# «ENVIRONMENT AND DEVELOPMENT The Changing Wealth of Nations ENVIRONMENT AND DEVELOPMENT A fundamental element of sustainable development is ...»

———. 2010. World Development Report 2010: Development and Climate Change. Washington, DC: World Bank.

WRI (World Resources Institute). 2009. “CAIT: Indicator Framework Paper.” World Resources Institute, Washington, DC.

## CHAPTER 5

** Intangible Capital and Development**

## IT HAS BEEN UNDERSTOOD SINCE AT LEAST THE TIME OF

Irving Fisher (1906) that income is the return on wealth. But if we scale up this idea to the level of the national economy, we arrive at a puzzle: if we measure wealth only as produced capital, we see from the national balance sheet accounts of countries such as Canada that wealth is only a small multiple of gross national income (GNI). This implies unrealistically high implicit rates of return on wealth.** Table 5.1 shows Canadian figures for 2009.**

The value of produced capital is less than three times GNI, while net worth (which includes commercial land and net financial assets) is a bit less than four times GNI. The implicit rates of return on wealth are correspondingly high, 35.9 percent and 25.4 percent respectively. Canadians appear to be a very productive bunch.1 The “solution” to this puzzle, of course, is that the national balance sheet accounts of the System of National Accounts (SNA) exclude values for many intangible assets, such as human capital and social/institutional capital.2 Moreover, the Canadian balance sheets highlighted in table 5.1 exclude the value of commercial natural resources.3 Since a “normal” rate of return on assets should be on the order of 5 percent, a comprehensive measure of national wealth should be approximately 20 times national income. The gap between such a measure

## 94 THE CHANGING WEALTH OF NATIONS

of comprehensive national wealth and the SNA balance sheet value is what we have termed intangible capital.

However, there is a risk that the intangible capital estimates derived in this book are simply a black box. We therefore revisit the analysis of the composition of intangible capital presented in chapter 7 of Where Is the Wealth of Nations?

(World Bank 2006), bringing to bear our new wealth accounts for 1995, 2000, and 2005. We extend this analysis by exploring the role of intangible capital in production. But we begin by presenting the theoretical underpinnings of the measure of total wealth and intangible capital.

Theoretical Considerations As documented in appendix A, total or comprehensive wealth is measured as the present value of future consumption, and intangible wealth is the residual derived by subtracting physical, natural, and net financial assets from total wealth. It is therefore important to understand in some detail how the total wealth estimates are derived.

Hamilton and Hartwick (2005) show how to estimate a comprehensive measure of national wealth for a competitive economy with constant returns to scale. For production function F F(K, L, R) with factors K (produced capital), labor L, natural resource flow R, and interest rate r, comprehensive wealth is given by

That is, comprehensive wealth can be measured either by adding up asset values K, H (human capital), and S (the value of the natural resource stock), or by measuring the present value of consumption C along the competitive development path. The intuition behind this result is clear: future consumption must be bounded by current wealth.

## INTANGIBLE CAPITAL AND DEVELOPMENT 95

To apply expression (5.1) we have to make assumptions about future consumption growth and the discount rate. To choose the discount rate we apply the Ramsey formula, which tells us how much a consumer would need to be compensated for deferring a unit of consumption from the current period to the next period. This is given by** r g, (5.2)**

where is the pure rate of time preference, is the elasticity of the marginal utility of consumption, and g is the growth rate of per capita consumption.

The discount rate is therefore the sum of the rate of impatience plus the rate of change of the marginal utility of consumption. If,, and g are constant, then expression (5.1) reduces to

Empirical estimates of are typically small (Pearce and Ulph 1999), on the order of 1–2 percent, while for they typically range from 1 to 2. However expression (5.3) implies that for 1, total wealth is a decreasing function of the growth rate of future consumption, a counterintuitive result. Based on this analysis, we therefore choose equal to 1.5 percent and equal to 1 in order to calculate total wealth.

As seen in expression (5.1), the underlying growth theory assumes an infinite lifetime for the analysis. As a practical matter, we have chosen to carry out the wealth accounting on a generational basis, assuming a maximum lifetime for all assets of 25 years. Our total wealth estimates are therefore calculated as the present value of the current level of consumption (held constant), taken over 25 years and discounted at the pure rate of time preference, 1.5 percent. We assume an optimistic future rate of per capita consumption growth of 2.5 percent (historical values are typically less than 1.5 percent), so that our calculated interest rate using the Ramsey formula is 4 percent.

Given these parameter choices, the logical next question is whether the resulting total wealth estimates are “reasonable.” We define reasonability in terms of the implicit rate of return on wealth, as we did in the discussion of table 5.1. To test this we derive the following additional result from Hamilton and Hartwick (2005): if interest rate r is constant, is the depreciation rate for produced capital, and FRR is the value of resource depletion, then net income is

**just equal to the return on total wealth. That is:**

** FIGURE 5.1 Distribution of Implicit Rates of Return on Comprehensive Wealth, 2005 number of countries —.**

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.0.0.0.0.0.0.0.0.0.0.0

Source: Authors’ calculations.

We use data from the World Bank’s World Development Indicators (2010) to calculate net income and then apply expression (5.4) in order to derive the implicit rate of return on comprehensive wealth in each country. The distribution of rates of return across countries is plotted in figure 5.1, which shows that 80 percent of the rates lie between 4 percent and 6 percent.

As this discussion makes clear, calculating a value for total wealth involves questions of judgment, including the choice of the pure rate of time preference, the elasticity of the marginal utility of consumption, and the lifetime over which present values are calculated. Alternatives to the choices we have made are clearly possible, but the calculation of the implicit rate of return on wealth provides an essential reality check for any total wealth estimates that result.

Finally, another caveat. Since intangible capital is measured residually, it implicitly includes all “missing” asset values. For example, since data on the value of diamond and fishery resources are not widely available, these natural assets are implicitly (and erroneously) included as part of the intangible capital for countries where these resources are important.

Explaining Intangible Capital Chapter 7 of Where Is the Wealth of Nations? (World Bank 2006) attempted to open the black box of intangible capital by analyzing the extent to which other factors could explain the total variation in intangible capital across countries.

## INTANGIBLE CAPITAL AND DEVELOPMENT 97

The factors chosen—measures of human capital and institutional/social capital— were selected on the basis of their plausibility as constituents of intangible wealth.Where Is the Wealth of Nations? estimated the composition of intangible wealth based upon a cross-sectional dataset of wealth estimates for the year 2000. This analysis had a number of limitations imposed by the cross-sectional nature of the data: in particular, there could be omitted variables relating to fixed country characteristics or to common shocks at a point in time that affect all countries.

In addition, the analysis used a particular functional form (Cobb-Douglas) to carry out the decomposition, without sufficient discussion of the underlying theory of wealth accounting. Finally, the measure of human capital used in the analysis, average years of schooling per capita, did not account for declining marginal returns to education or for the quality of human capital. In this chapter we address all of these shortcomings.

Marking an advance since the 2006 work, we now have a panel dataset with observations for 115 countries for the years 1995, 2000, and 2005. This permits the use of country and time fixed effects, which in turn helps mitigate omitted variable bias as long as the unobserved variables are constant over time and/or across countries.

With regard to measuring human capital, the current consensus approach in the literature uses a log-linear relationship between earnings and years of schooling, first formulated by Mincer (1974). It expresses the human capital per worker h as an exponential function of years of schooling, h e (s), where the function (s) represents the efficiency of a unit of labor with s years of schooling relative to one with no schooling. We follow common practice and use (s) s, where is the rate of return to education. Our benchmark is 8.5 percent return on years of schooling, as in Klenow and Rodríguez-Clare (1997, 2005). This is the average of returns to education in Psacharopoulos and Patrinos (2004). Our estimates of years of schooling per worker are from Barro and Lee (2001).

Next, we augment our indicator of human capital to account for the health of the population and of the workforce, based on the analysis by Caselli (2005), who introduces adult survival rates (equal to 1 minus the mortality rate for individuals between the ages of 15 and 60) as a proxy for health status. Shastry and Weil (2003) argue that differences in health status proxied by adult mortality rates map into substantial differences in energy and capacity for effort. For adult survival rate a we therefore calculate quality-adjusted human capital as

Adult survival rates are available in consistent form for a large cross-section of countries from World Development Indicators (World Bank 2010), while Weil (2007) estimates a value of = 0.653.

## 98 THE CHANGING WEALTH OF NATIONS

Turning to institutional quality, we follow Where Is the Wealth of Nations? in using a rule of law index from Kaufmann, Kraay, and Mastruzzi (2009) as the proxy measure. This index measures the extent to which agents have confidence in and abide by the rules of society. In particular, it measures the quality of contract enforcement, property rights, the police, and the courts, as well as the likelihood of crime and violence.4 The next issue is the functional form for estimating the constituents of intangible capital. The most parsimonious model is provided by expression (5.1). The underlying growth theory shows that total wealth (the present value of future consumption) is simply the sum of the different assets owned by a country. This**suggests a linear model specification for decomposing intangible capital:**

icit h wit. (5.6) i t h it w it Here ic is intangible capital, i is the country fixed effect, t is the time dummy, h is human capital, and w is the rule of law.

In estimating expression (5.6) we use three different models: (a) pooled data (no fixed effects or time dummies) with income dummies5 and human capital measured by years of schooling; (b) pooled data with income dummies and human capital measured as in expression (5.5); and (c) panel data with fixed effects, time dummies, and human capital measured as in expression (5.5).

The results of the estimation (the values of coefficients h and w) are shown in table 5.2.6 The first column in table 5.2 bears a strong resemblance to the results in Where Is the Wealth of Nations (World Bank 2006 chapter 7, table 7.4). A oneunit increase in the rule of law index (out of a possible 100 units) yields $3,000 of intangible wealth, while one additional year of schooling per capita yields $11,025. The second model uses the human capital index rather than years of

schooling. This index compresses the human capital scale, as shown in expression (5.5). In both models the rule of law index coefficient is statistically significant and close to $3,000. In the fixed effects model the rule of law index becomes insignificant, while the coefficient on human capital doubles and the time dummy (for 2005 relative to 1995) is positive and significant.

The results shown in table 5.2 require careful interpretation. With the theoretically preferred specification of human capital based on expression (5.5), the pooled data model shows that both human capital and institutional quality (proxied by the rule of law index) are statistically significant components of intangible wealth. However, the fixed effects model is preferred because it controls for unobserved variable bias.7 With this specification, rule of law ceases to be a significant determinant of intangible capital. This suggests that the country fixed effects in expression (5.6) are picking up the effects of institutional quality, which makes sense given the short time span involved; institutional quality likely did not vary that much from 1995 to 2005. But the country fixed effects are also picking up other important endowment effects, potentially including geography and history. The data do not permit us to dig deeper into these other constituents.

The other point to note in table 5.2 is the large coefficient on the passage of time from 1995 to 2005, over $10,000. This coefficient of time is typically considered to be a proxy measure of technical progress. The table can therefore be interpreted as saying that there is evidence for a considerable increase in intangible wealth per capita associated with technological change.