Macro inovation dynamics and the golden age

The contri-bution of Phelps had emphasized, in its application to a setup with a Cobb-Douglasproduction function, that the golden rule requires that the savings rate is equal to theincom

Macro Innovation Dynamics and

the Golden Age

Paul J J Welfens

New Insights into Schumpeterian

Dynamics, Inequality and Economic Growth

Macro Innovation Dynamics and the Golden Age

Jean Monnet Chair for European Economic Integration and Chair for MacroeconomicsPresident of European Institute for International Economic Relations (EIIW) at theUniversity of Wuppertal

Wuppertal, Germany

Non-resident Senior Research Fellow

AICGS/Johns Hopkins University

Library of Congress Control Number: 2017930939

# Springer International Publishing AG 2017

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Innovations were responsible for driving the Industrial Revolution in the eighteenthand nineteenth centuries The twentieth century has witnessed the combination ofmultinational companies’ foreign direct investment dynamics and product as well

as process innovations; and the early twenty-first century is shaped largely bydigital innovation dynamics While innovations have been analyzed by manyeconomists—beginning, in particular, with Schumpeter—there is surprisingly lim-ited research carried out on the role of innovations in Macroeconomics (as atextbook, Aghion/Howitt’s Endogenous Growth Theory summarizes manyapproaches) With my book, “Innovations in Macroeconomics”, I have tried tocontribute to closing some of the knowledge gaps and emphasis has been given tothe role of foreign direct investment (FDI), innovations and trade The role of FDI isgrowing in the context of economic globalization and it requires the making of adistinction between GDP and gross national product—typically neglected in openeconomy macroeconomics so far This point has already been emphasized inInnovations in Macroeconomics Consumption in an economy with trade and FDI

is proportionate to GNP, not to GDP; and imports are also proportionate to domesticGNP The export volume is proportionate to foreign GNP—not to GDP For manycountries there is a considerable difference between GNP and GDP

In this complementary book, I present my papers for the Brisbane conference ofthe Schumpeter Society, the paper for the Jena conference of the SchumpeterSociety as well as my paper on innovation and growth for a Sino-German proj-ect—here funding from the German National Science Foundation is gratefullyacknowledged—plus a new approach to the golden age in the presence of a researchsector Moreover, the last chapter—my paper for the Montreal conference of theInternational Joseph A Schumpeter Society—suggests an innovative approach thatuses a knowledge production function that can be plugged directly into a macro-economic production function and hence enables a straightforward way for newendogenous growth approaches from both a theoretical and empirical perspective.The main ideas in this book are to include innovations into the Mundell-Flemingmodel and to take a broad, fresh look at the golden age in neoclassical growththeory In a broader view that includes environmental aspects, the question of agolden rule that maximizes per capita consumption is even more important than theclassical contributions in this field: An economy that has a capital intensity

v

exceeding that which is required by the golden rule is not achieving the maximumper capita consumption on the one hand, on the other hand, in the case of a closedeconomy, one may emphasize that the amount of physical capital produced andemployed—this is associated with the use of resources and energy (leading tohigher CO2emissions)—is too high: the environmental quality is thus worse than

a situation in which the golden rule was observed would imply

The golden age, characterized by maximum per capita consumption in the steadystate, has, in the original contribution of Edmund Phelps (1961), been dubbed “afable for growthmen” and indeed the golden rule has not been considered as aserious element of economic policy—it was rather discussed as a very theoreticalpoint of neoclassical growth analysis; with the adoption of endogenous growththeory the golden rule seemed to become a remote corner of analysis The contri-bution of Phelps had emphasized, in its application to a setup with a Cobb-Douglasproduction function, that the golden rule requires that the savings rate is equal to theincome share of capital and the output elasticity of capital This interpretation is notfully consistent to the extent that it is understood to imply that all profits must beinvested if per capita consumption is to be maximized; rather a certain combination

of the savings rate of capital owners and of workers is also compatible with thegolden age An alternative condition for the golden rule is to require that the growthrate of output should be equal to the real interest rate and one may argue that profitmaximization and competition will bring about this equality Hence the only task ofgovernment then is to implement competition and to encourage profit maximiza-tion There are, however, three difficult problems for competition policy: (1) Com-petition policy in small open economies is not easy to implement effectively in aworld economy with multinational companies playing an increasing role; while inthe tradables sector free trade policy effectively is competition policy, the problem

in the non-tradables sector is much more difficult—often the presence of just onemultinational company already covers the entire domestic market so that there islittle room for actual or potential competition (the non-tradables sector couldrepresent between 20% and 40% of output in OECD countries and NewlyIndustrialized Countries; and even more in developing countries) (2) Profit maxi-mization is not always the natural behavior of relevant economic actors; thegovernment sector itself and government-owned firms should be considered as apotential problem or to put it differently: here, looking at the sectoral implication ofthe golden rule would be particularly useful, but no minister of finance and nocouncil of economic advisers has so far seriously emphasized the golden rule as apolicy element This point will be rather neglected in the subsequent analysis: There

is (3) the question of negative external effects from production How can negativeexternal environmental effects—related to production—be integrated in a simplegrowth model? Finally, there is the problem that the more innovative the economy

is, the less likely one should expect full competition to characterize the economy:Whenever there are product innovations or patents—the latter giving an effectivemonopoly over several years to the innovator—one may face the problem thatproduction factors are not simply rewarded in line with marginal productivity:Market power could play a crucial role in factor markets, possibly less so insmall open economies than in big economies

Moreover, deviations from the golden age are not in practice an irrelevantproblem of reality and economic policy, respectively It should be rather obviousthat in rather poor countries a lack of growth-enhancing economic policy will bringabout starvation, so that pushing governments to consider the implications of thegolden rule should be a natural element of modern development policy and UN orWorld Bank projects for stimulating economic development in the South of theworld economy.

This book has been completed in 2015 and 2016 in Beijing and Washington DC,respectively In China another project financed by the German National Foundationhas commenced Again, we are grateful to Mu Rongping and Reinhard Meckl whohave initiated the projects that have a broad focus on innovation dynamics, includ-ing green innovation dynamics (the first book edited by Rongping/Meckl wasInnovation for Green Growth; Beijing: Science Press: 2014) In Washington DC Ipresented at both the Congressional Research Service and at the IMF (on June

27 and 28, 2016, respectively) a theoretical and empirical paper on the knowledgeproduction function—a joint paper with Andre Jungmittag in which we haveconducted an empirical analysis covering 20 EU countries between 2002 and

2014 and also suggested ways of plugging the empirical results into a nomic production function This paper, which looks at the creation of new knowl-edge, is not included here, however, part of the theoretical basis is shown in the lastchapter of this book (those interested can find the EIIW paper No 212 on the website

macroeco-of the European Institute for International Economic Relations:www.eiiw.eu)

I am grateful for the research support of Jens Perret and Tony Irawan (EIIW andthe Schumpeter School of Business and Economics, respectively) I am alsograteful for the editorial support of David Hanrahan, Samir Kadiric and EvgeniyaYushkova (EIIW) As regards our China research projects, I would also like tothank Mu Rongping (Chinese Academy of Sciences), Rainer Walz (FraunhoferInstitut ISI, Karlsruhe), Klaus Rennings (ZEW) and Reinhard Meckl (Universita¨tBayreuth) for discussions on the subject matter, as well Raimund Bleischwitz(University College, London) and, in the field of innovation and growth, colleagues

at the International Joseph A Schumpeter Society—the bi-annual meeting inDenmark was particularly stimulating (unfortunately I was unable to attend theBrisbane meeting but Tony Irawan has presented my paper) Special thanks go toAndre Jungmittag from the Frankfurt Applied University; discussions about trade,innovation and economic stability with IMF colleagues are also acknowledged, as

is the hospitality of AICGS/The Johns Hopkins University, Washington, DC, overmany years The responsibility lies, however, with the author only

Wuppertal, Washington and Beijing

About the Book

This book is organized in five chapters: Following a short introduction, Chap 1suggests some new ideas on innovation, growth and income inequality The inno-vative approach presented introduces a modified neoclassical growth model whichincludes a new bias of technological progress in a quasi-endogenous growth model

in which part of labor is used in the research & development sector The tion of a macroeconomic production function and a new progress function, plus theassumption that the output elasticity of capital is positively influenced by the size ofthe R&D sector, sheds new light on innovation and growth as well as on incomeinequality: Thus there is a new approach for explaining Piketty’s historical findings

combina-of a medium term rise combina-of the capital income share in industrialized countries—both

in the earlier and later part of the nineteenth century and in 1990–2010 (thiscontribution has been published originally in the Journal International Economicsand Economic Policy) A rising share of capital income can be explained within thisapproach by the increase in the output elasticity of capital, which has been devel-oped in a new way, namely in the context of R&D In the approach presentedherein, the golden rule issues are also highlighted and it is shown that choosing theright size of the R&D sector will bring about maximum sustainable per capitaconsumption While the basic new model is presented for the case of a closedeconomy, one could easily accommodate both trade and foreign direct investmentand thereby get a better understanding of complex international investment, tradeand FDI dynamics—including with respect to the envisaged Transatlantic Tradeand Investment Partnership between the US and the EU

The second chapter is my revised contribution from the first Sino-Germanproject The analysis links R&D, foreign direct investment, output and CO2emissions in a simple growth model Based on the modified neoclassical growthmodel, key issues can be raised with respect to sustainable growth and severalconclusions can be drawn with respect to economic welfare and optimum consump-tion per capita, respectively It may be argued that in several industrializedcountries—and China—investment-GDP ratios in certain periods are above thelevel that is consistent with optimum per capita consumption; the capital intensityexceeds the ratio of capital to workers (in efficiency units) that is consistent with amaximum long-run per capita consumption CO2emission levels could be reduced

in an efficient manner on the basis of a broad approach that emphasizes

ix

Schumpeterian dynamics: Taxing emissions and giving subsidies for innovationscould be useful elements of innovation-enhancing policy Promoting greeninnovations—including the sustainability design of products-, renewable energyand realizing adequate genuine savings could be key policy elements for a consis-tent strategy to achieve sustainable growth Moreover, green ratings for companieslisted on the stock market could be crucial options for combining sustained growth,modernization and innovation Part of the analysis is based on the EIIW-vita globalsustainability indicator.

A further analytical contribution is presented in Chap.3 Economic growth is, inreality, not a smooth process and it is not clear why economic growth is ratherunstable across OECD countries and the global economy Economic growth iscertainly influenced by many factors, including innovation dynamics and technol-ogy, respectively Technological progress can have domestic sources and is, then,largely related to the innovation system, but in open economies the subsidiaries offoreign MNCs can also play a role in the host country Moreover, there could beinternational technology spillovers, part of which are related to international tradeand FDI dynamics Foreign direct investment has rarely been included in theanalysis of economic growth, despite the fact that economic globalization hasclearly reinforced the role of multinational companies in world investment From

a macroeconomic perspective, the presence of MNCs’ subsidiaries should not onlybring effects on capital accumulation and technology transfer; rather it is important

to consider that a distinction has to be made between GDP and GNP Thisdistinction, which concerns the specification of the savings function as well asother functions, has been much neglected in the literature; it is relevant both inmedium term macro models and in long run growth models In the standardneoclassical growth model with exogenous technological progress a rise of theprogress rate leads to a fall of the level of the growth path and a higher permanentgrowth rate of output This suggests that a technology shock should bring about aquasi-growth cycle and such a phenomenon—with a temporary fall of output—is,however, not observed in newly industrialized countries The empirical patterns ofgrowth and innovation dynamics do not show such a paradoxical temporary fall ofincome and income per capita, respectively The paradoxical result of the standardgrowth model is avoided in a model in which the output elasticity of capital depends

on the progress rate; certain parameter restrictions apply which are highlighted inthe analysis; furthermore, we get additional insights into the issue of the golden ruleand maximization of per capita consumption, respectively Moreover, it is interest-ing to consider the role of foreign direct investment for the growth model of an openeconomy and technological progress, respectively In this semi-endogenous set-up,the focus is mainly on asymmetrical foreign investment, namely inward FDIinflows Foreign direct investment inflows have a direct impact on the steadystate solution, namely both on the level of the growth path and the permanentgrowth rate—the latter to the extent that we consider a technological progressfunction in which both the foreign progress rate and the share of the capital stockowned by foreign investors are considered The relative impact of domestic

progress and internationally induced progress is discussed Finally, the issue of aconsistent investment function which takes into account both the short term and thelong run consistency is considered and the impact of changes in the progress rate arepointed out—along with broader policy conclusions of the analysis presented Atthe bottom line it is shown that a positive impact of the progress rate on the outputelasticity of the capital stock can bring a smooth transition to both a higher level ofthe growth path and a higher permanent growth rate The perspectives on the role ofFDI inflows in a two-country model with symmetrical flows have to be explored infurther analysis Key policy conclusions concern the question of to what extentgovernment should try to achieve a golden state while adequately taking intoaccount the role of foreign direct investment inflows Within a broader group ofcountries it would also be useful to consider options for cooperation in growthpolicies—certainly to the extent that there are symmetrical or asymmetric interna-tional technology spillover effects.

Chapter 4 presents a new multiplier analysis for a Schumpeterian Fleming model Traditional open economy macro models have focused on themix of fiscal and monetary policy while completely neglecting innovation policy.The new model presented is the first macro model that explicitly considers productinnovations in an open economy model Product innovations are considered in theconsumption function, the investment function, the export function, the importfunction as well as the money demand function; plus the net capital inflow function.The policy multipliers are derived for fiscal policy, monetary policy and innovationpolicy In an extended version of the model, the role of foreign direct investment isconsidered, in an approach for a small open economy Domestic and foreignproduct innovations are considered and their impact on policy multipliers isanalyzed Finally, the role of supply-oriented, innovation-enhancing fiscal policy

Mundell-is dMundell-iscussed Moreover, the empirical evidence for product innovation dynamics Mundell-isconsidered

Chapter 5 can be summarized as follows: The macroeconomic productionfunction is a traditional key element of modern macroeconomics, as is the morerecent knowledge production function which explains knowledge/patents by certaininput factors such as research, foreign direct investment or international technologyspillovers This study is a major contribution to innovation, trade, FDI and growthanalysis, namely in the form of a combination of an empirically relevant knowledgeproduction function for open economies—with both trade and inward FDI as well

as outward foreign direct investment plus research input—with a macro productionfunction Plugging the open economy knowledge production function into a stan-dard macroeconomic production function yields important new insights for manyfields: The estimation of the production potential in an open economy, growthdecomposition analysis in the context of economic globalization and the demandfor labor as well as long run international output interdependency of big countries;and this includes a view at the asymmetric case of a simple two country world inwhich one country is at full employment while the other is facing underutilizedcapacities Finally, there are crucial implications for the analysis of broad regionalintegration schemes such as TTIP or TPP and a more realistic and comprehensiveempirical analysis

At the bottom line, there are many good arguments for integratingSchumpeterian aspects into open economy macroeconomics The technology factor

in International Economics—with people concerned about the environment—isincreasingly important (here Lucas Bretschger’s research at ETH Zürich hasmade crucial contributions over many years) The modified neoclassical growthmodels are rather simple in the basic setting, however, this type of modeling is stillvery useful for considering key issues and topics

1 Green Innovations and CO2in a Growth Perspective:

A Neoclassical Model 1

1.1 A Rational Approach to Promotion of Green Innovation 6

1.1.1 Taxation and Subsidies as a Means to Internalize External Effects 6

1.1.2 Economic Growth 10

1.1.3 Traditional Neoclassical Growth Modeling 11

1.2 Technological Progress and R&D 17

1.2.1 Golden Rule Aspects in an Economy with Technological Progress 19

1.2.2 Extensions of the Neoclassical Growth Model 22

1.2.3 Growth Model with R&D and Emissions 25

1.2.4 Growth in a World with Negative External Effects: CO2Emissions and Hybrid Welfare 27

1.3 Policy Perspectives 28

1.3.1 Taxation, Risk, and Innovation 30

1.3.2 Liability Rules and Insurance Costs 31

1.3.3 Green Rating and Capital Markets 31

1.3.4 Double Sustainability 32

Appendix 37

References 49

2 Innovation, Inequality, and a Golden Rule for Growth in an Economy with R&D 51

2.1 New Quasi-endogenous Growth Model with Biased Technological Progress 62

2.2 Policy Conclusions 66

Appendix 70

References 78

xiii

3 Technological Progress, Output Elasticity, FDI, and Growth

Cycles 81

3.1 A Growth Model with Foreign Direct Investment 84

3.2 Technology, the Production Function, and the Impact of a Shift in the Progress Rate 87

3.3 Asymmetric FDI Inflows and the Role of Induced International Technology Transfer 90

3.4 Policy Conclusions 94

Appendix 95

References 96

4 Product Innovations in a Schumpeterian Mundell–Fleming Model 97

4.1 Theoretical Approach: Schumpeterian Open Economy Macro-model with Product Innovations 98

4.1.1 Basic Theory 98

4.1.2 New Analytical Approach: A Schumpeterian Mundell–Fleming Model Without and with FDI 106

4.2 Empirical Analysis 107

4.3 Policy Implications 108

Appendix 110

References 124

5 Schumpeterian Macroeconomic Production Function for Open Economies 125

5.1 Knowledge Production Function and Macroeconomic Production Function 130

5.2 The Schumpeterian Macroeconomic Production Function 134

5.2.1 Output Elasticity with Respect to Foreign Knowledge 137

5.2.2 Endogenous Growth Model 138

5.2.3 Golden Rule 139

5.3 Labor Market Demand and Other Macro Aspects 139

5.4 Hybrid Medium-Term Macro-model 140

5.5 Further Extensions 142

5.6 Policy Conclusions 142

Appendix 144

References 147

List of Figures

Fig 1.1 Subsidizing the innovation sector and imposing a Pigou tax on

the sector with emissions 8Fig 1.2 Gross investment-GDP ratios in selected countries Data Source:

International Monetary Fund (2010), World Economic

Outlook Database 11Fig 1.3 Investment-GDP ratio and net savings ratio in selected

countries Data Source: World Bank, World Development

Indicators & Global Development Finance; International

Monetary Fund (2010), World Economic Outlook Database 12Fig 1.4 Golden rule in a standard neoclassical growth model

(E1F¼ C/L) 13Fig 1.5 (a) Shares of renewables, (b) genuine savings rate/World Bank,

(c) volume-based RCAs for “green exports.” Data Source:

WDI Online, own calculations (RCA) 16Fig 1.6 Impact of a rise of the growth rate of knowledge on the level of

per capita income (y) and the growth rate of per capita income(tgα ¼ a) 18Fig 1.7 Real interest rate and growth rate of real GDP in selected

countries Data Source: European Commission Ameco Database,OCED (2008), [Real long-term interest rate based on GDP

deflator (%)]; World Bank, World Development Indicators &

Global Development Finance [Real interest rate

(real lending rate) (%), GDP growth (annual %)] 20Fig 1.8 Genuine savings rate for selected countries Note: Adjusted

net savings are equal to net national savings plus education

expenditure, minus energy, mineral and net forest depletion,

and carbon dioxide and particulate emissions damage

Data Source: World Bank, World Development

Indicators & Global Development Finance 22Fig 1.9 Golden rule with real money balances and R&D sector

employment 26Fig 1.10 Double sustainability 34Fig 1.11 Global sustainability indicator 35

xv

Fig 2.1 Rise of the R&D sector in the quasi-neoclassical growth model 66Fig 3.1 Traditional and Schumpeterian growth models 82Fig 4.1 Product innovations in a Schumpeterian MundellFleming

model 99Fig 4.2 Basic regression model for product innovations in 25 EU

countries: 2006–2012: panel correct standard error (PCSE)

regression and feasible generalized least square (FGLS)

regression results; data for product innovations from EU

surveys 108

List of Tables

Table 2.1 Capital income share as a % of GDP 55Table 2.2 Gini coefficient 56Table 2.3 Imported R&D services from abroad which is used as

intermediate input (as a % of GDP/total value added) 57Table 2.4 Total R&D services which is used as intermediate input

(as a % of GDP/total value added) 58Table 2.5 Total domestic R&D services which is used as intermediate

input (as a % of GDP/total value added) 59Table 2.6 Total intramural R&D expenditure (GERD) (as a % of GDP) 60Table 2.7 Total factor productivity (2010¼ 100) 61Table 4.1 Multiplier for Schumpeterian MundellFleming model 105Table 4.2 Multiplier for innovation dynamics and FDI inflows in a

Schumpeterian MundellFleming model 106Table 4.3 α* multiplier 106Table 5.1 Knowledge production function: patent applications at the

European Patent Office explained by researchers (full time

equivalent), per capita GDP (PPP, constant dollars), inward

FDI–GDP ratio: panel data analysis for 20 EU countries,

2002–2012; all variables in logs 128

xvii

Green Innovations and CO2 in a Growth

Economic growth is a key field of modern Economics and indeed since theIndustrial Revolution sustained economic growth of per capita income has beenobserved in the world economy In the USA, the twentieth century stands for a long-run per capita growth rate of about 2%, the 1990s even 3% per year was achieved.Japan and several Asian Newly Industrialized Countries have recorded 5–8% overmore than a decade in the 1960s, 1970s, and 1980s, China even achieved 8–10% inthe first decade of the twenty-first century, but there is, of course, not much doubtthat the growth rate of China will reduce to 2–3% over time, as its per capita income

is converging towards that of the US or leading EU countries Economic growth iswelcomed by both ordinary citizens and politicians; however, the rise of per capitaincome typically also means that there is an increasing use of natural resources andfossil energy sources—the exploitation of natural, nonrenewable resources is effec-tively reducing the effective (adjusted) savings rate as is emphasized by the WorldBank, which adds education expenditures to the traditional definition of savings andthus gets rather different savings rates than the traditional view on gross savingssuggests Moreover, the use of fossil fuels implies that the growth of output in theworld economy goes along with CO2and other emissions (particulate matter) thatimply risks for physical assets and human life in the long run The question as tohow CO2emissions, as a negative externality of production, could be included in agrowth model is considered subsequently; in this context, one may also point to thenew sustainability book with the EIIW-vita global sustainability indicator (Welfens

et al.2015)

The basic neoclassical closed economy growth model, with a savings rate (s), agrowth rate of population (n), and a growth rate of knowledge (a), results in thesteady state solution for the ratio of real GDP (Y ) to labor in efficiency units y # :¼(Y/(AL)¼ (s(1  τ)/(a + n))β/(1  β), whereβ is the output elasticity of capital K, andthe production function isY¼ Kβ(AL)1 β(A is the stock of knowledge, L is labor,τ

is the income tax rate, # indicates the steady state; 0< β < 1) Note that the onlyfiscal variable that can be considered here is the income tax rate; the growth rate of

Y in the steady state is a + n Under certain conditions, the neoclassical model is

# Springer International Publishing AG 2017

P J J Welfens, Macro Innovation Dynamics and the Golden Age,

DOI 10.1007/978-3-319-50367-7_1

1

equivalent to the modern growth model as presented in Aghion and Howitt (1998):The modeling is more complex, the ingredients are Utility-maximizing households(infinite time horizon), and the utility function isU(C)¼ (C(1  ε)– 1)/(1 ε); theintertemporal elasticity of substitutionη ¼ 1/ε The relevant Euler equation is heregiven by –ε(dC/dt)/C ¼ ρ – r, (where r is the real interest rate; note (1/(1 + ρ) is thediscount factor;ρ > 0 This gives the fundamental equation for the growth rate g0

¼ (ρ – r)η

According to the above equation, in the decade after the Transatlantic BankingCrisis, the growth rate should have increased strongly since the real interest rate hasfallen massively in the USA, Europe, and Asia This is not what we see however.The frictions observed in the new post-Lehman Brothers reality are particular, andthe new world with almost zero real interest rates implies many distortions.This book is really about the normal world and complementary aspects ofeconomic growth (e.g., environmental aspects in the subsequent analysis)—andone may hope that the OECD countries will have returned to a normal economysetting by the end of 2025 (BREXIT is, however, another destabilizing impulse forthe EU and the OECD, respectively) A modified neoclassical growth model is stillquite useful Additionally, the implications of some modern endogenous growthmodels are not fully convincing; e.g., in the context of a simple Romer model—with λ denoting a productivity parameter in the research sector where productvarieties are produced that feed into output (output parameterα00 > 0)—one getsfor the growth rateg0in steady state:g0¼ (α00λL – ρ)/(α00+ε); it is a bit strange thatthe size of the economy (L ) affects g0, although in a digital world the number ofpeopleL could play a positive role for economic growth—namely in the context ofdigital network effects The digital economy itself raises, however, certain critical

key issues and topics, including certain environmental aspects of growth

People have a natural interest in achieving high living standards, which thusgenerates analytical interest in the topic of economic growth At the beginning ofthe twenty-first century, the dynamics of global warming have added one importantelement, namely to consider the role of CO2emissions and other greenhouse gasemissions, respectively Innovation dynamics—including green innovations—can

be considered in various ways in growth models (e.g., Bretschger 1999, 2008,

2011); some economists have argued that green innovations and the diffusion ofenvironmentally friendly new products could contribute to climate change mitiga-tion in an efficient manner and create new opportunities for economic growth (e.g.,Aghion et al.2009; Popp et al.2009) Environmental issues and growth dynamicscan also be considered in the broader context of trade (e.g., WTO1999) and foreigndirect investment (Welfens 2011; Erdem2010,2015) In a broader perspective,issues may also be raised related to capital markets and investment incentives—subsequently, part of the analytical focus will be on the role of green ratings:Companies are rated on the basis of the sustainability of production processes andproducts sold

Green innovations are not easy to launch since innovation risks and costs areoften high, while established, less environmentally friendly technologies andproducts dominate many markets However, once green innovations have success-fully been launched, there are good prospects that competition in markets will lead

to rapid diffusion of more environmentally friendly products (Acemoglu et al

2009; Aghion et al.2009) If companies with a green innovation project are afraidthat they cannot fully capture the Schumpeterian innovation rents, becausepolicymakers will effectively push for accelerated diffusion, there is risk of under-investment in green innovations (Jaffe et al 2005; Newell 2009) The role ofinnovations for sustainable growth—sustainable consumption and production—has been emphasized by many authors (e.g., Iges2010; Erdem2010) The role ofinformation and communication technology, including concepts of green IT, hasalso been emphasized (e.g., Welfens2010b)

With some degree of uncertainty, green innovations (Walz 2010) can bemeasured and also countries can be identified on the basis of their innovationdynamics International patent applications are highly correlated with per capitaincome, except for most OPEC countries It is well known that resource richcountries face Dutch Disease problems, which is to say that the high share ofvalue added in the capital-intensive resource extraction sector only gives weakimpulses for the modernization of the industry—and only with a relatively highshare of modern manufacturing industries and a modern innovation system will acountry generate significant contributions to green innovations The market power

of OPEC countries has ambiguous effects on CO2emissions and global innovationdynamics, respectively:

• As regards impulses for reducing CO2emissions it might be argued that OPECcountries’ market power indirectly stimulates CO2-emission-saving technologies

in OECD countries and some Newly Industrialized Countries

• While the above argument may be valid to some extent, it should not beoverlooked that the industrial modernization of OPEC countries in a worldeconomy with lower prices of nonrenewable energy sources is likely to haveadvanced faster than it currently is and this would mean that global innovationdynamics might be stronger without OPEC market power; whether a generalincrease in innovation dynamics also implies more green innovation dynamicshas to be clarified on the basis of empirical analysis

The broad international consensus to limit greenhouse gas emissions in themedium term and to cut emissions in the very long run has contributed to a broadpolicy debate in OECD countries on how energy efficiency and resource produc-tivity could be raised The broad need to implement eco-efficiency principles inproduction implies certain adjustment requirements and the need to adopt newinitiatives for green innovation dynamics The OECD (2009, p 28), with respect tothe EU and the USA notes: “Such tasks are not trivial for manufacturing companiesand places great demands on their organizational management capability Thedevelopment of environmental management systems (EMSs) has tied many of the

1 Green Innovations and CO 2 in a Growth Perspective: A Neoclassical Model 3

environmental monitoring and management principles together, providing a work to move towards eco-efficient production [ .] An EMS is meant to providecompanies with a comprehensive and systematic management system for continu-ous improvement of its environmental performance Once implemented, the systemrelies on a structure that is typically characterized by four cyclical, action-orientedsteps: i) plan; ii) implement; iii) monitor and check; and iv) review and improve[ .]”; and with respect to the European Union, the OECD analysis states (p 38):

frame-“In the last few years, many companies and consulting firms have started usingeco-innovation or similar terms to present positive contributions by business tosustainable development through innovation and improvements in production pro-cesses and products/services A few governments and the European Union (EU) arenow promoting the concept as a way to meet sustainable development targets thatkeep the industry and the economy competitive In the EU, eco-innovation has beenconsidered to support the wider objectives of its Lisbon Strategy for competitive-ness and economic growth In 2004, the Environmental Technology Action Plan(ETAP) was introduced to promote the development and implementation ofeco-innovation The ETAP defines eco-innovation as ‘the production, assimilation

or exploitation of a novelty in products, production processes, services or inmanagement and business methods, which aims, throughout its life cycle, to prevent

or substantially reduce environmental risk, pollution and other negative impacts ofresource use (including energy)’ The action plan provides a general road map forpromoting environmental technologies and business competitiveness by focusing onbridging the gap between research and markets, improving market conditions forenvironmental technologies, and acting globally Eco-innovation now forms part ofthe EU’s Competitiveness and Innovation Framework Program 2007-13, whichoffered EUR 28 million in funding in 2008 to stimulate the uptake of environmentalproducts, processes and services especially among SMEs In the United States,environmental technologies are also seen as a promising means of improvingenvironmental conditions without impeding economic growth, and are being pro-moted through various public private partnership programs and tax credits [ .] In

2002, the Environmental Protection Agency laid out a strategy for achieving betterenvironmental results through innovation [ .] Based on this strategy, it set up theNational Center for Environmental Innovation and is promoting the research,development and demonstration of technologies [ .] In Japan, the government’sIndustrial Science Technology Policy Committee introduced the term ‘eco-innovation’ in 2007 as an overarching concept which provides direction and avision for the societal and technological changes needed to achieve sustainabledevelopment.”

A study by the European Commission (Conte et al.2010) has presented a based approach of cost-efficiency of alternative EU climate policy options throughwhich innovation dynamics could be encouraged to contribute to an environmen-tally sustainable growth path The innovative model, which is based on theCommission’s QUEST Dynamic Stochastic General Equilibrium Model, assessesdifferent policy options in order to identify the best policy mix of environmentaland innovation market instruments in terms of their cost-effectiveness The key

model-finding of the authors is that an adequate policy mix should strongly stimulateresearch and development in the short-term and phase it out by spreading theinnovation support to all sectors in the economy in the medium run Moreover,the authors emphasize the role of the supply chain (Conte et al.2010, p 1): “Theessential contribution of our approach is to consider that green innovation occursalong the supply chain and is not necessarily bounded within a single sector Theintroduction of an exhaustive sectoral input-output matrix allows us to capture thedevelopment and use of environmentally friendly products substituting dirtyproducts across different sectors of the economy Such a “green” multi-sectoralversion of the model allows us to evaluate the marginal economic effects of sector-wide measures compared to economy-wide policy intervention in the environmentaland innovation markets In applied terms, this model is calibrated on our newlyconstructed dataset that includes green R&D and CO2emissions for five sectorswith a distinctive potential for nesting green activities.”

Sustainable growth is a key challenge for Europe, Asia, and other regions of theglobe in the twenty-first century The concept of double sustainability will beemphasized here; sustainability in the traditional sense of environmental economicsmeans that future generations should have the opportunity to enjoy at least the samelevel of well-being as current generations (a notion of sustainability developed inthe Brundtland Report that largely shows the perspective of industrialized countriesand does not emphasize the obvious desire and need of developing countries tocatch up with OECD countries) The second notion of sustainability emphasizedhere is related to financial markets—sustainability means that banks, investmentfunds, and insurance companies, as well as other investors, have a long-runperspective This second notion suggests emphasizing a stronger role for thegreen rating of companies listed on the stock market, and such a rating should be

a signal for investors interested in thoughtful long-run decision-making able development has a natural connotation with growth analysis, namely in thesense that the growth modeling typically looks into the conditions of long-rungrowth and a stable steady state solution

Sustain-Besides the long-run growth analysis, medium-term adjustment and growthdynamics can also be looked into (Barbier2009) has argued that governments’spending programs aiming to overcome the Transatlantic Banking Crisis should bemore focused on the promotion of environmentally friendly growth, so that theglobal economy could be stimulated and new employment would be created, at thesame time, carbon dependency could be reduced, the degradation of the ecosystemcould be reduced, and the problem of water scarcity could be tackled moreeffectively Moreover, the Millennium Development Goal of overcoming extremepoverty by 2015 could be achieved The approach of Barbier is comprehensive butleaves many questions open, including whether or not the chosen analytical basis isconsistent Many policymakers prefer to rely on DSGE models that stand for acomplex approach while neglecting key elements of globalization, which in turn arerelevant for greenhouse gas emissions; e.g., the role of foreign direct investment(FDI) is ignored, although FDI is quite important for international technologytransfer and green growth in many countries In a rather simple neoclassical growth

1 Green Innovations and CO 2 in a Growth Perspective: A Neoclassical Model 5

framework, many key analytical challenges of green innovation and green growthcan easily be incorporated.

While a DSGE model is certainly useful for certain analytical perspectives, thefollowing analysis will largely be confined to a simple modified neoclassicalgrowth model The analysis presented first looks at the basics of green innovationdynamics (Sect 1.1) In Sect 1.2, aspects of modified neoclassical growthmodeling—including the role of the golden rule—are discussed Section 1.3presents some policy conclusions

At the bottom line, analytical progress is developed subsequently and somerough calculations on the impact of CO2emissions on true gross domestic productare also presented; for many OECD countries the corrected gross domestic productfigures—taking into account the quasi-negative value-added of CO2emissions—are rather small relative to official figures from the System of National Accounts.However, there are also industrialized countries in which imputed negative value-added from CO2emissions are rather big: China, a country where CO2emissionshave so far not been internalized through policy intervention, is an interesting casewhere the negative value-added from CO2 emission is in the range of 2–3% ofofficial gross domestic product (the range is a function of the opportunity costs of

CO2 emission reduction) The analysis presented argues that green innovationdynamics could play a crucial role in sustainability and long-run growth Informa-tion and communication technology is a sector that is highly innovative and couldparticularly contribute to green growth—despite some rebound effects in the field

of green ICT One of the most important green potentials that could be exploited byICT is a much more efficient use of machinery and equipment: By introducingvirtual markets and creating virtual machines, individual demand curves at anypoint of time can be aggregated rather effectively, namely in a way that raises thecapacity utilization of real machinery and equipment: The demand collected viacomputer systems and assigned to virtual machines can be assigned in a second step

to real machines and this two-stage system will allow to operate the existing capitalstock in many sectors in a much more efficient way than prior to the expansion ofICT This special aspect will subsequently be neglected However, many other keyaspects of green innovation and green growth will be discussed It will be arguedthat rather simple growth models allow to gain important new insights in the field ofgreen growth analysis

1.1 A Rational Approach to Promotion of Green Innovation

Effects

A government in a market economy has several tasks: creating institutions sary for transactions in markets, stabilization of the economy, and internalizingnegative as well as positive external effects Promoting innovations is a standard

neces-task of government, however, before paying subsidies for research and ment; the economy should be opened up for trade and competition in goods andfactor markets introduced; China has been among the countries that have madeenormous progress in this field since 1990, and membership of the WTO in 2001has been an important signal The EU’s eastern enlargement also stands for aremarkable experience in the field of trade liberalization, privatization, and compe-tition With the ongoing discussion about greenhouse warming and other environ-mental problems—including nuclear risks—there is a special need to emphasizegreen innovation dynamics Innovation dynamics will be high if there are five keyelements present:

develop-• Strong competition

• Sufficient emphasis on human capital formation and the expansion of digitalnetworks which are important for both fast diffusion of technologies and forcreating internet-based innovation networks (with more emphasis ontechnology-intensive production, there will be a growing demand for humancapital so that there is some trade-off between rising government expenditures

on education and rising promotion of innovation)

• Efficient innovation system

• International technology flows—typically partly related to trade and foreigndirect investment inflows

• Adequate incentives: such incentives should tax emissions and provide R&Dsubsidies

As regards innovations, there are often positive external effects from innovations

in a certain sector (or from certain innovative firms in this sector) so that subsidiesfor innovators and research & development are justified In the market for R&Dservices, the social benefits are higher than the private benefits (DD1is above DD0;

DD1indicates private benefits from R&D;q is the quantity) so that the optimumallocation of resources—the optimum quantity of R&D (q1)—is only obtained if themarginal costs curve in the innovation sector (k0i) is shifted downwards in a way that

we get an output that internalizes the positive external effect In the left-hand panel

b, we consider an industryj with emissions, that is, a sector j with negative externaleffects is shown so that the social marginal benefits (DD01) are below the privatesocial benefits (DD00); Q stands for the quantity of the good with emissions Byimposing an adequate Pigou tax on producers, the supply curve—the marginal costcurve—can be shifted upwards k0j1¼ k0

j0ð1þ t0Þ

wheret0is the Pigou tax rate (seeFig.1.1): Thus, the optimal outputQ1is obtained and not the outputQ0, whichwould result in an economy without government intervention The Pigou tax—ortradable emission permits—helps to correct a partial market failure, which wouldnormally characterize the market for goods with emissions If there were no sectorwith Pigou tax, the income tax would have to be raised in order to finance thesubsidies for innovative firms

As regards the economy in the real world, in a framework of Schumpeterianinnovation dynamics and emissions, it may be emphasized that there are two types

of market failures at the same time that can, however, be solved through a combinedpolicy: Subsidies are given to innovative firms in order to internalize the positiveexternal effects from innovation; these subsidies can be financed partly or fullyfrom revenues arising from a Pigou tax on emissions (or from government sellingtradable CO2emission permits to firms) For the sake of simplicity, focus will beplaced on a Pigou tax where the tax rate is τ0, so that the government budgetconstraint reads:G +τ00η00Y¼ τY + τ0η0Y

G denotes real government consumption,τ00is the subsidy rate for the shareη00ofproduction activities that are subsidized;τ is the income tax rate, η0is the share ofoutput, which is subject to the Pigou tax (seigniorage from “producing money” isignored here) This problem of an adequate tax and subsidization system is consid-ered here in a principal way Paradoxically, the emissions are welcome to someextent because this allows government to finance subsidies for innovations andresearch & development, respectively—without any deadweight loss; in theabsence of emissions and an emission tax, respectively, the subsidization ofinnovations would require to raise the income tax rate, which in turn would reducethe level of the long-run growth path in a growth model; and under certainassumptions could even reduce the long-run growth rate of output, namely if theincome tax rate would negatively affect the technological progress rate It may also

be noted—taking due account of well-known results from endogenous growthmodels in the context of the Lucas–Uzawa approach (see Appendix A.4 for asimple model without tax considerations)—that a progressive income tax rate

system might to some extent undermine the incentive to invest in human capital andcould thereby reduce the long-run growth rate.

A few formal aspects of the link between R&D subsidies and emission taxationshould also be highlighted Let us rewrite the government budget constraint asfollows:

τ ¼ γ  τh 0η0ð Þ  ττ0 00η00
τ00 i ð1:1ÞHere, γ : ¼ G/Y; it has been taken into account that η0

¼ η0(τ0)—with ∂η0

/∂τ0

< 0—and that η00¼ η00(τ00)—with ∂η00/∂τ00> 0 This implies that the income taxrate can be reduced ifτ0η0(τ0)> τ00η00(τ00), and a lower income tax rate will raise thelevel of the growth path An interesting case is an economy without any income tax;therefore, the government budget constraint will read (withη00¼ (1  η0) ):γ ¼ τ0η0(τ0)

τ00[1 η0](τ00) Taking the total differential, we can write:

dγ ¼ η0dτ0þ τ0η0

τ 0dτ0þ τ00dη0 η00τ00dτ00 ð1:2ÞSincedη0¼ η0

As regards externalities, it is quite important to make a distinction betweenconsumption and investment goods It has been assumed that negative externalitiesfrom emissions are from both sectors and that there is no difference between the twotypes of goods Unfortunately, the OECD/IEA does not offer adequate data onsector differences in CO2emissions—some of the relevant data for the BRICS aregiven in Appendix A.3

Different sectoral externalities can broadly be analyzed within a two-sectorapproach If there are only positive externalities in the capital goods sector—and

if these are internalized through a subsidy—and if all negative externalities(emissions) are in the consumption goods sector, key issues can be analyzed within

a one sector model: The positive externality shows up in the equation for profitmaximization, namely that the real interest rate should be equal to the net marginalproduct of capital, which isβkβ  1–δ + τ00 (assuming that per capita outputy¼ kβ,

wherek is the capital intensity K/L; K is capital and L is labor) Moreover,τ ¼ γ + τ00will have to be taken into account, which is relevant for the savings function—since

savings S¼ sY(1  τ), where 0 < s < 1 It can be shown that the subsidy forinnovations in capital accumulation paradoxically implies a reduction in the level

of the growth path within a neoclassical growth model If all emissions are in theconsumption sector, the golden rule relevant for maximum sustainable per capitaconsumption has to be modified adequately

Among the leading economies—including China (and India)—there seems to be anongoing quest for high growth rates For countries with a low per capita income,high economic growth seems to be a natural goal of policymakers since growth iskey for economic catching up High investment-GDP ratios are typically considered

to be crucial pillars for high economic growth (gY) of real GDP becausegY¼ (I0

/

Y )∂Y/∂K, where I0 is real net investment andK is the capital stock It should benoted that the growth rate of GDP can be raised by:

• Increasing the net investment-GDP ratio

• Raising the marginal product of capital (with a Cobb–Douglas productionfunction ∂Y/∂K ¼ βY/K; the parameter 0 < β < 1); an important aspect of themarginal product of capital is that it does not only depend on net investment,rather it also depends on the gross investment output ratio with technologicalprogress in a vintage model Stoleru (1978) has shown that in the case of a Cobb–Douglas function, higher technological progress amounts to raising the capitaldepreciation rateδ

It should also be noted that traditional growth theory—read the Solow model andmany refinements following this approach—has ignored the fact that production isassociated with emissions and hence a “true national accounting system” wouldhave to reflect that one should consider at least three output data in an enhancedsystem of economic statistics:

• GDP (Y )

• Net domestic productYδK

• “Net net domestic product” which could be defined asYδKV where V is theeconomic negative value-added of emissions (and waste); innovations wouldhelp to reduceV and if V¼ v00Y the key challenge is to reduce v00over time.The latter aspect has so far been ignored in official statistics and in the literature.The traditional growth literature has, however, developed an important concept,which is indirectly related to the emission problem of many countries—the concept

is normative and comes under the heading of maximum per capita consumptionC/L(C is real consumption, L is the population and the workforce, respectively) in thesteady state If it is assumed that the individuals’ utility function isU(C), it seems

wise for government to maximize steady state per capita consumption (C/L )#,where # denotes the steady state—read: the long-run equilibrium.

Capital accumulation is crucial for economic growth The investment-GDP ratio

of Germany and Japan has declined in the two decades after 1990; the GDP ratio was about 20% in 2009/2010, slightly higher than in the USA This isgreatly in contrast to the rising investment-GDP ratio of China, which reachedabout 40% at the beginning of the twenty-first century This raises doubts thatChina’s investment dynamics is sustainable and rational, respectively If adjustednet savings are considered—according to World Bank Data—we can see that thedifference betweenI/Y and the adjusted net savings ratio in the period 1990–2008has reached about 12% in 1990–2001 (see Figs 1.2 and 1.3), after 2001 thedifference that indicates capital depreciations has strongly increased The adjustednet savings ratio takes the depletion of natural resources into account as well asexpenditures on human capital formation

investment-Besides physical capital accumulation, focus may be placed on accumulationdynamics in human capital, which has been emphasized in the Lucas–Uzawaapproach While the Lucas–Uzawa approach—with emphasis on human capital—

is useful for certain questions, it may be pointed out that refinements of thetraditional Solow model also has its merits and therefore the subsequent analysislooks at key aspects of refining the approach of Solow (1956)

The growth model of Solow (1956) is based on the assumptions that savingsS¼ sY(and hence S/L¼ sY/L) and that there is a well-behaved neoclassical productionfunction F(K,L ); assuming a linear-homogeneous production function, we can

Fig 1.2 Gross investment-GDP ratios in selected countries Data Source: International Monetary Fund ( 2010 ), World Economic Outlook Database

write for per capita outputY/L : ¼ y ¼ f(k)—where k : ¼ K/L is the capital sity—and imposing the goods market equilibrium conditionδK + dK/dt ¼ sY yields

inten-a different equinten-ation for the cinten-apitinten-al intensityk Assuming a constant growth rate (n)

of the population and considering that dk/dt¼ (dK/dt)/L – nk and imposing theequilibrium conditionS/L¼ (dK/dt)/L + δk, we can write:

This equation can be used to determine the equilibrium condition, namely thesteady state value k# (a stable k# implies dk/dt¼ 0; if dk/dt ¼ 0, the grossinvestment-GDP ratio is equal tosf(k#) and this term is equal to (n +δ)k#; therefore(n +δ)k# is the amount of per capita investment needed to maintain the steady statecapital intensity) The Solow equation is modified in a simple way, namely byassuming a Cobb–Douglas production function Y¼ KβL1 β so that y¼ kβ

(0< β < 1) The steady state solution for k# is:

The optimum growth literature (Phelps1961; Von Weizsa¨cker1962) puts focus

on the equation and how per capita consumptionC/L can be maximized, which isgiven by the following function in the steady state of a closed economy withoutgovernment consumption:

Investment minus Adjusted net savings

Fig 1.3 Investment-GDP ratio and net savings ratio in selected countries Data Source: World Bank, World Development Indicators & Global Development Finance; International Monetary Fund ( 2010 ), World Economic Outlook Database

C=L ¼ y k#ð Þ  n þ δð Þk# ð1:7ÞMaximizingC/L is obtained under the golden rule; here this requires for the case

of the Cobb–Douglas functiony¼ kβthat

If profit maximization of firms brings about the equality of the real interest rate

r and the net marginal product of capitalβkβ  1 δ, we get the golden rule that

r must equal the growth rate of output (here the growth rate is n); alternatively, wecan state that in the golden age—equivalent to the golden rule—the sum of [n +δ]y

is equal to the marginal product of capital If, initially, per capita savings are given

bys0y(k), the steady state capital intensity is equal to k#0 However, the goldenrule—maximizing per capita consumption in the steady state—requires that wechoose that capital intensity, which is characterized by a tangent to the productionfunctiony(k), where the slope must be equal to that of n +δ (point E1; see Fig.1.4).The capital intensitykgoldbrings about the maximum sustainable per capita con-sumption, which is equal to the distance E1F This capital intensity can be reached ifthe savings rates is reduced to s1

Alternatively to the conditionr¼ n, we can state that s ¼ β, because from d(C/

L )/dk¼ βkβ  1– (n +δ) ¼ 0 we have the equation k#gold¼ [β/(n + δ)]1/1  β, while

the accumulation dynamics of the growth model for the steady state imply that

k #¼ [s/(n + δ)]1/1  βand this implies (Welfens2011)

α α

Fig 1.4 Golden rule in a

standard neoclassical growth

model (E1F ¼ C/L)

rate If the initial savings rates were too low—that is k#< k#gold—the governmentshould raise the savings rate.

If the actual steady state capital intensity exceeds the capital intensity required

by the golden rule, the per capita consumption and the ratioC/Y will be lower thanwould be possible in the “golden age.” SinceC + I¼ Y, it holds—with g denotinggrowth rate—thatgY¼ (C/Y)gC+ (I/Y )gIand in the steady stategY¼ gC¼ gI There-fore, it holds that if theI/Y is higher than required by the golden rule (and I/Y¼ S/Y),

we can draw the following conclusion:d ln (k0# /k0gold)/d ln s¼ 1/s—if the savingsrate is compatible with the golden rule capital intensity and we then increase thesavings rates by 1% the elasticity, indicates that an increase in the savings rate by1% raises k0#/k0gold by 2.5% (1/s) At the same time we know that “an excesssavings rate” of 1 percentage point will reduce the consumption GDP ratioC/Y by

1 percentage point (we will pick this up in the case of China subsequently).The standard assumption for the size of the output elasticity of capital is that it isabout 1/3 in OECD countries Hence, if s¼ Igross

/Y, any investment-GDP above33% would seem excessive Excessive investment is not only a doubtful exercisefrom the perspective of maximum per capita consumption but also because anexcess capital intensity implies an excess per capita GDP and—assuming that CO2/

L is proportionate to y—an unnecessarily high level of emissions per capita Theemission aspect has never been considered in the traditional neoclassical growththeory, but it will be covered subsequently Note that if Germany, the USA or Chinaraises its gross investment-GDP ratio and the capital intensity, respectively, beyondthe value that is compatible with the golden rule, there will be three main effects:

• The consumption per capita will be lower than possible in principle; ifk#> kgold

,

we get an abundance of resources, and C/L is smaller than it could be under amore optimal government and economic system—and this can bring aboutpolitical instability since the politico-economic system will not be judged onthe basis of per capita GDP but on the basis of long-run per capita consumption

• Emissions will be higher than necessary, therefore the respective country’scontribution to global warming will be higher than necessary; and the price of

CO2emissions certificates will be higher than it would be under the (modified)golden rule (the necessary modification is considered subsequently)

• This basic logic applies to all countries, and therefore it is particularly necessary

to reduce the capital intensity in those countries that face excess capital intensity(there could be symmetrical problems in some countries, namely that the capitalintensity is below the golden rule capital intensity, but it seems likely that bothpoliticians and investors might rather have a tendency for overinvestment thanfor underinvestment)

• A crucial question in reality concerns the size of the savings rate and the size ofthe depreciation rate Following the World Bank concept of genuine savings,serious doubts may be raised about the significance of the official savings rate.The genuine savings rate that takes a broader definition of capital into account—physical capital, human capital, and the stock of natural resources—often looksdifferent from the official savings rate Countries with huge depletion rates of

natural resources typically have genuine savings rates that are lower than theofficial savings rates from traditional statistics The savings rate is, of course, ofkey importance in growth modeling It should be pointed out that the differencebetween the gross savings rate from the System of National Accounts and thegenuine savings rate is large in many countries (see Appendix A.1).

• Since emissions enter a hybrid welfare function—with per capita consumptionand emissions per capita—with a negative sign it is important to consider theshare of renewables (almost zero CO2emissions within the life cycle analysis)

• The international specialization of countries in the field of innovation matters forgreen progress Here, it is interesting to see how specialization patterns change.Looking at revealed comparative advantage, it is clear that some countries arepositively specialized, and others are negatively specialized

In a broader perspective, key aspects of innovativeness and the genuine savingsrate have to be taken into account The subsequent graph shows the share ofrenewables, the genuine savings rate, and the revealed comparative advantage forenvironmentally friendly products for selected countries

Policymakers’ focus on the maximumC/L in the steady state is only plausible tosome extent The problem that any given capital intensityk and GDP per capita,respectively, is associated with certain emissions needs to be considered, and it may

be assumed that emissions enter the individual utility function with a negative sign.Current and future negative external effects of production can be quite impor-tant As regards negative external effects, it should be emphasized that such effectscould be so large that the post-internalization quantity is zero Nuclear energy is aform of energy that has very large potential negative external effects: the risk of anuclear accident and the social costs of a nuclear fall-out (emissions of cesium,strontium and plutonium) after the greatest possible accident is very large; there-fore, private nuclear power plants in OECD countries cannot find full insurancecoverage in the private insurance market At the beginning of the twenty-firstcentury, nuclear energy is economically viable in OECD countries only becausegovernments have not imposed strict insurance requirements on the nuclear powerindustry

The share of renewables differs considerably across countries, and severalcountries have problems in sustainability in so far as the genuine savings rate(adjusted net savings rate according to World Bank) is negative—moreover,RCAs for “green exports” are positive only for few countries, including the USA(Fig.1.5)

To the extent that nuclear power generation companies are not required by law tohave full liability insurance, there will be a major distortion of inter-fuel competi-tion In Germany, nuclear power generation companies have liability insurance for2.5 billion euros, while a major accident is likely to cause damages of more than

100 billion euros or even 500 billion euros In Switzerland, the government hasraised required liability insurance for nuclear power facilities from SFR 1 billion to1.8 billion, and the damage assessment of a major nuclear accident is also close to

500 billion euros

Fig 1.5 ( a) Shares of renewables, (b) genuine savings rate/World Bank, (c) volume-based RCAs for “green exports.” Data Source: WDI Online, own calculations (RCA)

1.2 Technological Progress and R&D

Subsequently, we will use the production function Y¼ Kβ(AL)1 β—where A isknowledge and L is labor, 0 < β < 1); by assumption, knowledge is labor-augmenting, but other types of technological progress can also be considered.Note that∂Y/∂K ¼ βY/K Using the production function Y ¼ Kβ(AL)1 βand assum-ing that the growth rate of knowledgedlnA/dt¼ a is exogenous and has a specificadvantage, we can write (withk0: ¼ K/(AL)):

Here,AL is dubbed labor in efficiency units; therefore, the mechanics of theneoclassical model are roughly the same as in the simple Solow model Using asavings function S¼ s(1  τ)Y—where τ is the income tax rate—and hence S/(AL)¼ s(1  τ)y0, we obtain a differential equation ink0, namelydk0/dt¼ s(1  τ)y0– (a + n +δ)k0

and, taking into account that y0¼ k0 β, the solution of the Bernoulli

differential equation is (withC0to be determined from initial conditions int¼ 0;

e0is the Euler number):

Fig 1.5 (continued)

This differential equation is converging to the steady state valuek0# if 0< β < 1which has been assumed Settingt¼ 0, we get k0

state is given by the parametera, the growth rate of Y in the steady state is (a + n)

• The role of the rate of technological progress rate (a) is important and inparticular it holds that (see the subsequent Fig 1.6 where the initial path isABD):

• A rise in the progress ratea (in tT) will reduce the level of the growth path

• At the same time, a rise ina increases the steady state growth rate of y

If the government’s time horizon is sufficiently long, the government willundertake measures that raise the rate of technological progress: Government will

Fig 1.6 Impact of a rise of

the growth rate of knowledge

on the level of per capita

income ( y) and the growth

rate of per capita income

(tg α ¼ a)

understand that the short-term impact of a rise in the progress rate is that the level ofthe growth path is reduced, while the long-term impact implies—due to the rise inthe permanent growth rate—that a higher per capita income can be reached thanwithout the rise in the progress rate Only in countries where government extremelydiscounts future income gains associated with a higher rate of technologicalprogress will government likely not have an increased progress rate.

it might be argued that China’s economy is not in a steady state, the subsequentgraph raises some doubts about the wisdom of China’s growth policy: As the realGDP growth rate has been above the real interest rate for 30 years, the hypothesismight be stated that China’s aggressive growth policy has systematically raised thecapital intensity above a level which is consistent with the golden rule Theelasticity of (k0#/k0gold) with respect to the savings rate is 2.5 as has already beenpointed out (assuming that China’s savings rate is initially 0.4 which is alreadyhigh; there are some good argument why the elasticity could be even higher) Thus,China’s government faces the risk that its policy contributes to high growth rates ofoutput, while households/voters are partially dissatisfied because per capita con-sumption is relatively low (China’s increasing investment-GDP ratio mainlybenefits Germany, Japan, and the USA as major exporters of machinery andequipment) Looking at the subsequent Fig.1.7for Germany, Japan, Russia, andthe USA, it seems that Germany, Japan, and the USA have an economic perfor-mance which is largely in line with the golden rule

Note that from the steady state solution fork0#, we can draw the conclusion that

we have the following in the steady state:

Ifβ exceeds s—a typical perception based on standard statistics of the OECD—the income tax rate should be negative However, government must have sometax revenues in order to be able to run the political system; without a stablepolitical system, there is no stable economic system and therefore no sustainablegrowth.

A broader analysis which takes into account the genuine savings ratio(Fig.1.8)—as published by the World Bank—however, leads to different results:The genuine savings ratio considers standard savings activities but also investment

in human capital (this raises the savings rate) and the depletion rate of naturalresources (depletion of nonrenewables reduces the savings rate) as well as someother activities

1.2.2 Extensions of the Neoclassical Growth Model

A modified production function could also be considered where three modificationscould be particularly interesting:

• Real money balances M/P (M is the nominal stock of money, P is the outputprice level) could be entered into the production function so that the productionfunction isY¼ M=Pð Þβ0Kβð ÞAL 1 ββ 0

; 0 < β0< 1 It may be assumed that M/P

is held by households, but their holding of money balances enters the firms’production as a positive external macroeconomic effect—effectively usingmoney reduces information and transaction costs If it is also assumed, based

on standard portfolio theory, thatM/P¼ α00K (in a broader approach it may beconsidered thatα00is a negative function of the nominal interest ratei), we get aquasi-Romer effect in the sense that at the macroeconomic level the outputelasticity of capital is greater than at the level of the individual firm Note that

in the portfolio theory—following Tobin (1958)—risks associated with holdingreal money balances are negatively correlated with the risks associated withholding physical capital; therefore, under risk, considerations of real moneybalances and physical capital are complementary The production functionnow reads Y¼ α00 β

Kβþβ0ð ÞAL 1 ββ 0

or y¼ α00 β

kβþβ0A1ββ0 The main effect ofreal money balances is that we get a higher output elasticity, and this raises thelevel of the growth path in the steady state; the same holds with respect to theimpact of parameter α00 Inflation would raise the nominal interest ratei andhence reduceα00in a setting in whichα00is considered to be a negative functioni.The steady state inflation rate π # ¼ μ  (a + n), as the ratio (M/P)/(AL) in thesteady state is constant (μ denotes the growth rate of the nominal money supply)

Adjusted net savings (genuine savings rate), including particulate emission damage

Fig 1.8 Genuine savings rate for selected countries Note: Adjusted net savings are equal to net national savings plus education expenditure, minus energy, mineral and net forest depletion, and carbon dioxide and particulate emissions damage Data Source: World Bank, World Development Indicators & Global Development Finance

The approach suggested here is to consider the role of real money balances in theproduction function and not to follow the monetary growth model of TOBIN(1961) whose approach was to argue that household savingsS is proportionate toenhanced real GDP, namelyY + (dM/dt)/P πM/P In the Tobin growth model, astandard aggregate production function is used, based on capital and labor asfactor inputs In the monetary growth model of TOBIN, the steady state capitalstock is smaller than in a standard neoclassical growth model This effect comesfrom the modified goods market equilibrium condition S¼ dK/dt + δK + H(whereH is transfers to households) and the government budget constraint G+H – T¼ μM/P; note that the assumption G ¼ T implies that per capita transfersH/L¼ μ(M/P)/L The Tobin monetary growth model is not considered as theo-retically convincing here, since an enhanced real income in a monetary economyshould simply read Y(K,L,A,M/P), which implies for the case of a linear-homogeneous production function, that Y¼ YKK + YLL + YAA + YM/P(M/P),where Y accompanied by a lower case letter denotes the respective marginalproduct; this implies that enhanced income isY + YM/P(M/P) and not Y + (dM/dt)/

P πM/P Here, we prefer a production function Y ¼ M=Pð Þβ 0

Kβð ÞAL 1 ββ 0

and

it is noteworthy that the inflation problem can be integrated by considering that

in an inflationary economy the output elasticity of real money balances is nolonger β but it is equal to β00

¼ β0–v0π, where v0is a positive parameter, whichindicates by how much the output elasticity is reduced at the margin via inflation.Hence, β0 is the output elasticity of real money balances in an economy withprice stability

• An important aspect of economic globalization and economic growth concernsthe role of foreign direct investment (Welfens2011): In a nutshell, it may beemphasized that foreign direct investment inflows (FDI inflows) and the exis-tence of multinational companies require several refinements in the growthmodel; the simplest model to be considered is a two country world withasymmetric FDI inflows: country I is the only host country, country II the onlysource country of FDI It is crucial that a distinction be made between GDP andgross national income (Z ), which is equal to GDP minus profits earned bysubsidiaries of foreign multinational companies Let us start with the observationthat in an economy with competition in goods markets and factor markets, profits

of foreign subsidiaries in country I—the host country—will be equal toα*βY,whereα* denotes the share of the capital stock owned by investors from abroad(country II) This is so because under competition—implying that productionfactors are rewarded in accordance with the respective marginal product ofcapital—profits will be equal to βY The users’ side of the household incomenow reads Y(1 α * β) ¼ C + S + T, where S is savings and T stands for taxpayments; denoting the income tax rate as τ, we have T ¼ τY Assuming thatconsumption is not proportionate to GDP but to disposable gross nationalincome Z(Z¼ Y(1 – α * β)) and that national income is taxed (T ¼ τ(1  α * β)

Y ), we can write Y(1 α * β) ¼ c(1  τ)Y(1  α * β) + S + τ(1  α * β)Y, whichimplies that the savings function is given by S¼ [1  c(1  τ) – τ](1  α * β)

Y¼ (1  τ)s(1  α * β)Y where s ¼ 1  c By implication, we get a modifiedSolow model for a setup with asymmetric FDI; the steady state capital intensity

is k0# ¼ [s(1  α * β)(1  τ)]1/1  β; a simple technological progress function

a¼ a0+ϕα * a* may be considered, where a0 is the exogenous progress rate,while a* is the foreign exogenous progress rate;ϕ is a positive parameter thatindicates how strongly the foreign progress rates feed via cumulated FDI into thehost country economy Output per worker in efficiency units isy0¼ {[s(1  α * β)(1 τ)]/(a0+ϕα * a * + n + δ)}β/(1  β) so that the level of the growth path is

reduced by the presence of multinational companies and cumulated FDI, tively However, the trend growth rate ofy0in the steady state has been increased

respec-by FDI since the progress rate (a) has been raised respec-by the termϕα*a*

• One potential refinement could be to consider the role of energy E—ofnonrenewablesN and renewables R—in a modified production function If theproduction function readsY¼ KβEβ00ð ÞAL 1 ββ00 0< β00

< 1

, profit tion will lead to the consideration of relative prices of input factors; similarly, if

maximiza-we have a production functionY¼ KβðNþ RÞβ00ð ÞAL 1 ββ00, there is one tional relative price, the price ratio of nonrenewables to renewables Technolog-ical progress might also be considered in the field of nonrenewables where the

Y ¼ KβðNþ BRÞβ00ð ÞAL 1 ββ00 Society has to decide how big the share ofresearchers ρA allocated to labor-saving knowledge A is and how large theshare of researchers ρB allocated to nonrenewable-enhancing technologies is,

so thatdB/dt reaches an adequate or optimal speed The share of nonrenewablesused in production could normally decline over time as the consequence of aquasi-Hotelling pricing rule for nonrenewables The intertemporal optimization

of nonrenewable resource owners (in OPEC countries plus Russia, Norway, etc.)will be governed by the intertemporal arbitrage condition that the yield from thecurrent exploitation of resources is (P00 H)i ¼ (dP00/dt), where P00is the price ofthe nonrenewable,H is the unit cost of exploitation nonrenewable sites, and dP0/

dt is the yield obtained from a marginal unit of nonrenewable resources left inthe ground (see Welfens (2011) on a modified Hotelling rule—with technologi-cal progress: here the basic equation is (P00 H)i ¼ (dP00/dt)(1 z00) wherez00isthe expected substitution rate of nonrenewables by renewable energy resourcesand z00 is determined by technological progress) Leaving the resource in theground brings a yield, which is equal to the (expected) rise in the price ofnonrenewables, producing and selling a unit of nonrenewables in the currentperiod brings a cash flow ofP00 H, and this revenue can be invested at thecurrent interest ratei so that the yield is (P00 H)i The nominal interest rate i isthe sum of the real interest rater and the (expected) inflation rateπ, which can bewritten asπ ¼ λ0π0+λπ00+λπ000 (π0is the inflation rate of nonenergy goods,π00isthe inflation rate of nonrenewables, andπ000is the inflation rate of renewables;λ0,

λ00, andλ000 are weights adding up to unity) The quasi-Hotelling rule reads—after dividing by P00: (1 H00)(r +λ0π0+λπ00+λπ000)¼ π00 whereH00 is defined as