Espacios. Vol. 36 (Nº 05) Año 2015. Pág. 16
Alena KAURYHA 1; Paul VALDIVIESO 2
Recibido: 15/02/2015 • Aprobado: 20/02/2015
1. Section 1: Implication of neoclassical and endogenous growth models
2. Section 2: Spatial data analysis of intra-national income dynamics in germany and the U.S.
3. Section 3: Quantitative results of data testing for convergence in germany and the U.S.
4. Section 4: Qualitative assessment of the hypothetical observation
The most significant difference in the approach of new growth theory in comparison to the neoclassical view is escaping from treating factors such as technological progress and human capital as exogenous, and perceiving them as endogenous. The convergence issue has been of crucial importance in economic geography and regional economics for making predictions and building long-run regional growth policies.
It is difficult to evaluate the empirical success of the theoretical constructs, since the theories of long-run growth do not take into account fluctuations in business cycles. When data is assembled into decades rather than years the benchmark of growth significantly varies and is affected by cyclical movements in output. Additionally, cross-country comparisons of growth rates appear to be complicated by the difficulty of controlling for political and social events (and indicators) that have apparent impact on the growth process over the long run.
In this work, empirical research was organized to evaluate the potential convergence in German and U.S. regions across the time period of 1960-2010. From the analysis, it can be concluded that convergence is not the natural evolutionary path for all economies or regions; however, low-wage regions can grow faster in terms of income level as long as capital flows into the poorer regions faster than labor flows out. Moreover, technical progress needs to be stimulated through the diffusion of knowledge towards poorer regions while taking into account the region's unique profile, its advantages and disadvantages toward knowledge use and its exploitation.
As mentioned by Armstrong and Taylor (2000, p. 71), "according to both neoclassical and endogenous growth theories, the major components of economic growth are achieved due to the growth of labor force, capital stock and technological progress". The rate of output growth is dependent on the evolution of these factors. In order to explain the reasons for growth, it is necessary to observe the reasons for the divergence of the rates for these factors between regions.
An important pattern having an impact on regional growth differences is interregional factor migration. As the neoclassical model assumes, capital and labor move to those regions where the highest rates of return are offered, whereby workers tend to move to the regions where they can find the highest wages and the producers are expected to choose the most profitable location for their business with the lowest rent price levels. The difference in the rates of capital stock can be caused by the disparities of investment inside the country and inflow of capital from other regions. Consequently, the rates of output growth will be higher if the saving rate increases while the capital stock will grow due to larger investment, whereas labor force will grow not only due to the population growth but also because of net in-migration from other regions. With this respect, it is of interest to evaluate which regions tend to grow the fastest according to neoclassical growth framework assuming perfect mobility of factors of production.
Regions with a high capital/labor ratio are expected to have high wages and low yield on investment, and, therefore, an inflow of labor and outflow of capital, the opposite being true for regions with low capital/labor ratio. In short, high-wage regions will attract workforce and lose capital and low-wage regions attract capital and lose workforce. It is hardly possible to make forecasts, since the rate of growth will depend on the speed of factor mobility. As Armstrong and Taylor (2000, p. 73) identified, "if the capital flows into low-wage regions faster than labor flows out of these regions, then low-wage region will experience the higher rates of output growth (which seems to be more likely)".
Essentially, it can be said that "convergence takes place when capital flows to the low-wage region and labor flows to the high-wage region until returns to capital and labor become equal" (Armstrong and Taylor (2000, p. 81). Furthermore, poor regions benefit from their absorptive capacity and catch up with rich regions. This catching-up can be measured by the parameter of convergence: beta-convergence (-convergence) and sigma-convergence (-convergence).
A number of efforts were implemented in order to measure the speed of intra-national and cross-country -convergence. One of the first empirical investigations was outperformed by Robert J. Barro and Xavier Sala-i-Martin in 1991 that tested the convergence across the 48 contiguous U.S. states. As a result, clear evidence of convergence was found in the sense that poor regions show tendency to grow faster than rich ones with respect to income per capita. "The wealth level of the regions with the lowest income per capita in 1880 grew fastest over the subsequent century (1880-1988) and the regions with the highest income per capita in 1880 grew the slowest" (Armstrong and Taylor, 2000, p. 82). However, the observers suggested quantitative reconciliation to neoclassical model by the condition that diminishing returns to capital to set in very slowly. Armstrong and Taylor (2000, p. 83) summarized also that later empirical studies in 1996 by Barro and Sala-i-Martin that identified the tendency of regional convergence of wealth levels to be very slow in industrialized economies.
Table 1. Estimates of convergence of regional per capita income levels.
Number of regions
Source: Armstrong and Taylor (2000, p. 83).
Table 1 represents some of the research results for Germany and the U.S. regions, which show that -convergence occurred in each of the study country within the period 1950-1990. The value of -convergence at around 2 per cent per annum or often even less indicates that the process of convergence is very slow. The rate of 2 per cent which seems to be typical to the US implies it takes 35 years for initial regional disparity to be halved, while the rate of 1 per cent explored in Europe suggests a period of 70 years. Such slow rates of convergence raise questions on the validity of the neoclassical model.
The speed of cross-country -convergence was also measured by William J. Baumol (1986) who analyzed data series collected by Angus Maddisson (1982) for the time period 1870-1979. The data collection for 16 industrialized economies was observed with a particular emphasis on the U.S. The outcome of the research was the existence of convergence of the productivities and growth rates among the industrialized countries. It was discovered that the U.S. productivity growth rate was unexpectedly steady, and there was no antecedent of any long term slowing-down in growth of either total factor or labor productivity. Strong evidence of convergence was found after the World War II. However, the sample included only a set of developed economies; therefore, it promoted a tendency in equalization of income levels between countries. "If the sample is extended by including under-developed and undeveloped economies, the existence of convergence will tend to be disclaimed. It will not be valid for the poorer countries to grow faster than the richer, and there will be no tendency for the cross national dispersion of GDP per capita to diminish over time" (Baumol, 1986, p. 1075). Therefore, the previous research supports the idea that if the sample set of data is restricted by including only industrialized and richer economies, absolute convergence may be identified.
This promoted the development of convergence research suggesting the hypothesis of "club convergence". It argues that only regions or countries with similar initial circumstances and traits of infrastructure can converge to one other. Hence, the developed countries generate one convergence club, the developing another, and underdeveloped another. As Alexiadis (2013) found out, the hypothesis of club convergence has been tested empirically by Chatterji (1992) for both world economies and for regions of individual countries. The set of data for countries over the period 1960-1985 was employed for regression analysis. The outcome of the research was similar, standing for the existence of two separate clubs: one "poor" and one "rich". The leading position was occupied by the U.S. at both initial and terminal times.
In spite of differences in preferences, technological level, formal and informal institutions between regions, these differences are proved to be smaller than those across countries. Companies and households have access to similar technologies; have similar tastes and values while the government provides the same infrastructure and institutional set-ups. Such relative homogeneity implies that the absolute convergence is more likely to occur across regions than across countries. Furthermore, factor mobility is also more attributable in regional analysis than in cross-country, since the cultural, linguistic, legal and institutional barriers are easier to overcome.
In short, the recent research of the speed of -convergence derived the following evidence (Angus Maddisson, 1982; Baumol, 1986; Barro and Sala-i-Martin, 1991; Chatterji, 1992; Rey and Montouri, 1999; Armstrong and Taylor, 2000): the poor regions tend to grow faster than the richer, but this convergence mostly occurs within the groups of developed, under-developed or undeveloped countries ("club convergence"). -convergence observed in the range of industrialized countries happened at a very slow rate – at around 2 %. Absolute convergence and factor mobility is more attributed to regional disparities than across countries.
The following section considers the initial hypothesis, data collection process, comparative analysis of initial data and testing design, concerning the concept of potential convergence in German and the U.S. regions across the time period of 1960-2010.
Empirical testing of the concept of income convergence will be implemented with the application of an econometric model. In the time series model proper specification and methodology of estimation need to be clearly stated. For convenience, we will assume that specifications are based on the hypothetico-deductive reasoning.
Depending on parameter values, the model can lead to convergence or divergence in the growth rates of GDP per capita. The initial hypothesis that needs to be tested is that poor regions grow faster than rich regions over the long run causing the convergence of incomes per capita.
The endogenous growth model application needs to be tested on the cross-regional data with the help of the concept of -convergence. We employ the data set of cross-regional GDP per capita in 11 regions of Germany and 51 states in the U.S. within 50 years and per each decade of the sample in period 1960-2010. The inter-decade regression is computed so as to investigate relative variation between relevant indicators and to decrease the potential effects of business cycles and labor migration in the intra-national level.
In the German case, the average annual growth rates (real GDP per capita) for German regions have slowed down from 3.57 % during the 1960s to 2.67 % during the 1970s, to 1.91 % during the 1980s, to 1.27 % during the 1990s, and remained the same during the first decade of millennium. It is relevant to mention that income level of the richest state Hamburg in 1960 (12.0 thousand Euro) almost twice exceeds the level of the poorest state Schleswig-Holstein (7.5 thousand Euro). The standard deviation of experimental data varies significantly between base and current period, which says how much of the variation exists from the mean. A low standard deviation (or dispersion) of 1.57 % in 1960 indicates that the GDP per capita tend to be very close to the mean; high standard deviation of 7.79 % indicates that the data points are spread out over a large range of values. The variability of the regional GDP per capita in 2010 is higher than of those in 1960.
In case of the U.S., it experienced increasing growth rates in terms of per capita income from 1.79 % to 2.54 % during 1970s and a decreasing tendency during 1980s, 1990s and 2000s (from 1.97 to 1.58 and 1.38 % respectively).
The standard deviation of GDP per capita across the U.S. regions gradually increases within the study period, which shows the volatility of the income levels between regions. A low standard deviation (or dispersion) of 0.43 % in 1960 indicates that GDP per capita tends to be very close to the mean. This implies that in 1960 all the states approached almost the same wealth level. Increased standard deviation of 7.10 % in 2010 indicates that the data points are spread out over a large range of values. The mean value of income levels across states has increased almost 20 times over the half-century period, which reflects how stable economic welfare has improved in the U.S. The coefficient of variation is slightly fluctuating: decreasing from 20.49 % to 14.71 % during 1960s and 1970s and then increasing from 16.51 % to 17.75 % during two recent decades. From the geographical point of view, southern states are catching up with the northern states and tend to converge in terms of income per capita over the study period.
In conclusion, the data series of regional income levels in Germany during the period of 1960-2010 indicate a pattern of divergence of income levels across states. This suggests the possibility of divergence in the sense of tendency of faster growth in terms of GDP per capita between regions that are further above the steady state position. There is a gap between western regions, which are richer and better developed, and eastern regions which are poorer and need to catch up with western states. In contrast, the data collection in the U.S. indicates the tendency of income equalization across the regions over study period. The southern states are catching up with northern states. This justifies the prediction of neoclassical and endogenous growth theories of convergence, which mostly rely on technological factor and human capital. Thus, less innovative regions are able to catch up with the leading regions due to externalities and spillover effect of knowledge and, hence, grow faster. Meanwhile, more innovative regions tend to create clusters that can promote better diffusion and exchange of knowledge and human capital.
This section includes the testing of the hypothesis through the application of econometric tools: Ordinary Least Squares Method and EViews 7.0. econometric software. The initial hypothesis is stated as follows: Poor regions grow faster than rich regions over the long run causing the convergence of incomes per capita. The data series of 1960-2010 have been employed for the analysis of economic income convergence across 51 states in the U.S. and 11 regions in Germany. The research testing relies on the negative correlation between growth of income per capita and its initial log form.
Under the null hypothesis it is assumed that there is no correlation between growth of GDP per capita and its initial log form; and, therefore, the conclusion of no convergence of income levels between the regions in the sample can be made. The alternative hypothesis stands for the existence of negative correlation between growth of GDP per capita and its initial log form so that regions tend to converge over study period. In order to prove the hypothesis of divergence of income levels, the results of analysis should contain positive correlation between growth of GDP per capita and its initial log form together with significant level of test statistics.
Empirical research was organized and developed. Firstly, the intra-national data series of real GDP per capita were tested for the whole study period of 1960-2010 for 51 states in the U.S. Afterwards; it was divided into 5 sub-periods for every ten years, thus limiting possible effects of political changes and economic cycles. A similar data test was executed for 11 German regions for a long term period of 1960-2010 and for each ten year period.
After testing, it is possible to conclude that Germany could have experienced convergence of GDP per capita during the 1970s and 1980s, but the data series testing failed to prove the tendency of equalization of income level due to the lack of significance in the regression. This non-reliability could emanate from the substantial differences in the levels of development and urbanization between Western and Eastern regions after World War II. Additionally, the effects of unification in 1989 and currency transition from German mark to Euro in 1999 could have an impact of distortion of the data series or on speed of convergence.
On the other hand, analysis of the cross-regional GDP per capita levels in the U.S. for the half-century period of 1960-2010 identified that the process of convergence of income levels occurred at a rate of 0.4720 %; tending to a slower rate of 0.2741 % during 1960s and to a rate of 0.1548 % during 1970s. In the recent three decades, data analysis does not seem to prove the existence of convergence or divergence due to insignificant values of estimation parameters. It is unambiguously related to the identified trend of slowing down growth rates across the U.S. states since 1980s and to a tendency of diminishing standard deviation of income per capita that proves the existence of -convergence during 1960s and 1970s. The phenomenon of disappearance of income convergence since 1980s in the U.S. can be related to interregional factor mobility. Interregional mobility of knowledge and technology leads to an equalization of incomes.
Considering the labor mobility factor, the U.S. experienced a persistent labor inflow from low-wage states to high-wage areas during the period of stable convergence before 1980. If capital is assumed to be more mobile than population, the low-wage region achieved faster income growth since the capital flowed into poorer regions faster than labor flows out which is consistent with the prediction of the neoclassical and new growth theory.
Ganong and Shoang (2012) highlight that over the recent three decades the difference between the housing prices in rich and poor regions of the U.S. significantly increased relatively to the difference of income. As a result, labor flows from poor to wealthy regions has slowed down. Highly-qualified labor continues to move to high-wage areas, whereas low-wage labor is now flowing to the regions with low nominal income but high nominal income net of housing costs. Hence, labor inflow to richer states decreased and disparities between skill and qualification levels slowed down the process of convergence.
Additionally, there is the influence of technological and innovation factor referring to the new policy approach implemented in the U.S. after 1980s in which a significant shift in spending trends in R&D occurred after 1980 in the U.S. After "having grown at an average rate of 6% per year in real terms during 1980–1985, inflation-adjusted federal R&D spending declined at an average rate of roughly 1% per year during 1985–1995" (Mowery, 1998, p. 640). This reduction of financial support from the government could have constrained the diffusion of knowledge and technological progress and, consequently, restrained the process of convergence between the states from the 1980s onwards.
More detailed analysis is needed to review the income equalization pattern between U.S. regions. Perhaps, it should be made across districts in the regions of the U.S. as "Club convergence" might have occurred across most developed states in the north and less developed states in the south of the U.S.
The slow speed of convergence in the U.S. and the finding that innovative activities in certain technological fields tend to be clustered in space, suggests that the main growth processes operate in different across regions or that development occurs unevenly over space. Several possible reasons can be given for the diversification of regional development, among which it is possible to name: the significance of spatial consequences of externalities and increasing returns to the production of output; the importance of education and human capital in regional and agglomeration economies; and the significance of innovations, technological transfer and spillover effect between regions.
Lack of empirical evidence for convergence in Germany can be explained by substantial economic diversification between Western and Eastern regions of the country. The period since the re-unification in 1989 can be characterized not only by the start of technological catch-up process, but also by significant labor migration from Eastern to Western region. Moreover, highly-qualified and educated labor was of greater demand in Western Germany, this together with essentially no restrictions on migration. This labor migration, motivated by political and economic events, promoted economic growth of Western Germany and slowed down the development of lagging Eastern region. An increased gap between Western and Eastern Germany have caused regional disparities and divergence of income levels across the country.
During the 1991 to 2009 period, the U.S. takes the leading position in comparison to Germany by investing more capital in knowledge development and R&D. However, from a dynamic perspective, Germany has been progressively raising its R&D investment and tends to catch up with the U.S., which resulted in Germany outperforming the U.S. and the European Union in patent applications (nearly doubling U.S. applications and the E.U. average). However, endogenous growth model stands for the idea that increases in investments into R&D lead higher growth rates with the positive relationship between the growth of GDP and a level of R&D. Nevertheless, empirical testing that this is not necessarily the case, as the share of GDP spent on R&D rose for the recent decades while the growth rate of GDP did not. More importantly, this situation highlights the need to consider growth-oriented policymaking as a holistic exercise rather than as stand-alone measures.
For further research, it could be useful to split the time series in the periods from 1960 to 1989 and from 1989 to 2010. The convergence could have occurred in two ways: for the period after World War II, and for the period of reunification. This could be relevant as it could mitigate to some extent the effects of political issues associated to the reunification process, including, partially, migration flows and the numeric effects of data distortion due to currency conversions.
In addition to this, more detailed analysis is needed to investigate the income equalization pattern between the U.S. regions. Perhaps, it should be made across districts in the regions of the U.S. "Club convergence" might have occurred across most developed states in the north and less developed states in the south of the U.S.
The major implication of the endogenous growth theory is concerned with the convergence of income levels and GDP growth rates between regions and states. The recent research on the speed of -convergence concluded that poor regions tend to grow faster than richer, but this convergence mostly occurs within the groups of developed, under-developed or undeveloped countries ("Club convergence").
The data series of regional income levels in Germany during the period of 1960-2010 indicate a pattern of divergence of income levels across states. This suggests the possibility of divergence in the sense of a tendency towards faster growth in terms of GDP per capita between regions that farther exceed the steady state position. There is a gap between western regions, which are richer and better developed and eastern regions which are poorer.
In contrast, the data collection in the U.S. indicates a tendency of income equalization across the regions over study period. The inference is that southern states are catching up with northern states. This justifies the prediction of neoclassical and endogenous growth theories of convergence, which mostly rely on technological factor and human capital. It may be concluded that less innovative regions are able to catch up with the leading regions due to externalities and spillover effect of knowledge and, hence, grow faster. Meanwhile, more innovative regions tend to create clusters that can promote better diffusion and exchange of knowledge and human capital.
Empirical testing for -convergence showed a trend of diminishing standard deviation in per capita level during 1970s, 1980s and 2000s in 11 regions of Germany and during 1970s and 2000s in the 51 regions of the U.S. The phenomenon suggests the fluctuating tendency for the German regions and American states to equalization of income levels over the period from 1960 to 1980. According to the empirical analysis, Germany could have experienced -convergence of GDP per capita during the 1970s and 1980s, but the data series testing failed to prove the tendency of equalization of income level due to the lack of significance of the regression, which could be due to substantial differences in the levels of development and urbanization between western and eastern regions after World War II, and the effects of re-unification, and currency transitions.
Empirical analysis of the cross regional GDP per capita levels in the U.S. for the half-century period of 1960-2010 identified that the process of convergence of income levels. This proves the hypothesis that poorer southern states tended to grow faster than richer northern states in terms of incomes per capita due to technological catching-up process and spillover effects of knowledge. The recent three decades data analysis does not seem to prove the existence of convergence or divergence due to insignificant values of estimation parameters. The identified phenomenon of disappearance of income convergence since 1980s in the U.S. can be related to interregional labor and technological factor mobility. Firstly, a significant increase of housing prices relatively to the growth of income could cause the decrease of labor inflow to richer states over the recent three decades. Secondly, significant declining shift in spending trends in R&D system occurred after 1980 in the U.S, which could have constrained technological progress as well as diffusion of knowledge and, consequently, slowed down the process of income convergence across the states.
Regions with a comparatively low level of technological progress have an opportunity to catch up with the leader in an environment of favorable socio-political conditions. The phenomenon of regional growth disparities can be explained by: the spatial consequences of externalities and increasing returns to the production of output; the education and human capital in regional and agglomeration economies; the intensity of innovative activities, technological transfer and spillover effect between regions.
Given the differentiated results of convergence in the U.S. and absence of convergence in Germany, subsequent research should focus on the reasons why two highly industrialized economies exhibit different patterns. It can be concluded that low-wage regions grow faster in terms of income level if the capital flows into poorer regions faster than labor flows out. Technical progress needs to be stimulated through the diffusion of knowledge towards poorer regions while taking into account the region's unique profile, its advantages and disadvantages toward knowledge use and its exploitation. More importantly, the analysis highlights the need to consider growth-oriented policymaking as a holistic exercise rather than as stand-alone measures.
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