## Executive Summary — Peru’s Closing Ethnic Gaps Amidst Sustained Economic Growth (wpiea2022180-print-pdf)

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### Context and motivation
- Peru’s social stability has been frequently threatened by resentment over lingering economic ethnic gaps related to its European colonization, which started almost five hundred years ago.
- A surge of ethnic-based discontent could fuel populism and weaken political support for the macroeconomically prudent policies that have sustained Peru’s growth.
- Analysis is based on an annual series of National Household Surveys (Peru’s ENAHOs).

### Scope and groups analyzed
- Focus on three largest ethnic groups: White, Mestizo, and Native American.
- Afro-Peruvians and Asian-Peruvians together account for about 3 percent of the population.

### Main findings: evolution of ethnic gaps (2004-06 baseline to 2016-18 recent distributions)
- Overall trend:
  - Substantial narrowing of ethnic economic inequalities over the past two decades.
  - Mestizo surpassed White in income/expenditure per capita by 2016-18.
  - Native American gap relative to White narrowed but more slowly than Mestizo.
  - The very top of the wealth distribution shows a modest but growing presence of non-White households.
- Drivers of Mestizo gains:
  - Rural-to-urban migration.
  - More years of schooling.
- Native American dynamics:
  - Slower rural-to-urban migration contributed to slower gap-narrowing.
  - If 2004–2018 pace is extrapolated, Native American would reach average income of White by the mid-2040s.

### Distributional and poverty statistics (preserve exact figures)
- 2004-06 baseline:
  - Almost 90 percent of Native American had an income per capita below 5,000 LCUs.
  - 75 percent of White had an income per capita below 5,000 LCUs.
  - Two-thirds of the Native American population was poor at the start of the 21st century.
  - One quarter of the Native American population was extremely poor at the start of the 21st century.
  - In 2004-06, almost 40 percent of the Native American population lived in the poorer rural areas; only 15 percent of the White group lived in those areas.
  - Native American had an average of only five years of schooling in 2004-06.
- Changes 2004-06 to 2016-18:
  - Poverty declined by about 15 percentage points for both Native American and Mestizo.
  - Poverty of White declined by 8 percentage points.
  - Extreme poverty of Native American declined by 7 percentage points (the highest decline among the three groups).
  - Cumulative distributions 2016-18: share of Native American below 5,000 LCU fell by about 25 percentage points between 2004-06 and 2016-18.
- Inequality:
  - Gini declined from 0.48 in 2006 to 0.42 in 2016.
  - The top expenditure quintile still accounts for about 50 percent of total expenditure despite a decline in its share.

### Sectoral and labor-structure drivers
- Occupational shifts 2005 to 2018:
  - Mestizo: agriculture share fell by about 15 percentage points; services increased by an equivalent amount.
  - Native American: shifted from agriculture to urban services but to a much lower degree than Mestizo.
  - White: lowered share in manufacturing and increased share in agriculture (linked to higher-paid agricultural export jobs).
- Sector incomes and incentives:
  - Urban services have much higher average income relative to agriculture, incentivizing migration.
  - Mestizo experienced faster income growth than other ethnicities within sectors.
- Informality:
  - Informality gaps largely unchanged between 2012-14 and 2016-18.
  - ILO statistics: non-agricultural informal employment fell from 90 to 60 percent since the start of the century.
  - Regression evidence indicates a negative effect of informality on income.

### Econometric methodology and key estimates
- Mincerian semi-logarithmic income regressions estimated for 2004-2018 (OLS and GMM).
  - Baseline Mincer form: ln(wi) = α + β1 Educi + β2 Expi + β3 Expi2 + B Xi + μi.
  - Experience proxy: agei − Educi − 6.
- Endogeneity approach:
  - GMM instrumented years of schooling with father’s and family years of schooling and used the household average schooling instrument suitable given high migration.
- Key coefficient findings:
  - OLS: an additional year of education associated with 5-6 percent additional income.
  - GMM estimates yield higher schooling coefficients than OLS.
- Decomposition approach:
  - Two-step growth contribution: estimate elasticities by ethnic group, then multiply changes in determinants (2004→2018) by elasticities.
  - Model-predicted change in Mestizo’s income relative to White ≈ 0.21, about 80 percent of the actual change.

### Ethnicity, discrimination, and informality coefficients
- Ethnicity dummy (White = 1, Native American = 0):
  - 2004-18: belonging to White associated with a 9 percent higher income (≈ one and a half years of schooling).
  - Time evolution: 2004-06 association ≈ 22 percent higher income; 2016-18 association ≈ 8 percent higher income.
  - Comparison: Ñopo (2012) estimated a 17 percent advantage for White.
- Informality (available in surveys since 2012; regressions for 2014-18):
  - Being informal associated with about 30 percent lower income.

### Policy recommendations — four broad areas
- Overarching recommendation: preserve Peru’s growth policy pillars and focus on Pareto-efficient reforms to reduce ethnic and overall economic inequality.
- (i) Expand public services:
  - Education expansion prioritized: OLS implies if Native American increased years of schooling to Mestizo levels it could narrow its income gap relative to White from 0.62 to 0.8; GMM suggests practically eliminating this gap.
  - Priorities: health services, water access, poverty-alleviation programs targeting the extremely poor, rural transport and telecommunications to improve market access and enable migration.
  - Subnational capacity issues: subnational governments have weaker spending capacity than the central government.
  - Cash transfers: expanding cash transfers, including Cash-for-oil initiatives, subject to rigorous cost-benefit evaluation.
- (ii) Increase government revenue to finance public services:
  - IMF 2021 Article IV Staff Report indicates revenue measures can yield additional 1 percentage point of GDP in revenues.
  - Sales tax accounts for about half of central government revenues; direct taxes contribute relatively little.
  - Example: transferring an additional 1 percentage point of GDP to the 6.5 million poor individuals (2019 pre-pandemic) would provide them with a stipend of about US$30 per month.
  - US$30 per month would fund about a third of the minimum consumption basket.
  - In theory, cash transfers of 1 percentage point of GDP could fully eradicate extreme poverty.
  - Political constraints: revenue mobilization should be matched with visible expansion of public services or cash transfers.
- (iii) Reduce informality:
  - Doing Business ranking fell from 39th in 2010 to 76th in 2019; cumbersome procedures to start a business and pay taxes may have reversed informal employment declines after 2012.
  - Minimum wage context:
    - Firms required to pay 14 minimum monthly salaries per year.
    - Minimum wage: 930 LCU until recently; increased to 1,025 LCU in May 2022.
    - 2019 ratio of annual minimum wage to average income per capita in Peru: 0.58 (in the highest fifth among upper-middle income countries).
    - International average ratio in 2019: 0.4; aligning to this would require lowering the minimum wage to 641 LCU.
    - Annual minimum wage divided by average income of Native American (survey estimate): 0.99.
    - Minimum wage that would align this ratio to the international average: 366 LCU.
  - Policy options: increase productivity of informal firms, control excessive minimum wage growth, or consider segmented minimum wages (by firm size, region, sector) though politically challenging.
- (iv) Promote competition:
  - Rationale: increase mobility at the top and respond to public demand for less concentrated market structures.
  - Banking sector: top four banks account for 83 percent of bank assets; banks’ high profit ratios and lending–deposits spreads above 10 percent noted.
  - Approach: technical identification and regulation of oligopolistic markets, strengthen legal and institutional frameworks for competition, market conduct, and consumer protection.

### Political-economy considerations at the top of the distribution
- Survey limitations for top wealth echelons; cited listing: 3 out of 17 top Peruvian families belong to Mestizo and the rest to White.
- Emergence of several Mestizo and Native American family groups indicates increasing top-end ethnic diversity, seen as conducive to political stability.

### Concluding remarks and research agenda
- Main conclusion: openness to international trade and macroeconomic stability that sustained growth and poverty reduction have been consistent with narrowing postcolonial ethnic inequalities.
- Policy stance: pursue technically sound redistribution that preserves macroeconomic stability and market incentives; avoid ISI-style policies that historically contracted income per capita.
- Suggested further research:
  - Impact of 1990s structural reforms on ethnic inequality and ISI period evolution.
  - Role of fiscal policy and redistribution via taxation and social safety nets.
  - Role of public investment scaling in facilitating rural-to-urban migration and socioeconomic progress.
  - Trajectory of ethnic gaps as the economy approaches the Lewis turning point.

*Source: wpiea2022180-print-pdf — Annex VI presents histograms of labor income by gender.*

### Executive Summary ......................................................................................................

### Executive Summary

### Context and motivation
- Peru’s social stability has been frequently threatened by resentment over lingering economic ethnic gaps related to its European colonization, which started almost five hundred years ago.
- A surge of ethnic-based discontent could fuel populism and weaken political support for the macroeconomically prudent policies that have sustained Peru’s growth.
- This analysis is based on an annual series of National Household Surveys (Peru’s ENAHOs).

### Scope and groups analyzed
- The paper analyzes the recent evolution of economic gaps among the country’s three largest ethnic groups: White, Mestizo, and Native American.
- Other ethnic groups include Afro-Peruvians and Asian-Peruvians, both adding up to about 3 percent of the population.

### Main findings: evolution of ethnic gaps
- The past two decades have seen a substantial narrowing of ethnic economic inequalities.
- The Mestizo ethnic group has surpassed the White group in income/expenditure per capita.
- The Native American population also experienced a narrowing of its gap relative to White, albeit at a slower pace than Mestizo.
- The very top of the wealth distribution has a modest but growing presence of the non-White group.
- The Mestizo progress mainly resulted from:
  - rural-to-urban migration, and
  - more years of schooling.
- The slower narrowing for Native American partly reflects its slower rural-to-urban migration.

### Historical background and persistence of discontent
- The discontent narrative emphasizes that colonizers violently settled in the Andes, largely tore down its civilization, and seized its most important production factors, leaving substantial economic gaps between Peruvians of European and Native American origins.
- Colonizers and their descendants historically monopolized ownership of the country’s main natural resources, subjugated and enslaved large segments of the Native American labor force, thwarted their human capital formation, and heavily taxed their economic activities.
- The Inca empire is noted for a markedly communitarian and distributive framework that contrasts with later colonial outcomes.
- Large-scale 20th century migration of indigenous Peruvians to cities led many to thrive informally and face exclusion from formal urban institutions and public services.

### Data and robustness
- Analysis is based on National Household Survey data and focuses on monetary income from individuals’ principal and secondary economic activities.
- Annexes analyze alternative measures (total income including transfers and nonmonetary income; monetary expenditure; labor income excluding zeroes) and show main conclusions are robust across these indicators.
- Key temporal markers used in analysis: 2004-06 (baseline distributions) and 2016-18 (recent distributions).

### Policy recommendations: accelerating narrowing of ethnic gaps
- Based on statistical findings, the paper suggests public policy action in four areas:
  - expansion of public services,
  - government revenue mobilization,
  - reduction of informality,
  - enhanced market competition.
- These reforms could more rapidly allow the country to move on from its historic ethnic-related animosities and to fully take advantage of its ethnic diversity asset.

*Executive Summary from IMF Working Paper: Peru’s Closing Ethnic Gaps Amidst Sustained Economic Growth*

### Annex VI presents histograms of labor income by gender.

### wpiea2022180-print-pdf - Annex VI presents histograms of labor income by gender.

### Distribution of labor income and poverty by ethnicity (2004-06 baseline)
- Almost 90 percent of Native American had an income per capita below 5,000 LCUs in 2004-06.
- 75 percent of White had an income per capita below 5,000 LCUs in 2004-06.
- Two-thirds of the Native American population was poor at the start of the 21st century.
- One quarter of the Native American population was extremely poor at the start of the 21st century.
- The White group had a headcount poverty rate about half of that of Native American.
- The White group’s share of extreme poverty was about a quarter of the share of Native American.
- Mestizo poverty rate was closer to that of Native American; Mestizo extreme poverty was closer to that of White.
- In 2004-06, almost 40 percent of the Native American population lived in the poorer rural areas, while only 15 percent of the White group lived in those areas.
- Native American had an average of only five years of schooling in 2004-06.
- Illiteracy: Native American had substantially higher illiteracy than White and Mestizo; illiteracy of Mestizo and White was broadly the same.
- Informality was much higher among Native American; Mestizo had a slightly lower level of informality than White.

### Changes during the growth period (2004–2018)
- The Mestizo ethnic group experienced strong gains:
  - Its average labor income per capita surpassed that of White by 2016-18.
  - Its per capita total income, monetary expenditure, and labor income excluding zeroes also surpassed White (see annex charts referenced in source).
  - By 2016-18, the share of Mestizo with income above 20,000 LCU was slightly superior to the share of White.
- Native American experienced slower improvement:
  - Prosperity increased and the gap relative to White narrowed, but at a much slower pace than Mestizo.
  - Recent stagnation in average labor income per capita of Native American in 2016-18 was observed; however, their average total income and labor income excluding zeroes continued to grow in those years.
  - If the pace of gap-narrowing between 2004 and 2018 is extrapolated, Native American would reach the average income of White by the mid-2040s.
- Urban-rural dynamics:
  - The Native American income gap narrowed faster in urban areas than overall; in urban areas average income of Native American did not as significantly stagnate in 2016-18.
  - Mestizo experienced the largest rural-to-urban migration between 2004-06 and 2016-18; Native American migration was much less significant.
- Distributional evidence beyond means:
  - Median and 25th–75th percentile ranges of labor income by ethnicity show gap-narrowing across distributions.
  - Cumulative distributions 2016-18: Mestizo had a lower share below 5,000 LCU than White; Native American share below 5,000 LCU fell by about 25 percentage points between 2004-06 and 2016-18.

### Poverty and inequality trends (2004-06 to 2016-18)
- Poverty declines by ethnic group between baseline and 2016-18:
  - Poverty of both Native American and Mestizo declined by about 15 percentage points.
  - Poverty of White declined by 8 percentage points.
  - Extreme poverty of Native American declined by 7 percentage points (the highest decline among the three groups).
- Expenditure distribution:
  - Between 2003 and 2017, all expenditure quintiles except the top one increased their share of total expenditure.
  - The lowest two quintiles experienced the highest expenditure growth; the top quintile saw a decline in its share of total expenditure.
  - Despite the decline, the top quintile still accounts for about 50 percent of total expenditure.
- Gini coefficient:
  - Gini declined from 0.48 in 2006 to 0.42 in 2016.
  - Peru’s Gini in 2016 is more significantly below the median for Latin America and the Caribbean, but above the average for emerging market economies (EME), particularly East Asia comparators.

### Sectoral and labor-structure drivers
- Occupational shifts 2005 to 2018 (selected highlights from Table 1):
  - Mestizo: share in agriculture fell by about 15 percentage points; share in services increased by an equivalent amount.
  - Native American: shifted from agriculture to urban services but to a much lower degree than Mestizo.
  - White: lowered share in manufacturing and increased share in agriculture (possible link to higher-paid agricultural export jobs).
- Sector incomes:
  - Urban services have much higher average income relative to agriculture, providing incentives for migration to urban areas.
  - Mestizo experienced faster income growth than other ethnicities within sectors.
- Informality:
  - Informality gaps were largely unchanged between 2012-14 and 2016-18; ILO statistics indicate non-agricultural informal employment fell from 90 to 60 percent since the start of the century.
  - Regression analysis (described in source) provides evidence of a negative effect of informality on income.

### Econometric evidence on drivers of equalization
- Methodology:
  - Mincerian earnings regressions for 2004-2018 were estimated (OLS and GMM).
  - Two-step growth contribution analysis: estimate elasticities by ethnic group, then multiply changes in determinants between 2004 and 2018 by elasticities.
  - GMM instrumented years of schooling with father’s and family years of schooling to address endogeneity.
- Key regression findings:
  - Coefficients had theoretically expected signs and high statistical significance for practically all variables.
  - OLS point estimates suggest an additional year of education is associated with 5-6 percent additional income.
  - GMM estimates corroborate the significance of education with higher coefficients.
  - For parsimony, OLS results were used in the decomposition while noting OLS may underestimate the impact of education relative to GMM.
- Main drivers attributed to gap-narrowing:
  - Rural-to-urban migration (agglomeration and access to higher-paying urban services).
  - Increases in educational attainment, particularly for Mestizo (by 2016-18, Mestizo surpassed White in years of schooling).
  - Sectoral shifts from agriculture to services for Mestizo and, to a lesser degree, Native American.
  - Other factors implicit in regressions (see methodological annexes referenced in source).

### Political-economy considerations at the top of the distribution
- Household survey improvements are less informative about the very top wealth echelons.
- A listing cited in the source indicates 3 out of 17 top Peruvian families belong to Mestizo and the rest to White; however, emergence of several Mestizo and Native American family groups suggests increasing top-end ethnic diversity over time.
- Greater non-White presence at the very top is viewed as conducive to political stability given historical allegations of a White-dominated elite and potential ethnic tribalism affecting support for social policies.

*Source: wpiea2022180-print-pdf - Annex VI presents histograms of labor income by gender.*

### 18. Including this variable does not significantly affect coefficients and statistical of other variables as seen in the

### 18. Including this variable does not significantly affect coefficients and statistical of other variables as seen in the

### Mincerian regression findings and contributions to income change
- Work experience: negative and insignificant impact in some regressions; note this variable is computed as current age minus schooling years less six years and may weaken coefficient accuracy.
- Education: OLS coefficient of education is broadly in line with estimates presented in Montenegro and Patrinos (2014). Instrumental variables produce higher schooling coefficients than OLS, consistent with Card (1995).
- Time trend: regressions include year of observation as a time trend; its coefficient is positive and statistically significant, reflecting trend growth of the Peruvian economy during this period.
- Migration and schooling were the most significant contributors to Mestizo income progress between 2004-06 and 2016-18; Table 4 highlights increased years of schooling and migration-related variables (Agriculture, Lima, Rural) as the largest contributors to Mestizo gains.
- Native American: increase in years of schooling was an important determinant of income growth but to a lower extent than Mestizo; lower migration of Native American yields low estimated contribution of migration-related variables to income growth.
- Model predictions:
  - Model-predicted change in Mestizo’s income relative to White’s is about 0.21, which is about 80 percent of the actual change in their relative incomes during this period.

### Ethnicity dummy (discrimination) analysis
- Race dummy (White = 1, Native American = 0):
  - For 2004-18, estimated dummy coefficient implies that belonging to White as opposed to Native American has been associated with a 9 percent higher income.
  - This effect is equivalent to about one and a half years of additional education.
  - Ñopo (2012) estimated a larger effect: belonging to White associated with a 17 percent higher income.
  - Time evolution of dummy coefficient:
    - 2004-06: being White vs Native American associated with a 22 percent higher income.
    - 2016-18: being White vs Native American associated with an 8 percent higher income.
- Informality (available in household surveys since 2012; regressions for 2014-18):
  - Estimated coefficient implies being informal is associated with about 30 percent lower income.

### Recommended policy areas (four broad areas)
- Main recommendation: preserve Peru’s growth policy pillars and focus on Pareto-efficient reforms to reduce ethnic and overall economic inequality.
- Four policy areas suggested:
  - (i) Further expanding education and other public services.
  - (ii) Increasing government revenue to finance public services.
  - (iii) Reducing informality.
  - (iv) Promoting competition.

### Expanding public services — details and rationale
- Rationale: increased years of schooling had a large estimated impact in reducing ethnic gaps.
- Quantitative implications:
  - OLS estimates suggest if Native American increased years of schooling to Mestizo levels it could narrow its income gap relative to White from 0.62 to 0.8.
  - GMM estimates suggest such an increase would practically eliminate this gap.
- Priority service areas to expand:
  - Health services and water access: Covid-19 exposed vast inequalities and increased demand to eliminate gaps.
  - Poverty-alleviation programs: existing programs contributed to poverty and inequality reduction (Ramirez-Rondan and others, 2020) but must better reach the extremely poor.
  - Rural connectedness: transport and telecommunications infrastructure to improve market access and enable rural-to-urban migration.
- Subnational spending and cash transfers:
  - Subnational governments are largely responsible for key public services but have significantly weaker spending capacity than the central government.
  - A complementary route: expand cash transfers, including Cash-for-oil initiatives that directly transfer hydrocarbon and mineral revenues to the population (Devarajan and others, 2013; Moss and others, 2015), subject to rigorous cost-benefit evaluation.

### Revenue mobilization to finance public services
- IMF 2021 Article IV Staff Report: revenue measures suggested can yield additional 1 percentage point of GDP in revenues.
- Current tax structure: sales tax accounts for about half of central government revenues; direct taxes contribute relatively little, suggesting room to increase intake by addressing evasion and expanding the tax base.
- Example impact of additional revenue:
  - If an additional 1 percentage point of GDP in revenue were transferred to the 6.5 million poor individuals (2019 pre-pandemic), it would provide them with a stipend of about US$30 per month.
  - US$30 per month would fund about a third of the minimum consumption basket.
  - In theory, cash transfers of 1 percentage point of GDP could fully eradicate extreme poverty.
- Political constraints: recent corruption scandals create skepticism; revenue mobilization should be matched with measurable progress in expanding public services or cash transfers to make benefits visible (e.g., transferring some share of mining revenues to the population).

### Reducing informality — constraints and options
- Informality reduction could significantly help reduce the Native American income gap, since this group has higher informality rates associated with much lower income.
- Regulatory environment:
  - Peru’s Doing Business ranking fell from 39th in 2010 to 76th in 2019; particularly cumbersome procedures to start a business and pay taxes may have reversed the trend reduction in informal non-agricultural employment after 2012.
- Minimum wage and formalization:
  - Firms are required to pay 14 minimum monthly salaries per year.
  - Minimum wage: 930 LCU until recently; increased to 1,025 LCU in May 2022.
  - 2019 ratio of annual minimum wage to average income per capita in Peru: 0.58 (in the highest fifth among upper-middle income countries).
  - International average ratio in 2019: 0.4; aligning to this would have required lowering the minimum wage to 641 LCU.
  - Annual minimum wage divided by average income of Native American (estimated from household surveys): 0.99.
  - Minimum wage that would align this ratio to the international average: 366 LCU.
- Policy options:
  - Conceptually lowering the high ratio could be achieved by lowering the minimum wage and/or increasing productivity of informal firms.
  - Lowering the minimum wage is politically challenging; practical solution should focus on increasing productivity through continued economic growth while controlling excessive minimum wage growth.
  - Another alternative: segment the minimum wage by groups (by firm size, region, or economic sector), though technically and politically challenging.

### Promoting competition
- Rationale: increase mobility at the top of the wealth distribution where there is still a small presence of non-White; public demand for less concentrated market structures.
- Sectoral evidence and considerations:
  - Banking sector: IMF 2018 FSAP noted the top four banks in Peru account for 83 percent of bank assets and banks’ very high profit ratios can be related to high lending–deposits spreads (above 10 percent).
  - High concentration does not necessarily imply lack of contestability (Moron and others, 2010).
- Policy approach: technical identification and regulation of oligopolistic markets, enhance legal and institutional frameworks to oversee competition, market conduct, and consumer protection.

### Concluding remarks and research agenda
- Main conclusion: openness to international trade and macroeconomic stability that sustained strong growth and poverty reduction in Peru have been consistent with narrowing postcolonial ethnic inequalities.
- Policy guidance: further reduce ethnic gaps while preserving growth pillars, concentrating on Pareto-efficient reforms and avoiding ISI-style policies that historically contracted income per capita.
- Mincerian analysis summary:
  - Expanding education and rural-to-urban migration were the main factors narrowing ethnic gaps.
  - Ethnicity remains an important income determinant but much less so than at the start of the century.
- Suggested further research questions:
  - Impact of specific structural reforms in the 1990s on ethnic inequality and evolution during the ISI period.
  - Role of fiscal policy in reducing income inequality; how redistribution via taxation and social safety nets affected income inequality.
  - Role of public investment scaling in socioeconomic progress and facilitating rural-to-urban migration.
  - What happens to ethnic gaps as the economy approaches the Lewis turning point (no more excess rural labor) and implications for ethnic inequality projections.
- Policy stance: advocate technically sound redistribution that preserves macroeconomic stability and market incentives; refrain from more controversial measures (e.g., affirmative action, ethnic emphasis in all public policies) pending further analysis.

*IMF Working Papers — Peru’s Closing Ethnic Gaps Amidst Sustained Economic Growth*

### Annex I. Mincerian Regressions: Methodological

### Annex I. Mincerian Regressions: Methodological

### Semi-logarithmic income function (Mincer, 1974)
- Baseline specification:
  - ln(푤푖) = 훼 + 훽1 퐸푑푢푐푖 + 훽2 퐸푥푝푖 + 훽3 퐸푥푝푖2 + 퐵푋푖 + 휇푖
- Definitions:
  - ln(푤푖) is the natural logarithm of the income of individual i.
  - 퐸푑푢푐푖 is years of schooling.
  - 퐸푥푝푖 represents the approximate years in the labor market (as estimated by agei − 퐸푑푢푐푖 − 6).
  - X_i is a vector of control variables including gender, rurality, economic sector, marital status, among others.
  - Coefficients 훽i can be interpreted as the average rate of return on income of the related explanatory variable.

### Endogeneity of schooling and instruments
- Concern:
  - Years of schooling could be endogenous to income (see Card (1995) and Card (1999)).
- Instrument strategies cited:
  - Angrist and Krueger (1991a): calendar quarter-of-birth dummies.
  - Angrist and Krueger (1991b): quarter-of-birth and date-of-birth interaction in addition to quarter-of-birth effects.
  - Gong (2018): years of schooling of an individual’s parents as a more suitable instrument in countries with high migration.

### Instrument choice for Peru and estimation framework
- Rationale:
  - Given the high migration rate in Peru, the Gong (2018) proposed instrument is used in addition to the household’s average years of schooling.
- Estimation method:
  - GMM two-stage regression framework with small sample correction (Windmeijer, 2005).

### First-stage specification (predicting schooling)
- First-stage equation:
  - 퐸푑푢푐푖 = 휆1 퐹푎푡ℎ푒푟푖 + 휆2 퐹푎푚푖푙푦 + 퐵푍푖 + 푣
- Definitions:
  - 퐹푎푡ℎ푒푟푖 and 퐹푎푚푖푙푦푖 are years of schooling of the individual’s father and family, respectively.
  - Z_i is the vector of explanatory variables in X_i (from equation 1) in addition to exp and exp^2.

### Second-stage specification (predicted schooling in earnings function)
- Second-stage equation:
  - ln(푤푖) = 훼 + 훽1 퐸푑푢푐̅̅̅̅̅̅̅푖 + 훽2 퐸푥푝푖 + β3 퐸푥푝푖2 + 퐵푋푖 + 푢
- Note:
  - 퐸푑푢푐̅̅̅̅̅̅̅푖 is the predicted years of schooling from the first-stage regression.

*Closing Peru’s Ethnic Gaps Amidst Sustained Economic Growth. Working Paper No. WP/2022/180*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022180-print-pdf.pdf_