No.68-Estimate the Income Inequality using Engel Curve Approach
Ding, Haiyan; He, Hui; Zhu, Dongming
Published: 2017/9/8 2:42:50    Updated time: 2017/9/9 18:52:28
Abstract: Adopting a simple demand system, we aim to re-estimate China.s income inequality using the Urban Household Survey (UHS) data assuming the expenditure data is well measured. We find income inequality growth exceeds the growth rate of consumption inequality, although income inequality is still lower than consumption inequality over the period 2003-2009. We also .nd that the increase of income inequality is mainly due to the increase of inequality between the middle expenditure group and the high expenditure group, while the income inequality between the middle-expenditure group and the low-expenditure group slightly decreases. This not only confirms the presence of pervasive grey income, also implying that grey incomes mostly exist in the high-expenditure stratum. Following Aguiar and Bils (2015), we assume that the Engel coeffcient is log-linear and that the income elasticities are constant over time. In the robustness test, we relax the assumptions and find that the estimation results are still robust.
Keywords: Engel Curve Method; Income Income; Grey Income

Version: 2017/9/6


Haiyan Ding (Visiting scholar at China Institute for Income Distribution (CIID), BeijingNormal University)

Hui He(Correspondent author, Senior Economist, Asian Division Institute for Capacity Development (ICD), International Monetary Fund)

Dongming Zhu (Associate Professor, School of Economics, Shanghai University of Finance and Economics)



In the past three decades, China has experienced rapid economic growth. China has become the second largest economy in the world by 2010. According to World Bank, China.s nominal GDP is 5.87 trillion, more than Japan.s 4.04 trillion. Mean-

while, China also has transformed from a relatively homogeneous society into decentralized wealth distribution society, and inequality has drawn the attention of the community. With the Chinese economic system reform process accelerated, people increasingly call for the reform of the social system. Some inharmonious phenomena in the society, such as the existence of pervasive grey income, generally affect the public mood and spark speculation and dissatisfaction among the community. Grey income makes the rising income inequality more severe actually. According to Wang (2010), the ratio between the top 10% of household incomes and the bottom 10% in urban areas widens to 26 times rather than offcially published 9 times in 2008. This re.ects that there may be some systematic measurement errors in the offcial survey data of China, especially the income data.

We use the Urban Household Survey (UHS) data to compute average household's saving rate in two ways: one equals self-reported savings divided by total income; another imputed from total consumption and total income equals 1 - Consumption/Income . We find saving rates from the two different methods are inconsistent, which implies household budget constraints can't hold. In addition, we use flow of fund of China to calculate the household savings rate that is far higher than the one obtained from the urban household survey data. This inconsistency implies the urban household survey data, especially the income data, may have some under-reported problems. We find household's savings mainly come from the rich families, rather than from the poor families by computing di¤erent income quintiles' saving rate using UHS data. Combined with the existence of pervasive grey income, we think the income data exists under-reported, especially from the high-expenditure stratum.

A recent paper, Aguiar and Bils (2015), estimates US consumption inequality from a demand system and compares it to income inequality assuming the latter is well measured. However, it is likely that both income and expenditure data are poorly measured in China, and there is more mis-measurement in household income data than in expenditure data due to pervasive grey income, especially in most recent years. We adopt a similar demand system to estimate China.s income inequality using the urban household survey data assuming the expenditure data is well measured.

Different from Aguiar and Bils (2015), we divide household groups according to total household consumption instead of total household income. First, we sort by total consumption, according to the quintile into .ve expenditure groups, including 0-20, 20-40, 40-60, 60-80, 80-100. Then, we sum total income and total consumption of each household, calculating the average values of each group. Finally, we put the average income (consumption) ratio of the high-expenditure group (80-100) to the low-expenditure group (0-20) as the primary measure of the income (consumption) inequality. The Engel Curve estimation method is based on two key assumptions that the di¤erent income elasticities of various kinds of goods are log-linear approximation and constant over time. Relative income growth is estimated on how the high-expenditure group and low-expenditure group allocate their spending between luxuries and necessities over time. Intuitively, the high-expenditure group will shift expenditure towards luxuries more dramatically than low-expenditure group if income inequality is increasing substantially over time. The key advantage of this method is that it does not require that the total incomes of households be well measured. Starting from consistent estimates of Engel Curve, the ratio of spending across two goods with di¤erent income elasticities the household's total income. Income inequality across expenditure groups is then estimated by comparing their respective ratios.

In order to let everyone understand our estimation method more intuitively, we follow Aguiar and Bils (2015) and use a simple example to illustrate our method. We take nondurable entertainment as a luxury and food at home as a necessity to explain this method. Based on the Engel Curve approach, we .nd that the ratio of nondurable entertainment fees relative to the expense of food at home by the high-expenditure group increased by 64% from 2003 to 2009 using the urban household survey. At the same period, the ratio of nondurable entertainment fees relative to the expense of food at home by the low-expenditure group just increased by 15%. This means that the total income of high-expenditure group and low-expenditure group increase by 57% (log points) and 14% (log points), respectively. Thus, income inequality increases 43% (log points) from 2003 to 2009. Given the presence of idiosyncratic shock, the measure is not accurate enough. A more precise estimate can be obtained using the detailed consumption data of UHS and control the heterogeneity of the family. We .nd income inequality growth exceeds the growth rate of consumption inequality (29% and 17%, respectively), although income inequality is still lower than consumption inequality (Table 2) over the period 2003-2009. In contrast, we .nd the growth rate of after-tax income is 5% by reported income over time period 2003-2009. We also estimate the income inequality between the middle-expenditure group (40-60) and the low-expenditure group, and the income  inequality between the high-expenditure group and middle-expenditure group. We find that the increase of income inequality is mainly due to the increase of inequality between the middle expenditure group and the high expenditure group, while the income inequality between middle-expenditure group and low-expenditure group slightly decrease (31% and -2%, respectively). This not only con.rms the presence of pervasive grey income, also implying that grey incomes mostly exist in the high-expenditure stratum.

We are not the first to identify the existence of grey income in urban China. Wang (2010) is the earlier study to estimate the scale of China.s grey income based on the Engel Curve. The results of their study are extensively discussed owing to the quality and representative of their survey data (for example, Luo, Yue, and Li 2010). China Household Finance Survey (CHFS) is a nationally representative survey on household .nance in China conducted by Southwestern University of Finance and Economics under the direction of Li Gan. This survey is also devoted to obtain reliable income data, and as far as possible to avoid the omission of high income people. Bai, Tang, and Zhang (2015) also estimate the scale of urban China's grey incone and recalculate the Gini index based on Engel.s law using the UHS. They adopt Engel single equation model and its semi logarithmic function in the quadratic form, and so they ignore the information about the structure of other commodity expenditures except food. This is likely to result in inaccurate results. Ge, Xue, and Mao (2017) investigate the relationship among anti-corruption, hidden income and public earning premiums using the CHIP data.

Following Mark Aguiar and Mark Bils (2015), we assume that the Engel co-effcient is log-linear. This hypothesis provides a feasible mechanism to deal with systematic errors of income in UHS. In the robustness test, we relax the log-linear assumption, adding second-order term. Our results show that our estimation results are very robust. Another important assumption is that the income elasticities are constant over time. Although people's living standard has been greatly improved in the rapid economic development period, the Engel coe¢ cient may change over time. But we are mainly concerned the period from 2002 to 2009, with the income elasticities in 2002 as a benchmark, so the income elasticities change not much during such a short period. We .nd that the correlation coeffcient between the income elasticities in 2002 and the income elasticities in 2009 is 0.94. We do robustness test using the income elasticities of 2009, and .nd that the estimation results are still robust.

The paper is organized as follows. We introduce our data set, document the fundumental facts including the trend in income and consumption inequality and analyze the saving rates from di¤erent data sources in Section 2. Section 3 presents our econometric methodology. Section 4 shows the robust check results by relaxing two key assumptions. Section 5 concludes.


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