Growth and distribution, technological progress, and economic policy

This dissertation consists of three essays rooted in the growth and distribution literature with a focus on technological progress and economic policy. The main objective is to integrate technological progress into the growth and distribution framework and to explore its implications for economic dynamics. To this end, I explore seemingly different topics such as the historical development of theoretical perspectives on technological progress, the application of the Keynesian growth and distribution model to the economics of pensions, and the role of induced technological progress in sustainability of old-age public pension schemes. This dissertation draws on the existing Keynesian economic literature. Specific emphasis is placed on the Cambridge-Keynesian view concerning the long-run position of capitalism and the distribution of income between wages and profits.

GROWTH AND DISTRIBUTION, TECHNOLOGICAL PROGRESS, AND ECONOMIC POLICY by Up Sira Nukulkit A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Economics The University of Utah December 2019 Copyright © Up Sira Nukulkit 2019 All Rights Reserved The University of Utah Graduate School STATEMENT OF DISSERTATION APPROVAL The dissertation of Up Sira Nukulkit has been approved by the following supervisory committee members: Codrina Rada , Chair 7/12/2019 Date Approved Cihan Bilginsoy , Member Date Approved Korkut Erturk , Member 7/12/2019 Date Approved Rudi von Arnim , Member 7/12/2019 Date Approved Jessie X. Fan , Member 7/12/2019 Date Approved and by Norman Waitzman the Department/College/School of and by David B. Kieda, Dean of The Graduate School. , Chair/Dean of Economics ABSTRACT This dissertation consists of three essays rooted in the growth and distribution literature with a focus on technological progress and economic policy. The main objective is to integrate technological progress into the growth and distribution framework and to explore its implications for economic dynamics. To this end, I explore seemingly different topics such as the historical development of theoretical perspectives on technological progress, the application of the Keynesian growth and distribution model to the economics of pensions, and the role of induced technological progress in sustainability of old-age public pension schemes. This dissertation draws on the existing Keynesian economic literature. Specific emphasis is placed on the Cambridge-Keynesian view concerning the long-run position of capitalism and the distribution of income between wages and profits. TABLES OF CONTENTS ABSTRACT....................................................................................................................... iii LIST OF FIGURES ........................................................................................................... vi PREFACE ......................................................................................................................... vii Chapters 1. GROWTH, DISTRIBUTION, AND TECHNOLOGICAL PROGRESS ...................... 1 1.1. Introduction: Growth and distribution ................................................................ 1 1.2. Accounting of macroeconomic variables............................................................ 4 1.3. The theories of value and the distribution of income ......................................... 6 1.3.1 Endogenous distribution .......................................................................... 8 1.3.2 Exogenous distribution ............................................................................ 9 1.4. Economic growth and the Cambridge equation ................................................ 11 1.4.1 Saving causality ..................................................................................... 12 1.4.2 Demand causality ................................................................................... 14 1.4.3 The Cambridge equation and the long -period rate of profit ................. 14 1.5. Technological progress ..................................................................................... 17 1.5.1 Technological frontier and the choice of technique of production ........ 19 1.5.2 Neutral balanced growth, elliptical technological frontier, and the rate of profit ........................................................................................................... 22 1.6. Conclusion: Long-period full employment and inequality ............................... 27 2. NEUTRAL TECHNICAL PROGRESS AND THE MEASURE OF VALUE: ALONG THE KALDOR-KENNEDY LINE .................................................................................. 29 2.1. Introduction ....................................................................................................... 29 2.1.1. Outline of the debate on neutral technical progress and the measure of value ................................................................................................................ 32 2.2. Technical progress and the measure of factors of production .......................... 34 2.3. Stylized facts and the existence of neutral technical progress .......................... 43 2.4. Neutral technical progress along the Kaldor-Kennedy line .............................. 54 2.5. Conclusion ........................................................................................................ 57 3. KEYNESIAN SOCIAL SEUCRITY AND INDUCED TECHNICAL PROGRESS .. 60 3.1 Introduction ........................................................................................................ 60 3.2 The US pension system and the old-age pension funding debate ...................... 63 3.3 Theoretical framework ....................................................................................... 67 3.3.1 A Keynesian model with Social Security .............................................. 68 3.3.2 Pension funding with technical progress ............................................... 72 3.3.2.1 Induced technical progress ........................................................... 73 3.3.2.2 Technical progress in a Keynesian model with Social Security .. 74 3.4 Keynesian pension tax funding in a Structuralist cycle model of growth ......... 76 3.4.1 A structuralist formalization of the Keynesian model with Social Security and technical progress ……………………………………………..79 3.5 Rising old-age dependency and the Social Security Trust Fund ....................... 81 3.6 Conclusions: Social Security tax, technical progress, and macro variables ...... 84 REFERENCES ................................................................................................................. 87 v LIST OF FIGURES Figures 1.1 Neutral Technical Progress ......................................................................................... 20 1.2 Viable Marx-Biased Technical Progress .................................................................... 22 1.3 Growth and Distribution Schedule of Neutral Technical Progress ............................ 24 1.4 Growth and Distribution Schedule of Marx-Biased Technical Progress .................... 26 2.1 Real Capital ................................................................................................................. 41 3.1 Comparison of Social Security to Private DB and DC ............................................... 65 3.2 401(k) Individual Asset Value .................................................................................... 67 PREFACE To my friends, my teachers, and my family. I am grateful for their support, patience and understanding. This dissertation consists of three chapters rooted in the growth and distribution literature with a focus on technological progress and economic policy. The main objective is to integrate technological progress into the growth and distribution framework and to explore its implications for economic dynamics. To this end, I explore seemingly different topics such as the historical development of theoretical perspectives on technological change, the application of the Keynesian growth and distribution model to the economics of pensions, and the role of induced technological progress in sustainability of old-age public pension schemes. This dissertation draws on the existing Keynesian economic literature. Specific emphasis is placed on the Cambridge-Keynesian view concerning the long-run position of capitalism and the distribution of income between wages and profits. The first chapter introduces the reader to the growth and distribution theory and to several perspectives on the conceptualization of technological progress. It starts with an overview of the growth and distribution model with the objective of discussing and comparing distinct features of the model from the neoclassical, classical, and Keynesian perspectives. The chapter draws on three major textbooks: Pasinetti (1974), Marglin (1987), and Foley and Michl (1999). I provide a concise description of the main building blocks of the model, main assumptions and closures. The chapter further discusses the effect of technological progress on the distribution of income following Joan Robinson's discussion of various types of capitalist systems (Robinson, 1960, 1962). The second chapter is a contribution to the history of economic thought literature. It examines the development of modern technological progress theories during the Cambridge Capital Theory Controversy, with a focus on the debates between neoclassicalKeynesian and the post-Keynesian economists in the postwar period. The chapter builds on the apparent inconsistencies regarding the measure of value in the formalizations of technological progress by various perspectives. The debates taking place between postKeynesian and neoclassical-Keynesian economists concerned the nature of technological progress and the nature of bias in innovation. The chapter reviews similarities and differences between each competing technological progress theory and implications for the determination of factor prices and factor income shares resulting from behavioral assumptions on the choice of innovation. The chapter highlights the Innovation Possibility Frontier theory developed by Kennedy (1964) using Joan Robinson's concept of Real Capital for the measure of value as a possible consistent theory of technological progress. The objective of the third chapter is to develop a Keynesian macroeconomic model of pension funding with different regimes of technological progress and derive their implications for sustainability of pay-as-you-go pension schemes. In an attempt to provide a context for the application of theory, the chapter starts with a brief empirical assessment of the US pension system and the role that Social Security has in old-age income funding. Next, I examine the distributive impact of pension funding by using the Kaleckian growth framework. With technological progress and under certain conditions, the pension tax induces economic growth, and hence it appears to increase the sustainability of a pay-as- viii you-go funding scheme. The chapter closes with a discussion of economic policy geared towards public pension funding in the presence of technological progress. My hope is that this dissertation provides useful intuitions on the effect of technological progress on growth, distribution, and economic policy. Overall, I emphasize the Cambridge-Keynesian point of view concerning the neutral character of technological progress that benefits both capital and labor in market-based economies. However, the dissertation does not discuss the bias technological progress that creates inequality between capital and labor, which is an important topic in current public discussions. I hope to address this issue of bias of technological progress in my future research. ix CHAPTER 1 GROWTH, DISTRIBUTION, AND TECHNOLOGICAL PROGRESS This chapter reviews the neoclassical, classical, and Keynesian theories of growth and distribution. The chapter serves as an overview of differences in economic perspectives used in my dissertation. It introduces the reader to the distinct features of each economic theory, with specific attention paid to the Cambridge-Keynesian interpretation of economic growth. I focus on the long-run Keynesian adjustment to full employment, treating labor and capital as given. The model's advantage is in its simplicity, which bypasses the capital and labor markets and avoids the problem of the measure of value. The chapter extends the analysis by discussing technological progress in the context of these growth and distribution frameworks. 1.1. Introduction: Growth and distribution The modern growth and distribution literature was developed during the postwar period during the debates between the Keynesian economists in Cambridge, England and those in Cambridge, Massachusetts. The literature since has been interpreted from many points of view. This chapter draws on three major textbooks: Pasinetti (1974), Marglin (1984), and Foley and Michl (1999). The textbooks were written at different times, and they provide different treatments of the growth and distribution model. They all review the 2 neoclassical, classical, and Keynesian economic theories, but they approach and emphasize the issues of growth and distribution from different angles. In this paper, I focus on the Cambridge-Keynesian interpretation, which highlights the Keynesian adjustment to the long-run full-employment position of capitalism, as the basis for my presentation of the problem of growth and distribution. Of the three textbooks, I base my core analysis on Pasinetti (1974), who represents the Cambridge growth and distribution tradition and focuses on the theories of value. The book provides a comprehensive assessment of the growth and distribution theory as a concluding remark in the aftermath of the Cambridge Capital Theory Controversy. In his textbook, Marglin (1984) emphasizes the distinct behavioral aspects of neoclassical, classical, and Keynesian perspectives. Marglin highlights the effects of different closures. Assumptions of individual agents, labor market bargaining, and firms' investment decisions from various economic perspectives provide different insights. Lastly, Foley and Michl (1999) improve the presentation of the growth and distribution modeling framework with a rigorous macroeconomic accounting. The book highlights the dynamic of macroeconomic variables under different scenarios of technical progress. The uniqueness of the Cambridge-Keynesian growth and distribution interpretation is its focus on the Keynesian adjustment to the full-employment position. The quantities of capital and labor are determined according to the condition of full-employment but this assumption remains controversial. However, I argue that it is explicit in the writings of the Cambridge-Keynesians. Nicholas Kaldor emphasized the condition of full employment in his solution to Harrod-Domar’s instability result (Kaldor, 1955). Joan Robinson wrote extensively about the golden age of capitalism in her two books on growth and distribution 3 (Robinson, 1960, 1962). The position was also assumed in the neoclassical-Keynesian Solow-Swan model (Solow, 1956; Swan, 1956). The early writings on growth and distribution from both Cambridge, England and Cambridge, Massachusetts economists focused on the long-run adjustment. Pasinetti (1974) summarized the position in the "Cambridge equation," which describes the relationship between capital accumulation and the rate of profit. We will discuss the Cambridge equation as it appears in the static model in section 1.4.3. The Cambridge-Keynesian approach to growth and distribution has evoked criticisms (Dutt, 2010; Garegnani, 1992; Harcourt, 1963; Samuelson, 1964), including that it does not provide convincing evidence on the mechanism through which the economy reaches its full-employment position. There are no theories of capital and labor markets. The model also lacks microfoundations of the real economy. Moreover, the CambridgeKeynesian approach fails to provide the connection between the short-period and the longperiod of the capitalist system and effective demand. These are valid criticisms. However, in my opinion, the Cambridge-Keynesians are more concerned with the complications presented by the measure of value as debated during the Cambridge Capital Theory controversy. They have to assume that the amount of labor and capital is given and that the system adjusts to the long-run full-employment position. The writings of Robinson, Kaldor, and Pasinetti on growth and distribution omit these narratives in order to avoid theoretical inconsistencies in the measure of capital and labor. Furthermore, the Cambridge-Keynesians were the first group of modern economists to analyze the effect of capital accumulation and technological progress on the economy. I discuss the development of technological progress theories in depth in my 4 second chapter, which also relates to my third chapter on induced technological progress as a response to changes in income distribution following a change in economic policy. In this chapter, however, I review technological progress theories and the choice of improvement. The last section follows the work of Joan Robinson (1956, 1962) in her analysis of the classification of capital and labor improvements, with the goal of explaining the effect of technological progress on the distribution of income. This approach is different from endogenous growth theories, which explain the source of growth rather than the effect of growth. Aside from this introduction, the next section describes the macroeconomic accounting relations that enter the baseline growth model, following Foley and Michl (1999). The third section focuses on the theories of value and the determination of the wage rate and the profit rate from different perspectives. The fourth section discusses the model’s closures. The fifth section analyzes technological progress and the choice between laborbias and capital-bias improvements. 1.2. Accounting of macroeconomic variables The relation between economic growth and the distribution of income is first looked at through macroeconomic accounting. I start with the output-income identity which states that income is distributed between wage and profit: 𝑌 = 𝑤𝐿 + 𝑟𝐾 (1.1) where 𝑌 is income or output, 𝑤 is the wage rate, 𝐿 is the amount of labor, 𝑟 is the profit rate, and 𝐾 is the amount of capital. 5 Following the classical economists and Sraffa (1956), modern economic growth and distribution theories posit that the wage rate and the profit rate have an inverse relation. This is also known as the real wage-profit rate schedule (Foley & Michl, 1998), or the factor price frontier (Marglin, 1984; Samuelson, 1962). The relation is shown in equation (1.2). 𝑌 𝐿 𝑟 = 𝐾 (1 − 𝑤 𝑌) (1.2) To determine the distribution of income the first task is to find the wage rate and the profit rate in each period. Equation (1.2) highlights the trade-off between the wage rate and the profit rate. Similarly, if we divide equation (1.1) by output (Y), we have the distribution of 𝑤𝐿 𝑟𝐾 income between the wage share ( 𝑌 ) and the profit share ( 𝑌 ): 1 = 𝑤𝐿 𝑌 + 𝑟𝐾 𝑌 . The wage share is the ratio of the wage bill (the wage rate multiplied by the amount of labor) over output. The profit share is a ratio of profits, or the profit rate multiplied by the amount of 𝑟𝐾 capital, and output ( 𝑌 ). The wage share and the profit share always sum up to 1. If the wage share increases, the profit share will decrease by the same percentage points. The distribution of income between workers and capitalists affects economic growth. The wage rate-profit rate schedule, as in Equation (1.2), has a direct relation to the rate of capital accumulation. Workers receive their wages and use the income for consumption and retirement. Capitalists receive returns from their past investments and make decisions about seeking new profits from new investments. We can construct a growth-consumption trade off in the same manner as the wage rate-profit rate trade off. The overall output will be divided between consumption (𝐶) and investment; 𝑌 = 𝐶 + 𝐼 = 𝑐𝐿 + 𝑔𝐾. Equation (1.3) shows the growth-consumption schedule, where 𝑔 is the rate of growth and 𝑐 is the rate of social consumption. 6 𝑌 𝐿 𝑔 = 𝐾 (1 − 𝑐 𝑌) (1.3) Neoclassical, classical, and Keynesian economics provide different views on the distribution of income and economic growth. The determination of the endogenous variables in equation (1.2) and (1.3) in each economic perspective comes from the assumptions made and the so-called closures, which, in simple terms, trace the overall causal structure of the model as discussed in sections 1.3 and 1.4 below. In the CambridgeKeynesian approach, capital ( 𝐾 ), and labor ( 𝐿 ) are predetermined. We have four endogenous variables (𝑟, 𝑤, 𝑔, 𝑐) we need to solve for. In this section, I describe two main building blocks of the model: the wage-profit rate schedule and the growth-consumption schedule. For a determinate system of equations, we need two more equations which are presented in sections 1.3 and 1.4. They show different ways to solve the growth and distribution model based on distinct economic perspectives. 1.3. The theories of value and the distribution of income The determination of the distribution of income is a matter of dispute among economic approaches. The central issue is the theory of value. We have two main approaches to the determination of the real wage and the profit rate: the marginal theory of value and the labor theory of value. First, the marginalist approach assumes that the real wage and the profit rate are endogenous to a production function of a resource-constrained economy. This view is inherent in neoclassical economics. Second, the labor theory of value treats the distribution of income as determined by prevailing norms and institutions, an assumption used in both classical and Keynesian economics. 7 The marginal theory of value, which spread in the period referred to as the marginal revolution (Jevon, 1871; Menger, 1871; Walras, 1874) and further developed into the capital theory (Bohm-Bawerk, 1890; Clark, 1899), relies on an assumption of diminishing marginal productivity. Labor and capital are factors of production. Each factor will be paid according to its productivity determined by the marginal principle of resource allocation and factor scarcity. In Wicksell's proof (1901), the Cobb-Douglas type of production function is used in accordance with Euler's theorem to show the distribution of income to each factor input that expends all output. The marginal theory of value posits that factor prices, the wage rate (𝑤) and the profit rate (𝑟), are endogenous and determined by the marginal productivity. In comparison, the labor theory of value of classical economics (Marx, 1867; Ricardo, 1817; Smith, 1776) has been revived by the neo-Ricardians and the CambridgeKeynesians (Pasinetti, 1974; Sraffa, 1960). Their analyses focus on the relations between the quantity of labor and the price of commodity output. The classical economists assert that the concept of factors of production is related to human labor. The value of a commodity is determined not just by the labor time used in its production, but also the amount of labor value of the machines or capital employed in the production. Capital in the classical approach is measured through past labor. The value of a commodity is a combination of the immediate labor from workers and the past labor embedded in capital goods, such as machines and plants. Through this concept of labor and labor value, the distribution of income is determined by the bargaining process or political economy over the distribution of income between labor and capital. 8 Modern growth and distribution models rely on the foundation of these two theories of value in determining the distribution of income. In the next section I discuss the endogenous and exogenous approach to the distribution of income. Differences between the two theories center on the determination of the real wage and the profit rate. 1.3.1 Endogenous distribution The wage rate (𝑤) and the profit rate (𝑟) in the marginal theory of value are determined according to productivity and the scarcity of factors of production. A simple illustration of this approach is to assume a neoclassical production function with constant elasticity of substitution, i.e., a Cobb-Douglas production function. Output (𝑌) is a function of labor (𝐿) and capital (𝐾): 𝑌 = 𝐹(𝐿, 𝐾) (1.4) Taking the first derivative for marginal productivity of labor and capital of a homogenous function of degree one and according to Euler's theorem we get: 𝑌= 𝜕𝑌 𝜕𝐿 𝐿+ 𝜕𝑌 𝜕𝐾 𝐾 (1.5) Neoclassical economics assumes perfect competition in the labor and capital markets and a firm's profit-maximization behavior. Retaining the concept of supply and demand in the labor and capital markets, the wage rate and the rate of profit are equal to their marginal productivities. Comparing equation (1.5) to equation (1.1), the wage rate is: 𝑤= 𝜕𝑌 𝜕𝐿 (1.6) and the profit rate is 𝜕𝑌 𝑟 = 𝜕𝐾 In the case of Cobb-Douglas production function (1.7) 9 𝑌 = 𝐿𝛼 𝐾 1−𝛼 (1.8) The wage share then becomes: 𝜓= 𝜕𝑌 𝐿 𝜕𝐿 𝑌 = 𝛼 (1.9) while the profit share is: 𝜕𝑌 𝐾 𝜋 = 𝜕𝐾 𝑌 = 1 − 𝛼 (1.10) Alpha (𝛼) comes from the intrinsic structure of the production function. The CobbDouglas production function has been popularized by the Solow-Swan neoclassical model as a tool to solve the Harrod-Domar adjustment problem. The neoclassical production function relies on the substitution assumption between capital and labor. Each factor of production will be used in the full amount available. The wage-profit schedule is determined according to the amount of labor and capital and the productiveness of both factors of production. 1.3.2 Exogenous distribution In contrast to the marginal productivity theory of value, classical and Keynesian economics rely first on an exogenous determination of the real wage based on the assumption that the determination of wages and profits depends on the political economy of class structure between workers and capitalists. There are two approaches to the determination of the real wage. The first approach is to assume that the wage rate is at a certain subsistence level (Marx, 1867; Ricardo, 1817). Following from equation (1.2), which is a trade-off relation, the profit rate is thus a residual of economic production. The second approach focuses on the share of the distribution of income (Foley & Michl, 1999). 10 This is known as the conventional wage share, which is the modern-macroeconomic interpretation of the classical wage theory. First, the classical wage theory posits that the wage rate is given. Workers receive an amount of income that enables them to survive and continue economic production. Although Ricardo and Marx have different treatments of subsistence wage, they both assume that the wage rate is determined outside of economic production. The wage rate is at a certain level, shown in equation (1.11). 𝑤= 𝑤 ̅ (1.11) The distribution of income of the wage share will be 𝐿 𝜓=𝑤 ̅𝑌 (1.12) From equation (1.2) of the trade-off relation between wage and profit, the profit rate with subsistence wage is 𝑌 𝐿 𝑟 = 𝐾 (1 − 𝑤 ̅ 𝑌) (1.13) The profit share will be 𝐾 𝐿 𝜋 = r 𝑌 = (1 − 𝑤 ̅ 𝑌) (1.14) In this approach, the classical economists assert that the wage rate is exogenously given. Second, the conventional wage share approach is a modern macroeconomic adaptation of the classical wage theory. Due to the observed fact that the wage rate changes over time, the wage rate increases due to an increase in labor productivity from technical change and labor market bargaining. Modern macroeconomics uses the conventional wage share instead of the wage rate as a tracking variable that is more stable than the classical wage rate. Equation (1.12)' shows the conventional wage share determined at a certain level, which is the ratio of the real wage to labor productivity in the parentheses. 11 ̅̅̅̅̅̅̅ 𝐿 𝜓 = (𝑤 𝑌) = 𝜓̅ (1.12)' The profit share is a residual of the wage share. 𝜋 = 1 − 𝜓̅ (1.14)' Exogenous determination of the distribution of income is a characteristic of classical and Keynesian economics. Both the subsistence wage and the conventional wage share highlight class conflict and political economy over the distribution of income between wages and profits. 1.4. Economic growth and the Cambridge equation Economic growth and the distribution of income are interrelated. Equation (1.2) and equation (1.3) look almost the same except that we replace the wage rate and the profit rate with the rate of growth and the rate of social consumption. The integration of the growth-consumption and the wage-profit tradeoff is called the growth and distribution schedule. The growth and distribution schedule is still bounded by the income accounting identity in equation (1.1). Neoclassical, classical, and Keynesian economics differ in their interpretation of sources of economic growth. Equation (1.2) of the wage rate-profit rate schedule has a direct effect on equation (1.3) of the growth-consumption schedule. Although both workers and capitalists are involved in economic production, it is the capitalists who make investment decisions. Workers receive their wage, and capitalists expect their returns from investment. Both classes will decide what to save or invest from their income for the next period. This section concludes the growth and distribution model with a focus on closures. I review two closures. First, the saving closure arises from the consumption-saving 12 decisions of individuals with rational preferences. The decision to save creates investment, which is the source of economic growth. Second, the demand closure reflects the Keynesian view that investment demand induces savings. In other words, capitalists’ profit-seeking behavior and workers' consumption demand generates economic growth. However, at the steady state, economic growth has to be within the limit of the Cambridge equation and the natural rate of growth (𝑔𝑛 ). In comparison to other interpretations of the growth and distribution dynamic presented in this chapter (Marglin, 1984; Michl & Foley, 1999), I emphasize the long-run solution of the Cambridge equation (Pasinetti, 1974) to the Harrod-Domar problem, which is the origin of the modern growth and distribution model. In my opinion, there should be more consideration of the importance of the Cambridge equation. 1.4.1 Saving causality The saving causality is emphasized by the supply-side economics, which includes neoclassical economics and most of classical economics. The source of growth in this view comes from individual consumption preferences that create available savings. Economic agents make rational decisions to abstain from consuming their immediate income because they expect additional benefits from returns on saving in the next period. A simple consumption-saving behavior is shown below. Assuming that an individual lives for two periods, the decision to save and consume in the first period (𝐶1 ) depends on the utility maximization behavior of the prospect of consumption in the next period (𝐶2 ). Samuelson (1958) sets up the consumption-loan model as an optimization of a convex utility function to individual budget constraints. Since savings is the residual of consumptions, 𝐶 = 1 − 𝑆, 13 Samuelson determines the consumption-saving rate through the relation between utility function and the lifetime budget constraint below. 𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑖𝑛𝑔 𝑈(𝐶1 , 𝐶2 ) = 𝑈(1 − 𝑆1 , 1 − 𝑆2 ) 𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑆1 + 𝑅𝑡 𝑆2 = 0 where 𝑅𝑡 is the prospective profit individuals expect to get in the second period. The optimum consumption-saving is the solution to the above optimization problem. Hence, according to the supply-side approach, the decision to save and consume originates in assumptions about microeconomic behavior. The consumption ratio is a function of utility optimization of the prospective profit, 𝑐 = 𝑓(𝑈𝐶 , 𝑟). Causality runs from available savings to economic growth. This is known as Say's law, which states that production of economic goods creates its own demand or that any available savings generates its own investment. The principle that supply creates its own demand is prominent in classical economics and has been inherited by neoclassical economists. The classical Ricardian system accepts Say's law, and neoclassical marginalism assumes that the economy is resource constrained. Hence, supply-side economics asserts that saving will create investment; 𝑆 → 𝐼. 𝑔 = 𝑠(𝑈𝐶 , 𝑟) (1.15) We can close the growth and distribution system with equation (1.15) as the fourth equation. The supply side closure is adopted in both neoclassical and classical models of economic growth. 14 1.4.2 Demand causality In contrast, the principle of effective demand reverses the causality to emphasize the role of an independent investment demand function. The principle of effective demand has existed since the time of classical economics. Malthus and Marx had written about the crisis of under consumption and over production. However, the view had never been accepted until the writings of Keynes and Kalecki. Investment demand has become the focus of Keynesian economics and a branch of classical economics. Joan Robinson (1962) and Nicholas Kaldor (1961) introduced the view that entrepreneurs decide to invest based on the prospective rate of profit. This view appears as well in the classical-Marxian approach, which highlights capitalistic competition (Shaikh, 2014). The decision to invest determines aggregate savings: 𝐼 → 𝑆 . Through profit seeking, the rate of growth and the rate of profit have a relationship that is the source of economic growth. Equation (1.16) shows the demand closure of economic growth that depends on the rate of profit. 𝑔 = 𝑖(𝑟) (1.16) We have a complete system of growth and distribution. To reiterate, our system has four endogenous variables: 𝑟, 𝑤, 𝑔, 𝑐 . The four equations described so far show how different economic perspectives approach the growth and distribution model of economic growth. 1.4.3 The Cambridge equation and the long-period rate of profit We have assumed throughout sections 1.2, 1.3, and 1.4 that the amount of capital and labor is given. Following the Cambridge-Keynesian tradition, I avoid discussing the 15 determination of labor and capital in the labor market and the capital market. With an assumption of Keynesian adjustment to the full-employment position, the amount of labor and capital is determined in the long-run. There have been many criticisms to this Cambridge-Keynesian position (Bortis, 1993; Harcourt, 1963; Samuelson, 1964). The approach does not provide enough narrative of how the full employment position is reached and lacks the microfoundations of the real economy. However, this perspective has an advantage with regard to its treatment of the measure of value. I follow Pasinetti here to close the static growth and distribution model in an interpretation concerning the long-run position of capitalism. This interpretation is summarized by the Cambridge equation, which was advanced by Pasinetti (1974) in the aftermath of the Cambridge Capital Theory Controversy. As stated before, modern growth and distribution theory can be traced back to the Harrod-Domar problem (Domar, 1946; Harrod, 1939), which propounded that there is no guarantee for the rate of growth of the economy (𝑔) to be equal to the natural rate of growth (𝑔𝑛 ) that ensures economic stability. So far, we have assumed that 𝑔 is endogenous. The Harrod-Domar knife-edge problem(s) has been defined in various ways and in relation to different definitions of economic growth. Specifically, the literature has concerned itself with the actual rate of growth, the warranted rate of growth, and the natural rate of growth, all of which are, in Harrod-Domar’s formulation, assumed exogenous. Hence, the occurrence of the steady-state becomes a fluke. In the Harrod-Domar model, the warranted rate of growth refers to the growth rate of economy’s capacity that is made possible by available savings. The actual growth rate (g) is, in turn, the growth rate that follows from aggregate demand. Finally, the natural rate of growth refers to the growth rate given by the 16 growth rate of effective labor force, which is the result of population growth and technological change. In the long-run, the actual rate of growth, the warranted rate of growth, and the natural rate of growth have to be equal in order to ensure stability of the economy. In what follows, I summarize Pasinetti's take on Harrod-Domar's dilemma which focuses on the long-period full employment and hence the natural rate of growth. Pasinetti’s focus on the long-run equilibrium restates the Harrod-Domar equilibrium in terms of the natural rate of growth, 𝑔𝑛 , and the warranted growth rate, which 𝐾 is the ratio of the saving rate (𝑠) over by the capital/output ratio ( 𝑌 ). 𝑔𝑛 = 𝑠 𝐾 ( ) 𝑌 (1.17) There is no guarantee that the saving rate and the capital/output ratio will be equal to the natural rate of growth that ensures full employment. One of the two variables has to adjust accordingly in order to ensure equality to the given natural rate of growth. Two solutions emerge. The first is to assume a production function with perfect substitution between capital and labor, as in subsection 1.3.1. Such a production function implies a smooth 𝐾 variation of the capital/output ratio ( 𝑌 ). This view of economic growth and economic dynamics has been captured by the Solow-Swan model (Solow, 1956; Swan, 1956). Given a certain amount of labor (𝐿∗ ) and capital (𝐾 ∗ ), there exists a capital/output ratio that uses all available labor and capital, leaving no unemployment and maintaining the economy at its full capacity. The second solution to the Harrod-Domar problem is to assume an adjustment of the saving rate. Kaldor-Pasinetti's formulation (Kaldor, 1957; Pasinetti, 1962) is shown below, where 𝑠𝑤 is the workers' saving rate and 𝑠𝑐 is the capitalists' saving rate. Equation (1.18) is an accounting relation of the saving rate and the growth rate similar to equation (1.2) and (1.3), which I borrow from Pasinetti (1974, p. 122). 17 𝑔𝑛 𝐾 𝑌 = 𝑠𝑤 𝑤𝐿 𝑌 + 𝑠𝐶 𝑟𝐾 𝑌 (1.18) under the condition that the capitalists' saving rate is more than the workers' saving rate. 𝐾 𝑠𝑤 < 𝑔𝑛 𝑌 < 𝑠𝑐 (1.19) Pasinetti (1962) provides a solution from equations (1.18) and (1.19) that reduces to the relation between the rate of growth (𝑔), the rate of profit (𝑟), and capitalists' saving rate (𝑠𝑐 ). 𝑟= 1 𝑠𝑐 𝑔𝑛 (1.20) Equation (1.20) is the "Cambridge equation," which can also be solved easily if we assume that the saving rate of workers in equation (1.18) is zero (Kaldor, 1956). The Cambridge equation, in a nutshell, represents the long-run growth and distribution equilibrium. The rate of profit in an expanding economy is determined through the natural rate of growth and the saving rate. The Harrod-Domar problem concerns the adjustment of macroeconomic variables such that the economy achieves a steady-state. The problem is still being debated, and many attempts have been proposed to reconcile short-period adjustment and the role of aggregate demand to the long-period position (Cesaratto, 2015; Dutt, 2011; Garegnani, 1992). An assessment of the Cambridge equation can be found also in Bortis (1993). In this chapter, I follow Pasinetti (1974) and his solution regarding the adjustment problem from a Keynesian perspective. 1.5. Technological progress Technological progress is considered the main source of growth across economic perspectives. In this section, I focus on the choice of technological progress between labor- 18 bias improvement and capital-bias and the effects of this choice for the distribution of income. This approach to the dynamic of income distribution through the lens of capital accumulation and technological progress is based on Joan Robinson's (1960, 1962) breakthrough analysis of various types of capitalist systems. This focus on bias in technological change is different from the current view of endogenous growth theories (Acemoglu, 2007; Tavani & Zamparelli, 2017). Endogenous growth theories explain the process of economic growth, whereas technological change and bias improvement theories aim to look at the effect of economic progress on the distribution of income. The type of technological improvement is the result of capitalists’ decisions. In the standard technical progress theories, the output to capital ratio is assumed to be constant, meaning that technological progress is, so-called, neutral. However, technological progress can also be of a bias type with a rising or a declining output/capital ratio depending on the choice of bias in improvement. Firms will decide to develop labor-bias or capital-bias improvements based on prevailing economic conditions. I describe below the constraint of technological frontier and the capitalists' behavior that determine the direction of technological progress. I will also follow Foley, Michl, and Tavani (2018) for an illustration of the effect of different biases of technological progress on the growth and distribution schedule of equations (1.2) and (1.3). Furthermore, in the second chapter of my dissertation, I discuss at length the historical development of modern technological progress theories. 19 1.5.1 Technological frontier and the choice of technique of production The modern economic interpretation of technological progress takes into account the constraints imposed by the innovation possibility frontier (Kennedy, 1964) and the maximizing behavior of economic agents. The frontier represents a trade-off between the choice of capital-bias improvement (𝜒) and labor-bias improvement (𝛾). The innovation possibility frontier shown below in equation (1.21) is concave: ∅ (𝜒, 𝛾) = 0 (1.21) The shape of the frontier is exogenous depending on the feasibility of the innovation. Given the frontier trade-off between labor-bias and capital-bias improvements, capitalists will choose the improvement that benefits them the most. We have three formalizations for capitalists' choice of technological improvement. The behavioral equations are set up as an optimization budget set that is constrained to equation (1.21) of the technological frontier. The first theory is the earliest attempt to explain the nature of economic improvement by looking at factor prices. This theory originates with Hicks (1932) and Salter (1960). Capitalists observe the price of capital (𝑝𝐾 ) and the price of labor (𝑝𝐿 ) and then decide to innovate based on which input is cheaper, as they attempt to minimize the overall cost of capital and labor. 𝑝𝑟𝑖𝑐𝑒 𝑐ℎ𝑜𝑜𝑠𝑖𝑛𝑔 = 𝜒𝑝𝐾 + 𝛾𝑝𝐿 (1.22) Equation (1.22) shows such a budget set based on prices of capital and labor. The choice of innovation between capital-bias improvement (𝜒) and labor-bias improvement (𝛾) can be solved using the Lagrangian optimization method from equation (1.21) to equation (1.22). Figure 1.1 provides an illustration of the optimization between a concave function and a linear budget constraint. This price-choosing theory has an advantage regarding the 20 Figure 1.1 Neutral Technical Progress hypothesis that the price of capital ( 𝑝𝐾 ) becomes cheaper, leading to capital-bias innovation, which will increase labor productivity and the wage rate. However, this theory of price-choosing behavior has a major weakness regarding the measure of capital. Capitalists need to be able to observe the price of capital and labor ex-post after input prices change. This view has largely been abandoned because of the unrealistic ex-post price assumption, as it remains unclear how to determine the price of capital. This weakness led to the development of the currently accepted assumption on distributive-shares explained in the next paragraph. The second theory is the standard theory of improvement-choosing behavior. The formulation comes from Kennedy (1964). The unique feature of this theory is its focus on the cost shares of capital and labor. The theory uses capital and labor factor "shares" instead of factor prices to resolve the inconsistencies in the measurement of capital. The theory 21 does not need to know the exact measure of capital and bypasses the measurement of factors of production to the share between capital and labor. 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑜𝑠𝑡 = 𝜒𝜋 + 𝛾𝜓 (1.23) Equation (1.23) shows the function for a reduction of cost. Capitalists choose bias improvement (𝜒, 𝜓) according to the prevailing capital share (𝜋) and labor share (𝜓). They optimize the reduction of cost share in equation (1.23) given the innovation possibility frontier in equation (1.21) in the same manner as the Lagrangian optimization in Figure 1.1. The theory is the standard approach to technical progress due to its ingenious solution based on factor shares. The third theory of choice of the technique of improvement focuses on the rate of profit, and it is based on the classical-Marxian view of competition (Dumenil & Levy, 1995; Foley, 1999; Shaikh, 2014). The rate of profit is central to the dynamic of the economic system, and it is the driving force of capitalism market-based economy. The capitalist will choose bias improvement that is viable for the competitive rate of profit. Taking the total derivative of equation (1.2) to the biases in improvement (𝜒, 𝛾) (Michl, 1999), we have 𝑟̇ = 𝑌 𝐾 𝑑𝜋 𝑌 𝑑𝑡 𝐾 ( ) = (𝜒𝜋 + 𝛾𝜓) (1.24) Equation (1.24) shows that the change in the rate of profit as a function of the capital/output ratio and technological change bias, given the innovation possibility frontier in equation (1.21). This perspective still retains the wage share and the profit share similar to equation (1.23). Graphically, it is illustrated in Figure 1.2. We have three setups for the behavioral function for the choice of improvement: 1) price choosing, 2) reduction in cost share, and 3) a competitive optimization of the profit 22 Figure 1.2 Viable Marx-Biased Technical Progress rate. The choice between capital-bias improvement and labor-bias improvement is constrained by the feasibility of the concave innovation possibility frontier in equation (1.21). In Joan Robinson's textbooks, the source of economic growth originates in capital accumulation. In comparison to modern endogenous growth theories, we determine the direction of changes in macroeconomics variables through the choice of capital-bias improvement and labor-bias improvement discussed above. We will analyze the implications of these choices on the distribution of income further in the next subsection. 1.5.2 Neutral balanced growth, elliptical technological frontier, and the rate of profit The accepted hypothesis on the effect of technological progress on the distribution of income is one of neutral technological progress. In the neoclassical growth and distribution model, the Cobb-Douglas production function ensures a neutral tendency of 23 technological progress due to its property of elasticity of substitution between capital and labor equal to one. This concept of elasticity of substitution between capital and labor was developed by Hicks (1932). If the elasticity of substitution is equal to one, an increase in capital from factor accumulation will raise the marginal productivity of both capital and labor in the same proportion, which will result in a neutral balanced growth that is a winwin for both capital and labor. The elasticity of substitution measures the proportionate change of substitution between the amount of capital and labor to the input's marginal productivities. 𝐿 𝐿 𝐾 𝐾 𝑑 / 𝜎 = 𝑑𝑀𝑅𝑆 𝐾𝐿 /𝑀𝑅𝑆𝐾𝐿 = 𝐾 𝐿 𝑀𝑃 𝑑 ln 𝐾 𝑀𝑃𝐿 −𝑑 ln (1.25) However, a unitary elasticity of substitution is an exceptional property of the CobbDouglas production function. In the neoclassical literature, the elasticity of substitution is likely to be less than one, as shown in empirical studies of CES (constant elasticity of substitution) production functions (Chirinko, 2008; Leon-Ledesma & Satchi, 2018). During the early development of neoclassical endogenous growth theory, Samuelson noted that capital accumulation would eventually yield to diminishing returns. Hence, Samuelson (1964) adopted the innovation possibility frontier discussed above in equation (1.21) and the unit-cost-share reduction in equation (1.23) to retain the neutral-balanced growth assumption and explain the capital-bias improvement. In the neoclassical literature, the bias in improvement is one of capital-using/labor-saving type at point A; see Figure 1.1. Neutral technical progress is also the dominant theory in the Keynesian growth and distribution model. It has been adopted partly as a result of a desire to maintain consistency with stylized facts (Kaldor, 1957; Robinson, 1956), which show constant income shares, a constant rate of profit, and capital/output ratio describing the long-period position of 24 capitalism. Neutral technical progress leads to an increased in wage rate leaving other variables constant. The growth and distribution schedule of equations (1.2) and (1.3) shifts out vertically on the wage rate axis; see Figure 1.3. The wage rate increases from 𝑤 to 𝑤 ′ , while the rate of profit stays the same. However, the current direction of market-based systems is toward inequality and a falling rate of profit in contrast to the previous hypothesis of a (neutral) win-win economic dynamic (Dumenil, Glick, & Rangel, 1987). The modern classical theorists have developed a theory of biased technological progress (Dumenil & Levy, 1995; Foley, 1999; Michl, 1999; Shaikh, 1987) in order to explain the contrasting empirical facts of a rising profit share and falling rate of profit. According to classical political economics, capitalists choose the type of technological progress according to a range of viable improvements for the competitive profit rate. The bias of technological progress that increases the profit share and decreases the profit rate is a result of the choice of improvement on an elliptical innovation possibility Figure 1.3 Growth and Distribution Schedule of Neutral Technical Progress 25 frontier. Figure 1.2 shows the viable improvement based on equation (1.24) above the red line, the elliptical innovation possibility frontier of equation (1.21), and the mean adopted ̅ Capitalists choose viable improvements above the red line that improvement at point 𝑋. make them competitive in the market place. However, the mean adopted improvement lies heavily on the negative capital bias improvement quadrant, given the elliptical share of the technological feasibility frontier. As a result, the capital/output ratio increases. The technique of production changes such that more capital is used to produce one additional unit of output. With this, Marx-biased technological progress and the assumption that workers negotiate for an increase in their wages, the growth and distribution schedule that combines equations (1.2) and (1.3), rotates clockwise; see Figure 1.4. The intersection of the profit rate axis shifts down from 𝑟 to 𝑟 ′ , and the intersection of the wage rate axis shifts up from 𝑤 to 𝑤 ′ . The wage-profit rate can be anywhere within the schedule. However, we can see that it is very likely that the rate of profit will fall due to the inward shift of the intersection of the rate of profit axis. 1 This deviation of the capital/output ratio in Marx-biased technological progress is in sharp contrast to the Cambridge-Keynesian long-period constant capital/output ratio. In this section, I have discussed technological progress theories proposed by different economic approaches. I have focused on the innovation possibility frontier and the three choice-of-improvement equations. Neutral balanced growth is the standard 1 Marx's falling rate of profit requires that the capital-output ratio increases in a higher 𝐾 ̂ proportion than the profit share: 𝑌 > 𝜋̂. The profit rate will fall even though there is a positive change in the profit share. 26 Figure 1.4 Growth and Distribution Schedule of Marx-Biased Technical Progress position of modern technological progress theories. However, the fear of disruptive technology has deep roots in economic analysis, e.g., the Ricardian view on machinery, Schumpeter's view of creative destruction, and many other economists' treatment of technological progress as an uncontrollable shock (Mokyr, Vickers, & Ziebarth, 2015). Economists use technological progress theories to explain this dynamic change of capitalism. The direction (or bias) of technological progress remains an ongoing debate. The pattern of technology that capitalists choose has an effect on the distribution of income. The focus of this section therefore has been on the bias in technological change and its effects on the economic system. However, there is no general agreement about the direction of technological progress, as explanations of mechanisms behind the choice of improvement remain largely untested. 27 1.6. Conclusion: Long-period full employment and inequality This chapter reviews the main tenets of the growth and distribution model emphasizing the Cambridge-Keynesian viewpoint. The unique character of the CambridgeKeynesian interpretation is on the long-run position of capitalism and its connection to classical political economy. The narrative follows three major textbooks: Pasinetti (1974), Marglin (1984), and Foley and Michl (1999). In section 1.2, I discuss the accounting building block of the model and, specifically, the wage-profit and the growth-consumption schedules. Section 1.3 presents the formalization of income distribution. In section 1.4, we discuss a fourth relation, which concerns the saving and demand closure of the model. The chapter highlights differences between economic approaches to the causal structure in the canonical growth and distribution model. We have a determinate static model of four equations and four unknowns. Section 1.5 turns to a review of technological progress theories and the dynamic of capital accumulation following Robinson (1960, 1962). The choice of bias in the direction of technological change affects the distribution of income and therefore the dynamics of the economic system. However, the growth and distribution model in the Cambridge-Keynesian viewpoint is still a work in progress. Samuelson (1965) acknowledged that the technical progress theory still cannot answer questions related to the nature of the rate of profit. Robinson (1962) warned about the ambiguous relation between the rate of profit and the rate of accumulation. Finally, Pasinetti urged us that "One must investigate first the relation, if there is any, between technology and the rate of profit" (1974, p.131). This recommendation remains especially relevant in the current atmosphere of rising inequality 28 as it relates directly to the question of the long-run position and stability of a market-based economy. It also speaks to the public discourse on the role of government policies and democratic process in economic adjustment. The present chapter on growth and distribution model reviews foundational ideas that are relevant for the remaining chapters in this dissertation. In the second chapter, I discuss technological progress and income distribution within the framework of the Cambridge Capital Theory Controversy. In my third chapter, I introduce a Social Security tax into the Keynesian model of growth under different regimes of technological progress. CHAPTER 2 NEUTRAL TECHNICAL PROGRESS AND THE MEASURE OF VALUE: ALONG THE KALDOR-KENNEDY LINE This chapter investigates "the effect of progress upon distribution" based on the analyses of Hicks (1932), Robinson (1937), Harrod (1937), Salter (1960), Kaldor (1957), Samuelson (1965), and Kennedy (1962). The chapter aims to address a neglected and controversial theoretical argument about the role of neutral technical progress for the measure of value in the context of the Cambridge Capital Theory Controversy. I focus on Kennedy's writings and his solutions to the complications between the measure of value and technical progress. Important intuitions behind the measure of value are crucial to the formulation of neutral technical progress theories in both the post-Keynesian and the neoclassical-Keynesian endogenous growth models. The chapter concludes with mathematical illustrations of neutral technical progress theories. 2.1. Introduction The foundation of value theories in the growth and distribution literature is not rigorous, with inconsistencies in the mathematical formulations of growth models regarding the measure of factors of production. The most renowned modern incident was the Cambridge Capital Theory Controversy (Harcourt, 1972; Harcourt & Cohen, 2003). 30 The controversy came to the attention of the public when Joan Robinson (1953-54) initiated a conversation questioning the validity of the neoclassical production function. The public debate was summed up by Paul Samuelson (1966), who acknowledged the reswitching and capital-reversing theory. The controversy covered a large body of literature, including the value theory, price theory, capital theory, growth theory, and issues related to methodology. Harcourt "found it impossible to disentangle them and… not being able to do so is no bad thing anyway" (2015, p. 243). More importantly, the Cambridge Capital Theory Controversy raised questions about the foundations of the growth and distribution literature. Specifically, the controversy has direct implications for the analysis of inequality between capital and labor income. Income inequality and capital accumulation is the topic of Thomas Piketty’s Capital in the Twenty-First Century. 2 Prior to Piketty or the Cambridge Capital Theory Controversy, classical and Keynesian economies were concerned with the effect of technical progress on the distribution of income, in terms of dynamic nature of the wage share and the profit share, which depends on the measure of value. The debate about technical progress and the measure of value that preceded and then continued to the period of the formal Cambridge Capital Theory Controversy has been, however, overlooked as a peripheral theoretical issue. Hicks, Robinson, and Harrod argued about the theoretical formulation of technical progress in the early 1930s. The issue then resurfaced again almost 2 decades later in the writings of Salter, Kaldor, Kennedy, and Samuelson. The Keynesians focused on the effect of technical progress on income 2 See Martin (2016). See also Harcourt's assessment (2015b) of Piketty's Capital in the Twenty-First Century. 31 distribution because it was not clear how to measure and determine the value of factors of production. For example, it is impossible to know the exact value of new machines introduced by economic progress. More importantly, we do not know how to distribute the added value from technological progress to the factors of production that created it. Above all, neutral technical progress and the measure of value provide a critical connection between post-Keynesian economics and neoclassical-Keynesian economics. Robinson's objections to the neoclassical production function attracted MIT's attention due to her use of a linear formal model. "Samuelson and Solow believed that they understood because it related directly to their recent work" (Backhouse, 2014, p. 256). They were focusing on linear-programming models, which exhibit a "balanced growth" path.3 Solow recalled that when he was in England enduring Joan Robinson's repetitive metaphysic, he finally forced her to admit that "a constant capital-output ratio will do" (2007, p. 4). A constant capital/output ratio implied a long-period neutral position, which was their mutual hypothesis. The neoclassical concept of balanced growth was analogous to Kaldor's stylized facts and Robinson's golden age. 4 After the publication of Piero Sraffa's Production of Commodities by Means of Commodities, the issue of linearity became even more relevant. Samuelson considered the problem of the measure of value as his lifelong quest. Toward the end of his life, he engaged in discussions with the neo-Ricardians regarding the implicit assumption of constant returns in Sraffa's system (Garegnani, 2007; Samuelson, 2000a; 2000b). 3 Dorfman, Samuelson and Solow, 1958, Ch. 12. See also Harcourt (2015a, p.247) cited from Gram (2010, p.362). The neoclassical production function is discussed extensively in Felipe and McCombie (2013). 4 See Robinson (1956, p. 99). 32 In contrast to Piketty's inequality conclusion, the two Cambridges focused on the neutrality of the wage and profit shares. This chapter emphasizes the relation between the measure of value and the existence of neutral technical progress in the framework of the Cambridge Capital Theory Controversy. The goal here is to address the foundation of endogenous growth models of both the post-Keynesians and the neoclassical-Keynesians.5 2.1.1. Outline of the debate on neutral technical progress and the measure of value Sir John Hicks introduced the question of "the effect of progress upon distribution" to modern economics (Hicks, 1932, p. 112). Hicks's writings were the origin of the controversial neoclassical aspect of the "elasticity of substitution.'' He used the neoclassical marginal productivity theory, which implies price-based substitution to determine the effect of technical progress on the value of capital and labor. Neutral progress that increases the income of capital and labor in the same proportion requires an elasticity of substitution equal to one. Joan Robinson (1937) followed Hicks’s framework in her analysis of of technical progress in Essays on the Theory of Employment. However, her approach received a negative response from Sir Roy Harrod, who criticized Robinson's handling of the elasticity of substitution, as it implied a controversy regarding the measurement of capital and the interest rate. This period was the beginning of modern economic analysis of the growth and distribution theory. At the time, the theoretical differences between postKeynesian and neoclassical-Keynesian economics were still not clearly understood. 5 See also Tavani and Zamparelli (2017) for a survey of endogenous technical progress. 33 Decades later, the effect of technical progress reemerged as a subject of interest. Nicholas Kaldor argued that the stylized facts of constancies in the distributive share, the profit rate, and the capital/output ratio are inexplicable in the neoclassical production function. With capital deepening, the neoclassical assumption of diminishing returns implies that the profit rate will fall. Neoclassical economics found a solution to the stylized facts only when Paul Samuelson (1965) adapted Charles Kennedy's "Induced Bias in Innovation and the Theory of Distribution" (1964) to neoclassical theories. However, Kennedy disapproved of Samuelson's approach. Kennedy was well aware of the complications in the measurement of value and the production function. He had "hoped that the innovation-possibility frontier might be able, so to speak, to swallow up the traditional production function and replace it altogether" (Kennedy, 1966, p. 442). Prior to Kennedy and Samuelson's argument about the production function approach, W. E. G. Salter (1960) had developed a best-practice productivity movements model through price-based substitution that explained the dominance of labor-saving invention via the cheapening of the price of capital goods. In disagreement, Kennedy countered with a theory that avoided price substitution, instead describing neutral technical progress through bias in innovation from the relative share of capital and labor. Kennedy was indebted to Hicks for the development of his theory. 6 At first, Kennedy's primary concern (Kennedy, 1961; 1962a; 1962b) was the measure of value to distinguish the effect of innovations in the factors of production. He questioned whether new investment is needed under technical progress: The value of existing capital has to rise, or it requires an accumulation of new machines. His question is fundamental to the argument that Robinson 6 See Thirlwall (1999). 34 and Harrod had earlier. Kennedy seemed to suggest the possibility of a consistent measure of value. He drew a curious conclusion that Hicks's neoclassical definition of neutral technical progress and Harrod's definition of neutral technical progress were equivalent. It should be noted that Kennedy's conclusion about the Hicks and Harrod neutral equivalency would likely come as a surprise to modern growth theorists. Notice here that Kennedy did not need to rely on the neoclassical production function or the restrictive assumption of constant elasticity of substitution. We now have two concerns about technical progress: the measure of value and the neutrality of wage and profit in growth models. The two concerns are usually analyzed separately. This chapter will analyze both concerns, adopting a method of analysis that belongs to the history of economic thought field. The goal here is to clarify potential complications in the measurement of value concerning technical progress that engaged our predecessors. Questions regarding the measure of value and the existence of neutral technical progress should receive more consideration. Next, I describe the mathematical formulations of neutral technical progress and provide intuitions behind the measure of value suggested by Kennedy. The second section goes over the concerns regarding the measure of value and technical progress. The third section analyzes neutral technical progress in growth models. The fourth section provides intuitions behind the mathematical assumptions of the Kaldor and Kennedy theories. 2.2. Technical progress and the measure of factors of production To have labour measure. It implies that the average of money rewards paid to workers never rises… Is it not a little sadistic to seek to deprive men of this increment of pleasure, for the sake of —what? —a mere academic preference. (Harrod, 1948, p. 29) 35 The measure of value of factors of production is crucial to determining the change in the distributive share due to technical progress. Harrod was well aware of this complication, and he refused to use labor as the measure of value. This section sets out the difficulties faced by our Keynesian predecessors concerning these two issues of technical progress and the measure of value. It describes, in brief, what these difficulties are and how to resolve them. Hicks was the first among his contemporaries to raise the question of the effect of progress upon distribution. He coined the term "elasticity of substitution" in his book The Theory of Wages (Hicks, 1932, 1963) as a criterion for assessing income distribution. Hicks was very clear in stating that his analysis was based on the neoclassical marginal productivity theory of distribution and value. If the elasticity is equal to one, "the increase in one factor will raise the marginal product of all other factors taken together in the same proportion as the total product is raised" (Hicks, 1932, p. 117). The elasticity of substitution determines the change in relative price as affected by the increase in the factor of production. If the elasticity of substitution is biased toward labor, an increase in the supply of capital tends to move the relative share toward labor. However, Hicks's criterion was inadequate because the marginal productivity theory is ambiguous about the notion of capital. The question of how to measure the value of capital remained unresolved. Furthermore, a more serious difficulty in Hicks' theory concerned the characteristics of invention. Technical progress is a term applied to the whole system, whereas invention relates specifically to a particular sector. An invention implies two separate effects: a saving of the volume of the factor of production and an increase in the value of its marginal product. First, an invention increases the efficiency of production by 36 saving the amount of input factor used in production. The invention can be labor-saving, capital-saving, or neutral if it affects labor and capital in the same proportion. Second, in addition to the saving efficiency aspect, Hicks also defined bias-saving innovation as an unequal increase in each factor's marginal productivity. A contradiction surfaced because in the former, saving invention refers to an existing volume of factors of production, whereas in the latter an increase in the marginal productivity assumes a rise in the value of factors of production. There is no problem identifying the amount of labor from the marginal product of labor. However, it is not clear how to determine the value of capital. For example, the amount of capital stock might stay the same, but the price of it has to increase with the marginal product from an invention. If the volume of capital stock increases simultaneously with the invention, we need Hicks's criterion of elasticity of substitution to determine its effect on distribution, assuming that we know the exact measure of capital. On the post-Keynesian side, Robinson and Harrod argued about the same theoretical problem in the measure of value. Robinson (1937) wrote about technical progress in her chapter titled a "Long Period Theory of Employment" published in the Essays in the Theory of Employment. Her book was an attempt to expand Keynes's ideas to various branches of economics. However, Harrod reviewed her chapter on technical progress with skepticism. Robinson used terminologies and theories laid down earlier by Hicks to determine the effect of progress on growth and distribution theory in the context of long-run equilibrium. The tangled relationship between the elasticity of substitution and invention described earlier made her analysis incoherent. Robinson retracted many of her propositions in her second edition (Robinson, 1947) as a result of her exchange with Harrod. 37 The definition of neutral invention was the focus of the exchange between Robinson and Harrod. With Hicks's definition, a neutral invention was an increase in the marginal product of capital and labor in the same proportion. Robinson applied Hicks's neoclassical foundation to analyze the long-period equilibrium and stated, "thus if a neutral invention occurs in conjunction with an elasticity of substitution equal to unity, the relative share of labour is unchanged" (Robinson, 1937, p. 133). A unity(one) elasticity of substitution implies that the share of labor relative to the share of capital is unchanged when there is a change in the supply of labor or capital. With a neutral invention that increases both the efficiency of capital and labor in the same proportion, the distributive share will be constant in the long run. Once again, Robinson's experiment with marginal productivity theory implied that we can find a measure of value of capital. Harrod (1937) criticized Robinson, and suggested instead an alternative definition to characterize inventions that is more general. Harrod proposed to "divide inventions into those which at a given interest rate, and an infinitely elastic supply of capital at that rate, increase, leave unchanged or diminish the length of the productive process" (Harrod, 1937, p. 329). Invention is characterized according to the length of the productive process. Harrod made two assumptions. The first concerned the interest rate and an infinitely elastic supply of capital. He claimed that an infinitely elastic supply of capital is in agreement with Keynes's optimism about the supply of capital. A horizontal supply will guarantee the existence of a constant interest rate. Second, Harrod asserted that the length of the productive process "is the most fundamental concept in defining the quantum of capital" (Harrod, 1961, p. 300). He chose to leave the interest rate and the measure of capital untouched. In effect, he did not have to consider the change in relative price that is 38 associated with the elasticity of substitution. A neutral invention by Harrod's definition was summarized as an invention that "at a constant rate of interest, does not disturb the value of the capital coefficient" (the capital/output ratio) (Harrod, 1948, p. 23). Joan Robinson responded in defense of her position with "Classification of Inventions" (Robinson, 1938). She accepted Harrod's criticism of the measurement of capital, but she insisted on using Hicks's conceptual framework. She illustrated graphically that an invention classified by Harrod as neutral is identical to an increase in the supply of labor. Neutral technical progress, therefore, is an overall increase in the efficiency of labor. In response to Harrod's criticism, Robinson argued that her illustration did not contradict her former analysis by using Hicks's classification. Consider, for instance, the case in which an invention raises the average productivity curve of capital iso-elastically (so that the invention is neutral in Mr. Harrod's sense). In this case (with a constant rate of interest) the relative share of capital in the total product is unchanged by the invention: it follows from my former analysis that if, in this case, the elasticity of substitution with the new technique is equal to unity, then the invention must be neutral in Mr. Hicks's sense, while if the elasticity of substitution is less or greater than unity, the invention must be capitalsaving or labour-saving, to a corresponding extent, in Mr. Hicks's sense. (Robinson, 1938, p. 141) Hicks neutral and Harrod neutral technical change theories did have some congruities. In effect, Robinson jeopardized the argument even more because she asserted that both Harrod's method and Hicks's method were compatible as a classification of inventions. This early debate among Hicks, Robinson, and Harrod has the same implications for the measure of value as the Cambridge Capital Theory Controversy. These scholars were arguing over the measure of value within a growth and distribution framework. Harrod noticed theoretical inconsistencies in the neoclassical foundation of the theory of distribution and value. Robinson, however, introduced a creative procedure different from 39 those of her contemporaries to classify inventions. After Robinson's Classification of Inventions, interest in the theoretical formulation of technical progress concerning the measure of value died down, leaving many questions unanswered. Years later, Joan Robinson raised the problematic issue of the measure of value again in her famous paper "The Production Function and the Theory of Capital" (1953-54) and her book The Accumulation of Capital (1956). She questioned the concept of a unit measure of capital and introduced "real capital," which marked the starting point of the formal Cambridge Capital Theory Controversy. Robinson's real capital, "reckoned in terms of labour time" (Robinson, 1956, p. 123), shows that the change in the distribution of income creates "perverse" relationships among the techniques of production. Robinson's measure of real capital was one of the appealing aspects of her argument in the Cambridge Capital Theory Controversy. However, in contrast to the earlier dispute, Robinson's focus was not on technical progress. She was skeptical about the neutral characteristic of invention in relation to capital accumulation. The prospect of neutrality in the measure of real capital "depends also upon how much accumulation took place while the technical change was being made. As we have seen, for the factor ratio to remain unchanged, when the inventions have been neutral, capital must have increased in the same proportion as output" (Robinson, 1953-54, p. 102). Robinson subsequently chose to focus on other problems more important than the neutrality aspect of progress. It was Charles Kennedy who attempted to reconcile this issue of technical progress and the measurement of new accumulated capital stock. In "Technical Progress and Investment" (Kennedy, 1961), he asked whether a new investment is needed for technical progress. The question, he noted, depends on the standard of measure of capital. "If a labour 40 standard of value is chosen, no new saving is required: if, on the other hand, a good standard is chosen, as Harrod himself prefers, an increase in the capital stock is necessary" (Kennedy, 1961, pp. 232-233). Kennedy perceived a possible solution to the problem of capital accumulation in the labor standard of measure. If the labor standard is chosen, there is no need for a change in the volume of capital. Kennedy illustrated this by using Joan Robinson's measure of real capital and her diagram (Robinson, 1953-54, 1956): see Figure 2.1. The horizontal axis represents real capital in terms of labor, and the vertical axis measures the quantity of output. A shift due to an invention will raise the overall output: line NQ shifts to NQ'. Output per worker increases from OP to OP'. The wage follows through from W to W'. Furthermore, a higher wage increases the value of capital when multiplied by real capital. The volume of capital (OR, real capital) can stay the same, but the aggregate value of capital will rise because of the growth of wage from invention. In effect, we have a rise in the value of capital with a rise in wage that leaves the interest rate constant, which is the definition of neutral technical progress.7 This question about the new accumulation of capital stock for neutral technical progress was crucial to the measure of capital. Prior to Kennedy's formulation, Kaldor had expressed his skepticism about separating the movement along the production function from the shift of the production function curve. Movement along the production function referred to an increase in capital stock, whereas the shift of the curve was an effect of technical progress. He noted that the distinction was "artificial and arbitrary" (Kaldor, 7 However, Kennedy also pointed to the complications of a multisector scheme and the obsolescence/depreciation of capital. Neutral technical progress in the system as a whole would complicate the matter and require some net investment (accumulation). 41 Figure 2.1 Real Capital 1957, p. 596). For this reason, Kaldor avoided the use of the unit measure of capital. In contrast, Kennedy questioned Kaldor's method and suggested that the measure of real capital can cope with both the movement and the shift effects. In his second paper, "The Character of Improvements and of Technical Progress" (Kennedy, 1962), Kennedy expanded his theory to a multisector model to address the problem of accumulation. Kennedy suggested comparing the new accumulated machine to the old machine in labor cost (wage-unit). "For example, if the old machine is taken as standard, and the new machine costs x times as much as the old machine in terms of wageunits, then the quantity of capital embodied in the new machine can be said to be x standard "machines""(Kennedy, 1962a, p. 908). By specifically situating invention in the investment sectors, an improvement from invention will lower the labor cost of a machine, which will lead to an accumulation of more machines per worker. If the improvement is neutral, real capital (labor cost multiplied by the number of machines) will be unchanged. The aggregate real capital in terms of labor embodied stays the same as a reduction in the labor cost in capital production is offset by a new accumulation in the number of machines. Kennedy 42 used this complex counting procedure to clarify the ambiguity of capital accumulation under technical progress. Output increases through invention. The value of capital increases through a rise in the wage. The rate of growth of the value of capital and wage will be the same. With unchanged real capital, the capital/output ratio stays constant. Kennedy summarized his accounting among the number of machines, labor(wage-unit) cost, and real capital in the following passage: The relationship between these three measures of capital is straightforward. If we multiply the number of machines by the cost of a machine in terms of wage-units, we obtain Mrs. Robinson's real capital. If we multiply real capital by the real wage, we obtain the value of capital in terms of the product. (Kennedy, 1962a, p. 903) Neutral technical progress leaves real capital per worker unchanged, but the value of capital increases with the wage. Capital in terms of machines in the investment sector accumulates, but the aggregate real capital remains unchanged. Kennedy later used this mechanism to address Samuelson's objection to his accumulation scheme. Kennedy's labor measure of real capital attracted Harrod's attention. Harrod had analyzed this issue before in his dialogue with Robinson, as discussed earlier. Harrod (1961) wrote an article in response to Kennedy's and reiterated his definition of neutral technical progress, stressing his view on the measurement of capital. In a rejoinder, Kennedy (1962b) pointed out that Harrod in fact had shown that the Harrod's and Hicks' definitions of neutral technical progress are equivalent. According to Kennedy’s analysis, neutral technical progress implies that real capital per worker will remain unchanged. With a constant interest rate, Harrod neutral technical progress leaves the capital/output ratio unchanged. An increase in the wage rate leads to a rise in the value of aggregate capital. Kennedy asserted that this narrative of Harrod neutral technical progress can be translated 43 into a rise in the marginal product of both capital and labor in the same proportion, which is Hicks's neoclassical definition of neutral technical progress. The controversy over the two competing definitions was created because of the "lack of care in the measurement of capital" (Kennedy, 1962b, p. 250). Kennedy had provided an alternative measure for capital in Robinson's concept of real capital. However, Kennedy warned that "because of the very restrictive assumptions made, too great claims should not be made" (Kennedy, 1962a, p.909). The analysis in this section has set out the difficulties in measuring value and technical progress. The problem at the center of the debate was to find a consistent measure of value to explain the neutrality in the distribution of income. This overlooked theoretical debate merits further consideration. 2.3. Stylized facts and the existence of neutral technical progress The third part of this chapter describes the intuitions behind the modifications of the definition of neutral technical progress in growth and distribution models. The focus of this section concerns the existence of the neutral technical progress conditions. Our Keynesian predecessors were arguing about the mechanism that explained this neutrality. We have two theories describing the existence of neutral technical progress. The first theory was from Nicholas Kaldor, who introduced the technical progress function that fits his stylized facts. For the second theory, Charles Kennedy provided a different treatment of neutral technical progress by using the biased character of invention. Neoclassical economics failed to replicate the neutral results when the elasticity of substitution was less than one until Samuelson adopted Kennedy's method. However, Samuelson's use of the 44 production function started a dispute with Kennedy because of the complications in the measurement of value described earlier. Toward the end of this section, the chapter discusses Salter and Kaldor's vintage method, which focuses on net investment due to the complication on the measure of capital. This section aims to provide a clearer picture of the neutral technical progress theoretical puzzle. It is crucial to define our question first as some assertions are not consistent with the current literature (e.g., on the equivalence of Hicks and Harrod neutral technical progress). The last section started with a quote by Harrod in which he refused to use labor as the measure of value. Perhaps Harrod forgot about the more important aspect of technical progress: that it explains a rise in labor productivity and the wage. If technical progress is neutral, the economy moves to a higher stage with constancies in the distributive share, the rate of profit, and the output/capital ratio. The wage is predetermined to rise along with economic growth. Neutral technical progress is a win-win for both capital and labor. Laborsaving inventions are acknowledged as dominant forces in the economy. However, the empirical outcomes of this mechanism were implicit in the analyses of Hicks, Harrod, and Robinson. It was Kaldor's narrative of stylized facts that emphasized these properties and attracted a wider audience. In contrast to his Keynesian contemporaries, the previously implicit properties of technical progress became explicit in Kaldor's writings. He suggested that economists should build a model that conformed to economic stylized facts of constancies in the distributive share, the capital/output ratio, and the rate of profit. Kaldor proposed the technical progress function that fits the narrative and explains the interdependencies among economic variables. As a result, Kaldor provided the first endogenous growth model of 45 neutral technical progress that conforms to the stylized facts and shows the irrelevancy of the neoclassical production function. Kaldor (1957, 1961) stressed that the neoclassical production function was incompatible with the stylized facts. The production function "is assumed to be a unique relationship between capital and output, which conforms to the general hypothesis of diminishing productivity, but this relationship is constantly shifting with the passage of time" (Kaldor, 1961, pp. 203-204). Kaldor asserted that technical progress is treated as a simple exogenous shift of the production function. The existing capital stock represents the optimal state on the production curve, but it has to separate the effect of technical progress from new accumulation. As Kaldor pointed out, it is difficult to distinguish between a shift in the production function, i.e., technical progress and a move along the production function. Marginal productivity theory cannot guarantee that factors will be paid since the shift in the production function and movement along the production function blur the concept of the factor of production. Kaldor concluded that "any sharp or clear-cut distinction between the movement along a 'production function' with a given state of knowledge, and a shift in the 'production function' caused by a change in the state of knowledge is arbitrary and artificial" (Kaldor, 1957, p. 959). Kaldor proposed instead the "'technical progress function' which postulates a relationship between the rate of increase of capital and the rate of increase in output and which embodied the effect of constantly improving knowledge and know-how, as well as the effect of increasing capital per man, without any attempt to isolate the one from the other" (Kaldor, 1961, p. 207). In effect, Kaldor had integrated both a shift in the production function and a movement along the production function into one postulate of his technical 46 progress function. The capital/output ratio is constant because of the equal rate of growth for both capital and output. With full employment, technical progress will be neutral, with constancy in the distributive share. Kaldor's technical progress function conforms to his previous observation on the stylized facts. However, according to Kennedy, Kaldor's model was a theoretical description of the stylized facts, not an explanation. The technical progress function did not set out an adequate mechanism to explain why the rate of growth of capital should equal the rate of growth of output. 8 Instead of using the nature of invention as did his contemporaries, Kaldor relied on assumptions of entrepreneurial investment behavior. Entrepreneurs will invest according to a prospective rate of profit that has adjusted to maintain a constant output/capital ratio. Kaldor provided a lengthy comment on the nature of entrepreneurs' expectations. In the case that the rate of accumulation is less than the rate of growth of output, the output/capital ratio is higher than the equilibrium rate. As a result, entrepreneurs will see the prospect of higher profits. They will increase the accumulation rate to adjust to equilibrium. Invention will appear to be labor-saving or capital-saving according to the adjustment of the rate of accumulation to the curve of the technical progress function. The capital/output ratio will adjust to the same rate. However, the adjustment mechanism of Kaldor's technical progress function had weaknesses. Kaldor relied on the behavior of the representative firm in the investment function instead of the nature of invention. Kennedy commented that in Kaldor's formulation, the output/capital ratio was assumed constant a 8 Harcourt (1963, p.24, 1982, p.72) commented that "it is unrealistic to assume that businessmen desire to maintain a constant relationship between capital invested and output." This argument came from James Meade and Hugh Hudson, which Kaldor addressed in the Corfu Capital Theory Conference (1961, p.212). See also Harcourt (2006, p.114) for further discussion. 47 priori. The deficiency of Kaldor's technical progress function was that "Mr. Kaldor had already assumed what he was trying to prove" (Kennedy, 1962a, p. 910). The existence of neutral technical progress was the more important question. Hicks had previously commented on the dominance of labor-saving inventions in the real economy. He suggested that labor-saving inventions are a predictable outcome because the cost of labor is high compared to the cost of capital. Capitalists will choose to develop an invention that saves the cost of labor. Hicks's theory of bias in innovation relied on the assumption that we know the factor price substitution between labor and capital, which we discussed in the last section. Salter (1960, 1966) put forward his argument on technical progress based on Hicks's framework of the elasticity of substitution, but he argued that entrepreneurs are interested in reducing total cost, and so there should not be an induced bias toward labor-saving inventions. Neutral technical progress is seemingly a result of price substitution from cheaper capital.9 Salter assumed an ex-ante neoclassical production function in his theory of investment decision-making. In each successive period, new technical knowledge changes the shape of the production function. "Parallel with the improving technical knowledge are changing relative factor prices. Both combine to determine the nature of the flow of new techniques coming into use—best-practice techniques" (Salter, 1966, p. 23). The two components—new technical knowledge and factor prices— determine the character of technical progress. If labor-saving invention is not already inherent in the new technical knowledge, there is no reason invention will be labor-saving. Hence, in contrast to Hicks's theory of induced invention, Salter asserted that 9 See also Kennedy and Thirlwall (1972, p.21) and Harcourt (1962, p. 390). 48 it could only be the cheaper price of capital that substitutes for labor, thus resulting in laborsaving bias. Kennedy noticed the defects in Salter's argument concerning price substitution. Kennedy's theory was an accumulation of his previous inquiries. He was hoping to retain some of Hicks's intuitions and provide a concise theoretical foundation for neutral technical progress that did not have to use price substitution and the production function as in Salter's theory. Kennedy made use of his analyses of the value of capital and the equivalency of Hicks and Harrod neutral technical change to build a model of biases in innovation. He asserted that "changes in relative factor price are not essential for a theory of induced bias in innovation" (Kennedy, 1964, p. 542). In Kennedy's formulation, the constancy of the distributive share from neutral technical progress is the result of an adjustment of unit cost reduction constraint on the condition of innovation. Kennedy considered the share, instead of factor price, in the cost of production as a whole. Bias in innovation affects then the share of labor cost and capital cost: 𝜆𝑝 + 𝛾𝑞 = 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑢𝑛𝑖𝑡 𝑐𝑜𝑠𝑡, where 𝜆 is labor cost share, 𝛾 is capital cost share, and 𝑝 and 𝑞 are labor and capital saving improvement, respectively. The reduction in unit cost depends on the interaction of labor (𝑝) and capital (𝑞) saving improvement with their share in the cost of production. Furthermore, the reduction in the unit cost constraint adjusts according to the feasibility of invention. The "innovation possibility frontier" between labor-saving innovation and capital-saving innovation is concave, ∅(𝑝, 𝑞) = 0. "If the labour costs are high relative to capital costs (𝜆 > 𝛾) he will search, ceteris paribus, for a labour-saving innovation. If capital costs are high relative to labour costs he will search for a capital-saving innovation" (Kennedy, 1964, p. 543). The reduction in unit cost 49 is subjected to a trade-off between labor and capital improvement. Kennedy structured his theory as a straightforward optimization of the reduction in unit cost constraint (𝜆𝑝 + 𝛾𝑞 = 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑢𝑛𝑖𝑡 𝑐𝑜𝑠𝑡) to the concave innovation possibility frontier (∅(𝑝, 𝑞) = 0). If 𝑝 ≠ 𝑞, there will be an adjustment with bias in innovation. An improvement will alter the cost share according to the innovation possibility frontier. The system will adjust until 𝑝 = 𝑞 , when there will be no change in the distributive cost share ( 𝜆, 𝛾 ). At equilibrium, the distributive share will not alter in the next period. The system exhibits Hicks neutral technical change, where the rate of labor-saving and capital-saving innovations are the same. Moreover, the equilibrium tangent determines the distributive share between capital and labor. Kennedy asserted that "in the long run the equilibrium values of the distributive shares will be determined by the characteristics of the purely technological innovation possibility function" (Kennedy, 1964, p. 545). Notice here that the distributive share does not change in the next period only when 𝑝 = 𝑞 with Hicks's definition of neutral technical progress. Furthermore, in the second part of his paper, Kennedy went beyond his previous assumption of no capital accumulation. If improvement occurs in the investment sector, Kennedy assumed that there will be accumulation of new machines, which will leave the real capital unchanged due to the fall in capital cost with the same amount of labor. The improvement in the investment sector disturbs the previous equilibrium when 𝑝 = 𝑞. The system adjusts to maintain equilibrium by focusing on endogenous labor-saving inventions. More machines will be augmented to the previous equilibrium condition of Hicks neutral technical progress. The system adjusts to Harrod’s neutral technical progress 50 with a labor-saving invention bias. Kennedy asserted that Kaldor's stylized facts "are to be explained by the neutrality of technical progress for the economy as a whole, a neutrality in which the generally labour-saving character of individual improvements is balanced by the fact that some of the improvements take place in the capital sector" (Kennedy, 1962a, p .911). Kennedy concluded that Hicks neutral technical progress is equivalent to Harrod neutral technical progress as discussed in the last section. Without considering complications in the measurement of value, Samuelson (1965, 1966) adapted Kennedy's innovation possibility frontier for the neoclassical production function when the elasticity of substitution is less than one to answer the question posed by Kaldor's stylized facts. However, Samuelson significantly deviated from Kennedy's formulation. Samuelson insisted on using factor price theory derived from the production function and did not consider the equivalency of Hicks and Harrod neutral technical progress. Samuelson's forceful introduction of factor price changed the previous assumption about the cost share of the factor of production. According to the marginal productivity theory, factor price is determined by factor scarcity. Hence, Samuelson's distributive share is determined in the competitive market, which is in sharp contrast to Kennedy's endogenous determination of the distributive share on the innovation possibility frontier. Samuelson simulated Kennedy's results using a purely neoclassical method. If the innovation possibility frontier is symmetric and the factor input ratio does not change, Samuelson obtains stable equilibrium results from Hicks neutral technical change and a strange equal dividend of factor share.10 Samuelson showed that his use of factor price on 10 Kindleberger effect (Samuelson, 1964, p. 346). 51 the innovation possibility frontier can also yield results similar to Kennedy's. The outcomes are due to the restrictions that there is no factor accumulation and the innovation possibility frontier is symmetrically given. However, with steady capital accumulation, Samuelson asserted that Kennedy's results for Hicks neutral technical change were inconsistent. Samuelson demonstrated his argument by dropping an assumption of a fixed factor ratio and "replacing it by the more realistic recognition that capital is 'deepening relative to labor'" (Samuelson, 1965, p. 348). If the elasticity of substitution is less than unity, labor's relative share will tend to rise more than capital's relative share. There has to be a bias in invention that offsets diminishing marginal productivity from accumulated capital. Samuelson showed that this scenario happens only under Harrod neutral technical progress with a labor-saving invention. It is impossible to retain Hicks's neutrality as in Kennedy's model. Output will keep up with the constant capital/output ratio with labor-augmented invention and less efficiency for capital. The concept of elasticity of substitution and bias technical change are to remain in neoclassical endogenous growth models (Acemoglu, 2003; León-Ledesma & Satchi, 2015). Kennedy (1966) objected to Samuelson's use of the production function. 11 He demonstrated that Samuelson's capital accumulation could be reconciled with his theory: "in Kennedy's case, the Harrod-neutral result is not 'supposed to come about,' it does come about" (Kennedy, 1966, p. 442). The disagreement between Samuelson and Kennedy echoes the complication of value we discussed in the second section. Because of their different treatments, Samuelson would deny the equivalency between Hicks and Harrod 11 Kennedy criticized Samuelson's use of mathematic weight in the production function as improper because there were intercorrelations from the production function that would alter the innovation possibility frontier. 52 neutral technical progress, whereas Kennedy insisted otherwise. As a result, Samuelson established Harrod's definition instead of Hicks's as the standard exposition of neutral technical progress in the growth and distribution literature. Their disagreement about the theory of neutral technical progress, which aimed to abide by the stylized facts, was due to the controversy over the measurement of capital. Furthermore, Samuelson's solution on bias in innovation was to address an empirical evidence that the elasticity of substitution is less than one. When the production function exhibits constant elasticity of substitution, i.e., the Cobb-Douglas production function, capital accumulation will always be neutral to the distribution of income in the neoclassical "balanced growth" concept. It can be shown that Kaldor's technical progress function is just another form of neoclassical production function (Black, 1962). Due to criticisms of his linear technical progress function, Kaldor put forward another endogenous growth model: A New Model of Economic Growth (Kaldor & Mirrlees, 1962), which addressed and clarified many of the criticisms of his previous models. As noted earlier, although Salter relied on neoclassical production function and price substitution, Kaldor, in an attempt to discard any connections to the production function, used the vintage method pioneered by Salter. The Salter process12 focused on the initial investment in each period due to technical progress. Salter was aware of the complications in measuring capital. He proposed instead to focus on an analysis of obsolescence and scraping of each vintage of machines. Salter (1965) compared his theory to Ricardo's quasi-rents. The investment decision to replace the existing capital stocks 12 Harcourt commented that the Salter process "is worthy to be called a major breakthrough" (1972, p.66, p.73). 53 depends on the prospect of quasi-rents the capital stocks have in the next period. A new investment is encouraged by the change in conditions, making the quasi-rents of the existing capital stocks go down in each successive period. Focusing on the initial investment, there is no need to measure capital directly. Salter proposed that "by replacing capital in the production function by this less ambiguous concept of investment, we are forced to recognize the time element in technique decisions" (Salter, 1966, p.18). Kaldor used Salter's concept to modify his technical progress function. Previously, Kaldor had set up the technical progress function as a relation between the rate of growth of output and the rate of growth of capital. In the New Model of Economic Growth (Kaldor, 1962), the new technical progress function instead depicts a relation between the rate of growth of productivity per worker and the rate of growth of investment per worker. Notice that it is the rate of growth of investment that comes from Salter's theory. Kaldor was more explicit in avoiding the measure of capital stock, addressing the previous critique that his technical progress function was just another form of the neoclassical production function. This section has described the intuitions behind the modifications of neutral technical progress in growth and distribution models. Kaldor made explicit statements about the nature of economic growth and the fact that wage was predetermined to rise. The focus of this section concerns the existence of the neutral technical progress conditions. Kaldor had assumed an automatic process based on the technical progress function. Kennedy relied on the framework of bias in innovation. His modification went back to the complication in the measure of value debated in the early years of the Keynesian revolution. In contrast, Samuelson had fulfilled the task of neoclassical economics by attaching the marginal productivity factor price theory to neutral technical progress. 54 Neoclassical economics had discarded this complication in the measure of value and confined to Samuelson's formulation. On the other hand, Kaldor introduced a vintage method pioneered by Salter that focused only on investment to avoid the use of the measurement of capital. I want to emphasize Kennedy's solution for neutral technical progress and the measure of value. Kennedy's model based on Joan Robinson's real capital did not get the credit it deserved. The next section focuses on the mathematical formulations of neutral technical progress theories. 2.4. Neutral technical progress along the Kaldor-Kennedy line The effect of progress upon distribution is a long-period analysis. Both Kaldor and Kennedy assumed that the profit rate and employment are constant. Kaldor had been teased by Samuelson before as "Jean Baptiste Kaldor" (Samuelson, 1964, p. 235) because of these long-period assumptions. The neutral long-period tendency of the effect of technical progress was the central question they had in mind. This section will describe differences in mathematical assumptions used by Kaldor and Kennedy using income accounting. Both models provide the same conclusion of neutral technical progress. However, their intuitions are different, as captured by the behavior of their main variables. At the end of the section, I use the concept of labor measure to provide another intuition on neutral technical progress. Distributive income accounting is shown by 𝐿∗ 𝐾 1 = 𝑤 𝑌 + 𝑟∗ 𝑌 (2.1) 55 Labor (𝐿∗ ) and profit (𝑟 ∗ ) are assumed constant. The remaining variables are wage (𝑤), capital (𝐾), and output (𝑌). The neutral technical progress model needs to explain the behavior of these variables to achieve the neutrality result. Kaldor explained neutral technical progress through the relation between capital (𝐾) and output (𝑌). His technical progress function depicts an equal rate of growth between capital and output. Kaldor relies on assumptions of entrepreneurial investment behavior. If the rate of capital accumulation is less than the rate of growth of output, entrepreneurs will see the prospect of profitability. A new investment will increase the accumulation rate such that it adjusts to the rate of growth of output. Invention will appear to be labor-saving or capital-saving according to the adjustment of the rate of accumulation that offsets the technical progress function. In effect, the investment behavior of entrepreneurs will maintain the constancy in the capital/output ratio. The distributive income accounting identity will change as shown in equation 2.2. 𝐿∗ 𝐾 ∗ 1 = 𝑤 𝑌 + 𝑟 ∗ (𝑌 ) (2.2) With constancy in the capital/output ratio, an increased output will increase capital in the same proportion. Because of constant profit rate and employment in the income identity, technical progress will leave the profit share of income identity unchanged. It follows that the wage will increase in the same proportion as a result of an increase in output. Kaldor obtained his stylized facts with the same rate of growth of output, capital, and wage. In the case of Kennedy, neutral technical progress is the result of bias in innovation. In contrast to Kaldor's investment behavior, Kennedy adopted Hicks's insight on the character of invention to explain the neutrality. The economic system optimizes the cost share between capital and labor to the innovation possibility frontier. An endogenous labor- 56 saving invention is due to an improvement that occurs in the investment sector, thereby disturbing the previous distributive share. Endogenous bias in innovation induced from the disturbance in distributive share will adjust the system to the same distribution. Notice that it is the distributive share that now controls the behavior of the equation. The income accounting identity would change as in equation 2.3 with constancy in the distributive share in parentheses. 𝐿∗ ∗ 𝐾 ∗ 𝑌 𝑌 1 = (𝑤 ) + (𝑟 ∗ ) (2.3) Technical progress increases the amount of overall output. With Kennedy's bias in innovation, the distributive shares are constant. The denominator (𝑌) increases in both sets of parentheses. Since the distributive share is constant, any increase in output from technical progress will benefit capital and labor in the same proportion. Wage (𝑤) will increase along with the value of aggregate capital (𝐾). Equations (2) and (3) show the basis of Kaldor's and Kennedy's models for implementing neutral technical progress on the distributive income accounting identity. First, Kaldor used the equal rate of growth of capital and output. Second, Kennedy focused on the character of cost share optimization. Their approaches to neutral technical progress were efforts to overcome the complications in the measure of value, which affected income distribution. However, Kennedy was more explicit about the measure of value. He suggested using labor as a measure. If capital is a function of labor measure 𝐾 = 𝑓(𝑤, 𝐿∗ ), it follows that the income accounting identity would change as indicated in equation 2.4. 𝐿∗ 1 = 𝑤 𝑌 + 𝑟∗ 𝑓(𝑤,𝐿∗ ) 𝑌 (2.4) 57 The function of the labor measure 𝐾 = 𝑓(𝑤, 𝐿∗ ) has to take a specific form for the effect of technical progress to be neutral. As shown by Kennedy, using Joan Robinson's real capital: 𝐾 = 𝑤𝐿∗ , the value of capital depends on the wage. Capital will increase only when wage increases because of the behavior of labor measure. With an increase in output, the rate of growth of output will be equal to the rate of growth of capital and the rate of growth of the wage: 𝑔𝑦 = 𝑔𝑘 = 𝑔𝑤 . Equation 4 shows that Joan Robinson's labor measure also gives the same result along the Kaldor-Kennedy line of neutral technical progress.13 2.5. Conclusion The 100 per cent pseudo labour theory of value is no labour theory of value at all! (Samuelson, 1998, p.330) This chapter describes the development of the analysis of the effect of technical progress along Kaldor-Kennedy lines of thought. Crucial theoretical problems concerning the measurement of capital and the character of technical progress deserve more attention. Particularly, the effect of technical progress theory is related to the famous Cambridge Capital Theory Controversy. Although overlooked, the intuitions behind the analysis of neutral technical progress are rich and profound. Hicks, Robinson, and Harrod had written about the relation of the measure of value to the effect of technical progress prior to the 13 Moreover, the conflict between Kaldor and Robinson was from their claims on Keynesian distribution theory, see King (1998). Robinson has provided a lengthy analysis on the effect of technical progress. However, it was Kaldor who dominated the literature of endogenous growth models. Their writings seem to be disconnected. This paper hopes that the analysis of neutral technical progress and the measure of value can bridge some gaps between their contributions. 58 controversy. Their inquiries led to the establishment of the criteria to distinguish the effects of technical progress on the distributive shares. Kaldor raised the question again when he put forward the stylized facts of constancies in the distributive share, the profit rate, and the capital/output ratio. Although he was aware of the complications on value, Kaldor proposed the technical progress function, which did not relate to the measure of value pioneered by Salter. In contrast, Kennedy attempted to solve both problems: the measure of value and the neutrality of technical progress. Kennedy suggested that Joan Robinson's measure of real capital was consistent with the neutral technical progress analysis. Kaldor and Kennedy's theories are the foundation of the modern endogenous growth model. The long-period position of the neutral technical progress theory implies a win-win capitalist system. The neoclassical-Keynesian balanced growth theory is analogous to the post-Keynesian neutral technical progress. Although Kaldor later changed his mind to focus on his Mark 2 models (Harcourt, 2006), concentrating on history versus equilibrium and Adam Smith's increasing returns, it is worthwhile to examine the connection of our Keynesian predecessors to the long-period analysis of the classical political economy first. Furthermore, in the last 2 decades of his life, Samuelson (2000a, 2000b) came back to address Sraffa's interpretation of classical economics regarding linear analysis and returns to scale. Thus, the debate on neutral technical progress is connected to the classical theory of value. The implications of the measure of value for neutral technical progress are significant. They suggest the possibility of reconciling a consistent theory of value with the growth and distribution literature. The post-Keynesians and the neoclassical-Keynesians 59 share a common concept of neutral technical progress. This chapter describes the history of thought behind the analysis. There are useful intuitions from the effect of technical progress debate to be reconsidered regarding the measure of value in the framework of the Cambridge Capital Theory Controversy. CHAPTER 3 KEYNESIAN SOCIAL SECURITY AND INDUCED TECHNICAL PROGRESS This chapter explores the economics of pensions from a Keynesian perspective using a model with induced technical progress. The focus is on parsing out the implications of old-age income funding through a Social Security tax on the distribution of income and economic growth. Given the possibility of induced technical progress, I explore whether a pension scheme funded through a public income tax could potentially generate sustainable funding for a growing share of retirees. 3.1 Introduction This chapter analyzes the effects of old-age income funding on the distribution of income and economic growth, focusing on the pay-as-you-go system that is akin to US Social Security. Old-age pension funding impacts both private decision-making and public regulatory structures. Moreover, pensions affect the distribution of income and economic growth on the transition path as well as at the steady state (Rada, 2012). The economics of pensions describes the process of income funding for nonworking retirees (Barr & Diamond, 2006). Pension related policies remain a hot topic of the public debate. In simplified terms, the focus has been on the implementation of two types of pension system: 61 the fully funded (FF) and the pay-as-you-go (PAYG) pension schemes. An FF pension is a form of savings preparation where funding depends partially on individual preferences. In contrast, a PAYG pension is an income transfer scheme from working generations to retirees, mostly associated with public and union pensions. The debate centers around which of the two systems of pension funding is more sustainable. Indeed, there are growing concerns over the sustainability of pensions in many developed countries. Increasing oldage dependency raises questions about the prospect of a sufficient stream of output to fund old-age retirement income. Moreover, financial instability increases the risk of losing retirement savings and the guarantee of steady income to retirees, which has led scholars, policymakers and politicians alike to propose reforms of pension systems. The focus of this chapter is on the effects of pension funding on the economy, and specifically on income distribution and economic growth. The analysis is rooted in the Keynesian perspective, which, in simplified terms, identifies demand as the most binding constraint to economic growth. Economic growth in turn is required for the sustainability of any pension funding system. The typical Keynesian model of growth is extended to allow the possibility of endogenous growth through induced technical progress. In this way, a direct connection is being made between pension funding which affects income distribution and technological change, which, as formalized here, responds to changes in factor income shares. In the US, the Social Security system is at the center of the public debate. Social Security is the largest federal mandatory expenditure, supplying income to most US retirees. There are various points of view, both policy and theory relevant, about the workings of US Social Security. For the classical economic approach to pensions (Michl 62 & Foley, 2004), Social Security can be considered fully funded, if workers save and receive a return from the Social Security Trust Fund. However, from a policy perspective, Social Security is mostly regarded as a pay-as-you-go pension scheme, better described by the transfer of output from working population to the retirees through the income tax. This fiscal aspect of the transfer of income from Social Security tax is in accordance with the Keynesian approach. From the Keynesian perspective, pensions are social institutions (Cesaratto, 2005a), and pensions affect the distribution of income and important macroeconomic variables such as consumption, investment and output (Rada, 2017). The transfer of income from workers to retirees introduces a distributive conflict between economic classes. The conflict is not only between workers and retirees; capitalists are responsible for mitigating the distributive conflict, since they are the class that controls investment and therefore economic production. As a result, old-age pension funding is seen as introducing a new economic class, that of retirees, to the Keynesian model of growth. The challenge of Social Security, as in the case of any other pension system, is in providing sustainable funding for retirees. Arguments in support of Social Security have to consider the problem of economic and demographic shocks and how these may affect sustainability of old-age pension funding. There are various discussions on the bestpractice policies from different economic perspectives (Barr, 2002; Michl & Foley, 2004; Musgrave, 1981; Palley, 1998). These discussions focus on the mechanism of funding and the steady stream of income. Population aging, which is a feature of many developed countries, poses challenges to their pension systems. Privatization of the public pension system, which entails the establishment of a fully funded system, has been the solution often proposed to address rising old-age dependency rate. However, a fully funded pension 63 system is not necessarily more effective or shock-proof (Barr & Diamond, 2009; Cesaratto, 2005b; Ghilarducci et al., 2012). One aspect that has been understudied by the literature, and which this chapter tackles, concerns the effects that the distributive conflict described above may have on technological change and therefore on economic growth, a required ingredient for the sustainability of any pension system. The chapter illustrates the role of public pension tax policy for both static and dynamic behaviors of main macroeconomic variables. Section 3.2 provides a brief empirical description of the US pension system and reviews the main public debate. Section 3.3 discusses the theoretical framework behind the model and provides comparative statics for a Keynesian pension funding model with technical progress. Section 3.4 analyzes the stability of pension policies in dynamic cycle. Section 3.5 discusses the implications of rising old-age dependency. 3.2 The US pension system and the old-age pension funding debate Pension systems in most countries began as pay-as-you-go funding schemes or as social insurance programs. The history of the modern US pension system traces back to the New Deal era, when pressures from economic hardship brought about by the Great Depression of the 1930s prompted reforms to improve economic welfare. The Social Security Act was enacted during that time as a public pay-as-you-go scheme. However, the US is seeing a change in public opinion towards fully funded private pensions. This transition is the result of the congruence of various concerns about the sustainability of pension funding. 64 Although the US has seen a rise in private pension funds, Social Security is still the pension plan that provides most of the old-age income coverage to Americans. Social Security is also the largest mandatory federal budget fiscal expenditure. Figure 3.1 shows the size of Social Security claims compared to private defined-benefit (DB) and definedcontribution (DC) pensions in billions of dollars from the Bureau of Economic Analysis data. Social Security provided $896.5 billion in claims for benefits in 2016 in comparison to $526.7 billion from DC and $363.9 billion from DB. The amount of claims in public Social Security roughly matches the amount of claims in private pensions. The US pension system depends on public expense in contrast to the conventional understanding that individual retirement funds support most of the US retirees' income. Furthermore, private pension funds are mostly concentrated in the middle to upper income brackets. Using the Survey of Consumer Finance data, Devlin-Foltz et al. (2016), Wolf (2015), and Poterba (2014) show that the bottom half of households depends on Social Security as the source of retirement wealth, whereas members of the middle to upper classes have an alternative with their individual retirement accounts. In contrast, Social Security has supplied, and continues to supply, most of the replacement income for most Americans regardless of their income class. The suggestion to transform and weaken the public Social Security is meant to address concerns over the sustainability of income funding and the benefits provided to retirees. First, a pension system has to consider the issue of old-age dependency and the sustainability of income streams to retirees. Funding of pension schemes depends on the availability of output, or, equivalently, on income in the next period. In other words, regardless of the pension system in place, a portion of total output must be provided to 65 Figure 3.1 Comparison of Social Security to Private DB and DC pensioners. The younger generation may not be able to produce enough output for both retirees and for themselves. The old-age dependency rate, the ratio of the nonworking population to the working population, is rising in the US. An increase in old-age dependency means that a larger proportion in total output must be provided to retirees. In a labor constrained economy, rising old-age dependency poses a risk for the prospect of economic growth in the sense that the labor force may not be large enough to maintain economic production and a sufficient income stream. Many developed countries face adverse demographic changes, which raises concerns about the sustainability of pension funds and economic production. Proponents of the transition toward private pensions argue that private saving accounts prepare workers for old-age retirement because: 1) savings are solvent in the next period and thus ensure retirees' consumption, and 2) fully funded pensions provide the saving required for capital accumulation and labor productivity growth. In other words, in an economy with saving driven investment, a fully funded pension system can mitigate the 66 effects of rising old-age dependency. As a result, 401(k)/Individual Retirement Accounts have become popular as instruments of privatization policies. Figure 3.2 shows that the average 401(k) individual asset value increased from $37,000 in 1996 to $76,000 in 2014. The trend demonstrates the effect of the move toward individual saving plans. Workers and employers contribute to saving accounts to prepare for their retirement. The transition to a fully funded system shifts the responsibility to private individual as workers have to provide for their own retirement. However, opponents of the privatization of the Social Security system point out that workers' own savings are very often inadequate for their retirement. The average values plotted in Figure 3.2 come from individuals who have private pensions. They do not include most of the population who do not have access to private pensions. Even though there has been an increase in private pension accounts, the savings are not enough compared to the previous benefits from the old pension system, while only workers in the top half can afford private pensions. Figure 3.2 also shows the volatility of 401(k) pensions during economic recessions. The value of individual 401(k) assets fell sharply during the financial crises in 2001 and 2008. Ghilarducci et al. (2012) and Ghilarducci et al. (2015) point out that the transition to fully funded private pensions has a destabilizing effect because the administrative cost of private pensions is high, and often a large part of the gains are transferred to the financial sector. From a policy perspective, various changes to the prevailing pension systems have been proposed. Behind the analysis conducted in this chapter one important condition is that each pension policy must seek the sustainability of income funding and the benefits provided to retirees discussed above, given that old-age income funding has transitive and 67 Figure 3.2 401(k) Individual Asset Value steady state effects on the economy. The importance of Social Security has been stressed in both the neoclassical approach (Diamond, 2004; Diamond & Orszag, 2004) and the classical approach (Michl & Foley, 2004; Michl, 2007). This chapter contributes to this literature an analysis of the Social Security system from a Keynesian perspective. 3.3 Theoretical framework This section describes the theoretical framework of this chapter. The pivotal difference between Keynesian and neoclassical and classical economics is its emphasis on the role of demand. The closure of the Keynesian model of growth is from the demand side in contrast to the supply closure associated with Say's law and adopted by classical and neoclassical economics. Moreover, the distribution of income in the Keynesian perspective can be either exogenous or endogenous. The premise of the analysis in this chapter is that 68 political actions and public policies impact, eventually, the distribution of income between wages and profits even when these are not directly targeted by the intervention in the economy. Hence, the claim of this chapter is that old-age income funding and pension policies affect income distribution and important macroeconomic variables. Furthermore, public policy impact on the distribution of income can become relevant in the context of the induced technical progress mechanism. But first let me describe the static Keynesian model with pension funding. 3.3.1 A Keynesian model with Social Security The model setup follows the framework put forth by Rada (2017). Workers contribute a portion of their income to the Social Security Trust Fund through the income tax, and they save for retirement through privately managed pension funds. The transfer of income to retirees takes place via two mechanisms of taxation and saving. Equation (3.1) shows the accounting for an economy with pension funding and three economic classes: workers, retirees, and capitalists. First, workers' consumption is a residual of their savings (𝑠𝑤 ) applied to their wage bill (𝜓𝑋) net of deductions for the Social Security tax (𝜌). Second, retirees' consumption is possible due to the income they received as transfers from workers' wages (𝜌𝜓𝑋) and the profit income that results from their holding of a share of capital ( 𝜂𝐾 ). Third, capitalists' consumption is given by their consumption (or one minus propensity to save, 1 − 𝑠𝜋 ) out of their profit income after paying retirees' their dividend income (𝜂𝐾𝑟). 𝑋= ⏟ (1 − 𝑠𝑤 )(1 − 𝜌)𝜓𝑋 + ⏟ 𝜌𝜓𝑋 + 𝜂𝐾(1 + 𝑟) + ⏟ (1 − 𝑠𝜋 )(𝜋𝑋 − 𝜂𝐾𝑟) + 𝐼 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 𝑟𝑒𝑡𝑖𝑟𝑒𝑒𝑠 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 𝑐𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑠𝑡𝑠 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 (3.1) 69 The Keynesian closure entails that economic activity in terms of quantity of output and employment responds to changes in autonomous demand components (Bhaduri & Marglin, 1990; Dutt, 1984). Retirees are introduced here as a new class that affects aggregate demand, and specifically consumption. Starting from the macroeconomic equilibrium condition in equation (3.1) and normalizing by the capital stock, we get the solution for capacity utilization, which shows the quantity variable that adjusts in the short run to reestablish equilibrium in the economy. The model solves for capacity utilization 𝑢 = 𝑋 𝐾 ; see Rada (2017) for the full derivation of equation (3.2). 𝑢= 𝑔+𝜂 𝑠𝜋 𝜋(1−𝜂)+𝑠𝑤 𝜓(1−𝜌) (3.2) With the introduction of the new class, capacity utilization is a positive function of the rate of accumulation g, and retirees' consumption from their share of capital over the rates of savings of workers and capitalists. Note that the Keynesian approach focuses on the effect that pensions have on aggregate demand. As discussed in section 3.2, the Social Security system provides universal support to every retiree, and pension systems perform largely as a transfer of income across generations. The chapter focuses here only on the effects of the tax transfers to retirees. In such a system with pensions funded only through Social Security, workers do not save for their retirement (𝑠𝑤 = 0) which means they do not hold a share of capital (𝜂 = 0). Thus, capacity utilization is determined only by capitalists, which resembles the Cambridge equation, where capitalists control production (Pasinetti, 1962). Notice here the system turns back to the baseline assumption of post-Keyensian and classical economics where economic activity is affected only by investment demand, g, and capitalists' saving rate. Equation (3.2) becomes 70 𝑢= 𝑔 (3.3) 𝑠𝜋 𝜋 But how does the introduction of Social Security affect the economy? As I have mentioned above, the tax affects the distribution of income and specially the after-tax income received by workers. Workers, in turn, may bargain with capitalists for higher wages, which, if successful, will result in a reduction in the profit share. Following Rada (2017), the profit share becomes an inverse endogenous function of the pension tax shown by: 𝜋 = 𝜌𝜎 (3.4) where 𝜎 < 0 captures the bargaining power of workers, and 𝜌 is the Social Security tax. The assumption of an inverse relation of profit share to the negative pressure of the workers' wages dates back to classical economic theory. The capitalists control the decisions on production and are responsible for providing a necessary wage to the workers. The effects of distributive income tax policy in a model with a demand closure can be shown using the baseline Kaleckian model, which models investment demand as a function of capacity utilization, a proxy for economic activity, and of the profit share, a proxy for profitability (Bhaduri & Marglin, 1990; Dutt, 1984). 𝑔 = 𝛼 + 𝛽𝑢 + 𝛾𝜋 (3.5) Using equations (3.3-3.5), we can solve for the equilibrium values of u and g and trace the effects of the Social Security tax on economic activity. Notice that, compared to the standard Kaleckian story, the emphasis here is on the tax rate (𝜌). 𝛼+𝛾𝜌𝜎 𝑢∗ = 𝑠 𝜋𝜌 𝑔∗ = 𝜎 −𝛽 𝛼+𝛾𝜌𝜎 1− 𝛽 𝑔𝜋 𝜌𝜎 Taking the total derivative of (3.3) to (3.5) with respect to 𝑢, 𝜋 and 𝜌, we have (3.6) (3.7) 71 𝑑𝑢 𝑔𝑖 −𝑔𝑠 = 𝑔𝜋𝑠 −𝑔𝜋𝑖 = 𝑑𝜋 𝑢 𝑑𝜋 𝑑𝜌 𝑢 𝛾−𝑢𝑠 (3.8) 𝑠𝜋−𝛽 = 𝜎𝜌𝜎−1 (3.9) To meet the short-run Keynesian stability condition it is necessary that the denominator in (3.8) be positive. Hence, a redistribution towards profits stimulate the economy if the effect of profitability (𝛾) is strong and the saving rate of capitalists (𝑠𝜋 ) is not too high. In this case the economy is said to be profit-led. Alternatively, the economy is wage-led and the economic activity in equation (3.8) will be negative. Combining (3.8) and (3.9), we can now discuss an effect of the pension tax on capacity utilization: 𝑑𝑢 𝑑𝜌 𝛾−𝑢𝑠 = 𝜎𝜌𝜎−1 𝑠𝜋−𝛽 (3.10) In a wage-led economy a rise in the Social Security tax combined with a materializing 𝑑𝑢 bargaining power of workers will lead to an increase in economic activity (𝑢), since 𝑑𝜋 < 0 and 𝑑𝜋 𝑑𝜌 < 0. The total derivative of equation (9) with respect to 𝜌 provides insights into the effect of the Social Security tax on capital accumulation: 𝑑𝑔 𝑑𝜌 𝑑𝑢 𝑑𝜋 𝑑𝑢 𝑑𝜋 𝑑𝜋 = 𝛽 𝑑𝜌 + 𝛾 𝑑𝜌 = 𝛽 𝑑𝜋 𝑑𝜌 + 𝛾 𝑑𝜌 (3.11) If the economy is profit-led, capacity utilization reacts positively to an increase in the profit 𝑑𝑢 𝑑𝜋 share: 𝑑𝜋 = (+). Since the pension tax (𝜌) has an inverse relation to profit share (𝜋), 𝑑𝜌 𝑑𝑢 𝑑𝜋 will be negative, and 𝑑𝜋 𝑑𝜌 is therefore always negative in a profit-led economy. On the 𝑑𝑢 𝑑𝑢 other hand, for a wage-led economy, the derivative 𝑑𝜋 is negative, and therefore 𝑑𝜌 is positive. The second part of equation (3.12) is always negative. Thus, the possible signs of the effect of pension on the rate of accumulation are 72 𝑑𝑔 𝑑𝜌 = 𝛽(+, −) + 𝛾(−) (3.12) It follows that, if the economy is profit-led, an increase in the tax rate has an adverse effect on the rate of accumulation. However, the effect of an increase in the tax rate is not clear in the case of a wage-led economy. A positive effect from a higher wage share on utilization could possibly overcome the negative effect of a higher tax rate on profitability. Nevertheless, the effect of an increase in the pension tax likely reduces the rate of accumulation and further exacerbates the conflict over the distribution of income complicating pension funding. Thus, it is possible that a rise in the Social Security tax will hurt accumulation and growth. Next, the chapter introduces technical progress that arises from the conflict over the distribution of income. 3.3.2 Pension funding with technical progress Technical progress has been a subject of interest for economists since the time of the industrial revolution. Overall, economic history points out that rapid economic growth and technological changes took place in a relatively very short period of time in human history. This optimistic view of economic progress in market-based economic systems is explicit in Adam Smith's writings on human cooperation and the division of labor. In the second chapter of this dissertation, I have discussed at length theories of technical progress that underline a win-win scenario. In this chapter, I delineate the conditions under which such a win-win outcome may result in the context of the Social Security system and policies related to it. Still, there are limitations to the impact that technological progress may have on the economy. 73 The section above analyzed the effects of old-age pension funding through Social Security tax transfer of income. However, the scenario did not consider the possibility of technical progress. This section introduces the mechanism of induced technical progress based on the theory of induced bias in innovation (Kennedy, 1964). The idea is the following: If a higher Social Security tax forces workers to negotiate for higher wages, the capitalists will be pressured to innovate and save on the labor cost. The system will move towards a labor-saving innovation due to the pressure from pension related tax policies on the distribution of income 3.3.2.1 Induced technical progress According to the theory of induced bias in innovation (Kennedy, 1964), technical progress is endogenous to changes in the distribution of income. Although Kennedy's theory is associated mostly with classical growth models, the idea can be useful for Keynesian growth models due to its emphasis on changes in the distribution of income. Kennedy asserts that technical progress comes from the pressure of higher input costs. If, for example, the share of costs due to labor goes up, the capitalists will be pressured to innovate and save on labor costs. The system will move toward labor-saving innovation. Note that this is an economy where capitalists have control over the production process and manage the cost of production through changes in techniques of production. Hence, the distribution of income affects the pattern of innovation, which is ultimately chosen by the capitalist class. Kennedy structured his theory as a straightforward optimization problem of a reduction in the unit cost of production (equation (3.13)) given a concave innovation 74 possibility frontier (equation (3.14)). The problem is formalized in terms of total cost of production, which is a function of the wage share (1 − 𝜋 ), the growth rate of labor productivity (𝜀), the profit share (𝜋), and the growth rate of capital productivity (𝜒). Following Foley and Michl (1999), firms' optimization problem is specified as: max = (1 − 𝜋)𝜀 + 𝜋𝜒 (3.13) subject to the innovation possibility frontier (Kennedy, 1964) 𝜙(𝜀, 𝜒) = 0 (3.14) The solution of equations (3) and (4) is given by: 𝜋 𝜙 ′ (𝜀) = 1−𝜋 (3.15) It follows that technical progress, which addresses labor productivity, is an inverse function of the profit share or a positive function of the wage share (Shah & Desai, 1981). 𝜀 = 𝑓(𝜋), 𝑓 ′ (𝜋) < 0 (3.16) The premise of this chapter is that a higher pension tax forces workers to demand higher wages to pay for the retirees' consumption. Labor cost share increases, in turn, force capitalists, who control production, to choose a technique that optimizes the reduction in the cost of production. I discuss this effect of pension tax on technological progress in more detail in the following sections. 3.3.2.2 Technical progress in a Keynesian model with Social Security Consistent with the assumption that capitalists control economic production in equation (3.4), the distributive conflict introduced by the pension tax forces workers to demand higher wages to pay for retirees' consumption. The profit share decreases, which then forces the capitalists to innovate in order to save on labor costs. In order to capture the 75 role of technical progress, we introduce it in the Kaleckian model through the investment demand function on the basis that higher labor productivity growth has spillover effects on the economy, including on capital accumulation. Accordingly, we have: 𝑔 = 𝛼 + 𝛽𝑢 + 𝛾𝜋 + 𝑓(𝜀) (3.17) Taking the total derivative of (3.17) with respect to 𝜌 we get: 𝑑𝑔 𝑑𝜌 𝑑𝑢 𝑑𝜋 𝑑𝜋 = 𝛽 𝑑𝜌 + 𝛾 𝑑𝜌 + 𝑓′ 𝑑𝜌 (3.18) The third part of equation (3.18) captures the effect of induced technical progress initiated by the change in the distributive share. Previously, an increase in the pension tax decreased the profit share and likely had an adverse effect on the rate of accumulation. The effect of the pension tax on the rate of accumulation would depend on whether the system is wageled or profit-led, but it would not be definitive as in the case of the effect on economic activity. However, with induced technical progress, the sign of the third term in equation (3.18) is positive: 𝑓′ 𝑑𝜋 𝑑𝜌 > 0. If induced technical progress responds strongly to a change in the distributive shares, it can overcome the effects on capacity utilization and investment from a lower profit share. The economy does not need to rely entirely on wage-led/profitled differentiation in order to ease the negative impact of a pension tax on distribution and therefore on the economy, especially in the profit-led case. The sign of the effect of the pension tax on the rate of accumulation could arguably be positive due to the mechanism of induced technical progress: 𝑑𝑔 𝑑𝜌 > 0. In this case, the combination of a higher tax rate that is necessary to support old-age income and the productivity effect can ease the overall constraints on the economy. 76 The first part of this section extended the Keynesian approach to pension proposed by Rada (2017) with an analysis of the effects of Social Security tax on economic activity and capital accumulation. Without induced technical progress, the pension tax is likely to have an adverse effect on the rate of accumulation no matter whether the economy is profitled or wage-led. The second part of this section introduced technical progress to the baseline Kaleckian model. The model suggests that induced technical progress is a crucial mechanism that may induce a positive effect of a Social Security tax on investment. In the next section, I introduce the above ideas of induced technical progress in a cyclical model and illustrate the role of tax distributive income policy in a dynamic setup. 3.4 Keynesian pension tax funding in a Structuralist cycle model of growth This section introduces the Social Security tax and, generally, pensions in a structuralist modeling framework that emphasizes cyclical dynamics between income distribution and economic activity. Distributive cycles are at the center of the debate on growth dynamics in the recent post-Keynesian literature (Skott, 2015; von Arnim & Barrales, 2015; Zipperer & Skott, 2011). The pension tax, which has a redistributive effect, plays an additional adjustment role in the economy as discussed above. Furthermore, induced technical progress can, arguably, provide a supplementary feature to the Keynesian cyclical model. Following Marx, and using the classical assumptions of saving driven investment and an elastic supply of labor, Goodwin (1982) introduced a model that builds on a predatory-prey dynamic between the employment rate and the wage share: This dynamic gives rise to closed-loop counterclockwise cycles between the two variables. This type of 77 adjustment is consistent with the empirical evidence in many developed economies (Kiefer & Rada, 2014; Nikoforos & Foley, 2012). Post-Keynesian economists have adapted the Goodwinian framework to the Keynesian perspective on effective demand. Following Kalecki, the rate of employment has been replaced by capacity utilization as the main variable measuring economic activity (Barbosa-Filho & Taylor, 2006; Taylor, 2009). This chapter uses the Goodwin-Kaleckian structuralist framework to trace the effects of a pension tax and induced technical progress on economic activity and income distribution. Following Taylor (2004), the model consists of two differential equations. Capacity utilization (𝑢) is measured by the ratio of output (𝑋) to capital stock (𝐾), while the wage share (𝜓) is defined as the ratio of the real wage (𝑤) and labor productivity (𝜖). ̂ 𝑢̂ = 𝑋̂ − 𝐾 (3.19) 𝜓̂ = 𝑤 ̂ − 𝜖̂ (3.20) Firstly, output is expected to rise with the introduction of pension. Following from equation (3.18) in the last section, the distributive conflict due to the pension tax forces capitalists to innovate and, in the process, potentially ease the conflict over the old-age income 𝑑𝑔 funding and, by extension, the primary distribution of income: 𝑑𝜌 > 0. Investment demand is assumed to increase as a result of induced technical progress, which in turn increases output. I assume here that the rate of growth of output reacts positively to an exogenous pension tax. Furthermore, for simplicity, the Keynesian stability condition is satisfied: Investment demand responds positively to higher economic activity, but proportionally less than saving: 𝜆1 is positive. The system can be profit-led or wage-led: 𝜆2 ≷ 0. 𝑋̂ = 𝛾𝜌 − 𝜆1 𝑢 ∓ 𝜆2 𝜓 (3.21) 78 Secondly, the rate of growth of capital (𝐾̇ ) or capital formation is usually assumed to respond positively to capacity utilization and negatively to the wage share. Capacity utilization indicates the level of economic activity, which also impacts demand for investment. Moreover, the distribution of income captures profitability as explained above. The effect of the wage share on capital formation is negative since it has an adverse effect on profitability. In this model, the rate of capital accumulation is also affected by technical progress, 𝑓(𝜖̂). The role of technical progress on the accumulation function has not been explored before in the Structuralist Cycle in this manner. The main assumption here is that of a neutral balanced growth path of technical progress, which implies a constant capital/output ratio. ̂ = 𝛼1 𝑢 − 𝛼2 𝜓 + 𝑓(𝜖̂) 𝐾 (3.22) Thirdly, in the labor market, workers are the only class that directly funds pensions through the Social Security tax. They negotiate for higher wages as a function of the pension tax. Following Taylor (2004), wages depend positively on capacity utilization, which affects the employment share and thus the bargaining share of workers, and on the wage share. In the labor market, workers have more leverage in negotiating their wage when the level of economic activity or capacity utilization is high. Furthermore, the level of the wage share is a proxy for the political bargaining power of workers. Notice here that the model focuses on the real side without price inflation formalized in any specific way: 𝑤 ̂ = 𝛽𝜌 + 𝛳1 𝑢 + 𝛳2 𝜓 (3.23) Lastly, the rate of growth of labor productivity (𝜖̂) is the variable of interest in this section. An increase in labor productivity comes as a result of technical progress. In the next section I analyze two scenarios of technical change and show their effects on pension funding 79 based on the following dynamic system, which can be summarized by the Jacobian for equations (3.19), (3.20) and using equations (3.21), (3.22), (3.23) to get: 𝑢̅(𝑌𝑢 − 𝐾𝑢 ) 𝐽= [̅ 𝜓(𝑤𝑢 − 𝜖𝑢 ) 𝑢̅(𝑌𝜓 − 𝐾𝜓 ) ] 𝜓̅(𝑤𝜓 − 𝜖𝜓 ) (3.24) 3.4.1 A structuralist formalization of the Keynesian model with Social Security and technical progress To show the role of the Social Security tax, I analyze first a case where technical progress is exogenous. The distributive conflict following a change in Social Security has no effect on technical progress. If technical change is exogenous, labor productivity increases at an autonomous rate of (𝜀̂) that comes from outside the economy. Equations (3.19) and (3.20) become 𝑢̇ = 𝑢[𝛾𝜌 + (−𝜆1 − 𝛼1 )𝑢 + (∓𝜆2 − 𝛼2 )𝜓 − 𝑓(𝜀̂)] (3.25) 𝜓̇ = 𝜓[𝛽𝜌 + 𝛳1 𝑢 + 𝛳2 𝜓 − 𝜖̂] (3.26) With respect to exogenous technical progress, the sign pattern of the system's Jacobian at the steady state is: 𝐽= [ 𝑢̅(−𝜆1 − 𝛼1 ) 𝜓̅𝛳1 𝑢̅(∓𝜆2 − 𝛼2 ) − ] =[ + 𝜓̅𝛳2 ∓ ] + (3.27) The phase diagram shows a negatively sloped distribution schedule with a possibility of both wage-led and profit-led demand. If the system is wage-led, the determinant of the Jacobian is negative, showing a saddle-point stability. If the system is profit-led, the phase diagram is inconclusive. In either case, the implications of exogenous technical change are counterintuitive and overall uninteresting. 80 Next, I analyze the role of induced technical progress. Endogenous technical progress plays a mediating role for the distributive conflict. Labor productivity becomes a function of distributive share as described in equation (3.16). 𝑓 ′ (𝜓) > 0 𝜖̂ = ℎ(𝜓), (3.28) The system dynamics of demand and distributive share change to 𝑢̇ = 𝑢[𝛾𝜌 + (−𝜆1 − 𝛼1 )𝑢 + (∓𝜆2 − 𝛼2 )𝜓 − 𝑓(ℎ(𝜓))] (3.29) 𝜓̇ = 𝜓[𝛽𝜌 + 𝛳1 𝑢 + 𝛳2 𝜓 − ℎ(𝜓)] (3.30) The sign pattern of the system's Jacobian at the steady state becomes 𝐽= [ 𝑢̅(−𝜆1 − 𝛼1 ) 𝜓̅𝛳1 𝑢̅(∓𝜆2 − 𝛼2 − 𝑓 ′ ℎ′) ] 𝜓̅(𝛳2 − ℎ′) (3.31) Endogenous technical change overcomes the negative feedback of a higher wage share to capital accumulation identified in the static Kaleckian model:∓𝜆2 − 𝛼2 − 𝑓 ′ ℎ′ is negative. Endogenous technical change can also relieve the pressure from workers' demands for an increase in real wage: 𝛳2 − ℎ′ becomes negative. The sign pattern of the system's Jacobian changes to: − 𝐽 = [+ − −] (3.32) The system produces a stable counterclockwise cycle. The model shows that endogenous technical change is an adjusting mechanism, which can replicate the result of counterclockwise cycle acknowledged in the current established models and empirical trends (Shah & Desai, 1981). In this model, the counterclockwise behavior is due to the assumption that capitalists control the production process. The pension tax affects the previous level of distribution of income, which in turn forces capitalists to innovate, generating a counterclockwise adjustment. This section advances the Keynesian approach 81 to Social Security to the dynamic analysis of the Structuralist cycle model. It further demonstrates the role of induced technical progress from a tax transfer policy on economic adjustment. The stability analysis shows that endogenous technical progress induced by the conflict in the distribution of income is a crucial mechanism for a stable cycle consistent with established models. The condition for stability also requires that induced technical progress reacts more strongly than the parameters from the distribution of income and capacity utilization. 3.5 Rising old-age dependency and the Social Security Trust Fund This section examines the sustainability of the Social Security system with respect to demographic shocks. In the public policy sphere, the problem of rising old-age dependency is at the center of the pension debate. Proponents of Social Security privatization argue that saving-based pensions provide a smooth transfer of income during demographic shocks. Mainstream economics generally embraces the transition to private pension systems through this intergeneration solvency argument. According to this view, the public pension system, which relies on taxes, cannot provide enough income to retirees, and the Social Security Trust Fund will be depleted once the demographic shock kicks in. However, such argument relies on the capital theory, which has been contested in the recent literature (Cesaratto, 2002; 2005). Capital is not solvent, and it is therefore impossible to transform savings into output across periods. In contrast, Keynesian economics provides a theoretical solution to the problem of rising old-age dependency in a different way by focusing on the production side. Due to the demand closure, induced technical progress can potentially sustain the level of output 82 growth despite a downward trend in labor supply. The induced technical progress is a response to the redistributive income policy from the pension tax. The Keynesian perspective on technical progress provides a strong argument in support of the refusal of the myth of the Social Security crisis (Baker & Weisbrot, 2001; Beland, 2005), which presses that the Social Security system is unsustainable. 𝑅 Consider an economy where the ratio of retirees to workers is 𝑑 = 𝐿 . If the old-age dependency rate is increasing, the supply of output in the next period declines as a result of a reduction in the labor force. Unless there is induced technical progress that increases labor productivity, workers will have to divert a larger proportion of their incomes to 𝑝𝑅 retirees. The tax rate needed to fund pensions is 𝜌 = 𝑤𝐿 = 𝑑 𝑤 𝑝 , where 𝑝 is the level of pension and 𝑤, as before, is the wage rate. Transforming the relation in growth terms yields: ̂ 𝑤 𝜌̂ = 𝑑̂ − 𝑝 = 𝑑̂ − 𝜖̂ (3.33) where 𝜖 is the rate of increase in labor productivity, given the assumption that retirees demand a constant level of income, 𝑝, and workers receive wages that increase according to their labor productivity growth. In the short run, the demographic change (𝑑̂ ) applies pressure on the Social Security tax, which in turn has a negative effect on the profit share as in equation (3.4). Similar to the last two sections, I employ the induced bias in innovation theory (Kennedy, 1966) to parse out the effects of distribution on economic activity and capital accumulation. The effect of induced technical progress will ensure the sustainability of the Social Security Trust Fund as sketched below. I assume that the sustainability of the 83 trust fund depends on the actual tax rate less the required tax rate (𝜌𝑡 − 𝜌̅ ) , which determines the amount of funds available for old-age income. ̂ = 𝜌𝑡 − 𝜌̅ = 𝑑̂ − ℎ(𝜓) 𝑆𝑆𝑇𝐹 (3.34) Combining (3.34), (3.29), (3.30), the model analyzes the stability of the steady state tax rate in the PAYG old-age pension funding scheme. The Jacobian of the endogenous Social Security tax from the problem of rising old-age dependency is: 𝑢̅(−𝜆1 − 𝛼1 ) 𝑢̅(∓𝜆2 − 𝛼2 − 𝑓 ′ ℎ′) 𝐽=[ 𝜓̅𝛳1 𝜓̅(𝛳2 − ℎ′) 0 𝜌̅ (−ℎ′) 𝑢̅𝛾 𝜓̅𝛽 ] (3.35) 0 The stability of the Social Security tax will depend on the effect of technical progress. Similar to section 3.3, stability condition requires that the effect of induced technical progress must compensate for the impact of other variables. The sign of the Jacobian becomes: − 𝐽 = [+ 0 − − − + +] 0 (3.36) which meets the Routh-Hurwitz conditions under certain assumptions. First, the traces are negative. Second, the determinant is negative. Third, −𝑇𝑟[𝐽](∑ 𝐷𝑒𝑡[𝐽𝑡 ]) + 𝐷𝑒𝑡[𝐽] > 0, which can be shown to hold if the effect of technical progress is strong. In regard to the problem of rising old-age dependency, the steady state effect on the Social Security Trust Fund will depend on the magnitude of induced technical progress. Equation (3.35) shows that induced technical progress can mitigate the depletion of the Social Security Trust Fund. Moreover, if the effect of induced technical progress is stronger than the problem of rising old-age dependency, the Social Security Trust Fund can actually operate with a surplus. This section shows that, under the Keynesian framework, the US Social Security 84 system is sustainable even given rising old-age dependency from its distributive income tax mechanism in regard to induced technical progress. The sustainability of Social Security Trust Fund has been debated repeatedly in the public policy spheres. There have been many attempts over the years to reform the structure of the public pensions system that have addressed the sustainability of the Social Security Trust Fund as it relates to the ability to collect enough contributions in the context of economic crises or population aging. In this chapter, I advance the idea that technical progress might be able to mitigate potential crises of Social Security. However, there are limitations on the extent to which technological progress may contribute to sustainability of a pension system. For example, if class conflict and bargaining power are such that they favor a certain economic class, technological progress may instead foster income inequality. If inequality increases to the detriment of workers, technological progress is not expected to contribute to the Social Security system sustainability. In the short run, through the transition path, workers might end up being the only class that provides for retirees' income. 3.6 Conclusions: Social Security tax, technical progress, and macro variables This chapter provides an analysis of Social Security tax on the economy and assesses the old-age pension-funding problem using a Keynesian model with technical progress. First, the chapter discusses the US pension system and the debate on pension policies reform. Second, the chapter proceeds to analyze the pension tax in the Keynesian/Kaleckian static model by focusing on comparative statics that emphasize 85 different demand regimes. Third, the chapter introduces the pension tax in the so-called structuralist cycle. Fourth, the chapter summarizes the problem of the sustainability of the Social Security Trust Fund in regard to rising old-age dependency rate. Overall, the chapter brings to the forefront the implications of induced technical progress applied to the public tax transfer of income. In contrast to classical and neoclassical economics, the Keynesian approach focuses on the demand causality and emphasizes that pension systems are social institutions, which have effects on aggregate demand, income distribution, and therefore economic growth. We formalized the link to income distribution by assuming that taxes in support of retirees will lead to a change in the primary distribution of income between workers and capitalists. This will in turn affect consumption and investment decision and therefore important macroeconomic variables, such as capital accumulation and labor productivity growth. Furthermore, the Keynesian model of pension benefits from an extension that includes formalization of induced technical progress. The aspect of technical progress is unexplored in the context of old-age pension funding from a Keynesian perspective. The public tax transfer of income from Social Security affects the distribution of income, which in turn influences the economic system to innovate due to the distributive conflict. The chapter uses this interaction between the distribution of income and induced technical progress to analyze the effect of pension tax policy. Applying the current debate on the sustainability of the US Social Security, the chapter provides a theoretical argument that Social Security can, under certain conditions, be sustained. An adjustment effect from induced technical progress mitigates the problem of demographic shocks. 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