Competing theories of growth models and their forecast ability of actual output growth By Dembe Netshipale 671613 Supervisor: Dr. Tshepo Mokoka A dissertation submitted to the Faculty of Commerce, Law and Management (CLM) University of the Witwatersrand Johannesburg School of Economic and Business Sciences (SEBS), in fulfilment of the requirements for the degree of Master of Economic Science 30 March 2020 http://www.google.co.za/url?sa=t&rct=j&q=&esrc=s&source=images&cd=&cad=rja&ved=0CAQQjRw&url=http://rufreshmeat.blogspot.com/2008_10_01_archive.html&ei=3KoPU6KsM8iVhQfBi4GIAw&usg=AFQjCNEhYnvUQrrdyEv1yGgozXveZu27iw&bvm=bv.61965928,d.ZG4 i Declaration I Dembe Netshipale, declare that this dissertation, competing theories of growth models and their forecast ability of real output growth which I hereby submit for the degree of Master of Economic Sciences at the University of Witwatersrand is my own work and has not been submitted before for any degree at any other University. Signed……………………………………………. Name of Student: Dembe Netshipale April 2020 ii Dedication This dissertation is devoted to the following people: Masindi Maluta Mbulaheni “Shamula”, Todani Ndou, Eric Ndifheleni Netshipale, Ndorovheni Netshipale, Mulamuleli Randima, Mutondiwa Netshipale, Rolamulelwa Ritshidze Netshipale, Nthungeni Ndou, Avhafunani Netshipale, Mashudu Netshipale, Ndavhelelo Netshipale, Magondo M.E. & M, Maanda Magondo, Louisa Netshipale, Thimaliswi Netshipale, Azwianewi Netshipale, Ndamulelo Netshipale, Mulisa Nenzhelele, Emmanuel Mudzanani, Bongani Senyolo, Breezman Chabalala, Mpfunzeni Makhanya, Ramilane Mohlakoane, Aaron Alovokpinhou, Bonga Mdletshe, Ntsieni Thanyani, Aluwani Mulovedzi, Rotshidzwa Nedzingahe, Phalandwa Rendani, and Mafanywa Given. Iwe Dembe Netshipale! “Dzulani zwanu MuDzanani, mukhwa vhusuto, mukhwa mulavhu, mukhwa govha, mutaulu muila gumbo. Songozwi thavha ya Dzanani”. Shamula!!!!!!!! UF Jema!!!!!!!!!!!!!!!!!!!! iii Acknowledgements I thank God, and my supervisor Dr. Tshepo Mokoka for his critical feedback, kind support and guidance in the process of writing this dissertation. iv Abstract This dissertation examines correlation between real output growth and projected output growth for diverse schools of thought. In this research study, we measure projected output growth of Australia, Brazil, France, Germany, South Korea, South Africa (S.A.), the United Kingdom (U.K.) and the United States (U.S.), using the Domar model, Solow model, extended Solow model, Goodwin’s model, AK model, Lucas model and Romer model for the period from 1970 to 2017, then compare it to the actual output values to see if there exist a co - movement between the two variables and the correlation. We use both the ordinary least squares (OLS) regression and root mean square error (RMSE) to compare the performance of projected output growth for the above-mentioned period. The OLS results show that the Solow model, the extended Solow model, Goodwin’s model, and Lucas model the impact of projected output growth on real output growth is positive for all the countries and statistically significant. For the Domar model, the parameter term is significant, and the model predicts a positive impact on projected output growth, except for SA. We also present the graphic representation of real output growth and projected output growth for seven growth models. The results show a strong co-movement between real output growth and projected output growth for extended Solow, Solow and Domar model. The RMSE estimate of real output growth and projected output growth for Solow model and extended Solow model provides superior estimate ability. Lastly, we use in-sample and out-of-sample forecasts, by utilizing RMSE, to determine which model possess the most superior forecasting ability for the one year, two year and three year time horizon. The in-sample results illustrate that, generally, the Goodwin model outperforms other models followed by extended Solow model then The AK and Lucas models. The out-of-sample results yield the following results: The extended Solow model generally outperforms the other models, followed by Solow model then Domar and Lucas models. Keywords: projected output growth, actual output growth and forecasting ability v Table of Contents 1. Introduction ............................................................................................................................................. 1 1.1 Background of the study ..................................................................................................................... 1 1.2 Motivation for the study ...................................................................................................................... 4 1.3 Objective of the study ......................................................................................................................... 5 1.4 Problem statement ............................................................................................................................... 6 1.5 Research questions .............................................................................................................................. 7 1.6 Contribution of the study .................................................................................................................... 7 2. Literature review .................................................................................................................................... 9 2.1 Introduction ......................................................................................................................................... 9 2.2 The evolution of growth theories and growth facts .......................................................................... 11 2.2.1 The importance of long run economic growth ........................................................................... 11 2.2.2 Growth miracles and disasters ................................................................................................... 11 2.2.3 The question of why the whole world is not rich? ..................................................................... 12 2.2.4 The world income distribution ................................................................................................... 13 2.2.5 Determinants of economic growth ............................................................................................. 13 2.3 Convergence ..................................................................................................................................... 14 2.3.1 Concepts of convergence hypothesis ............................................................................................. 15 2.4 Sources of Economic convergence ................................................................................................... 17 2.5 School of thoughts ............................................................................................................................ 18 2.5.1. Keynesian School (Domar’s model) ......................................................................................... 18 2.5.2. Neoclassical School (Solow and extended Solow models). ...................................................... 19 2.5.3. Marxian School (Goodwin’s model) ......................................................................................... 22 2.5.4. New Growth School - [NGT - The AK, Lucas and Romer models] ......................................... 23 2.6 The role of potential output ............................................................................................................... 27 3. Methodology .......................................................................................................................................... 29 3.1 Introduction ................................................................................................................................... 29 3.2 Keynesian School: Domar model ................................................................................................ 30 3.3 Neoclassical School: Solow model ............................................................................................... 31 3.4 Neoclassical School: Extended Solow model ............................................................................... 32 3.5 Marxian School: Goodwin model ................................................................................................. 33 3.6 New growth theories ..................................................................................................................... 35 3.7 The Root Mean Square Error (RMSE).......................................................................................... 41 vi 3.8 Models variables and data sources ................................................................................................ 42 3.8.1 Collective Data ........................................................................................................................... 42 3.8.2 Models variables ........................................................................................................................ 42 4. Results .................................................................................................................................................... 44 4.1 The Analysis ..................................................................................................................................... 44 4.2 The Table .......................................................................................................................................... 45 4.2.1 Domar model results .................................................................................................................. 45 4.2.2 Solow model results ................................................................................................................... 46 4.2.3 Extended Solow model results ................................................................................................... 46 4.2.4 Goodwin model results .............................................................................................................. 47 4.2.5 The AK model results ................................................................................................................ 48 4.2.6 Lucas model results .................................................................................................................... 49 4.2.7 Romer model results .................................................................................................................. 49 4.2.9 Summary of the table results ...................................................................................................... 50 4.3 Robustness checks ............................................................................................................................ 51 4.3.1 Domar model results .................................................................................................................. 51 4.3.2 Solow model results ................................................................................................................... 52 4.3.3 Extended Solow model results ................................................................................................... 52 4.3.4 Goodwin model results .............................................................................................................. 53 4.3.5 The AK model results ................................................................................................................ 54 4.3.6 Lucas model results .................................................................................................................... 54 4.3.7 Romer model results .................................................................................................................. 55 4.3.8 Summary of the table results ...................................................................................................... 55 4.4 Output growth rate and projected output growth rate ....................................................................... 57 4.4.1 Domar model ............................................................................................................................. 57 4.4.2 Solow model .............................................................................................................................. 61 4.4.3. The extended Solow model ....................................................................................................... 65 4.4.4 The Goodwin model................................................................................................................... 69 4.4.5 The AK model ............................................................................................................................ 73 4.4.6 Lucas model ............................................................................................................................... 77 4.4.7 Romer model .............................................................................................................................. 81 4.4.8 Summary of figures results ........................................................................................................ 83 4.5 The RMSE results ............................................................................................................................. 84 vii 4.6 Empirical forecasting of GDP growth .............................................................................................. 85 4.6.1 In Sample forecasting................................................................................................................. 86 4.6.2 Out of Sample forecasting .......................................................................................................... 89 4.6.3 The RMSE of in sample and out of sample results .................................................................... 92 4.7 Robustness checks on Empirical forecasting of GDP growth .......................................................... 98 4.7.1 Robustness of in Sample forecast .............................................................................................. 98 4.7.2 Robustness check of out of sample forecast ............................................................................ 102 4.8 Reinforcement of findings .............................................................................................................. 106 5. Conclusion ........................................................................................................................................... 108 5.1 Policy Implications and Recommendations ................................................................................ 109 6. Appendix A .......................................................................................................................................... 111 A.1 The potential output versus real output growth .............................................................................. 112 A.2 The output gap ............................................................................................................................... 114 A.3. Unit root test and stationarity test ................................................................................................. 115 A.3.1 Australia ...................................................................................................................................... 115 A.3.1.1 Stationarity test result for actual output growth ................................................................... 115 A.3.1.2 Stationarity test for estimated output growth for Solow Model ........................................... 115 A.3.1.3 Stationarity test for estimated output growth for Extended Solow Model ........................... 116 A.3.1.4 Stationarity test for estimated output growth for Domar Model .......................................... 116 A.3.1.5 Stationarity test for estimated output growth for Goodwin Model ...................................... 117 A.3.1.6 Stationarity test for estimated output growth for The AK Model ........................................ 117 A.3.1.7 Stationarity test for estimated output growth for Lucas Model ............................................ 118 A.3.1.8 Stationarity test for estimated output growth for Romer Model .......................................... 118 A.3.2 Brazil ........................................................................................................................................... 118 A.3.2.1 Stationarity test result for actual output growth ................................................................... 118 A.3.2.2 Stationarity test for estimated output growth for Solow Model ........................................... 119 A.3.2.3 Stationarity test for estimated output growth for extended Solow Model............................ 119 A.3.2.4 Stationarity test for estimated output growth for Domar Model .......................................... 120 A.3.2.5 Stationarity test for estimated output growth for Goodwin Model ...................................... 120 A.3.2.6 Stationarity test for estimated output growth for The AK Model ........................................ 121 A.3.2.7 Stationarity test for estimated output growth for Lucas Model ............................................ 121 A.3.3 France .......................................................................................................................................... 122 A.3.3.1 Stationarity test result for actual output growth ................................................................... 122 viii A.3.3.2 Stationarity test for estimated output growth for Solow Model ........................................... 122 A.3.3.3 Stationarity test for estimated output growth for extended Solow Model............................ 122 A.3.3.4 Stationarity test for estimated output growth for Domar Model .......................................... 123 A.3.3.5 Stationarity test for estimated output growth for Goodwin Model ...................................... 123 A.3.3.6 Stationarity test for estimated output growth for The AK Model ........................................ 124 A.3.3.7 Stationarity test for estimated output growth for Lucas Model ............................................ 124 A.3.3.8 Stationarity test for estimated output growth for Romer Model .......................................... 125 A.3.4 Germany ...................................................................................................................................... 125 A.3.4.1 Stationarity test result for actual output growth ................................................................... 125 A.3.4.2 Stationarity test for estimated output growth for Solow Model ........................................... 125 A.3.4.3 Stationarity test for estimated output growth for extended Solow Model............................ 126 A.3.4.4 Stationarity test for estimated output growth for Domar Model .......................................... 126 A.3.4.5 Stationarity test for estimated output growth for Goodwin Model ...................................... 127 A.3.4.6 Stationarity test for estimated output growth for The AK Model ........................................ 127 A.3.4.7 Stationarity test for estimated output growth for Lucas Model ............................................ 128 A.3.4.8 Stationarity test for estimated output growth for Romer Model .......................................... 128 A.3.5 South Africa ................................................................................................................................ 128 A.3.5.1 Stationarity test result for actual output growth ................................................................... 129 A.3.5.2 Stationarity test for estimated output growth for Solow Model ........................................... 129 A.3.5.3 Stationarity test for estimated output growth for extended Solow Model............................ 129 A.3.5.4 Stationarity test for estimated output growth for Domar Model .......................................... 130 A.3.5.5 Stationarity test for estimated output growth for Goodwin Model ...................................... 130 A.3.5.6 Stationarity test for estimated output growth for The AK Model ........................................ 131 A.3.5.7 Stationarity test for estimated output growth for Lucas Model ............................................ 131 A.3.6 South Korea ................................................................................................................................. 132 A.3.6.1 Stationarity test result for actual output growth ................................................................... 132 A.3.6.2 Stationarity test for estimated output growth for Solow Model ........................................... 132 A.3.6.3 Stationarity test for estimated output growth for extended Solow Model............................ 133 A.3.6.4 Stationarity test for estimated output growth for Domar Model .......................................... 133 A.3.6.5 Stationarity test for estimated output growth for Goodwin Model ...................................... 133 A.3.6.6 Stationarity test for estimated output growth for The AK Model ........................................ 134 A.3.6.7 Stationarity test for estimated output growth for Lucas Model ............................................ 134 A.3.6.8 Stationarity test for estimated output growth for Romer Model .......................................... 135 ix A.3.7 United Kingdom .......................................................................................................................... 135 A.3.7.1 Stationarity test result for actual output growth ................................................................... 135 A.3.7.2 Stationarity test for estimated output growth for Solow Model ........................................... 136 A.3.7.3 Stationarity test for estimated output growth for extended Solow Model............................ 136 A.3.7.4 Stationarity test for estimated output growth for Domar Model .......................................... 136 A.3.7.5 Stationarity test for estimated output growth for Goodwin Model ...................................... 137 A.3.7.6 Stationarity test for estimated output growth for The AK Model ........................................ 137 A.3.7.7 Stationarity test for estimated output growth for Lucas Model ............................................ 138 A.3.7.8 Stationarity test for estimated output growth for Romer Model .......................................... 138 A.3.8 United States ............................................................................................................................... 139 A.3.8.1 Stationarity test result for actual output growth ................................................................... 139 A.3.8.2 Stationarity test for estimated output growth for Solow Model ........................................... 139 A.3.8.3 Stationarity test for estimated output growth for extended Solow Model............................ 140 A.3.8.4 Stationarity test for estimated output growth for Domar Model .......................................... 140 A.3.8.5 Stationarity test for estimated output growth for Goodwin Model ...................................... 140 A.3.8.6 Stationarity test for estimated output growth for The AK Model ........................................ 141 A.3.8.7 Stationarity test for estimated output growth for Lucas Model ............................................ 141 A.3.8.8 Stationarity test for estimated output growth for Romer Model .......................................... 142 7. References ............................................................................................................................................ 143 List of Figures 1. Projected output growth of the Domar model results ........................................................................... 57 2. Projected output growth of the Solow model results ............................................................................ 61 3. Projected output growth of the extended Solow model results ............................................................ 65 4. Projected output growth of the Goodwin model results ....................................................................... 69 5. Projected output growth of the AK model results .................................................................................. 73 6. Projected output growth of the Lucas model results ............................................................................. 77 7. Projected output growth of the Romer model results ........................................................................... 81 8. Real output growth and one year ahead in sample forecasts. ............................................................... 86 9. Real output growth and two year ahead in sample forecasts ................................................................ 87 10. Real output growth and three year ahead in sample forecasts ........................................................... 88 11. Real output growth and one year ahead out of sample forecasts ....................................................... 89 12. Real output growth and two year ahead out of sample forecasts ....................................................... 90 13. Real output growth and three year ahead out of sample forecasts .................................................... 91 x List of Tables 1.Estimated parameters of the Domar model ............................................................................................ 45 2.Estimated parameters of the Solow model ............................................................................................. 46 3.Estimated parameters of the extended Solow model ............................................................................. 46 4.Estimated parameters of the Goodwin model ........................................................................................ 47 5.Estimated parameters of the AK model................................................................................................... 48 6.Estimated parameters of the Lucas model .............................................................................................. 49 7.Estimated parameters of the Romer model ............................................................................................ 49 8.Robustness Check: Estimated parameters of the Domar model ............................................................. 51 9.Robustness Check: Estimated parameters of the Solow model .............................................................. 52 10.Robustness Check: Estimated parameters of the extended Solow model ............................................ 52 11.Robustness Check: Estimated parameters of the Goodwin model ....................................................... 53 12.Robustness Check: Estimated parameters of the AK model ................................................................. 54 13.Robustness Check: Estimated parameters of the Lucas model ............................................................. 54 14.Robustness Check: Estimated parameters of the Romer model ........................................................... 55 15.The RMSE error of the competing models............................................................................................. 84 16.The RMSE error of the competing models in sample forecasts ............................................................ 92 17.The RMSE error of the competing models for out of sample forecasts ................................................ 95 18.Standard deviation of the competing models in sample forecasts ....................................................... 98 19.Standard deviation of the competing models out of sample forecasts .............................................. 102 1 1. Introduction 1.1 Background of the study Throughout the history of economics, since its advent in the late 15th century, there has been the development of many diverse schools of economic thought. Many have arisen due to the needs and economic crises of their times, and how well they cope and explain the said crises. A predominant amount of the theories was influenced by the question, if the growth rate of a country the right instrument to measure the standard of living? However, the schools’ ability to be effective over differing periods (to their period of genesis) is what determines how fundamentally accurate or strong the prevailing theories and assumptions of that time are. A school of thought that functions for only a twenty-year period is not nearly as valuable as one that can be used to determine trends over a century. As different models have different underlying theories, it is also important to compare diverse schools over a common topic - to this end, the following study will analyse and contrast the diverse schools over the common topic of long-term growth. The economic growth review and models paper by Piętak (2014) outlines economic growth critics as follows: Firstly, not embodying the “black market” on the extracted output data from all different sources. Secondly, the welfare of the society measurement excludes the effort spent on work. Thirdly, the economic growth rate calculations exclude negative economic activities - notably air and environmental pollution. Regardless of the critics, the economic growth theory and models remains crucial for measuring a country living standard. Before developing the main idea of this study, the development of the economic growth theory is worth highlighting. The concept of economic growth emerged in the 15th century by Mercantilism, whereby a country’s wealth is stored using precious metals (gold and silver etc.) and maintaining a trade surplus. Where the government encouraged trade surpluses through subsidy incentives in exports and the imposition of tariffs on imports. The Mercantilist theory is a “zero sum” game where the two countries trade against each other in such a manner that if country A gains country B loses and vice-versa (Berhani, 2015). The Marxian theory pointed out the weakness of 2 Mercantilism theory as being exclusive of industrial and non-agriculture labour from determining this wealth. The Mercantilist economic theory was replaced during the 18th century by Physiocrats who believed that wealth is dependent on the agricultural land and products worth - where the growth in agricultural production is proportional to technological changes. The Adam Smith theory criticized the mercantilist belief of holding precious metals and Physiocrats belief of agricultural land and product. Furthermore, Adam Smith pronounces that the wealth of a country is determined by its industrial and agricultural production and views trade as “winning sum” game by incorporating the absolute advantage concept (Berhani, 2015). The following economist: A. Smith, T. Malthus and D. Ricardo discovered the theory of classical growth, where the theory suggests that changes in real output per capita are determined by the population growth (Çalışkan, 2015). In his influential book “An Inquiry into the Nature and Causes of the Wealth of Nations” Adam Smith (1776) professed the classical growth theories, which point out that the wealth is generated through trading not holding of precious metals. Furthermore, he argues that enhancement of peoples’ wealth is related to factor inputs (i.e. land, labour, and capital) that produce output which results in a higher labour productivity. The book emphasizes on the key role played by population growth to extensive growth. However, Smith believed that the capital accumulation and population growth are constant at the equilibrium state. The comparative advantage theory discovered by Ricardo (1821) is viewed as one of the most influential works under the classical growth economics. Piętak (2014) identifies that the trade of goods and services transacted through money which Ricardo just viewed it as a medium of exchange. Contrary to the absolute advantage in Smith theory, Ricardo’s theory of the corporative advantage postulates that free trade can be mutually beneficial to all participant countries (Berhani, 2015). In addition, Ricardo advanced Smith by considering the effects of diminishing marginal returns from input on Smith’s growth model. Malthus (1959) on his “Essay on the principle of Population” opposes Smith’s idea to say that the relationship between population growth and production tends to be negative (Sharipov, 2015). Thus, the food supply grows slower than the population growth as it grows arithmetically whereas population is geometrically (Berhani, 2015). Lastly, the classical growth theory got summed up by Keynes (1936) who argues about long term economic trend - the long-term population growth is 3 stimulated by an increase in capital. Joseph Schumpeter (1934) introduced the innovative growth theory, which is driven by business and entrepreneur innovator competition for economic long run development (Nijkamp & Poot, 1998). The Keynesians theory of economic growth was developed by J.M. Keynes (1936), to provide a better understanding of economic activity of an economy. Keynes believed that factor demand determined economic growth, existing solely because of the development and processes around a macroeconomic steady state. An impediment of Keynes’ theory is that the tools of analysis are focused on the short-run, subsequently, Harrold and Domar examined the outcomes of growth theory for the long-run. Harrold, (1939) establishes that output growth is determined by the growth rate of labour and capital productivity whereas Domar, (1946) emphasizes more on the role of the marginal propensity to save (MPS) and average productivity of investment. Consequently, the combination of Harrold-Domar is extensively used in the recent literature because the two methods yield the same conclusion regarding a country’s continuous sustainable development. The neoclassical economists were against the idea of Keynes that during recessions a government should intervene to enhance business activity. The study by Sharipov (2015) points out three weaknesses of Keynesian and Post-Keynesian growth theories as follows: Firstly, economic growth being only determined by investment growth - excluding factors like technological progress. Secondly, the lack of an ability to interchange between the share of capital and labour - the neoclassical school of thought proves output can be achieved by different combination of inputs. Lastly, Inability of achieving a market mechanism for automatic rebalancing - only believe that stability is brought by government rather than competitive market system. The Solow (1956; 1957) model show that output per capita growth is determined by the combination of, technological progress, labour, and investments. Solow’s theory puts considerable emphasis on technological progress as a main determinant of sustainable economic growth - measured by per capita income. Furthermore, the countries with a high population experience a lower capital per labour which means low incomes. During 1980s the issue of imperfect competition, research and development (R&D) theory and the role of possible changes in the profit rate became of interest by Paul Romer (1986, 1987&1990) and Robert Lucas (1988). This resulted from the neoclassical critics of diminishing marginal productivity of capital, from taxation and government spending not being able to affect long term 4 economic growth. Sharipov (2015), shows the impact of economic growth as the savings rate only. The endogenous growth models believe that technological progress is not the only determinant of long-term economic growth, it emphasizes that the following factors need to be considered: Human capital, government intervention for science, technology development and protection in terms of property rights. 1.2 Motivation for the study Following Parente (2001), examines the endogenous and exogenous growth theories to see which one best explain the evolving income distribution of all countries. However, the endogenous growth theory fails to encapsulate the following: It is unable to explain the growth miracles which occurred restrictively in poor countries and is unable to explain that the modern economic growth for late entrants that have the ability to double their respective income than that of early entrants. Therefore, endogenous growth theory is not a convenient tool to measure economic development. This influenced the chosen variables through assessing which models best project the actual output through the better-known models of economic growth such as Solow, the extended Solow, Domar, Goodwin, The AK, Lucas and Romer models. Following Boldeanu and Constantinescu (2015), the issues of enhancing active population, human capital investment, natural resources and research and development advancement impact on economic growth led to assessment of this variables impact on economic growth which are directly impacted. Furthermore, the assessment of the factors that affect the economic growth indirectly such as institutions, saving rates and investment rates, fiscal policies and the efficiency of government and financial systems etc. This influenced the study to consider both the variables that have a direct and indirect impact on economic growth when projecting the actual output growth. In most studies, authors have focused on the issues of determinants and sources of economic growth; world income distribution; convergence of the countries and their long run impact. Firstly, the study is driven by the lack of consensus in the literature for exogenous and endogenous growth theory on examining the relationship between real output growth and projected output growth. The study by Adak (2009) examined the causality between total factor productivity (TFP) growth and economic growth using the Solow model for Turkey. The author’s finding shows a significant linear relationship between TFP growth and economic growth rates. Furthermore, the study by Khan (2005) analyses the co-movement and the correlation between real output growth and 5 projected output growth for Pakistan. Where the author’s finding shows the identical behaviour between real output growth and projected output growth for the entire period of analysis and a high degree of correlation. The second motivation that influenced the study originates from the crucial role played by macroeconomic variables such as unemployment, Gross Domestic Product (GDP) and inflation in the considerations of politicians and central banks when forecasting the future (Pilström & Pohl, 2009). We examine these long run growth models of Domar, Solow, extended Solow, Goodwin, the AK, Lucas and Romer models to see which model best predict the economic growth. GDP is a significant macroeconomic variable used by politicians, central banks, consumers, and firms to make future economic decisions. Uncertainty about macroeconomic fluctuations induces challenges for the economic ecosystem, consequently a thorough understanding of each respective model provides value for each economic agent. The comparisons of all the 7 models using 8 diverse countries to see which one best predict real output growth rate will assist in remedying the issue of uncertainty. The debate on which model best predict real output growth among above mentioned models has not been settled in the literature. We conduct this study for Australia, Brazil, France, Germany, South Korea, South Africa, United Kingdom, and the United States. The chosen diverse group of countries were chosen from the stand point of different levels of research and development, productivity growth and economic activity, their monetary policy mandate to achieve price stability in the economy this is a crucial part of their monetary policy conduct when forecasting the actual output growth. 1.3 Objective of the study The objective of this study is to revisit the importance of economic growth models in the following ways: Firstly, study the importance of both endogenous and exogenous growth models and their limitation. Secondly, examine the relationship between projected output growth and real output growth. Lastly, examines which of the considered economic growth models best forecast economic growth. Pilström and Pohl (2009), pointed out that this information is crucial for central bank when it comes to managing interest rate and prices which affect economic growth of a country. Therefore, it is crucial to identify a general model that best forecast the economic growth. To this 6 end, the analysis will cover the period from 1970 until 2017 across the above-mentioned countries. Such an analysis not only provides insight through comparable nations, such as the first world developed France and Germany, but also through contrasting very distinctly different nations, such as SA and the US. As there is a clear range in the types of economies analysed. The analysis allows greater discernment and interrogation of the models - under what circumstances are they most accurate? And to what lengths of time? 1.4 Problem statement The problem statement emanates from the following studies Adak (2009), Khan (2005) and Liu, Li, and Tan (2012) where their studies examines the correlation between the TFP and the actual output growth from the standpoint of the Solow growth model. Their results show a Significant relationship between the TFP and the actual output growth. This brought the argument to examine the correlation and the co-movement between the TFP and the actual output growth using other exogenous growth models such as Domar model and the Goodwin model and also the main endogenous growth models such as the AK, Lucas and Romer Model. Furthermore, the study by Diebolt and Monteils (2000) analyses the sources and the policy implications of the endogenous growth models, through deriving projected output growth of the AK, Lucas and Domar model. The Solow model were already derived by Solow (1957) study then, this stimulated us to derive the Domar model using Domar (1947) and Lianos (1979), and the Goodwin model using the Goodwin (1982). Therefore, this led to a question of comparison and contrasting long term growth models from the competing schools of thought. The following studies emphasizes on the importance of GDP growth role which plays an important indication role for the central banks, world banks, companies etc. to forecast the future (Pilström & Pohl 2009, Andersson 2007 and Monokroussos 1999). This stimulated the question to know which outperforms the others under a different time horizon. To this end, the analysis will cover the period from 1970 until 2017 across the above-mentioned countries. Such an analysis not only provides insight through comparable nations, such as the first world developed France and Germany, but also through contrasting very distinctly different nations, such as SA and the US. As there is a clear range in the types of economies analysed. The analysis allows greater discernment and interrogation of the models - under what circumstances are they most accurate? And to what lengths of time? 7 1.5 Research questions The research problem outlines three main questions: I. Between the economic growth models, which one best explains real output growth? II. Is there a significant relationship between projected output growth and economic growth? III. Which economic growth model best forecast real output growth? 1.6 Contribution of the study Firstly, the study derives the projected output growth from endogenous and exogeneous growth models, then compares them to the actual output growth to examine the relationship between the two variables. The issue of economic growth is a major challenge for developing countries, it is either there is a negative growth, or the country is growing at a very slow rate. This results from the issue of economic delinquency were the level of growth is not sufficient to address the issue of poverty and inequality (Bhorat and Tarp, 2016). This has important implications on long run growth rate to alleviates poverty and inequality through enhancing employment opportunities and labour productivity. Therefore, the projected output growth and the actual output growth plays a crucial role in determining the rate at which the economy will expand in the long run and also provides the implications for the outlook of inflation and economic growth. This also offers a significant information on stock market by the investors as they attention to the fluctuations of projected and the actual output growth. Lastly, the study compares the performance of competing growth theories in forecasting the actual output growth to test which one produces the best forecasting of actual output growth one, four and eight years ahead, respectively. This is crucial for monetary policy since the actual output growth is one of the main variables used by the central banks and other institutions to predict the future. Most of the existing studies focus mainly on addressing problems such as convergence, income distribution and inequality. We contribute to the existing knowledge by shedding light on the best growth models that explain real output growth better. This allows us to point out the gap between the models and which model describes best the dynamics of the economy. This is the current gap in economic knowledge as there is no literature that covers such a wide spread of cross-sectional data nor models in terms of determining which model most accurately depicts long term growth. 8 Furthermore, we need to distinguish between policies that can be effective for decades and implemented from the short, medium and long run effects as this is noted to have no impact on the needs of development economics by Hicks (1965) study. This results from inadequate exploring of exogenous growth model (Solow model and the extended Solow model). On the other hand, for endogenous growth models this study examines the dynamics of the long run growth effect of the economy as it have been neglected - majority of the studies mainly focuses on the long run growth effect of the policy. However, for a developing country endogenous with optimising agents. This is due to complexity of the parameter’s derivation and non- linearity structure of the model estimation using a time series for a country specific (Rao and Cooray, 2012). This also shades light as the study examines the long run dynamics of endogenous and exogenous growth models, mainly concentrated on the projected and actual output growth and link them with the policies that can have a positive impact on the development of a country in the long run. 9 2. Literature review 2.1 Introduction The issue of economic growth has become a subject of interest in the past 50 years because of the industrial revolution and subsequent two world wars. There have been competing models of growth from diverse schools of thought, with each trying to explain economic growth. The mercantilists argue that the accumulation of gold and silver as the engine of country’s state of wealth. However, The Wealth of the Nations book by Adam Smith (1776) favours the labour force productivity as an appropriate measure of wealth rather than the holding of precious metals (Parente & Prescott 1993). In addition, after the industrial revolution, output growth has overtaken population growth, but these models lack growth path comparisons between different countries over lengthy periods of time (Grossman and Helpman, 1994). A recent study by Pietak (2014) re-emphasizes that majority of the growth models were developed in the 20th century. Furthermore, Sharipov (2015) documents the economic growth models and theory through outlining the evolution of the literature on growth theories. The study by Çalışkan (2015), defines economic growth as a rise in the number of tools and products required to meet human needs in any country, where it is primarily determined by capital accumulation, technology advancements, a rise in population and work force. Isaksson (2007) outlined that the TFP enhances the welfare of the people in the economy. This stimulated many authors to focus on recent contributions of TFP growth on economic growth. During the 19th century the issue of economic growth became of interest by many neoclassical economists, especially after the World War II. However, Economic historians have recommended industrialization based on historical experience. Grossman and Helpman (1993) point out that the industrial revolution that facilitated an output expansion that superseded population growth from 19th to 20th century and diverse growth path for over a relative longer period among the countries. This stimulated many economists to focus on recent contributions of economic growth. During the 20th century Harrod (1939) “An essay in dynamic growth” discovers the concept of warranted rate growth, actual (geometrical) rate of growth and natural rate of growth, which influenced many economists to analyse the causes of economic growth; which saw the emergence of two problems. 10 Firstly, the savings rate determines the actual growth rate and labour determines the natural growth rate. The assumptions of fixed wages, labour and capital consumption in the identical ratio resulted in the actual growth to equal the natural growth. Secondly, the Harrod model exhibited unstable economic growth consequently, this had the potential of explosive growth occurring when real output growth slightly deviated from natural rate growth, with a stagflation as a possible outcome (Hagemann, 2009). The assumption of the fixed proportion of labour and capital became a major criticism of the Harrold-Domar model. The Solow (1956) model of economic growth relaxes the assumption of fixed wages, labour and capital consumption. The Solow’s model focuses on the capital accumulation and his findings shows that the opposition among the unwarranted and natural growth rate of capital is not easily achievable if the constant returns to scale and variable proportions holds under neoclassical assumptions. This means that the knife edge case, found in Harrod-Domar economic models, is not attainable. Swan (1956) studies the relationship between the capital accumulation and the output growth using two diagrams based on theory of Adam Smith, Stuart Mill, Lewis and Ricardo. Abramowitz (1956) answers questions relating to the resource and output trends (the net increase in aggregate output per capital, evidence of change in the output per labour growth and fluctuations that affect the growth rate of output) in the U.S. for the periods of 1870 to 1953: Firstly, Abramowitz (1956) find that the population tripled and the net national output per labour in constant prices quadrupled. Secondly, growth rate of total output and output per capita shows no significant trends in rates. Lastly, he finds uniform change of the output growth rate. Additionally, these points outline the fact that capital should be broadened to include the following categories: health, education and training and research. One may therefore attribute the founding ideas of endogenous technological change to Abramowitz (1956), just that he did not present it in a formal way. Romer (1986) challenged the exogenous growth theory, where they discovered the endogenous growth models which emphasize on contribution by researchers and entrepreneurs as the engine of economic growth. Furthermore, Jones (2019) considered Romer (1990a) paper as a turning point in economic growth as it provided a key insight to nonrivalry of ideas and the rival of standard goods in classical economics, and clarity on the implications for economic growth. This key turning point led authors into publish papers under the key topic endogenous growth theory. 11 The literature review next sections are as follows: section 2.2 discuss the evolution of growth theories and growth facts, section 2.3 discuss convergence as a whole, section 2.4 provides sources of economic growth, section 2.5 diverse schools of thought and lastly Section 2.6 the role of potential output. 2.2 The evolution of growth theories and growth facts 2.2.1 The importance of long run economic growth The long run economic growth plays a crucial role in explaining the factors that determines economic growth within a specified country of interest and explains the cross country differences in income and growth rates (Soylu, Çakmak, and Okur, 2018). The standard of living determines the economic growth which is the productive capability of an economy, measured by the quantity of goods and services (Palmer, 2012). The long run economic growth theory state that the higher level of investment and savings rate results in temporarily increase in output growth (Kahn, 1992). 2.2.2 Growth miracles and disasters The growth miracle occurs when the income inequality of a country is higher than the actual position at a steady state (Jones 1997). Young, 1995 argues that the capital growth rate explains “growth miracles”, whereas for most of the economists may have considered to be driven by the higher TFP growth. During 1960 to 1990, South Korea average yearly growth rate of output per labour rose to 6.1 percent. Hlavac, (2010) point out that the South Korea economy recovered after the Second World War through encouragement of inflow of foreign capital, international trade, and international completion among powerful countries. Furthermore, Singapore, Hong Kong and Japan reported similar growth miracles from 1960 to 1980 where there was an improvement by 40 percent from the initial start of 20 percent in the year 1960 (Jones, 1997). The South Korean income rose, relative to the US GDP per capita, from 11 percent in 1960 to 38 percent in 1988, where the average yearly growth rate of output per labour rises to 6.1 percent, average yearly growth rate of capital amount to 10.8 percent, with the average yearly growth rate of labour and TFP growth amount to 2.6 and 2.3 percent, respectively (Lui, 2007). The other countries that reported a relative high-income growth are as follows: Botswana (from 5 to 20 percent), Romania (from 3 to 12 percent) and Lesotho (from 2 percent to 6 percent). Although, the countries’ modest growth attribute to a large change, they did not catch the attention 12 of economists’, for the period same period as South Korea. Contrastingly, during the same period Venezuela faced a crucial period where their income of 84 percent U.S. income fell dramatically to only 55 percent. Chad is the other country that experience growth disaster from 8 percent to 3 percent in relative income (Jones 1997). 2.2.3 The question of why the whole world is not rich? Following Wolla (2017), GDP measures the value of final goods and services produced within a year. As mentioned under the importance of long run economic growth it measures a country standard of living. The difference between the poor country and the rich country, determined by the level of income, wealth, goods, and services. The whole world is not rich because GDP per capita is used to measure the country’s standard of living (Economic well-being of a country). This question got addressed by the following models Harrold (1939) and Domar (1946) model, Solow model (1956) and endogenous growth models (Barro and Salai-i-Martin, 1995 and Aghion and Howitt, 1998) Following Felipe, Kumar, and Abdon (2014), outlines three reasons why the whole world is not rich question. Firstly, the low level equilibrium trap which is formalised by Nelson (1956) – occurs when the capital stock and population is growth at a similar rate which mean a constant change in capital per worker, were this change also impact per capita income as it result in a constant economic growth of a country. This shows the interdependence of the three mentioned variables. Therefore, low level equilibrium trap occurs when the population super pass the per capita income. Secondly, the issue of economic development under the structural transformation literature which occurs when new ideas replace the old ones, their impact on economic activity and their interactivity (Felipe, Kumar, and Abdon, 2014). Following Chenery, Robinson, Syrquin, (1986), Kuznets (1966) or Kaldor (1967) the structural changes focuses more on industry such as composition of demand, the occupation of the labour force and international trade unlike agriculture sector only. Lasty, the issue of higher real wage earnings which makes a country to become rich (Sutton, 2001). The Sutton argues that the source of growth is through a gradual build-up of “scarce capabilities” which is through network of firms which contrasts from that of the neoclassical model that capital per labour ratio results in higher real wages (Felipe, Kumar, and Abdon, 2014). Furthermore, 13 Hidalgo et al (2007) argues that the production and exports of technology, capital, skills, and institutions as a product progress enhance countries growth. 2.2.4 The world income distribution Sala-i-Martin (2003) examines the issue of how income spreads vary amongst countries by means of a microeconomic survey and aggregate GDP data for the period 1970 to 2000. The author’s findings show that the world per capita GDP progressed to 95 percent1. During 1970 to 1978, the total population rises by more than 1.6 billion whereas number of poor people increased by 20 million. This shows that the population growth offset the poverty rate - this rate decreased by a factor of 3 during this period since 1970. Therefore, growth plays a significant role in eliminating the world poverty (Barro and Salai-i-Martin, 2004, pa.8). The issue of income distribution in the future under the new growth theories assumption of technological progress as the engine of economic growth shows in the long run that the creation of ideas stimulates the output per capita (Jones, 1997). Since ideas are non-rival this means that the other countries can share the ideas, therefore, this implies that the countries that can catch up with each other and growth at the equivalent rate of world knowledge (Eaton and Kortum, 1994). 2.2.5 Determinants of economic growth Following Barro and Salai-i-Martin (2004), the issue of economic growth plays a significant role in standard of living, income levels of individuals and world poverty. Their study stresses on the importance of determinants of economic growth both theoretically and empirically. Barro (2003) examines initial levels of state variables, policy variables and national characteristics as a determinant of economic growth using a panel empirical study. The author’s findings show that holding GDP per capita and high human capital constant, the fertility rate, the inflation rate and the ratio of government consumption to GDP affects growth rate negatively whereas rule of law and the international openness stimulates growth and the effect of democracy being ambiguous. This effect of democracy consists of political models-which impact democracies negatively as it 1 The world per capita is equivalent to GDP of 126 countries then divided by world population. 14 influences the transfer of political power and private sector capital accumulation expropriation - henceforth a democracy becomes productive when government does not expropriate. The following inputs: R&D, capital stock and human capital have been proved to be the main sources of growth. The issue of investment in physical capital shows that the Solow-Swan model in the long run is expected to be independent of the investment rate, because of the diminishing returns. This shows that the there is a correlation that appears in the data between the investment rates and growth rate (Temple, 1999). The issue of human capital on MRW analysis raises two problems, firstly the issue of output per person being overstated by fluctuations in human capital (Benhabib & Spiegel, 1994), lastly the data set shows that the growth rate of educational capital shows no effect on the growth rate output per labour (Pritchett, 2001). The study by Dieckmann (1996), examines the effect of cultural determinants on economic growth under endogenous growth model using theoretical and empirical analysis. The theoretical part found cultural determinants to provide a country with a highest growth rate whereas the effect of empirical study still needs clarity. Also, the effect of cultural determinants cannot be examined under neoclassical growth model since the competitive equilibrium methods under growth accounting is not adequate. 2.3 Convergence During 1980s the questions were asked about the degree of income distribution changes across countries. If there exist absolute convergences or not in future decades? These led to the convergence debate to be of an interest among economists. Following Romer (1996, pa.30), the reasons for economists to study convergence got influenced by the Solow model when forecasting that countries tends to converge to their own equilibrium state, which indicates that the rate of return of capital is low for rich countries and delays in the spread of knowledge. Furthermore, Barro and Sala-i-Martin (2004, pa.47) point out that the neoclassical growth models plays an important role in the prediction of conditional convergence, which occurs when we have heterogeneity (group of countries) across the countries and different steady states. 15 Baumol (1986) and Abramovitz (1986) observe the level of output per labour and growth in the long period after the world-war II, they found that there exists an inverse relationship in the estimation among the poor and rich countries. The catch-up hypothesis further shows that the level of technology includes a country’s capital stock acts as a catalyst, where the latecomer’s country performance (which is initially backward) accelerates with leading country. The diminishing returns in capital yields high rates of return, under the neoclassical model of growth in a closed economy, which is the reason why it led to absolute convergence (Barro & Sala-i-Martin, 1990). 2.3.1 Concepts of convergence hypothesis Following Barro and Sala-i Martin (2004, pa.462), the absolute convergence hypothesis holds when poor countries tends to grow faster than the rich countries - implies a catch-up effect with the rich ones. They assume the following parameters to be identical: population growth, depreciation rate, savings rate, and factors of production. The absolute convergence hypothesis depends on the structural attribute namely, “technologies, preferences, population growth, government policy and factor market structure” which are significant for the attainment of a country’s long run steady state (Galor, 1996). Barro (2003) examines the relationship between the output per capita growth rate and log output per capita in 1965 for sample of 113 countries for the period 1965 to 1995. The author’s outcomes show that the no relation between absolute convergence and cross section of countries. During 1870 to 1979, the study by Maddison (1977) examined the absolute convergence for OECD countries for 13 advanced countries and found strong evidence that support this convergence after World War II period. However, Martin and Sunley (1998) criticized the findings and argue that the study consists of countries that are the same - in the sense that the cross-section of countries is rich before thus are subjective to convergence. The authors suggest that they should have used ex ante sample countries that are expected to be industrialized in 1870, which when combined with ex post, provides evidence of convergence. However, for the relationship between annual growth rate for the period 1880 to 2000 and log personal income per capita in 1880 across U.S. states as 16 well as the relationship between log of GDP per capita in 1960 and growth rate from 1960 to 2000 all support the hypothesis of absolute convergence (Barro & Sala-i Martin 2004, pa.462). Barro (1991) and Quah (1996) validates that the absolute advantage hypothesis is wrong in their empirical studies built on cross - country regression and dynamics of income distribution across countries, respectively. The other concept of convergence is conditional convergence hypothesis (𝛽 𝐶𝑜𝑛𝑣𝑒𝑟𝑔𝑒𝑛𝑐𝑒), which occurs when we drop all the assumptions that the parameters in the absolute convergence are the same across countries (Barro & Sala-i Martin 2004, pa.464). The study by Barro (1996), postulates that for conditional convergence to occur when initial real GDP per capita is less than equilibrium state position, the lower the real GDP per capita infers the higher the likelihood of a higher growth rates. In other words, given the identical structural characteristics across countries except for the initial real GDP per capita, the countries are anticipated to converge to the equivalent equilibrium state position of real GDP per capita (Galor, 1996). Therefore, the conditional convergence is a necessary condition however not a sufficient condition for absolute convergence (Martin & Sunley, 1998; Nelson, 1981). The conditional convergence and club convergence are the two types of unconditional convergence, which were studied by Fischer and Stirböck (2006) who examine two key developments of basic convergence regression that resulted from the analysis of a constrained group of richer OECD countries that support hypothesis of absolute convergence. According to Martin and Sunley (1998), the existence of club convergence result from testing of multiple equilibrium state through adding successive powers of log (𝑦𝑖𝑡) in the basic growth regression. Following Islam (2003), unconditional convergence occurs when there is only one steady state amongst all countries, while conditional convergence occurs when each country has its own equilibrium state. The club hypothesis convergence - arises when per capita income of regional countries is the same in both structural features and initial conditions converge to one another in a long run (Galor, 1996). Further, Baumol (1986) introduce the unconditional convergence, where the author examines the long run growth and convergence among 16 advanced countries using Maddison (1983) data for the period 1870-1979. The author’s findings illustrate a high coefficient of correlation which infers that, with a higher initial income per person in 1870 then the growth rate changes at a slower rate 17 until 1979 denoting perfect convergence and support the evidence of unconditional convergence. However, the author findings were criticised for being mostly dubious which results from the sample selection - the countries used are utmost developed and measurement error - the estimated real output per worker in 1870 is vague (DeLong 1998). Azariadis and Drazen (1990) argue that club convergence occurs when there exists a multiple equilibrium state in the Diamond model. Furthermore, the club convergence may also occur when the cross country reaches steady state given that they have identical location. Therefore, these different concepts of convergence depend on the initial position and some other factors. Following Islam (2003), condition of technological change under the neoclassical growth models requires the following assumptions: technological innovation not driven by resources, it should benefit everyone equally and benefits should be for free. Therefore, if all these assumptions hold, these yield a growth rate that satisfies the convergence hypothesis. If the assumption of production functions being identical in all countries holds then this yields the income level convergence. 2.4 Sources of Economic convergence Rassekh (1998) identifies three main sources of conditional convergence and find its past origin. Firstly, diffusion of technology for poor countries the transfer of technology and low wages results in a faster growth than the rich countries. Secondly, the neoclassical growth model argued that the assumption of diminishing returns to capital results in conditional convergence. Lastly, the role of globalisation - where the terms of trade favours the developed countries and widens the income gap. According to Elmslie (1994), David Hume and Josiah Tucker established the convergence hypothesis during the mid-18th century. Hume’s view is that during economic development, growth experienced a natural inclination of convergence across countries while Tucker’s view is in line with the existence of international economic inequality forever. In addition, Hume discussed the following factors low wages and transfer of technology as the driving force for absolute convergence (Irwin, 1996 and Rassekh, 1998). Gerschenkron (1952) promoted and clarified on the suggestion that there is an advantage in being technologically backward country. Abramovitz (1986) uses Maddison data to hypothesize that being technological backward carries a potential for faster growth, which occurs when a leading country abandons old stock and change it. 18 During 17th and 18th centuries, the two classical economists John Stuart and Adam Smith has suggested the possibility of limit to growth. During 1776, Smith in his “Wealth of the Nations” forecasts that real GDP per capita reaches a maximum state for each country and does not touch on convergence. In addition, Smith criticizes Hume’s theory of technological transfer and low wages in poor countries. Furthermore, Rassekh (1998) shows that Smith argues that higher productivity in developed economies benefit them to lead over deprived countries regardless of having to pay higher wages. Mills (1998) in his “Principles of political economy” emphasizes concentrating on a spread of wealth instead of focusing on increasing it for rich countries, which makes poor countries catch up - convergence applies. Solow (1956) points out that even if the countries are not trading to each other, the neoclassical growth model forecasts income convergence across countries with similar initial per capita GDP. However, Rassekh (1998) argues that international trade is a determining factor of convergence/divergence process. This is because more trade benefits the incomes of the trading partners. Whether more trade leads to convergence of countries is dubious. There are several empirical works that concentrate on examining the relationship between income convergence and international trade. The study by Ben-David (1996) uses a sample of major trade partners and found a positive relationship between convergence and trade - through a decline in the sample of countries income discrepancies overtime. The author clarifies that an increase in trade openness instead of the volume of trade that leads to equalisation of incomes. 2.5 School of thoughts 2.5.1. Keynesian School (Domar’s model) Domar’s model, in isolation, has a fundamental issue with regards to unemployment and inflation (Aricó, 2003). The derivation of equilibria is defined as, “on a knife’s edge,” where any slight deviation results in prolonging or growing of either of these ills, due to the lack of stabilising forces.- the model is not stable (Sato, 1964). The model assumes fixed and equal proportions of factors of labour and capital which is extremely problematic and at the core of the criticisms. Swan (1956) began this critique of long-term growth theory, that capital and labour were key determinants, and such assumptions were misleading and inaccurate. This was in accordance with 19 neoclassical theory, reinvigorated by the development of Solow’s model in the same year (Solow, 1956). Domar’s model, while claiming to refute the original Marxian Reproduction Scheme only serves to rediscover and reinforce the arguments Marx made in a modern context. Domar begins with an analysis of the investment process, declaring a dual nature to the function. Specifically, that investment initially as, spending in the economy that creates income for others, as well as an increase to the productive capacities of the system (Lianos, 1979). Domar (1947) originally stated that, “investment is at the same time a cure for the disease (of unemployment) and the cause of even greater ills in the future.” The parallels between Domar and Marx’s models extend further beyond the definition of investment - the same rate of growth of investment must equal the MPS multiplied by the average productivity of investment. That is, the underlying fundamentals, if their economic reasoning in both models are equivalent. Domar’s implementation of the Keynesian savings rate should not be misinterpreted, it is equivalent to Marx in that the savings rate is estimated in a class society where labourers have no marginal or average propensity to save. This means that the savings rate constructed is the same as Marx’s Capitalists saving’s function. These stark similarities continue into the determination of long-term growth - the income growth rate must be equivalent to the MPS multiplied by the average productivity of investment. These realisations are exactly those of Marx, whose model preceded these revelations by eighty years. 2.5.2. Neoclassical School (Solow and extended Solow models). The neoclassical economists were against the idea of Keynes stating that during the recession the government should intervene to enhance business activity. Firstly, the theory of new neoclassical growth theories was discovered in the article economics of growth by Abramovitz (1952) through his basic notations. However, this was neglected since those basic notations were not articulated formally. The difference in the new neoclassical models assumes perfect foresight, this helped to overcome neglecting or misspecification of important parts of technological change and economic growth. Chandler, et al (2009) and Lazonick and Lazonick(1990) articulate the finding that, during end of 19th century and the start 20th century, the US exceeded the UK in economic performance 20 because of differences in management and organizational structure among both countries firms. Furthermore, Womack et al. (1990) shows that after World War II the Japanese economic growth performance increased unexpected, this resulted from organization of Japanese firms. The Solow growth model is the fundamental model for estimation in growth theory. Solow (1957) studies, US technological change that isolate shift of the output per labour from the movements of the available capital per labour, for the period 1900 to 1949. The findings show that technological change is neutral on average, it accounts for an average of 1 percent in the first half and an average of 2 percent in the remaining half-this results from the upward shift in the production function and increase in technological change approximately double by contributing 87.5 percent of gross output per labour. Since the Mankiw, Romer and Weil (MRW) (1992), MRW going forward, empirical study focused on the rate of growth rather than variation of the income levels, Jones and Hall (1997) study point out that the importance of income levels for 133 countries lies in the differences in output per labour which is basically connected to differences in institutions and government policy (social infrastructure). This is a result of MRW failing to account for income in the cross-country differences through endogenous variables such as lack physical infrastructure. Sachs and Warner (1997) use a cross-country regression to examine geographical factors and economic and international framework factors that affect the slow growth in Sub-Saharan Africa. The authors’ finding shows that the factors mentioned above influenced slow growth, where the GDP per capita accounts for 65 percent in 1965 then dramatically falls to 35 percent in 1990. This is a fall by 25 percent over 25 years. For several years, the issue of whether the growth models with multiple equilibria outline the differences in the long-term income levels were left unaddressed. The Benhabib and Gali (1995, pa.195) study addresses this by coming up with “model based, and conditional on a number of auxiliary hypothesis” method, where their evidence supports multiple equilibria role in explaining the difference in income levels. The study by Klenow and Rodriguez-Clare (1997) examines how the human capital and international productivity difference are measured, by re-estimating the MRW methodology incorporating primary schooling by running a Mincer regression. The findings show that 50 percent or more of 1985 GDP per worker at level difference result from the productivity difference. The MRW calculation of school enrolment data experiences difficulties since it was not clear which proxy is represented amid investment in human capital and investment stock. This is a 21 result of population or labour force data on average schooling being currently accessible which means that it is going to be a poor (Temple, 1999). 2.5.2.1 Technology progress as the Engine of Growth The neoclassical growth theory founded by Solow (1956) focuses on method of capital formation with the assumptions of constant returns to scale (CRTS) and fixed technology, where a country that begins with a low capital per labour ratio drive a high marginal product of capital. However, Grossman and Helpman (1994) criticize the neoclassical growth theorist as being unable to anticipate undesirable outcome of long run forecasts for the aggregate economy. The original Solow growth model influenced researcher to review the issue of growth in different ways. Some, such as MRW (1992) using a sample of 98 countries investigate the difference between the Solow growth model and the augmented Solow model - includes human capital, are consistent in international variations and speed of convergence in the standard of living, for the period 1960-85. The findings show almost 80 percent of international variations in income per unit of labour are generated by the augmented Solow model which shows improvement in the performance variations of income per labour than in the Solow model. The results were influenced by the correlation of human capital accumulation with the savings and population growth, which solves the bias results of the coefficient of savings and population growth. Furthermore, Nonneman & Vanhoudt (1996) study shows that the augmented Solow models best explains the international variations in the income per labour through savings, education, and population. The results show a 60 percent accuracy than of original Solow model. Romer (2006) identifies Solow model as the current foundational base of long-term growth theory. The other key issue that economist encountered under neoclassical growth theory is what TFP change measures? The study by Lipsey and Carlaw (2004) solves the different interpretation of what TFP change exactly measures. This resulted from different conclusion of what it measures where studies; Barro (1991) and Young (1992) show that it measures the rate of technological progress. However, Hulten (2001); Jorgenson and Griliches (1967) believes that it measures the 22 super normal benefits (R&D, and externalities) of technological progress. The findings support the super normal benefits preposition as a measure of technology progress since this is based on investing in new technology rather than investing in an existing technology, which represent an imperfect measure of returns. Hulten (1975, 1978), Rymes (1971), and Cas and Rymes (1991), show that if the Solow conditions hold, the TFP is measured as a shift in the production function. They further clarify that; marginal propensity to invest under capital accumulation should contribute to economic growth. However, in the growth process the TFP residual model “overstate” the role of capital and “understate” the role of innovation as results of exogenous capital assumption (Chen, 1997.). The Solow model of growth has been contrasted against the Domar model in Sato’s 1964 paper. In it, is a note made of the relative strength of the two models, and that Solow’s model is superior as long run instability, with regards to unemployment and inflation, is improbable. This is due to neoclassical assumptions on variable proportions and constant returns to scale. However, latter assumption is criticised by Shaikh (1974) for making the model “infallible” - that is, the model functions on the mathematics of the production function, and not on underlying economic theory. It is a coincidence of the mathematics. Furthermore, For Industrialized and developing countries the neoclassical growth model were criticized for being unable to address the divergent growth paths issue, where this led to economists coming up with an endogenous growth model which address the differences in growth rates and output per person (Morana, 2003). 2.5.3. Marxian School (Goodwin’s model) Goodwin’s model of long-term growth is formulated around considerations of distribution and growth in the economy. From his analysis, there is a clear instability in the capitalist framework and system. This is due to the struggle of all economies to distribute value. This results in perpetual disequilibrium as the economy oscillates between varying levels of employment and wages. The author states that the economy is disaggregated into two classes: the capitalist class and the working class (Goodwin, 1965). The core issue is that value is constantly absorbed from the system at large by the capitalist class from the poor working class, in a manner that is not unlike the gravitational pull from a black hole. This simile of the rich eating the poor is only broken by Volterra’s uneasy predator-prey relation that Goodwin’s model has been contrasted against 23 (Volterra, 1926). As the rich require the poor, there is a need for sustainability in the system, otherwise it collapses. This “collapse” is seen throughout history through mass revolt and/or mass starvation. To sustain the system the economy needs to grow, through an increase in employment and wages, until the point of overheat and implosion. Then wages start to diminish, and employment levels drop, and such the system begins anew. Throughout this cycle, the capitalist class are rarely the afflicted group, that burden is left to the working class. This has changed slightly in the modern economic era, where the rate of brutality has reduced, however the rate of exploitation has increased. Goodwin’s model too has received criticism, as the labour share and proportion of employed labourers in the economy can exceed the value of one - violating core a priori expectations making the model estimation nonsensical. However, modern adaptations of the model have accounted for these issues, but as we are estimating Goodwin’s original model, these issues still lie in the underlying fundamentals of the framework (Desai, et al., 2006). 2.5.4. New Growth School - [NGT - The AK, Lucas and Romer models] During 1980s a large body of economic research analysis focused on studies into endogenous growth which is one of the crucial research areas on causes of economic growth (Gualerzi, 2002). In addition, the disregard of determinants and subsequent impact of technological progress by neoclassical model stimulated the new growth models (Belloumi, 2014). This is due to neoclassical economic growth failing to consider R&D, public expenditure, and education as a critical input in the production. The above-mentioned input variables were incorporated into research by Romer (1986) and Lucas (1988) who discovered the theory of endogenous growth. This was done through the relaxing of the neoclassical growth model and theory assumption of exogenous technological change. Furthermore, the NGT value of capital which currently includes human capital and knowledge. Lucas (1988) examines models that place emphasis on; “physical capital accumulation; technological change, human capital through schooling; and human capital accumulation through learning by doing” and evaluate if the variables are sufficient for economic development. The author’s findings for physical capital accumulation model portray that convergence occurs in the 24 income and asymptotically for the rate of growth levels equally for countries that have identical technology and preferences. The accumulation of capital models through schooling shows a consistent cross-country difference in the income per capita that is permanent education. Romer’s model in the seminal work “increasing returns and the long-run growth” shows that the knowledge is an input in production of endogenous technical change model and exhibit increasing returns in marginal product (Romer, 1986). Gilson and Roe (1993) as well as Nelson (1993), outlined how the difference in national institution as a factor that influence the country growth performance: the financial sector and the universities. The critique about new neoclassical growth model is that it hardly deals with institutions, and firms are treated in an extremely simplified manner. Romer (1990) outlines, the reason why the new growth theories formalized certain thoughts for understanding technological advances and economic growth, the ideas include uncertainty. The reason being that the NGT model’s agenda is to be as close as possible to the principles of general equilibrium theory. According to Hulten (2001), the important assumption of NGT is the constant marginal product. However, the human capital and research are important determinants of economic growth. Furthermore, Gualerzi (2002), points out that the growth per capita in capital is the engine for the neoclassical growth model. However, the problem with the assumption of diminishing return to capital is that the Solow (1956) model fails to consider the continuing improvement in technology as a result the per capita growth comes to an end (ceases). Cuñado et al, (2009), points out that the convergence hypothesis is the important difference between the neoclassical and endogenous growth model prediction. In addition, convergence hypothesis outlines that the per capita outcome in an economy for endogenous growth models and finds that it’s unlikely for income to converge. However, the neoclassical growth model will converge at equilibrium state growth rates of output per capita. Thus, the growth of neoclassical model is determined by technological change which is exogenous in nature (Gualerzi, 2002). Rabelo (1991), formulated the AK model based on human capital as well as R&D as the engine for endogenous growth. This model assumes that fixed factors are not re-producible and can’t be accumulated so they don’t form part of the model, the factors can be land, labour and raw materials etc. However, Lucas (1988); Azariadis and Drazen (1990) stress the importance of education as the engine for the economic growth and in Lucas (1988) model the self-maintained process as the 25 engine of growth. Following Diebolt and Monteils (2000), the production and the education sector in Lucas model occurs simultaneously. The process occurs as follows: goods are produced from human capital and capital stock, then through some part of human capital in production sector not utilised and human capital through itself. According to Barro and Lee (1993), the level of education positively affects the gross national product (GNP) growth rate directly. This study was conducted for the period 1960 to 1985; it examines levels of adult population at primary, secondary, uneducated, and higher education stochastic rate of success. The NGT is supported by Charlot (1997) and Barro (2003), who pointed out that the returns on the education are cumulative and positively impact on output growth rate. However, Benhabib and Spiegel (1994) show that the effect on growth rate of per capita output is not significant by the growth rate of human of the working population (calculated as number of years of education). This indicates that the human capital is no longer considered as factor of production since it only enhances rate of income per capita rather than growth rate, this study contradicts with the endogenous growth theory. The abovementioned contradicting conclusions are due to endogenous growth hypothesis not directly tested (Monteils, 2002). Hulten (2001) point out that the economic growth in the TFP model cannot be explained only by the production function and marginal productivity conditions, since it does not describe how the inputs and technology changes over time. The Solow (1956) overcomes the change over time problem by assuming that labour and technology are exogenous, and investment is a constant fraction of the output. Furthermore, they investigate the importance of technological change in the neoclassical economic growth which shows that the long run growth is not explained by the capital formation. This arises since capital is endogenous and dependent on technological innovations that enhance output which further lead to an increase in the investment and the result being an increase in capital stock. According to Hulten (2000), the TFP models derived from production function are based on a view that productivity growth occurs through advancements in the “transforming of input into output”. However, no clarity on the TFP models’ view about the dimension of innovation. Grossman and Helpmann (1991) point out that the production of better goods contributes a lot to welfare gains that the production of new goods in terms of innovation, where this is referred as increasing the quality ladder. However, the better goods outcome of innovation is not part of the 26 TFP residual; it only measures the production of more goods. Solow (1956) and Johansen (1959) shows that the efficiency approach solves the problem of the two types innovation (the introduction of new goods and quality of products developments) - through the model of capital embodied technological change. According to Nelson (1997), during 1950s the technological advance remains acknowledged as the engine for “formal” neoclassical models of economic growth. However, many studies on the “formal” neoclassical models inarticulate the sources of technological advance. This resulted in the establishment of the new formal neoclassical growth model (Aghion and Howit, 1990; Grossman and Helpman, 1989 and Romer 1990). A distinguishable contrast between the neoclassical growth models is that the new formal neoclassical growth model includes R&D and assumes the imperfectly competitive markets whereas in the “informal” neoclassical growth model assumes the perfectly competitive market. The technological advance in endogenous models has been considered differently as some models take it as a creative destruction and some as externalities: research, and development investment and education activities. 2.5.4.1. Research and Development (R&D) In the AK models the permanent changes in the capital growth rate leads to a temporary effect on the output growth rate rather than permanent changes. This led to NGT to consider the R&D as a significant source of growth for industrial economics. The R&D models got influenced by AK models because of their inconsistency with regards to long run growth time series test and cross- sectional empirical literature (Jones, 1995). In the NGT, the R&D models in the long run concentrates on technological progress and R&D, where the technological progress is an outcome from the search for innovations through discoveries ideas. R&D considers the significance of externalities, spillover and increasing returns for growth theory (Griliches, 1991). The study by Griliches (1979) examines the effect of R&D on economic growth, using the historical case studies and the econometric production function approach-where the aggregate inputs variables also embodies the R&D investment. However, the historical case study is difficult to implement due to data and time expensiveness. Following Parente (2001), R&D is costly, and it excludes poor countries from participating forcing these countries to enhance their output per person through implementing the existing technological 27 developments of rich countries. After World War II, Japan and South Korea are examples of poor countries that implemented existing R&D then became rich countries as the output per person largely increased. Solow (1994) criticize that the R&D activity is affected less by product improvement and cost reduction, where the author shows that it is mainly affected by production labour, process engineers, and even customers. Furthermore, enhancing productivity through resources is not sufficiently measured by the R&D expenditure. 2.5.4.2 The issue of measurement Following Griliches (1979), this issue arises as result of output being measured in terms of inputs and does not account for improvement in productivity through R&D investments - which is consistent of defence, space, and health subdivisions. This implies that the data for R&D sectors were totally unmeasured and mis-measured as it is problematic to trace it out. The following have been the main issues for measurement of capital: R&D of capital may not impact economic growth since its process takes time and its adjustment takes place after several years; the previous R&D investment losses value and becomes out of date; and the level of knowledge of R&D Investment being rival among industries (Griliches 1979). 2.5.4.3 Econometric problem Griliches (1979) outlines multicollinearity and simultaneity as econometric analysis problems for estimation of measured capital and output in R&D to economic growth. The multicollinearity occurs because numerous series focused more on moving observations which are jointly correlated for a given period. The possible remedy for multicollinearity uses micro-time series data “at the individual firm”. The simultaneity occurs because of causality between R&D and output, where the possible solutions are the use of instrumental variables and assumptions of independent relationship between error term and independent variables. 2.6 The role of potential output 28 Slevin (2001); Fedderke and Mengisteab (2017) and Butler (1996), defined the potential output as the maximum level of output that the country can sustain if all the resources (labour, technology and technology) are used efficiently and while inflation held constant. In addition, the output gap is defined as the percentage deviation between real output growth and the potential output growth - an indication of supply and demand pressures of a country at a given time (Kemp, 2011 and De Brouwer, 1998). The GDP is measured by the level of Real GDP - the demand over the business cycle (Slevin, 2001). Therefore, the positive output gap suggests an excess demand which may result in inflationary pressure. On the contrary, the negative output gap suggests a shortage of demand which may results in declining inflationary pressure (Fuentes, et al 2007). Most central banks have a common mandate to achieve consistent price stability. Therefore, the output gap represents a variable provide a significant information in economic policy formulation by policy makers when measuring a country macroeconomic performance, setting inflation targets and fiscal policies. (Fedderke & Mengisteab, 2017; Kemp, 2011 and Arora & Bhundia, 2003). However, these variables are unobservable - becomes a challenge to quantify. In the literature there are various methods of calculating potential output growth such as: a production function, Univariate and Multivariate and structural vectors. This section focuses on the production function approach to evaluate potential output like the Solow model approach used to project output growth. Musso and Westermann (2005), point out that the growth accounting method plays an important part in the medium to long run growth, as the output growth and the supply side factors (where the aggregate supply of the country can be represented by the potential output growth (Slevin 2000). Furthermore, the key benefit of using this method is that it does not rely on forecasting but the actual results. In a monetary policy sense the unemployment is defined as output level that is steady with the constant rate of inflation in the short run (Butler, 1996). The derivation and the results of potential output and output gap are shown in Appendix A. 29 3. Methodology 3.1 Introduction The economists during the 20th century examine the issue of economic growth due to rapid changes in the US economic growth post - World War II. This section focuses on deriving the projected output growth rate of different