The Role of Technological Progress in Testing Adjusted Net Savings: Evidence from OECD Countries

Ecological Economics 164 (2019) 106382

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Analysis

The Role of Technological Progress in Testing Adjusted Net Savings: Evidence from OECD Countries

T

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Rui Pedro Mota , Maria A. Cunha-e-Sá NOVA School of Business and Economics, Universidade Nova de Lisboa, Portugal

A R T I C LE I N FO

A B S T R A C T

JEL Classification: Q56 E01 Q55

In this paper we investigate the relationship between comprehensive measures of savings and changes in future consumption in OECD countries. This relationship is at the basis of the interpretation of adjusted net savings as a weak sustainability indicator, and so, evidence of its validity provides support to the use of this indicator. We construct various measures of comprehensive savings for 20 OECD countries to include depletion from nonrenewable resources, human capital investment and technological progress. Given their importance, especially for rich countries, we focus on the role of technical progress and human capital, in the form of changes in education level. We do not find strong evidence in favor of including green adjustments in the conventional net savings. However, we find compelling evidence for the inclusion of technological progress. Since this involves a forward looking term, the above result suggests that to construct an indicator of weak sustainability from conventional net savings, some estimate of future technological progress is needed.

Keywords: Adjusted net savings Indicators of weak sustainability Technological progress Comprehensive accounting

1. Introduction In the last decades there have been important contributions on how to adjust national accounting aggregates to indicate welfare improvement or sustainability by including green terms like the depletion of resources and pollution (e.g., Pearce and Atkinson, 1993; Hamilton and Atkinson, 1996; Hamilton and Clemens, 1999), technological progress or human capital (e.g., Aronsson and Löfgren, 1995; Weitzman, 1997). Of these contributions, the leading indicator of weak sustainability is the adjusted net savings (ANS) proposed and estimated by the World Bank (Hamilton and Clemens, 1999; Lange et al., 2018). Two definitions of weak sustainability are typically associated to the use of comprehensive savings indicators like the ANS.1 One postulates that development at a particular moment is sustainable if current consumption can be maintained forever (Pezzey, 2004), while the other assumes that development is sustainable if welfare is not decreasing (e.g. Arrow et al., 2012). In both cases, if comprehensive savings is negative, development is not sustainable. However, having positive comprehensive savings does not guarantee that consumption will not decrease (Asheim, 1994; Pezzey, 2004), and in this sense the indicator is of

unsustainability.2 Both definitions refer to weak sustainability, by allowing savings or investments in other forms of capital to compensate the consumption of natural capital. In contrast, a definition of a stronger sustainability emerged challenging the feasibility of unlimited substitution between forms of capital (Dietz and Neumayer, 2007). The theoretical model used to understand how to measure welfare changes and to indicate weak sustainability is a general model of economic growth. Irrespectively of the definition of sustainability adopted, this underlying model relates comprehensive savings to future welfare changes and it is this relationship that supports the use of comprehensive savings as an indicator of sustainability. Although welfare (e.g., present value of utility flows) is not observable, in fairly general conditions the present value of future changes in consumption can signal changes in welfare, and changes in comprehensive savings can be used to measure the present value of future consumption changes (Asheim, 2007). So, finding evidence that comprehensive savings measure present value of future consumption changes, as predicted by the theory, provides support for the use of comprehensive savings as practical indicators of sustainability. Since this indicator is based on a general neoclassical growth model, this evidence also supports the underlying

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Corresponding author at: Universidade Nova de Lisboa, Nova School of Business and Economics, Campus de Carcavelos Rua da Holanda, n.1, 2775-405 Carcavelos, Portugal. E-mail address: [email protected] (R.P. Mota). 1 We adopt the term comprehensive savings to refer to a general adjusted measure of savings constructed from a more comprehensive system of national accounts, for instance including natural capital. 2 For a discussion and historical overview of sustainable development definitions in economic models see Pezzey (1992) and for a discussion of the sustainability significance of comprehensive savings see e.g., Pezzey (2004) and Asheim (2003). https://doi.org/10.1016/j.ecolecon.2019.106382 Received 29 June 2018; Received in revised form 19 June 2019; Accepted 25 June 2019 0921-8009/ © 2019 Elsevier B.V. All rights reserved.

Ecological Economics 164 (2019) 106382

optimal growth theory (see e.g. Pezzey et al., 2006). There is a growing literature devoted to check whether comprehensive savings are better at predicting the present value of future consumption changes than conventional indicators from the system of national accounts (SNA). This literature found some support to include green adjustments in conventional measures of savings, but for rich countries the evidence is weaker (Ferreira and Vincent, 2005; Hamilton, 2005). The result for rich countries has been justified by the fact that estimates of comprehensive savings have ignored technical progress, which is thought to be more relevant in these countries. Developments of the theory of comprehensive accounting to include technological progress can be found in Pemberton and Ulph (2001) or Weitzman and Löfgren (1997). Most recent tests of the theory already include an adjustment for technological progress in their measures of savings. These tests are available for a few countries, namely, Scotland, Portugal, UK, USA, Germany, Sweden and Australia (see Table 1). In this paper, we extend this list to 20 OECD countries with the advantage of using a more homogeneous dataset, therefore, facilitating the comparison of the results. Existing tests provide some evidence that including technological progress improves the fit with the theory. Moreover, the value of time is typically the largest adjustment to comprehensive net savings and significantly affects its value (see e.g. Mota et al., 2010 or Greasley et al., 2014). Since including technological progress involves estimating a forward-looking term (Pezzey, 2004), then, to signal future economic development some estimate of future technological progress is needed. Given its importance in the value of the indicator, this in turn, would amount to assume future welfare improvement and sustainability rather than measuring it. Moreover, the measure of technological progress to be included in the indicators depends on the capital stocks considered in the underlying growth model (Pemberton and Ulph, 2001). So far, the tests performed use exogenous technological progress while at the same time considering investments in human capital (Pezzey et al., 2006; Mota and Domingos, 2013). In this context, considering human capital changes when measuring technological progress would be more appropriate to test the theory. If it turns out that the value of technological progress does not contribute significantly to explain future consumption changes then the use of comprehensive savings to indicate welfare changes or sustainability is strengthened. For these reasons, we adjust total factor productivity (TFP) to include changes in human capital, in the form of changes in education level (see Section 3.2). This paper is organised as follows. Next section reviews the literature that tests the comprehensive accounting theory. Section 3 presents estimates of the comprehensive savings, and Section 4 the results of the tests of the theory. Section 5 concludes the paper.

Minerals, educ., TFP (T = 20) with pasture land, pop Iron, forest, air flow pollutants, educ., TFP (T = 20, 30) and pop.

(1), time series (1), time series

20, 30, 50, 100 50 20, 50, 100 Mineral, educ., TFP (T = 20), CO2.

This section addresses the theoretical and empirical literature on testing macroeconomic indicators of weak sustainability. First we present the theory that supports the sustainability and welfare significance of comprehensive savings, as well as its testable expressions. We then use a specific model to derive the indicators to be estimated in Section 3. We discuss, in Section 2.2, the results of the empirical tests in the literature, highlighting some inconsistencies in the estimates of the various comprehensive savings indicators.

Australia, 1870–2011 Sweden, 1850–2008

UK, USA, Germany, 1870–2000 Germany, 1850–2009

(1), time series

20, 30, 50 Minerals, forest, educ., TFP (T = 20), pop.

(1), time series and panel

(1), time series 20, 50, 100

2. Literature Review

Greasley et al. (2017) Lindmark et al. (2018)

Blum et al. (2017)

Hanley et al. (2016)

2.1. The Theory and its Testable Expressions Greasley et al. (2014)

Mota and Domingos (2013)

Ferreira et al. (2008)

Great Britain, 1760–2000

(1)–(5), time series 5, 10

Minerals, forest, flow air pollutants, educ., TFP (T = 17, 100). Minerals, forest, educ., TFP (T = 20, 30), pop.

20

β1 ∈ [−0.7.0.6]. Population did not improve estimates. Green savings better. QI performs better than Y. Best model: β1 = 1.1 with Qt and no educ. β1 ∈ [0.4.1.5] Best model: β1 = 1.1 without Qt and T = 100. β1 ∈ [0.6.1.5] Better to have Qt without educ. Best model for UK, USA, Germany: β1 = (1.2,1.0,1.2) without Qt and T = (20,30,20), resp. Best model: β1 = 1.2 using GS without Qt. β1 increases with T. Better to have Qt without educ. Best model: β1 = 2.5 with mineral depletion. Best model: β1 = 0.4, T = 20 without Qt, with resource depletion and pollution. β1 ∈ [−0.1.0.43] (1), panel

–

Minerals, forest, fish, air flow pollutants, TFP (T = 20), oil price changes, educ. Minerals, forest. Pop. Pezzey et al. (2006)

64 developing countries, 1970–1982 Portugal, 1990–2005

(2)

10, 20 20 Ferreira and Vincent (2005) Hamilton (2005)

139 countries, 1970–2001 Countries in WDI (2002), 1977–1980 Scotland, 1992–1999

Forest and mineral, educ. Minerals, forest, pop.

ΔY much bigger, or QI much smaller than prediction.

β1 ∈ [0.1.0.6]. No relation for OECD. β1 ∈ [0.3.1.3]. Worse for rich countries.

Correlation in (5) but mixed results in (4). β1 ∈ [0.2.0.8] 10 Vincent (2001)

Latin America, 1973–1986

Forest and mineral.

(4) and (5), cross-section and panel (5), panel (1), cross-section

Selected findings Expressions/Method T Adjustments Countries/Years Reference

Table 1 Overview of tests of comprehensive accounting theory. Y represents a measure of comprehensive income. QI a measure of comprehensive savings or investment. “forest” means depletion of commercial timber stocks. “educ.” refers to education expenditures and “pop” to varying population growth. T refers to the time horizon considered in PVΔC. β1 refers to regression results of (7). “Best model” means β1 closest to 1 using the same T in the value of time and in PVΔC.

R.P. Mota and M.A. Cunha-e-Sá

The general comprehensive accounting model (Asheim and Weitzman, 2001; Pezzey, 2004) considers an economy with constant population where utility at time t, U(C(t)), depends on C(t), a vector of consumption flows that includes all determinants of current instantaneous utility. See Asheim (2004) for a discussion of welfare measures with a changing population. K+(t) is a vector of capital stocks that contains all determinants of current net productive capacity (e.g., 2

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human capital (that does not depreciate), so that K̇H = F H (h) . Also, QR is the vector of resource prices and fR the vector of marginal costs of resource extraction. Along the optimal path, comprehensive net investment is given by

man-made capital, environmental assets or human capital), and therefore, net investment, I+, is K̇+ = I+. The superscript + means an augmented vector of capital stocks where, following Pemberton and Ulph (2001) or Pezzey (2004), we consider time as a form of capital, i.e., K+ = (K, t) and I+ = (I, 1). This means that the model is able to include exogenous technical progress. The production possibilities are a convex set S that depends on K+, so that (C, I+) is feasible given K+ if and only if (C, I+) ∈ S(K+). Within this set we assume that there is a resource allocation mechanism that, for any K+, determines the values of consumption and net investment flows (Arrow et al., 2003; Asheim, 2007). This defines a path for C(t), I+(t) and K+(t) that is not necessarily an optimal path. In this context, Asheim (2007) shows that the present value of future consumption changes equals the value of net investments, i.e., ∞ ∫t p (s ) Ċ (s ) ds = q+ (t ) I+ (t ) , where p and q+ are the present value consumption and investment prices, respectively. Using a constant real interest rate, R, then,

Q+I+ = K̇ + K̇ f + (FhH )−1F H + (Q R − f R) Ṡ + Qt where Qt =

∫ (P (s) Ċ (s))e−R (s−t ) ds = Q+ (t ) I+ (t ) t

t

(1)

+

where P(t) and Q (t) represent the real prices of consumption and investment deflated by a Divisia consumer price index (CPI), respectively, and Q+(t)I+(t) is comprehensive savings (Asheim and Weitzman, 2001). Most tests in the literature use this expression (see Table 1). For more information on the properties of the Divisia consumer price index as well as the relationships between utility prices and the money prices necessary to translate observable market values into statements about welfare see Asheim and Weitzman (2001) and Asheim (2007). Defining comprehensive income (often denoted by green net national income) in real prices as Y(t) = P(t)C(t) + Q+(t)I+(t), Asheim and Weitzman (2001) show that

Y ̇ (t ) = RQ+ (t ) I+ (t )

(2)

This last equality was used as an empirical test of the theory in Pezzey et al. (2006) and Mota and Domingos (2013). Using (2) and the definition of Y(t) we obtain

PV ∆C = Y ̇ (t )/ R,

(3)

tested in Mota and Domingos (2013). Assuming discounted utilitarianism and constant returns to scale, Asheim (2003) shows that along an optimal path, real comprehensive income equals the interest on real wealth, i.e.,

∫t

∞

P (s ) C (s ) e−R (s − t ) ds = Y (t )/ R

(4)

Expression (4) was tested in Vincent (2001) and Mota and Domingos (2013). Using the definition of Y(t), another expression that has been used to test the theory is obtained,

R

∫t

∞

P (s ) C (s ) e−R (s − t ) ds

− P (t ) C (t ) =

Q+ (t ) I+ (t )

PV ∆Ct = β0 + β1 Q+I+ + εt t+T ∑s = t

(7)

R)−(s − t )

where PV ∆C ≈ and PCt is real con(PCs − PCs − 1)(1 + sumption at time t. Sections 3.1 and 3.2 describe how the variables for Eq. (7) are estimated.

(5)

This last expression was used in Vincent (2001), Ferreira and Vincent (2005) and Mota and Domingos (2013). These are the expressions used to test the theory of comprehensive accounting and their indicators of weak sustainability. To derive an expression for comprehensive savings, Q+(t)I+(t), we assume that K = (K, Kf, KH, S) includes domestic man-made capital, K, net foreign capital, Kf, human capital, KH, and a vector of stocks of natural resources, S, so that F(K+) is the production function of manmade capital.3 Time as an argument of the production function represents any productivity change that is not related to investments in existing capital forms (Pemberton and Ulph, 2001). For the change in the stock of human capital we assume, as in Hamilton and Clemens (1999), that a function FH(h) transforms education expenditures h into 3

∫ ∂F (∂Ks . s) e−R (s − t ) ds (Pezzey, 2004). If time is not included in

K+, then Qt = 0 and technical progress is fully captured by changes in stocks. Pemberton and Ulph (2001) label this as “purely endogenous technical progress”, and argue that whether there is a need to correct national accounts' aggregates for technical progress “depends on the view one takes regarding the extent to which technical progress is endogenous or exogenous”. When human capital is not included as a capital stock we are in the presence of an exogenous growth model and ∂F ∂s represents TFP growth. If, however, the vector of capital goods K includes human capital, as the model used by the World Bank to estimate ANS (Hamilton and Clemens, 1999) then estimates of TFP growth must include human capital changes. By the same token, a correction in TFP for natural capital should be considered. This has been done for OECD countries in Brandt et al. (2017) and included in wealth estimates of the World Bank (Lange et al., 2018). Brandt et al. (2017) conclude that the change in TPF growth from the correction for natural capital (only sub-soil assets) is very small even in resource rich countries. Given these small adjustments and since data exists for a short period of time only this correction is not applied here, and is left for future work “as better and more extensive data on natural capital becomes available” (Brandt et al., 2017). In our framework, the terms K̇ + K̇ f would correspond to conventional net savings (NS) if the distinction between consumption and investment in the SNA was correct. The SNA treats important items as consumption, which by their nature are investments instead, notably education expenditures (Hamilton and Clemens, 1999). Hence, if CSNA denotes consumption as estimated by the SNA, since current (as opposed to capital) operating expenditures in education are treated strictly as consumption, then it is necessary to subtract education expenditures from CSNA to obtain consumption, PC, in our setup. Assuming, as Hamilton and Clemens (1999), that (FhH)−1FH can be approximated by current education expenditures, then to estimate expressions (1), (3), (4) and (5) it is necessary that PC = CSNA − (FhH)−1FH. This correction is neglected in the literature that tests the comprehensive accounting model although used in Hamilton (2003). Here we test expression (1), by estimating,

∞

PV ∆C ≔

(6)

∞

2.2. Review of Empirical Studies Expressions (1) to (5) have been used to understand whether greener national accounting aggregates provide better indicators of long-run economic possibilities. To this end, several proxies for savings or income are used to test different hypotheses, e.g. the exact verification of the expressions or estimates being closer to expected values when measures are more comprehensive. Table 1 presents an overview of the literature highlighting selected findings. Earlier studies used panel data or cross-section methods on comprehensive accounting measures that included depletion of natural capital (mineral and forest depletion), and human capital (reclassification of education expenditures as investment) (Vincent, 2001; Ferreira and Vincent, 2005; Ferreira et al., 2008). More recently, time-series have been preferred since the theoretical expressions were essentially

See Sections 3.1 and 3.2 for more details the stocks considered. 3

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include TFP growth without including education expenditures (Table 1). One reason for this could be that the value of time is estimated using TFP data that do not include changes in human capital, and, therefore it measures exogenous technical progress, which is not suitable for testing a model that includes human capital (Mota and Domingos, 2013; Pezzey et al., 2006). A more suited model would estimate an endogenous measure of TFP including changes in human capital. Interestingly, although recent studies use very long-run series, increasing the time horizon did not lead to a clear improvement of the fit with the theory, even though the results were more robust. For instance, Lindmark et al. (2018) conclude that β1 does not approach 1 with longer time horizons. Note that in order to understand the effect of increasing the time horizon, the same T should be used in both PVΔCt and Qt. In the literature, however, it is common to vary the time horizon in PVΔCt while leaving the T in Qt fixed (see Table 1). Comparing the results in the literature of regressions that use the same time horizon it is not clear that having longer time series results in estimates of β1 closer to 1. Regarding the inclusion of changing population growth rates in the tests, this requires an estimate of the value of all capital stocks. In Ferreira et al. (2008) these are produced and natural capital, with natural capital calculated as the discounted sum of mineral and timber rents over 20 years (the same time horizon as in PVΔCt). In the absence of data on stocks the remaining literature uses a top-down approach where wealth equals the discounted sum of real consumption, e.g. in Greasley et al. (2014) wealth is the present value of a 3 year average of consumption over 25 years with a discount rate of 1.5% (in PVΔCt the discount rate used is 2.5% and T=20, 50, 100 years). This approach assumes that consumption is such that leaves the capital stock intact (World Bank, 2011). Thus, for the years ANS is negative a measure of sustainable consumption must be used instead of current consumption; the World Bank (2011) uses ANS subtracted from consumption. However, including changing population growth rates did not substantially improve the empirical relation between current savings and future consumption changes in Hamilton (2005) or Ferreira et al. (2008), and led to worse results for the longer time horizons in Greasley et al. (2014) arguably due to measurement errors and the invalidity of the assumption that wealth is equal to the present value of a consumption stream. For these reasons we decided not to include changing population growth rates. Finally, note from Table 1 that given the various assumptions used in the literature, a comparison of their results is difficult.

derived for welfare comparisons over time for a single country. Regarding the theory of welfare comparison between countries see Weitzman (2001) and Asheim (2010). We see from Table 1 that studies where income and savings measures are compared conclude that savings measures usually perform better, and are therefore preferred as proxies of future welfare changes (Vincent, 2001; Mota and Domingos, 2013). Most regressions in the literature indicate that when including some correction for the depletion of natural resources better measures of welfare changes are obtained in the sense that regressions results of Eq. (7) are more in accordance with the theory. Thus suggesting that these adjustments add value to the national accounts even if natural resource data are far from perfect (Ferreira and Vincent, 2005; Hamilton, 2005; Ferreira et al., 2008). It is important to refer that the appreciation of renewable resources is neglected in the World Bank's forest depletion time series. Net forest depletion is calculated as the product of unit resource rents and the excess of roundwood harvest over natural growth, implying that if growth exceeds harvest no adjustment to ANS is made (Lange et al., 2018). For this reason, in most developed countries net forest depletion is zero. To understand the contribution of each term, Vincent (2001) tested disaggregated expressions of comprehensive savings concluding that due to the significance of the stock appreciation variables, “genuine savings estimates that include only the depletion-related component are wrong from a theoretical standpoint, and this mistake is empirically significant.” This then makes the World Bank's measure of net forest depletion unsuited to test the theory of comprehensive accounting. Using data from the World Bank, Ferreira and Vincent (2005) found no evidence supporting expression (5) for OECD countries. Using education expenditures in ANS worsened the results and the best savings measure simply considered depletion of mineral and timber stocks. When increasing the time period from 10 to 20 years all indicators performed better. Overall, their estimates suggest that either savings are overstated or that consumption changes are understated. Moreover, the authors used consumption without excluding education expenditures and timber depletion that ignored the appreciation of stocks. With these results in mind, Hamilton (2005) did not correct for education expenditures. Though, the author still found poor results for high-income countries. Of the indicators tested, net savings corrected for the depletion of resources without including varying population growth performed better. Moreover, Hamilton (2005) adds that “the bad fit in rich countries probably reflects factors other than capital accumulation being key for the growth performance of these economies, in particular technological innovation”. Given the lack of correlation between saving measures and future consumption changes for rich countries, Ferreira et al. (2008) focused on developing countries. Education expenditures were not included, and again, the best performing savings measure turned out to be net savings corrected only for the depletion of natural resources. These results motivated the introduction of technological progress in empirical estimates of comprehensive accounting indicators. Pezzey et al. (2006) included TFP changes in their estimates of ANS for Scotland (as well as capital gains) but the authors still concluded that the growth in comprehensive income is much higher than the interest on ANS, thus contradicting expression (2). Moreover, Mota and Domingos (2013) tested expressions (1) to (5) for Portugal and concluded that a savings measure with exogenous TFP performs better. Subsequent literature suggests that, besides being one of the largest terms in comprehensive savings measures, and although there is some evidence that favors the inclusion of the value of time, this has produced mixed outcomes with respect to the fit with the theory. In recent papers, i.e. since Greasley et al. (2014) in Table 1, the savings expressions that best fit the theory do not include the value of time. This conclusion is reached when comparing the estimates that use the same time horizon, T, in both PVΔCt and Qt. Moreover, the results in the literature suggest that it is better to

3. Methods and Estimates of Net Savings This section presents the data used to construct the various comprehensive savings as well as their estimates. We consider, by including different terms in QI and PC, four models that are particular cases of the general growth model in Section 2.1. Namely,

• Model 1: QI1 = NS, where NS is net savings from the SNA, and PC1 = C . • Model 2: QI2 = NS + Ed − Depl and PC2 = C − Ed, where Ed is SNA

SNA

• •

education expenditures, and Depl is depletion from non-renewable resources. Model 3: QI3 = QI2 + Qt and PC3 = PC2, where Qt represents the value of time. Model 4: QI4 = QI2 + QHt, where QHtis the value of time including changes in human capital, and PC4 = PC2.

According to (1) we expect that in expression (7) β0 = 0 and β1 = 1, or that β1 approaches 1 as the savings and consumption measures are more comprehensive. The time series were tested for stationarity (ADF and KPSS tests) and the regressions tested for cointegration (Johansen test). The results 4

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considered an investment in capital and therefore included in the Gross Fixed Capital Formation. If investment in human capital is included in the model to be tested, then to estimate PVΔC it is necessary to subtract from CSNA the part that corresponds to education expenditures, reclassified as investment. This adjustment was not done before in the literature on testing sustainability indicators. The reason for not including CO2 emissions is because the atmospheric concentration of CO2 is a function of global emissions not just on an individual country's emissions (Ferreira and Vincent, 2005). Regarding particulate matter, assuming that it does to not accumulate it may be modelled as a flow pollutant. Pezzey et al. (2006) and Mota and Domingos (2013) include flow pollutants that enter the utility function. Modelled this way, particulate matter should not enter ANS as flow pollutants do not accumulate, or affect another stock, and comprehensive savings measures changes in stocks. If, however, a flow pollutant affects human or health capital, it should be included in comprehensive savings, but in this case human capital should include health and not just education as considered by the World Bank (Hamilton and Clemens, 1999). Lindmark et al. (2018), for instance, include flow pollutants in their measures of savings by considering the depreciation that these pollutants produce on man-made capital. However, this can lead to double counting when using net man-made capital stock. Moreover, available data only exists after 1990. For all these reasons, the version of the World Bank's ANS better suited to test the theory includes the adjustments for education expenditures and mineral depletion, i.e., QI2.

are presented as supplementary material (tables S1 to S4). Most time series show evidence of being non-stationary and most regressions do not show evidence of cointegration. It is expected though that longer time series show evidence of cointegration in accordance with the theory, just as more comprehensive estimates of the variables should. This is however not clear from our results. Similar results have been found in the literature, e.g., Hanley et al. (2016), where more comprehensive indicators and longer time series do not necessarily result in cointegrated regressions. In any case, we find that for almost all countries a cointegration relation is found between PVΔC and Q+I+ for some model and some time horizon. Another econometric issue concerns the possible endogeneity in regressions of models with the value of time. Given the forward-looking nature of both the dependent and the explanatory variables, there may be a simultaneous relationship between variables in both sides of Eq. (7), namely, a change in consumption in PVΔC and GDP in Qt (see Section 3.2). This risk may be reduced since GDP in Qt is being weighted by TFP growth and the discount rate. For a similar reason Greasley et al. (2017), following Ferreira et al. (2008), use instrumental variables and two stage least squares (2SLS) for models where population and wealth-dilution are included (although not in all models with the value of time). The set of instruments typically used in the literature are a time trend, and lagged values of comprehensive savings, GNI, real interest rates, real exchange rates, labor, the proportion of the population of working age, produced capital, population or population growth rate. Besides being correlated with comprehensive savings, the validity of an instrument requires arguing that it cannot be a direct determinant of PVΔC, and that it is not correlated with some omitted determinant of PVΔC. In this sense, the validity of the above instruments is not justified in the literature, and in fact it may not be easy to find good instruments since many macroeconomic variables are interrelated. We tested several subsets of the above instruments and the vast majority does not pass the Sargan test for the validity of the instruments. Moreover, given that lagged values of the dependent variable are less influenced by current PVΔC shocks, we opt to use these as instruments in the 2SLS regressions of models 3 and 4. Since the results of the OLS and the 2SLS do not differ significantly and given that the sample size is not large, we opt to present the results for the OLS. For comparison, Figs. S5 to S7 of the supplementary material, replicate Figs. 4 to 5 using 2SLS in models 3 and 4.

3.2. Models 3 and 4: The Value of Time and Human Capital Models 3 and 4 are set to understand whether the value of time, accounting for technological progress, is an important adjustment to savings measures when compared to Models 1 and 2. The value of time t+T  −(s − t ) , where A t is TFP growth in Model 3 is Qt ≈ ∑s = t A s × Ys (1 + R ) rate, estimated in the AMECO database with the production function Y /Y Yt = AtLtαKt1−α to obtain At / A0 = (L / L )αt(K 0/ K )1 − α . The index 0 means 0 0 t t the initial year of the time series, Yt is the current GDP at 2010 prices (deflated with CPI), Kt is the net capital stock at 2010 prices deflated by the price deflator of Gross Fixed Capital Formation, Lt is the total employment and α is the cost share of labor in total production. For α, CE

(

L

)

AMECO uses the average of Y t L −tSE where CE is compensation of t t t employees and SE is self-employment. Net capital stock at time t is calculated in the AMECO database (code OKND) by adding the net fixed capital formation to the previous year's net capital stock. Net fixed capital formation (i.e., net of consumption of fixed capital) is obtained using data from the Eurostat namely Gross fixed capital formation (definition P.51 g of the European System of Accounts 2010). To account for human capital in the estimates of TFP we adapt AMECO's calculations of TFP to include changes in the education levels. The value of time with human capital, QHt, is estimated using the production function Yt = At′HtαKt1−α, where human capital is Ht = eϕ(St) Lt, with ϕ(S) = rpSp + rsSs + rtSt and At′ is used as endogenous TFP. The superscripts p, s, and t in ϕ(S) represent primary, secondary and tertiary education levels where Si is the average years of schooling with education level i and ri is the average return to schooling from education level i. Average years of schooling until 2010 were obtained from Barro and Lee database (Barro and Lee, 2013), whereas returns on education are the averages of the values in table A1 of Psacharapoulos and Patrinos (2004). If there is no information on a country's returns on education we follow Caselli (2005) and use rp = 0.134, rs = 0.101 and rt = 0.068, which are, respectively, the average returns of sub-Saharan countries, the world average returns and average returns of OECD countries. We estimate PVΔC and the value of time for the time horizons of T = 5, 10 and 20 years.

3.1. Models 1 and 2: Conventional and Green Savings The AMECO database (annual macro-economic database of the European Commission's Directorate General for Economic and Financial Affairs) was used to obtain the SNA's data for Models 1 and 2. The countries included are: Belgium, Denmark, Ireland, Greece, Spain, France, Italy, Luxembourg, Netherlands, Austria, Portugal, Finland, Sweden, United Kingdom, Iceland, Norway, United States, Japan, Canada and Australia. Other countries in the AMECO were left out due to missing data, particularly CPI and the data needed to estimate TFP growth. All variables were deflated to the 2010 prices using the CPI. For the real interest rate we used the average of the real long-term interest rates from AMECO, except for Australia where the average of the real interest rate from the World Bank's Development Indicators data was used. While Model 1 tests whether conventional savings indicate future consumption changes, Model 2 is motivated by the World Bank's ANS. ANS is calculated as net savings plus public education expenditures minus resource depletion (energy, mineral and forest) and pollution damages (carbon dioxide and particulate matter). Adding education expenditures corresponds to a reclassification from expenditure into investment in human capital. Current operating expenditures in education include teachers' salaries and the purchase of books and are treated strictly as consumption in the SNA (Hamilton and Clemens, 1999). Capital investments in buildings and equipment is already 5

Ecological Economics 164 (2019) 106382

R.P. Mota and M.A. Cunha-e-Sá

Fig. 1. Average values of the different components of comprehensive savings by country (% GNI). Q and QH, mean, respectively, the value of time without and with changes in education level, for T = 5.

3.3. Estimates of QI and PVΔC

savings, namely, QI2 and QI4, for T = 5 years. We observe that for several countries (e.g., USA, UK, Iceland or Australia), while PVΔC seems to vary differently from savings adjusted with education expenditures and depletion of minerals (QI2), comprehensive savings with the value of time seem to follow closely the PVΔC. This suggests that the value of time is a relevant component to predict changes in future consumption. Next section investigates this by analyzing the regressions of Models 1 to 4.

Fig. 1 shows the average for the whole period (1970–2010) of the terms in comprehensive savings, expression (6). Net savings and the value of time are the most significant terms, followed by education expenditures and depletion of non-renewable resources (negligible for many countries, except for Australia, Canada, Norway, Netherlands, UK and USA). In some countries Qt (even just for T = 5) is considerably higher than NS. As expected, in general, including changes in education level decreases the value of time. According to (1) it is expected that the present value of future consumption changes closely resembles the evolution of comprehensive savings. Fig. 2 shows the time series of PVΔC and two measures of

4. Results and Discussion This section presents the regression results of Eq. (7) for the Models 1 to 4. The estimates of β1 are presented in Figs. 3, 4 and 5. Table S1 of

Fig. 2. Comprehensive savings and present value of consumption changes for T = 5 (Mrd2010 LCU). The horizontal line represents x-axis. 6

Ecological Economics 164 (2019) 106382

R.P. Mota and M.A. Cunha-e-Sá

usa uk swe prt nor nld lux jpn ita

Model 1

isl

Model 2

irl

Model 3

gre

Model 4

fra fin esp dnk can aut aus 0

1

2

3

β1 Fig. 3. Estimates of β1with p-value < 0.05 for T = 5 years. Horizontal bars indicate the 95% confidence interval using an heterokedasticity and autocorrelation consistent (HAC) estimator.

the supplementary material presents all the regression results. A first conclusion is that most estimates of β1 are positive but smaller than 1. This evidence, that most measures of comprehensive savings move in the same direction but understate the true value of PVΔC, is not uncommon in the literature. Moreover, models without the value of time, i.e. Models 1 and 2, seem perform worse for larger time horizons. For instance, with T = 20 years most regressions using models 1 and 2 estimate a negative β1. A negative relationship was also found in Ferreira and Vincent (2005), between ANS and the difference between current and average future consumption for OECD countries

(expression (5)). There also seems to be no strong evidence in favor of one of the savings measures QI1 or QI2, although for the 5 year time horizon QI2 presents a better fit with the theory. The typical adjustments to obtain ANS from conventional savings (subtracting mineral depletion and adding education expenditures) in general do not improve savings to better indicate future consumption changes. Comparing the results from Models 1 and 2 in Figs. 3, 4 and 5, it can be seen that, although for some countries it is better to use QI2 (e.g., Canada with T = 5), for most countries it is either worse (e.g., Iceland with T = 10) or indifferent

usa uk swe prt nor nld lux jpn ita

Model 1

isl

Model 2

irl

Model 3

gre

Model 4

fra fin esp dnk can bel aut aus −2

0

2

4

β1 Fig. 4. Estimates of β1 with p-value < 0.05 for T = 10. Horizontal bars indicate the 95% confidence interval using a HAC estimator. 7

Ecological Economics 164 (2019) 106382

R.P. Mota and M.A. Cunha-e-Sá

usa uk swe prt nor nld lux jpn ita

Model 1

isl

Model 2

irl

Model 3

gre

Model 4

fra fin esp dnk can bel aut aus −5.0

−2.5

0.0

2.5

β1 Fig. 5. Estimates of β1 with p-value < 0.05 for T = 20. Horizontal bars indicate the 95% confidence interval using a HAC estimator.

conventional net savings (Model 1) did not improve the regressions. Comparing models 3 and 4, Fig. 6 suggests no significant advantage of introducing changes in education level in the value of time. Regarding the time horizon, for longer time horizons adjusting net savings with the value of technological progress improves the fit, but the shorter time horizon of 5 years has the most regressions for which with β1 = 1 cannot be rejected. This is also suggested by the results of the Wald test (Fig. S4 of supplementary material), where most models for which the exact verification of expression (1) is not rejected use T = 5. As in Lindmark et al. (2018) there is no strong support to the conclusion that using longer time horizons provides a better fit with the theory.

(e.g., USA with T = 10) to predict future consumption changes with QI1 or QI2. It is interesting to see from Figs. 3 to 5 that focusing on countries with considerable depletion (from Fig. 1: aus, can, dnk, nld, nor, uk, usa), then QI2 is a better indicator of future consumption changes than QI1 for all time horizons. The most striking result though is obtained when measures of savings are adjusted to include the value of time, either Qt or QHt. Although for a few countries including a measure of the value of time does not improve the relationship with future consumption changes (e.g., Sweden), for most countries, the regressions present a better fit with the theory, in the sense that β1 is closer to 1 with narrower confidence intervals (e.g., Portugal). For longer time horizons the improvement from using the measures QI3 or QI4 is more evident. So, including the value of time in current estimates of comprehensive savings seems to be relevant for its practical use as an indicator of welfare changes and weak sustainability. However, the existence of this large (see Fig. 1) forward-looking term undermines the practical use of the indicator since some estimate of future technological progress is needed. Regarding the introduction of changes in education level in the estimate of TFP, the results suggest that, although this has an impact on the estimates of the value of time (Fig. 1), there seems to be no gain in explanatory power. Considering all the results (Figs. 3, 4 and 5), for most countries it is indifferent to include changes in education level. This suggests that alternative measures of human capital changes, or adjustments other than the education level could be considered in TFP to decrease the magnitude of the value of time in comprehensive savings while improving the fit with the theory. Extending the factors of production to include natural resources use may be relevant (e.g. Brandt et al., 2017). In order to check whether there is evidence of exact verification of expression (1) we test the hypotheses (i) β1 = 1 with a t-test, and (ii) β0 = 0 ∧ β1 = 1 with a Wald test. Regarding (i), Fig. 6 shows the regressions for which we cannot reject expression (1) except for a constant. There are 14 countries for which the data does not reject the possibility that β1 = 1 for some model. Considering all the time horizons, models with the value of time (Models 3 and 4) have more regressions for which β1 = 1 is not rejected, while model 2 performs worst. It seems that including green adjustments (Model 2) to

5. Conclusions The comprehensive accounting theory predicts that a measure of net savings equals the present value of future consumption changes. The relevance of this statement is that the use of savings as indicators of welfare change and weak sustainability depends on the confirmation of this relationship. This paper presents the results of testing various measures of savings, with a focus on the value of technological progress, thus contributing to better understand (i) the power of those measures in predicting the present value of future consumption changes, (ii) the adjustments to net savings that are more important to include. The motivation for analyzing the importance of the value of technological progress on indicators of weak sustainability is twofold. First, early tests did not find evidence of a relationship between adjusted net savings and the present value of future consumption changes for rich countries. A possible argument is that in rich countries the accumulation of capital other than man-made capital (e.g., human capital) may have a stronger contribution than in developing countries, and, therefore, should have been included in the savings measures. Second, having a large forward-looking term in an indicator of future development hinders its applicability, since an estimate of future technological progress is necessary. In this sense, having a high value of TFP growth reflects our inability to measure current productive capacity, and consequently does not allow for foreseeing future consumption possibilities. So, if this adjustment is a relevant term to include 8

Ecological Economics 164 (2019) 106382

R.P. Mota and M.A. Cunha-e-Sá

Fig. 6. Results of the t-test with H0 : β1 = 1 for the various time horizons, using HAC estimators. Circles represent model/country pairs where the p-value of the test is higher than 0.1 (do no reject H0).

measures of savings to indicate future changes in consumption, further research is required to understand whether conventional TFP (i) is being overstated, or (ii) can be reduced by extending the capital base of when performing growth accounting. In this paper, we have extended TFP to include changes in education level. The main conclusion from our results is that, for the countries analysed, including a measure of technological progress improves the fit with the theory. However, including changes in human capital in the estimate of TFP growth does not result in significant improvements. Therefore, adjustments other than the education level should be considered in TFP to attempt to decrease the magnitude of the value of time in comprehensive savings, for instance with alternative measures of human capital changes or by including natural capital use as a factor of production. This means that bringing together the literature of economic indicators of sustainable development with growth accounting, is a potentially interesting area of research not only to construct better measures of weak sustainability but also to provide support for the construction of economic growth models.

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Acknowledgments This work was funded by Fundação para a Ciência e a Tecnologia FCT - (UID/ECO/00124/2013 and Social Sciences DataLab, Project 22209), POR Lisboa (LISBOA-01-0145-FEDER-007722 and Social Sciences DataLab, Project 22209) and POR Norte (Social Sciences DataLab, Project 22209). Rui Mota acknowledges the financial support by FCT (SFRH/BPD/81880/2011). Maria A. Cunha-e-Sá acknowledges the support from FCT under the project UID/ECO/00124/2013. Appendix A. Supplementary Data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ecolecon.2019.106382. References Aronsson, T., Löfgren, K.-G., 1995. National product related welfare measures in the presence of technological change: externalities and uncertainty. Environ. Resour. Econ. 5, 321–332. Arrow, K.J., Dasgupta, P., Mäller, K.-G., 2003. Evaluating projects and assessing sustainable development in imperfect economies. Environmental and Resource Economies 26, 647–685. Arrow, K.J., Dasgupta, P., Goulder, L.H., Mumford, K.J., Oleson, K., 2012. Sustainability and the measurement of wealth. Environ. Dev. Econ. 17, 317–353. Asheim, G.B., 1994. Net national product as an indicator of sustainability. Scand. J. Econ.

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