. Beta Convergence for Virginia CountiesTable III contains the estimates of the regressions based on equation (2). Of crucial importance is the estimate of . The firs
43、t row of results in the table shows the estimates for the full sample, 1959-1999. The estimate of is correctly signed and statistically significant, indicating beta convergence for the full sample period. The overall explanatory power of the regression is reasonably impressive ( = 0.513). We also 2R
44、12present evidence for four 10-year sub-periods in the last three rows of the table. The results for the sub-periods from 1959 to 1969 and 1969 to 1979 give the strongest evidence in favor of convergence and those results seem to dominate the other two sub-periods. For the decade from 1979 to 1989,
45、the sign of the is negative, but not significantly different from zero. However, in the last available decade, the 1990s, the estimate of once more has the correct sign (for beta convergence) and is statistically significant. All of these results are consistent with the earlier evidence on sigma con
46、vergence.To summarize the results in for beta convergence for this sample, we find that initially poorer areas (in 1959) grew faster over the succeeding forty year period than those areas that were initially richer in terms of per capita income. The economic meaning of this is that the poorer areas
47、were catching up to those counties/cities that were initially richer, a result consistent with the predictions of the Solow-Swan neo-classical growth models. Congruent with the results on sigma convergence, there was a break in the 1980s when convergence was not evident, only to resume in the 1990s.
48、 We offer some possible explanations of this phenomenon in the following section.13TABLE 1: REGRESSIONS FOR PERSONAL INCOMES ACROSS VIRGINIA COUNTIESPeriod 2RSeeFull Sample1959 19990.02449(0.00364) 0.513 0.0048Sub-period1959 19690.033083(0.00367) 0.491 0.0092Sub-period1969 1979 0.036314(0.00493) 0.3
49、87 0.0093Sub-period1979 1989-0.00893(0.00467) 0.019 0.0110Sub-period1989 1999 0.011534(.003299) .0938 .0078(standard errors in parentheses, see = standard error of the estimate, n = 124, all regressions include an unreported constant term.)Considering the results for the full sample, the degree of convergence suggested is similar to that found in other studies. Sala-i-Martin 8 finds convergence for US states (from 1880 to 1990) to be on the order of 2% per year; these results suggest convergence
