Paul J J Welfens Macro Innovation Dynamics and the Golden Age New Insights into Schumpeterian Dynamics, Inequality and Economic Growth Macro Innovation Dynamics and the Golden Age Paul J J Welfens Macro Innovation Dynamics and the Golden Age New Insights into Schumpeterian Dynamics, Inequality and Economic Growth Paul J J Welfens Jean Monnet Chair for European Economic Integration and Chair for Macroeconomics President of European Institute for International Economic Relations (EIIW) at the University of Wuppertal Wuppertal, Germany Non-resident Senior Research Fellow AICGS/Johns Hopkins University Washington, DC USA Research Fellow IZA Bonn, Germany ISBN 978-3-319-50366-0 ISBN 978-3-319-50367-7 DOI 10.1007/978-3-319-50367-7 (eBook) Library of Congress Control Number: 2017930939 # Springer International Publishing AG 2017 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface Innovations were responsible for driving the Industrial Revolution in the eighteenth and nineteenth centuries The twentieth century has witnessed the combination of multinational companies’ foreign direct investment dynamics and product as well as process innovations; and the early twenty-first century is shaped largely by digital innovation dynamics While innovations have been analyzed by many economists—beginning, in particular, with Schumpeter—there is surprisingly limited research carried out on the role of innovations in Macroeconomics (as a textbook, Aghion/Howitt’s Endogenous Growth Theory summarizes many approaches) With my book, “Innovations in Macroeconomics”, I have tried to contribute to closing some of the knowledge gaps and emphasis has been given to the role of foreign direct investment (FDI), innovations and trade The role of FDI is growing in the context of economic globalization and it requires the making of a distinction between GDP and gross national product—typically neglected in open economy macroeconomics so far This point has already been emphasized in Innovations in Macroeconomics Consumption in an economy with trade and FDI is proportionate to GNP, not to GDP; and imports are also proportionate to domestic GNP The export volume is proportionate to foreign GNP—not to GDP For many countries there is a considerable difference between GNP and GDP In this complementary book, I present my papers for the Brisbane conference of the Schumpeter Society, the paper for the Jena conference of the Schumpeter Society as well as my paper on innovation and growth for a Sino-German project—here funding from the German National Science Foundation is gratefully acknowledged—plus a new approach to the golden age in the presence of a research sector Moreover, the last chapter—my paper for the Montreal conference of the International Joseph A Schumpeter Society—suggests an innovative approach that uses a knowledge production function that can be plugged directly into a macroeconomic production function and hence enables a straightforward way for new endogenous growth approaches from both a theoretical and empirical perspective The main ideas in this book are to include innovations into the Mundell-Fleming model and to take a broad, fresh look at the golden age in neoclassical growth theory In a broader view that includes environmental aspects, the question of a golden rule that maximizes per capita consumption is even more important than the classical contributions in this field: An economy that has a capital intensity v vi Preface exceeding that which is required by the golden rule is not achieving the maximum per capita consumption on the one hand, on the other hand, in the case of a closed economy, one may emphasize that the amount of physical capital produced and employed—this is associated with the use of resources and energy (leading to higher CO2 emissions)—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 steady state, has, in the original contribution of Edmund Phelps (1961), been dubbed “a fable for growthmen” and indeed the golden rule has not been considered as a serious element of economic policy—it was rather discussed as a very theoretical point of neoclassical growth analysis; with the adoption of endogenous growth theory the golden rule seemed to become a remote corner of analysis The contribution of Phelps had emphasized, in its application to a setup with a Cobb-Douglas production function, that the golden rule requires that the savings rate is equal to the income share of capital and the output elasticity of capital This interpretation is not fully consistent to the extent that it is understood to imply that all profits must be invested 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 the golden age An alternative condition for the golden rule is to require that the growth rate of output should be equal to the real interest rate and one may argue that profit maximization and competition will bring about this equality Hence the only task of government then is to implement competition and to encourage profit maximization There are, however, three difficult problems for competition policy: (1) Competition policy in small open economies is not easy to implement effectively in a world economy with multinational companies playing an increasing role; while in the 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 one multinational company already covers the entire domestic market so that there is little room for actual or potential competition (the non-tradables sector could represent between 20% and 40% of output in OECD countries and Newly Industrialized Countries; and even more in developing countries) (2) Profit maximization is not always the natural behavior of relevant economic actors; the government sector itself and government-owned firms should be considered as a potential problem or to put it differently: here, looking at the sectoral implication of the golden rule would be particularly useful, but no minister of finance and no council of economic advisers has so far seriously emphasized the golden rule as a policy element This point will be rather neglected in the subsequent analysis: There is (3) the question of negative external effects from production How can negative external environmental effects—related to production—be integrated in a simple growth 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 effective monopoly over several years to the innovator—one may face the problem that production factors are not simply rewarded in line with marginal productivity: Market power could play a crucial role in factor markets, possibly less so in small open economies than in big economies Preface vii Moreover, deviations from the golden age are not in practice an irrelevant problem of reality and economic policy, respectively It should be rather obvious that in rather poor countries a lack of growth-enhancing economic policy will bring about starvation, so that pushing governments to consider the implications of the golden rule should be a natural element of modern development policy and UN or World Bank projects for stimulating economic development in the South of the world 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 Foundation has commenced Again, we are grateful to Mu Rongping and Reinhard Meckl who have initiated the projects that have a broad focus on innovation dynamics, including green innovation dynamics (the first book edited by Rongping/Meckl was Innovation for Green Growth; Beijing: Science Press: 2014) In Washington DC I presented at both the Congressional Research Service and at the IMF (on June 27 and 28, 2016, respectively) a theoretical and empirical paper on the knowledge production function—a joint paper with Andre Jungmittag in which we have conducted an empirical analysis covering 20 EU countries between 2002 and 2014 and also suggested ways of plugging the empirical results into a macroeconomic production function This paper, which looks at the creation of new knowledge, is not included here, however, part of the theoretical basis is shown in the last chapter of this book (those interested can find the EIIW paper No 212 on the website 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 and the Schumpeter School of Business and Economics, respectively) I am also grateful for the editorial support of David Hanrahan, Samir Kadiric and Evgeniya Yushkova (EIIW) As regards our China research projects, I would also like to thank Mu Rongping (Chinese Academy of Sciences), Rainer Walz (Fraunhofer Institut ISI, Karlsruhe), Klaus Rennings (ZEW) and Reinhard Meckl (Universitaăt Bayreuth) 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 in Denmark was particularly stimulating (unfortunately I was unable to attend the Brisbane meeting but Tony Irawan has presented my paper) Special thanks go to Andre 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, over many years The responsibility lies, however, with the author only Wuppertal, Washington and Beijing Summer 2016 Paul J J Welfens 保罗 威尔芬斯 Reference Phelps ES (1961) The golden rule of capital accumulation Am Econ Rev 51:638–643 About the Book This book is organized in five chapters: Following a short introduction, Chap suggests some new ideas on innovation, growth and income inequality The innovative approach presented introduces a modified neoclassical growth model which includes 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 combination of a macroeconomic production function and a new progress function, plus the assumption that the output elasticity of capital is positively influenced by the size of the R&D sector, sheds new light on innovation and growth as well as on income inequality: Thus there is a new approach for explaining Piketty’s historical findings of a medium term rise of the capital income share in industrialized countries—both in the earlier and later part of the nineteenth century and in 1990–2010 (this contribution has been published originally in the Journal International Economics and Economic Policy) A rising share of capital income can be explained within this approach by the increase in the output elasticity of capital, which has been developed in a new way, namely in the context of R&D In the approach presented herein, the golden rule issues are also highlighted and it is shown that choosing the right size of the R&D sector will bring about maximum sustainable per capita consumption While the basic new model is presented for the case of a closed economy, one could easily accommodate both trade and foreign direct investment and thereby get a better understanding of complex international investment, trade and FDI dynamics—including with respect to the envisaged Transatlantic Trade and Investment Partnership between the US and the EU The second chapter is my revised contribution from the first Sino-German project The analysis links R&D, foreign direct investment, output and CO2 emissions in a simple growth model Based on the modified neoclassical growth model, key issues can be raised with respect to sustainable growth and several conclusions can be drawn with respect to economic welfare and optimum consumption per capita, respectively It may be argued that in several industrialized countries—and China—investment-GDP ratios in certain periods are above the level that is consistent with optimum per capita consumption; the capital intensity exceeds the ratio of capital to workers (in efficiency units) that is consistent with a maximum long-run per capita consumption CO2 emission levels could be reduced in an efficient manner on the basis of a broad approach that emphasizes ix x About the Book Schumpeterian dynamics: Taxing emissions and giving subsidies for innovations could be useful elements of innovation-enhancing policy Promoting green innovations—including the sustainability design of products-, renewable energy and realizing adequate genuine savings could be key policy elements for a consistent strategy to achieve sustainable growth Moreover, green ratings for companies listed 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 global sustainability indicator A further analytical contribution is presented in Chap Economic growth is, in reality, not a smooth process and it is not clear why economic growth is rather unstable across OECD countries and the global economy Economic growth is certainly influenced by many factors, including innovation dynamics and technology, respectively Technological progress can have domestic sources and is, then, largely related to the innovation system, but in open economies the subsidiaries of foreign MNCs can also play a role in the host country Moreover, there could be international technology spillovers, part of which are related to international trade and FDI dynamics Foreign direct investment has rarely been included in the analysis of economic growth, despite the fact that economic globalization has clearly reinforced the role of multinational companies in world investment From a macroeconomic perspective, the presence of MNCs’ subsidiaries should not only bring effects on capital accumulation and technology transfer; rather it is important to consider that a distinction has to be made between GDP and GNP This distinction, which concerns the specification of the savings function as well as other functions, has been much neglected in the literature; it is relevant both in medium term macro models and in long run growth models In the standard neoclassical growth model with exogenous technological progress a rise of the progress rate leads to a fall of the level of the growth path and a higher permanent growth rate of output This suggests that a technology shock should bring about a quasi-growth cycle and such a phenomenon—with a temporary fall of output—is, however, not observed in newly industrialized countries The empirical patterns of growth and innovation dynamics not show such a paradoxical temporary fall of income and income per capita, respectively The paradoxical result of the standard growth 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 in the analysis; furthermore, we get additional insights into the issue of the golden rule and maximization of per capita consumption, respectively Moreover, it is interesting to consider the role of foreign direct investment for the growth model of an open economy and technological progress, respectively In this semi-endogenous set-up, the focus is mainly on asymmetrical foreign investment, namely inward FDI inflows Foreign direct investment inflows have a direct impact on the steady state solution, namely both on the level of the growth path and the permanent growth rate—the latter to the extent that we consider a technological progress function in which both the foreign progress rate and the share of the capital stock owned by foreign investors are considered The relative impact of domestic About the Book xi progress and internationally induced progress is discussed Finally, the issue of a consistent investment function which takes into account both the short term and the long run consistency is considered and the impact of changes in the progress rate are pointed out—along with broader policy conclusions of the analysis presented At the bottom line it is shown that a positive impact of the progress rate on the output elasticity of the capital stock can bring a smooth transition to both a higher level of the growth path and a higher permanent growth rate The perspectives on the role of FDI inflows in a two-country model with symmetrical flows have to be explored in further analysis Key policy conclusions concern the question of to what extent government should try to achieve a golden state while adequately taking into account the role of foreign direct investment inflows Within a broader group of countries it would also be useful to consider options for cooperation in growth policies—certainly to the extent that there are symmetrical or asymmetric international technology spillover effects Chapter presents a new multiplier analysis for a Schumpeterian MundellFleming model Traditional open economy macro models have focused on the mix of fiscal and monetary policy while completely neglecting innovation policy The new model presented is the first macro model that explicitly considers product innovations in an open economy model Product innovations are considered in the consumption function, the investment function, the export function, the import function as well as the money demand function; plus the net capital inflow function The policy multipliers are derived for fiscal policy, monetary policy and innovation policy In an extended version of the model, the role of foreign direct investment is considered, in an approach for a small open economy Domestic and foreign product innovations are considered and their impact on policy multipliers is analyzed Finally, the role of supply-oriented, innovation-enhancing fiscal policy is discussed Moreover, the empirical evidence for product innovation dynamics is considered Chapter can be summarized as follows: The macroeconomic production function is a traditional key element of modern macroeconomics, as is the more recent knowledge production function which explains knowledge/patents by certain input factors such as research, foreign direct investment or international technology spillovers This study is a major contribution to innovation, trade, FDI and growth analysis, namely in the form of a combination of an empirically relevant knowledge production function for open economies—with both trade and inward FDI as well as outward foreign direct investment plus research input—with a macro production function Plugging the open economy knowledge production function into a standard macroeconomic production function yields important new insights for many fields: The estimation of the production potential in an open economy, growth decomposition analysis in the context of economic globalization and the demand for 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 in which one country is at full employment while the other is facing underutilized capacities Finally, there are crucial implications for the analysis of broad regional integration schemes such as TTIP or TPP and a more realistic and comprehensive empirical analysis 134 Schumpeterian Macroeconomic Production Function for Open Economies inward FDI capital variable as well as the outward FDI capital variable—plus x and j as indicators of trade intensity—is the key point of departure for the next section With respect to a more general knowledge production function—and its empirical implementation—an alternative formulation of the knowledge production function 00 could be the equation A ẳ 1ỵX=LịH 1ỵJ=LịV z00 Y ịV 1ỵ*K=Y ịV 1ỵK*=Y*ịV* so that the case of a closed economy with no trade and no foreign direct investment could also be covered 5.2 The Schumpeterian Macroeconomic Production Function The Schumpeterian Macro Production Function (SMPF) is obtained from plugging the knowledge production function into the macroeconomic production function 00 For the sake of simplicity, a Cobb–Douglas production function Y ¼ (1 À z )Kβ(AL)1 À β will be considered, and it is assumed here that the share z00 of R&D output in GDP is an intermediate product The knowledge production function is A(Y * /Y, y, L , α, α*, j, x) where all partial derivatives are positive Using the rather compact specification of the knowledge production function developed here, one can easily plug it into the macroeconomic production function and in the end get a macroeconomic long-run supply function (with L0 denoting the number of researchers): Y ¼ Y ðK; L; L0 ; Y*; α; α*; x; jÞ ð5:11Þ The partial derivatives are all positive Hence, let us consider the explicit result of plugging the knowledge production function for the open economy into the macroeconomic production function which gives the integrated Schumpeterian production function (with nested knowledge production function A( .)): Y ¼ ð1 À z00 ÞK β ðALÞ1Àβ 0 00 00 A ¼ ðxY*=Y ịH jV yHỵV ỵV z0 L0 ị *=r ịV *=r*ịV* Y ẳ 1z00 ịK  x Y* Y H jV Y HỵV ỵV 00 L V ð5:12Þ ð5:13Þ 1Àβ 00 ðz0 L0 ÞV ðα*β=r ÞV ðαβ*=r*ÞV* L  1Àβ 00 00 00 À Á 0 HỵV ỵV ẳ 1z00 ịK xH Y *H Y H jV Y HỵV ỵV L1 z0 L0 ịV ðα*β=r ÞV ðαβ*=r*ÞV* L  1Àβ 00 00 00 0 HỵV ỵV V ẳ 1z00 ịK Y V ỵV ị1ị xH Y *H jV L1 z0 L0 Þ ðα*β=r ÞV ðαβ*=r*ÞV* L  1Àβ 00 00 00 00 0 0 V ẳ 1z00 ịK Y V ỵV ị1ị xH Y *H jV L1HV V z0 L0 ị *=r ịV *=r*ịV* Y 1V ỵV Þð1ÀβÞ  1Àβ 00 00 0 ¼ ð1Àz00 ÞK β xH Y *H jV L1ÀHÀV ÀV ðz0 L0 ÞV ðα*β=r ÞV ðαβ*=r*ÞV* ð5:14Þ 5.2 The Schumpeterian Macroeconomic Production Function 135   1 1 V0 ỵV100 1ị 00 00 0 ị V Y ẳ 1z00 ịK xH Y *H jV L1ÀHÀV ÀV ðz0 L0 Þ ðα*β=rÞV *=r*ịV* 5:15ị   1 1 V0 ỵV100 1ị 00 00 0 ị Yẳ 1z00 ịK xH Y *H jV L1ÀHÀV ÀV ðz0 L0 ÞV ðα*β=rÞV ðαβ*=r*ÞV* β   1Àβ00 00 00 00 00 0 0 Y ẳ 1z00 ị1V ỵV ị1ị K 1V ỵV ị1ị xH Y *H jV L1HV V z0 L0 ịV *=rịV *=r*ịV* 1V ỵV ị1ị lnYẳ ln1z00 ịỵ lnK 00 00 V ỵV 1ị V ỵV 1ị   00 00 1Àβ 0 V ln xH Y *H jV L1ÀHÀV ÀV ðz0 L0 Þ ðα*β=rÞV ðαβ*=r*ÞV* þ À 00 Á 1À V þV ð1ÀβÞ ẳ fln1z00 ịỵlnKỵ 00 V ỵV 1ị ẫ 00 00 1ị HlnxỵHlnY * þV lnjþ 1ÀHÀV ÀV lnLþV lnðz0 L0 ÞþVlnðα*β=rÞþV*lnðαβ*=r*Þ ð5:16Þ It is obvious from the logarithmic equation that a positive growth rate dln(L0 /L) will contribute to economic output growth in the long run To get a better understanding as to what extent the level of the growth path and the trend growth rate itself will be affected, one will have to consider a modified neoclassical growth model The result obtained for the Schumpeterian macroeconomic production function looks fairly compact Real gross domestic product is a positive function of • • • • • • • The capital stock The export–GDP ratio and foreign GDP The import–GDP ratio Total labor The share of researchers in the total labor force The ratio of the inward FDI capital stock relative to the total capital stock The ratio of the outward FDI capital stock relative to the total capital stock abroad • The real interest rate at home and abroad has a negative impact on the production potential The latter is quite interesting since it allows a direct link to the real money supply: if money market equilibrium—in an economy with a stable price level at home and abroad—is written as M/P ¼ hY/(h0 r) in the home country and as M*/P* ¼ h*Y*/(h0 *r*) in country (with positive parameters h, h0 , h*, and h0 *), one gets r ¼ hY/(h0 M/P) and r* ¼ h*Y*/(h0 *M*/P*), respectively, and thus obtains an analytical basis for monetary growth models; defining h/h0 :¼ h00 and h*/h0 *¼ h00 *, one can see that real money balances at home and abroad are contributing to 136 Schumpeterian Macroeconomic Production Function for Open Economies real GDP in an open economy with inward and outward FDI (an alternative new approach in a closed economy has been suggested by Welfens (2011) who considers real monetary balances held by private households as an implicit production factor of firms, namely on the basis of positive external effects for companies) Real GDP thus can be written as follows: β 1Àβ  00 À 00 00 ÁV À ÁV* 1V0 ỵV00 ị1ị 00 00 0 Y ẳ 1z00 ị1V ỵV ị1ị K 1V ỵV ị1ị xH Y *H jV L1ÀHÀV ÀV ðz0 L0 ÞV α* β=r αβ* =r * β 00 00 00 00 0 V Y ẳ 1z00 ị1V ỵV ị1ị K 1V ỵV ị1ị @xH Y *H jV L1HV V z0 L0 Þ 00 1Àβ  * V * !V* 1V ỵV00 ị1ị * h M * h0 M* A YhP h* Y * P* 1Àβ 00 11ịẵV ỵV ỵV  * V * !V* 1V ỵV 00 ị1ị * 00 00 00 00 00 αβ* h0 M* 0 0 V} α βh M A Y 1ÀðV ỵV ị1ị ẳ 1z00 ị1V ỵV ị1ị K 1V ỵV Þð1ÀβÞ @xH Y *H jV L1ÀHÀV ÀV ðz0 L0 Þ hP h* Y * P* 00 1V ỵV0 ị001ị !V* 11 V0 ỵV 11ịẵV ỵV þV Š 00 > >   * β ð 1Àβ Þ V * ð Þ = < 00 00 00 00 00 α* βh0 M αβ* h0 M* 0 V A Y ẳ 1z00 ị1V ỵV ị1ị K 1V ỵV ị1ị @xH Y *H jV L1HV ÀV ðz0 L0 Þ > > hP h* Y * P* ; : Y 00 ẳ 1z ị 00 11ị V ỵV ỵV ẵ K 11ịẵV0 ỵV00 ỵV @xH Y *H jV L1HV 00 ÀV 00 ðz0 L0 ÞV 00 1Àβ  * V * !V* 11ịẵV ỵV 00 ỵV * α βh M αβ* h0 M* A hP h* Y * P* ð5:17Þ There are two key insights here: • The real GDP thus is a positive function of both real money balances at home (M/P) and real money balances abroad (M*/P*) • The exponent for K and the exponent for the large bracket term are smaller than before so that taking into account money market equilibrium conditions at home and abroad implies that the effective output elasticity with respect to capital and all variables in the large bracket terms are smaller than before This effective Schumpeterian production potential could be the basis for a new monetary growth model (one may, however, argue that a true monetary growth model should be based on a production function in which M/P enters directly as a productive input, namely in the form of positive external effects of households’ holding of real money balances M/P: Welfens 2011) Let us return to the formulation of the production potential with r and r* It is obvious here that if Y* is growing in a sustained way—hence the foreign economy is already in a steady state—the implication is that the home economy is growing too, and here exports are the key driver As the long-run level of output growth is a negative function of the real interest rate, monetary policy can be considered in a quasi-monetary growth approach If the equilibrium condition for the money market is M/P ¼ hY/(h0 r), monetary policy—defined as a change of (M/P)/Y— can reduce the real interest rate, the level of output, and thus raise output Moreover, it can be shown that the effective Schumpeterian macro production function implies 5.2 The Schumpeterian Macroeconomic Production Function 137 that output per capita for the special case of β ¼ 0.5 is a positive function of capital intensity, the ratio of R&D workers in the total labor force, exports per capita, imports per capita, inward FDI intensity (α), and outward FDI intensity (α*) For the general case 0< β 5:23ị k# ẳ Q0:5=v ððsð1 À τÞ À z00 Þð1 À z00 Þ=nÞ 1=10:5=vị ; 5:24ị 0:5=vị=10:5=vị 5:25ị Q0:5=v y# ẳ Q0:5=v À z00 Þððsð1 À τÞ À z00 Þð1 À z00 Þ=nÞ   00 V =v ðα*β=r ÞV=v ðαβ*=r ÞV*=v y# ¼ xH=v Y*H=v LðÀHÀVÀV Þ=v ðz0 L0 Þ Á Âð1 À z00 Þ1=ð1À0:5=vÞ ðsð1 À τÞ À z00 Þ=n ð0:5=vÞ=ð1À0:5=vÞ ð5:26Þ One can rewrite Y*/L as (Y*/L*)(L*/L) and—with y0 *:¼ Y*/(A*L*)—therefore Y*/L ¼ y0 *A*0e0 a*t Therefore, one can restate the equation as follows:   00 00 V =v y# ẳ xH=v y*H=v L*=LịH=v LV HVV ÞH=v ðz0 L0 =LÞ ðα*β=r ÞV=v ðαβ*=r ÞV*=v Á ð1 À z00 Þ1=ð1À0:5=vÞ ðsð1 À τÞ À z00 Þ=n ð0:5=vÞ=ð1À0:5=vÞ 5:27ị If abroad S * ẳ (1 *)Y* andassuming that dln(A*)/dt ¼ a* and constant and n* is constant—the steady state solution for y0 * can be written as (s * (1 À τ*)/(a * + n*))β * /(1 À β*); the economy in country 2, for the sake of simplicity, thus is characterized by a standard neoclassical (Solow) growth model result 5.3 Labor Market Demand and Other Macro Aspects 139 y#  00 V =v ¼ xH=v s*1*ị=a*ỵn*ịị*H=1*ị=v L*=LịH=v z0 L0 =Lị *=r ịV=v *=r ịV*=v 1z00 Þ1=ð1À0:5=vÞ ðsð1ÀτÞÀz00 Þ 00 00 Á *H=v Â=n ð0:5=vÞ=ð1À0:5=vÞ L0 V HVV ịHV =vvị A0 e0 a*ỵnịH=vịt 5:28ị Thus, the steady state growth rate of y is (a*+n)(H/v) 5.2.3 Golden Rule The golden rule that maximizes per capita consumption is given by the condition dY/dK ¼ (a* + n)(H/v) and, recalling the definition of v:¼ 1À(V0 + V00 )(1 À β), therefore also by the condition: 11     V* !1Àβ v 00 H β β@ 0 * * V A a* ỵ nị ẳ K v ð1 À z00 Þ xH Y *H jV LN ðz0 L0 Þ v v r r* ð5:29Þ If one assumes profit maximization in the form marginal product of capital YK ¼ r (r is the real interest rate), the implication is that r ¼ (a * + n)(H/v) which is quite interesting since in the case of a big country 2, the reading is that the real interest rate is determined by the foreign variable a* and the domestic population growth rate n as well as the parameters H and v; recall v:¼ 1À(V0 + V00 )(1 À β) so that four supply side parameters determine r in this new setup, namely the output elasticity β negatively while the knowledge production parameters H, V0 , and V00 have a positive impact on the real interest rate It is noteworthy that a rise of β—e.g., caused by the expansion of information and communication technology—will reduce the real interest rate 5.3 Labor Market Demand and Other Macro Aspects The marginal product of overall labor YL is given by (with N0 :¼ À H À V À V0 ) YL 11  V  V* !1Àβ v 00 00 N 1ị 1ị1HVỵV ị1 @ * * V A v L ẳ 1z00 ịK xH Y *H jV ðz0 L0 Þ v r r* ð5:30Þ 140 Schumpeterian Macroeconomic Production Function for Open Economies Clearly, obviously the marginal product of labor is a positive function of both the domestic and foreign capital stock, the foreign level of knowledge, the employment abroad, the number of researchers, the inward FDI parameter α*, the outward FDI parameter α The demand for labor therefore is (with N0 :¼ À H À V À V0 ): Ld   v    00 1 1ị1HVỵV00 ị1 00 1ị1HVỵV ị1 00 H *H V 0 V α*β V αβ* V* ¼ N ðvw ð 1Àz ÞK x Y j ð z L Þ r r* 1ÀβÞ ð5:31Þ The demand for labor thus depends on many interesting variables As regard the marginal product of capital, it can be written as 11    V  V* !1Àβ v 00 β β@ * * 0 V A 5:32ị YK ẳ K v ð1 À z00 Þ xH Y *H jV LN ðz0 L0 Þ v r r* The marginal product of researchers is given by 00 V ð1ÀβÞ v Y L0 ẳ L @1 z00 ịK xH Y *H jV LN z0 V 0 00 11     !1Àβ v α*β V αβ* V* A r r* ð5:33Þ Denoting the nominal wage of researchers by W0 and the real wage by w0 , profit maximization will lead to w0 ¼ Y L Under profit maximization, the implied demand for skilled labor (researchers) is given by the condition: 0d v V 1ị L ẳw 00 @1 z00 ịK xH Y *H jV L z 0 N 0V 00  α*β r 1 V   !1Àβ ÀV00 ð1ÀβÞ αβ* V* A r* ð5:34Þ Thus, one gets a comprehensive view for the case of an open economy on how many domestic and foreign influences affect the marginal product of labor and researchers, respectively Trade intensity as well as FDI globalization parameters and foreign output determine the demand for researchers 5.4 Hybrid Medium-Term Macro-model If in reality goods market equilibrium in the medium run is characterized on the aggregate demand side by both current income and steady state income (Welfens 2011) so that an adequate medium-term macro-model would have to consider a 5.4 Hybrid Medium-Term Macro-model 141 weighted composite effective real income Z (with Ω0 denoting the weighting factor of permanent income in the form of steady state income Y#, < c < 1; < c0 < 1; for the sake of simplicity, no discounting of future income takes place and foreign GNP is already in the steady state) Assuming a Cobb–Douglas production function in each of the two countries considered, we can write for Z and Z*, respectively (α denoting the share of capital owned by foreign investors from country in country 2; α* denoting the share of capital owned by foreign investors from country in country 1; and q*:¼eP*/P, where e is the nominal exchange and P the price level): Z ¼ Y *ị ỵ *Y*q* 5:35ị Z* ẳ Y*1 *ị ỵ *Y=q* 5:36ị Here, gross national income is Y plus real net profit transfers from abroad— profits of country subsidiaries amount to α*βY in country provided there is competition in goods and factor markets Profits accruing from subsidiaries abroad are αβ*Y* and to express those profits in domestic goods units of country 1, αβ*Y* has to be multiplied by q*; profits of foreign subsidiaries in country are α*βY in good units of country (when expressed in goods units of country 2, the term α*βY/q* has to be considered) Hence, if one assumes that consumption and imports are not proportionate to GDP but rather to Z—and exports to Z*— one can state as a mediumterm condition for goods market equilibrium (Welfens 2011) 0 Y ¼ ð1 À Ω0 Þcð1 À τÞð1 À α*β À ÞY þÀ Ω c ð1 À Á τÞY#ð1 À α*βÞ 00 þb ðβY=K À r Þ þ G þ x Y*# * q* ỵY jẵ1 ịc1 ịY *ị ỵ c0 À τÞð1 À α*βÞY#Š ð5:37Þ The first term [ .] on the right-hand side is planned consumption Exports depend, of course, on real income abroad and imports are a positive function of disposable real GNP (here the investment function is simply b00 (βY/KÀr) and G is government consumption) The difference between GDP(Y ) and GNP(Z) is net income from abroad, namely profits obtained from subsidiaries abroad minus profits paid to foreign subsidiaries in country It is obvious that the fiscal multiplier now looks different and that other multipliers also differ from traditional macro-models The steady state GDP has to be calculated from an endogenous growth model One may also emphasize that Ω0 might have varying numbers over time, if the economy is in the full employment steady state solution, between and otherwise 142 5.5 Schumpeterian Macroeconomic Production Function for Open Economies Further Extensions There are many opportunities for additional research to be conducted Since the Schumpeterian Macro Production Function includes Y*, one could also focus on a situation of an asymmetric international business cycle where country is at full employment while country is facing underutilization of the production potential so that Y* could be covered by a Keynesian macro-model with technology included—e.g., A* would enter the investment function and the export function (Welfens 2011) Moreover, in a full macro-model with an additional equilibrium condition for the money market and the foreign exchange market, one also will get new insights into the equilibrium exchange rate To the extent that (with positive 00 parameter b0 and b00 ) a medium-term investment function I ¼ b (YK – r) + b (A/A*) is used, the logic of the knowledge production function and the macroeconomic production function will enter even a compact open economy macro-model via the investment function via YK, A, and A*; a compact export function (with positive 00 parameters x0 and x00 ) could be X ¼ xZ * + x A * /A + x q* and the import function 00 would read J ¼ jZ À j A/A * À j q*, where j0 and j00 are positive parameters In an international full employment perspective, it is also possible to model Y* in an analogous way as Y in country so that a Schumpeterian macroeconomic production function is relevant in country and country This is a useful approach to study long-run international output interdependency The production function as well as the knowledge production function could additionally include information and communication technology as a distinct input so that this important strand of research also could be analyzed in future research in a more consistent open economy context—possibly including international spillover effects plus network effects 5.6 Policy Conclusions There are some important conclusions to be drawn here In a world economy characterized by globalization and innovation dynamics, it is highly relevant to carefully consider the knowledge production function in an open economy and its implications for the macroeconomic production function As regards the knowledge production function of EU countries, there is clear evidence (Jungmittag and Welfens 2016) that the number of researchers, the per capita income, and the inward FDI stock relative to GDP significantly raise the number of patent applications Patents, in turn, raise real GDP so that government’s R&D policy has to consider a complex perspective It is not only important to ask whether the marginal social domestic benefits exceed private innovators’ benefits, rather one should take into account that higher patent applications and actual patents granted, respectively, will also contribute to international real income effects provided that the country considered is big This international output transmission effect will have a positive real income feedback on the home country—assuming two big countries to be considered (e.g., the EU and the USA)—macroeconomic 5.6 Policy Conclusions 143 externality This positive per capita effect—assuming the population in country and country to be given—in turn stimulates R&D efforts and patent applications, respectively, so that there is a positive intertemporal spillover effect of innovations that so far has not been considered in the literature in this context It might, however, have been covered to some extent indirectly and implicitly in studies looking at path dependency of innovation dynamics If there are such positive external effects of researchers and inward FDI stocks, there would also be new arguments why government should not only subsidize R&D activity but inward FDI flows—relative to GDP—as well A specific question could be to focus on the optimum R&D activity level (see Appendix A.1) The impact of globalization on factor income shares also could be considered in a new way; however, a CES function is adequate for this (some aspects are highlighted in Appendix A.2) The internalization of positive international external effects should guide corporate tax policy; however, there is an international coordination problem since without coordination of tax policy there is the risk of excessive subsidization which could distort factor allocation considerably In a two-country model (with two big countries), there could be a problem of international R&D policy interaction so that an R&D subsidy race could occur; if it brings countries closer to the optimum R&D intensity, this should not be considered to be a major problem Rather, in open economies with rising export–GDP ratios—including exports of the R&D sector and of innovative intermediate products, respectively—there is some probability that part of R&D efforts will contribute to raising foreign real income so that the problem of low government incentives for an optimum R&D promotion could increase in the context of economic globalization In such a context, international R&D cooperation might be required The supply-side formulation of the production potential in an open economy with trade, FDI, and research is also important for long-run output multiplier effects In an analogy to a Schumpeterian production function for country 1, a similar production function can be stated for country 2, and on this basis the longrun equilibrium Y, Y* and Y#, and Y*#, respectively, can be considered Moreover, the optimum innovation policy at home and abroad can be discussed in a more realistic setup Long run as well as medium-term fiscal and monetary policy could be analyzed within the new framework Generally, one may expect that policymakers will get a much better understanding of the role of innovation dynamics at home and abroad Some of the important findings of Piketty (2014) on changes in income distribution could also be analyzed in a better way (see also Welfens 2014, 2015) It also becomes clear that from a supply-side perspective, globalization—assuming an interplay of both two-way FDI and trade—is not neutral for both small countries and big countries The Schumpeterian dimension of the macroeconomic production function should be emphasized more clearly, and certainly the important role of multinational companies’ international investment should become a standard feature of International Macroeconomics The reflections presented here are both a modest contribution to Schumpeterian Economics and a clear statement in favor of 144 Schumpeterian Macroeconomic Production Function for Open Economies a more realistic open economy macroanalysis as well as an approach in favor of taking a broader look at modern regional integration analysis Finally, there are crucial implications for the analysis of broad regional integration schemes such as TTIP or TPP and a more realistic and comprehensive empirical analysis The interaction of trade, foreign direct investment, and innovation is crucial to understand in the context of regional integration and integration policies Moreover, the economic policy debate can be quite misguided if FDI and innovation effects are ignored in deep integration projects (such as TTIP and TPP)—the TTIP study of Francois et al (2013) for the European Commission that looks mainly at trade effects and to some extent also at FDI aspects while neglecting innovation effects is a typical case This official study puts the economic welfare effect in the context of trade creation at 0.5% for the EU and 0.4% for the USA, but this clearly seems to be a considerable underestimation for the two countries (“EU” as a country in an analytical sense) that stand for the two top source countries of international patents and innovation dynamics, respectively, and that also represent the two leading FDI source countries and two of the three global FDI host countries It is noteworthy that the approach presented can, or course, be applied to a comparative regional analysis in countries with regions with FDI inflows/outflows so that the EU, the USA, Canada, Australia, and China could be analyzed in a broader regional globalization context At the bottom line, there are many interesting implications of the new approach presented and much further research will be needed Appendix A.1 Optimal Choice of the Size of the R&D Sector In the above equation (V) in logs, one can replace z0 L0 by z00 L since z00 Y ¼ z0 L0 y (recall that z00 Y is the output of the R&D sector), and z00 Y/y ¼ z0 L0 and z00 Y/y ¼ z00 L so that z00 L ¼ z0 L0 and hence ln(z0 L0 ) can be replaced by ln(z00 L) The research share z00 in output that maximizes Y thus can be derived (or one maximizes y with respect to z00 ) Taking the derivative dlnY/dz00 and setting it equal to zero gives the necessary condition (while assuming: V0 + V00 < 1)    À  00 dlnY=dz00 ¼ ðÀ1=ð1 À z00 ịị 1= V ỵ V ị     00 00 ỵ ịV 1=z00 ị= V ỵ V ị ẳ   00 00 00 1= z ỵ òịV =z ẳ ð5:38Þ ð5:39Þ Appendix 145 00 z00 =ð1 À z00 Þ ¼ ð1 À βÞV   00 1=z00 ¼ ỵ 1= ịv 5:41ị    00 z00 ẳ 1= ỵ 1= βÞv ð5:42Þ ð5:40Þ Assume 1/((1 À β)v00 ) is close to zero   00 lnz00 % 1= ð1 À βÞv ð5:43Þ Note: dlnz00 /dβ < 0; dlnz00 /dv00 > For a maximum, the second derivative should be negative and it is given by the expression d2 lnY=dz00 ¼ h     i 00 À1=ð1 z00 ị 1= V ỵ V ð1 À βÞ n   o Á  00 À 00 À ð1 À βÞV 1=z002 = À V ỵ V ị [ .] f .g=½ .Š >    À 00 1=ð1 À z00 Þ = ð1 À βÞv =z002 < 1=  ÀÀ  Á 00 2z00 ỵ z002 =z002 βÞv < À Á 00 1= 1=z002 À 2=z00 þ > ð1 À βÞv À1=z002 þ 2=z0 > ỵ lnv f z0 ị > ỵ lnv 00 00 ð5:45Þ ð5:46Þ ð5:47Þ ð5:48Þ ð5:49Þ ð5:50Þ An alternative approach could be to consider an endogenous growth model based on the Schumpeterian macroeconomic production function and then one considers the steady state situation and maximizes steady state per capita consumption through optimal choice of z00 Governments eager to obtain the maximum golden rule consumption per capita will have to consider the profit maximization condition of the R&D sector and on this basis should allocate an adequate subsidy rate to the R&D sector An extended approach would then additionally include the government budget constraint G + f0 Y ¼ τY if one assumes that there is no government debt ( f0 is the subsidy ratio that should reflect the difference between the social rate of return on innovation and the private rate of return on innovation 146 Schumpeterian Macroeconomic Production Function for Open Economies and G is government consumption—with G/Y:¼ γ to be considered the relevant exogenous variable) This then leads to an optimum tax analysis where τ ¼ f0 + γ A.2 Schumpeterian CES Function The knowledge production function is given by 00 00 A ẳ xY*=Y ịH jV yHỵV ỵV z0 L0 ị *=r ÞV ðαβ*=r*ÞV* V ð5:51Þ The CES production function—compared to the Cobb–Douglas function, it is better suitable for analyzing income distribution issues—is given by 00 h i 00 00 À1=v Y ẳ ịALịv ỵ K v 5:52ị ( > 0; < Ω < 1; ! v00 ! 1; v00 6¼ 0, elasticity of substitution σ 00 ¼ 1/(1+v00 ); λ > 0) Inserting (i) in (ii) gives: Y "  H V HỵV ỵV 00 ẳ 1ị xY*=Y ị j y v00 00 z L ị *=r ị *=r*ị L ỵK v 0 V 00 V #À1=v00 V* ð5:53Þ 00 Y Àv " 00 v ẳ  H V HỵV þV 00 ð1ÀΩÞ ðxY*=Y Þ j y Àv00 00 ðz L ị *=r ị *=r*ị L ỵK v 0 V 00 V # V* ð5:54Þ We can solve in a meaningful way for Y if one assumes that v00 ¼ V0 +V00 : 00 Y À2v " ¼λ Àv 00  H V0 0 V 00 V V* HÀV ÀV ð1ÀΩÞ ðxY*Þ j ðz L Þ *=r ị *=r*ị L 00 v00 ỵK=Y ị v 00 # ð5:55Þ Y "  H V0 0 V 00 V V* 1HV V 00 ẳ 0:5 1ị ðxY*Þ j ðz L Þ ðα*β=r Þ ðαβ*=r*Þ L Àv00 þΩðK=Y Þ 00 #À1=2v00 Àv ð5:56Þ 00 Dividing (iv) by Kv gives: References 147 Y=K " ịị ẳ v #  Àv00 00 00 00 0 ð1ÀΩÞ ðxY*=Y ÞH jV yHỵV ỵV z0 L0 ịV *=r ịV *=r*ịV* L =K=Y ịv ỵ1 00 5:57ị " #  v00 00 00 00 H V HỵV ỵV V V* v 0 V Define z : ẳ 1ị xY*=Y Þ j y ðz L Þ ðα*β=r Þ ðαβ*=r*Þ L =K=Y ị ỵ1 5:58ị 0 Hence, taking logs and using the approximation ln(1 + Z ) % Z —for Z0 close to zero—we can use the approximation: À 00 00 00 À3v lnðY Þ À ln ðΩÞ v lnK ị ẳ v lnị ỵ Z0 lnY Þ ¼ È À 00 00 É À ln ị v lnK ị ỵ v lnị Z =3v ð5:59Þ 00 ð5:60Þ References Abdih Y, Joutz F (2005) Relating the knowledge production function to total factor productivity: an endogenous growth puzzle IMF Working Paper, WP/05/74 Aghion P, Howitt P (1998) Endogenous growth theory MIT Press, Cambridge, MA Asian Development Bank (2015) Asian economic integration report: how can special economic zones catalyze economic development? 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