Measures of Income Inequality and Economic Growth

1、Measures of Income Inequality and Economic Growth Measures of Income Inequality and Economic Growth Sept. 2004 Pak Hung Mo Hong Kong Baptist University, School of Business Kowloon Tong, Hong Kong. 1 Abstract There are many measures of income inequality and also many discussions on the differences be

2、tween the measures. In this study, we find that several measures of income inequality do capture different effects on economic behavior and performance. If we want to predict the effects of inequality on economic growth and socio-political stability, the middle-quintile income share outperforms the

3、commonly adopted Gini coefficient. We open up a new way for looking into how different measures of inequality in affecting economic growth and some commonly suggested transmission channels. JEL Classification: O15, O31. 2 I. Introduction There are many measures of income inequality and also many dis

4、cussions on the differences between the measures. However, most of the discussions are only of theoretical interest. To our best knowledge, there are no comparative studies on the empirical implications of various measurements. It is widely recognized that there can be no single best measure of inco

5、me distribution inequality. The choice of a measure depends on the particular aspect of inequality in which one is interested. Among various measures, the most popular one is the Gini coefficient. However, there are several disadvantages of the measure. The coefficient is insensitive to changes in i

6、ncome distribution and to errors of measurement. The observed range of variation within a country over time is small when comparing with the possible sampling errors. Moreover, the ratio does not distinguish between different locations of inequality within the income range; for example, between the

7、effects of unemployment increasing at the low end during depressions, and the effects of dividends increasing it at the high end during prosperity. Bronfenbrenner, 1971 In particular, we can say that a distribution is more equal than the other according to the Gini measurement if the Lorenz curve of

8、 a distribution lies entirely above that of another. However, when the Lorenz curves of two distributions intersect each other, the measurement becomes inconclusive. A simple statistical measure of inequality is the range, the difference between the largest and smallest of the data. It can be comput

9、ed very easily by observing the extreme values. It was dismissed by Sen as it does not make use of the information provided by the other observations. However, it is considered by Wiles (1974) as one of the best measures of inequality on the argument that there is usually little difference in the re

10、lative incomes of people in the intermediate levels, and therefore what is needed is a measure of the extent to which the top incomes differ from the bottom incomes. In most studies the ratio between the incomes of the top and bottom 10 or 20 percent of the population is employed to capture the extr

11、emity of income distribution. Although this measure ignores much of the 3 information collected, it describes how big the difference is in the standard of living between the richest and the poorest members in a society that may have substantial effect on the performance of an economy as well as of m

12、uch interest to the general public. Moreover, it is more sensitive than most other measures in the sense of being much more variable between societies and over time.1 (Sundrum, 1990) Similar discussions and comments on various measures can be endless. In recent empirical studies on the effects of in

13、come inequality, apart from the commonly used Gini coefficient, the measurements include the income share of the top 20% of population and the income share of the bottom 40% of population as in Park (1998) and the middle-quintile income share as in Partridge (1997). However, the merits, demerits and

14、 the empirical contents of various measurements have never been understood. In this paper, we investigate the empirical implications on the economic performances of several common inequality measures, namely, the ratio between the top and bottom income shares, middle-quintile income share and the Gi

15、ni coefficient. The following section is an introduction of the analytical framework. Section three reports the descriptive data and empirical results. The last section concludes our findings. 2. Analytical Framework This section can be substantially shorten in publication Following the model set in

16、 Mo 2000, 2001, the input-output relationship is characterized by a general production function of the form: (1) Y=Tf(K,L), where Y is the total output level, T is total factor productivity, K and L is the capital stock and labor respectively. Total differentiation of Y gives: 1 In this study, we fi

17、nd that this measure do have higher coefficient of variation relative to other measures. However, economic growth is not most sensitive to this measure. 4 (2) dY=fdT+T(fKdK+fLdL). Divide (2) by Y, we have: dYdTdKfLdL(3) =+TfLK+. YTYfL Simplifying the expression: (4) GR=Fg,IY,dLL, where GR and are th

18、e growth rates of real GDP and total factor productivity respectively, IY is the investment output ratio and dLL is the growth rate of labor. F equals 1, FIY is the marginal product of capital and FdLL is the elasticity of output to labor. We then have to decide the factors affecting the growth rate

19、 of total factor productivity. Based on prior works in the literature, the initial level of real GDP per capita is used as the basic control variable which is expected to have negative effect on the growth rate. This convergence tendency is usually considered as the effect of knowledge gap between c

20、ountries in the literature of endogenous growth. The larger the knowledge gap, the easier will be for a country to raise their productivity by learning, imitating and adapting technology from leading economies Barro and Sala-I-Martin, 1995. The initial per capita output is commonly used to capture t

21、his effect on the growth of total factor productivity between countries. Recent investigations have found empirical evidences on a positive relationship between inequality and sociopolitical instability Mo, 2000; Alesina and Perotti, 1996). The instability creates uncertainty in property rights 5 pr

22、otection and hence reduces investment and productivity. Consequently, income inequality has negative effect on economic growth. Redistributive policy is another channel suggested through which income distribution inequality affects economic growth. The more unequal the income distribution is in a so

23、ciety, the more income redistribution is sought by the majority of the population. These redistributive policies will reduce growth by introducing economic distortions and disincentives Alesina and Rodrik 1994; Persson and Tabellini 1994; Layard and Nickell, 1986. Another suggested influence of inco

24、me distribution on growth is through its effect on human capital formation. Individual investment in education involves opportunity cost in the form of current earnings that the family unit forgoes as well as the direct costs for education. Families with subsistence earning may be trapped in a low-e

25、ducation and low-income cycle as they cannot afford to invest in education. It is widely suggested that income inequality will therefore result in a lower rate of human capital accumulation and hence lower human capital stock and economic growth for example, Galor and Zeira 1993. Political instabili

26、ty (PINSTAB), the ratio of government transfer in GDP (TRANY) and human capital (HUMAN) are therefore included as the major transmission variables. Finally, income distribution inequality (INE) is included as the focus of our research. The expected sign of INE is negative according to various studie

27、s like Mo 2000, Perotti 1996, Alesina and Rodrik 1994, and Persson & Tabellini 1994, among others. In notation: (5) g=g(INE,y0,PINSTAB,TRANY,HUMAN), where INE is a measure of income distribution inequality, y0 is the initial GDP per capita 2. 2 Although there may have many possible variables aff

28、ecting economic growth, such as corruption , land distribution inequality (Mo, 2000, 2003) and possibly many others, it does not mean that we have to include all the possible variables into the models. If the variables have causality 6 According to the findings in Benhabib and Spiegel 1994, human ca

29、pital stock has positive effect on the growth rate of total factor productivity. The basic idea is that educated labor force is better at learning, creating and implementing new technologies, thereby generating a higher rate of productivity growth. For the determination of the investment ratio, we b

30、orrow the idea of Schumpeter 1912, 1939. Investment is driven and made possible by the existence of profit. However, without development or equivalently, an increase in total factor productivity, there will be no profit. Only when new techniques of production are employed to produce a certain produc

31、t or if a new product is introduced, profit can arise. Otherwise profit is driven to zero in a competitive market. It is the change in the fund of technical knowledge that is responsible for the change in the stock of producer goods. The investment ratio is therefore positively related to the growth

32、 rate of total factor productivity. That is: IY= IY(), with IY > 0. Since the inequality is expected to have negative effect on the growth rate of total factor productivity, we should expect that the INE has negative effect on the investment ratio as well. However, there is a common belief that t

33、he rich save proportionately more than the poor, so that greater income inequality tends to be associated with higher savings. Consequently, we do not have an expected overall effect of income inequality on the investment ratio3. Substituting (5) into (4) and introducing the inequality as a direct d

34、eterminant of the investment ratio, we have: relationship with the variable concerned or the variables are not highly correlated with the concerned variable, the absence of the variables will have no substantial effect on our major conclusions even though the missing variables affect economic growth

35、. We therefore include only those variables that are found to have substantial effect on economic growth and are likely to be highly correlated with the concerned variable. Apart from the variables discussed in this section, we also include the level of political rights as the basic control variable

36、s as it is likely to have substantial effect on the transmission variables as well as the growth rate. (Przeworski and Limongi,1993). The consistency of our results among different models and with the findings in Mo (2000) provides supports to our specifications and conclusions. 3 In our empirical s

37、tudies, the latter effect of the inequality on investment is not substantial. 7 (6) GR=F4g(INE,y0,PINSTAB,TRANY,HUMAN),IY(g,INE),dLL. The growth of total factor productivity not only drives the growth of GDP directly, but also raises the profitability of investment and hence the investment ratio. Ac

38、cordingly, the total effect of inequality on the growth rate can be decomposed into the direct effect on the productivity, the effects on productivity through the transmission variables and finally, the effect on the investment ratio. The total effect can therefore be decomposed according to equatio

39、n. dGR臝GR螔臝GR臝TV臝IY臝g臝IY(7) =臝+(臝臝)+F(). dININETVINE臝+EIYTVg臝INE臝INEwhere TV equals PINSTAB, TRANY and HUMAN. Equation (7) states that the total effect of INE on the growth rate of GDP equals to the summation of its effect on total factor productivity and its overall effect on the investment ratio w

40、eighted by the marginal product of capital. Empirically the total effect of income inequality on economic growth, its effect on the respective transmission variables and private investment can be estimated. We can cross check whether the estimates behave according to equation 7. For the purpose, thr

41、ee sets of specifications will be estimated, the first set is: (8) GR=g(INE,y0,TV,dLL,IY). 4 In reality, other than the productivity growth rate and income inequality, the investment ratio is also driven by some exogenous variables such as culture, demographic factors, and historical experience of a

42、 country. Perfect collinearity between IY and the development variables will not happen. 8 Regression based on (8) will generate the estimates of the marginal product of capital, the partial effects of the transmission variables and the direct impact of income inequality on the rate of productivity

43、growth. The second set is: (9) IY=q(INE,y0,dLL), and (10) TV=5k(INE,y0,dLL). They will provide the estimates of the effects of INE on the investment ratio and the transmission variables. Lastly, we will estimate: (11) GR=h(INE,y0,dLL). Equation (11) is the reduced form of equation (9). The only diff

44、erence between equation (11) and (9) is the absence of the transmission variables and the investment ratio. Regression based on (11) can provide the estimate of the overall effect of INE on the growth rate. If the relationship of the estimates generated from (8), (9), (10) and (11) matches the impli

45、cation as in equation (7), we will have more confidence on the validity of the analytical framework and the empirical results. 3. Data and Descriptive Statistics Apart from the data on income inequality, all data are obtained from the data set assembled by Robert Barro and J-W Lee. It is a panel dat

46、a set starting from 1960 to 1985 divided into five 5-year subperiods. In the periods before 1970, we find that some essential variables have a large number of missing observations. Meaningful estimations can only start from 1970. Recent financial crises in the world reveal that the short-term GDP gr

47、owth rate of a country can fluctuate wildly according to its country-specific conditions. To study the determinants of the growths in total 9 factor productivity and capital stock, we need to observe their performance over a longer period. The period 1970 to 1985 is therefore chosen for this study.

48、For the measures of income inequality, we use the cross-country data set assembled by Deininger and Squire. It includes Gini coefficients and the cumulative quintile shares measured in different years. The stage of development is likely to be correlated with GDP growth rate and income distribution a

49、t the same time. Since the stage of development can last for decades, using the inequality indexes measured at the beginning of or before the period studied may not be able to solve the spurious correlation problem between the growth rate and income distribution. To deal with this problem, the two s

50、tages least square method is employed in our regressions. The inequality measures are regressed with the regional dummies, initial human capital stock and the right-hand-side variables in various specifications. The predicted value is used as the instrumental variable for the income inequality measu

51、res. If a country has more than one observation, we take the one that is closest to the beginning of the period, that is, year 1970 as the indicator of income inequality. Furthermore, we include the year of the chosen inequality observation, the initial per capita income and the level of political r

52、ights as the basic right-hand-side variables in all regressions to reduce the possible spurious correlation problem. The instruments used in the regressions are listed in the note to Table B. After trying different sets of instruments, we find that our conclusions are generally robust. All the varia

53、bles in the following empirical study match closely with the analytical framework. The average schooling years in the total population over age 25 is used as the proxy for the stock of human capital. The annual growth rate of a variable is approximated by fitting the compound interest rate formula.6

54、 5 The growth rate of labor is also used as the basic control variable in all regressions as the demographic factor is likely to have widespread effects on an economy. 6 For example, the annual growth rate in GDP is estimated by finding r in the formula: GDP70*(1+r)15=GDP85, where GDP70(85) is the r

55、eal gross domestic product in 1970 (1985). 10 The correlation and descriptive statistics of the major variables used in this study are summarized in Table A. The variables are defined in the footnote to the table and the original acronyms and sources of data are summarized in the Appendix Table. Ins

56、ert Table A about here Table A: Correlation Coefficients and Descriptive Statistics GR GINI EXTR2 EXTR1 MIDY INSTAB TRANY HUMAN GR 1 GINI 0.097 1 EXTR2 0.041 0.863 1 EXTR1 0.068 0.820 0.925 1 MIDY -0.186 -0.874 -0.760 -0.727 1 INSTAB -0.265 0.083 -0.034 -0.085 -0.038 1 TRANY -0.130 -0.461 -0.303 -0.

57、283 0.413 -0.292 1 HUMAN -0.204 -0.598 -0.430 -0.341 0.527 -0.299 0.506 1 IY 0.387 -0.300 -0.266 -0.188 0.279 -0.298 0.242 0.426 HUM70 -0.208 -0.589 -0.419 -0.323 0.531 -0.286 0.503 0.984 YEAR 0.045 0.118 0.010 0.018 -0.0973 0.046 -0.010 -0.223 y70 -0.317 -0.594 -0.405 -0.343 0.544 -0.320 0.450 0.878 POPG 0.199 0.656 0.490 0.461 -0.640 0.195 -0.575 -0.754 PRIGHT 0.160 0.533 0.445 0.379 -0.498 0.352 -0.405 -0.716 MEAN 3.8207 42.856 5.3964 11.224 14.69 0.2846 0.0556 5.1823 (S.D.) (2.303) (9.985) (