China Economic Review

China Economic Review 23 (2012) 205 222 Contents lists available at SciVerse ScienceDirect China Economic Review Residual wage inequality in urban China, 1995 2007 Chunbing XING, Shi LI Beijing Normal University, No 19, Xinjiekouwai Dajie, Beijing, 100875 China article info abstract Article history: Received 25 August 2010 Received in revised form 20 October 2011 Accepted 24 October 2011 Available online 30 October 2011 JEL classification: C14 J31 O15 Keywords: Wage inequality Residual China We use three waves of urban household survey from 1995 to 2007 to investigate the trends of residual inequality and its determinants. First, we find that the enlargement in both the overall and residual inequality was larger at the upper half of the wage distributions between 2002 and 2007. Between 1995 and 2002, however, it is the lower half that experienced larger increase in inequality. Second, by using two complementary semi-parametric methods, we find that composition effect is negligible. Instead, the change in skill prices plays a dominant role in the rise of residual inequality. Finally, by constructing a panel data at the city level, we find that ownership restructuring is an important factor that has caused the skill price to rise, especially in the earlier period. Another finding is that China's export share of GDP has a positive effect on the enlargement of residual wage inequality, especially in the period from 2002 to 2007. 2011 Elsevier Inc. All rights reserved. 1. Introduction China's urban wage inequality increased continuously in the last two decades (Li, Zhao, & Lu, 2007; Park, Song, Zhang, & Zhao, 2006). According to Li et al. (2007), the Gini coefficient of urban wages increased from 0.238 in 1988 to 0.364 in 2003. Not surprisingly, wage structure and how it is affected by various factors have attracted much attention (see Meng, 2000; Knight & Song, 2008; Meng, Shen, & Sen, 2010 still among many others). Most of the existing research on China's wage inequality focuses on wage gaps betweenwell-defined groups, for example those between different education groups. Although between inequality is important, there are still large proportions of wage variations that cannot be explained by those observable characteristics. We define the unexplained part as residual inequality or within inequality. In a standard Mincer wage equation, where wage (in log form) is modeled as a function of education, experience, plus an error term, the between inequality is captured by the distribution of these observable characteristics and their coefficients, and residual inequality is captured by the error term. It is well known that the explanatory power of education and experience is seldom more than 30%. 1 Meanwhile, both casual observations and academic research indicate that within group difference is becoming increasingly manifested both in China (Meng et al., 2010) and in other countries (Lemieux, 2008). Therefore, exploring how the unexplained (residual) part evolves and its underlying reasons are important for understanding the behavior of overall inequality. The increase in residual inequality may be due to several reasons. One important reason is the increase in the price of unobserved skills. Holding the skill distribution constant, the rise in skill price will increase residual inequality. The increase of unobserved skill price having caused the increase in residual inequality appears to be a dominant view in U.S. (Acemoglu, Corresponding author. E-mail addresses: xingchunbing@gmail.com (C. Xing), lishi@bnu.edu.cn (S. Li). 1 For example, in Meng et al. (2010, page 30), the explanatory power of the observables (experience and education dummies, as well as province dummies) in wage regressions is around 30% especially after late 1990s. In another research by Knight and Song (2008, pages 228 229), the explanatory power is around 35% for both year 1995 and 2002. The dependent variables include dummies for sex, minority status, party membership, ownership, province, education, occupation and age. 1043-951X/$ see front matter 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.chieco.2011.10.003

206 C. Xing, S. Li / China Economic Review 23 (2012) 205 222 2002; Juhn, Murphy, & Pierce, 1993; Katz & Autor, 1999). However, when looking into the residual structure, we may come up with very different conclusions. Loosely speaking, the overall residual distribution is a weighted average of within distributions of all well-defined groups, the weights being the shares of these groups in the whole sample. Because within inequalities of different groups are not necessarily identical, composition change in observable characteristics alone can cause change in the overall residual inequality. Considering this, Lemieux (2006b) finds that the increase in residual inequality in U.S. is partly due to composition effect. Besides price effect and composition effect, other factors that may affect residual inequality include measurement error and change of unobserved skill distribution (Meng et al., 2010). 2 In this paper, we use data from three waves of urban household survey in 1995, 2002, and 2007 to investigate the trends of residual inequality and its determinants. First, we describe overall and residual wage inequality in detail. From 2002 to 2007, one important new pattern is that, the rise in both the overall and residual inequality mainly happened at the upper half of the wage distributions. In the former period of 1995 to 2002, however, the rise in inequality mainly occurred at the lower half. Second, by constructing counterfactual residual wage inequality using two semi-parametric methods, DFL (DiNardo, Fortin, & Lemieux, 1996) and quantile regression based approach (Machado & Mata, 2005 3 ; Angrist, Autor, & Chernozhukov, 2004), we consider the effect of composition change on residual inequality. Surprisingly, although skill composition changed significantly, both approaches indicate that the composition effect is negligible. This result provides supportive evidence for researches that directly link the change in residual inequality to the change in skill price, without considering composition effect. However, we would like to point out that the price effect includes the effects of changes in measurement error and in unobserved skill distributions within groups. Although these two effects are difficult to address, exercises in the latter part indicate that they are not very large. Finally, by constructing a panel data at city level, we find that ownership restructuring is an important factor in causing the skill price to rise, especially in the 1995 2002 phase. This result is consistent with most of the existing research on China that emphasizes institutional change (Cai, Chen, & Zhou, 2010; Meng et al., 2010; Zhang, Zhao, Park, & Song, 2005). Another finding is that China's export surge has raised residual inequality. This finding helps differentiate this paper from the existing ones further. We are now only aware of one research emphasizing globalization's effect on urban inequality, Cai et al. (2010). By pooling all data from 1992 to 2003 together, they do not document the structural change between different periods of time. Although the research on residual inequality of urban China is relatively few, there are some exceptions. Using data from the Urban Household Income and Expenditure Survey (UHIES), Cai et al. (2010) decomposes the income inequality into between group inequality and within group inequality. 4 They find within group variation accounts for over 60% of the overall inequality. They also uncover explanations (economic restructuring, urbanization and globalization) for the acceleration of urban inequality. They do not consider the price effect versus composition effect issue. Meng et al. (2010), by decomposing the increase in the variance of earnings into observable price effect, composition effect and within cell variance, find that within group inequality is the major force that drove up the overall earning inequality. However, they do not consider the composition effect and price effect of residual inequality. The decomposition exercises in both studies are based on variance decomposition, unable to give a complete description if the residual distributions are not normal. By using two complementary semi-parametric approaches, we can study the whole distribution of residual distributions. Two relatively earlier researches are Park et al. (2006), and Li et al. (2007). Both researches find a substantial increase in within group inequality in the 1990s 5 and that the returns to unobserved skills measured by regression residuals explain much of the increase in overall inequality. But they do not provide explanations for the rise in skill prices. Compared to these studies, our dataset is more recent, allowing us to detect some new patterns. This paper is organized as follows. Section 2 describes data. Section 3 introduces how we decompose the residual wage inequality. Section 4 presents the decomposition results, highlighting the role of skill price change in causing the rise of residual inequality. In Section 5, we aggregate our data at the city level and estimate fixed effects models to uncover factors that affect residual inequality (and kill prices). Section 6 concludes. 2. Data and the trends of residual wage inequality in urban China In this paper, we use data from three waves of China Household Income Project Survey (CHIP) in 1995, 2002, and 2007, each year covering 11, 12, and 16 provinces respectively. The surveys for 1995 and 2002 were conducted in the same provinces. 6 Four more provinces (Shanghai, Zhejiang, Fujian, and Hunan) were included in the survey in 2007. We do not include them in our analysis so that the data cover the same provinces over time. 7 We keep both male and female observations of 18 to 60 years old. The annual wages used in this paper include regular wages, subsidies, and other labor incomes. Observations without wage data or with zero wages are dropped. All wages are deflated into 1995 RMB using the national CPI. As the residuals in the following analysis are obtained with province dummies being controlled for, whether to use deflators at the provincial level will not affect our results. We use annual rather than hourly wages because the 2 To be more rigorous, there are two types of composition effects. One is due to the change in the distributions of observable characteristics the other is due to change in distributions of unobserved skills. The first one is our focus in this paper. 3 We use the terms QR approach and quantile regression based approach interchangeably. 4 The income data they use include wage earnings, business income, asset income and transfer income (Cai et al., 2010, p389). 5 Both studies use urban household survey data, and the data cover 1988 to 1999 and 1988 to 2003 respectively. 6 Chongqing was included in the 1995 survey as a city of Sichuan. It was separated from Sichuan as a directly administered municipality in 1997, and was included in the 2002 survey. The other provinces (or municipalities) include Beijing, Shanxi, Liaoning, Jiangsu, Anhui, Henan, Hubei, Guangdong, Yunnan, and Gansu. 7 Whether or not to include these four provinces in the analysis do not have significant effect on our results.

C. Xing, S. Li / China Economic Review 23 (2012) 205 222 207 working time information is not consistent between 1995 and 2002 and it is not collected in 2007. But we have evidences suggesting that using hourly wage is unlikely to change our results significantly. 8 Because the sampling process of these surveys is based on formal residence registration (hukou), the data we use exclude most migrant households in urban areas without formal residence permit. Considering the large amount of rural-to-urban migrants (Cai, Du, & Wang, 2009) and the fact that they are usually worse off than urban local workers (Démurger, Gurgand, Li, & Yue, 2009), our data may produce biased urban inequality. However, by focusing on a subsample with urban hukou, there is less need to consider the monetary value of hukou. If, instead, both native and migrant workers are considered, neglecting hukou value will bias urban inequality because hukou status is often associated with many benefits. 9 Due to the lack of data on migration and the complication of hukou value, it is hard to assess precisely to what extent our data bias urban inequality. The findings in this paper should therefore be interpreted with these caveats in mind. Consider the changing patterns of the wage levels and inequalities first (see Table 1). For both genders, average wages increased from 1995 to 2002 and from 2002 to 2007, with the increases for females being relatively slower than male, especially in the latter period. For male, the variance of log wages increased from 0.41 in 1995 to 0.54 in 2002 and to 0.80 in 2007. The differential of log wages between 50th and 10th percentiles increased from 0.72 to 0.87, while that between 90th and 50th percentiles increased from 0.60 to 0.68. Over 65% of the increase in the differential between 90th and 10th percentiles happened in the lower half. This pattern reversed in the second period. Around 60% of the increase in the 90 10 percentile gap happened in the upper half. In words, the inequality increased mainly because the poor were left behind in the first period, in the second however, it is mainly because the rich got richer much faster. Female inequality also increased in both periods. Unlike male, the increase in inequality concentrated in the upper half in the first phase (1995 2002), but in the lower half in the second phase (2002 2007). To see the importance of residual inequality, we predict residuals after running wage regressions for male and female by years. 10 The observables (education, experience, their full interactions, and province dummies) can explain around one quarter of the total variance for both genders in various years, and the wage dispersions are still large after purging out the between-group differentials. 11 For male, the changing patterns of the residual inequality patterns are similar to those of the overall wage inequality. For female, the increase of residual inequality from 2002 to 2007 concentrates on the upper half of the residual distribution, which is in contrast to the change of overall wage inequality during the same period. Controlling ownership, sector, and occupation dummies increases the explanatory power of the wage equation (in particular in 2007), but still, there are large proportions of variation unexplained (see panel C in Table 1). For both genders, the increase in residual inequality from 2002 to 2007 happens mainly on the upper half distribution. Next, we divide the sample of each year into 24 education experience cells for both male and female. We have 6 categories for education, namely primary and below, junior middle school, high school, technical school, professional school, college and above, and 4 categories for experience, namely below 10 years, 11 20 years, 21 30 years, 31 years and above. For each group, we calculate the variance of log wages (see Tables 2 and 3,columns1 5). At a given point of time, the within group variance varies with education and experience subgroups. In all three years, variances of wages are relatively larger for less educated and less experienced subgroups. Within most of the education experience cells, the variance of wages increased during both periods of time. But some groups with education level lower than technical school (inclusive) and with less than 10 years of experience tend to witness decrease in within group inequality. Two points are noteworthy regarding the within group inequalities. First, the patterns we have got here are inconsistent with both theoretical predictions and empirical evidences in developed countries (see Lemieux (2006b) for example). This is probably because wages are set according to rigid rules under the traditional planning system. As educated and experienced individuals are more likely to be employed in public sector, it is natural that their within group dispersion is lower. With the deepening of China's economic reform, employers have more autonomy to set wages according to the employees ability other than education and seniority. Therefore, we expect the dispersions of higher skills to increase further. Second, the fact that wage dispersions of different groups are different means that changes in distribution of observable skills can potentially influence residual inequality, i.e. the composition effect. Table 2 and 3 (columns 6 10) show clearly that the labor force became more educated and more experienced between 1995 and 2002. During the second period however, the trend is not obvious. Another way to see this is to run regressions with year dummies as dependent variables. We pool the data of 2002 with that of 1995 and 2007 respectively. Let the dichotomous dependent variable equal to one if the individual belongs to the sample of 2002 and zero otherwise. The results reported in Table 4 confirmed our conclusion that the skill composition did change significantly. The results also indicate that most of the change occurred in the first period, and the changes for female are more significant. 3. Decomposing residual wage inequality We assume that wages are determined according to a Mincer type wage equation: y it ¼ X it β t þ ε it ð1þ 8 Using information from the 1995 and 2002 surveys, we find a negative correlation between hourly wage rate and annual working hours, suggesting a larger inequality for (residual) hourly wages. Under the assumption of negative correlation between wage rate and working time, the changing pattern of (residual) wage inequality and decomposition results will not change substantially. Detailed results are available upon request. 9 The bias can be in either direction. One scenario is that people with urban local hukou have higher wages possibly because of discrimination against migrant workers. On the other hand, people may accept lower wages because of their urban hukou can guarantee them of other benefits. For a more detailed discussion of China's hukou system, see Fan (2008). 10 We use OLS to obtain residual wages. Using other methods such as FGLS or median regression does not have substantive effect on residual inequality. 11 Other inequality measures (90 10 gap, for example) indicate a similar pattern. However, they cannot be neatly decomposed into the inequality of between inequality and residual inequality as the variance.

208 C. Xing, S. Li / China Economic Review 23 (2012) 205 222 Table 1 Wage inequality and residual inequality. 1995 2002 2007 1995 2002 2007 Male Female A: Real log wage Mean 8.630 9.120 9.594 8.398 8.880 9.181 90th percentile 10th percentile 1.315 1.555 1.882 1.524 1.693 2.016 50th percentile 10th percentile 0.717 0.871 1.004 0.894 0.910 1.103 90th percentile 50th percentile 0.598 0.684 0.879 0.630 0.784 0.912 Variance 0.414 0.544 0.799 0.607 0.593 1.076 B: Residual of log wage (Residual I) a 90th percentile 10th percentile 1.095 1.325 1.530 1.233 1.412 1.738 50th percentile 10th percentile 0.580 0.751 0.846 0.707 0.801 0.948 90th percentile 50th percentile 0.514 0.574 0.684 0.525 0.612 0.790 Variance 0.311 0.407 0.611 0.475 0.430 0.823 C: Residual with more controls (Residual II) b 90th percentile 10th percentile 1.044 1.254 1.361 1.148 1.342 1.394 50th percentile 10th percentile 0.550 0.682 0.723 0.651 0.746 0.716 90th percentile 50th percentile 0.493 0.572 0.638 0.497 0.596 0.678 Variance 0.286 0.364 0.426 0.386 0.379 0.426 Note: the residual is predicted after running regression of ln(wage) on education dummies, experience dummies, their full interactions, and province dummies. Occupation dummies, ownership dummies, industry dummies, as well as education dummies, experience dummies, their full interactions, and province dummies are controlled in the wage equations. Where y it is the log form of real wages, X it stands for observable skills such as categories of potential experience (age-years of schooling-6), education levels, their interaction terms, and province dummies. ε it is the error term. According to Chay and Lee (2000) and Lemieux (2006b), the residual is assumed to be a product of some unobserved skills (e it ) and the price of unobserved skills (p t ), plus measurement error (v it ): ε it ¼ p t e it þ v it : ð2þ Table 2 Variance and composition change by education and experience, male. Within group variance Labor force share (%) Change Change 1995 2002 2007 95-02 02-07 1995 2002 2007 95-02 02-07 Primary and below (EDU=1) 0 10 0.76 1.87 0.32 1.11 1.56 0.14 0.19 0.20 0.04 0.01 11 20 0.35 0.44 0.89 0.09 0.45 0.53 0.28 0.21 0.25 0.07 21 30 0.57 0.43 0.50 0.14 0.07 1.86 0.78 0.51 1.08 0.27 31+ 0.83 0.44 0.85 0.40 0.42 1.91 1.29 1.19 0.62 0.10 Middle school (EDU=2) 0 10 0.78 0.9 0.47 0.13 0.44 3.78 1.68 1.38 2.09 0.30 11 20 0.52 0.86 0.87 0.33 0.01 6.55 4.93 3.28 1.61 1.66 21 30 0.27 0.47 0.65 0.20 0.18 12.73 8.71 6.49 4.02 2.22 31+ 0.61 0.49 1.23 0.12 0.74 4.91 8.63 9.59 3.73 0.95 High school (EDU=3) 0 10 0.48 0.69 0.62 0.21 0.07 5.29 3.92 2.52 1.36 1.40 11 20 0.33 0.57 0.67 0.24 0.10 9.22 6.73 4.61 2.49 2.12 21 30 0.29 0.38 0.91 0.09 0.53 5.59 12.2 10.08 6.61 2.12 31+ 0.44 0.44 0.90 0.00 0.45 2.45 3.63 7.07 1.17 3.44 Technical school (EDU=4) 0 10 0.38 0.69 0.53 0.31 0.16 3.82 2.19 2.14 1.64 0.05 11 20 0.26 0.35 0.51 0.09 0.16 3.82 2.54 3.20 1.28 0.65 21 30 0.16 0.27 0.47 0.11 0.20 5.11 2.99 2.49 2.12 0.50 31+ 0.42 0.49 1.01 0.07 0.53 3.50 3.01 2.40 0.50 0.60 3 Year college (EDU=5) 0 10 0.35 0.47 0.60 0.12 0.13 3.50 4.26 4.30 0.76 0.04 11 20 0.20 0.34 0.44 0.14 0.10 6.20 7.25 6.69 1.05 0.56 21 30 0.22 0.25 0.36 0.03 0.11 6.13 7.16 7.77 1.03 0.62 31+ 0.23 0.28 0.53 0.05 0.26 2.41 4.82 6.14 2.42 1.32 4 Year college and above (EDU=6) 0 10 0.39 0.42 0.55 0.03 0.14 2.12 2.77 4.02 0.65 1.25 11 20 0.22 0.36 0.59 0.14 0.23 2.33 5.42 5.80 3.09 0.38 21 30 0.14 0.29 0.35 0.15 0.06 3.46 2.71 5.57 0.75 2.86 31+ 0.38 0.46 0.48 0.08 0.03 2.64 1.91 2.36 0.74 0.45 Note: 0 10, 11 20, 21 30, 31+ refer to potential experience calculated as age minus years of schooling minus 6.

C. Xing, S. Li / China Economic Review 23 (2012) 205 222 209 Table 3 Variance and composition change by education and experience, female. Within group variance Labor force share (%) Change Change 1995 2002 2007 95-02 02-07 1995 2002 2007 95-02 02-07 Primary and below (EDU=1) 0 10 0.54 0.82 0.31 0.29 0.51 1.00 0.66 0.34 0.34 0.32 11 20 0.88 0.55 1.10 0.33 0.55 1.81 0.54 0.30 1.26 0.24 21 30 0.86 0.27 1.84 0.59 1.57 2.77 0.89 0.70 1.87 0.19 31+ 2.58 0.55 1.58 2.03 1.03 0.58 0.28 0.55 0.30 0.27 Middle school (EDU=2) 0 10 0.70 0.67 0.98 0.03 0.31 5.68 3.27 2.43 2.41 0.85 11 20 0.49 0.62 0.72 0.13 0.10 9.92 6.74 4.02 3.19 2.71 21 30 0.54 0.45 0.73 0.09 0.28 14.69 8.24 6.30 6.45 1.95 31+ 1.68 0.41 3.12 1.27 2.71 2.10 2.66 4.65 0.56 1.99 High school (EDU=3) 0 10 0.58 0.62 0.64 0.04 0.02 6.42 4.36 2.90 2.06 1.45 11 20 0.34 0.54 0.69 0.19 0.16 13.51 9.44 6.90 4.07 2.54 21 30 0.35 0.44 0.83 0.09 0.39 5.56 14.67 13.41 9.12 1.26 31+ 3.38 0.41 1.70 2.97 1.29 0.68 1.72 4.84 1.04 3.12 Technical school (EDU=4) 0 10 0.71 0.62 0.70 0.09 0.09 4.87 4.07 2.90 0.80 1.17 11 20 0.30 0.48 0.47 0.18 0.01 5.07 4.10 3.74 0.97 0.36 21 30 0.34 0.38 0.77 0.03 0.39 5.63 4.95 3.51 0.68 1.44 31+ 1.32 0.70 2.26 0.63 1.57 1.98 2.03 2.48 0.04 0.46 3 Year college (EDU=5) 0 10 0.36 0.55 0.72 0.18 0.18 3.23 6.52 6.62 3.30 0.10 11 20 0.23 0.30 0.38 0.06 0.08 4.52 8.60 9.28 4.07 0.68 21 30 0.17 0.29 0.61 0.12 0.32 4.07 6.05 8.19 1.99 2.14 31+ 0.49 0.33 0.91 0.16 0.58 0.75 2.21 3.38 1.46 1.16 4 Year college and above (EDU=6) 0 10 0.43 0.56 0.54 0.13 0.02 1.74 2.54 4.67 0.81 2.12 11 20 0.15 0.66 0.35 0.51 0.31 1.33 3.46 4.67 2.13 1.20 21 30 0.17 0.23 0.33 0.06 0.10 1.51 1.53 2.30 0.02 0.76 31+ 0.59 0.36 0.78 0.22 0.42 0.60 0.45 0.93 0.15 0.48 Note: 0 10, 11 20, 21 30, 31+ refer to potential experience calculated as age minus years of schooling minus 6. The unobserved skills can be linked to any productive attributes of the workers that cannot be accounted for by education and experience, including school quality, intrinsic ability, specific skills, and effort, etc. Residual wage inequality is the inequality of residual ε it. Consider the marginal distribution of the wage residual: F t ðε i Þ ¼ F εjx ðε i jx; t ε ¼ tþdg X ðxt j X ¼ tþ: ð3þ ε it 's distribution in time t can be written as its conditional distribution given X (F ε X ( )) integrated over the distribution of X (G X ( )). Eq. (3) highlights the fact that residual distribution (inequality) may be different for different observed skills. In theory, Mincer (1974) pointed out that differential investments in on-the-job training will cause the wage dispersion to increase as a function of experience. Farber and Gibbons (1996) reach the same conclusion in a simple learning model. Using a random coefficient model, Lemieux (2006a) shows that the variance of wages should be larger for more educated workers, and that the variance should increase more for more educated workers when the price of education increases. Empirically, the wide use of quantile regressions to estimate wage equations reflects researchers concern about the dependence of residual distribution on X (or heteroskedasticity, see Koenker & Bassett, 1982; Autor, Katz, & Kearney, 2005). The evidence from China also suggests heteroskedasticity (Luo, 2008; Xing, 2007), but the pattern is different from that of U.S, as we will see later. Next, assume that measurement error v it and unobserved skill e it do not change over time. 12 Eq. (3) can be rewritten as: F t ðε i Þ ¼ F εjx p t e i þ v i X; t p ¼ t dg X ðxt j X ¼ tþ ð3 Þ The increase in residual inequality can come from two sources: rising skill price p t and the composition change in G(X t). One central task of this paper is to determine the relative importance of price effect and composition effect. For such a task, it is essential to construct counterfactual distributions, keeping skill composition or skill price constant over time. Consider the change of residual inequality from t=0 to t=1. What would the residual distribution be like in time 1 if the skill composition is held at time 0? 13 Under the assumption that the skill distribution change has no effect on the conditional 12 This is a strong assumption. We will see to what extent does this assumption holds in Section 5. 13 We can also construct the following counterfactual distribution: F C (ε i )=F c (ε i t X =1, t p =0). In this paper, we use different combinations of skill distribution and skill prices to construct counterfactuals. Our results are not sensitive to how we construct the counterfactual distributions. See the last paragraph in Section 4 and footnote 19.

210 C. Xing, S. Li / China Economic Review 23 (2012) 205 222 Table 4 Probit models. In year 2002=1/otherwise=0 Male Female 1995 vs 2002 2002 vs 2007 1995 vs 2002 2002 vs 2007 Middle school 0.632** 0.128 0.081 0.158 (0.304) (0.283) (0.155) (0.205) High school 0.342 0.330 0.018 0.105 (0.300) (0.275) (0.152) (0.202) Technical school 0.485 0.067 0.153 0.190 (0.303) (0.278) (0.154) (0.202) 3 year college 0.029 0.060 0.711*** 0.368* (0.301) (0.273) (0.154) (0.196) 4 year college and above 0.007 0.178 0.506*** 0.766*** (0.305) (0.274) (0.167) (0.202) Experience_11 20 0.452 0.183 0.451** 0.047 (0.350) (0.359) (0.194) (0.279) Experience_21 30 0.670** 0.258 0.408** 0.232 (0.314) (0.305) (0.176) (0.238) Experience 30+ 0.405 0.134 0.157 0.785*** (0.310) (0.287) (0.245) (0.282) MiddleXexper11 20 0.764** 0.000 0.578*** 0.165 (0.362) (0.376) (0.209) (0.295) MiddleXexper21 30 0.921*** 0.163 0.412** 0.186 (0.325) (0.322) (0.190) (0.256) Middle Xexper31+ 1.229*** 0.276 0.654** 0.234 (0.322) (0.305) (0.266) (0.301) HighXexper11 20 0.462 0.208 0.459** 0.002 (0.357) (0.368) (0.205) (0.291) HighXexper21 30 1.344*** 0.393 1.227*** 0.050 (0.322) (0.314) (0.189) (0.251) High Xexper31+ 0.848*** 0.814*** 0.948*** 0.098 (0.322) (0.299) (0.280) (0.301) TechnicalXexper11 20 0.542 0.354 0.445** 0.068 (0.363) (0.374) (0.212) (0.295) TechnicalXexper21 30 0.663** 0.165 0.452** 0.274 (0.328) (0.324) (0.194) (0.257) TechnicalXexper31+ 0.652** 0.001 0.284 0.478 (0.324) (0.306) (0.268) (0.304) 3yearcolXexper11 20 0.440 0.144 0.416** 0.008 (0.358) (0.366) (0.209) (0.287) 3yearcolXexper21 30 0.639** 0.324 0.170 0.062 (0.323) (0.313) (0.194) (0.249) 3yearcolXexper31+ 0.715** 0.280 0.339 0.536* (0.322) (0.297) (0.277) (0.298) 4yearcolXexper11 20 0.829** 0.005 0.810*** 0.271 (0.364) (0.368) (0.230) (0.295) 4yearcolXexper21 30 0.326 0.462 0.077 0.371 (0.331) (0.318) (0.224) (0.266) 4yearcol Xexper31+ 0.062 0.034 0.269 0.740** (0.329) (0.305) (0.315) (0.334) Constant 0.058 0.333 0.399*** 0.155 (0.298) (0.269) (0.149) (0.194) Pseudo R2 0.041 0.034 0.060 0.040 N 11407 11422 9774 9518 Note: Standard errors in parentheses. *significant at 10% level, **significant 5% level, ***significant at 1% level. Province dummies are controlled. Primary education and 0 10 experience category are reference groups. distribution of residuals, the counterfactual distribution is the conditional distribution of time 1 integrated over the skill distribution of time 0: F C ðε i Þ ¼ F c ε i t X ¼ 0; t p ¼ 1 ¼ F εjx p t e i þ v i X; t p ¼ 1 dg X ðxt j X ¼ 0Þ ð4þ Two approaches are proposed to construct such counterfactuals. The first is based on quantile regressions (QR approach). By running quantile regressions at different quantiles using data of time 1, we obtain a detailed description of its conditional distribution. The estimated skill price structure (conditional distribution) can then be applied to data (skill distribution) of time 0, through multiplying the quantile coefficient matrix of time 1 by the data matrix of time 0. 14 Clearly, this approach estimates the conditional distribution explicitly, 14 An alternative procedure proposed by Machado and Mata (2005) relies on a re-sampling process. Angrist et al. (2004) show that greater precision can be obtained by multiplying the entire g(x) distribution by the quantile regression coefficient matrix. Therefore, we do not use the re-sampling procedure in this paper.

C. Xing, S. Li / China Economic Review 23 (2012) 205 222 211 Table 5 Decomposition results using DFL approach. Male Price of unobserved skill Female Price of unobserved skill 1995 2002 2007 1995 2002 2007 A: Residual I a 90th percentile 10th percentile 1995 1.095 1.388 1.527 1.233 1.468 1.785 2002 1.054 1.325 1.541 1.177 1.412 1.722 2007 1.054 1.325 1.530 1.186 1.424 1.738 50th percentile 10th percentile 1995 0.580 0.804 0.828 0.707 0.831 0.950 2002 0.563 0.751 0.847 0.656 0.801 0.932 2007 0.561 0.751 0.846 0.661 0.812 0.948 90th percentile 50th percentile 1995 0.514 0.584 0.698 0.525 0.637 0.836 2002 0.491 0.574 0.694 0.520 0.612 0.790 2007 0.493 0.574 0.684 0.525 0.612 0.790 Variance 1995 0.311 0.444 0.615 0.475 0.469 0.803 2002 0.299 0.407 0.635 0.457 0.430 0.766 2007 0.299 0.390 0.611 0.583 0.420 0.823 B: Residual II b 90th percentile 10th percentile 1995 1.044 1.221 1.308 1.148 1.376 1.261 2002 1.093 1.254 1.330 1.075 1.342 1.429 2007 1.187 1.310 1.361 1.227 1.393 1.394 50th percentile 10th percentile 1995 0.550 0.654 0.650 0.651 0.748 0.636 2002 0.609 0.682 0.688 0.568 0.746 0.715 2007 0.676 0.707 0.723 0.599 0.759 0.716 90th percentile 50th percentile 1995 0.493 0.568 0.658 0.497 0.628 0.626 2002 0.484 0.572 0.642 0.508 0.596 0.714 2007 0.511 0.603 0.638 0.629 0.634 0.678 Variance 1995 0.286 0.325 0.327 0.386 0.346 0.281 2002 0.570 0.364 0.394 0.294 0.379 0.405 2007 0.593 0.381 0.426 0.251 0.400 0.426 a The residual is predicted after running regression of ln(wage) on education dummies, experience dummies, their full interactions, and province dummies. b Occupation dummies, ownership dummies, industry dummies, as well as education dummies, experience dummies, their full interactions, and province dummies are controlled in the wage equations. with some risk of imposing strong restrictions on its structure. Meanwhile, no effort is needed to estimate the composition change parametrically. An alternative approach proposed by DiNardo et al. (1996) is like a mirror image of the QR approach. The insight of DFL is that counterfactual distribution can be estimated by re-weighting the residual sample of time 1 using the following weight, θ ¼ Prðt ¼ 0jXÞ= ð1 Prðt ¼ 0jXÞÞ ð5þ Pooling the data of time 0 and time 1 together, the composition change can be estimated explicitly by running probit models Pr(t=0 X). The predicted probability is used to calculate the weight (^θ) for each observation. Using residual data in time 1 and corresponding weights, the counterfactual density and various counterfactual inequality measures can be estimated. To be intuitive, consider the composition change from 1995 to 2002. With the gradual expansion of higher education, we expect more college graduates in the 2002 sample than in 1995. Using the residual wage sample of 2002 to construct the counterfactual holding skill composition at the 1995 level, we should give college graduates less weight. The probability of a graduates being in the 1995 sample will be lower than that in the 2002 sample holding other characteristics constant. The weight of an observation with college degree will be less than one. The two approaches, DFL and QR, are conceptually similar. As neither one can claim global superiority over the other, we use them both. 15 It turns out that they produce similar results. As the QR approach gives more volatile results and is time consuming, after presenting the benchmark results, we use the DFL approach to do decomposition exercises. 15 Autor et al. (2005) extended the QR approach to investigate composition effect and price effect in the change of wage inequality. Comparing their results to Lemieux (2006b), who used re-weighting approach, they find its substantive differences with the latter are not consequential for their conclusions.

212 C. Xing, S. Li / China Economic Review 23 (2012) 205 222 Finally, we define a real-valued functional v(f), which can be thought of as rules to map distributions (Fs) to real numbers. It can be statistical measures of F such as variance, percentiles, and the difference between percentiles. It is straightforward to decompose the change of any distribution statistics into two parts: vf ð 1 ðε i ÞÞ vðf 0 ðε i ÞÞ ¼ ½vF ð 1 ðε i ÞÞ vðf C ðε i ÞÞŠþ½vF ð C ðε i ÞÞ vðf 0 ðε i ÞÞŠ ¼ Δ v þ Δv X P ð6þ The term in the first bracket is the change due to composition effect (Δ X ), while that in the second is the change due to skill price effect (Δ P ). 16 4. Counterfactual residual inequality and decomposition results 4.1. Conditional distribution and quantile regression based decomposition We estimate quantile regressions for both genders and for each year at various percentiles in this section. If the conditional distribution of wage residuals does not depend on observable characteristics, there should be no systematic difference in coefficients across percentiles. The results indicate that this is not the case. In particular, we estimate returns to various levels of education and experience. 17 The results for male of different years are reported in Fig. 1. InFig. 1a, one obvious feature is that the coefficients for education and experience in lower quantile regressions are higher than those in upper quantile regressions. This pattern changed significantly in 2002. For lower levels of educations, the relationship between coefficients and quantiles becomes inverted U-shaped. For higher levels of education (professional college, and college graduates), the relationships are still downward sloping, but to a lesser extent. The same is also true for experience dummies. In 2007, the coefficient quantile relationships become more flatter. The results for female, which are not reported to save space, show similar patterns. The evolution of quantile regression results indicate a dramatic change in the conditional distribution from 1995 to 2007. Moreover, the coefficient differences across quantiles confirm that the conditional residual distributions are dependent on observable characteristics, and composition change may have substantive effect on the overall residual inequality. We construct counterfactual residual distributions to evaluate the relative importance of price effect and composition effect. Take the counterfactual distribution combining 2002 skill price and 1995 composition for example. First, we estimate quantile regressions using the 2002 data. In all quantile regressions, residual wage is the dependent variable and education and experience dummies, their interactions, and province dummies are regressors. The quantile regressions are run at the (1, 1.5, 2,, 98, 98.5, 99)th percentiles. After estimating each quantile regression, the coefficient vector is applied to the 1995 data. Therefore the 1995 data are used 197 times to predict residual wages. All these predicted residuals are used to estimate the counterfactual residual distributions. The main results are reported in Fig. 2a and b, for male and female respectively. In Fig. 2a and b, the long dash line is the counterfactual distribution combining 2002 skill price (quantile regression coefficients) and 1995 composition. The dash-dot line is the counterfactual combining skill price of 2002 and skill composition of 2007. These two lines almost overlap with the actual distribution for 2002. As all lines are based on skill price of 2002, their differences are due to composition change. Panels A and B in Fig. 2 indicate a very small composition effect for both genders. 4.2. DFL decomposition Next, we apply the re-weighting approach to estimate the counterfactual residual kernel densities. The same variables (education dummies, experience dummies, their interactions and province dummies) are included in the probit models as in the wage regressions (see Table 4 for the results). 18 The predicted probabilities from the probit models are used to calculate the weight according to Eq. (5). We have two counterfactuals and one actual residual distribution. The two counterfactuals are constructed using the residual data of 2002. By re-weighting the observations according to composition change from 1995 to 2002, and from 2002 to 2007, we are holding the price of unobserved skills constant at the 2002 level and letting the skill composition to change. Similar to the results of QR approach, Fig. 2c and d show that the counterfactual distributions for 1995 and 2007 are very close to the actual one for 2002, suggesting that the composition change has little effect on the residual inequality. An alternative way to see the role of price effect and composition effect is to calculate the change in percentiles. Take male from 1995 to 2002 for example. Fig. 3a plots the change of each percentile from 1995 to 2002. The solid line depicts the actual change at various percentiles. The long dash line depicts the difference between the actual percentiles of 2002 and the counterfactual percentiles of 1995, which is due to composition change. The dash-dot line depicts the difference between the actual and counterfactual percentiles of 1995, which is due to price change. The latter one is very close to the actual difference, indicating a 16 If the counterfactual distribution is constructed as follows F C (ε i )=F c (ε i t X =1, t p =0), v 1 v c will be skill price effect, and v c v 0 will be composition effect. 17 For ease of interpretation, we do not consider the interaction terms between education and experience here. In constructing the counterfactual using quantile regressions, we do include interaction terms. 18 As the predicated weights will be affected by model specifications, we have tried several alternative specifications for the probit model: (1) controlling for the 6 education dummies and 4 experience dummies, but excluding the interaction terms; (2) Instead of using 4 experience categories, using 8 experience categories (0 5/6 10/11 15/16 20/21 25/26 30/31 35/36+), education dummies (6 categories) and their full interactions with experience dummies being controlled; (3) Using each experience as one category. Education dummies (6 categories) and their full interactions with experience dummies are controlled for; (4) using continuous experience and its quadratic and cubic terms as well as their interaction terms with the education levels as independent variables. All these alternative specifications produce similar results.

C. Xing, S. Li / China Economic Review 23 (2012) 205 222 213 predominant role of price change in enlarging residual inequality. The composition effect is positive at lower percentiles and negative at higher percentiles. Thus composition change tends to decrease residual inequality. Although the composition effect plays a minor role on the whole, it seems to have large effect at the very low end of the distribution. This is also true for female between 1995 and 2002. In the second period, the changing pattern of the residual inequality is different from that of the first period. The role of price effect and composition effect do not change much however, with the latter playing an even more minor role. To see the robustness of our results, we calculate counterfactual inequality measures using different combination of skill prices and skill compositions. In Table 5, each column is under the skill price of a specific year, and each row is under the skill composition of a specific year. For example, the element at column 1 and row 2 is residual wage inequality (90th percentile minus 10th percentile) calculated using the counterfactual distribution with 1995 skill price and 2002 composition pattern, while the element at column 2 and row 1 is calculated using the counterfactual distribution with skill price of 2002 and composition pattern of 1995. 19 And so on so forth. Therefore, the change of inequality along the diagonal is the actual change, while the change along columns is due to composition change and the change along rows is due to price effect. Obviously, price change usually explains off the overall change, and the composition change plays a minor role, if not negligible. Using different counterfactuals gives similar results. 5. Caveat and explanations 5.1. Change of unobserved skills or measurement error? In Section 2, we make two assumptions: Both the distribution of unobserved skills within specific groups and the measurement error do not change over time. Whether or to what extent these assumptions hold have major implications for the interpretation of our results. Clearly, we cannot separate out the price effect if the distribution of unobserved skill (e it ) or (and) that of the measurement error (v it ) changes over time. However, with increase in the number of new students admitted to colleges accompanying the college expansion program (see Li, Whalley, Zhang, & Zhao, 2011; Li & Xing, 2010), we expect that the unobserved skill distributions within both high school graduates and college graduates to change accordingly, and this will contaminate the price effect. In Fig. 4, we calculate inequality measures (variance, the difference between the 90th and 50th percentiles, and that between the 50th and 10th percentiles) using a 1/5 random sample of 1% census data in 2005. Given more high school graduates being admitted to college or universities, we expect more heterogeneity and higher within group inequality within those groups. However for both male (Fig. 4a) and female (Fig. 4b), we do not find obvious increase in inequalities for the younger groups. Despite a sharp increase in the number of college student after 1999 (see Fig. 1 in Li & Xing, 2010), there are no obvious discontinuities in inequalities around this time. The inequality measures are even lower for those affected by the expansion program (i.e. those with fewer market experiences). For high school graduates, within group inequality is lower for the younger groups, but there are no sharp changes. As Fig. 4 uses only one cross sectional data set, we cannot separate the expansion effect from the age or cohort effect. According to human capital theory, the within group inequality for younger workers is lower. Therefore the younger age effect may counter balance the expansion effect. However, if this is true, the change in unobserved skill distributions will have little effect on our decomposition also. The reason is that even in 2007, those affected by the expansion policy are still young. The change in unobserved skill distribution needs time to have effect. 20 In Fig. 5, we perform similar exercises using the three CHIP surveys. As the samples are small, we put male and female samples together. Although still being volatile, the inequality-experience profiles for year 2002 and for 2007 are similar, especially for the younger groups. For older groups, within group inequalities in 2007 are larger than that in 2002 and than that in 1995. Yet for younger groups, it is hard to say that college or university within group inequalities have increased because of expansion. It is also hard to say that within group inequalities for younger high school graduates have declined. Therefore, evidences from both the census data and CHIP data show that the change in unobserved skill distributions is not a major problem that contaminates our decomposition. We do not exclude the possibility of significant change in the within group skill distributions. Instead, how education expansion has changed the within group ability distributions is still an open question, and more concrete evidences are needed. It is also hard to judge whether the measurement error has become more manifested. However, the three surveys being conducted by the same research team alleviates this concern. Furthermore, there seems no significant change in the volatility of those inequalityexperience profiles in Fig. 5. 5.2. Labor market segmentation and residual inequality Existing researches have shown that China's labor market is segmented (Knight & Song, 2008 for example). Individuals with identical observable and unobservable characteristics have different earnings because they are in different occupations, industries, or ownerships. Therefore, the price effect includes both real price of unobserved skill and rents between different sectors. However, it is more realistic to say that individuals sector affiliation is often closely related to education levels and unobserved ability, making it notoriously difficult to separate out the rent effect from the real price effect. 19 Let t=0, 1 denotes year 1995 and 2002, these two counterfactual distributions can be written as F C (ε i )=F c (ε i t X =1,t p =0)andF C (ε i )=F c (ε i t X =0,t p =1), respectively. 20 Higher education expansion and the change in within-group unobserved skill distributions are also a major concern in Meng et al. (2010). They do not find evidence for increase in within-group variance for the educated group either. They conjecture that within college variance decrease because unobserved skill prices decreased. With sharp expansion in higher education, unobserved skill prices must decrease significantly to offset the widening in unobserved skill distribution. However, the return to college increased in the 2000s (Fig. 4 in Meng et al., 2010).

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C. Xing, S. Li / China Economic Review 23 (2012) 205 222 215 Fig. 1. a Coefficients in quantile regressions, 1995 male. edul=2, 3, 4, 5, 6 refer to middle school, high school, technical school, 3 year college (dazhuan), and college, respectively; experc=2, 3, 4 refer to experience category of 11 20, 21 30, and 31+, respectively. b Coefficients in quantile regressions, 2002 male. c Coefficients in quantile regressions, 2007 male. To what extent the segmentation is correlated with unobserved ability also determines how far we should go when defining residuals. 21 Two extreme cases help illustrate this point. If segmentation is perfectly correlated with unobserved skills, the segmentation is just a result of different individuals selecting or being selected by different sectors. In this case, segmentation is a superficial phenomenon and will not be a concern. Another extreme case is that segmentation is totally uncorrelated with unobserved skills, and the differences between different sectors are just rents. In this case, it is more appropriate to have industry, occupation, and ownership dummies in the wage equation when predicting residuals. The exercise we do here is to include the industry, occupation, and ownership dummies when predicting the residuals. As already shown, residual inequalities decrease, but are still large (see panel C in Table 1). Next, we construct two sets of counterfactuals. In the first set exercises to get counterfactuals, the observations are re-weighted based on education and experience differentials, i.e. only education and experience dummies and their full interactions are included in probit models. The results are not reported, because they are very similar to previous results, and the composition effects are negligible. In the second set exercises, the observations used for constructing counterfactuals are re-weighted based on differentials in ownership, industry, and occupation, as well as education and experience. The decomposition results are reported in panel B of Table 5. Still, price change plays a major role. Composition change, however, plays an important role as well in many cases. Take male for example. The residual 90th 10th percentile differential increases from 1.044 in 1995 to 1.254 in 2002. If we use observations in 1995 to construct counterfactual distribution 23% of the increase in residual inequality is due to composition change. If observations in 2002 are used to construct the counterfactual, the explanatory power of composition effect will be 16%. From 2002 to 2007, 29% or 52% are due to composition change, depending on the data of which year is used to construct the counterfactuals. Considering other inequality measures gives similar results, and the above conclusions are also true for female. 21 If segmentation is perfectly correlated with observable characteristics such as education and experience, the discussion here will be trivial.