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---

### Introduction and motivation
- World population projected to grow by about 2.4 billion people in the next 40 years, almost all in developing countries.
- The large bulk of this increase will be between ages 15 and 64 (working age).
- For least developed countries, the share of working age population will continue to increase through 2050; for other less developed countries the share has been steadily increasing and will peak in the coming two decades.
- Mechanisms by which an increased working age ratio can raise economic growth:
  - People of working age are on average more productive than those outside this age group.
  - Workers save while dependants do not, so a bulge in the working age ratio contributes to higher savings rates, increasing domestic resources for productive investment.
  - Fertility decline may induce greater female labor supply and increase attention to primary education and health (Bailey (2006); Joshi and Schultz (2006)).

### Focus on India: scale and timing
- India accounts for about a quarter of the projected increase in the global population aged 15–64 years between 2010 and 2040.
- Working-age ratio in India set to rise from about 64 percent currently to 69 percent in 2040, reflecting addition of just over 300 million working-age adults.
- India will be the largest single positive contributor to the global workforce over the next three decades by an order of magnitude.
- China comparison: China’s population pyramid matured between 1960 and 2000; China’s working age population projected to decline while India’s will rise rapidly.

### Data, definitions, and sample construction
- Age distribution data source: successive rounds of the Census of India (COI) for years 1961, 1971, 1981, 1991 and 2001.
- Working age ratio definition: share of population aged 15–59 years (chosen for consistency across COI rounds).
- Per capita income constructed from net state domestic product (NSDP) and COI state population estimates.
- Panel: largely balanced panel of 22 states with data at ten year intervals from 1961 to 2001. States included: Andhra Pradesh, Arunachal Pradesh, Assam, Bihar, Gujarat, Haryana, Himachal Pradesh, Jammu and Kashmir, Kerala, Karnataka, Maharashtra, Manipur, Madhya Pradesh, Meghalaya, Nagaland, Orissa, Punjab, Rajasthan, Tamil Nadu, Tripura, Uttar Pradesh and West Bengal.
- Adjustments for state boundary changes:
  - 2001 data consolidated Bihar with Jharkhand and Madhya Pradesh with Chattisgarh so time series remain consistent with old geographical divisions (Jharkhand and Chattisgarh created in 2000).
  - For the 1966 creation of Haryana (from Punjab) and Chandigarh, COI 1971 ratios of combined Punjab, Haryana and Chandigarh were applied to 1961 population data by age group to construct consistent time series for Punjab and Haryana.

### Summary statistics (exact values preserved)
- Treating each state-time period combination as a separate observation:
  - Per capita income growth (percent): Mean 2.13; S.D. 1.67; Minimum -1.83; Maximum 6.26.
  - Working age ratio (percent): Mean 54.93; S.D. 3.37; Minimum 47.98; Maximum 64.4.
  - Working age ratio growth (percent): Mean 0.22; S.D. 0.38; Minimum -0.68; Maximum 0.85.
- Summary statistics across states (averaged over time):
  - Per capita income growth (percent): Mean 2.18; S.D. 0.79; Minimum 0.87; Maximum 3.8.
  - Working age ratio (percent): Mean 54.9; S.D. 1.89; Minimum 52.25; Maximum 59.7.
  - Working age ratio growth (percent): Mean 0.21; S.D. 0.19; Minimum -0.09; Maximum 0.55.

### Empirical approach and identification
- Panel conditional convergence framework where both the level and the growth rate of the working age ratio serve as explanatory variables for economic growth.
- Exploit heterogeneity across Indian states in levels and growth rates of working age ratios to estimate impact on economic growth.
- Robustness checks:
  - Corrections for possible response of inter-state migration to differential economic growth.
  - Two-stage procedure using lagged fertility decisions to instrument growth in working age population.

### Principal empirical conclusions (preserved wording)
- First, the demographic dividend is substantial. This result is robust to corrections for the possible response of inter-state migration to differential economic growth, and to a two-stage procedure in which lagged fertility decisions are used to instrument the growth in working age population. Our econometric estimates imply that from the 1970s onwards, between 40 to 50 percent of the per capita income growth was attributable to the ongoing demographic dividend. While policy reforms had an important role to play in the growth acceleration starting in the 1980s, the results caution that this was less so than commonly perceived once the concurrent rise in working-age ratios is taken into account.
- Second, unlike Bloom and Canning (2004), we do not find the demographic dividend to be conditional on specific policies or social environments. We read the evidence to say that the very features that lead to a demographic transition—mortality decreases followed by fertility decline—also reflect broader health and educational achievements that are conducive to the exploitation of the demographic dividend.
- Third, going forward, it is the poorest Indian states that stand to gain the most from the forthcoming demographic transition, since they are the ones that have so far lagged behind in both the transition and in income growth.

### Key empirical findings and estimates
- Working age ratio is as significant a correlate of per capita income growth as the literacy rate.
- Table 3 (pooled OLS, single regressor, no controls) selected coefficients:
  - Log Initial P.C. Income: Coefficient 0.01, Standard Error 0.006, Observations 81
  - Log Literacy Rate: Coefficient 0.015***, Standard Error 0.005, Observations 78
  - Log Working Age Ratio: Coefficient 0.155***, Standard Error 0.032, Observations 78
  - Log Population Growth: Coefficient -0.184, Standard Error 0.20, Observations 76
- Within-estimator (Table 4, Column 1) estimated demographic dividend:
  - Log initial working age ratio: Coefficient 0.188**, Standard Error 0.077
  - Growth rate of working age ratio: Coefficient 2.478**, Standard Error 1.026
  - Log initial income per capita: Coefficient -0.088***, Standard Error 0.0175
  - Adjusted R-squared 0.73, Observations 76, Groups 22
- Magnitude interpretations preserved:
  - A 0.01 increase in the log of the initial working age ratio (1 percent increase) → 0.2 percentage points increase in annual average per capita income growth.
  - Standard deviation of ti w, ln across states is 0.03 → one standard deviation increase → ~0.6 percentage points higher per capita income growth.
  - One standard deviation increase in the growth rate of the working age ratio is 0.19 → increases per capita income growth by about 0.5 percentage points.

### Migration adjustment and endogeneity checks
- Migration-adjusted growth rate constructed by assuming all migrants are of working age and subtracting net inward migrants from end-of-decade totals.
- Table 4, Column 2 (within estimator, migration-adjusted):
  - Log initial income per capita: Coefficient -1.01***, Standard Error 0.013
  - Log initial working age ratio: Coefficient 0.234***, Standard Error 0.081
  - Adjusted growth rate of working age ratio: Coefficient 1.57***, Standard Error 0.50
  - R-squared 0.69, Observations 72, Groups 22
- Conclusion: Migration does not appear to drive the demographic-growth correlation.

### Instrumental variables and exogeneity checks
- IV strategy: lagged birth rate as instrument (e.g., birth rate in 1961 instrumenting working age ratio growth 1971–81); additional instrument: lagged working age ratio.
- Table 5 summary:
  - Column 1 (within baseline): Log initial income per capita -0.088***; Log initial working age ratio 0.188**; Growth rate of working age ratio 2.478**.
  - Column 2 (IV: lagged birth rate): Log initial income per capita -0.076***; Log initial working age ratio 0.36***; Growth rate of working age ratio 4.13*.
  - Column 3 (IV: lagged birth rate + lagged working age ratio): Log initial income per capita -0.080***; Log initial working age ratio 0.38***; Growth rate of working age ratio 4.98**.
  - Standard errors (Column 1): 0.0175, 0.077, 1.026; (Column 2): 0.025, 0.12, 2.34; (Column 3): 0.025, 0.093, 1.98.
  - First stage F-statistics: Column 2 = 10.7, Column 3 = 8.3.
  - Overidentifying Sargan-Hansen statistic 0.23, p-value 0.63.
  - Difference-in-Sargan statistics: 0.032 (p-value 0.86) and 0.067 (p-value 0.79).
- Interpretation: IV estimates imply an even stronger impact of demographic variables though sample size smaller for IV (observations 48 and 47, Groups 18 and 18). Exogeneity tests fail to reject instrument validity; subsequent analysis uses the within estimator.

### Robustness: core controls and policy variables
- Core controls (Table 6): literacy rate, hospital beds per 1000 residents, sex ratio (females/males).
- Selected Table 6 coefficients (within estimator, robust SEs):
  - Column 4 (all three controls): Log initial income per capita -0.103*** (0.013); Log initial working age ratio 0.169*** (0.059); Growth rate of working age ratio 2.214** (0.928); Literacy rate 0.03 (0.02); Hospital beds 0.006 (0.007); Sex ratio 0.123*** (0.042); R-squared 0.76; Observations 76; Groups 22.
- Robustness findings:
  - Sex ratio is highly significant and positively associated with growth.
  - Literacy rate and hospital beds bear expected signs but are not statistically significant.
  - Demographic variables remain robust to inclusion of these controls.
- Additional policy/structural variables considered (sample limitations noted):
  - Social and economic expenditure per capita (development expenditure).
  - Scheduled commercial bank credit per capita.
  - Land concentration (land Gini).
  - Cumulative land reform index.
  - Cumulative labor reforms index.
- Summary:
  - Some evidence that development expenditure—particularly economic expenditure—can spur growth.
  - Land reforms appear negatively related to per capita growth in reported analyses.
  - Demographic variables remain robust where sample size permits.

### Additional regression results and interaction tests
- Point estimate on initial working age ratio significant in every specification and quantitatively stable.
- Growth rate of working age ratio significant in six out of seven specifications and falls in a narrow numerical range.
- Selected coefficient ranges across Tables 7–8 preserved in text (examples):
  - Log initial income per capita: values include -0.104***, -0.121***, -0.13***, -0.084***, -0.113***, -0.121***, -0.104*** with associated standard errors as reported.
  - Log initial working age ratio: values include 0.246**, 0.196**, 0.243***, 0.188*, 0.241***, 0.304***, 0.24*** with associated standard errors as reported.
  - Growth rate of working age ratio: values include 2.281, 2.549***, 2.925***, 3.14**, 2.945**, 2.928***, 2.272* with associated standard errors as reported.
- Interaction tests:
  - No significant interaction terms found between age-structure variables and social controls (education, health, gender bias).
  - Possible explanations: adequate preconditions may already exist; inadequate measurement of state-level policy variation; national-level reforms applied uniformly reducing state-level interaction effects.
  - Paper flags economic openness × demographic dividend interactions in cross-country work as a potential research area.

### Definition and formula for the demographic dividend used in simulations
- Per capita income growth inclusive of age-structure changes:
  - ln y_{i,t+1} - ln y_{i,t} = ρ + β1 ln w_{i,t} + β2 g_{w,i,t} + γ'X_{i,t} + η_t + ε_{i,t}.
- Counterfactual: working age ratio remains fixed at base-year level (w_{i,t} = w_{i,0}, g_{w,i,t} = 0).
- Demographic dividend DD_t (average annual increment in per capita income growth over the decade starting in year t attributable to age-structure changes):
  - DD_t = β1[ln w_{t+1} - ln w_{1}] + β2[ln w_{t+1} - ln w_{t}].
- Baseline point estimates used for simulations: β1 = 0.478 and β2 = 0.188 (from column 1, Table 5).

### Historical simulations — "The Dividend thus Far"
- Age distribution (percent of total population) by decade:
  - 1961: 0-14 = 41.0, 15-59 = 53.3, 60+ = 5.6.
  - 1971: 0-14 = 42.0, 15-59 = 52.0, 60+ = 6.0.
  - 1981: 0-14 = 39.6, 15-59 = 53.9, 60+ = 6.5.
  - 1991: 0-14 = 37.3, 15-59 = 56.7, 60+ = 6.0.
  - 2001: 0-14 = 35.4, 15-59 = 57.1, 60+ = 7.5.
- Decadal demographic dividend (increment to annual per capita income growth relative to 1961 working age ratio):
  - 1960s: -0.6 (percent)
  - 1970s: 0.4
  - 1980s: 1.4
  - 1990s: 1.3
- Per capita income growth (constant 1993–94 prices) and net of dividend:
  - Per capita growth by decade: 1960s = 2.1, 1970s = 0.9, 1980s = 3.1, 1990s = 3.4.
  - Net of demographic dividend: 1960s = 1.8, 1970s = 0.4, 1980s = 1.7, 1990s = 2.1.
- Interpretation: Demographic dividend small/negative in 1960s, small/positive in 1970s, and substantial in 1980s and 1990s; a considerable fraction of growth acceleration since the 1980s may be attributed to age-structure changes.

### State-level distribution of the dividend (selected states)
- Classification: Andhra Pradesh, Karnataka, Kerala, Madhya Pradesh, Rajasthan, and Tamil Nadu as pro-employer states; Gujarat, Maharashtra, Orissa, and West Bengal as pro-worker states; six other large states did not implement Industrial Disputes Act amendments over the period.
- Leaders (South and West) demographic dividend by decade (percent):
  - Tamil Nadu: 1960s = -0.1, 1970s = 0.8, 1980s = 2.2, 1990s = 2.7.
  - Karnataka: -0.3, 0.9, 2.4, 3.2.
  - Gujarat: -0.2, 1.5, 2.6, 3.0.
  - Simple average (leaders): -0.2, 1.0, 2.4, 3.0.
- Laggards (Heartland) demographic dividend by decade (percent):
  - Bihar: -0.3, -0.2, 0.8, 0.0.
  - Madhya Pradesh: -1.7, -0.4, 0.7, 0.3.
  - Uttar Pradesh: -0.9, -0.6, 0.4, -0.4.
  - Simple average (laggards): -0.9, -0.4, 0.6, 0.0.
- Per capita income growth rates (leaders, percent):
  - Tamil Nadu: 0.4, 0.1, 4.1, 5.1.
  - Karnataka: 2.0, 0.7, 3.0, 6.0.
  - Gujarat: 1.9, 0.9, 3.1, 3.6.
  - Simple average (leaders): 1.4, 0.5, 3.4, 4.9.
- Per capita income growth rates (laggards, percent):
  - Bihar: 0.3, 0.6, 2.7, -0.1.
  - Madhya Pradesh: -0.5, 0.6, 2.2, 1.1.
  - Uttar Pradesh: 0.7, 0.7, 2.6, 0.8.
  - Simple average (laggards): 0.2, 0.6, 2.5, 0.6.
- Net of demographic dividend:
  - Leaders simple average: 1.7, -0.5, 1.0, 1.9.
  - Laggards simple average: 1.1, 1.0, 1.9, 0.6.
- Interpretation:
  - Tamil Nadu, Karnataka, and Gujarat reaped large dividends: increment to per capita income growth of 2.4 percent per annum in the 1980s, rising to 3 percent in the 1990s.
  - Lagging Hindi Heartland states averaged 0.6 percent in the 1980s and zero in the 1990s.
  - Bulk of projected increases in working age ratio likely to come from laggard states (average 2001 working age ratio among leaders = 62.1 percent; laggards = 53.4 percent), implying potential for income convergence.

### Recent developments and anecdotal evidence
- Bihar experienced per capita income growth averaging 6.2 percent per annum from 2001 through 2009, up from about zero in the previous decade, and above the sample median growth rate for this period.
- Among four big Hindi Heartland states in that period: Rajasthan averaged 6.1% per annum; Uttar Pradesh 3.2%; Madhya Pradesh 2.7%; median growth rate was 5.7%.
- Notes governance and development reforms in Bihar as contributors to the turnaround and demographic contributions via increase in working age ratio from 52.5 percent in 2001.

### Future projections and simulations
- Projection sources: Census of India (projections through 2026), United Nations Population Division (UNPD, projections through 2050 medium-fertility variant), and IDB, US Census Bureau (projections through 2050).
- Demographic projection snapshots (percent of total population):
  - Census of India — 2001: 0-14 = 35.5, 15-59 = 57.8, 60+ = 6.9; 2011: 29.2, 62.7, 8.2; 2021: 25.1, 64.0, 10.7; 2026: 23.4, 64.0, 12.5.
  - United Nations Population Division — 2001: 35.5, 57.8, 6.9; 2010: 30.8, 61.6, 7.5; 2020: 26.7, 63.5, 9.8; 2030: 22.8, 64.8, 12.4; 2040: 19.7, 64.6, 15.6; 2050: 18.2, 62.2, 19.6.
  - IDB, US Census Bureau — 2001: 35.5, 57.8, 6.9; 2010: 30.1, 61.7, 8.2; 2020: 26.3, 63.5, 10.2; 2030: 23.5, 63.3, 13.2; 2040: 21.4, 61.9, 16.7; 2050: 19.8, 60.1, 20.1.
- Demographic dividend projections by decade (increment to annual per capita income growth relative to working age ratio fixed at 2001 level), in percent:
  - Census of India 2001 projections: 2000s = 2.0, 2010s = 2.2, 2020s = 2.04, 2030s = 2.16.
  - United Nations Population Division: 2000s = 1.6, 2010s = 1.95, 2020s = 2.27, 2030s = 2.10, 2040s = 1.17.
  - US Census Bureau (IDB): 2000s = 1.62, 2010s = 1.93, 2020s = 1.69, 2030s = 1.15, 2040s = 0.57.
  - Simple averages across projection sources: 2000s = 1.74, 2010s = 1.98, 2020s = 2.04, 2030s = 1.62, 2040s = 0.87.
- Interpretation:
  - All projections show rapid growth in the working age ratio from 2001 through 2021.
  - Demographic dividend projected to peak over the next two decades—adding about 2 percentage points to annual per capita income growth over the period.
  - Subsequently the dividend should begin to decrease gradually (UNPD) or decrease rapidly (IDB), though remaining positive for some decades.
  - Calculations suggest that over the current decade the increment to per capita income growth from demographic change has been between 1.5 to 2 percent points per annum.

### Conclusions and policy implications
- Both the level and the growth rate of the working age ratio have exerted a large impact on India’s economic growth; results robust to migration corrections, endogeneity checks, and a range of controls.
- Considerable gains already from age-structure changes; a substantial part of India’s growth acceleration since the 1980s can be attributed to demographic change.
- Looking ahead, continuing demographic transition will yield a growth dividend of about 2 percent per annum over the next two decades (projected peak).
- Bulk of remaining demographic transition concentrated in lagging states, raising the prospect of substantial income convergence among rich and poor states.
- Little empirical evidence for complementarities between demographic variables and various facets of social development or the policy environment at the state level; national-level reforms may have been the most complementary policies to demographic change.
- Research agenda: investigate policy complementarities (especially national-level policies or interactions with state industrial composition and trade exposure) to better understand growth trajectories.

*Source: _wp1138 (IMF working paper content unit).*

### References .............................................................................................................

### _wp1138 - References .............................................................................................................

### Introduction and motivation
- In the next 40 years, the world’s population will grow by about 2.4 billion people, almost all of them in developing countries.
- The large bulk of this increase will be between the ages of 15 and 64, the so-called “working age” population.
- For the least developed countries, the share of working age population will continue to increase through 2050; for other less developed countries, the share has been steadily increasing and will peak in the coming two decades.
- Mechanisms by which an increased working age ratio can raise economic growth include:
  - People of working age are on average more productive than those outside this age group.
  - Workers save while dependants do not, so a bulge in the working age ratio contributes to higher savings rates, increasing domestic resources for productive investment.
  - Fertility decline may induce greater female labor supply and increase attention to primary education and health (Bailey (2006); Joshi and Schultz (2006)).

### Focus on India: scale and timing
- India accounts for about a quarter of the projected increase in the global population aged 15–64 years between 2010 and 2040.
- The working-age ratio in India is set to rise from about 64 percent currently to 69 percent in 2040, reflecting the addition of just over 300 million working-age adults.
- India will be the largest single positive contributor to the global workforce over the next three decades by an order of magnitude.
- Comparison with China: China’s population pyramid matured between 1960 and 2000; over coming decades China’s working age population is projected to decline while India’s will rise rapidly.

### Data, definitions, and sample construction
- Age distribution data source: successive rounds of the Census of India (COI) for years 1961, 1971, 1981, 1991 and 2001.
- Working age ratio definition used: share of population aged 15–59 years (chosen for consistency across COI rounds).
- Per capita income constructed from net state domestic product (NSDP) and COI state population estimates.
- Panel: largely balanced panel of 22 states with data at ten year intervals from 1961 to 2001. States included: Andhra Pradesh, Arunachal Pradesh, Assam, Bihar, Gujarat, Haryana, Himachal Pradesh, Jammu and Kashmir, Kerala, Karnataka, Maharashtra, Manipur, Madhya Pradesh, Meghalaya, Nagaland, Orissa, Punjab, Rajasthan, Tamil Nadu, Tripura, Uttar Pradesh and West Bengal.
- Adjustments for state boundary changes:
  - 2001 data consolidated Bihar with Jharkhand and Madhya Pradesh with Chattisgarh so time series remain consistent with old geographical divisions (Jharkhand and Chattisgarh created in 2000).
  - For the 1966 creation of Haryana (from Punjab) and Chandigarh, COI 1971 ratios of combined Punjab, Haryana and Chandigarh were applied to 1961 population data by age group to construct consistent time series for Punjab and Haryana.

### Summary statistics (exact values preserved)
- Treating each state-time period combination as a separate observation:
  - Per capita income growth (percent): Mean 2.13; S.D. 1.67; Minimum -1.83; Maximum 6.26.
  - Working age ratio (percent): Mean 54.93; S.D. 3.37; Minimum 47.98; Maximum 64.4.
  - Working age ratio growth (percent): Mean 0.22; S.D. 0.38; Minimum -0.68; Maximum 0.85.
- Summary statistics across states (averaged over time):
  - Per capita income growth (percent): Mean 2.18; S.D. 0.79; Minimum 0.87; Maximum 3.8.
  - Working age ratio (percent): Mean 54.9; S.D. 1.89; Minimum 52.25; Maximum 59.7.
  - Working age ratio growth (percent): Mean 0.21; S.D. 0.19; Minimum -0.09; Maximum 0.55.

### Empirical approach and identification
- Use of a standard conditional convergence framework to derive a panel specification where both the level and the growth rate of the working age ratio serve as explanatory variables for economic growth.
- Exploitation of heterogeneity across Indian states in levels and growth rates of working age ratios to estimate the impact on economic growth.
- Robustness checks mentioned:
  - Corrections for possible response of inter-state migration to differential economic growth.
  - A two-stage procedure using lagged fertility decisions to instrument growth in working age population.

### Principal empirical conclusions (preserved wording)
- First, the demographic dividend is substantial. This result is robust to corrections for the possible response of inter-state migration to differential economic growth, and to a two-stage procedure in which lagged fertility decisions are used to instrument the growth in working age population. Our econometric estimates imply that from the 1970s onwards, between 40 to 50 percent of the per capita income growth was attributable to the ongoing demographic dividend. While policy reforms had an important role to play in the growth acceleration starting in the 1980s, the results caution that this was less so than commonly perceived once the concurrent rise in working-age ratios is taken into account.
- Second, unlike Bloom and Canning (2004), we do not find the demographic dividend to be conditional on specific policies or social environments. We read the evidence to say that the very features that lead to a demographic transition—mortality decreases followed by fertility decline—also reflect broader health and educational achievements that are conducive to the exploitation of the demographic dividend.
- Third, going forward, it is the poorest Indian states that stand to gain the most from the forthcoming demographic transition, since they are the ones that have so far lagged behind in both the transition and in income growth.

### Organization of the paper (section map)
- Section 2: Reports state-specific trends in the age structure of the population and correlations with income growth.
- Section 3: Describes an econometric framework.
- Sections 4 and 5: Use the framework to estimate the demographic dividend, with robustness considerations.
- Section 6: Uses regression coefficients to quantify the contribution of the demographic dividend in the past four decades and in the decades beyond.
- Final section: Concluding remarks.

*Source: _wp1138 - References .............................................................................................................*

### 2.6 standard deviations (across state-time observations). Figure 3 illustrates these trends

### _wp1138 - 2.6 standard deviations (across state-time observations). Figure 3 illustrates these trends

### Key empirical findings
- The working age ratio is as significant a correlate of per capita income growth as the literacy rate.
- From Table 3 (pooled OLS, single regressor, no controls):
  - Log Initial P.C. Income: Coefficient 0.01, Standard Error 0.006, Observations 81
  - Log Literacy Rate: Coefficient 0.015***, Standard Error 0.005, Observations 78
  - Log Working Age Ratio: Coefficient 0.155***, Standard Error 0.032, Observations 78
  - Log Population Growth: Coefficient -0.184, Standard Error 0.20, Observations 76
- Estimated demographic dividend (within-estimator, Table 4, Column 1):
  - Log initial working age ratio: Coefficient 0.188**, Standard Error 0.077
  - Growth rate of working age ratio: Coefficient 2.478**, Standard Error 1.026
  - Log initial income per capita: Coefficient -0.088***, Standard Error 0.0175
  - Adjusted R-squared 0.73, Observations 76, Groups 22
- Magnitudes interpreted in text:
  - A 0.01 increase in the log of the initial working age ratio (1 percent increase) → 0.2 percentage points increase in annual average per capita income growth.
  - Standard deviation of ti w, ln across states is 0.03 → one standard deviation increase → ~0.6 percentage points higher per capita income growth.
  - One standard deviation increase in the growth rate of the working age ratio is 0.19 → increases per capita income growth by about 0.5 percentage points.

### Estimation framework
- Baseline theory: Conditional convergence equation (Barro and Sala-i-Martin (1995), following Bloom and Canning (2004)):
  - gz = λ(z* - z) where z is log income per worker, gz is growth in income per worker, z* steady state, λ speed of adjustment.
  - Steady state depends on determinants X with parameters β: gz = λ(βX - z)
- Demographic identity and logs:
  - Income per capita equals labor productivity times participation rate times working age ratio.
  - Log notation: z = y - p - w  (equation (2) in text)
  - Growth decomposition: gy = gw + gz  (equation (3))
- Empirical specification (equation (5)):
  - Dependent variable: annual average growth rate of per capita income in state i over the decade beginning in year t (ti y g , _ )
  - Main regressors: log of initial per capita income, log of initial working age ratio, average annual growth rate of the working age ratio over the decade.
  - Controls: ti X , time-invariant fixed effects i f , decade dummies t η .
  - Estimation: within estimator with heteroskedasticity-robust standard errors.

### Migration adjustment and endogeneity concerns
- Migration could contemporaneously affect the growth rate of the working age ratio; evidence suggests limited inter-state responsiveness to income differentials.
- Migration-adjusted growth rate construction (Table 4, Column 2):
  - Assume all migrants are of working age; subtract net inward migrants from end-of-decade total population and working age population to compute adjusted growth rate.
- Table 4, Column 2 results (within estimator, robust SEs, migration-adjusted growth rate):
  - Log initial income per capita: Coefficient -1.01***, Standard Error 0.013
  - Log initial working age ratio: Coefficient 0.234***, Standard Error 0.081
  - Adjusted growth rate of working age ratio: Coefficient 1.57***, Standard Error 0.50
  - R-squared 0.69, Observations 72, Groups 22
- Conclusion: Migration does not appear to drive the demographic-growth correlation; demographic variables remain significant after adjustment.

### Instrumental variables and exogeneity checks
- IV strategy (Table 5):
  - Instrument: lagged birth rate (e.g., birth rate in 1961 instrumenting working age ratio growth 1971–81).
  - Additional instrument in Column 3: lagged working age ratio.
- Table 5 estimates:
  - Column 1 (within baseline): Log initial income per capita -0.088***, Log initial working age ratio 0.188**, Growth rate of working age ratio 2.478**.
  - Column 2 (IV: lagged birth rate): Log initial income per capita -0.076***, Log initial working age ratio 0.36***, Growth rate of working age ratio 4.13*.
  - Column 3 (IV: lagged birth rate + lagged working age ratio): Log initial income per capita -0.080***, Log initial working age ratio 0.38***, Growth rate of working age ratio 4.98**.
  - Standard errors: Column 1 (0.0175, 0.077, 1.026), Column 2 (0.025, 0.12, 2.34), Column 3 (0.025, 0.093, 1.98).
  - First stage F-statistics: Column 2 = 10.7, Column 3 = 8.3.
  - Overidentifying Sargan-Hansen statistic 0.23, p-value 0.63 (cannot reject instruments uncorrelated with errors).
  - Difference-in-Sargan statistics: 0.032 (p-value 0.86) and 0.067 (p-value 0.79) — fail to reject exogeneity of the instrumented regressor.
- Interpretation: IV estimates imply an even stronger impact of demographic variables on income growth, though sample size is smaller for IV (observations 48 and 47, Groups 18 and 18) and error bands encompass baseline point estimates. Given exogeneity test results and larger OLS sample, subsequent analysis uses the within estimator.

### Robustness: core controls and policy variables
- Core control variables introduced (Table 6): literacy rate, hospital beds per 1000 residents, sex ratio (females/males).
- Table 6 (within estimator, robust SEs) selected coefficients:
  - Column 1 (adding Literacy rate): Log initial income per capita -0.096*** (0.0133); Log initial working age ratio 0.226*** (0.056); Growth rate of working age ratio 2.375** (0.917); Literacy rate 0.03 (0.019); R-squared 0.74; Observations 76; Groups 22.
  - Column 2 (adding Hospital beds per 1000): Log initial income per capita -0.09*** (0.017); Log initial working age ratio 0.177** (0.084); Growth rate of working age ratio 2.52** (1.019); Hospital beds 0.003 (0.005); R-squared 0.73.
  - Column 3 (adding Sex ratio): Log initial income per capita -0.092*** (0.016); Log initial working age ratio 0.147* (0.076); Growth rate of working age ratio 2.22** (1.040); Sex ratio 0.133** (0.053); R-squared 0.75.
  - Column 4 (all three controls): Log initial income per capita -0.103*** (0.013); Log initial working age ratio 0.169*** (0.059); Growth rate of working age ratio 2.214** (0.928); Literacy rate 0.03 (0.02); Hospital beds 0.006 (0.007); Sex ratio 0.123*** (0.042); R-squared 0.76; Observations 76; Groups 22.
- Robustness conclusion:
  - Sex ratio is highly significant and positively associated with growth.
  - Literacy rate and hospital beds bear the expected signs but are not statistically significant.
  - Demographic variables (initial working age ratio and its growth) remain robust to inclusion of these controls.

### Policy-relevant additional variables (sample limitations noted)
- Additional policy and structural variables considered (but not fully tabulated here due to sample-size attenuation):
  - Social and economic expenditure per capita (development expenditure).
  - Scheduled commercial bank credit per capita (proxy for investment/financial deepening).
  - Land concentration (inequality in agricultural land holdings).
  - Cumulative land reform index (tenancy reforms, abolishing intermediaries, land ceilings, consolidation).
  - Cumulative labor reforms index (degree to which cumulative legislation has been pro-worker).
- Summary from text:
  - Some evidence that development expenditure—particularly economic expenditure—can spur growth.
  - Land reforms appear negatively related to per capita growth in the reported analyses.
  - Crucially, demographic variables remain robust to introduction of these policy variables where sample size permits.

*Italic: Source — content unit: _wp1138 - 2.6 standard deviations (across state-time observations). Figure 3 illustrates these trends (PDF chapter/section).*

### introduction of these diverse control variables. The point estimate of the coefficient on the

### _wp1138 - introduction of these diverse control variables. The point estimate of the coefficient on the

### Key regression findings on age-structure and growth
- The point estimate of the coefficient on the initial working age ratio is significant in every specification and quantitatively fairly stable.
- The growth rate of the working age ratio is significant in six out of seven specifications, and falls within a narrow numerical range.
- Selected coefficient estimates from Tables 7–8 (dependent variable: Annual per capita income growth):
  - Log initial income per capita: -0.104***, -0.121***, -0.13***, -0.084*** (with standard errors 0.018, 0.0131, 0.018, 0.025 respectively in the first block) and -0.113***, -0.121***, -0.104*** (with standard errors 0.0196, 0.009, 0.016 respectively in the second block).
  - Log initial working age ratio: 0.246**, 0.196**, 0.243***, 0.188* (standard errors 0.114, 0.075, 0.070, 0.105) and 0.241***, 0.304***, 0.24*** (standard errors 0.072, 0.068, 0.0809).
  - Growth rate of working age ratio: 2.281, 2.549***, 2.925***, 3.14** (standard errors 1.51, 0.841, 0.878, 1.426) and 2.945**, 2.928***, 2.272* (standard errors 1.124, 0.881, 1.187).
- Core control coefficient examples (Table 7, part 1):
  - Log literacy rate: -0.007, -0.029, -0.017, 0.047 (standard errors 0.032, 0.033, 0.033, 0.034).
  - Log hospital beds per 1000 residents: -0.002, -0.002, -0.002, 0.009 (standard errors 0.011, 0.009, 0.011, 0.007).
  - Log sex ratio (females / males): 0.094, 0.073*, 0.057, 0.451*** (standard errors 0.086, 0.039, 0.044, 0.146).
- Policy control coefficient examples:
  - Log social expenditure per capita: 0.001 (standard error 0.019).
  - Log economic expenditure per capita: 0.029** (standard error 0.014).
  - Log development expenditure per capita: 0.035* (standard error 0.017).
  - Log scheduled commercial bank credit per capita: -0.004 (standard error 0.006).
  - Log land gini co-efficient: 0.092 (standard error 0.074).
  - Cumulative land reforms index: -0.003** (standard error 0.001).
  - Cumulative labor reforms index: -0.001 (standard error 0.003).
- Goodness of fit and sample sizes:
  - R-squared values reported: 0.76, 0.82, 0.80, 0.81 (first block) and 0.78, 0.82, 0.76 (second block).
  - Observations: 58, 58, 58, 57 (first block) and 55, 58, 58 (second block).
  - Groups: 16, 16, 16, 21 (first block) and 15, 16, 16 (second block).

### Interaction tests and interpretation
- Specifications with age-structure variables interacted with control variables (following Bloom and Canning (2004)) were estimated.
- No significant interaction terms were found between age-structure variables and social controls (education, health, gender bias) — implying health and educational preconditions may be sufficient conditions for exploiting the demographic dividend.
- Lack of significant interactions with policy variables may reflect inadequate measurement of state-level institutional/policy variation or may reflect that major reforms (dismantling of industrial licensing, trade policy reforms, greater exchange rate flexibility) were applied at an all-India level, reducing observable state-level interaction effects.
- The paper flags economic openness × demographic dividend interactions found in cross-country panels as a potential counterpart worthy of future research.

### Definition and formula for the demographic dividend used in simulations
- Per capita income growth inclusive of age-structure changes between period t and t+1 is given by:
  - ln y_{i,t+1} - ln y_{i,t} = ρ + β1 ln w_{i,t} + β2 g_{w,i,t} + γ'X_{i,t} + η_t + ε_{i,t}  (equation (5) form; variables preserved in original notation).
- Counterfactual: working age ratio remains fixed at base-year level (w_{i,t} = w_{i,0}, g_{w,i,t} = 0).
- Demographic dividend DD_t (average annual increment in per capita income growth over the decade starting in year t attributable to age-structure changes from period zero onwards) is:
  - DD_t = β1[ln w_{t+1} - ln w_{1}] + β2[ln w_{t+1} - ln w_{t}]  (equation (7) representation preserved in original structure).
- For historical and future simulations the baseline point estimates used are β1 = 0.478 and β2 = 0.188 (from column 1, Table 5).

### Historical simulations — "The Dividend thus Far"
- Using the formula with historical working age ratios and β1 = 0.478; β2 = 0.188, Table 9 reports India’s past age distribution and demographic dividend by decade relative to a 1961 counterfactual.
- Age distribution (percent of total population) by decade:
  - 1961 age groups: 0-14 = 41.0, 15-59 = 53.3, 60+ = 5.6.
  - 1971: 0-14 = 42.0, 15-59 = 52.0, 60+ = 6.0.
  - 1981: 0-14 = 39.6, 15-59 = 53.9, 60+ = 6.5.
  - 1991: 0-14 = 37.3, 15-59 = 56.7, 60+ = 6.0.
  - 2001: 0-14 = 35.4, 15-59 = 57.1, 60+ = 7.5.
- Decadal demographic dividend (increment to annual per capita income growth relative to 1961 working age ratio):
  - 1960s: -0.6 (percent)
  - 1970s: 0.4
  - 1980s: 1.4
  - 1990s: 1.3
- Per capita income growth (growth in per capita net domestic product in constant 1993–94 prices) and net of dividend:
  - Per capita growth by decade: 1960s = 2.1, 1970s = 0.9, 1980s = 3.1, 1990s = 3.4.
  - Net of demographic dividend: 1960s = 1.8, 1970s = 0.4, 1980s = 1.7, 1990s = 2.1.
- Interpretation: The demographic dividend was small/negative in the 1960s, small/positive in the 1970s, and substantial in the 1980s and 1990s. A considerable fraction of India’s growth acceleration since the 1980s may be attributed to changes in age structure.

### State-level distribution of the dividend (selected states)
- Method classifies Andhra Pradesh, Karnataka, Kerala, Madhya Pradesh, Rajasthan, and Tamil Nadu as pro-employer states; Gujarat, Maharashtra, Orissa, and West Bengal as pro-worker states; six other large states did not implement Industrial Disputes Act amendments over the period.
- Table 10 (selected states — leaders vs laggards) reports demographic dividend and growth rates (in percent) by decade:
  - Leaders (South and West) — Demographic dividend by decade:
    - Tamil Nadu: 1960s = -0.1, 1970s = 0.8, 1980s = 2.2, 1990s = 2.7.
    - Karnataka: -0.3, 0.9, 2.4, 3.2.
    - Gujarat: -0.2, 1.5, 2.6, 3.0.
    - Simple average demographic dividend (leaders): -0.2, 1.0, 2.4, 3.0.
  - Laggards (Heartland) — Demographic dividend by decade:
    - Bihar: -0.3, -0.2, 0.8, 0.0.
    - Madhya Pradesh: -1.7, -0.4, 0.7, 0.3.
    - Uttar Pradesh: -0.9, -0.6, 0.4, -0.4.
    - Simple average demographic dividend (laggards): -0.9, -0.4, 0.6, 0.0.
  - Per capita income growth rates (leaders, percent):
    - Tamil Nadu: 0.4, 0.1, 4.1, 5.1.
    - Karnataka: 2.0, 0.7, 3.0, 6.0.
    - Gujarat: 1.9, 0.9, 3.1, 3.6.
    - Simple average (leaders): 1.4, 0.5, 3.4, 4.9.
  - Per capita income growth rates (laggards, percent):
    - Bihar: 0.3, 0.6, 2.7, -0.1.
    - Madhya Pradesh: -0.5, 0.6, 2.2, 1.1.
    - Uttar Pradesh: 0.7, 0.7, 2.6, 0.8.
    - Simple average (laggards): 0.2, 0.6, 2.5, 0.6.
  - Net of demographic dividend (leaders simple average): 1.7, -0.5, 1.0, 1.9.
  - Net of demographic dividend (laggards simple average): 1.1, 1.0, 1.9, 0.6.
- Interpretation:
  - Tamil Nadu, Karnataka, and Gujarat reaped large dividends: increment to per capita income growth of 2.4 percent per annum in the 1980s, rising to 3 percent in the 1990s.
  - Lagging Hindi Heartland states averaged 0.6 percent in the 1980s and zero in the 1990s.
  - The bulk of projected increases in working age ratio is likely to come from laggard states (average 2001 working age ratio among leaders = 62.1 percent; laggards = 53.4 percent), implying potential for income convergence.

### Recent developments and anecdotal evidence
- Bihar (worst-performing laggard historically) experienced per capita income growth averaging 6.2 percent per annum from 2001 through 2009, up from about zero in the previous decade, and above the sample median growth rate for this period.
- Among the four big Hindi Heartland states in that period: Rajasthan averaged 6.1% per annum; Uttar Pradesh 3.2%; Madhya Pradesh 2.7%; median growth rate was 5.7%.
- The paper notes governance and development reforms in Bihar as contributors to the turnaround while also noting likely demographic contributions via an increase in the working age ratio from 52.5 percent in 2001.

### Future projections and simulations
- Projections of India’s age distribution used: Census of India (projections through 2026), United Nations Population Division (UNPD, projections through 2050 medium-fertility variant), and IDB, US Census Bureau (projections through 2050).
- Table 11: demographic projection snapshots (percent of total population):
  - Census of India — 2001: 0-14 = 35.5, 15-59 = 57.8, 60+ = 6.9; 2011: 29.2, 62.7, 8.2; 2021: 25.1, 64.0, 10.7; 2026: 23.4, 64.0, 12.5.
  - United Nations Population Division — 2001: 0-14 = 35.5, 15-59 = 57.8, 60+ = 6.9; 2010: 30.8, 61.6, 7.5; 2020: 26.7, 63.5, 9.8; 2030: 22.8, 64.8, 12.4; 2040: 19.7, 64.6, 15.6; 2050: 18.2, 62.2, 19.6.
  - IDB, US Census Bureau — 2001: 0-14 = 35.5, 15-59 = 57.8, 60+ = 6.9; 2010: 30.1, 61.7, 8.2; 2020: 26.3, 63.5, 10.2; 2030: 23.5, 63.3, 13.2; 2040: 21.4, 61.9, 16.7; 2050: 19.8, 60.1, 20.1.
- Projection differences arise from different age-specific fertility and mortality assumptions.
- Table 12 reports demographic dividend projections by decade (increment to annual per capita income growth relative to working age ratio fixed at 2001 level), in percent:
  - Using Census of India 2001 projections: 2000s = 2.0, 2010s = 2.2, 2020s = 2.04, 2030s = 2.16 (note: 2021–2026 for Census of India), 2040s and beyond not provided in Census series in the table.
  - Using United Nations Population Division: 2000s = 1.6, 2010s = 1.95, 2020s = 2.27, 2030s = 2.10, 2040s = 1.17.
  - Using US Census Bureau (IDB): 2000s = 1.62, 2010s = 1.93, 2020s = 1.69, 2030s = 1.15, 2040s = 0.57.
  - Simple averages across projection sources: 2000s = 1.74, 2010s = 1.98, 2020s = 2.04, 2030s = 1.62, 2040s = 0.87.
- Interpretation:
  - All projections show rapid growth in the working age ratio from 2001 through 2021.
  - The demographic dividend is projected to peak over the next two decades—adding about 2 percentage points to annual per capita income growth over the period.
  - Subsequently the dividend should begin to decrease gradually (UNPD) or decrease rapidly (IDB), though remaining positive for some decades.
  - Calculations suggest that over the current decade the increment to per capita income growth from demographic change has been between 1.5 to 2 percent points per annum.

### Conclusions and policy implications
- Both the level and the growth rate of the working age ratio have exerted a large impact on India’s economic growth; results are robust to corrections for inter-state migration, to endogeneity concerns, and to a range of control variables.
- There have already been considerable gains from changes in the age structure; a substantial part of India’s growth acceleration since the 1980s can be attributed to demographic change.
- Looking ahead, the continuing demographic transition will yield a growth dividend of about 2 percent per annum over the next two decades (projected peak).
- The bulk of the remaining demographic transition will be concentrated in lagging states, raising the prospect of substantial income convergence among rich and poor states.
- Little empirical evidence is found for complementarities between demographic variables and various facets of social development or the policy environment at the state level; national-level reforms may have been the most complementary policies to demographic change.
- The paper highlights research into policy complementarities (especially those applied at national level or that interact with state industrial composition and trade exposure) as a worthwhile future agenda to better understand growth trajectories.

*Source: IMF working paper content unit _wp1138 - introduction of these diverse control variables. The point estimate of the coefficient on the*

### REFERENCES

### _wp1138 - REFERENCES

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- U.S. Census Bureau, “International Data Base: Population Estimates and Projections Methodology”, June 2010. (http://www.census.gov/ipc/www/idb/)

*Source: _wp1138 - REFERENCES*

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