Convergence of per Capita Income in the United States, Essay Example

Economists have always had the inherent need to study and measure any underlying economic disparities between distinct geographic areas and regions. In order for distinct regional areas to develop and sustain regional growth, they have to be engaged in a process that institutes monetary and economic amalgamation and drive these economic regions towards a single market. One of the main schools of thought in the integration theory if the regional convergence theory. This theory, as postulated by Barro and Sala-i-Martin, states that complete and optimal integration that results in the development of a single currency across regions will mitigate the economic and social disparities that existed between these regions. In the long-run, this is expected to lead to the convergence of a number of economic factors and indicators, such as income. The United States of America, as depicted in Barro and Sala-i-Martin’s study, has considerably adopted economic integration, embodied in a single currency, the US Dollar, used in all member states.

The Convergence Theory

The convergence theory is made up of two main approaches that is used to quantify the relationship between convergence and the economic growth process.

Sigma Convergence

This is the traditional approach towards quantifying the relationship between convergence and the economic growth process. Sigma convergence is based on analyzing the standard deviation in real per capita income between regions over time. As the standard deviation of per capita income depicts the underlying differences in economic conditions, when it appears to fall over time, it indicates the general decline in the economic differences between the regions in question. Barro and Sala-i-Martin’s study depicted that in the United States, standard deviation in per capita income decreased over time, since its inception. This is evidence of an underlying convergence of factors and real per capita income.

When sigma convergence depicts an increase in deviation in real per capita income between different regions, it indicates divergence. However, a state of mixed convergence, characterized by alternate periods of convergence and divergence, lead to a general state of no deviation. Sigma convergence can alternatively be obtained by mathematical application of division of standards deviation of a given sample by its mean. When the value of the coefficient of variation declined over time, it indicates that at here is regional convergence present in the given region of interest. Divergence is depicted by an increasing coefficient of variation over time.

Beta Convergence

Neoclassical models employ the beta convergence to depict per capita income growth for a given period of time, founded on a given base period. This means that the analysis is usually executed by comparing the initial level of per capita income of a given base period. Beta convergence employs the use of regression analysis where a negative beta coefficient sign show that the regions that initially experienced low per capita income are experiencing faster growth than the regions with initially high levels of per capita income. This is designated by the following non-linear expression

• is the real per capita income of a given regionat time
• is the initial per capita income of a given region
• are the exogenous variables that have an influence on per capita income growth rate
• is the length of time for which the per capita growth rate is measure
• is the stochastic error of the equation
• is the constant that is determined and influenced by per capita income growth rate and the technological factors influencing the analysis of the given region of interest.
• is the convergence coefficient that is derived from estimation using non-linear mathematical application.

Types of Convergence

The neoclassical models highlight two types of convergence. Namely; (1) unconditional convergence, and (2) conditional convergence. Unconditional convergence is characterized by the general assumption that the given regions in question converge towards the steady state point. This is where all regions converge towards a common terminal point. Here the structural variables,, are not taken into consideration when determining. This is because all distinct regions are presumed to have similar states of structural variables such as human capital qualification, investment ratio and technological levels. As such, unconditional convergence is commonly detected and applied in regions with homogenous systems and structures. Regions found within the same sovereign state, characterized by a common legal system, technology and economic structure, usually depict homogenous characteristics of structural variables that influence growth rate of per capita income.

Economies with differing structural variables are presumed to be converging at different steady state points. This kind of convergence is largely dependent on the influence that the structural variables have on per capita income growth rate. The convergence coefficient,, is determined by taking into account the implication of these structural variables.

The convergence theory under the neoclassical models depicts the poor regions have a faster-growing per capita income as compared to rich regions. This is due to the law of diminishing returns that is engrained in the neo-classical models. The law of diminishing returns of capital infers a negative relationship between stock of per capita income per head and the rate of return, i.e., ceteris paribus, regions with high levels of capital stock per head grow much slower than those with lower levels if capital stock per head.  

According to Barro and Salis, the equation highlighted above, has been employed to study per capital personal income in 48 states in the USA and depicts beta convergence of 2% every year. However, the study also notes that there is no stable beta convergence throughout the years for which the analysis was performed. The beta coefficient varies with the chose time period. This is largely owing to the difference in the economic environment with time.

Statistical Interpretation

Income convergence in the United States has experienced a considerable decline since the study conducted by Barro and Sala-i-Martin and the population flow to areas of considerable wealth, relative to the nation’s average wealth. The changes in income convergence can be linked to three vital economic factors; housing prices in highly productive areas have gone up, skill-specific returns in highly productive areas have experienced divergence and the movement of unskilled labor from areas of high productivity. The model employed in this study takes into consideration the effect that growing house prices have on unskilled migration and income convergence. The model postulates that growing housing prices tends to slow down the convergence of income while deterring unskilled migration in areas of high productivity. According to the data analysis performed, the convergence of per capita personal income has declined from the initial 1.8% to 2% per year, to less that 0.9% annually. Interestingly, the period just before the great recession experienced negligible, and at times zero convergence.

The cost of living, largely affected by the cost of housing considerably influences the flow of migration. Barro and Sala-i-Martin depict this fact in their study that revealed population flow to areas that generate wealth, i.e. highly productive areas. However, an increase in population in a given area of interest. This develops a relationship between per capita personal income and population growth. However, the data analysis performed depicts a decline in this relationship in the past three decades. Wages, the marginal product of labor, is inversely related to population growth. At the onset, most rich states experienced unconstrained housing supply. This attracted individuals from all levels of skilled labor towards areas of high productivity. However, over time, the influx in the population serves to drive down the marginal product of labor within these areas. The high demand for housing and the constriction of its supply brings up the cost of housing in these areas as well. The declining levels of marginal product of labor leads to income convergence. However, since unskilled labor is particularly responsive to the cost of living, the rising cost of housing reverts the income convergence that had been initially recorded.

Statistical Model

The statistical model employed in this study, take into consideration the 48 states in the USA, but concentrates on two specific areas of interest. These areas, within a single national market, are handpicked from the North of the USA, where it is deemed to be more productive, and the less productive Southern States. The model takes into consideration that all individuals living in these areas have to consumer two types of goods. Namely; tradable numeraire and non-tradable housing.

The model also take into consideration the interregional allocation of labor. At the beginning, wages are seen to be lower in the Southern States as productivity is low. Migration flows to the Northern states owing to the attractive levels of marginal returns to labor. As a result, the increasing population drives down the marginal returns to labor while increasing demand for housing and straining its supply. The reduction in population in the south raises wages as labor is in short supply and its demand goes up. it also serves to creating considerable availability of housing within the South, reducing the cost of housing and the cost of living. These forces of demand and supply working in poosite directions in the North and South serves to bring about convergence.

As the North continues to realize a net increase in population, the cost of construction may go up as a result of an increase in the demand for housing. This further increases the cost of housing in the north and constrains the flow of migration into these regions. Income convergence under these conditions slows down with time, further compounded by the fact that these areas are now filled with skilled labor.

Conclusion

Per capital income in the United States had realized convergence in the past century, during the time of Barro and Sala-i-Martin’s study. However, the increase in availability of labor in areas of high productivity led to the eventual reversion of the inter-regional conversion of income. This was largely due to the influx in net population flow in areas of high productivity from areas of low productivity. ­this served to slow down income convergence in the United States. The data depicts how migration patterns from low productivity area to high productivity areas have changed the relationship between housing prices and income.

Works Cited

Barro, Robert J and Xavier Sala-i-Martin. “Convergence across States and Regions.” Convergence across States and Regions (1991): 107-182. Electronic Source.

Cortes , Patricia. “The Effect of Low-Skilled Immigration on U . S . Prices : Evidence from CPI Data Patricia Cortes.” Journal of Political Economy 116.3 (2008): 381-422. Print.

DiCecio, Riccardo and Charles S Gascom. “Convergence Across States and People.” Economic Synopses 1.2 (2008): 1-2. Electronic Source. 5 May 2015. <http://research.stlouisfed.org/publications/es/08/ES0802.pdf>.

DiCecio, Riccardo and Charles S Gascon. “Income Convergence in the United States: A Tale of Migration and Urbanization.” Annals of Regional Science 45 (2008): 365–377. Print.

Ganong, Peter and Daniel Shoag. Why Has Regional Income Convergence in the U.S. Declined. Harvard University, 2014. Electronic Source. 5 May 2015. <http://isites.harvard.edu/fs/docs/icb.topic1121952.files/Papers%20Fall%202012/SHOAG%20paper.pdf>.