1. Introduction

Income distribution is a major concern for most economists. Classical economists, who took the income distribution theory as the core for economy, argued that the distribution rules among different classes for the production process of commodities should be the major research theme of political economics. New Classical economists inherited from Classical ones, studying the distribution rules from production factors, developing the income distribution theories which now are basic elements in economics textbooks. In 1950s, the research centre of income distribution shifted to individual distribution, i.e., from the distribution of national income between wages and profits to the inequality of income distribution among individuals described by Gini coefficient. The relationship between income inequality and economic growth has been widely studies. It has been one of the growing points in the macroeconomics and the economic theory during the past 20 years.

The relationship between income inequality and economic growth has been studied by economists within different data source and models since 1950s. However, the conclusion is still not clear. The income equity in East Asia accompanied with the economic growth in resent years, while the income gap expands along with the economic growth in South American. It was generally believed that the income inequity had positive effects on economic growth researches before 1980s, and again most researches hold an opposite opinion after that. However, very recently various empirical data based models have been used to study this question by scholars, which show positive effects of inequity on economic growth.

Economists in the mid-20th century studied this question via the saving-investment aspect. People from rich class, who contributed main savings and investments for society, had more savings rate than others; thus the income inequality could promote savings and investments, hence enhanced the economic growth (Kaldor, 1957; Lewis, 1954; Pasinetti, 1962). Theories of income distribution have widened the explanation of the effect of inequality and economic growth nowadays by some in-depth studies from political economics, education and fertility decision, social stability and market demand aspects.

This essay introduced some theories of distribution inequality and economic growth, including political and economical model, fertility and education, social unrest factors and demand model. In addition, it took an insight study and explanation of Forbes (2000) model, discussing the economic growth affected by inequality, income, education, etc.

2. Theoretical analysis

2.1 General analysis

In the early stage of economic development, the inequality distribution of income would cause the effective concentration of resource. Especially inequality distribution among different areas, would benefit to the positive formation of economic growth, and promote the development of economy. Economic development will likewise improve people’s income. In the process of income improvement, high income owner may have faster income growth speed, resulting in a continually expansion of inequality.

However, when economic level was sufficient to provide necessary support for low-income class, the economic market and the government would have positive effect on narrowing the income gap. In addition, the economic growth would change the cost structure of enterprises. It would cost much more to employ high-income employees than lower ones. Competitive enterprises then would search for lower cost labours. The competitiveness between high and low income staffs would result in lower ones receiving higher wages, and also limit the income growth rate for high-income people, which could finally decrease the inequality scope. For regional differences, along with the economic development, resource depleted in developed areas, which leads to enterprises investigated in less developed areas where resources are relatively sufficient. This would promote the economic growth of less developed areas, and reducing the distribution inequality. The government’s policies are likely to promote economic growth of less development areas, to change the economical environment and attract investment in those areas, reducing inequality among areas. Meanwhile, the economic development could increase the human capital investment, providing more educational opportunities for low-income people, and improve their future income.

2.2 Political and economical model

The distribution inequality and economic growth in these models were considered mainly to be determined by economic and political balances. The initial distribution of income would affect the political process, i.e., the preferences of voters, through which affects the distribution policies and finally economic growth (Alesina & Rodrik, 1994; Bénabou, 1996; Bertola, 1993; Perotti, 1993; Romer, 1986).

In the Alesina & Rodrik (1994) model, the government production service which was used as an indicator of distribution was added to the economic growth model. With the principle of median-voter theorem, it was proved a negative relationship between distribution inequality and economic growth. This was consistent with some empirical results. There was a key index σi i∈ [0, ∞) ) indicating each individual’s relative factor endowment, which was a monotonic relationship index between income distribution and economic. The bigger of σi meant the more unequal of distribution. Government assessed upon capital tax to provide public services. Those public services were productive and must be used for producer in production.

This aspect was similar to Romer (1986) model: Economy could also be considered as goods in production, and the best economic growth rate was closely related to government capital tax rate which was nonlinear. In the low tax rate period, the increase of tax rate could increase the economic growth rate; in the high tax rate period, the increase of tax rate would be harmful to economic growth, i.e., a bell shape relationship between capital rate and economic. On the other hand, government policies were to choose an optimal capital tax rate to maximize the total welfare of society. According to the median-voter theorem, policies decision was influenced mainly by the major median-voters. Voting here was not fully based on political processes, but reflected profits of most people. People from different income classes had different ideal tax preference: people with low income preferred a higher tax tare which high income preferred lower tax rate. Results finally showed that in an inequality society, the capital tax rate was not in the level which had the fastest economic growth rate, but lower this level. Lower income of median-voters than social average income, the government would choose a higher capital tax rate, hence damaged to economic growth. Therefore, in those models, income inequality would have negative effects on economic growth rate.

2.3 Fertility and education decision

According to (Perotti, 1996), rich families would have higher human resource investments than poor ones, and fertility decisions are the weighing results of parents decided for human resource investment costs and direst costs of rearing children. Higher human resource investments parents would have larger opportunities cost as well as education cost, with less demand for child number, and vice versa.

The above theory could therefore infer the following conclusion: first, the decline of distribution inequality would increase the human resource capital investment and decrease the fertility rate; second, the increase of human resource capital and decrease of fertility rate would improve the economic growth rate; and therefore, the decline of distribution inequality would improve the economic growth rate. This hypothesis was tested by Perotti (1996) who found that the greater proportion of middle-class incomes came with the lower fertility rate and higher economic growth rate. This conclusion had statistically significant. Therefore, it would be a promising research direction to study the relationship between distribution inequality and economic growth from the fertility and education aspect.

2.4 Social unrest factor

The unequal distribution of wealth and income would lead to the social unrest such as crime and riots participated by poor people, resulting in the waste of social resource; on the other hand, cost economic and labour efforts to prevent those unrest, and finally harmful to economic growth (Alesina & Perotti, 1996; Benhabib & Rustichini, 1996; Benhabib, 2003).

The distribution inequality would cause dissatisfy of low-income people to social economic status when facing rich ones, and would require the reform of social system. Social reformation would bring instability of the political system. This instability would lead to the uncertainty of legal and regulations for a short term, and causing the negative impact on economic growth. On the other hand, inequality prompted low-income people to engage in crime, violence and other destructive activities, while those activities would not be put into production but threaten investment which mainly determined by property right. Therefore, inequality would lead to social unrest, decreasing investment levels and production, and damage to economic growth. In addition, the nature of a government, democratic or authoritarian, although does not have same effects as social unrest on economic growth, also has negative effects on economy when transforming from dictatorship to democracy for a short term (Alesina & Perotti, 1996).

2.5 Demand model

Demand is the main driver for economic growth. The distribution equality would directly affect demand level, and hence influence the industrialization and economic growth (Murphy et al., 1989).

During the development process of a country, the improvement of agricultural productivity or exports expansion increases people’s income and then their demand for industrial products, and eventually promotes the development of industrialization. However, if the increased income from agricultural productivity or exports does not cause the increased demand of industrial products and the domestic industrial market still is relatively small, then industrialization cannot be realized. Therefore, the demand structure which was restricted by income structure, i.e., income distribution, would affect the industrialization process. The expansion of domestic demand, particularly for industrial products, needs the supportive form middle class people. Generally, rich people demands for senior crafts or luxury import goods, rather than common domestic industrial products. The increase gross from agricultural productivity or exports are mainly concentrated in a small number of rich people, so that distribution equality would have negative effect on economic growth.

3. Forbes Model

3.1 Model introduction

Many economists are trying to measure the relationship between inequality and economic growth from various independent variable models. Most of these studies found a negative effect of distribution inequality on economic growth, and the statistical significance was not very strong (Alesina & Perotti, 1994; Rodrik & Alesina, 1994).

However, Kristin Forbes (2000) found an opposite result – positive relationship between income inequality and economic growth. According to Forbes (2000), the previous studies for the negative impact result are not robust; most measurements rely on exogenous variables, such as total wealth, political systems and development levels; all previous empirical studies do not have high quality data, with measurement bias caused by measuring the income inequality error and ignoring some relevant variables, leading to invalid estimates. Based on the disadvantages of previous studies, Forbes’s growth equation was similar to previous ones, but use Deininger and Squire (1996) of the high quality inequality data and new method to evaluate the income inequality and economic growth; the inequality was measured by gini coefficients. The economic growth was set as dependent variable, with independent variable including initial inequality index, income level, men and women education, country’s market distortions, country dummies and period dummies. The initial equation was:

Growthit = β1Inequalityi, t – 1 + β2Incomei,t – 1 + β3MaleEducationi,t – 1 + β4FemaleEducationi,t – 1 + β5PPPIi,t-1 + αi + ηt + uit.

In this equation, i represents a country and t for a certain time period, where t = 1, 2, 3, … T. Growthit represents the average annual growth for country i during time period t; Inequalityi, t – 1 represent the inequality level for country i during time period t – 1; hereafter the same meaning for the Incomei,t – 1 , MaleEducationi,t – 1, FemaleEducationi,t – 1 and PPPIi,t-1 representing income, male education, female education and market distortion for country i during time period t – 1. αi, ηt, and uit represent country dummies, period dummies and error term, respectively. β1 to β5 are coefficients that need to be evaluated.

3.2 Model estimation, simplification

Forbes used four different techniques to estimate this equation. There are: fixed effects, random effects, Chamberlain’s p-matrix technique, and generalized method of moments (GMM) by Manuel Arellano and Stephen R. Bond (1991). A 5-year time period data was used when estimation. Different estimate techniques have different significant value. When testing the validity of each estimation method, Arellano and Bond’s GMM were consistent and efficient. Testing results from GMM are mainly discussed.

In this essay, to make it more understandable, the equation could be idealized as

Y = B1X1 + B2X2 + B3X3 + B4X4 + B5X5 + C,

where Y represents depend variable economic growth; X1 to X5 independent variables represent inequality, income, male education, female education and market distortion; C represents country dummies, period dummies and error term. Since only inequality, income, education and market distortion are mainly considered here, variable C could not be taken account in this ideal equation. Then the equation is:

Y = B1X1 + B2X2 + B3X3 + B4X4 + B5X5,

where B1 to B5 are coefficients that we care about.

Coefficients

B1

B2

B3

B4

B5

Estimated value

0.0013

– 0.047

– 0.008

0.074

– 0.0013

p value

0.0006

0.008

0.022

0.018

0.0001

Table 1. The regression results from Arellano and Bond GMM method in Forbes (2000); estimation were virtually identical for the period from 1970 to 1995 with 135 observations according 45 countries; p value shows the regression significance.

Table 1 shows the estimated coefficient values from Forbes (2000) with the technique of GMM. Data was from 45 countries with 135 observations from 1970 to 1995, within five-year periods. Results showed that all estimated values were significant under the confidence level of 5 %. Throughout this results, there was positive effect of the inequality on economic growth were estimated (B1 = 0.0013, p = 0.0006); negative effect for income and market distortion (B2 = 0.047, p = 0.008; and B5 = 0.0013, p = 0.0001); male and female education have different effects on economic growth, specifically, negative for male education (B3 = 0.008, p = 0.022) and positive for female education (B4 = 0.074, p = 0.018), although significant value was not very strong.

3.3 Model Discussion

In Forbes’ model, five-year panels were used when estimations variable impacts (indeed another ten-year period panels were utilized in fixed effects in his results, no discussion here). However, there are no criteria when choosing the time period and five-year was the author’s subjective choice. Because of lacking of sufficient data, there is no observation from a long-term, 30 years or even 50 years, to test those effects. We can only say from Forbes’ model that inequality has positive effect on economic growth from a shot term time period (5 years). In fact, Forbes argued that the result was not indeed contracted with study taken by Perotti (1996) who found negative relationship between inequality and economic growth because Perotti’s model was from a relative long term relationship.

Data if inequality value would have measured problems that there is a deviation of the dummy variables among countries. Data from a province or state of a country might be more accurate. In addition, to some developing countries, the income inequality would effect economic growth via education and investment, where investment would have a larger proportion. Hence, economic growth is more likely to be affected by investment than inequality, while investment driver was not included in Forbes’s model.

4. Conclusion

There are many studies for the relationship between inequality and economic growth. Theoretical studies include political and economical factor, social stability factor, fertility and education, etc. Empirical ones mainly use the latest data stetting panel model and simultaneous equation to study this relationship across and within countries. Those conclusions have positive effects on determining the nature and interaction mechanisms between inequality and economic growth, which is useful for policies makers.

However, there are some limitations in those researches. First, there is still no consistent conclusion of the relationship between inequality and economic growth. Second, although many theories have been used to explain this relationship, different explanations could hardly be combined. Third, there is no unique and standard index could be used to measure the inequality distribution, thus conclusion would be different even for the same area and same time period. Fourth, there is no long term observation for economic growth and we can not have the conclusion for the long term impact of inequality on economic growth. Fifth, most economists studied their relationship from one-way aspect, i.e., the effect of inequality on economic growth, or economic growth on inequality, but few from interaction aspects. Finally, new measurement methods might have a prior conclusion when study the relationship between inequality and economic growth, but the difference in sample selection, estimation model method and data processing would all lead to a different conclusion.

Overall, from either empirical or theoretical aspects, the relationship between the income inequality and economic growth is still not clear. Inequality and economy relationship are a complicated issue. It can be affected by many economic and non-economic factors, and different factors vary much when influencing their relationship. Results also vary under different economical development stages, different economic systems and social systems, and different economic structures. It is hard to draw a same conclusion. While the formulation of policies needs theoretical and certain conclusions. Therefore, more studies should be taken to understand their relationship. Deeper but wider theoretical studies, better measurement methods with  more reliable data researches are very necessary, to give a theoretical support for policy makers.

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