Aggregate implications of occupational inheritance in China and India

2.1 IOM rates vs. GDP per capita

In this section, we use the IOM rate as an indicator of intergenerational occupational mobility. By definition, the IOM rate is the proportion of children that choose an occupation that is different from that of their fathers. As the IOM rate increases, the degree of occupational inheritance decreases. First, denote by πL=(π1L,π2L,…πML) the distribution of fathers’ occupations. In addition, P=[pij]M×M denotes the intergenerational occupational transition matrix, where row i corresponds to fathers’ occupations and column j corresponds to sons’ occupations; p_ij is the possibility of a worker choosing occupation j, conditional on the fact that his father works in occupation i. Therefore, diagonal elements of the transition matrix, p_ii, represent the possibility of occupational inheritance for children with father working in occupation i. The IOM rate is then calculated as

where diag(P)=(p11,p22,…,pMM) is the vector of all diagonal elements of the transition matrix P.

It is usually more convenient to think about the percentage of sons that inherit their fathers’ occupations, i.e. (1 − IOM), and therefore, Equation (1) can be re-written as

Equation (2) suggests that (1−IOM) is equal to the summation of the probabilities of all children inheriting their father’s occupations and can be called the Intergenerational Occupational Inheritance (IOI) rate for convenience. The IOI rate is a complement to the IOM rate, and they sum to 1. As the IOI rate increases, the degree of occupational inheritance increases.

Figure 1:

(1−IOM) vs. GDP per capita. (A) First Occupation; (B) Current Occupation.

We first calculate (1 − IOM) based on the respondent’s first occupation,^[7] and then repeat the same procedures using the respondent’s current occupation. Figure 1 presents the correlation between (1 −IOM) and real GDP per capita based on these two different specifications. Both graphs report a significant correlation between (1 − IOM) and GDP per capita; the slopes of the linear fitted line are reported in the first two rows of Table 1. According to the first row of this table, the slope for Figure 1A is −2.90⋅10−4, which implies that if the GDP per capita differs by $40,000 between two countries, the IOM rates should differ by 11.6%. In the second row of the table, the slope for Figure 1B is −1.75⋅10−4 and statistically significant. Comparing these two figures, the GDP per capita correlation for the IOM rate based on the first occupation is larger than the correlation for the IOM rate based on the current occupation. Our quantitative exercises will be based on the current occupation, and therefore, our estimates provide a lower bound for the potential gains from removing barriers to IOM for China and India.

As previously mentioned, the ISSP 2009 data do not include India. In order to include India, we simply calculate (1 − IOM) from the IPUMS International data and put all the data points on top of Figure 1B and produce Figure 5 in Appendix C. The IPUMS International data provide five extra data points: China in 1982 and 1990, and India in 1993, 1999, and 2004. It can be seen that these observations all display very high (1 − IOM) rates, which suggests that (1 − IOM) decreased dramatically for China from the 1980s to 2009. Since these five extra data points are from a different dataset, we do not include them when calculating the correlation between (1 − IOM) and GDP per capita in Table 1 to prevent strong outlier effects.

It might be a concern that farmers, as the majority of the labor force in many developing countries, will completely dominate the results. If sons of farmers are also more likely to be farmers and the labor force is composed predominantly of farmers, the correlation between (1 − IOM) and GDP per capita would be significant even if there is no inheritance of other occupations. Of course, the barriers that impede sons of farmers from moving to new occupations also fits our topic, but if that is the case, a simpler analysis considering only farmers and non-farmers, similar to Adamopoulos et al. (2017), would serve not only the agricultural sector but also the whole economy. Therefore, we would like to know the extent to which farmers drive these results. We investigate this issue by removing all farmers from the data and reproducing the results. The graphs appear the same, with similarly significant and negative slopes, but on a smaller magnitude, which can been seen in Figure 3 and Figure 4 in Appendix C and in Table 1. Farmers explain part of the occupational inheritance phenomenon, but much remains to be explained by all other occupations.

2.2 Altham statistics vs. GDP per capita

The IOM rate includes information on the distribution of fathers’ occupations and the diagonal elements of the intergenerational occupational transition matrix; therefore, alone, it cannot disentangle interaction from prevalence, as discussed in Long and Ferrie (2013). Prevalence refers to the difference arising from fathers’ occupational distribution, while interaction refers to the conditional probability that sons will switch to occupations that are different from their fathers’ occupations. The problem of farmers in the previous subsection also involves excluding the effect of prevalence from interaction. Although both effects fit our topic, we follow Long and Ferrie (2013) to further explore empirical facts.

The interaction effect is determined by the intergenerational occupational transition matrix. In order to directly analyze the properties of the transition matrix, Long and Ferrie (2013) propose using the Altham statistic. For any two matrices P={pij}r×s and Q={qij}r×s, the Altham statistic is defined as

The Altham statistic d(P, Q) represents the distance between the row-column associations between matrices P and Q. In our case, P is the transition matrix for each country, and Q is the benchmark matrix, i.e. a matrix with all elements set at 1. The economic interpretation of Q is that children from any type of family will have an equal opportunity to enter any occupation. In addition, here, r = s because the transition matrix is square.

To further understand the mathematical implications of the Altham statistic, we would like to transform equation (3) into a more straightforward form. Define aij=log(pijqij). Following some derivations as shown in Appendix B, we re-write Equation (3) as

According to Equation (4), the items at the core of the equation are aij−matrix mean−column deviation−row deviation=residual. That is, d(P,Q)2 is a sum of squares of the residual of the matrix {aij}. In other words, the Altham statistic d(P,Q)2 is the F test statistic of a two-way analysis of variance (ANOVA) between the transition matrix P and the benchmark matrix Q. The two-way ANOVA F statistic can detect the interaction effects between the row variable and the column variable. By calculating d(P, Q), we know the extent to which the rows and columns of P are associated. Following a simple calculation, one can find that d(Q,Q)=0. That is, we should find a smaller d(P, Q) for countries in which sons are relatively freer to deviate from their fathers’ occupations.

We present the relationship between Altham statistics and GDP per capita in Figure 2. Again, the two subfigures are based on respondents’ first occupations and current occupations, respectively. As before, we also use data from IPUMS International to calculate Altham statistics for China in 1982/1990 and India in 1993/1999/2004, and they appear in red in Figure 6. The slopes of the regression lines are listed in Table 1.

Figure 2:

Altham statistics vs. GDP per capita. (A) First Occupation; (B) Current Occupation.

According to Figure 2, the correlation between Altham statistics and GDP per capita is negative but on the margin of being significant (t = −1.55), which suggests that interaction is not the only determinant of differences in IOM rates between different countries. That is, both the the distribution of fathers’ occupations π^L and the intergenerational occupational transition matrix P play a role in determining occupational inheritance levels. Moreover, compared with China, India shows very high Altham statistics in multiple years. This result implies that, regardless of their family background, workers in India will always find it very difficult to transfer from their fathers’ occupations to new occupations. This finding partly explains why, in our counterfactual experiment, the effect of reducing barriers in India is much larger than that in China.

2.3 China and India

In this section, we discuss our countries of interest, China and India, in detail. We first explain why we target China and India and then introduce some background information on labor market frictions and barriers to human capital accumulation in China and India.

3.1 Model setup

The model is a closed-economy version of Eaton and Kortum (2002) that is embedded with heterogeneous individuals making occupational choices, following Roy (1951). An individual’s work efficiency (or quality) is a combination of innate talents and acquired human capital, but there exist different levels of barriers in acquiring human capital and frictions in allocating workers from different family backgrounds. Based on one’s own innate talent draw and frictions in the labor market, an individual chooses his or her optimal occupation, consumption, and schooling investment. The collective decisions of all individuals will then determine aggregate productivity.

More specifically, there is a unit measure of individuals grouped by their fathers’ occupations (denoted by i), and a total of M different occupations (J={1,2,…,M}) in the economy. Each individual is born with innate talent ϵ=(ϵ1,ϵ2,…,ϵj,…,ϵM) across occupations that is determined by an idiosyncratic draw, where ϵ_j is his particular innate talent for jth occupation. Each individual lives one period, but we further decompose it into two sub-periods to distinguish between the period of accumulating human capital (“childhood”) and the period of work (“adulthood”). We denote by s schooling time, and therefore, (1−s) is leisure time, and we denote by e the expenditure on human capital acquisition. In childhood, the acquired human capital h is produced using schooling time input s and resource input e with a Cobb-Douglas production function h=δsϕeη, where δ is a parameter measuring the barriers to accumulating human capital. Ultimately, an individual’s work efficiency (or overall quality) is ϵh, a combination of innate talent and acquired human capital. In adulthood, each individual works in an occupation j ∈ J and earns a labor income subject to labor market frictions τ, that is, (1−τ)⋅wϵh, where w is the wage for one unit of effective labor. Then, the individual repays education input e and consumes the rest c.

In this model, innate talent ϵ is public information and determines an individual’s state jointly with family group i. Individuals face different levels of barriers to acquiring human capital and labor market frictions depending on the family group and working occupation. In other words, δ and τ come with subscripts i and j, where δ_ij and τ_ij are the corresponding terms for an individual from group i and working in occupation j. We will infer these barriers and frictions from the data – the key component of the quantitative exercise of this paper. When i = j, we expect a high value of δ and a low value of τ, as working in the same occupation as one’s father could potentially occur as a result of the transfer of knowledge within the family, social networks, etc.

In the model, an individual makes an occupational choice decision and decides on schooling timing and resource input and consumption based on this state. The optimization process could be decomposed into two-step backward induction. In the first step, given a particular occupation, an individual chooses the optimal schooling timing and resource input and consumption and calculates the indirect utility for this occupation; in the second step, an individual compares the indirect utility of different occupations and chooses the best occupation.

According to the model setup, the individual maximization problem can be written as

Innate talents are drawn from a Frechet distribution as in Eaton and Kortum (2002):

The parameter T_ij governs the location of the distribution: a larger T_ij implies a greater likelihood of high talent in occupation j for group i; the parameter θ is the shape parameter and governs the dispersion of the distribution.

The total amount of effective labor supply in occupation j can thus be written as

As defined in Section 2, π^L is the distribution of fathers’ occupations, that is, the distribution of groups, and p_ij is the probability of choosing occupation j conditional on group i. Therefore, πiLpij is the total measure of people who are from group i and work in occupation j. Ei[hijϵij|j] is the conditional mean of worker quality for all individuals from group i working in occupation j. As a result, πiLpij⋅Ei[hijϵij|j] is the total amount of effective labor that individuals from group i provide to occupation j, and the total amount of effective labor supply in occupation j is a simple summation over all groups.

There is a representative firm that hires all occupations of workers and produces final goods according to the CES production function:

where A_j is occupation-specific productivity. According to this production function, the marginal output of an individual depends not only on his own quality but also on the occupation productivity. In equilibrium, this A_j would determine the occupation-specific wage w_j for each unit of effective labor.

3.2 Model solution

Due to the properties of the Frechet distribution, this model has a solution that is dependent solely on wages. We present key equations in this subsection, and further details can be found in Appendix A.

An important statistic that links individual choice and macroeconomic variables is every group’s probability of choosing each occupation. To solve for this, we first solve the individual maximization problem using two-step backward inductions. First, for an individual with endowment ϵ from group i, calculate his indirect utility in occupation j, that is, Uij(ϵ) as in Equation (22) in Appendix A. Second, compare across j ∈ J to search for the best occupation. Then, we can integrate individual choices over the distribution of innate talent and solve for p_ij:

We can also solve for another important statistic – the average quality of workers from group i working in occupation j – by taking advantage of the Frechet distribution:

From Equation (14), we can solve for the average income of workers from group i working in occupation j:

Holding group i constant, we determine Equation (16) by comparing children’s average income of different groups for any occupation:

We further define an overall measure of barriers and frictions κ with the following equation:

By definition, κ should capture the strength of the elements that impede growth. As κ increases, these elements’ strength increases, and the economy suffers a larger productivity loss. From the occupational choice perspective, the variable affects each individual’s occupational choices and determines the aggregate intergenerational occupation transition pattern on the macro level. Estimating κ is a crucial step in our quantitative exercise, and thanks to the model’s design, we can directly infer κ from the data. Combining Equations (12), (16) and (17), we reach a key equation:

The average income for groups and occupations and an intergenerational occupational transition matrix can be directly estimated from the data. That is, we can instantly compute the last two terms on the right-hand side of Equation (18). Then, the right-hand side degenerates to the parameter T, which governs how innate talent can be transferred between generations. Additionally, from Equation (18), we can estimate κ, but we cannot further distinguish between δ_ij and (1 − τ_ij). Therefore, our quantitative exercises will continue by assuming two polar cases, that is, the case that τ_ij = 0 and the case that δ_ij = 1.

4.1 Data

Similar to the empirical analysis in Section 2, we rely on the ISSP 2009 and IPUMS International as data sources. However, we use mainly census data from IPUMS International in this section because we need to estimate the occupation transition matrix in the quantitative exercises. If there are M occupations in the economy and, consequently, M² elements in the transition matrix, we therefore, on average, have only 1/M2 of the total number of observations to estimate each cell. This problem could be even more serious because the occupation distribution is not even; therefore, a large sample size is required, and thus, census data are a better choice.

More specifically, we use China’s 1982 and 1990 censuses, the Indian Employment Survey for 1993, 1999, and 2004, and US census data from 1990, 2000, 2005, and 2010. The US census data include 5% percent of the population for 1990 and 2000 and 1% of that for 2005 and 2010. That is, we have 12,501,046 observations for 1990, 14,081,466 observations for 2000, 2,878,380 observations for 2005, and 3,061,692 observations for 2010. We still consult IPUMS 2009 data for two reasons: (1) neither of China’s censuses includes income information, but these data are available in the ISSP 2009; and (2) China’s 2010 census data are not available to the public, and we must therefore use the ISSP 2009 as a substitute to calculate the productivity gain for China from the 1980s to date.

For all data, we use the ISCO88 1-digit occupation classification. There are 10 occupations at this level, but we drop “Armed Forces” because it is difficult to measure its output, and in many countries, being a soldier is only a temporary occupation. The detailed 1-digit ISCO88 is listed in Table 11 of Appendix C.

We use four sets of data to parameterize the whole model: (1) intergenerational occupational transition matrix P={pij}; (2) average occupation income {INCi}; (3) average income ratios across all groups; and (4) average schooling in one particular group (i.e. farmers). These four sets of data include M(M−1), M, M − 1, and 1 moments, respectively. In total, we use M(M+1) moments for the estimation process.

We pool data from the 1982 and 1990 Chinese censuses to generate Table 3, and we pool the 1993, 1999, and 2004 Indian Employment Survey data to generate Table 4. We pool these data to eliminate short-term fluctuations and because there is no significant difference between datasets. We also report the intergenerational occupational transition matrix for the US in Table 12 in Appendix C.

A quick glimpse of the table illuminates several observations: 1) In comparing the diagonal elements between China and India, which indicate the degree of occupational inheritance, China’s occupational inheritance occurs mainly among farmers (cell (6,6)) and craft and related trade workers (cell (7,7)), while India has universally high occupational inheritance among all occupations; and 2) in both China and India, farming is the occupation with the highest inheritance rate, while for the US case, the occupational inheritance rate is around the median across all occupations.

In addition, we calculate the average income for each occupation in China and India. For China, data are reported as the annual occupational income in CNY; for India, it is reported as the weekly wage and salary income in INR; for the US, it is reported as the yearly wage and salary income in USD. When we feed these data into the model, they would be normalized internally so that direct comparisons are justified. Similarly, we also calculate relative average incomes across groups for each country.

4.2 Estimation and calibration of the parameters

Parameters {θ,η} govern the distribution of talent; however, the distribution of human talent is not directly observable. Fortunately, we can still infer this distribution from income information. According to the model, the distribution of income within an occupation for a particular group is Frechet, and the shape parameter is θ(1−η), which decides the moments of the distribution. Similar to HHJK (2016), we first regress income on occupation-group dummies using census data. The variance in the residuals would be exactly equal to the variance of a Frechet distribution with a shape parameter θ(1−η). Therefore, we can pin down that θ(1−η) is 4.32 for China, 2.44 for India, and 3.13 for the US. The parameter η is the resource input share in the production of acquired human capital and is equal to the ratio of human capital accumulation spending and output. Following Hsieh et al. (2016), we use the ratio of the share of education spending of output to the labor share of output as a proxy for η. We determine the share of education spending in GDP for China from the China’s Bureau of Statistics website^[8] and that for India from the OECD’s World Education Indicators 2005.^[9] In addition, we determine the average labor shares of China and India from the Karabarbounis and Neiman (2013) data. Ultimately, we find that η is 0.111 for China and 0.156 for India. We obtain the value 0.103 for the US directly from HHJK (2016).

In the model, β determines the Mincerian return, i.e. how one’s length of education is reflected in his or her income. A survey of the Mincerian return in China suggests a wide range of estimation results, starting from 3.29%^[10] in Johnson and Chow (1997), 10.24% in Zhang (2011), and 17.26% in Awaworyi and Mishra (2014), and the situation is very similar for India. To simplify, we choose the level β = 0.693 to match the Mincerian return in the US of 12.7% as shown in HHJK (2016) as the benchmark.^[11] In addition, we choose the elasticity of substitution between different sectors σ = 3, following the literature. We calculate the average years of schooling among farmers in China and India using census data, which are 4.8 years and 5.2 years, respectively. This step helps us calibrate the schooling of a benchmark occupation s₀, and we then further calibrate ϕ using Equations (19) and (29) in Appendix A. Finally, we determine occupation-specific A_j to clear labor markets for all occupations.

Parameter T determines how innate talent, the human capital determined by “nature” when one is born, is transferred between generations. It is not impossible that men in certain occupations would father children born with superior abilities for certain occupations. For example, the children of athletes are likely to be physically stronger or faster than average children. Unfortunately, it is impossible to directly evaluate these differences. In addition, if this mechanism is truly significant in magnitude, we should observe very serious occupational inheritance in well-developed market economies such as the US, while in fact, we observe very limited inheritance from the data. Therefore, we begin with the assumption that “all men are created equal”. That is, we assume that the distribution of talent is constant across all groups, and T_ij = 1. We will relax this assumption in an extension in Section 5.4 to check the extent to which this assumption affects the results.

Finally, we aim to infer the aggregate measure of the previously discussed impediments, matrix {κij}M×M, for China, India, and the US. We consider these {κij}M×M as the deep parameters that distinguish developed countries from developing countries. We normalize κ_ii = 1 for all i, i.e. when sons inherit their fathers’ occupations, the impediments they face are normalized to 1. Then, the estimation of {κij}M×M simply follows Equation (18), which uses elements in the intergenerational occupational transition matrix and income information as inputs.

5.1 Benchmark experiments

The results of the counterfactual experiments are listed in Table 5. These results indicate that both China and India can experience gains by a large magnitude by reducing the impediments to IOM. Comparing these two countries, we find that the gain for India is especially large. According to our previous empirical results, we can attribute this gain to the fact that it is very unlikely for Indian workers to move to a new occupation, regardless of their fathers’ occupations. The caste system is likely the most important reason for this result.

5.2 Accounting for China: the 1980s – 2009

As discussed in previous sections, China has made significant improvements in several dimensions in recent decades. First, China’s reform and opening-up policy has relaxed constraints such as “hukou” (household registration), which tied farmers to field work and restricted internal migration, and as a result, many young farmers have moved to coastal cities to work in new occupations. Second, the rapid expansion of the market economy on the coast has gradually mitigated the “guanxi” problem. Compared with state-owned enterprises, private firms facing intense international competition are less willing to hire simply because of “guanxi”. Due to the expansion of the market economy, the relative proportion of state-owned enterprises has decreased dramatically since the 1980s. Third, China has improved its general academic and vocational school education, as discussed in Section 2.3.3.

In order to examine the extent to which China has gained through reductions in occupational inheritance, we again use data from the ISSP 2009 and calculate the intergenerational occupational transition matrix as in Table 6. It can be directly observed from this table that the diagonal elements are very moderate, that is, the occupational inheritance rate is not high for any occupation.

The counterfactual experiment results are listed in the second row of Table 7. We also list the results from the benchmark counterfactual from Section 5.1 in the first row for comparison. In the third row, we list the realized growth potential for China from the 1980s to 2009. Our results suggest that China has realized 74–89% of the growth potential from the US counterfactual experiment in recent decades. These results indicate that China has made great progress towards reducing occupational inheritance; however, the country also needs to find other ways to continue its sustainable growth in the future.

5.3 Implications for intergenerational income correlation

In addition to affecting occupational choices and hurting productivity, barriers to human capital accumulation and labor market frictions can impact intergenerational income elasticity. If children from low-income families are constrained from moving away from low-income occupations, the economy would display very high intergenerational income elasticity. Our model incorporates occupational-level income information for both generations, and therefore, it allows us to analyze the relationship between the incomes of both generations. More specifically, for fathers, we have the distribution of occupations (πL=(π1L,π2L,…,πML)) and the average income for each occupation (w1=(w11,w21,…,wM1)), where superscripts denote the first generation. We can also calculate for both the real data and the counterfactual experiment equilibrium the intergenerational occupational transition matrix P and the average income for each group (w2=(w12,w22,…,wM2)). Based on the above information, we can calculate the correlation between the two generations’ incomes with the following equation:

We should note that this intergenerational income correlation measure does not include intra-occupation income variation, which would generate a higher value. This issue does not trouble us because we do not intend to analyze this value itself; instead, we aim to focus on the change in this measure after implementing the counterfactual experiment. For example, for the benchmark experiment, our research question is essentially this; we know from Section 5.1 that if impediments to occupational change were reduced to the US level, China and India could increase their labor productivity – but how would this affect the intergenerational income correlation?

According to Table 8, removing barriers and frictions are helpful in reducing intergenerational income correlations. Both China and India experience very large magnitudes of reduction, approximately 0.53~0.54 for China and 0.42~0.43 for India. The difference between China and India is minor and is likely to to the more uneven distribution of labor market frictions across occupations in China than in India. In the second experiment, China also experiences a reduction in intergenerational income correlations, but the magnitude of the change is not as significant as in the first experiment. This result indicates that the removal of barriers to human capital accumulation and labor market frictions between the 1980s and 2009 is uneven across occupations for China, and its effect on relaxing productivity constraints is greater than that on promoting income equality across society.

Regardless of the differences in magnitudes, we aim to emphasize the general conclusions that removing elements impeding intergenerational occupational change not only helps in improving productivity but also reduces inequality. This option promotes efficiency and social justice simultaneously, which should be considered by policymakers when dealing with “hukou” policy in China and the caste system in India.

5.4 Experiment: relaxing equal innate talent assumption

So far, we have assumed that the parameters of innate talent distribution are constant regardless of group and occupation, i.e. T_ij = 1. However, it may be true that men working in certain occupations may father children with greater innate talent to work in the same occupation. In this case, we would expect T_ij to vary across i and j. However, we are unlikely to completely estimate or correct the exact value of T_ij. Instead of attempting to find correct values for T_ij, we simply assign values to T_ij with reasonable alternative assumptions and check the extent to which our results are sensitive to this assumption.

Since the occupation for which children are born with superior ability is most likely to be the family occupation, we will change only the values of T_ii but maintain the assumption that Tij=1,∀i≠j. In addition to conducting the benchmark counterfactual experiment, we impose three different sets of T_ij and reproduce the results in order to determine how our results rely on this assumption. The three sets of values that we choose for this experiment are (1) Tii=1.5θ; (2) Tii=2θ; and (3) Tii=(skill level)θ. The skill level in case (3) is introduced by International Labour Office (1990) to measure the degree of complexity and skill requirement for occupations in ISCO88. There are four skill levels, which range from 1 to 4, and details can be found in Table 11.

How large are our values of T_ii in these experiments? Here, we aim to provide some straightforward intuition. Assume that innate talent follows a Frechet distribution, as in Equation (8). According to the property of the Frechet distribution, it follows that Ei(ϵj)∝Tij1θ. In other words, when we impose Tii=2θ, a worker working in the same occupation as his father would, on average, be twice as efficient as one working in a different occupation. Therefore, we consider that the three sets of values are large enough to detect problems in our results if the equal innate talent assumption is violated. The results for this experiment are listed in Table 9. According to this table, relaxing the equal innate talent assumption may shift the results slightly; however, this shift does not fundamentally change our conclusion.

5.5 Extension: allowing for an additional distortion creating the public sector earnings premium

In this section, we want to link the misallocations implied by the intergenerational occupational choices with the public-private wage premium in Cavalcanti and Santos (2015). In order to make such link, the first issue to solve is that we classify jobs by occupations in this paper while it is done by sectors in Cavalcanti and Santos (2015). Fortunately, China provides a particular case to overcome this problem. In the early 1980s, China was mostly a socialistic country with most enterprises being state-owned. In fact, most workers in the country were on the government’s payroll in the broad sense except farmers and the self-employed. It was impossible for the government to provide an income premium for all its employees especially for the unskilled workers considering their large number. Therefore, if the public sector earnings premium existed, it was intended for occupations with relatively high social status rather than all employees of the government. We pick three occupations (“Legislators, senior officials and managers”, “Professionals”, and “Clerks” ) as best candidates for wage premiums, and we would treat them as “the public sector” in this Section. The choice of occupations designated as the public sector would not change our conceptual analysis on the interactions of different distortions, but it is possible to make some quantitative differences.

We revise our model setup to allow for the public-private wage premium by revising the income Equation (6):

where the term (1+tij) stands for the distortion of the public sector earnings, and it could be further simplified to t_j if we maintain the assumption that the public sector wage premium is independent of an individual’s group. To effectively represent a public sector wage premium, t_ij should be greater than 0 when j is the public sector and 0 otherwise. Adding such a new term would change all the equilibrium conditions of the model, but only up to the level that we now replace (1 − τ_ij) by (1+tij)⋅(1−τij). For example, the Equation (13) is now:

Since the occupation choice pattern is still determined by ψ_ij as in Equation (12), the new distortion also affects the allocation of talents into different occupations according to Equation (20).

When we reduce the barriers of occupational choices by reducing τ_ij, (1+tij) would magnify the amount of barrier being removed. This is how the existence of this new distortion increases productivity gains when removing barriers of intergenerational occupational choices. However, if (1+tij)⋅(1−τij) is greater than 1 in the counterfactual, the public sector becomes too attractive and would induce inefficiently too many workers into the sector through the interactions with intergenerational occupational choices, which could potential hurt the labor productivity. Therefore, the overall effects of the interactions of the two misallocation sources really depend on their quantitative details.

We do not have data on the t_ij. Instead of arbitrarily choosing the values of t_ij, we use a “detour” method: we construct a new equilibrium with designated levels of the public sector earnings premium and running counterfactual experiments based on this new equilibrium. More specifically, we implement quantitative exercises following the following procedures:

Step 1: Calibrate the model just as in the benchmark case in the Sections 5.1.

Step 2: Add the new public sector wage distortion as in Equation (19), and calculate the new equilibrium with this new public sector. This new equilibrium would be the starting point for further counterfactual experiments. By construction, the public sector wage premium is completely a result of the corresponding underlying distortion.

Step 3: Keep the new public sector wage distortion but remove the occupational choice barriers in the counterfactual. This is again similar to the benchmark case in the Sections 5.1.

Step 4: Compare the equilibrium outcomes in the Step 2 and Step 3, and calculate the productivity gain of removing occupational choice barriers under the existence of the new public sector wage premium distortion.

This “detour” method relieves us from taking stand in the level of the public sector wage premium. In addition, since we are able to choose the designated level of the new public sector wage premium distortion, we are able to further explore how the size of the new distortion could affect the gains of productivity when removing the occupational choice barriers.

We list the results in the Table 10. Because we want to study different sources of misallocation, here we only focus on the case that δ_ij = 1 because in the other case that τ_ij = 0, the occupational choice distortions would be shut down. Column (1) is the productivity gain of the benchmark case in the Sections 5.1. It is effectively the case with zero public sector wage premium and we list it here for comparison. Column (2) is the productivity gain when the public sector wage distortion is set to be 25% uniformly for all workers just as in Cavalcanti and Santos (2015). In Column (3), we allow t_ij to vary by group. It is the productivity gain when the new public sector wage distortion is set to be 40% for workers whose fathers are farmers and 25% for all the rest groups. Since workers from the farmer family are usually the unfavorably treated group in China, this could be considered as a government policy to help this socially vulnerable group.

Comparing Columns (1) and (2), the results suggest that with presence of the public sector earnings premium, the gains of productivity by reducing occupational inheritance become slightly larger. This is especially true if the government gives additional favor to workers grown up in the farmer family as suggested in Column (3). In other words, in China’s case, the public sector earnings premium aggravates the effects of the barriers to intergenerational occupational choices on the labor productivity, even though the magnitude is not large.