UNIVERSITY OF PISA
SANT’ANNA SCHOOL OF ADVANCED STUDIES
Department of Economics and Management Master of Science in Economics
SCHUMPETERIAN GROWTH THEORY:
Comparative Analysis of Neo-classical and Evolutionary Models
Candidate: Supervisor: Edoardo Lolini Giovanni Dosi
Abstract
This thesis presents a comparative analysis of the neo-classical and evolutionary theories of growth, both from a theoretical and an operational point of view. The focus of attention is the “Schumpeterian approach” to economic growth. Both perspectives, in fact, have invoked Schumpeter’ insights as major sources of inspiration. Given such common framework, they become closer and closer in terms of sources and mechanisms that drive growth, and some outcomes of their models result very similar. In short, it seems that a sort of convergence is taking place between the two perspectives. However, despite these similarities, the theoretical comparison, which is done looking at their major theoretical building blocks, has maintained the two perspectives separated one from the other, so that they are not converging to a common paradigm. More than this, it resulted that the theoretical foundations do not have a theoretical impact only, but also an operational one. That, in fact, reverberates in how, and how well, formal models can deliver “predictions” on major macroeconomic aggregates. The operational comparison is done looking at formal models’ ability to jointly replicate the major stylized facts concerning output and its main components. Although with some differences, both the neo-classical “Schumpeterian” and the “pure Schumpeterian” evolutionary models analysed, have brought unsatisfactory results. Both, in fact, are resulted not able to replicate the major empirical regularities concerning the variables of interest. In that, it can be argued that the Schumpeterian apparatus alone is not sufficient to fully account for the effects that the process of economic growth has on macroeconomic variables. An evolutionary agent-based model that bridges Schumpeterian innovation theory and Keynesian economic theory is analysed to clarify this point. The “Keynes-augmented” evolutionary model robustly generates many macroeconomic stylized facts, accounting for both short-run business cycle fluctuations and long-run growth dynamics.
CONTENTS
INTRODUCTION 1
CHAPTER I – MACROECONOMIC EMPIRICAL REGULARITIES 5
CHAPTER II – NEO-CLASSICAL AND EVOLUTIONARY PERSPECTIVES
1.1. Introduction 10
1.2. The neo-classical perspective 11
1.2.1. Exogenous growth models 11
1.2.2. Endogenous growth models 14
1.3. The evolutionary perspective 22
1.3.1. Macroeconomic interpretation 22
1.3.2. Microeconomic interpretation 26
1.4. Analysis of essential differences 30
1.4.1. Agents’ rationality and equilibrium 32
1.4.2. Technological knowledge 33
1.4.3. Heterogeneity 35
1.4.4. Uncertainty 36
1.5. Discussion 37
CHAPTER III – NEO-CLASSICAL SCHUMPETERIAN MODEL
2.1. Introduction 41
2.2. Basic model 42
2.2.1. The setup 42
2.2.2. Labour market clearing and research arbitrage equations 43
2.3. Steady-state growth 48
2.3.1. Comparative statistics 49
2.3.2. Equilibrium profits, aggregate R&D, and growth 50
2.4. Simulation results 53
CHAPTER IV – “PURE SCHUMPETERIAN” EVOLUTIONARY MODEL 3.1. Introduction 59 3.2. Formal modelling 62 3.3. The model 68 3.3.1. Technical change 69 3.3.1.1. “Satisficing” behaviour 70 3.3.1.2. Local search 70 3.3.1.3. Imitation 72 3.3.1.4. Profitability testing 72 3.3.2. Investment 73 3.3.3. Entry 73
3.3.4. The labour market 74
3.4. Main results and implications 74
3.5. Simulation results 77
3.6. Discussion 85
CHAPTER V – “KEYNES-AUGMENTED” EVOLUTIONARY MODEL
4.1. Introduction 89
4.2. The model 92
4.2.1. The timeline of microeconomic decisions 92
4.2.2. The capital-good industry 93
4.2.3. The consumption-good industry 96
4.2.4. Schumpeterian exit and entry dynamics 99
4.2.5. The labour market 99
4.2.6. Consumption, taxes, and public expenditures 100
4.3. Simulation results 100
4.4. Discussion 105
CONCLUSIONS 106
List of Figures and Tables
Figure 1. Aggregate output time series (logs) [Stock and Watson] 6 Figure 2. Cyclical component of aggregate output [Stock and Watson] 6
Figure 3. Level of GDP (logs) [Stock and Watson] 7
Figure 4. Band-pass filtered GDP (trend) [Stock and Watson] 7 Figure 5. Band-pass filtered GDP (cycle) [Stock and Watson] 7 Figure 6. Band-pass filtered total consumption (cycle) [Stock and Watson] 8 Figure 7. Band-pass filtered total investment (cycle) [Stock and Watson] 8 Figure 8. Band-pass filtered total employment (cycle) [Stock and Watson] 8
Figure 9. Phases of GPT cycles 21
Figure 10. Steady state equilibrium 49
Figure 11. Comparative statistics 50
Figure 12. Logarithmic growth of final output 52
Figure 13. Single simulation output, investment, and consumption time series (logs) [AH] 56 Figure 14. Level of output (logs) [Aghion and Howitt] 56 Figure 15. Band-pass filtered output (cycle) [Aghion and Howitt] 57 Figure 16. Interaction mechanisms in Nelson and Winter models 62 Figure 17. Technique array in input coefficients space 66 Figure 18. Technique array in input coefficients space (logs) 66 Figure 19. Dynamics of the Nelson and Winter growth model 75 Figure 20. “Replicator dynamics” in Nelson and Winter growth model 80 Figure 21. Single simulation output, investment, and consumption time series (logs) [NW] 80 Figure 22. Labour input coefficients time series [Nelson and Winter] 81 Figure 23. Capital input coefficients time series [Nelson and Winter] 81
Figure 24. Wage rate time series [Nelson and Winter] 81
Figure 25. Output per worker and capital per worker time series [Nelson and Winter] 82 Figure 26. Level of output, investment, and consumption (logs) [Nelson and Winter] 83 Figure 27. Band-pass filtered output, investment, and consumption [Nelson and Winter] 83 Figure 28. Single simulation output, investment, and consumption time series [NW (𝐵 = 2)] 86 Figure 29. Labour input coefficients time series [Nelson and Winter (𝐵 = 2)] 86 Figure 30. Capital input coefficients time series [Nelson and Winter (𝐵 = 2)] 87 Figure 31. Levels of output, investment, and consumption (logs) [Nelson and Winter (𝐵 = 2)] 87 Figure 32. Band-pass filtered output, investment, and consumption (cycle) [NW (𝐵 = 2)] 88
Figure 33. Interaction mechanism in K+S model 91
Figure 34. Probability density function of a 𝐵𝑒𝑡𝑎(𝛼, 𝛽) distribution 95 Figure 35. Levels of output, investment, and consumption (logs) [K+S] 102 Figure 36. Band-pass filtered output, investment, and consumption (cycle) [K+S] 103
Table 1. Correlation structure [Stock and Watson] 9
Table 2. Major theoretical building blocks of neo-classical and evolutionary theories 37 Table 3. Initial values and parameters [Aghion and Howitt] 54
Table 4. Output statistics [Aghion and Howitt] 57
Table 5. Initial values and parameters [Nelson and Winter] 78 Table 6. Output, investment, and consumption statistics [Nelson and Winter] 84
Table 7. Correlation structure [Nelson and Winter] 84
Table 8. “Benchmark” parameters [K+S] 101
Table 9. Output, investment, and consumption statistics [K+S] 103
1 INTRODUCTION
This thesis presents a comparative analysis of neo-classical and evolutionary theories of growth, both from a theoretical and an operational point of view. Among the wide literature on economic growth, I have decided to focus on “Schumpeterian” growth theories as they provide the more concrete framework to analyse the process of technical change, in this way allowing for a more defined explanation the process of economic growth.
The notion of economic growth explained by endogenous technological progress is a topic that can be found long ago in the works of the “classic”: Smith, Ricardo and Marx. For Smith, technological change took the form of further and further division of labour, enabling a productivity increase in the economic system. He was not focussed on the process of generation of innovations, but rather, on the relation among technological change, division of labour, and structural economic change. Ricardo, instead, analysed the technological progress both from an endogenous point of view, focussing on the relation among innovations, price reduction, and demand increase, and from an exogenous point of view, analysing the consequences on employment of technological progress (assessing that the innovations of his time were employment-reducing). Later, Marx claimed that the innovations are incorporated in standardized industry machines and that technological change (in form of labour-saving technological innovations) is the principal mean of capitalists for acquiring more “surplus value” decreasing labour costs and increasing profits.
Endogenous technological change is the principal topic in the works of Schumpeter (Schumpeter, 1934, 1939, and 1942). All his theories are characterized by the central role given to the technological innovations as major source of technological progress, economic growth, and economic development. He put forward the idea that the technological innovations, or “new combinations” in his term, are introduced in the economic system by non-economic forces. The human actor, the entrepreneurs, the researchers, and the firms, are the ones that perform most of research, and produce and implement most of innovations and, then, are the main sources of economic growth. He
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had particularly studied the so-called “radical innovations” rather than the incremental ones, analysing their impact on the economic system in term of economic growth, economic development and business cycles. In his most famous aphorism, he argued that the introduction and the diffusion of major innovations in the economic system lead to a process of creative destruction, which drastically changes the structure of economic system from within, “incessantly destroying the old one, incessantly creating a new one”. The Schumpeterian intuitions are of fundamental importance for understanding the processes of technical change and influenced the economic thinking during the subsequent years.
In the first growth models, developed between the 1940s and 1950s, technological change was introduced, however, as an exogenous phenomenon. These early growth models did not specifically analyse the relationship between technological progress and economic growth, but they were focussed primarily on issues like savings and stability of the macroeconomic growth path. Intuitive support for the assumption of exogenous technological progress can be found in the public good characterization of technological knowledge and innovations. The economic agents do not have to develop the innovation themselves, but can rely upon other agents to develop it and then, they can simply copy, imitate or buy it. The technological knowledge was represented as a sort of “manna from heaven” at which all agents can freely access.
It is only during the 1980s, that the interest in endogenous technological progress as a motor for economic growth is turned to be of crucial importance in the economic theory. Chronologically speaking, the first attempts to endogenize technological progress in a theory of economic growth can be found in the evolutionary literature, which can be traced back from the work of Nelson and Winter (1982). This kind of models assume out of equilibrium dynamics and bounded rational behaviour of agents as necessary elements to understand the processes of technological progress and economic growth. In that years, there were attempts to endogenize technological progress also in the neo-classical literature. The seeds of this new class of growth models can be found in Romer (1986) and Lucas (1988). These models analyse the process of economic growth on the ground of different concepts as perfect rational behaviour of agents, utility and profit maximization, and emphasising the equilibrium state of the economic system.
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The principal cause that lead to the born of both the neo-classical and evolutionary theories is, however, common and it must be sought in the dissatisfaction of the treatment of technological knowledge and of technological progress in the previous growth models. Both perspectives were indeed animated by the desire to treat technological change as an intrinsic result of economic mechanisms, rather than an exogenous factor. It can be noted that the main topics of research in both perspectives are the same as they both provide an explanation of economic growth based on technological progress and innovation. The development of the so-called “Schumpeterian approach” to economic growth made the two perspectives closer and closer in terms of concepts and outcomes. More precisely, both the evolutionary perspective, from Nelson and Winter (1982), and the neo-classical perspective, from Aghion and Howitt (1992), have explicitly invoked Schumpeter’s insights as major sources of inspiration, bringing the consequence that the sources and mechanisms that drive economic growth in their formal models become very similar one with the other. In short, the “Schumpeterian” approach to economic growth revolves around three distinctive features:
(𝑖) the main sources of technological progress, and, hence, of economic growth are the innovations;
(𝑖𝑖) the innovation process result from the uncertain research activities done by self-interested firms, entrepreneurs, and researchers who are motivated by the perspective of (some) monopoly rents;
(𝑖𝑖𝑖) the introduction and the diffusion of an innovation imply an incessant creative destruction in the economic system.
This common theoretical framework gives the possibility to compare the neo-classical and the evolutionary perspectives in a more defined way. The first questions that this thesis wants to address are: given the common Schumpeterian framework, how similar are the two perspectives? Are they “converging” to a common paradigm? If such convergence is taking place, is the Schumpeterian apparatus sufficient to maintain it? To answer to these questions, both perspectives are analysed in terms of their major theoretical building blocks, that is at the level of principal theoretical assumptions on which they are grounded on, rather than simply focusing on their common Schumpeterian features or by looking at the properties and the results of formal models.
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Despite the Schumpeterian insights, the two perspectives are grounded in completely different theoretical assumptions and the aspects in which they diverge are multiple. In short, neo-classical growth theories analyse the process of economic growth in a dynamic equilibrium framework, where rational behaviours of agents lead to a steady state result in the long-run; while evolutionary growth theories analyse the process of economic growth in a dynamic disequilibrium framework governed by choices of boundedly rational heterogenous agents.
Furthermore, this thesis wants more fundamentally to investigate on “operational” implications of the theoretical assumptions that govern neo-classical and evolutionary models, analysing the ability of such models in generating “predictions” of major macroeconomic aggregates. In this respect, the principal questions that this thesis wants to address are: which is the perspective that represents as well as possible the economic system and the process of economic growth? Is the Schumpeterian apparatus sufficient to account for both long-run growth dynamics and short-run business cycle fluctuations? To answer to this second group of questions, a neo-classical model and an evolutionary model are chosen, and evaluated in terms of their ability to jointly replicate the major stylized facts concerning the principal macroeconomic aggregates, namely output, consumption, investment and employment.
The thesis is structured as follows. In the first chapter, I have reported the major empirical regularities concerning growth and business cycles. In the second chapter, I have briefly analysed the neo-classical and evolutionary perspectives on technology and technological progress, summarizing their major insights to identify essential differences and similarities. In the third chapter, I have analysed the neo-classical Schumpeterian model of growth rooted in the work of Aghion and Howitt (1992). In the fourth chapter, I have analysed the first evolutionary formal model of growth, originally presented in the work of Nelson and Winter (1982). In the fifth chapter, I have analysed an agent-based model of growth, recently presented in the work of Dosi, Fagiolo, and Roventini (2010). Finally, in the last part I have summarized the major conclusions of this work.
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CHAPTER I – MACROECONOMIC EMPIRICAL REGULARITIES
A good test to measure the operational ability of growth models is to analyse their capability in robustly accounting for more than one macroeconomic stylized facts (SF), that is broad empirical evidence concerning macroeconomic variables. In that, several macroeconomic empirical regularities emerge from the literature on economic growth and business cycle. Here, the principal reference is Stock and Watson (1999) that, among others, provide the more complete analysis on the variables of interest (that is output, investment, consumption, and employment).1
The principal stylized fact concerning economic growth is that the logarithmic time series of aggregate output displays growth together with persistent fluctuations (see Figure 1 below). All the available statistical evidence suggests that recurrent fluctuations have characterized the whole history of U.S. economy, but this argument can be widely applied to all the industrialized economies. The time series of U.S. aggregate output shows prolonged periods of increases and declines. It must be noted that much of these fluctuations coincide with signal events of U.S. economy, for example: The Great Depression of the 1930s; the subsequent growth during the World War II; the sustained boom of the 1960s, partly associated to the spending on the Vietnam War; the recession of 1973-1975, associated with the first OPEC price increases.
The presence of persistent turbulences in aggregate output time series can be seen also when it is analysed at business cycles frequencies. The estimate was obtained by passing the series to the Baxter and King (1999) band-pass filter that isolates fluctuations at business cycles periodicities. The series displays a typical “roller coaster” dynamics, implying that the recurrent interchange of expansion and contraction are part of the very definition of the business cycles (see Figure 2 below).
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Figure 1. Aggregate output time series (logs) [Stock and Watson]
Figure 2. Cyclical component of aggregate output [Stock and Watson]
Figures 3, 4, and 5 below, show respectively the level of GDP time series, the band-pass filtered GDP trend and cyclical component. These graphs are relative to U.S. data on the Post-War period. This allows a clearer analysis of the GDP time series eliminating the greater part of the volatility caused by the Great Depression and the World War II.
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Figure 3. Level of GDP (logs) [Stock and Watson]
Figure 4. Band-pass filtered GDP (trend) [Stock and Watson]
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To analyse the empirical co-movements between output and investment, consumption, and employment, the cyclical component of each variable, obtained using the band-pass filter, is plotted along with the cyclical components of output (Figures 6, 7, and 8 below report, respectively, the results of total consumption, total investment, and total employment). These co-movements are quantified in Table 1 below, which reports the cross-correlation of the cyclical components of each series with the cyclical component of real GDP. From this analysis emerge that: investment is considerably more volatile than output; consumption, employment, and unemployment rate are less volatile than output; both investment and consumption tend to be pro-cyclical and coincident variables; aggregate employment tend to be a lagging and pro-cyclical variable, while unemployment rate tend to be a lagging and anti-cyclical variable.
Figure 6. Band-pass filtered total consumption (cycle) [Stock and Watson]
Figure 7. Band-pass filtered total investment (cycle) [Stock and Watson]
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Std. Dev. Cross-correlation with GDP (lags)
Series Abs. Rel. 𝑡 − 4 𝑡 − 3 𝑡 − 2 𝑡 − 1 0 𝑡 + 1 𝑡 + 2 𝑡 + 3 𝑡 + 4 GDP 1.66 1 0.03 0.33 0.66 0.91 1 0.91 0.66 0.33 0.03 Consumption 1.26 0.76 -0.07 0.21 0.51 0.76 0.90 0.89 0.75 0.53 0.29 Investment 4.97 2.99 0.04 0.32 0.61 0.82 0.89 0.83 0.65 0.41 0.18 Employment 1.39 0.84 0.49 0.72 0.89 0.92 0.81 0.57 0.24 -0.07 -0.31 Unemployment 0.76 0.46 -0.27 -0.55 -0.80 -0.93 -0.89 -0.69 -0.39 -0.07 0.19
Table 1. Correlation structure [Stock and Watson]
To summarize, the major macroeconomic stylized facts are:
SF1 Endogenous self-sustained growth with persistent fluctuations. SF2 Relative volatility of output, consumption and investment. SF3 Investment is more volatile than output.
SF4 Consumption is less volatile than output.
SF5 Investment and consumption are both pro-cyclical and coincident variables. SF6 Aggregate employment tend to be a lagging and pro-cyclical variable. SF7 Unemployment rate tend to be a lagging and anti-cyclical variable.
To recall, both the neo-classical and the evolutionary models are thus evaluated in their ability to jointly replicate the above empirical regularities concerning output, investment, consumption, and employment. To have objective results, the models are analysed with the same “standard procedure” that, in some way, follows the one of Stock and Watson:
1) the models are simulated over a time horizon of 600 time steps;
2) the models are replicated performing extensive Monte-Carlo analysis in order to wash away across simulation variability (all the results refer to across-run averages over 100 replications);
3) the first 100 time periods of the simulation are eliminated in the aggregate analysis to provide the models with a warm-up period;
4) the logarithmic time series of output and its main components are calculated; 5) the cyclical components of the series are calculated applying a band-pass filter; 6) co-movements of output and its main components are plotted and quantified in
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CHAPTER II – NEO-CLASSICAL AND EVOLUTIONARY PERSPECTIVES
1.1. Introduction
The principal aim of this chapter is to give a panoramic overview on the evolution of growth theory over the last sixty years, emphasizing the “Schumpeterian approach” to economic growth. Here, I intend not to give an accurate description of the whole neo-classical and evolutionary theories of economic growth, but, rather to present the key characteristics and the main insights of both perspectives on technological change, to compare them to identify essential differences as well as similarities.
Following Solow (1994), it can be identified three major stages in the history of economic growth theory over the last sixty years:
the first stage is associated with the development of Harrod-Domar model of economic growth;2
the second stage is related to the development of the traditional neo-classical models of economic growth in the 1950s;
the third stage is relative to the emergence of endogenous growth theories in the early 1980s, and their development in subsequent years.
For the purpose of this chapter, I have analysed the last two stages only as they represent the most relevant theories of economic growth and offer the majors arguments of comparison between the neo-classical and the evolutionary theories.
The traditional neo-classical models of economic growth were first developed by Solow and Swan in the 1950s. The authors independently developed relative simple models whose principal result is that, in the long run, economic growth is achievable only
2 These models were independently developed by Harrod (1939) and Domar (1946). They were originally developed as a help to analyse the business cycles, but they were later adapted to explain economic growth. Basically, these models suggest that an economy’s growth rate depends on the level of saving and productivity of capital investment, known as capital-output ratio (𝑘 = ∆𝐾/∆𝑌). The rate of economic growth is then simply given by the ratio of the above variable, i.e. 𝑔 = 𝑠/𝑘. Therefore, the rate of economic growth can be increase in one of two ways: increasing the level of saving (i.e. investment policies) or decreasing the capital-output ratio (i.e. increasing the productivity/quality of capital input). The Harrod-Domar model lead to an instable solution and its main suggestion is that there is no “natural” reason for an economy to have a balanced growth.
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through technological progress. However, the technological progress was assumed as exogenous and, then, rest unexplained by the models. Furthermore, the technological knowledge was assumed to be a public good, a “manna from heaven” at which all economic agents have freely access. For this reasons the models were strongly criticized in subsequent years as they explain the force behind economic growth by simply assuming it.
In the early 1980s, during an economics slow-down, dissatisfaction of the Solow-Swan model lead to the development of different theories that try to overcome these shortcomings. The two major alternatives to the traditional neo-classical model of economic growth are:
the neo-classical endogenous growth models, pioneered by Romer (1986) and Lucas (1988);
the evolutionary growth models, rooted in the work of Nelson and Winter (1982).
Even if from a completely different theoretical point of view, both the classes of models try to give a more accurate and realistic description of the complex process of technological progress and therefore try to accurately explain the economic growth. 1.2. The neo-classical perspective
In this section I have reported few examples of the neo-classical growth theory providing their main characteristics and analysing the mechanisms that drive growth. For a more complete survey on neo-classical growth models I refer, among others, to Aghion and Howitt (1998) and Verspagen (1992).
1.2.1. Exogenous growth models
The neo-classical growth theory is rooted in the models presented by Solow and Swan in 1956. The main aim of these models was to provide a theoretical framework to understand the growth of output and the persistent differences in output per capita among countries. The authors attempted to explain long-run economic growth by looking at capital accumulation, labour (or population) growth and increases in productivity, commonly referred to as technological progress.
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Due to its particularly attractive mathematical characteristics, the model has provided a convenient starting point for further extensions.3
The model assumes a closed economy, with no government or international trade, where a single commodity is produced. Aggregate output (𝑌) depends on capital stock (𝐾) and labour (𝐿) according to an aggregate production function that is homogeneous of degree one (which imply a constant return to scale production function) and that satisfies the Inada conditions. Technological knowledge is introduced in the term of aggregate parameter (𝐴), commonly called “effectiveness of labour” which reflect the labour-augmenting technological knowledge. Therefore, the aggregate parameter (𝐴𝐿) represents the effective units of labour of the economy.
Taking a Cobb-Douglas production function, we get that:
𝑌 = 𝐹(𝐾, 𝐴𝐿) = 𝐾𝛼(𝐴𝐿)1−𝛼, with 0 < 𝛼 < 1 (1)
Both the growth rate of technological knowledge (𝑔) and labour force (𝑛) are assumed to be exogenously determined. The number of effective units of labour (𝐴𝐿) therefore grows at rate (𝑛 + 𝑔). Stock of capital, instead, is assumed to depreciate over time according to a constant rate (𝛿). However, only a fraction of capital is consumed, leaving a saved share for investment.4 Also the growth rate of saving (𝑠) is assumed to be constant and exogenous in this model.
A crucial assumption of the above production function is that there are diminishing returns to capital accumulation at economy wide level, that is, the marginal productivity of capital on output decreases as capital accumulates. Indeed, because of diminishing returns to capital, output does not grow as fast as the capital stock, which in turns means that savings cannot grow as fast as depreciation. Therefore, in absence of population growth (i.e. if 𝐿 remains constant) and of technological progress (i.e. if 𝐴 remains constant) such economy cannot grow at a positive rate.
3 Among others, the most direct one is Mankiw, Romer and Weil (1992) whose developed an “augmented” Solow model including the human capital parameter (𝐻) as a crucial variable of the production function, i.e. 𝑌 = 𝐾𝛼𝐻𝛽(𝐴𝐿)1−𝛼−𝛽.
4 Formally, 𝑑𝐾
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The main interest of the model is to analyse the dynamics of capital intensity (𝑘)5,
which depends positively on the saving rate and negatively on the rate of population growth, the rate of technological progress and the depreciation rate, according to what become known as the “Solow equation”:
𝑘 = 𝑠𝑘𝛼− (𝑛 + 𝑔 + 𝛿)𝑘 (2)
This equation implies that capital converge to a steady state value of 𝑘∗, at which there
is neither an increase nor a decrease in capital intensity, which is defined by:
𝑘 = ( 𝑠
𝑛+𝑔+𝛿)
1 1−𝛼
(3)
Since there are constant returns to scale, output grows at the same rate. Therefore, the steady state or the balance growth equilibrium is defined by a situation in which output and capital grow at the same proportional rate. In essence, on the basis of the above assumptions, an economy, regardless of its starting point, converges to a balanced growth path where long-run growth of output and capital are determined only by the rate of labour augmenting technological progress and the rate of population growth. In this situation, the growth of output per worker is in turn determined only by the rate of technological progress. In others words, the economy converges to a steady state in which diminishing returns are exactly offset by the exogenous technological progress. As it can be noted, one of the main shortcoming of this model is that it takes as exogenous both the technological progress and the population growth rate, that is it take as given the behaviour of the variables that are identified as the driving forces of growth and, therefore, explain growth by simply assuming it. Furthermore, when the model is used for “growth accounting”, a methodology that was introduced by Solow in 1957, it turns out that it’s unable to explain growth rates of output by relying on the accumulation of physical inputs (labour and capital). When output growth is corrected for the increase in physical inputs, a large persistently positive residual remains, the so- called “Solow residual”. Then, factors other than capital accumulation and an increasing labour force could be responsible for most of the economic growth that has occurred. The Solow residual is often called our “measure of ignorance” as it captures the fundamental driving force behind the economic growth, namely technological progress.
5 That is the per capita stock of capital, or stock of capital in efficiency units (i.e. 𝑘 = 𝐾 𝐴𝐿).
14 1.2.2. Endogenous growth models
During the second half of the 1980s, there was the development of different theories that try to overcome the problems rest unsolved by the Solow-Swan model. Two were the main points of criticism. First, the unique source of long run growth in the steady state is a mystery variable, the “effectiveness of labour” (𝐴), whose exact meaning is not specified and whose behaviour is taken as exogenous. Then the model is turn to be unable to explain why the GDP per capita has been continuously growing in most industrialized countries. Second, as technological knowledge is assumed to be as a perfect public good at which all economic agents have access, the model predicted that poor and rich countries will converge to the same level and rate of growth of GDP per capita in the long run. This, however, was totally in contrast with the empirical evidence. Considering the above problems, economists started to explore models that would be able to really explain how technological progress can generate sustained growth and persistent differences between countries in the long run. This new wave of models takes the name of “neoclassical models of endogenous growth” as they try to endogenize the technological progress.
The endogenous growth economists assert that the economic growth is generated from within the economic system as a direct result of internal processes, and is not the results of exogenous external forces. In these models, growth is primarily driven, not only by capital accumulation and saving, but more fundamentally by entrepreneurial activities or innovations that are induced or facilitated by various aspect of the economic environment. These new growth theories are more deeply rooted in microeconomics (in particular, in theory of industrial organization) and, even if they treat capital accumulation and its role in production in ways that are similar to the earlier models, they try to specifically analyse the accumulation of technological knowledge modelling the determinants of its evolution over time.
Arrow (1962) can be considered one of the first attempts in this field. His model was based on the observation that productivity of labour increase even in absence of investments.6 He assumed that the growth rate of the effectiveness of labour is a result of workers’ cumulated experience in producing commodities, or the result of what is defined as learning by doing.
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With his work the labour productivity become endogenous and increasing function of cumulated aggregate investment by firms. However, Arrow still assumed diminishing marginal productivity of capital at an economy wide level for a given supply of labour. In such case increasing knowledge cannot fully compensate for diminishing returns of firm’s capital stock and long-run growth will cease unless the exogenous growth rate of labour is sufficiently high.
An important step forward was made by Romer (1986). The main idea of his approach is that technological knowledge grows in proportion to the macroeconomic capital stock. But “capital” here must be considered as a broader concept including human, physical and intangible capital. The basic idea of his model is that capital accumulation by any individual firm contributes to a collective process of creation of new technological and organizational knowledge through learning by doing or learning by imitating. Such knowledge creation, in turn, will permanently offset the effect of the diminishing marginal productivity of capital and thereby enable the economy to sustain a positive rate of growth in the long-run, under suitable assumptions on the learning externalities. Thus, investments in capital would have a “spill-over effect” on the economy as a whole that potentially offsets the effects of diminishing returns to capital accumulation.
In its basic formulation, this approach is become currently known as the “AK approach” because it results in a production function of the form 𝑌 = 𝐴𝐾 with (𝐴) constant. The individual firm’s production function is represented by the equation:
𝑌𝑖 = [𝐴𝑖(𝐾, 𝐿)𝐿𝑖]1−𝛼𝐾
𝑖𝛼 (4)
As in Arrow model, technological knowledge is considered as a public good that can be applied to each firm with zero costs. In this formulation, the index of knowledge available to the firm is linked to the economy wide stock of capital and labour. Accordingly, the change in each firm’s technology is related to the change in the external aggregate capital and labour stock, which the individual firm cannot influence. A simplifying specification of firm’s knowledge, in which the change in technology depends only on the rate of macroeconomic capital accumulation is:
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Aggregating over all firms, the aggregate production function becomes:
𝑌 = 𝐴𝐾𝛼+𝛽𝐿1−𝛼 (6)
In a special case, in which (𝛼 + 𝛽 = 1) and (𝐿) is normalized at 1, the production function becomes 𝑌 = 𝐴𝐾 with (𝐴) assumed constant. In this kind of model economic growth can be sustained in the long run without relying on exogenous technological progress, but rather on capital accumulation only.
The crucial assumption of this approach is that firm’s production is dependent on both the technological knowledge acquired by the firms themselves, but also on the aggregate technological knowledge in the economy. This assumption has important implications on the theory of economic growth. Firstly, it implies that there are important externalities concerned with the development of technological knowledge. In these circumstances, firms which invest for increasing their own productivity do not take into account the effect of these investments on the aggregate technological knowledge, and then on other firms’ production. Secondly, the presence of externalities in the innovation process is closely connected the existence of increasing returns to
scale in the aggregate production function.7
However, it must be noted that the existence of a steady growth path is strongly conditioned on the assumption of constant return to scale at individual firm level. In fact, any deviation from this assumption will have significant effects in the long-run: if the expression for growth contains the growing variable raised to the power of exactly one (𝛼 + 𝛽 = 1), there is steady state growth; if this variable is raised to the power of a parameter less than one (𝛼 + 𝛽 < 1), growth will cease; if the parameter is larger than one (𝛼 + 𝛽 > 1), there will be exploding growth.8
Although the presence of externalities and non-diminishing returns to scale are important characteristics of the basic AK model, subsequent developments have generalized this basic model in several ways. Rebelo (1991) demonstrated the feasibility of sustained growth without relying on constant returns to scale with respect to reproducible factors in the final goods sector and without the presence of externalities.
7 Because of the difficulties associated to work with increasing returns in a general equilibrium framework, the introduction of externalities makes possible a competitive equilibrium in which capital and labor receive their marginal products.
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Another important contribution was made by Lucas (1988). He proceeded in the same line of Romer, assuming that firm’s production is dependent on both the technology acquired by firms themselves and on the aggregate knowledge in the economy, and that there are important externalities associated with the development of technological knowledge. However, the characterization of his model is that knowledge is accumulated through human capital and that externalities are represented by a form of public learning which increases the stock of human capital at the economy wide level. The main shortcoming of this first generation of endogenous models is the treatment technological knowledge, considered as a perfect public good at which all firms have access with zero costs, freely available and easily transferable. Their models suggest that technological knowledge may be conceived as a non-rival good. This means that once new knowledge is produced by a firm (or by an economic agent who is accumulating human capital) this may benefit all the other firms as well. The public good characteristic of innovation introduces a positive externality in the economic system, consequently determining the existence of increasing returns to scale in the aggregate production function. That may explain the persistent differences in economic growth rates between countries that the Solow model left unsolved. However, the problem of this conception of technological knowledge rest in a question: why economic agents may decide to invest in the accumulation of knowledge and human capital? Where they take the incentive to invest?
This question was considered few years after by a second generation of models that become known as “multi-sector” models (Grossman and Helpman, 1990; Romer, 1990). Still grounded on the idea that there are important externalities associated to the public good feature of knowledge, these models argue that knowledge is a partly appropriable good, meaning that the fruits of technological progress may be appropriated by the producer in the form of monopoly rents.
These models represent a more realistic economy in which the agents decide in which sector invest their resources. The usual way to model intentional technological progress is to make a distinction between a research and development (R&D) sector and other sectors in the economy. The products of the R&D sector are typically of two types: “blueprints” of new intermediate goods and general technological knowledge. The crucial difference of these goods is related to their application in the production process.
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In fact, general technological knowledge cannot be applied directly in the production process, but in the research sector only and it’s used for the production of blueprints. It’s generally produced as a by-product of the innovation process which can be used not only by the entrepreneur who developed it, but also by other firms in the research sector. Therefore, general knowledge is assumed to be non-appropriable and public. Instead, blueprints are specific and provide the guidelines to produce a given type of intermediate or consumer good. The firms which operate in the research sector devote their efforts to producing and selling these blueprints because they enable producers of consumer or intermediate goods to produce at lower cost (process innovation’s blueprint) or higher quality (product innovation’s blueprint). The level of output in the research sector, in form of blueprints, depends on human capital input, general knowledge input and on a productivity parameter.
Then, the innovations are assumed to be produced in form of blueprints and once a new blueprint is found, the firm who produced it can appropriate its invention by patenting, so that becoming the monopolist producer of the new good. Consequently, the R&D sector is monopolistic competitive and not perfectly competitive. These models also assumed that the new good produced is insert in the market without having effects on the older ones. Thus, economic growth takes the form of an increasing variety of new intermediate goods. These models, in fact, define the so-called “product variety approach” to economic growth.
This second generation of growth models seems to answer to the questions left unsolved by Solow because the appropriability characteristic of knowledge explain the incentive to invest in innovative activities, while its public characteristic explains increasing returns to scale and then cross-countries differences.
In the trail of these models, soon after, there was the development of models that analyse deeply the innovation process assuming that its outcome is non-deterministic and uncertain. Grossman and Helpman (1991) and Aghion and Howitt (1992) are the first examples in this stream of research. Their models analysed a multi-sector economy composed by a R&D sector, an intermediate sector, and a consumer (or final-good) sector in which innovations operate through the improvements in the quality (or productivity) of consumer (or intermediate) goods. Their analytical models formalize the uncertain nature of innovative process by assuming that new blueprints are found
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according to a Poisson stochastic process, whose parameter represents the productivity of research sector. As the crucial parameter of the stochastic process is known, it is possible to calculate the average arrival rate of innovation, and consequently the average growth rate of the economy as a whole. Both models assumed that each new innovation is built on the previous one, so that the quality (productivity) of the new consumer (intermediate) good is always higher for next innovations. Then, the impact of an innovation is not only to raise quality (productivity) in the present period, but also in the periods that follow. Since innovations in future periods may be sold by different firms, the value of an innovation to society goes beyond its value for the innovating firm in the present period. Thus, there is a positive inter-temporal externality in the innovation process, i.e. knowledge spill-over effect. However, there is also a negative externality involved in the production of innovation that is due to the fact that a new innovator, by bringing his innovation on the market, destroys the monopoly rents for the previous innovator. This effect is called business stealing effect or “creative destruction effect”, in Schumpeterian terms. Each innovation, each new blueprint, makes the previous one instantaneously obsolete, so that the previous monopolist is driven out of the market as soon as an innovation is found. Obsolescence exemplifies an important characteristic of the growth process, namely that progress creates gains for someone as well as losses for someone else, embodying the Schumpeter's idea of creative destruction. This concept is specifically analysed in Aghion and Howitt (1992) and in their subsequent works. This paper represents the seeds of the neo-classical “Schumpeterian approach” to endogenous growth theory. The principal features of this approach are:
(𝑖) the main source of technological progress is innovation;
(ii) innovations, which lead to the introduction of new production processes, new products, new management methods, and new organization of production activities, are created by self-interested firms, entrepreneurs, and researchers who expect to be rewarded with (monopoly) rents in the event that their innovation is successfully implemented;
(iii) in general, these monopoly rents are eventually dissipated, as the new processes or products introduced by current innovators become obsolete when new innovations occur that compete with the current technologies and thereby drive them out of the market.
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The model of Aghion and Howitt is sometimes called one of “vertical innovation” as opposed to model of “horizontal innovation” defined by the model of Romer (1990). This distinction exemplifies the basic difference between the “Schumpeterian approach” and the “product variety approach”. Even if, in both approaches the driving force of long run growth are the innovations produced by a monopolistic R&D sector, in the latter approach new innovations do not generate better product in term of quality and productivity, but just more of them. In fact, even if they both assumed that there exist important externalities in the innovation process,9 the business stealing effect and, hence, the obsolescence of older innovations is completely absent for the product variety approach.
The most recent developments in neo-classical endogenous growth theories, concern the observation that different innovations may have different sizes and, hence, different impacts on the economic system. The distinction between radical and incremental innovations is explained with the notion of “general purpose technology” (GPT). Bresnahan and Trajtenberg (1995) define a GPT as a technological innovation that affects production and/or innovation in many sectors of an economy. Well-known examples in economic history include the steam engine, electricity, the laser, turbo reactors, and more recently the information-technology (IT). Three fundamental features characterize most GPTs. First, their pervasiveness: GPTs are used in a wide range of economic sectors in ways that drastically change their modes of operation and thereby generate evident macroeconomic effects. Second, their scope for improvement: once a GPT arrives, the radical innovations is not immediately ready to be used in the final good sector, but it needs to be implemented in the form incremental innovations, thus, GPTs tend to underperform upon being introduced and only later do they fully deliver their potential productivity growth. Third, innovation spanning: GPTs make it easier to invent new products and processes that is, to generate new secondary innovations of higher quality. The GPTs typically led to older technologies in all sectors of the economy to be abandoned as they diffuse to those sectors, i.e. they are Schumpeterian in nature as they involve the obsolescence of previous innovation. For this reason, the GPT models are developed using the Schumpeterian apparatus.10
9 i.e. the “knowledge spill-over effect” in the Schumpeterian approach and the “non-rivalry plus limited excludability” in the product-variety approach.
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This kind of models explore another effect related to the innovation process that emerge from the fact that although each GPT raises output and productivity in the long run, it can also cause cyclical fluctuations while the economy adjusts to it. This process is analysed in phases. The first phase is related to the emergence of the new GPT. When the new GPT is introduced in the economy much of resources are invested in the research sector to develop the new good and appropriate the related monopoly rents. This initial phase occurs when the old technology still has the higher productivity. Hence, at aggregate level the introduction of the new GPT results in a slow-down of economic activity that may last for many years. Later, when a certain number of intermediate good embodying the new innovation are developed, the profitability of the new technology increase and the GPT start to become dominant in the economic system causing the abandon of the older one. Then, in this second phase, the new GPT diffuses to the whole economy, and this may sustain the growth of aggregate productivity for the following years (until a new GPT is discovered and introduced in the economic system). Figure 1 below schematize this two-phase cycle (Aghion and Howitt, 1998, p. 249).
Figure 9. Phases of GPT cycles
These two phases of the growth cycle are assumed to repeat over time, and in the long run such a cyclical trend tends towards the steady state. The GPT formalize within a neo-classical framework the Schumpeterian theory of “long waves” (Schumpeter, 1939) aiming to explain the causes of long run accelerations and slow-downs in economic growth, which underlies the so-called “Kondratieff cycle”.
22 1.3. The evolutionary perspective
During the early 1980s, dissatisfaction of the traditional neo-classical model of growth has led also to a revival of the evolutionary tradition in economics, which goes back to Veblen (1898) and Schumpeter (1934, 1939, and 1942). The roots of this revival can be found in the works of Dosi (1982), Freeman (1982) and Nelson and Winter (1982). The last work can be seen as the evolutionary response to the shortcomings of the Solow model of economic growth.
The focus of evolutionary economics is on innovation as the main source of growth, and on economic change with the main driver being technological change. The idea that technological change is a fundamental driving force of economic development is at the heart of evolutionary theorizing about economics in general and economic growth in particular. Of course, the crucial role of technological progress has been recognized in neo-classical economics as well, but what distinguishes evolutionary economics from neo-classical economics is its theoretical framework. However, define the evolutionary economics theory through a stylized description of formal models is a very hard task, so I have preferred to use here a different approach describing firstly the evolutionary macroeconomic and microeconomic interpretation of technology and technological change and later summarizing its major formalization (see Chapter III, Section 3.2.). 1.3.1. Macroeconomic interpretation
A useful starting point to define the evolutionary view on technology is Dosi (1982). In this work the author defined the technology as “a set of pieces of knowledge, both directly practical ... and theoretical ..., know-how, methods, procedures, experiences of successes and failures and ... physical devices and equipment” (Dosi, 1982, p. 151). This view of technology is broader than the one given by the neo-classical theory and, relatedly, also the conception of technological progress takes a different form. Instead of the neo-classical viewpoint of technological change, based on well-behaved production function movements, he argued that “normal” technological change consists in relatively small improvements upon few drastic and bigger technological breakthroughs. He developed the hypothesis that main technological discoveries are grouped in technological paradigms.
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In analogy with what Kuhn (1962) defined “scientific paradigm” (or “scientific research program”), a technological paradigm is defined as “a model and a pattern of solution of selected technological problems, based on selected principles derived from the natural sciences and on selected material technologies” (Dosi, 1982, p. 152). As a scientific paradigm determines the field of enquiry, the problems and the tasks, so does the technology, defined in the broader sense. In other words, a technological paradigm could be approximately defined as an “outlook” or a “model” which defines the relevant problems to be addressed and the “patterns” of enquiry in order to address them. Technological paradigms are distinct from technological trajectories, namely “the pattern of the “normal” problem solving activity (i.e. of “progress”) on the ground of a technological paradigm” (Dosi, 1982, p. 152). A technological trajectory can be seen as the development of a technology along the lines set out by the technological paradigm. Thus, “normal” technological progress takes place along the direction set out by the discovery of a more general principle which provides the opportunity of application in several economic sectors. This view can be linked to the Schumpeterian innovation theory according to which the introduction of an important innovation creates a “bandwagon” effect of smaller follow up inventions and innovations. Thus, the so-called “radical innovations” can be interpreted as the innovations associated to a change in the technological paradigm, while the so-called “incremental innovations” can be seen as the normal technological progress that occur along a technological trajectory. The notion of technological paradigm stems from empirical observations in the history of technological change. There are many examples of fundamentals discoveries which opened possibilities for a wide economic application, thus giving rise to large productivity increases and the emergence of new products and services, like steam technology, electricity, chemical technology, internal combustion engine and semi-conductors. The actual achievement of these productivity gains and new products and services do not take place all in one time, but rather comprises a long period of “normal” technological change, that is of development along a technological trajectory. In this respects, an important characteristic of technological paradigms is related to the concept of their pervasiveness (Freeman et al., 1982). This concept may be understood as the influence that a technology has upon economic sectors. If the technological discovered only affects the production structure in one or few sectors, its effect upon the whole economy will be small. Instead, if the new technology affects the production
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structure in most sectors, i.e. the new technological paradigm is pervasive, the effect on economy will be large leading to a higher productivity increase and, hence, to a faster growth. The analysis of Freeman et al. (1982) is focused on the “Kondratieff wave” and on business cycle trying to formalize the Schumpeterian theory of long wave (Schumpeter, 1939). Basically, the idea behind this theory is that major technological breakthroughs would lead to a cyclical growth path and, hence, to a long wave pattern of long-run economic development. It is recognized that technological innovations play the central role both in creating such long wave and generating economic growth in the long run. Schumpeter, grounding on the observations that innovations are not distributed randomly over the economic system but arrive in clusters, suggested that some long wave can be identified within the 18th and the 19th century: the first long cycle of economic development was based on the diffusion of the steam engine and textile innovations; the second, largely on the railway and the associated changes in the mechanical engineering and iron industries; and the third on electrical power and combustion engine. In other words, the emergence of technological paradigms may determine a long wave pattern of economic development. When a new technological paradigm emerges, there is a big impulse in the economic system to adopt it, normal technological progress occurs and several incremental innovations are developed, the economic system enter in the boom phase of the long wave. Later, increased competition and market saturation, decreasing revenues from the new technologies and, hence, decline in firms’ profits lead to the recession and depression phase of the long wave. In such situation, when the “payoff” of the old technological paradigm started to diminishing, lot of efforts are devoted to find an alternative one.11 The discovery and introduction of the new paradigm give rising to another cycle of economic development. The process continues over and over and takes the form of a succession of long waves. Leaving aside the long waves cycle process, it’s important to analyse in what the technological paradigms are different and the process by which some are selected and introduced in the economy and some other are discarded or retarded.
First, prevailing technological paradigms differ over time and across fields regarding the nature of the knowledge underlying the opportunities for technological advances. In relation, they differ in the degree to which such knowledge has been gained largely
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through operating experience (i.e. through “learning by doing” and “learning by using”) or through scientific research (i.e. through the results of public and private R&D activities). These are the main sources of technological knowledge upon which a technological paradigm is drawn. Differences in such sources lead to different technological opportunities, different technological trajectories and, hence, different rate of technological advance for different paradigms. Secondly, another important feature which distinguishes different paradigms has to do with the cumulativeness of innovative successes. Cumulativeness captures the incremental nature of technological search, and, crucially, varies a lot across different innovative activities. The property captures the degrees to which “success breeds success” or, more formally, reflects the tendency to generate new technological knowledge by incrementally building upon what has been previously done. It can be analysed both at firm level or at sectoral level: at firm level, cumulativeness means that, today, the probabilities that innovators will innovate soon are higher than non-innovators will; while at sectoral level, cumulativeness means that new innovations are based on the previous ones and that technical change builds incrementally and continuously on existing knowledge.
As mentioned above, other important aspects are related to why a paradigm is selected, retarded, or abandoned. These aspects depend both on the economic potential of a paradigm itself and on the interaction among economic, social and institutional environment. Freeman (1991) suggested that the emergence or the retardation of technological paradigms can be seen as an evolutionary selection process. The process of evolutionary selection is essentially a process of competition. The relative competitiveness of different paradigms, together with the selective environment determines the outcome of such process. The paradigm competitiveness is analysed in terms of technological, economic and institutional factors. First, the technological competitiveness of a paradigm is related both to the potential decrease in the production costs (i.e. to the so-called “process innovation”) and to the potential increase in the quality of products (i.e. to the so-called “product innovation”). This kind of competitiveness, clearly, varies a lot over the technology lifetime due to cumulative nature of the innovation process, increasing and increasing as incremental innovations are developed, that is as the “normal” technological progress occurs.12 Second, the
12 In most of all technologies the presence of increasing returns, network externalities and path
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economic competitiveness of a paradigm is also crucial for its emergence. This factor principally operates through the profitability concept, following the basic economic principles. Demand-side factors can induce changes in the orientation of the creation and development of the new technology in different ways. First, within a particular paradigm, changes in relative prices or in demand or supply conditions may affect the orientation and the direction of search heuristics.13 For example, the increase in the price of gas leads to the development of diesel engine within the paradigm of internal combustion engines. Second, the actual or perceived environmental conditions can influence the problem-solving activities which agents decide to undertake, that is can affect the intensity of search between paradigms.14 For example, the recent passage from internal combustion engine paradigm to electric engine paradigm is partly due to the need perceived both by users and politicians for more ecological way of living. Finally, also institutional and social factors have crucial impact on paradigm competitiveness. There are strong interconnections between a technological paradigm and the institutional setting of the society. Factors like education, labour relation, politics, social conflicts, institutional actors and legal issue can empower or undermine a technological paradigm. For example, the labour conflict occurred in England in the 19th century acted as a powerful stimulus for the industry mechanization.
1.3.2. Microeconomic interpretation
For analysing the evolutionary microeconomic interpretation of technology and technological progress, the attention must be switched to the level of individual firm. Already Schumpeter (1934) placed the emphasis on non-economic forces as the main driver for growth. The human actor, the entrepreneur, and the firm are the ones that perform most of research and that produce and implement most of innovations and, then, are the main sources of economic growth and development. Nowadays, firms have become a central locus of “research” efforts and have been the economic entities that employ most new technologies, produce and market new products, and operate with new production processes. Most modern firm operates in environments that are changing over time, in ways that cannot be predicted in any detail. Technological advance is one of the primary forces causing continuing uncertainty, but other causes concern the nature of markets and competition.
13 This is what Rosenberg (1976) called “focusing” or “selective” device.
