metadata: authors: 0: author: Markandya,Anil
1: author: Pedroso-Galinato, Suzette
count: World
docna: 0: docna: How substitutable is natural capital ?
docty: Policy Research Working Paper
subtopic: Construction Industry,Common Carriers Industry,Food & Beverage Industry,General Manufacturing,Pulp & Paper Industry,Plastics & Rubber Industry,Coastal and Marine Resources,International Trade and Trade Rules,Energy Demand,Energy and Environment,Energy and Natural Resources,Energy and Mining,Business Cycles and Stabilization Policies,Global Environment
teratopic: Macroeconomics and Economic Growth,Environment,Finance and Financial Sector Development,Poverty Reduction
abstracts: cdata!: One of the recurring themes in the
            sustainability literature has been the legitimacy of using
            an economic framework to account for natural resources. This
            paper examines the potential for substituting between
            different inputs in the generation of income, where the
            inputs include natural resources such as land and energy
            resources. A nested constant elasticity of substitution
            (CES) production function is used to allow flexibility in
            the estimated elasticities of substitution. Also, with this
            specification, natural resources and other inputs are
            combined in different levels of the function, thus allowing
            for different levels of substitutability. Institutional and
            economic indicators are also incorporated in the production
            function estimated. Results show that the elasticities
            derived from functions involving land resources were
            generally around one or greater, implying a fairly high
            degree of substitutability. Furthermore, changes in trade
            openness and private sector investment have a statistically
            significant and direct relationship with income generation.
            No statistically significant relationship between income and
            any of the institutional indicators was found.
repnme: repnme: How substitutable is natural capital ?
display_title: How substitutable is natural capital
listing_relative_url: /research/2006/01/6523016/substitutable-natural-capital
topicv3: Natural Resources m1326446 1979,Manufacturing Sectors m1326521 1281,Energy and Extractives m1326595 507,Trade m1326924 698,Environment, Natural Resources and Blue
            Economy m1327391 566
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Environment,Finance and Financial Sector Development,Poverty Reduction
no_of_pages: 20
author_keys: 0: author_key: 321136
model_extractions: WPS3803

# **How Substitutable Is Natural Capital?**<sup>**1**</sup>

**Anil Markandya FEEM, The World Bank and University of Bath**

## **Suzette Pedroso-Galinato The World Bank**

### World Bank Policy Research Working Paper 3803, December 2005

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they represent. Policy Research Working Papers are available online at http://econ.worldbank.org._

> 1 This paper is drawn from a larger study on the ‘Where is the Wealth of Nations?’ (World Bank, 2005a).  We wish to thank Giovanni Ruta, Kirk Hamilton, Giles Atkinson and a number of others who have provided useful comments on earlier drafts.
2

# **Abstract**

One of the recurring themes in the sustainability literature has been the legitimacy of using an economic framework to account for natural resources. This paper examines the potential for substituting between different inputs in the generation of income, where the inputs include natural resources such as land and energy resources. A nested constant elasticity of substitution (CES) production function is used to allow flexibility in the estimated elasticities of substitution. Also, with this specification, natural resources and other inputs are combined in different levels of the function, thus allowing for different levels of substitutability. Institutional and economic indicators are also incorporated in the production function estimated. Results show that the elasticities derived from functions involving land resources were generally around one or greater, implying a fairly high degree of substitutability. Furthermore, changes in trade openness and private sector investment have a statistically significant and direct relationship with income generation. No statistically significant relationship between income and any of the institutional indicators was found.
# **I.  Background**

One of the recurring themes in the sustainability literature has been the legitimacy of using an economic framework to account for natural resources. Those critical of such an approach contend that wealth accounting assumes natural resource assets can be substituted by produced assets, such as human and physical capital, on a dollar for dollar basis. This, they argue, does not capture the limited degree to which such substitution is possible. A loss of some natural capital, such as an entire ecosystem, surely cannot be made up with an increase in physical capital if the very basis of social existence and well-being are destroyed in the areas affected by that system. This makes them skeptical of the kind of wealth accounts we are constructing here.

While we cannot hope to disentangle the full set of issues embedded in this line of reasoning, we can at least start by focusing on the degree of substitutability between the different assets. Underlying any wealth accounts is an implicit ‘production function’ which is a blueprint of the combinations of different assets with which we can achieve a given level of output. These blueprints are usually written as a mathematical function, which describes the precise relationship between the availability of different amounts of ‘inputs’, such as physical and human capital services, and the maximum output they could produce. The substitutability between inputs is then measured as an ‘elasticity of substitution’. In general terms, this captures the ease with which a decline in one input can be compensated by an increase in another, while holding output constant. More precisely, it measures how much the ratio of two inputs (e.g. physical capital and land) changes when their relative price changes (e.g. the price of land goes up relative to the price of capital)<sup>2</sup> . The greater the elasticity, the easier it is to make up for the loss of one resource by using another. Generally, an elasticity of less than one indicates limited substitution possibilities.

A commonly used production function, which implies elasticities of one between the inputs, is the ‘Cobb-Douglas’ form, written as: Income or output (Y) is expressed as a function of the levels of capital input (K), labor input (L), an exogenous technological factor (A) and the parameters α and β , which give the returns to capital and labor respectively. If the national production options could be captured by such a function, with natural capital services included, it would have considerable implications for sustainability. First, it would imply a degree of substitutability between natural and produced capital that would give some comfort to those who argue we can lose some natural capital without seriously compromising our well-being. Related to that it would validate the ‘Hartwick Rule’, which states that when exploiting natural resources you should ensure you save an amount equal to the rent from those resources if you are to sustain the highest possible level of consumption (Hamilton, 1995). This so-called ‘Hartwick Rule’ is a useful sustainability policy since it is open to monitoring – we can check whether or not it has been adhered to.

> 2 Where prices are not defined, we measure the change in the ratio of the inputs resulting from a change in the marginal rate at which one factor can be substituted for another (Chiang, 1984).   The discussion is complicated by the fact that there are other definitions of substitution in the literature.  We discuss this further below.
4 Economists have devoted a considerable amount of effort to estimating these elasticities, for inputs such as capital, labor and energy but **not** natural resources. Although, starting in the 1970s, there were theoretical studies that modeled neoclassical economic growth with nonproduced capital such as natural resources as factors in production (e.g., Stiglitz, 1974a,b; Mitra, 1978)<sup>3</sup> ; the empirical estimation of the underlying production functions was never carried out, largely because of a lack of data.

This paper is a preliminary attempt in that direction. It is part of a larger study undertaken by the Bank on the Wealth of Nations (World Bank, 2005a). In that study, a database of new wealth estimates has been developed which includes both produced and non-produced capital – renewable and non-renewable resources, and human resources. This allows us to estimate a production function that includes the services from these different resources as inputs. This paper examines therefore the economic relationship between total wealth and income generation and takes advantage of the new wealth estimates to estimate a production function based on a larger set of assets. Section II briefly discusses the definitions of elasticities and describes related studies on substitution between different inputs, including natural resources. Section III presents the estimation of the production function and Section IV concludes.

# **II.  Definitions of elasticities and results of earlier studies**

The definition of an elasticity of substitution given at the beginning of this paper applies unambiguously when there are only two inputs. With more than two inputs, however, the generalization depends on what is assumed constant when the changes in the inputs of interest are being calculated. The issues are familiar to economists – a summary can be found in Kang and Brown (1981). Based on work by Morishima, they define a ‘full elasticity of substitution between inputs ‘i’ and ‘j’ as _Fij_ where: _Xi_ and _Xj_ are levels on inputs ‘i’ and ‘j’ respectively. They are two of the ‘n’ inputs that go into producing output Y, as represented by the production function: and

> 3 A bibliographical compilation of studies can be found in Wagner (2004).  One exception to the observation that there is little empirical work is Berndt and Field (1981), who did look at limited natural resource substitution between capital, labor, energy and materials. The studies generally found low elasticities between capital and materials.  They did not, however, look at land as an input in the way we do here.  Nor did they work with national level data.
5 Unfortunately, not all studies report this full elasticity of substitution (Equation 2), which corresponds more closely to the concept of substitutability that we are interested in. More commonly the ‘Allen’ partial elasticity is reported, which, for inputs ‘i’ and ‘j’ is given by _Aij_ : where _sj_ is the share of total cost of production represented by input ‘j’ and _pj_ is the price of input _j_ . Readers will recognize _Aij_ as the weighted cross price elasticity of demand for input ‘i’ with respect to the price of input ‘j’. Kang and Brown ( _op. cit.)_ cite the result from Morishima which relates the full elasticities of substitution to the Allen elasticities as follows: _Eij_ is the simple unweighted cross price elasticity of demand for input ‘i’ – it gives the proportional change in the use of input ‘i’ for a proportional change in the price of input ‘j’. Given that in almost all conditions the own price elasticity ( _Ejj_ ) is negative, the full elasticity of substitution will be greater than the corresponding direct price elasticity. The relationship between the Allen and the Full elasticity is less clear but, as we will see below, the latter are typically smaller than the former.

In the simple case of two inputs, we note that the full elasticity of substitution cannot be negative. A negative elasticity of substitution is economically nonsensical – it implies that a decline in the availability of one input can be ‘made up’ by a decline in the availability of other factors. With more than two inputs it is theoretically possible for this elasticity to be negative but such a case is highly unlikely. It would require the cross price elasticity between two inputs to be negative (indicating they are complements) **and** to be greater in absolute value than the own price elasticity. Taking capital and natural resource inputs as an example, a negative full elasticity would imply that a one percent increase in the price of the natural resource would reduce inputs of that natural resources by a smaller percent than it decreased the inputs of capital. Note also that by the relation defining _Fij_ , the full price elasticity between ‘i’ and ‘j’ is not the same as that between ‘j’ and ‘i’ – i.e. _Fij ≠ Fji._ Estimates of the elasticities of substitution are either reported as Allen elasticities or Full elasticities but rarely both. Kang and Brown ( _op. cit.)_ have calculated the Full elasticities for some studies where the Allen elasticities are reported. Table 1 gives what estimates are available and indicates which elasticity has been reported.

Previous studies demonstrate Full elasticities that are considerably lower than the Allen elasticities. Moreover, they are almost all positive and less than one. The one exception is the Hudson and Jorgensen (1974) study which suggests that the capital-energy elasticity could be negative. As that study estimates the own price elasticity for energy to be positive, we can probably discount it.
6 The other result that has attracted a lot of attention is the difference between those studies that find capital and energy as complements (Allen elasticity is negative) and those that find the two factors as substitutes (Allen elasticity is positive). The differences between these studies have been attributed to a number of factors: use of time series versus cross-section data (Griffin, 1981), response of output to changes in relative prices (Solow, 1987), and different methods of aggregating capital (Garofalo and Malhotra, 1988).

We also note that there is little information in existing studies on the substitutability between natural resources and other inputs. The Parks (1971) study looks at different inputs used in manufacturing, including materials from the agricultural sector, capital and labor. In terms of Allen elasticity, the author finds a complementarity between capital and agricultural inputs, and a substitutability between agricultural inputs and labor. We could not recover the full elasticity but it is likely to be low. The Moroney and Trapani (1981) study finds substitutability between the inputs, labor and exhaustible mineral resources, in mineral-intensive production processes. The two studies are not comparable; nor do they really throw much light on the substitutability issues we are discussing here.

More recent studies have focused on the substitution between energy and another input, such as labor or capital, using the same definition of elasticity that we employ. Manne and Richels (1992) and Chang (1994) estimated the substitution possibilities between the ‘capital and labor nest’ and energy to be about 0.4; while Kemfert (1998) estimated the same to be about 0.5. On the other hand, Prywes (1986) found the substitution elasticity between the ‘capital and energy nest’ and labor to be less than 0.5. These studies use the variables capital, labor and energy as relating to stock of fixed assets, skilled and unskilled labor, and final energy consumption, respectively.

# **III. Estimation of Nested CES production function**

# **A.  The Nested CES production function and variables**

The estimation carried out here uses national level data on Gross National Income (GNI) or economic output and sees the extent to which variations in GNI across countries at any point in time can be explained in terms of the national availability of produced capital, human resources and natural resources (energy and land resources). A Cobb-Douglas production function of the form shown above is not appropriate for this estimation because it restricts the elasticity between factors to be one. In fact, one of our objectives is to estimate the elasticity of substitution between factors or groups of factors. A form that holds the elasticity constant but allows it to take values different from one is the ‘constant elasticity of substitution’ (CES) production function. In particular, this paper uses a **nested CES** production function. For example, a two level nested CES with three inputs takes the form:<sup>4</sup>

> 4 This model makes the further assumption of ‘homothetic weak separability’ for groups of inputs. _Homothetic weak separability_ means that the marginal rate of substitution between inputs in a certain group is independent of output and of the level of inputs outside that group (Chiang, 1984)
7 where _X_ is the gross output; _A, B_ and _C_ are inputs; and _XAB_ represents the ‘joint contribution’ of _A_ and _B_ to production. The first level of the estimation involves _A_ and _B_ ; while the second level models the production of output by _XAB_ and _C_ . A special feature of the nested CES function is that the elasticity of substitution between the first level inputs A and B can be different from the elasticity of substitution between the second level inputs XAB and C. In other words, by placing natural resources and other inputs in different levels of the function, we effectively allow for different levels of substitutability. So, for example, natural assets may be critical (low substitutability) while other inputs are allowed to be more substitutable among themselves.

In this paper we use related variables to estimate aggregate national level production functions. The variables used are<sup>5</sup> :

- a. _Produced capital (K)_ is an aggregate of equipments, buildings and urban land;

- b. _Human capital (H)_ has two alternative measures: human capital, which relates educational attainment with labor productivity (HE); or intangible capital residual (HR), which is obtained as the difference between a country’s total wealth and the sum of produced and natural assets. Part of the intangible capital residual captures human capital in the form of raw labor and stock of skills.  For further discussion of this variable and its rationale see World Bank (2005a; particularly, Chapter 3 and Chapter 10);

- c. _Production and net imports of non-renewable energy resources (E)_ includes oil, natural gas, hard coal and lignite<sup>6</sup> .

- d. _Land resources (L),_ which refer to the aggregated value of crop land, pasture land and protected areas.  Land is valued in terms of the present value of the income it generates rather than its market value.

The gross national income (GNI) and all inputs mentioned above are measured in per capita values at 2000 prices and are taken at the national level for 208 countries. GNI data are obtained from the World Development Indicators (World Bank, 2005). HE is derived based on the work by Barro and Lee (2000); while the remaining variables, K, HR, E and L are the components of wealth as described in World Bank, 2005a (Chapter 3).

The relationships of the production inputs to income are expressed in nested CES production functions described in the Annex. Three different nested CES approaches are examined – (a) one-level function, with two inputs; (b) two-level function, with three inputs; and (c) three-level function with four inputs. The combinations of the variables in the different CES approaches were varied to further investigate any possible differences among substitution elasticities for pairs of inputs.

The production function approach taken so far neglects an important set of factors that influence differences in national income. These relate to the efficiency with which productive

> 5 Per capita dollar values at nominal 2000 prices.

> 6 For energy it would be inappropriate to take the stock value of the asset, as what is relevant for production is the flow of energy available to the economy.  This is given by production plus net imports.  With the other assets (K, H and L) it is also the flow that matters but it is more reasonable to assume that the flow is proportional to the stock. We do note, however, in the conclusions that even this assumption needs to be changed in future work.
8 assets are utilized and combined and include both institutional as well as economic factors. In this study, we consider the following institutional indicators, which capture the efficiency with which production can take place; as well as economic indicators, which also capture the efficiency of economic organization:

- a. _institutional development indicators_ - indices on: voice and accountability (VA); political instability and violence (PIV); government effectiveness (GE); regulatory burden (RB); rule of law (RL) and control of corruption (CC). An increase in a given index measures an improvement in the relevant indicator. Hence, they are expected to have a positive impact on income and possibly growth.  These indicators were estimated by Kaufmann, et al, 2005.<sup>7</sup>

- b. _economic indicators_ - trade openness (TOPEN) is calculated as the ratio of exports and imports to GDP (World Bank, 2005b); and the country’s domestic credit to the private sector as proportion of GDP (PCREDIT), which represents private sector investments (Beck, _et al._ , 1999)<sup>8</sup> .

Two methods of incorporating the impact of these institutional and economic indicators were investigated. The first method involved the derivation of residuals from the regression of a nested CES production function. The residuals are the part of income not explained by the wealth components – physical capital, human capital, land resources and energy resources, and are regressed on the identified institutional and economic indicators. By using this method, however, a statistically significant correlation between the residuals and any indicator would imply that relevant variables have been omitted in the estimation of the nested CES production function. Thus, the estimated coefficients of the nested CES production function earlier derived will be biased and inefficient (Greene, 2000). Hence, another method is considered to be more appropriate. The influences of the institutional and economic indicators on income will be incorporated into the efficiency parameter of the production function, _A_ (see Annex).

Depending on the available data for the variables of the nested CES production function, the number of countries drops in the range of 67 to 93 countries. For a given nested CES approach, the reduction is caused by considering only those countries that have non-missing observations for their corresponding dependent and explanatory variables (i.e., _complete case method_ ).<sup>9</sup>

> 7 Data can be obtained from the website: _http://www.worldbank.org/wbi/governance/pubs/govmatters4.html_ . 8 Hnatkovska and Loayza (2004) use openness and credit as a measure of financial depth, which they find to have a positive impact on growth. Data for this indicator can be obtained from the following website: _http://www.worldbank.org/research/projects/finstructure/database.htm_ .

> 9 An “imputation method” was tried to fill the missing values for some of the countries to keep all 208 countries in the estimation. Most of the results, however, were not found to be reasonable.  For example, the imputed value of physical capital for a low income country turned out to be too high compared to the average value of physical capital of its income group.  Hence, the imputation method was not used since it poses more problems in the estimates than using the _complete case method_ .
9

# **B.  Regression results**

The nested CES production functions are estimated using a non-linear estimation method.<sup>10</sup> The sample size in each CES approach differs because countries with missing observations in any of the variables had to be dropped. Table 2 shows the estimated substitution elasticities corresponding to the case where human capital is part of the measured intangible capital residual (HR). All the statistically significant substitution elasticity estimates have a positive sign, which is encouraging. The lowest is that between K and E at 0.37 in the threelevel production function. It is also interesting to note that most of the significant elasticities of substitution are close to one.

A second round of regressions was carried out using the other measure of human capital that is related to schooling and labor productivity, HE. Table 3 shows the statistically significant elasticities of substitution, which also have a positive sign. A substitution elasticity approximately equal to 1 is likewise found for most of the nested functions.

The results provide some interesting findings. First and foremost, there is no sign that the elasticity of substitution between the natural resource (land) and other inputs is particularly low. Wherever land emerges as a significant input, it has an elasticity of substitution approximately equal to or greater than one. Second, by and large, the HE variable performs better in the estimation equations than the HR variable. Third, the best determined forms, with all parameters significant are those using HE, involving four factors and containing the following combinations: (a) K, HE and L are nested together and then combine with E; or (b) K, HE and E are nested together and then combine with L.<sup>11</sup> It is hard to distinguish between these two versions and so they are both used in the further analysis reported below.

From the nested CES production function estimations, the elasticity estimates of the institutional and economic indicators can be derived. Table 4 and Table 5 show the results for the four-factor production functions: [(K,HE,L)/E] and [(K,E,HE)/L] of Table 3, respectively. In both Tables, the variables on trade openness and private sector investment are found to be statistically significant. The elasticity estimates of these two variables are not very different from each other. The results imply that for every percent increase in trade openness, gross national income per capita increases by approximately 0.5 percent. None of the institutional indicators, on the other hand, has a statistically significant elasticity estimate.<sup>12</sup>

> 10 See Annex for more details.

> 11 “Inputs nested together” refers to the joint contribution of these inputs to the production of output, as indicated in Section III of this paper.

> 12 In the regression where the ‘residuals’ are expressed as a function of the institutional variables, we did find significant values for a few institutional variables, especially the rule of law, which was encouraging as that variable also emerges as important in other evaluations of inter-country differences in the World Bank (2005a) study. Unfortunately, the result did not hold when the more appropriate method was used.
10

# **C.  Simulation**

The predicted value of the dependent variable can be calculated by using the estimated coefficient estimates of the production function and the mean values of the explanatory variables. Through this method, we try to predict what will happen to the economic output (per capita GNI or GNIPC) if there is significant natural resource depletion. The natural resource considered in this exercise is “land resources (L)” and the four-factor nested CES production functions used are: [(K,HE,L)/E] and [(K,E,HE)/L] of Table 3. Table 6 presents the predicted average GNIPC as well as the change in GNIPC given a reduction in the amount of land resources, _ceteris paribus_ . Based on the production function [(K,HE,L)/E], economic output is reduced by 50 percent when the amount of L declines by about 92 percent, while holding other variables constant. For the production function [(K,E,HE)/L], on the other hand, it takes a reduction in the amount of L by about the same percentage, _ceteris paribus_ , to halve the economic output relative to the baseline.

# **IV. Conclusions**

In this paper we looked at the potential for substituting between different inputs in the generation of GNI. Among these are land resources, one of the most important natural resources. The estimation of a well-known production function form, which allows the elasticities of substitution to be different from one, was carried out. The resulting elasticities involving land resources (between L and other inputs such as physical capital, human capital and energy resources) were generally around one or greater, which implies a fairly high degree of substitutability. Moreover, it validates the use of a ‘Hartwick Rule’ of saving the rents from the exploitation of natural resources if we are to follow a maximum constant sustainable consumption path.

There are, of course, many caveats to this result. Land resources, as measured here include crop land, pasture land and protected areas. Each has been valued in terms of the present value of the flow of income that it generates. Such flows, however, under-represent the importance of protected areas for example, which provide significant non-monetary services, including ecosystem maintenance services that are not included. Further work is needed to include these values, and if this were done, and if the GNI measure were adjusted to allow for these flows of ‘income’, the resulting estimates of substitution elasticities might well change. We intend to continue to work along these lines and to improve the estimates made here.

Another shortcoming of the method applied here is the limited number of factors included in the original estimation. Generating national income depends not on the stock of assets but the amounts of the stocks that are used in production and the way in which they are used. For physical and human capital and land, we assume the rate of use is proportional to the stock. That assumption should be improved on, to allow for different utilization rates.

The treatment of institutional factors can also be improved. In this version, they are assumed to affect the overall efficiency of production rather than the efficiency of specific inputs, such as capital and labor. A modified estimation equation in which K, L and HE were
11 differently affected by different institutional factors would probably find greater significance for these factors than we have.

Finally, the paper also examined how the institutional and economic indicators will affect the generation of GNI. Estimation results show that income generation is significantly influenced by changes in trade openness and private sector investment. The institutional indicators, however, have no statistically significant impact on income generation.
12

# **Table 1: Estimates of elasticities of substitution in previous studies**

|**Inputs**|**Estim**<br>|**ates**<br>|**Study**|
|---|---|---|---|
||**Allen Elasticity**|**Full Elasticity**||
|Capital and natural<br>resourceinputs|-0.82<br>(0.47;1.08)<sup>a</sup>|-<br>-|Parks (1971)<br>Moroney andTrapani(1981)|
|Labor and natural<br>resourceinputs|0.90<br>(0.63 to1.33)<sup>b</sup>|-<br>-|Parks (1971)<br>Moroney andTrapani(1981)|
|Capital and Labor|0.12<br>1.09<br>1.01<br>(.06 : 0.39)<br>(0.60 : 0.95)<br>0.88<br>-|-<br>(0.56 : 0.74)*<br>-<br>(0.17 : 0.19)*<br>-<br>-<br>0.82**|Parks (1971)<br>Hudson and Jorgenson (1974)<br>Brendt and Wood (1979)<br>Griffin and Gregory (1976)<br>Moroney and Trapani (1981)<br>Prywes (1986)<br>Kemfert (1998)|
|Capital and Energy|-1.39<br>-3.22<br>1.03: 1.07<br>-1.35<br>2.17<br>-|(-0.09 : 0.24) *<br>0.26**<br>(0.33 : 0.92)*<br>-<br>0.87**<br>0.65**|Hudson and Jorgenson (1974)<br>Brendt and Wood (1979)<br>Griffin and Gregory (1976)<br>Prywes (1986)<br>Chang (1994)<br>Kemfert (1998)|
|Labor and Energy|2.16<br>0.65<br>(0.84 : 0.87)<br>0.88<br>0.35|-<br>-<br>-<br>-<br>-<br>0.42**|Hudson and Jorgenson (1974)<br>Brendt and Wood (1975)<br>Griffin and Gregory (1976)<br>Prywes (1986)<br>Chang (1994)<br>Kemfert (1998)|
|Labor and Capital<br>‘nest’ and Energy|-<br>-|0.40**<br>0.42**<br>0.50**|Manne and Richels (1992)<br>Chang (1994)<br>Kemfert (1998)|

The figures are rounded off to the nearest hundredth.

Unless stated otherwise, the elasticities above are calculated for the aggregate of the industry. Energy – the variable refers to total energy consumption a The given Allen elasticities are statistically significant only for two industries: primary aluminum and blast furnaces/basic steel, respectively.

b A range is given to cover the estimated elasticities for 4 of the 6 industries studied: primary aluminum, blast furnaces/basic steel, storage batteries and hydraulic cement.

(*) The full elasticity was calculated by Kang and Brown (1981)

- (**) The full elasticity was calculated by the authors

Study focus and estimation method: Parks (1971): Swedish manufacturing industry; Generalized Leontief Function Moroney and Trapani (1981): Mineral-intensive manufacturing industries; Translog cost model Hudson and Jorgenson (1974): U.S. manufacturing sector; Translog cost function Berndt and Wood (1979): U.S. manufacturing sector; Translog cost function Griffin and Gregory (1976): U.S. and U.K. manufacturing sectors, respectively; Translog cost function Prywes (1986): Manufacturing sector; Nested CES estimation. Manne and Richels (1992): Manufacturing sector; Nested CES Chang (1994): Taiwan manufacturing industry (aggregate); Nested CES and Allen elasticities of substitution Kemfert (1998): German manufacturing industry (aggregate); Nested CES
13 ˆ **Table 2: Substitution elasticities** (σ _i_ ) **, using intangible capital residual (HR)**

||**Inputs**|**Substitu**|**tion elasticity**|**R-squared**|**Adj. R-**|**Sample**|
|---|---|---|---|---|---|---|
|||_i_<br>σˆ|**Standard**||**squared**|**size**|
|**A. T**|**wo factors (One lev**|**el CES prod**|**error**<br>**uction function)**||||
|**(1)**|K/HR|1.00*|3.88E-10|0.9216|0.9131|93|
|**(2)**|K/E|-0.48|2.02|0.9958|0.9951|78|
|**B. T**|**hree factors (Two le**|**vel CES pr**|**oduction function**|**)**|||
|**(1)**|(K,HR)/L|||0.9375|0.9290|93|
||� K/HR<br>|6.79|13.92||||
||� (K,HR)/L<sup>1</sup>|1.00*|4.33E-10||||
|**(2)**|(K,HR)/E|||0.9089|0.8916|70|
||� K/HR|-0.78|1.31||||
||� (K,HR)/E<sup>1</sup>|1.00*|5.37E-10||||
|**(3)**|(K,E)/HR|||0.87667|0.8533|70|
||� K/E|0.65|0.69||||
||�(KE)/HR<sup>1</sup>|100*|396E-09||||
|**C. F**|, <br>**our factors (Three l**|. <br>**evel CES pr**|.<br>**oduction functio**|**n)**|||
|**(1)**|(K,HR,L)/E|||0.3435|0.1911|70|
||� K/HR|-0.90|0.70||||
||� (K,HR)/L<sup>1</sup>|0.97*|0.01||||
||� (K,HR,L)/E<sup>2</sup>|1.00*|5.46E-12||||
|**(2)**|(K,HR,E)/L|||0.9958|0.9951|78|
||� K/HR|-0.13|0.17||||
||� (K,HR)/E<sup>1</sup>|0.93*|0.18||||
||� (K,HR,E)/L<sup>2</sup>|1.00*|6.52E-09||||
|**(3)**|(K,E,HR)/L|||0.9350|0.9200|70|
||� K/E|0.37*|0.20||||
||� (K,E)/HR<sup>1</sup>|-0.64|0.55||||
||� (K,E,HR)/L<sup>2</sup>|1.00*|1.27E-09||||

Legend: K – physical capital; HR – intangible capital residual (captures raw labor and stock of skills); L – land resources; E – energy resources Notes: Inputs in parenthesis imply that they are nested. 1 two inputs in a nested function 2 three inputs in a nested function (*) denotes statistical significance at 5% level The substitution elasticities and their corresponding standard errors are rounded off to the nearest hundredth.
14 ˆ **Table 3: Substitution elasticities** (σ _i_ ) **, using human capital related to schooling (HE)**

||**Inputs**|**Substitu**|**tion elasticity**|**R-squared**|**Adj. R-**|**Sample**|
|---|---|---|---|---|---|---|
|||_i_<br>σˆ|**Standard**||**squared**|**size**|
|**A. T**<br>|**wo factors (One leve**<br>|**l CES prod**<br>|**error**<br>**uction function)**<br>||||
|**(1)**|K/HE|1.00*|2.50E-08|0.9061|0.8942|81|
|<br>**B. T**<br>|**hree factors (Two lev**<br>|**el CES pr**|**oduction function**|**)**<br>|||
|**(1)**|(K,HE)/L|||0.9203|0.9076|81|
||� K/HE|1.01*|0.01||||
||� (K,HE)/L<sup>1</sup>|1.00*|2.23E-10||||
|**(2)**|(K,HE)/E|||0.8952|0.8742|67|
||� K/HE|1.65*|0.12||||
||� (K,HE)/E<sup>1</sup>|1.00*|6.76E-11||||
|**(3)**|(K,E)/HE|||0.7674|0.7209|67|
||� K/E|0.17|0.19||||
||�(KE)/HE<sup>1</sup>|100*|822E-08||||
|**C. F**|, <br>**our factors (Three le**|. <br>**vel CES pr**|.<br>**oduction functio**|**n)**|||
|**(1)**|(K,HE,L)/E|||0.9037|0.8081|67|
||� K/HE|1.78*|0.11||||
||� (K,HE)/L<sup>1</sup><br>|1.14*|0.02||||
||� (K,HE,L)/E<sup>2</sup>|1.00*|2.52E-12||||
|**(2)**|(K,HE,E)/L|||0.9059|0.8828|67|
||� K/HE|-8.55|12.61||||
||� (K,HE)/E<sup>1</sup>|0.48*|0.17||||
||� (K,HE,E)/L<sup>2</sup>|1.00*|4.60E-11||||
|**(3)**|(K,E,HE)/L|||0.9062|0.8831|67|
||� K/E|1.57*|0.37||||
||� (K,E)/HE<sup>1</sup>|0.92*|0.02||||
||� (K,E,HE)/L<sup>2</sup>|1.00*|6.41E-11||||

Legend: K – physical capital; HE – human capital related to educational attainment and labor productivity; L – land resources; E – energy resources Notes: Inputs in parenthesis imply that they are nested. 1 two inputs in a nested function 2 three inputs in a nested function (*) denotes statistical significance at 5% level; (**) at 10% level The substitution elasticities and their corresponding standard errors are rounded off to the nearest hundredth.
15

# **Table 4:  Elasticity estimates of the economic and institutional indicators using the [(K, HE, L)/E] production function**

|Variable|Elasticity|Standard error|t-statistic|
|---|---|---|---|
|TOPEN|0.47|0.10|4.53|
|PCREDIT|0.51|0.12|4.25|
|VA|0.01|0.04|0.28|
|PIV|-0.01|0.02|-0.28|
|GE|0.04|0.10|0.40|
|RB|0.03|0.07|0.39|
|RL|-0.07|0.10|-0.73|
|CC|0.01|0.09|0.17|

Legends: TOPEN-trade openness; PCREDIT- variable for private sector investment; VA - voice and accountability; PIV- political instability and violence; GE - government effectiveness; RB - regulatory burden; RL - rule of law; and CC - control of corruption.

**Table 5:  Elasticity estimates of the economic and institutional indicators using the [(K, E, HE)/L] production function**

|Variable|Elasticity|Standard error|t-statistic|
|---|---|---|---|
|TOPEN|0.50|0.09|5.27|
|PCREDIT|0.51|0.11|4.83|
|VA|0.02|0.03|0.45|
|PIV|-0.01|0.02|-0.44|
|GE|0.06|0.09|0.62|
|RB|0.03|0.07|0.37|
|RL|-0.08|0.09|-0.86|
|CC|-0.02|0.08|-0.24|

Legends: TOPEN-trade openness; PCREDIT- variable for private sector investment; VA - voice and accountability; PIV- political instability and violence; GE - government effectiveness; RB - regulatory burden; RL - rule of law; and CC - control of corruption.

**Table 6: Level of Gross National Income per capita given a reduction in the amount of land**

|**Prod. function**|**Baseline***|**R**|**eduction inthe **|**amount of land b**|**y**|
|---|---|---|---|---|---|
|||**20%**|**50%**|**75%**|**92%**|
|**(K,HE,L)/E**|$8,638.10|$8,068.84|$7,019.27|$5,774.25|$4,297.16|
|_Difference_|_from baseline**_|_(-7%)_|_(-19%)_|_(-33%)_|_(-50%)_|
|**(K,E,HE)/L**|$9,096.20|$8,540.27|$7,477.97|$6,147.62|$4,455.06|
|_Difference _|_from baseline**_|_(-6%)_|_(-18%)_|_(-32%)_|_(-51%)_|

*Predicted per capita GNI at the mean values of the explanatory variables. **Rounded off to the nearest whole number Sample size of each production function = 67