Economic complexity, human capital and income inequality: a cross-country analysis

This paper investigates the relationship between economic complexity, a measure of economic structures, and income inequality. Using cross-country OLS regression analysis, we show that countries with economic structures geared toward complex products have less inequality. Human capital is found to magnify this correlation but with subtle interaction effects. Concerns about endogeneity bias in the OLS estimates stemming from reverse causality motivate us to estimate a dynamic panel data model, using a system GMM estimator. From the system GMM estimates we find that an increase in economic complexity provokes higher inequality, not less.


Introduction
Since the 1950s, there has been an intense discussion of the relationship between economic development and income inequality, following the path-breaking paper of Kuznets (Kuznets 1955). This line of research attempts to verify empirically the well-known inverted U-shaped "Kuznets curve", in which economic development at first increases inequality but eventually reduces it. Findings remain inconclusive, with some papers providing empirical support for the Kuznets hypothesis (Ahluwalia 1976;Barro 2008), others finding support for only the downward sloping part of the curve (Perotti 1996;Galbraith 2007;Palma 2011), and still others refuting any systematic relationship between economic growth and the level of income inequality (Deininger and Squire 1996).

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A glaring limitation of the above strand of literature is that scholars have typically made use of aggregate indicators of economic development, such as GDP or the total contribution to GDP of agriculture, manufacturing or services (Hartmann et al. 2017). Economists, however, contend that an aggregate monetary measure of economic size is an inadequate proxy for economic development when it comes to explaining variations in income inequality (Kuznets 1973;Stiglitz et al. 2010;Sbardella et al. 2017;Hartmann et al. 2017). The basic problem with aggregate monetary measures of economic development is that economic outcomes depend on what a country produces and exports. Development indicators based upon broad categories, therefore, fail to capture effectively the complexity level of what is produced. 1 By contrast, economic performance is not necessarily uniform across the diverse range of products. Analysis of the relation between economic development and income inequality requires a disaggregated approach.
Indeed, the relationship between a country's economic structures, reflecting what it produces and exports, and economic growth and income inequality, has long been recognized in the literature. Specifically, Lewis (1955), Rostow (1959), Kuznets and Murphy (1966), Kaldor (1967) and Chenery and Taylor (1968), among others, emphasize the role of economic transformation, that is, the process of moving from activities with lower productivity to those with higher productivity. Specialization in different activities is associated with differentiated economic outcomes. Countries whose economic structures are geared toward sophisticated commodities develop faster than those specializing in simple products (Felipe et al. 2012).
This paper goes beyond the current literature by investigating the relationship between economic complexity and income inequality. We build upon recent scholarship which argues that income distribution depends not only on economic growth but also on the type of growth (Hartmann et al. 2017). This line of research calls for better measures of economic development, ones that are not just aggregated indicators of income (Costanza et al. 2009;Stiglitz et al. 2010). Accordingly, economic development involves not only increases in economic size, but also entails variations in technology, human capital, and institutions. All these factors are defined as non-tradeable capabilities, which determine a country's productivity level (Hidalgo and Hausmann 2009). These capabilities are captured by the economic complexity index, which measures productive capabilities embedded in economic structures. The index is constructed based on the method proposed by Hidalgo and Hausmann (2009). An economy is complex if it can produce a diverse range of products (diversity) that are not widely produced by many other countries (ubiquity). Complexity reveals information about a country's human capital, technology, and institutions. It is strongly correlated with economic performance (Hausmann et al. 2007;Hidalgo and Hausmann 2009). Nevertheless, little is known about the extent to which complexity affects income inequality.
By examining the relationship between economic complexity and inequality, our study contributes to the literature in several dimensions. First, we employ an extended dataset of income inequality with the broadest coverage of countries and 1 3 The Japanese Economic Review (2020) 71:  years to examine the distributional effects of economic complexity. Second, using cross-country OLS regression, we demonstrate that countries with higher economic complexity enjoy a lower level of inequality. Furthermore, human capital magnifies this negative correlation. Breaking down the sample based on countries' income level, we find that secondary education and tertiary education interact differently with economic complexity in explaining inequality. Third, we note that the strong correlation between economic complexity and income inequality in the OLS estimates may not establish causality because of possible endogeneity bias. To address this concern, we estimate a dynamic panel data model, using a system GMM estimator that caters for the potential endogeneity bias. We differ from previous research by separating the short-and longer run effects of complexity on inequality. An immediate and a longer term increase in complexity is found to worsen income distribution.
The paper proceeds as follows. The Sect. 2 discusses economic complexity and its relationship with income inequality. Next, we present our econometric methods. The Sect. 4 examines empirical findings. The study concludes by summarizing the main results.

What is economic complexity?
Economic complexity, as constructed by Hidalgo and Hausmann (2009), is a measure of the set of productive capabilities available in a country. Here, capabilities are defined as non-tradeable inputs required to make a product (Hidalgo and Hausmann 2009). These inputs include human capital, technology, institutions, and the legal system. At the firm level, capabilities encompass the set of "know-how" or working practices, which are created when individuals interact and work closely together in a group. Broadly speaking, capabilities at firm level capture organizational capacity associated with the formation, management, and operation of production activities (Felipe et al. 2012). The diversity of these capabilities, as measured by economic complexity, determines a country's productivity level. Thus, economic complexity helps explain cross-country divergence in income per capita (Hidalgo and Hausmann 2009). Hidalgo and Hausmann (2009) construct an economic complexity index based on the so-called "Method of Reflections". The authors calculate the Revealed Comparative Advantage (RCA) index to determine whether a country is effectively exporting each given product. 2 They define two concepts, "diversity" and "ubiquity", as the number of products a country can export with RCA and the number of countries that have an advantage in exporting a given product, respectively. A country is complex if it can export a diverse range of products with RCA (high diversity), while a product is complex if it is exported by few countries (low ubiquity). The basic reasoning is that producing a given commodity requires a set of productive capabilities. Hence, the diversity of these capabilities is revealed by the number of products a country exports with RCA. At the same time, complex products that require many hard-to-find capabilities are exported by few countries. Finally, economic complexity is obtained by combining information on country diversity and product ubiquity. A country is complex if it exports a diverse range of products (high diversity), including ones that are exported by few other countries (low ubiquity).
The calculation is shown below, following Hidalgo and Hausmann (2009): where c stands for the country, and p denotes the commodity. RCA cp is an indicator variable, taking the value of 1 if a country has a revealed comparative advantage in product p, and 0 otherwise. However, these two indicators, considered separately, are imprecise measures of economic complexity. For instance, a country may export a diverse range of products, simply because of its economic size. In this case, product diversity may provide biased information on the availability of capabilities within a country. To address this bias, Hidalgo and Hausmann (2009) propose the method of reflection to calculate economic complexity by computing jointly and iteratively the mean values of diversity and ubiquity. The formulae can be represented as follows: where N stands for the number of iterations.
By substituting Eq.
[4] into [3], we obtain the following equation (Hausmann et al. 2014): This can be rewritten as in which The Japanese Economic Review (2020) 71:  where M cc′ is a matrix connecting the countries exporting similar products. To discount common products, the matrix is weighted by the inverse of the ubiquity of a product. Then it is normalized by the diversity of a country (Hartmann et al. 2017). Finally, economic complexity is computed as where K c is the eigenvector of M cc′ , associated with the second largest eigenvalue. The vector associated with the largest eigenvalue is a vector of ones (Hausmann et al. 2014;Caldarelli et al. 2012).

Why does economic complexity matter for income inequality?
Hartmann et al. (2017) is the only paper we know of that documents a relationship between economic complexity and income inequality. Using OLS and panel fixed-effects regression, the authors demonstrate that economic complexity reduces income inequality. We replicate their findings using OLS regressions and find that countries with higher economic complexity exhibit less inequality. But this may reflect endogeneity bias stemming from reverse causality. Based on system GMM estimates, we show that within any one country, an increase in complexity is associated with higher inequality, a divergence from the previous literature. There are several mechanisms by which economic complexity improves a country's income distribution. Individuals living in a complex economy have higher employment and wider occupational opportunities, and possess a great diversity of disseminated skills and knowledge (Hartmann 2014). Economic structures geared toward a diverse range of sophisticated products are associated with a relatively flat occupational structure (Hartmann et al. 2017). Furthermore, workers in complex industries have more bargaining power, lowering income disparity. Complex economic structures are also associated with better institutions and higher unionization, which reduces income inequality (Hartmann 2014).
Considering a country whose economic structures are geared toward simple commodities (e.g., raw materials and agricultural products), inequality tends to proliferate because of the following reasons. First, the income of most workers in such a country depends on economic activities characterized by decreasing returns to scale and low productivity. By contrast, a small fraction of the population enjoys higher income, stemming from limited activities with higher productivity. Second, the diffusion of knowledge and skills would be confined to small groups of individuals, leaving them with an economic premium. Third, individuals at the bottom of the income distribution are constrained by limited learning and occupational opportunities. This further increases the income gap. Finally, the presence of one main sector producing primary commodities is associated with a vertical hierarchy in the occupational structure to manage a huge cadre of unskilled labors. By contrast, complex economic structures, characterized by products with increasing 1 3 returns to scale, reduce inequality by enhancing the lifetime earnings of workers who produce these products (Constantine 2017). A diverse range of opportunities also provides the poor with several means of moving up in the social stratification (Hidalgo 2015;Hartmann et al. 2017). Therefore, economic complexity helps to lower income inequality. We argue that within a country, an increase in economic complexity can be associated with a higher level of inequality. When economic structures become more complex, there appears a growing demand for qualified workers (Constantine 2017). This is attributable to changes in the set of required capabilities (Hodgson 2003). Specifically, this process results in some new capabilities emerging and becoming increasingly essential, in accordance with the growing richness of the complex economy. This is described as a creative-destruction process, which leads to the emergence of new sectors and the disappearance of traditional ones (Hartmann 2014). In this process, workers may find it difficult to switch from one specialty to another (Hartmann 2014). There would be opportunities for the low-income group to climb up the career ladder, but continual retraining would be of great importance in acquiring remunerative employment. It is much easier and less costly for skilled workers to advance because they are endowed with greater capabilities. Skilled workers with the capacity to adapt to the changing sets of capabilities eventually secure an improved economic premium and become active agents in society. For this reason, we argue that growing economic complexity benefits skilled workers more than unskilled workers, exacerbating the income gap within a country.
We suppose that human capital magnifies the negative correlation between economic complexity and inequality. Specifically, human capital plays an important role in tackling inequality when a country experiences structural transformation toward complex industries. Endogenous growth theory, attempting to explain cross-country income disparities, observes that human capital is an essential determinant of growth (Romer 2012). Furthermore, the literature has long acknowledged that economic development is a process of structural change in a country's productive structures (Rostow 1959;Lewis 1955). This occurs through resource transformation from simple to complex industries, achieved by accumulating new productive capabilities. In this process, human capital allows a country to learn and acquire more capabilities faster. Consequently, human capital helps a country to engage in the production of sophisticated commodities, thereby enhancing its economic complexity (Hidalgo and Hausmann 2009;Hausmann et al. 2014). Improvements in education also allow individuals to take advantage of diverse opportunities due to growing economic complexity. It, therefore, lowers the possibility that complexity worsens a country's income distribution due to skill bias. Hence, we argue that human capital is the key factor that intertwines with economic complexity in affecting income inequality.

Cross-country models
A cross-country model is used to test the hypothesis that more complex economies have more equal income distribution. We calculate the average value for each variable across the period from 1980 to 2014 to obtain cross-sectional data for 96 countries. 3 The dependent variable is the Gini coefficient, a measure of income inequality. This index is estimated using post-tax, post-transfer measures of household income in the Standardized World Income Inequality Database. The main variable of interest, economic complexity, is taken from MIT's Observatory of Economic Complexity (https ://atlas .media .mit.edu).
First, income inequality is regressed on economic complexity, controlling for the level of income, its square, years of schooling, population, trade openness, and FDI. The model specification is expressed as where i stands for country i, GINI represents the Gini coefficient for disposable income, ECI represents the Economic Complexity index, lnGDPPC and lnGDP-PCSQ are the natural log of GDP per capita and its squared term, respectively, Schooling denotes years of schooling, X is a vector of other control variables, and ε represents the error term.
Second, the effects of economic complexity on income inequality are conditional on human capital, as argued earlier. Therefore, an additional model is specified, including interaction terms between economic complexity and different measures of human capital. The model specification is presented below: From the results shown in the following section, most of the control variables included in Eq.
[5] are statistically insignificant. The basic reasoning is that some of the distributional effect of those factors (e.g., trade openness and FDI) may be captured by ECI. Hence, we do not include them in Eqs.
Finally, we estimate Eq. [6] using two different sub-samples, based on the level of income, to test whether different measures of human capital have differentiated effects in developing and developed countries (we find that they do have differentiated effects).
[5] and [6] requires some attention to reverse causality that may run from income inequality to economic complexity. A higher level of income inequality impedes the development of education, and affects health outcomes, investment, and the social consensus (Persson and Tabellini 1994;Benabou 1996;Alesina and Perotti 1996;Easterly 2007;Berg and Ostry 2013). In addition, economic complexity is a correlate of a country's innovative outcomes, its increasing innovative capacity, and the implementation of those innovations (Sweet and Eterovic Maggio 2015). A high level of income inequality, which deters economic development, can (5) also lower the innovation creation process by limiting the demand for innovative products and services (Zweimüller 2000). We may well think that income inequality dampens incentives to innovate. These incentives are essential for a country to obtain new productive capabilities, which allow it to engage in more sophisticated production activities. Thus, the estimates of effects of complexity on inequality may reflect reverse causation. This potential bias is ignored by Hartmann et al. (2017), which is the only study linking complexity and inequality. The consistency of estimates requires using an instrumental variable that affects income inequality only through economic complexity. This is a challenging task, given that the main determinants of economic complexity have direct effects on income inequality (e.g., government consumption, the abundance of arable land, and capital per worker). 4 This motivates us to estimate a dynamic panel data model in the following section.
In short, we estimate Eqs.
[5] and [6] using OLS, albeit recognizing that some endogeneity bias may exist. Hence, the strong correlation between economic complexity and income inequality, as demonstrated later, may not necessarily imply causality.

A dynamic panel data model
To test the effects of an increase in economic complexity on income inequality in a dynamic model, this section analyzes an unbalanced panel dataset, comprising 113 countries with 5-year averages from 1965 to 2014. The motivation for taking 5-year averages for all time-variant variables is that we can reduce short-run fluctuations due to business cycles. In addition, our main variables of interest, including economic complexity, GDP and inequality, change slowly year-over-year. This paper follows Blundell and Bond (1998) to estimate the following model: where i denotes country i (i = 1, 2,…113). The time dimension runs from 1 to 10, denoting 10 successive periods of 5-year averages from 1965 to 2014. GINI it represents the disposable income Gini coefficients of country i in period t. GINI it−1 reflects the dynamic characteristics of the model. Schooling it is years of schooling of country i in period t. 5 Population it is the total population; δ i is the country fixed effects; γ t stands for time effects; ε it is the error term; and β is the vector of estimated coefficients. 6 (7) 4 See Daude et al. (2016) and Zhu and Fu (2013).
5 Data for years of schooling is obtained from Barro and Lee (2013), but this data is available at 5-year intervals. Therefore, we assigned the educational data at the beginning year of every period. For instance, data on years of schooling in 1965 will be used for the first period (1965)(1966)(1967)(1968)(1969), and data on years of schooling in 2010 will be used for the final period (2010)(2011)(2012)(2013)(2014). Years of schooling represent the stock of human capital, accumulated over every 5 years. Hence, we can match them with 5-year averages data to estimate Eq.
[7]. 6 Unlike the OLS models, the panel data models do not include institutional variables because data is relatively sparse.

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The Japanese Economic Review (2020) 71:695-718 The reason why we include lagged inequality as an explanatory variable in Eq.
[7] is that aggregate indicators, such as GDP or inequality, exhibit high time persistence. Indeed, serial correlation of income inequality across time has been well established in the literature (Banerjee and Duflo 2003;Kurita and Kurosaki 2011). This motivates us to estimate a linear dynamic panel data. 7 We include both current and lagged economic complexity to capture the shortand long-run effects of an increase in economic complexity on income inequality. 8 In particular, the current economic complexity reflects the distributional effects of an immediate increase in economic complexity. We also compute the long-run effects, following Wooldridge (2013, p. 635). It is necessary to conduct formal tests of selecting the appropriate lag length of ECI when calculating the long-run effect. However, this task is challenging given that our time-series dimension is relatively short. We also tried including the second and third lag of ECI, and the estimated coefficients are positive but statistically insignificant. Including further lags of ECI also results in the model suffering from instrument proliferation when we have too many endogenous regressors. For these reasons, we include only the one-period lag of ECI.
Estimation of Eq.
[7] requires the following issues to be addressed. First, the lagged dependent variable, included as an explanatory variable, is endogenous. Second, estimating the distributional effects of economic complexity, GDP, and human capital suffers from endogeneity bias due to measurement errors, omitted variable bias, and reverse causality, as argued earlier. The solution to these problems is to use an exogenous instrument that satisfies the exclusion restrictions. This is a challenging task, as we discussed in the previous section. Motivated by this issue, we estimate Eq. [7] using internal instruments, which are the higher order lags of our endogenous variables. 9 Arellano and Bond (1991) propose the use of first differences of the variables to remove bias arising from unobserved country heterogeneity. The first-difference equation can be expressed as follows.
in which Δ stands for the first difference operator. It is easy to recognize that ΔGINI it−1 is endogenous in this case because 7 Income inequality varies slowly within countries over years. This suggests that there exist some unobserved factors explaining this time persistence. In this case, fixed-effects estimates are biased if these factors are correlated with our explanatory variables. Addressing this issue requires including the past income inequality levels as an explanatory variable. 8 We sincerely thank an anonymous referee for this suggestion. 9 We treat all variables on the right-hand side, except population, as endogenous variables.
Under the assumption that the error terms in Eq.
[7] are serially uncorrelated ( cov i,t , i,t−j = 0 if j ≠ 0 ), the moment conditions for the difference-GMM estimator are specified as follows: Hence, two periods or further lags of the dependent variable are valid instruments for ΔGINI i,t−1 in Eq. [8]. 10 We apply the same logic to address the second problem caused by reverse causality running from inequality to complexity. Under the assumption that E ECI i,t i,j ≠ 0 for j ≤ t and E ECI i,t i,j = 0 for j > t , the moment condition is specified as Hence, two periods or further lags of economic complexity are valid instruments for both ΔECI i,t and ΔECI i,t−1 . The difference GMM employs two sets of moment condition [9] and [10] to estimate Eq. [7]. However, the difference estimation method suffers from the problem of weak instruments, given the high time persistence of the dependent variable and the short time dimension (Arellano and Bover 1995;Blundell and Bond 1998). This problem can be addressed using the system GMM estimator, developed by Blundell and Bond (1998). The basic idea is to specify additional moment conditions by adding the level form equation to the difference equation. The lagged differences of the explanatory variables are used as instruments for the equations in levels. The additional moment conditions can be described as below: In short, the system GMM employs the moment conditions [9], [10], [11], and [12] to estimate Eq. [7]. Because our dependent variable is time persisting, as discussed above, the system GMM estimator is more suitable. Furthermore, it can address the potential endogeneity of our variables using appropriate lags of endogenous variables as valid instruments.
Finally, we perform several specification tests to check the validity of our results. First, the Arellano-Bond AR(2) test is used to test the absence of second-order autocorrelation. Failure to reject the null of the AR(2) test implies no autocorrelation in the second-differenced errors, validating the moment conditions. In this case, we can perform the system GMM estimation without changing the instrument sets. By contrast, rejection of the null of the AR(2) test supports the presence of autocorrelation in the error term of order one or higher. This requires re-estimating the models using further lags (Cameron and Trivedi 2005). For this reason, we perform (9) E GINI i,t−j Δ i,t = 0 for t = 3, 4, … T and j ≥ 2.

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The Japanese Economic Review (2020) 71:695-718 the Arellano-Bond AR(3) test to check the absence of third-order autocorrelation in the error term. Failure to reject the null validates our instruments used in the modified system GMM estimator. Second, we check the Hansen J test of over-identifying restrictions. The null hypothesis is that the over-identifying restrictions are valid, of which the failure to reject substantiates the overall validity of the instruments and the model. Furthermore, the system GMM estimator may suffer from instrument proliferation problems because it employs a larger set of instruments, relative to difference GMM. We solve this problem by limiting the number of lags of the endogenous variables. 11 Table 1 Basic OLS estimates of the effects of economic complexity on income inequality Robust standard errors in parentheses ***p < 0.01, **p < 0.05, *p < 0.

OLS estimation
The OLS estimation results are presented in Tables 1, 2 and 3. We find a strong negative effect of economic complexity on income inequality. It can be observed from Table 1 that the estimated coefficients of economic complexity are negative and statistically significant at the 1% level in all models. This means that a country whose productive structures are more complex has less income inequality, ceteris paribus. This empirical finding is in line with the OLS estimates of Hartmann et al. (2017). It is also consistent with the argument that higher complexity flattens the hierarchical occupational structure and provides individuals with more occupational choices, better learning opportunities, and higher sustained incomes, all of which reduce income inequality. The other potential determinants of inequality, including trade openness, FDI, education and institutions, are statistically insignificant when ECI is used to explain cross-country differences in inequality. This shows that economic complexity is a strong predictor of income inequality across countries. Using cross-country average data from 1980 to 2014 for 96 countries, this paper provides empirical support for the validity of the Kuznets proposition after controlling for economic complexity. The coefficients for GDP per capita have a positive sign, and are statistically significant at the 1% level. Also, the estimated coefficients for the squared term of GDP per capita are negative and statistically significant at the 1% level. Hence, the inverted U-shaped curve is recovered, using this sample of 96 countries. Table 2 examines the effects of the interaction between economic complexity and human capital on income inequality. The effects of ECI on inequality at the mean value of the log of Schooling can be computed from column (1) of Table 1

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This is consistent with our findings in Table 1. Hence, it further supports the negative correlation between economic complexity and inequality, using the OLS estimation method.
The estimated coefficients of interaction terms between complexity and human capital are negative and statistically significant at the 1% level. The strong significance and the negative sign of the estimated coefficients suggest that human capital considerably bolsters the negative effect of complexity on income inequality. Our results are robust to using different measures of human capital. Countries that manage to complement social policies, which improve the quality of human capital, with industrial policies, which diversify toward more sophisticated products, will have less income inequality. Hartmann et al. (2016) argue that high-performing Asian economies (HPAEs) such as South Korea, Malaysia, and Thailand have managed to diversify their economic structures into more complex industrial products, creating wider employment opportunities. At the same time, they invested substantially in education that prepared workers for new occupational choices. Consequently, those countries maintained a lower level of income inequality from 1970 until 2010, along with growing economic complexity. By combining social and economic policies, the benefits of their growing level of economic complexity were spread into the whole society, evidenced by decreasing income inequality (Stiglitz 1996).
We further perform different regressions after dividing the observations into two sub-samples, one with developing and the other with developed countries. For both sub-samples, the estimated coefficients for secondary education and its interaction with complexity are noticeably higher than for tertiary education as shown in Tables 2 and 3. Estimation results indicate that secondary education has much stronger interaction effects on inequality than tertiary education, in both high-income countries and low-and middle-income countries. More importantly, the interaction between education and complexity has a positive effect on inequality in high-income countries, but a negative effect in developing countries. Hence, the negative joint effect when pooling data across countries (as shown in Table 2) is mainly driven by the group of developing economies. The reasons for this are various.
First, the link between income inequality and education expansion, measured by increasing years of schooling or by decreasing education inequality, has been subject to numerous empirical tests. Barro (2000) considers the effects of different levels of education on income inequality, and finds that secondary education is negatively associated with inequality while tertiary education is positively correlated with inequality. Examining the distributional implications of education in Greece, Tsakloglou and Antoninis (1999) find that public transfers in primary and secondary education are associated with a more equal distribution of income, while transfers in tertiary education have limited distributional effects. The explanation for such a finding is that investments in secondary education benefit the middle quintiles (the majority of households) while the impact of tertiary education is found only in the top quintiles. Hence, transfers in secondary education have much higher and stronger effects in decreasing inequality than transfers in tertiary education. Furthermore, stronger distributional effects of secondary education are found in other studies (Abdullah et al. 2015).
Second, these results are not surprising when considering that the majority of the sample consists of developing countries. Over recent decades, most developing economies with high economic growth rates have experienced rapid structural transformation, which is dominated by resource reallocation away from agriculture and toward manufacturing. According to Atkin (2016), this industrialization process is mainly driven by low-skill manufacturing exports. Thus, there has been a growing demand for low-skill manufacturing labor in most developing countries. To the extent that an improvement in secondary education responds to this increased demand and improves productive capabilities, the joint effect of secondary education and complexity is more pronounced in developing countries. The negative interaction effect is also mainly driven by developing countries.
Third, Zhu and Li (2017) argue that the stronger interaction effect between complexity and secondary education in developing countries can be explained by looking at the method of computing the economic complexity index. The first step in measuring the complexity level is to select products in which a country can produce and export with revealed comparative advantage. In developing countries, it is far more common to reveal comparative advantage in low-skill manufacturing and labor-intensive production activities, which mostly employ workers without higher education. Therefore, the labor market of developing economies is likely to absorb workers with secondary education. Also, complexity can be bolstered by employing workers with secondary education in the expanding industries.
Finally, the effect on income distribution of the interaction between complexity and human capital is found to be positive in high-income countries. This means that the higher quality of education, together with growing economic complexity, drives widening income disparities. While the structural transformation in developing countries has been driven by the resource movement toward manufacturing, it has been accompanied by service-based activities in developed economies. Wage variation in the manufacturing sector is usually lower than that in the service sector. Meanwhile, manufacturing jobs are characterized by the presence of labor unions and collective bargaining that act as impediments to worsening income inequality. Hence, the structural transformation in high-income countries from labor-intensive manufacturing to more service-intensive activities is associated with higher inequality. Furthermore, we argue this could be due to the saturation of high-quality human capital in developed countries. Highly complex economies usually require a smaller workforce as industries tend to be more highly automated and technologically advanced. Therefore, workers with highly advanced skills or advanced degrees will be rewarded by significantly higher income, but these industries also need fewer workers to drive the value chain. Therefore, higher inequality and income differences should be seen between workers with exceptional skills or advanced degrees compared with others. This suggests that the interaction effects of economic complexity and education on income inequality, as argued before, are more important in developing countries than in advanced countries.
We also test whether the quality of institutions magnifies the correlation between economic complexity and income inequality. Indeed, institutions act as a catalyst for new economic activities (North 1990). They are also beneficial for investment in productive capabilities, including new technologies and skills (North 1990), and 1 3 the so-called "self-discovery" process (Hausmann and Rodrik 2003). In addition, the quality of institutions promotes innovations through creating entrepreneurship, and disseminating knowledge and technologies (Schumpeter 1934;Brown 1999). Countries with better institutions, therefore, acquire productive capabilities faster, thus improving their economic complexity and income distribution. The estimated coefficients are significantly negative, supporting this argument. However, they are statistically insignificant when we include the interaction between human capital and ECI in the model. This indicates that human capital is the most important factor that interacts with complexity to affect inequality. 12 1 3 The Japanese Economic Review (2020) 71:695-718

System GMM estimates
Estimation results of the dynamic panel data, using a system GMM estimator, are presented in Table 4. The failure to reject the Hansen J test substantiates the model specifications and the validity of our instruments. However, the AR(2) test shows that the error terms are serially correlated. For this reason, we re-estimate our model, using an adjusted instrument set. The AR(3) test indicates the absence of serial correlation in the error term, validating our instruments. 13 The estimated coefficients of the lagged dependent variable are relatively large in magnitude, and are highly significant as shown in Table 4. This implies that income inequality shows high time persistence, which further justifies the relevance of the system GMM estimation method.
The estimated coefficients of ECI are positive and statistically significant at the 1% level. This indicates that an immediate increase in economic complexity provokes higher income inequality. Specifically, a one-standard-deviation increase in complexity is associated with approximately a 0.02-unit increase in inequality, as shown in column 6 of Table 4. It should be noted that this result is opposite to that of Hartmann et al. (2017), as discussed below.
Although the estimated coefficients of the lagged ECI are not statistically significant in several models, they are statistically significant at the 5% level after we control for schooling. Following Wooldridge (2013, page 635), we compute the longrun effects of an increase in economic complexity on income inequality, given the estimated coefficients in column 6 of Table 4. 14 Hence, a long-term increase in economic complexity is associated with an increase in the degree of income inequality. Specifically, a one-unit increase in ECI in the long-run results in a 0.116-unit increase in inequality. The magnitude of the long-term effects, however, is larger than the short-term effects.
13 We used the third and fourth lags of endogenous instruments to avoid the problem of instrument proliferation in system GMM estimator. This choice is also motivated by the criterion that the number of instruments should be ideally smaller than the number of countries (Roodman 2009) and the AR(3) test results. Our main findings are robust to limiting lags of endogenous variables used as instruments. 14 We can re-write Eq.
Our results suggest that when the economy manages to diversify its production activities and engage in the production of more complex products, the distribution of income becomes less equal. This empirical finding supports the arguments of Hodgson (2003) and Hartmann (2014). In particular, an increase in economic complexity is achieved when a country acquires new productive capabilities that allow it to make more complex products. On the one hand, this process brings about new employment and education opportunities, which tends to reduce inequality. On the other hand, it can also create a situation of "winner-take-all" that intensifies income inequality within and between countries because low-skilled workers and low-income countries are at a greater disadvantage. Hodgson (2003) argues that the growing diversity and sophistication of products are associated with the emergence of new specialties. Hartmann (2014) refers to this as the "creative-destruction" process in which new specialties emerge and replace outdated ones. Workers who have advanced and transferable skills can learn quickly, and are exposed to less risk when adapting to this structural change. Hence, they capture an economic premium.
Furthermore, economic complexity exacerbates inequality when it results in the problem of structural dependence and underdevelopment of a country's less developed areas (Myrdal 1957;Hartmann 2014). The growing diversity of complex industries in developed regions attracts inflows of qualified workers from a "periphery" of impoverished and underdeveloped areas, enriching the complexity levels of the former while worsening the economic issues of the latter. Consequently, the income disparity among regions increases. If we consider the issue from a crossnational perspective, growing complexity, which might be facilitated by automation and artificial intelligence, lowers the demand for low-skilled jobs in developing countries. This happens because developed nations are bringing back manufacturing and industrial jobs in which low-income countries traditionally have had a comparative advantage. Thus, income disparity between countries escalates.
It is important to compare our empirical findings with those of Hartmann et al. (2017). The authors perform a cross-country fixed-effects panel regression with 10-year averages from 1963 to 2008, and find that an increase in complexity lowers inequality. We also estimate a static panel data, using 5-year and 10-year averages, but employ another dataset of income inequality with the broadest coverage of countries and years. Fixed-effect estimates show that the estimated coefficient on ECI is consistently positive, but it is statistically insignificant in some cases. 15 However, as discussed earlier, fixed-effect estimates may be biased due to the potential endogeneity of complexity and the persistence of the dependent variable. Addressing these problems, we estimate a dynamic panel data, using a system GMM estimator. Furthermore, our paper also differs from Hartmann et al. (2017) in demonstrating that an increase in economic complexity is associated with higher degrees of inequality in both short and long runs, using the dynamic panel data estimation. The shortcoming of Hartmann et al. (2017) is that this paper is not including lagged ECI, thus failing to capture the long-run effects of an increase in complexity on inequality. Using a new dataset of inequality with the broadest coverage of countries and years, we find that an increase in economic complexity is associated with a higher level of income inequality, controlling for the potential endogeneity bias.
To sum up, we estimate a dynamic panel data, using a system GMM estimator. Results show that an increase in economic complexity results in higher income inequality in both short and long runs. The magnitude of the long-run effect is larger than that of the short-run effect.

Conclusions
This paper sheds light on the relationship between economic complexity and income inequality. It does so by estimating cross-country OLS regressions and a dynamic panel data model.
The cross-sectional OLS regressions show that countries with higher economic complexity enjoy lower levels of income inequality. This finding indicates that economic complexity is a strong predictor of income inequality. Furthermore, human capital magnifies the negative correlation between complexity and inequality. Countries endowed with better and improved human capital are better able to enhance their economic structures. Consequently, this reinforces the distributional effects of economic complexity, leaving them with a lower level of inequality. We also demonstrate that secondary education plays a more important role than tertiary education in interacting with economic complexity. Although these findings document a strong correlation, they do not necessarily imply causality because of potential endogeneity concerns.
Motivated by the possible endogeneity bias of OLS regressions, we estimate a dynamic panel data model to consider the time-varying effects and address the potential endogeneity bias, using a system GMM estimator. We also include economic complexity and its lagged term to capture the short-and long-term effects. We find that an increase in economic complexity is associated with a higher level of income inequality, which is in contrast with the OLS estimates. This is consistent with the notion that when the economy experiences structural changes toward more sophisticated products, the degree of income inequality increases. In particular, the estimated coefficients of lagged economic complexity are significantly negative. The calculation of the long-term effects shows a positive correlation between an increase in complexity and the level of inequality. Hence, an increase in economic complexity is associated with higher income inequality. The Japanese Economic Review (2020) 71:695-718  The quality of government basic dataset Dahlberg et al. (2016) 2009 N/A