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Dissertation on Calculating Measures of Sustainability

Info: 11318 words (45 pages) Dissertation
Published: 16th Apr 2021

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Tagged: EconomicsFinanceInternational Studies

Measuring the Sustainability of Indian States


This dissertation will calculate measures of genuine investment for 29 Indian States in the ten-year period between 2003-13. Genuine investment is a proxy for intergenerational well-being, more commonly known as sustainability, and is a measure of the change in society’s productive capacity or genuine wealth. Genuine wealth consists of various capital stocks. This study will look to derive a calculation of the natural, human, health, reproducible and institutional capital components of genuine wealth. The relationship between the computed sustainability measure and selected socioeconomic factors (corruption and female empowerment) will also be analysed.

  1. Introduction

“Gross National Product, now, is over $800 billion dollars a year, but that Gross National Product – if we judge the United States of America by that – that Gross National Product counts air pollution and cigarette advertising, and ambulances to clear our highways of carnage….. Yet the gross national product does not allow for the health of our children, the quality of their education or the joy of their play…. If this is true here at home, so it is true elsewhere in world.” Robert Kennedy, 1968.

India has consistently experienced GDP growth above 5% per year in the 21st century (MOSPI) whilst undergoing huge reductions in poverty. In 1999 the poverty rate stood at 37.4%, it had fallen to 17% by 2013.  There have also been impressive improvements in life expectancy, increasing by six years from 2000 to 2015[1]. However, there have been costs to India’s development, such as rising inequality due to a growing upper middle class. Most notably though are environmental concerns from rapid urbanisation and population growth. India is home to nine of the world’s 20 most polluted cities[2], with a day spent in Delhi equivalent to smoking 50 cigarettes[3]. Furthermore, India’s population is set to be the largest in the world for most of the century – a population of 1.6 billion by 2060 will be a huge drain upon resources[4]. While the poverty rate may have fallen substantially, India still has the largest number of people living in poverty of any country, and in comparison with China – with a poverty rate of 1.85% in 2013 –  much work is still to be done to achieve the Millennium Development Goal of ending extreme poverty by 2030[5].

The sustainability of India’s development, whether India can maintain current welfare in the future, therefore comes into question and is the subject this paper will seek to investigate between 2003-2013 in the States of India. Sustainable development, as coined by the Brundtland Commission in 1987, “is development that meets the needs of the present without compromising the ability of future generations to meet their own needs[6]. Future generations will only be able to meet such needs so long as they possess capital assets that can cater to these needs. Future societies require that the value of these capital assets are at least maintained to ensure sustainable development. More formally than ‘needs’, the definition of sustainability in this study will be taken to follow Arrow et al (2004): to achieve sustainability “intertemporal social welfare[7] must not decrease over time”. So, essentially is India’s current economic growth ensuring intertemporal social welfare is non-decreasing over time or is it instead exploiting India’s current wealth?

Simply considering GDP growth is insufficient in this context, as alluded to by the Bobby Kennedy quote; GDP disregards the depreciation of natural capital, whilst also ignoring the human capital stock. Essentially, the issue is that GDP, a flow, can be increased by depleting society’s capital stocks (for example deforestation) which would translate to a decrease in inter-temporal social welfare as future generations become worse off. As outlined in Arrow et al (2004), considering genuine investment – the change in genuine wealth – can instead answer the question as it offers a measure for changes in inter-temporal social welfare (if at a certain time, t, genuine investment is non-negative then intergenerational well-being is non-decreasing).


“Genuine investment can be expressed as the sum of the values of investments or disinvestments in each of society’s capital assets, where the value of each investment is the product of the change in the quantity of the asset times the shadow value” (Arrow et al , 2004).

Genuine wealth, predicated upon the weak sustainability theory, captures the productive capacity of the economy, and is measured in this study by calculating the stocks of natural, human, health, reproducible and institutional/knowledge capital[8] and multiplying them by their respective shadow prices. Shadow prices are the social values of the capital assets.

In this study, natural capital comprises land, forests, minerals & fossil fuels, human capital is proxied by education and health, and reproducible capital is calculated from measures which use the perpetual inventory method. These stocks are then valued by calculating their shadow prices, which are theoretically the price of a unit of the capital asset to society. However, these shadow values are unobservable and often instead proxied by using market prices minus costs of production. There are also data limitations preventing the perfect measurement of the stocks, such as newly discovered mineral and fossil fuel reserves increasing natural capital stocks. Additionally, there are components that simply can’t be measured due to a lack of data, such as environmental capital (air and water pollution) as well as institutional capital. However, whilst genuine wealth may have its imperfections, it is the best available measure of sustainability. Finally, the relationship between sustainability and two selected measures (corruption and female empowerment) are considered through regression analysis and as anticipated less corruption and greater female empowerment are found to improve sustainability.

In nearly all States across the ten-year period sustainable development occurs as genuine wealth per capita adjusted for TFP improves. The largest component of genuine wealth is health capital, which follows the findings of Arrow et al (2012). Improvements in health, human, institutional and most notably reproducible capital are responsible for the improved productive base of many Indian States. Yet, many people, given the conventional understanding of sustainability[9] would find that the Indian States have been unsustainable as natural capital per capita falls over the period. However, caution is advised in considering the results presented here, as assumptions upon which we calculate capital stocks as well as data limitations do impede the accuracy of our findings.

This paper will review the key literature on sustainability, particularly the two fundamental, already cited, Arrow et al papers (2004, 2012) and the Green Indian States Trust (GIST) methodology which inspired the measurements undertaken for human capital, forests and land. Next, the theoretical framework behind genuine wealth and sustainability, established in the Arrow et al papers, will be presented. The main part of this study will detail the methodology employed to compute the capital stocks which comprise genuine wealth. The calculated genuine wealth per capita will be analysed against corruption and female empowerment, to test the relationship these socioeconomic variables may have upon sustainability. Finally, the conclusion will evaluate the results and methodology used.

  1. Literature Review

The seminal papers Clemens and Hamilton (1999), Arrow et al (2004) and the recent addition to the latter, Arrow et al (2012), are the basis for the theoretical foundation espoused in this paper. Where available the ‘Green Accounting for Indian States & Union Territories Project’ (GAISP) monographs were followed to calculate the components of wealth, as these offer a more detailed approach to calculating capital assets than the brief methodologies provided by the seminal papers. The Green National Accounts in India[10] (2013), the most recent source, was also of general use as an up-to-date manual on sustainability and its measurement, as well as providing Indian specific details.

  1.  Clemens and Hamilton (1999)

Clemens and Hamilton (1999) develop the theory of genuine savings[11] (“traditional net savings less the value of resource depletion and environmental degradation plus the value of investment in human capital”) which the World Bank uses (although they call it ‘net adjusted savings’) and publishes data upon. They postulate the fundamental notion that the depletion, of a natural resource is equivalent to the loss of any other asset and therefore this should impact negatively upon measures of net savings. They establish that capital assets are the determinants of intergenerational wellbeing and therefore, sustainable development becomes a sum of these assets weighted by their respective shadow prices, which in turn constitutes society’s wealth.

  1.  Arrow et al (2004)


Arrow et al (2004), a joint paper by economists and ecologists, builds upon Clemens and Hamilton (1999) by considering intratemporal equity concerns – they forward the notion that social welfare should be defined as average welfare of individuals (rather than the sum of utilities of all individuals). Therefore, they stipulate that population should also be a capital asset (whilst Arrow et al (2012) further this by adding time as well). As intergenerational wellbeing is inherently a per capita measure, the fact that Clemens and Hamilton ignored adjusting their estimates of genuine savings for population growth, makes their results ambiguous. As such, the measure obtained in this paper is one of genuine wealth per capita – genuine wealth adjusted for population growth.

  1.  Arrow et al (2012)

The theoretical framework posited by Arrow et al (2012), which will be outlined in the next section, derives conditions that require genuine wealth per capita at constant shadow prices to be non-decreasing for development to be deemed sustainable. Hence why in this study genuine wealth for each period is calculated – a direct measurement – as opposed to solely the rate of change in wealth as compiled in Arrow (2004). In computing genuine wealth per capita, the more recent and wider remit used by Arrow et al (2012) to measure wealth is embraced[12].[13]

  1.  Gundimeda et al (2008)

Whilst the theoretical framework concerning intergenerational wellbeing and sustainability is inspired by the seminal papers by Clemens and Hamilton, and Arrow et al, the methodology used to calculate the components of the capital assets mainly arises from the work by the GIST. GIST outlines their methods and the approach that their series of monographs (which cover certain components of capital) takes in “Green Accounting Methodology for India and its States” (Gundimeda et al, 2008). They seek to build upon the System of Environmental Accounting (SEEA, 2003)[14] through developing “top-down” models of adjusted Gross State Domestic Product (GSDP) in the bid to create Green Accounts for India. However, in this study, the stocks (of capital) rather than the flows (of income) are instead adjusted, in line with the concept of intergenerational wellbeing. Forests, land and human capital measures are derived from the respective monographs published by GIST, whilst the approach used to value minerals and fossil fuels stocks comes from the ‘Green National Accounts’.

  1.  Aidt (2010)


A cross-country study of corruption on sustainability (also using the genuine wealth per capita measure), the paper provides the empirical specification used in the later analysis of corruption and female empowerment upon sustainability. Additionally, supports the use of the Hausman-Taylor model given the likely endogeneity of the two socioeconomic variables due to unobserved, time invariant, State-specific determinants of sustainability.

In terms of the contributions this study seeks to make to the outstanding literature; it is a country specific study conducted at State level, unlike the seminal papers which are cross country studies. Consequently, data research proves to be challenging with many, infrequent and often incomplete data sources having to be relied upon, rather than simply being able to call upon a centralised database of the World Bank or UN. However, given the interesting process of development that India has experienced in the 21st century as well as the diversity inherent in its States, (whether that be in size, income or the structure of their economies) the examination of sustainability this study undertakes proves to be pertinent. In addition, econometric analysis, investigating potential determinants of sustainability, is a further step that most papers which produce sustainability measures ignore.

  1. Theoretical Framework


The theoretical model derived below follows largely Arrow et al (2012), but also draws upon Arrow et al (2004) and GNA (2013).

3.1 Intergenerational Well-being

Intergenerational well-being at time (t) is denoted as

Vt. Time is denoted by



s≥t≥0) and is continuous. Let U(C(s)) be the society’s utility in a given period

s(flow), where C(s) is society’s consumption.

δ≥0, is the pure rate of time preference. Assume a closed economy. We have (1)

Vt= ∫t∞U(Cs)e-δ(s-t)ds


So, the discounted flow of utilities of present and future generations is what constitutes intergenerational well-being. Therefore, the sustainability criterion specified by Arrow et al (2004) is satisfied if

dVtdt≥0(change in intergenerational well-being is non-decreasing) at time t. As V(t) is forecasting periods in the future, the measure depends upon the genuine wealth of society in those future periods. Genuine wealth or the productive base is the stock of society’s capital assets (multiplied by their respective shadow prices), institutions and technology at time t. Assume for now population and technology/institutions are fixed. Let K(t) denote the stocks of capital assets. Naturally V(t) is a function of K(t) and also (t), so we have (2)



We take V to be dependent on (t) to account for time variant factors (which are assumed to be exogenous) such as population growth and technological change. As such, t also becomes an asset.

3.2 Shadow Prices

Differentiating the above equation (2) with respect to t and using

dVtdt≥0, gives (3):


This can now be linked to the shadow prices of the capital assets, where pi(t) is denoted the shadow price of Ki at time t. This is the value society places upon the asset and therefore the contribution each unit of the capital asset makes to V(t) (4):


Note, the shadow price of time is also (5):


The shadow price is a function of the capital stocks now and in the future, and the substitutability (assuming weak sustainability) between assets across time. Therefore, the difficulties with empirically measuring such social values quickly becomes apparent.

However, in certain cases we can use the marginal rates of transformation (which can be observable as market prices); this can be seen from the equations above which show shadow prices to be the marginal social rates of substitution. In the case where V(t) is maximised by society, the marginal rates of substitution equal the marginal rates of transformation. Generally, where the capital asset is traded upon a market, the market price is used as the shadow price (e.g. minerals and fossil fuels) in the following empirical analysis. However, the majority of the capital assets in question here do not feature in a marketplace and so, alternative methods are used to arrive at a shadow price for these stocks.

3.3 Genuine Wealth

The definition of genuine wealth follows now that shadow prices have been established (6):


Relating W(t) to V(t); intergenerational well-being increases if and only if genuine wealth increases, holding shadow prices constant. We can prove this statement by substituting the shadow price of a capital asset (4) and the shadow price of time (5) into (3). Let

∆represent an infinitesimal change (7) :


3.4 Genuine Investment


In terms of the relationship between intergenerational well-being and genuine investment, denote the rate of change of



Substituting this expression into (7) gives the genuine investment that occurs, when there is an infinitesimal change. So, the shadow value of genuine investment must be positive for intergenerational well-being to increase. The shadow value of genuine investment is the present discounted value of consumption changes (with the changes arising from the investment itself).

 3.5 Technological Change


This extension to the framework seeks to adapt the model for changes in knowledge and institutions that is proxied through the use of TFP growth in this study. Let A, as in a standard production function Y(t) = A(t)F(K(t)), be a capital asset representing society’s stock of knowledge (or technology) and institutions, so A denotes TFP. As mentioned earlier, incorporating time into the model as an additional asset was on the condition that it accounted for exogenous changes, so such changes in TFP were represented by (5). Combining this and the growth rate of TFP,

γ, and assuming a steady state, gives:


Assuming a zero genuine savings rate (which is approximately observed by Arrow et al (2004)) then

pAtA(t)∑ipi(t)Ki(t)≈1, in which case we are left with

∂V∂t=γ. This can be added to the genuine investment equation. This addition of TFP growth is used to augment genuine investment in the empirical analysis.

3.6 Population Growth


As discussed in the overview of the relevant literature, Arrow et al (2004) advocate that population is also a capital asset. If we’re unable to project future demographics, then population growth can be modelled like TFP growth – exogenously such that the shadow price of time incorporates it. For example, population growth effects upon the economy could be attributed as TFP, if the benefits of scale were felt. This allows population growth to be added to genuine investment as well.

Note that a further expression for intergenerational well-being, relating to genuine wealth per capita, can be derived from Dasgupta (2001) using dynamic average utilitarianism. This analysis, which requires several strong assumptions, is passed over given the empirical application will model population growth arising exogenously within r(t).

3.7 Discussion


This theoretical framework, like any economic model is simplified and as such dependent upon several assumptions which should be noted before implementing the model empirically. An inherent assumption is that of weak sustainability, whereby one form of capital can be said to substitute for another; for example, under this assumption natural capital depreciation can be sustainable if an equal or greater investment is undertaken in reproducible capital to maintain genuine wealth per capita. Additionally, nonlinearities are alerted to; when calculating genuine wealth per capita, the loss of natural capital, for example, is assumed to have a constant shadow price. However in reality the shadow price can be a function of the capital stock, the cost of the loss can be extremely nonlinear if a critical threshold is exceeded[15]. As such shadow prices will be severely underestimated; the results we obtain for natural capital are most likely to be lower bound estimates. Finally, the use of TFP estimates should be taken with caution given that TFP growth rates can be biased upward if an economy is depleting its natural capital at a growing rate.

Typically, a shadow price is calculated using the net present value (NPV) approach. A resource generates revenue from its use, LR, whilst being able to use the resource comes at a cost, C (the inputs needed to create the output). The asset value will equal this economic rent discounted, by r, for the life of the resource, T. For example, if we think of a plot of land generating output now and in future periods, but requires fertilisers and labour to do so. The formula for NPV is therefore:

Net Present Value NPV=∑t=1TLRt-Ct(1+r)t

However, practically issues arise with this approach as it rests on several assumptions. For instance, we require knowing not only future revenues and costs but also the life of the resource T, furthermore the analysis is heavily reliant on the choice of discount rate.

  1. Methodology

The following will detail the methods used to calculate the value of each capital asset that comprises genuine wealth per capita for Indian States between 2003-2013. Genuine investment is determined as the growth in genuine wealth per capita. To obtain constant shadow prices, the following price methods (NPV, net price, replacement cost etc) are averaged across the period 2003-2013, or if that isn’t possible taken from a particular year. Additionally, if not explicitly stated, the data used is at the State and year level.


  1. Natural Capital


Natural capital is measured here through valuing forests, land and minerals & fossil fuels stocks. As such, it becomes apparent many aspects of what we think of as natural capital are omitted due to data limitations: carbon damages to air, water, ecosystem services, etc. This emphasises that this method of environmental accounting is in its infancy, but whilst this natural capital measure is underestimated it is still useful in informing how Indian States are performing in maintaining natural capital.

To calculate the shadow price, and given the issues with the present value approach, the total rent approach or net price method (Repetto et al (1989)) is used for forests and minerals & fossil fuels. The net price is the market price of the resource minus the marginal cost of a unit (this marginal cost incorporates the cost of extraction, exploration and development). The value or user cost (UC) is therefore equal to the rent (P-C) multiplied by the stock of the resource, (R):


The method assumes an optimal extraction path and that the net price is the Hotelling rent, meaning growth of the rent is equal to the interest rate on an alternative investment – such that the discount rate is offset.[16]. For a discussion of alternative approaches for valuing stocks see Atkinson and Hamilton (2007).


  1.      Forests

The forests calculation is adapted from Gundimeda et al (2006) and Monograph 1 of the GAISP. The main data source is the Forest Survey of India’s (FSI) biannual[17] State of Forest Report (SFR).

The forests’ stock is divided into three main components: timber, carbon and non-timber forest products (NTFPs). Using timber and carbon is not a case of double counting as the stock of timber is contained within the protected forests and the stock of carbon within the reserved forests. This is because the protected forests are used for timber and fuelwood, whilst the reserved forests aren’t permitted to be logged and hence why their value is derived from the carbon they hold. The value of the three are calculated as follows:

Timber = Volume of growing stock* Net price of timber*Protected Forests%

Volume of growing stock is given in the SFR, the net price uses Gundimeda et al (2006) data and the percentage of protected forests (of total forests) is also from the SFR.

Carbon = Volume of carbon*Price of carbon*Reserved Forests%

Volume of carbon is calculated using the FSI Carbon Report which estimated the average carbon density per hectare for each State in 2004 (assumed to have remained constant for the ten-year period) multiplied by the ‘total forest cover’. The price of carbon is taken to be $20 per tonne as used in the monograph. Similarly, the percentage of reserved forests (of total forests) is also from the SFR.

NTFPs = Forest Cover*PV per hectare

Forest cover is given in the SFR. The present value per hectare is calculated using the net price method, where the value (price) per hectare comes from Gundimeda & Shyamsundar (2012) and the marginal cost is taken as zero as the sole input, labour,  are assumed to have no option to work elsewhere. The net price is divided by the social discount rate 4%[18] to give the present value; this adjustment to present value occurs as NTFPs, unlike timber, are generated every year. State level data upon the value per hectare was unavailable so a national average is instead used.

Unfortunately, we couldn’t obtain data on fodder and followed convention in our measurement of forests (through considering timber, carbon and NTFPs), however ecosystem services, ecotourism and genetic diversity could also be considered. In Gundimeda et al (2006) they find that the latter two are worth roughly 83% of the value of timber, carbon and NTFPs in India, and so could be worthwhile calculating in the future.

  1.      Land


Land, or specifically agricultural cropland and pastureland draws upon the methodology used in Monograph 2 of GAISP.


The value of agricultural cropland and pastureland can fall if the land is used for other purposes (e.g. urbanisation), if soil erosion occurs or the land becomes degraded such that they’re instead classified as wastelands.The Monograph also considers sedimentation costs (e.g. if restricting the capacity of a reservoir) that soil erosion causes, although these may not strictly impact the value of land given we’re already accounting for soil erosion, these costs will still affect natural capital (through water stock) so are included.


Data on stock of agricultural cropland and pastureland came from the Statewise Land Use Classification in India’ from Indiastat, where net area sown was taken to be the former and permanent pastures the latter. Land degradation was calculated by using the Wasteland Atlas and the SAC, these were only published in 2003, 2005, 2008 and 2013 so interpolation was used to arrive at the stock of degraded land for the other years. For soil erosion, the medium estimates total of soil erosion in India were used from Table 8 in the Monograph, divided by the total agricultural land in 2000 (the year of the medium estimate) as we assumed agricultural land was proportional to soil erosion. This estimate of soil erosion per sq km was assumed to remain constant throughout the period; to arrive at each State’s measure, this estimate was multiplied by the State’s agricultural land. For the calculation of loss of potassium, nitrogen and phosphorus, the fixed percentages from the Monograph of these minerals in soil were used and multiplied by the amount of soil erosion to give the total loss. Sedimentation was taken as 20% of soil erosion’s quantity, as used in the Monograph.

To value agricultural cropland the net present value method was used. To compute the NPV in theory required estimating the future net returns that the land would generate, this depends upon rainfall, quality of soil, cropping patterns etc. To model this we use the value of output of agriculture adjusting for constant 04/05 prices, published by the CSO but found on Indiastat, for each State from 1990. A linear regression model is fitted, where the dependent variable is output and independent variable is time, to predict the future net returns for 40 years[19] into the future. Similarly, for pastureland the NPV method was used. However, the calculation for pastureland used the output value of fodder (compiled from cereals, fibres, oilseeds, sugars and pulses data) which was only available for India as a whole. We multiplied the national figure of NPV per hectare for the share of a State’s agricultural output of total agricultural output.

To value soil erosion, the replacement cost method was adopted. This was as follows for nitrogen (with super phosphate and potash used for phosphorus and potassium respectively, in place of urea):

RCNitrogen=Price per kilogram of nitrate in urea × Content of nitrogen in urea

The maintenance cost method was implemented for land degradation, whereby the average cost of land reclamation was calculated (using data from several studies in Table 16 of the Monograph) and assumed to be constant across States and time. The cost of sedimentation was said to be $3 per tonne.

The final value for land was calculated as follows:

Land=(Cropland+Pastureland) –(Soil Erosion+ Land degradation+ Sedimentation)

  1.      Minerals & Fossil Fuels


The methodology used here draws upon the GNA and Arrow et al (2012).

The GNA’s recommendation of considering iron and limestone as minerals and coal, oil and gas as fossil fuels is followed, as the GNA says these make up 82% of mineral & fossil fuel value in India. Proven and probable reserves are used as our physical stocks, as done in Arrow et al (2012), the potential issues with using this classification are raised later.

Data for these stocks comes from the Indian Bureau of Mines’s (IBM) annual publication the Indian Mineral Yearbook which goes back to 2008, for the earlier years we used the Coal Directory and Indian Petroleum & Natural Gas statistics. However, iron and limestone data is available only quinquennially (2000, 2005, 2010, 2015) and so is interpolated. The estimate of oil and gas is a lower bound estimate as a substantial number of reserves are located offshore.

The net price method was used. The market price was calculated by dividing the value of production by the quantity produced (both of which were given in the Mineral Yearbook). The extraction cost was computed using the ‘Rental Rates’ given in Clemens and Hamilton (1999), assuming this stayed constant as a proportion of the price throughout the period.

The issue with the given method is that only proven and probable reserves are used as the physical stock; these are the reserves that are economically recoverable. There are of course other reserve classifications, and given the ever-improving extraction and exploration technology these lower reserves are often upgraded as they become economically feasible. This problem has occurred in the data, so for many years stocks increase which doesn’t seem reasonable, given the non-renewable nature of minerals & fossil fuels.

  1.  Human Capital


The method used in Monograph 5 of GAISP is largely adopted here. The definition they follow, and which will also be used here is that of the OECD (1998) for human capital: ‘the knowledge, skills, competences, and other attributes embodied in individuals that are relevant to economic activity”. The main data sources are the Indian Human Development Survey (IHDS) (2005, 2011) and the Census (2001, 2011).

To measure human capital we take inspiration from Becker (1966) and Mincer (1974) through estimating returns to education. The NPV approach is then used, with these estimated returns, to value future income streams given the level of education, rate of employment, mortality rate, likelihood of seeking more education (dependent on the underlying age cohort) and the discount rate.

Firstly, the Mincerian earning function is used, whereby the wage of an individual is regressed upon the level of education, sex, sector (urban or rural), job experience (proxy for on-the-job training) and social group.[20]

ln wage=β0+β1SEX+β2SECTOR+β3EXPER+β4EXPERSQ+β5SOCIAL+∑i=17β6iEDUCi+ε


Insert description of variables

Used this specification and data from the IHDS to obtain the predicted wages for different education levels and age cohorts in each State. To get these estimates we used the Heckman maximum likelihood estimation (Heckman, 1974)as there is reason to believe OLS gives biased estimates due to sample selection bias (from using the IHDS) being present (perhaps those who undertook the survey were more likely to be literate). We can also think that wages and education decisions are influenced by omitted variables such as parental characteristics, ability etc. Heckman used the joint maximum likelihood procedure precisely to adjust for such selection bias in wage regressions. Simultaneous equations are used, with the first stage using a probit estimate of the probability of being employed, whilst in the second stage the wage equation is used – this latter equation needs to be identified. For an accurate solution it is required that there are variables which strongly impact employment but not the actual wage, for example, for female employment the number of children would be such a variable. As such, we include the number of children and income from other sources (non-wage employment). In Figure 1, we can see that the Heckman model is viable as the Likelihood Ratio test tells us rho is statistically different from zero and additionally the lambda estimate is significantly different from zero which suggests wages are affected by unobserved varaibles.

To estimate the lifetime labour income for different education levels and age cohorts a formula based upon Jorgenson and Fraumeni (1989, 1992) and Wei (2001) was used with the predicted wages. As aforementioned this uses a NPV approach, weighted not only by the discount rate, but also the mortality rate and employment rate. Additionally, for the age cohort 15-30, the probability of seeking more education was also incorporated. This formula, from the Monograph (for age 15-30), is given below[21]:

HKaei=WaeiYaei+Enrolaei×Sa, a+1×HKa+1ei+1+(1-Enrolaei)×Sa, a+1×HKa+1ei×(1+g)(1+r)

where a = age, e = education, HK is human capital, W = employment rate, Y = annual labour income, Enrol = enrolment rate, S = probability of survival, g = growth rate of wages and r = discount rate (4%).

The employment rate came from the Census and the enrolment rate from the National Sample Survey (NSS) 71st “Status of Education and Vocational Training in India” (2014) using the net attendance ratio (NAR). The NAR is the ratio of the number of individuals in the age group attending a particular ‘class-group’ to the total number of individuals in the age group. The probability of survival used the Sample Registration System (SRS) abridged life tables from the Census. Calculated g=5% by looking at the growth rate over the period.

An individual aged 60 is considered retired and so lifetime income at this age is zero. The present value estimates for each education level and age cohort for each State were multiplied against the population within each category, obtained from the Census. The sum of these values (for each level of education and age) gave the human capital of that State.

The main issue with this method concerned data from the Census. The Census is completed only every 10 years so the years between 2001 and 2011 and the years after had to be interpolated and extrapolated respectively. Also, using the IHDS and calculating predicted wages for each education level and age cohort for each State led to some cases where there were relatively few observations. As we couldn’t get hold of the relevant NSS this was the best we could manage.

Fig 1

  1.  Health Capital


The framework used by Arrow et al (2012) is implemented here for health capital, with their approach inspired by Nordhaus (2002) and Becker et al (2005).

An improvement in health in this context means higher life expectancy and the value stems from the worth people place upon these additional years of life. The GNA details two possible methods for valuing health capital: (1) a “willingness to pay” approach or ‘stated preference’ which looks at how much people have paid for health improvements and (2) a “revealed preference” approach whereby we infer the value of health, we shall be using the latter.

As noted, health capital improvements result from greater life expectancy – additional years of life. Therefore, we need to estimate the value of an additional life year (which we take to be independent of age) which we can do through considering the value of a statistical life (VSL)[22]. The theoretical framework behind the health capital calculation is detailed in Arrow et al (2012), due to space it shall not be reproduced here. The outcome is the following formula for the value of an additional year of life (VSLY), h:



π(a)is the proportion of people of age a,

f(T|T≥a)is the conditional density of death at age T, given one has survived to age a and 0.04 is again the discount rate of 4%. Due to the data, people are assumed to die at 80.

So, the complex expression in the denominator is essentially expected discounted years of life remaining of the State’s population (which is the health stock). The proportion of population of a certain age is again from the Census, likewise the construction of the conditional density used data from the SRS abridged life tables (which, unlike population data, are available for each year).

Viscusi and Aldy (2003) find the VSL is positively correlated with income, arriving at the formula

VSL=bY0.6, where b is a constant and Y is GDP per capita. As Arrow et al (2012) do, we use the Environmental Protection Agency’s estimate for the VSL, but updated for 2004 of $6.6million, and given Viscusi and Aldy (2003) assume therefore that the VSL for Indian States is proportional to $6.6million at

(State NSDP 2004U.S GDP 2004)0.6. For the States’ NSDP, obtained from RBI Handbook of Indian States, we convert it into PPP adjusted dollars (using OECD conversion rates). This calculation gave us the VSLY or h for 2004, which is the shadow price. The VSL was calculated for each year by multiplying the constant VSLY by the expected discounted years of life. In turn health capital was computed as the product of this VSL and the population.

This analysis is very dependent upon the calculation of the VSL for India, and the genuine wealth more broadly given that health capital massively dominates any other form of capital. We should also be aware that we have assumed a VSLY that is independent of age, which in practice wouldn’t hold (see Murphy & Topel (2006) for an example of an age dependent value).

  1.  Reproducible Capital

The RBI’s Handbook of Indian States, the main source of macro level statistics for each State, unfortunately contained no measure of the reproducible capital stock. However, the NAS publishes such a figure – the ‘net capital stock’[23] – for India as a whole. The proportion of a State’s NSDP of total India GDP was used to proxy how much of the net capital stock a State has.

State’s Reproducible Capital=NSDPGDP×India’s Reproducible Capital

This means that our reproducible capital estimates are dependent on the level of NSDP and also on this NSDP performance relative to other States. This isn’t ideal, as NSDP is determined by capital stocks other than reproducible, such as human, natural and population. However, given the strong positive correlation we expect between NSDP and the reproducible capital stock and the seemingly accurate TFP estimates generated from such, we decide this is the best available method of estimation.[24]

  1.  TFP

The TFP calculation follows Klenow and Rodriguez-Clare (2005) as used by Arrow et al (2012). TFP is our proxy for the growth in institutional or knowledge capital, the capital stock of which can’t be directly measured.

Instead of using the formula they propose in their calculations, which looks to estimate human capital by using attainment and a Mincerian return to education, we use the actual human capital and reproducible capital data we’ve estimated. Therefore, their formula takes the following form:


Where y denotes output per worker, k denotes reproducible capital per worker and h denotes human capital per worker.

αis capital share of income,and is assumed from Klenow and Rodriguez-Clare (2005) to be

13. We calculate this TFP value for each year, and from this compute the growth rate of TFP.

  1. Results

Using the results presented in Tables 1- 4, the most noticeable finding is the magnitude of health capital compared to the other forms of capital (Table 4); this result was also found in Arrow et al (2012). Therefore, we have also presented results for genuine wealth excluding health capital (what has been termed ‘Wealth’ in the Tables) to see more clearly the dynamics of human, natural and reproducible capital.[25]

Genuine wealth has grown for all States between 2003 and 2013, as has genuine wealth per capita with Kerala the exception[26]. Such is health capital’s magnitude, the movements in genuine wealth are therefore a result of the steady growth of it due to life expectancy improving markedly over the period. There are also positive findings for wealth and wealth per capita, however these growth rates are considerably higher than those of genuine wealth. This is largely attributable to substantial increases in reproducible capital over the period (with per capita rates exceeding 200% for nearly all States), but there has been also steady growth in human capital due to higher levels of education. However, natural capital per capita falls for nearly all States due mainly to decreasing land and forest wealth. Whereas minerals & fossil fuels, as highlighted earlier, have risen for many States (due to the valuation method used) as such these results for natural capital are lower bound estimates.

Technological progress and institutional capital, as proxied by TFP growth, improved in the vast majority of States. Therefore, using genuine wealth per capita adjusted for TFP as the definition of sustainability, all but five States (Uttar Pradesh, Manipur, Jammu & Kashmir, Chahattisgarh and Rajasthan) have experienced sustainable development. In terms of wealth per capita adjusted for TFP, just two States have been unsustainable over the ten-year period: Arunachal Pradesh and Manipur. Both due to experiencing high population growth and large losses of natural capital.

Health capital comprises over 90% of all States’ genuine wealth in 2003 and 2013. This is because….On average human capital is five times larger than natural and reproducible capital in 2003 (with the latter two of a similar magnitude). However, reproducible capital grows considerably over the period (especially pronounced in the ‘Wealth’ measures), to be over three times larger than natural capital by 2013.

*Insert here four Powerpoint Tables*

  1. Corruption & Female Empowerment

We have obtained a measure of sustainability – genuine wealth per capita – through measuring the various capital asset components that make up the wealth of society. Given this measure, we can now look to investigate wider socio-economic factors that may influence the sustainability of a society. Here, we look to consider two such measures: corruption and female empowerment, both of which are especially pertinent to many developing countries whilst being important issues still in India.

6.1 Background

Firstly, corruption, the argument is whether corruption ‘greases or ‘sands the wheels of development (Aidt (2009)). The former concerns the fact that bureaucracy and legal frameworks can often cause there to be long delays and costs in decision making by government, and so corruption acts as a loophole, speeding up the process. The latter argument, is that corruption acts to impede sustainable development as funds meant for investment are siphoned off at each stage of the funding distribution; this can be thought to affect all forms of capital. This is a commonly found conclusion in the evaluation of aid effectiveness. For instance, funding to hospitals and schools being diverted into government agents’ pockets, would impact investments in health, human and also reproducible capital assets. Furthermore, the resource curse argument proposes that those nations blessed with valuable natural capital assets are also rife with corruption, and so these public assets are sold off for private gain (Shleifer and Vishny, 1993) where they are extracted, leading to depleted capital stocks. Needless to say, the weak sustainability theory can’t defend such extraction in these cases; the resource rents won’t be hypothecated, as is the case with Norway’s sovereign wealth fund for instance, given the now private ownership.

In terms of female empowerment, there is evidence from Beaman et al (2010) in India, that greater female representation on local councils can lead to greater investment in public goods in water infrastructure and also education, whilst finding these investments don’t lead to lesser investments in other areas as a result. Svaleryd (2009) uncovers similar findings in Sweden that would increase health and human capital formation. Greater female empowerment is also representative of greater female education and work opportunities, which further improve human capital.

6.2 Empirical Specification

The empirical specification is inspired by Aidt (2010), who similarly analysed the effect of corruption upon sustainable development. The control variables are the determinants of genuine wealth per capita that we have studied in this paper, namely institutions (which were proxied through TFP), capital asset stocks and their shadow prices. We shall look to first conduct a pooled regression, but given the endogeneity of corruption and female empowerment (from correlation with the random effect), we also use the Hausman-Taylor model (Hausman and Taylor (1981)) to control for such unobserved State random effects. The specification for corruption is as follows:



εirepresents the unobserved, time invariant, State-specific determinants of genuine wealth per capita. We retain the same design for measuring female empowerment.

6.3 Data Sources

The measure of corruption is a composite of experienced and perceived corruption, taken from Charron (2010) who forms the measure using surveys conducted by Transparency International (2005).Female empowerment is derived from the Gender Empowerment Measure (GEM)[27] created by the Ministry of Women and Child Development (MWCD) for all States in 2006[28]. The proxies for political institutions and legal institutions are the composite scores of quality of legislature and justice, law & order respectively from Mundle et al (2016)[29]. Both the corruption and institutions measures cover the 20 largest States (accounting for 96% of the population) for 2005 and 2011 respectively – hence the need for pooled OLS. For capital stocks, we use our measures of natural, human, health and reproducible capital (all in rupee billions) and population for each State and year. To proxy for the proximity of shadow prices to market prices we, like Aidt (2010), use a measure of trade openness from Maiti and Marjit (2010), this measure is for 2003 and covers 15 States. The full specification therefore includes 14 States, so trade openness has also been dropped in each regression to give a greater number of observations.


6.4 Results


The pooled OLS[30] estimates are highly significant (at 1% level) for both variables. The coefficient on corruption is positive, which supports the sanding the wheels hypothesis. However, the gender empowerment measure is negative when including the trade openness measure, suggesting that less female representation in society is beneficial to sustainable development. This counterintuitive finding could be due to the smaller number of observations when including this proxy for shadow prices or potentially it controls for the international openness of the State and this progressivity is a key determinant in female empowerment. As the specification of pooled OLS is reliant upon some time invariant independent variables, we have reason to believe corruption and female empowerment may be suffering from endogeneity. For example, this endogeneity could be due to State-specific culture that our specification fails to control for. We are unable to use a fixed effects estimator due to the time invariance of the corruption and female empowerment measures, whilst the customary random effects estimator can’t be adopted as these two variables are most likely correlated with the State-specific unobserved determinants of sustainability (Aidt, 2010). The Hausman-Taylor model avoids this latter issue and as such is used here.

The Hausman-Taylor estimation produces results which are also significant, however, with both coefficients as anticipated. The fact that we have controlled for the random effects using this model, suggests the results found under pooled OLS were biased due to endogeneity. However, the use of the Hausman-Taylor model implicitly assumes that corruption and female empowerment are uncorrelated with any time-varying unobserved determinants of genuine wealth per capita; this assumption seems unlikely to hold given that reverse causality or omitted variables could trigger such endogeneity.

We have conducted a brief analysis with our sustainability measure finding that greater corruption and poorer female empowerment lead to lower genuine wealth per capita and therefore less sustainable development. Future work would look to implement a more detailed econometric investigation: addressing the additional endogeneity concern through an instrumental variables approach, using panel data instead and investigating other socioeconomic variables closely tied with sustainable development.

  1. Conclusion

This study has found that the chosen 29 Indian States have almost all experienced sustainable development over the ten-year period from 2003-2013. The definition of sustainability has rested on the concept of non-decreasing intergenerational well-being linked by Arrow et al (2012) to the measure of genuine wealth per capita adjusted for TFP. To calculate this measure we have computed the stocks (and their respective shadow prices) of various forms of capital: natural, human, health, reproducible and institutional.

Health capital is found to be the most dominant capital asset of a magnitude ten times at least greater than the next, whilst reproducible capital experienced the largest growth such that Hartwick’s rule (Hartwick, 1977) held comfortably. If, we had instead assumed hard sustainability however, sustainability would have been jeopardised as the value of natural capital per capita fell for all but four States. As expected human capital per capita increased steadily, given the improved educational standards in India in the 21st century. Furthermore, with the economic performance of India over the period, it is unsurprising to find that institutional or technological capital also improves on the whole. As an addition to simply measuring sustainability, analysis was also undertaken to understand the wider determinants of genuine investment through investigating the relationship between it and selected socio-economic variables. Although we could only find measures of corruption, female empowerment and certain control variables for one particular year within the ten-year period, the Hausman-Taylor model allowed (through controlling for random effects) for us to conclude that less corruption and greater female empowerment lead to greater sustainable development.

However, the genuine investment measure used should be taken with caution given the assumptions the theoretical framework rests upon, the methodologies employed, the feasibility of assigning non-market assets monetary value and the data limitations encountered. Yet, whilst there is the omission of important components, especially of natural capital (such as air and water stocks), the method still encompasses many of the economy’s key assets and determinants that are typically ignored in national accounts.

The results are favourable to Indis’a economic growth path in the 21st century; the country has largely achieved impressive rates of economic growth whilst remaining sustainable. This is most likely due to the post-industrial nature of the growth being tertiary sector led and its consequent increases in reproducible capital, as well as the investments and improvements in health and education. However, the loss of natural capital is still a cause for concern given that this is most definitely a lower bound estimate and that the principle of valuing such capital (particularly linearly) is very much debateable.


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[1] https://data.worldbank.org/indicator/SP.DYN.LE00.IN

[2] http://www.who.int/phe/health_topics/outdoorair/databases/cities/en/

[3] https://www.vox.com/energy-and-environment/2017/11/22/16666808/india-air-pollution-new-delhi

[4] https://yaleglobal.yale.edu/content/indias-population-becoming-number-one

[5] https://openknowledge.worldbank.org/bitstream/handle/10986/25078/9781464809583.pdf

[6] http://www.un-documents.net/ocf-02.htm

[7] Intertemporal social welfare is used in Arrow et al (2004), whilst intergenerational well-being is used in Arrow et al (2012); the two are equivalent and can be used interchangeably.

[8] This measure is intangible, so we proxy its change through TFP growth.

[9] They’re are by no means wrong; we require the assumption of weak sustainability after all in this framework.

[10] ‘GNA’ from hereon

[11] ‘Genuine investment’ is instead used in this study, although the two are equivalent. Genuine investment is a better term as we commonly think of savings in macroeconomics as being private savings, whereas here they refer to the sum of private and public savings (hence the equality between the two terms). (Neumayer, 2013)

[12] Although due to data limitations not all measures that form their measure of comprehensive wealth can be used (considerations of international trade, adjustments for carbon damages).

[13] They use the term ‘comprehensive’ in place of ‘genuine’ although the two are again equivalent.

[14] SEEA, a UN manual, arose as a result of the earlier cited Brundtland Commission Report, to adjust conventional national accounts for environmental damages (or improvements).

[15] This is known as bifurcation: “a situation where the characteristics of the natural system change fundamentally”.

[16] However, the issue with this approach is that the marginal cost remains fixed whilst the market price, for optimality, must rise.

[17] So, interpolated for the years not given.

[18] Social discount rate of 4% arises from the GAISP and is used throughout this study.

[19] 40 years was chosen as the average of the values used in the Monograph.

[20] Ideally would include technical qualifications, however IHDS didn’t contain data on such.

[21] For the older age cohorts insert Enrol = 0 to get the relevant formula

[22] Commonly estimated through wage differentials from jobs with different levels of risk to life.

[23] This measure is calculated using the Perpetual Inventory Method (the standard estimation strategy for reproducible capital), see GNA for further details.

[24] Due to a lack of data on State-State and (foreign) country-State asset holdings, we did not adjust estimates for a State’s net asset position,

[25] Due to space, the Tables only consider the years 2003 and 2013, however data on each year has been generated.

[26] A surprising finding, this is due to its health capital growing by the lowest rate of all States because of an already high life expectancy in 2003, relatively low population growth and ageing population.

[27] The GEM captures `Political Participation and Decision-making Power’, ‘Economic Participation and Decision-making Power’ and ‘Power over Economic Resources’.

[28] Both corruption and female empowerment have been scaled, such that the composite scores run from 0 to 10.

[29] For the components of these measures, see the appendix 2. Unfortunately, we couldn’t obtain a democracy measure as used by Aidt (2010)

[30] Including State dummy variables and time fixed effects (not shown on the regression output).

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