Intergenerational Mobility of Earnings in China

Due to dataset limitations, existing studies on China’s intergenerational income mobility are unreliable. Using longitudinal data from the Chinese Health and Nutrition Survey, this study applied a modified version of the Zimmerman [Zimmerman DJ (1992) Regression toward mediocrity in economic stature. Am Econ Rev 82(3):409–429] model and estimated intergenerational earnings mobility based on a complete model with covariance restrictions. The new estimate demonstrates that intergenerational earnings elasticity in China is 0.54, a rather higher level relative to most developed countries.


Introduction
China's economic growth over the past 40 years was an amazing global event.
However, the other side of this coin is that China's income inequality has increased sharply and is close to that of the US (Piketty et al. 2019). This outcome increased academic attention on income inequality with the aim of understanding the extent of income disparities. A broad consensus is that the income disparities in China, measured with the Gini coefficient, are very close to those of the US, a country with one of the highest inequality among developed countries (Cheng 2007;Yang and Yang 2015).
Inequality of opportunity has become a tremendously salient issue for policy makers in China. In the three recent National Congresses of the Communist Party of China, the party called for the government to improve equality of opportunity. Equality of opportunity is measured by intergenerational mobility. Given the widespread concern about intergenerational mobility, it is astonishing that there is no any official document concisely presents the intergenerational elasticity (IGE) in earnings between fathers and sons, which measures the extent that individuals inherit their parents' position in the income distribution. Although several studies were conducted, these are of no help for ascertaining the degree of intergeneration mobility in China. Compared to the research in the US and Sweden, most studies on China's intergeneration mobility did not use an intergenerational sample from longitudinal data, but rather depended on cross-sectional or retrospective data on the incomes of parents at an earlier date (Wang 2005;Gong et al. 2012;Chen 2013;Deng et al. 2013;Fan 2016). With the application of longitudinal data, especially the Chinese Health and Nutrition Survey (CHNS), a limited number of studies used short panels to estimate intergenerational mobility (Yao and Zhao 2006;Labar 2007;Han 2010;Yan and Deng 2021). The estimates of the level of mobility in China as a whole are below 0.5, with the exception of Yao and Zhao's (2006) IGE estimates, which imply much lower levels of intergenerational mobility.
However, all the longitudinal datasets except the CHNS do not have a period long enough to conduct intergenerational analysis. Even the CHNS is also not a perfect data source, like the Panel Survey of Income Dynamics (PSID) in the US. Firstly, it is not nationally representative survey. In the last waves, the CHNS covered 15 provinces among 31 provinces in the mainland China, excluding Hong Kong, Taiwan and Macau.
Secondly, the survey does not follow family members as they formed new households.
As a result, parents and sons in the sample for intergenerational analysis is in co-residence condition. Few authors attempted to address the problems; hence, we should be cautious interpreting their conclusions.
In China's context, the CHNS is not too bad. The problems because of sampling design are less than expected. Indeed, the CHNS covers most provinces east of the Hu Line. This is significant because China's population is distributed unevenly, with about 94% living east of the Hu Line on about 43% of China's land area (Chen et al. 2016).
Additionally, the selection bias induced by the co-residence condition is far less serious than was earlier believed. In China, if a family only has one son, the parent and son will live in the same household until the parent dies. If a family has more than two sons, then the families will not be broken up until the sons marry. That is, parents and sons will live in the same households for a long time. Nevertheless, if we can collect as much information as possible about adult earnings, the risk for selection bias will be reduced.
In this study, we extend the Zimmerman's (1992) econometric model and estimate the IGE based on data from the CHNS. The results contain strong evidence that intergenerational earnings elasticity is 0.54 or even higher, depicting a much less mobile society than suggested by earlier studies.
The rest of this paper is organized as follows. Section 2 briefly review the relevant literature on intergenerational earnings mobility. Section 3 describes the CHNS data and data processing. In Section 4, we develop an econometric models and discuss the estimation methods. Section 5 presents the empirical results, and Section 6 concludes the main findings.

Literature Review
The most commonly measure for intergenerational income mobility is the elasticity of lifetime income between fathers and sons; that is, the estimate of  obtained from the following regression: where it v represents the error term. In a linear errors-in-variables model, the ordinary least square (OLS) estimator of  is downward biased if there is error in independent variable (Greene 2018).
Since 1990s, the intergenerational mobility literature, especially on measurement of the IGE, has flourished. The consensus among the social scientists is that sons' earnings should lag one generation, at least 15 years and even more, behind fathers' earnings to control for life cycle biases. Most influential studies in the US were based on survey data. A landmark study by Solon (1992), using PSID data, showed that the estimate using a single year of income were heavily downward biased. Using up to the five-year average of the father's earnings, Solon's (1992)  There should be a unified framework to address the measure error in both fathers' earnings and sons' earnings. Zimmerman (1992) made the earliest attempt. He assumed that it v followed a first-order autoregressive process and estimated all the parameters in a completed model with minimum distance estimation (MDE). Altonji and Dunn (2012) assumed it v followed a white noise or second-order moving average process and estimated the intergenerational correlation with the method of moments. The Zimmerman's (1992)  However, there has been process in recent years. Dickens (2000) developed a procedure to estimate and infer parameters in univariate variance component models with unbalanced panel data. Blundell et al. (2008) extended the procedure to examines the link between income and consumption inequality. We utilize their method to estimate China's IGE of earnings. The method enables all available information from randomised participants to be included, as well as from dropouts. Thus, all the paired samples with adult earnings are available, and our sample size is larger.

Data
The CHNS is an international collaborative project between University of North

Models
In the transitory component in equation (2), we assume that it v follows an AR (1) process: where it  represents white noise. The serial correlation coefficient,  , represents the rate of deterioration of the effects of random shocks that persist for many years. We obtain the process of it v recursively: where 0 i v represents the initial shock. The moments implied by equations (1) where () Var  and ( , ) Cov  represent cross-sectional variance and covariance respectively. Our model extends Zimmerman's (1992) specification. He assumed no correlation in transitory income between fathers and sons. This assumption is reasonable if fathers and sons are not observed at the same time. However, every survey in the CHNS always contains the earnings data for both fathers and sons; therefore, the innovations for transitory income and initial shock between parents and sons should be correlated. For sake of simplicity, we assume that the covariance of the innovations between fathers and sons are time-invariant; that is, We refer to the complete statistical model in (5)

Estimation Methods
Our measure of it y was defined as the deviation of observed log earnings from the mean. We follow the demeaning procedure from the most recent literature and adjust for year, age and region effects on average earnings in a pooled regression.
Next, we estimate the complete model using MDE, which minimizes the distance between the observed sample moments in the data, m, and the corresponding population moments in the model, f  () .  is the parameters in our model. The objective function is formulated below.
where W is the identity matrix as the weighting matrix to reduce small-sample bias (Altonji and Segal 1996). The variance-covariance matrix of  is ( ) is the Jacob matrix of f  () evaluated at  and V is the variance-covariance matrix of m.

Empirical Results
The first part of this section presents the estimate of IGE based on MDE. The second part is the results of robust analysis.

MDE Results
We applied MDE of the complete model laid out in Section 4. The first column in    Source: Authors' computation.
Note: standard errors in parentheses. ***, **, and * denote 0.01, 0.05, and 0.10 rejection levels of significance, respectively. Table 2 also presents the parameters on income dynamics, which are similar between fathers and sons. The simulation with equations (5)-(8) indicates that the transitory component of earnings account for 80 percent of the total variance. The result echoes Xu and Zhu's (2011) findings, suggesting that most of the earnings inequality in China is due to high inequality in the transitory component of earnings. In addition, the permanent share was approximately 0.5 in the US (Mazumder 2001). Therefore, the earnings process is obviously different between China and the US.

Sensitivity Analysis
In this case, we consider two variants of the Table 2 estimation for the base model.
Next, we exclude persons with only a single observation. Doing so shrinks the sample to 1, 085 father-son pairs and produces  = 0.689 (SE = 0.106).
Despite the variation in results, all the estimates are distinctly above 0.5.
Corresponding to China's Gini coefficient obtained from previous studies, we can conclude that China in the last 30 years became a country with high inequality and low intergenerational mobility.

Conclusions
Previous studies in China reported inconsistent estimates of the IGE given the data limitations. Based on an intergenerational data from the CHNS, this study estimated intergenerational earnings mobility with a complete model with covariance restrictions.
The results indicate that the IGE is 0.54. Combined with the Gini coefficient, we can conclude that China has a relatively higher outcome and chance of inequality. The empirical results also verify the validity of the "Great Gatsby curve" (Corak 2013).

Authors' contributions
WY finished drafting of the manuscript; JJ carried out critical revision of the manuscript.

Funding
This research was supported by a grant from Ministry of Education of the People's Republic of China (19YJCZH069) and Anhui Provincial Department of Education (SK2020A0020).

Availability of data and materials
CHNS data are free and available for registered users. CHNS files can be downloaded directly from the website (https://www.cpc.unc.edu/projects/china/dat a/datasets/data_downloads/).