The aggregate neoclassical theory of distribution and the concept of a given value of capital: a reply

In this reply to Paola Potestio, it is argued that there are cases in which both the “supply” of and the “demand” for “capital” can be conceptualised in an economically meaningful way and used in the conventional long-period neoclassical manner to determine an equilibrium or to investigate the adjustment process towards it. This conceptualisation is based on strict assumptions. If, for the sake of the argument, we concede these assumptions, the critique of the theory that tries to generalise the determination of distribution in a simple one-good model, or “corn-economy”, to multi-good models can be safely founded on the possibility of reswitching and capital reversing, contrary to Potestio's critique.     

The Incoherent Emperor: A Heterodox Critique of Neoclassical Microeconomic Theory

It is somewhat common for heterodox economists to come to the defense of neoclassical microeconomic theory. This is due to many reasons, but perhaps the commonest one is ignorance. It seems that most heterodox economists are not aware of the many critiques or that as a collective they completely undermine neoclassical theory. The objective of the article is to dispel ignorance by using the existing criticisms to delineate a systematic critique of the core components of neoclassical microeconomic theory: the supply and demand explanation of the price mechanism and its application to competitive markets. The critique starts by examining the choices, preferences, utility functions, and demand curves, followed by examining production, costs, factor input demand functions and partial equilibrium, and ending with perfect competition and the supply curve. In the conclusion, the implications of the results will be extended to the firm and imperfectly competitive markets, and then the question whether general equilibrium theory or game theory can save neoclassical microeconomic theory.     

C.E. Ferguson and the Neoclassical Theory of Capital: A Matter of Faith

In 1969 the American neoclassical economist C.E. Ferguson wrote that reliance on neoclassical aggregate production and distribution theory is a ‘matter of faith’ to be sorted out (he says ‘answered’) by econometricians. Ferguson was criticized on both sides of the debate for invoking this religious metaphor. Using the methodological framework of A.J. Cohen & G.C. Harcourt (2005), Introduction: capital theory controversy: scarcity, production, equilibrium, and time, in: A. Cohen, G.C. Harcourt & C. Bliss (Eds) Capital Theory, 3 Vols. Northampton, MA: Edward Elgar, this paper argues that faith plays a recurring role in all capital controversies and especially in modern theories of growth that rely wholesale on the aggregate production function. Ferguson's faith proves to be much more insightful than previously recognized.     

Neglected Implications of Neoclassical Capital-Labour Substitution for Investment Theory: Another Criticism of Say's Law

Abstract

Recent mainstream macroeconomic models take Say's Law for granted. This paper argues that the justification for this assumption is not found in general equilibrium theory but in the ‘neoclassical-synthesis’ (and then monetarist) criticism of Keynes, which relies in a fundamental way on a treatment of investment that turns out to depend not only on neoclassical capital-labour substitution (called into questioned by the Cambridge controversies) but also on an assumption of full labour employment that on the contrary should be a result of the analysis. This paper first criticizes the attempt to justify a negative interest-elastic investment function through adjustment costs, that is, without relying on traditional neoclassical capital-labour substitution, with special attention on the treatment in Romer's advanced textbook. Then it proceeds to its new contribution, the demonstration that an endogenous determination of labour employment raises questions about the capacity of decreases in the real wage to raise employment even accepting neoclassical capital-labour substitution, because when the latter is correctly understood the rate of interest does not suffice to determine investment; hence, there is an inevitable role for the accelerator (and Say's Law is thereby undermined). This was perceived by Dornbusch and Fischer but they did not realize that then reductions of real wages will reduce investment instead of raising it. Thus, the ‘neoclassical synthesis’ reply to Keynes is undermined even apart from the inconsistencies of neoclassical capital theory. So the paper exposes a deficiency of the neoclassical arguments in support of a tendency toward full employment, additional to the inconsistencies revealed by the capital critique.     

Uninsured idiosyncratic investment risk and aggregate saving

This paper augments the neoclassical growth model to study the macroeconomic effects of uninsured idiosyncratic investment, or capital-income, risk. Under standard assumptions for preferences and technologies, individual policy rules are linear in individual wealth, ensuring that the equilibrium dynamics for aggregate quantities and prices are independent of the wealth distribution. The analysis thus remains highly tractable despite the incompleteness of markets. As compared to complete markets, the steady state is characterized by both a lower interest rate and a lower capital stock when the elasticity of intertemporal substitution is higher than the fraction of private equity in total wealth. For empirically plausible parameterizations, this condition is easily satisfied, and the reduction in aggregate saving and income is quantitatively significant. These findings contrast with Bewley models, where idiosyncratic labor-income risk leads to higher aggregate saving and income.     

An unpleasant dilemma for contemporary general equilibrium theory

By examining the contributions of two prominent contemporary neoclassical economists, i.e. Lucas and Hahn, the article attempts to shed light on the problematic relationship between neoclassical theory and observation. It is argued that this approach must face the unpleasant dilemma of having to choose between endowing general equilibrium theory with an explanatory role that is marred by its illegitimate notion of capital as a single factor of variable form (Lucas); or alternatively, to consistently treat each capital good as a distinct factor of production, with the bitter implication that the theory must simply renounce to have a correspondence with observation (Hahn).     

Sraffa: the theoretical world of the ‘old classical economists’ *

Sraffa's mature work is seen here as a re-discovery and resumption of the ‘submerged and forgotten’ approach of the ‘old classical economists from Adam Smith to Ricardo’. Wages determined by broad economic and social forces entail there product prices determined independently of demand and supply functions. Some main questions raised for the modern economists by this radical reorientation of economic theory are then considered in order to conclude that it is aginst that background that Sraffa's mature work should be set with its three main contributions, of a rediscovery of the approach, of a complete and transparent solution of the problems of price determination it raises, and of its application to the critique of neoclassical theory. Among several developments originating from Sraffa's seminal work, two are singled out for mention: (i) the possibility of deficiencies of aggregate demand in the long period no less than in the short one; this follows naturally from the abandonment of the neoclassical theory of distribution, of which the role of the interset rate in equilibrating savings and investment is a corollary; (ii) the question of the distribution of the surplus between wages and profits in a modern economy where wages are no longer confined to subsistence.     

Joan Robinson and the three cambridge revolutions

Joan Robinson's association with three Cambridge ‘revolutions’—imperfect competition, effective demand and capital theory—is examined in the context of her personal and intellectual partnership with Richard Kahn, John Maynard Keynes and Piero Sraffa. Initially, imperfect competition appeared to have successfully extended marginal analysis to all market forms. It also allowed Richard Kahn and Joan Robinson to persuade Keynes to present the main argument of The General Theory in terms of aggregate demand and aggregate supply. By the early 1950s, however, Joan Robinson had rejected the Marshallian methodology and had become a strenuous censor of neoclassical theory. In this paper the origin of her critique is traced to her reading of Sraffa's Introduction to Ricardo's Principles.     

Self-fulfilling patience

This paper explores macroeconomic implications of investment in patience in a standard neoclassical growth model with Becker-Mulligan endogenous time preferences. The endogenous discount rate acts as a new margin for inter-temporal decisions, in addition to the standard margin that hinges on the marginal return of capital. This time preference margin alters the equilibrium dynamics and stability of the neoclassical growth model substantially. When the discount rate is positive, there may exist multiple steady states that are either saddle-point stable or unstable. When the discount rate is negative, the unique steady state is locally indeterminate due to self-fulfilling patience investment. Interestingly, the existence of the local indeterminacy does not need any externality. When the discount rate is zero, various types of bifurcations can happen, leading to rich equilibrium dynamics such as limit cycles and chaos. We show that opening up the closed economy can cause aggregate instability.     

The local bifurcation of Ramsey equilibrium

Summary The elasticity of substitution has been proposed as one factor in the generation of aggregate fluctuations in dynamic models with incomplete markets. We study the existence of periodic solutions in a one-sector neoclassical capital accumulation model under borrowing constraints with infinitely-lived heterogeneous agents. A dynamical system representing an equilibrium profile with only the most patient agent holding capital is analyzed when capital income is not an increasing function of total capital. Conditions for the linear approximation system at a steady state to have an eigenvalue of — 1 are found. A one-parameter family of maps based on a perturbation of the production function is introduced and the dynamical system is reduced to 1 dimension via an application of a center manifold theorem. Conditions for a stable flip bifurcation are shown to hold at the steady state.This paper is dedicated to Professor Nicolas Spulber, one of the great pioneers in the study of growth theory. He brought us together and encouraged our joint work on Ramsey equilibrium theory.We thank Nicolas Spulber for his usual insightful comments and we thank Michele Boldrin for a useful discussion. We also thank a referee for suggesting improvements in the paper as well as the seminar participants at the University of Rochester and Cornell University for their comments on the paper.     

Investment rates and the aggregate production function

In this paper we consider a simple version of the neoclassical growth model, and carry out an empirical analysis of the main determinants of aggregate investment across countries. The neoclassical growth model predicts that aggregate investment may be influenced by income growth, the capital income share, the relative price of capital, taxes, and other market distortions. We check these investment patterns for both OECD and non-OECD countries. We also decompose investment data into equipment and structures, and explore major factors affecting their relative prices. These empirical exercises shed light into the shape of the neoclassical production function.     

On the existence of a market for second hand physical capital: An empirical test of the Keynesian and neoclassical assumptions

In this paper we test Keynesian and neoclassical assumptions concerning the existence of second-hand markets for physical capital. These alternative views of the dynamic profit maximizing firm lead to distinct equilibrium price equations. We use a sample of 4-digit SIC consumer goods and capital goods industries over 1967–1975 to test the relative goodness of fit of the competing price equations. We find consumer goods industries conform better to the Keynesian assumptions and capital goods industries more nearly approximate the neoclassical view of the world. We investigate the policy implications of our finding of sector heterogeneity by constructing a three-sector macro model with a Keynesian consumption goods sector, a neoclassical capital-for-consumption-goods-production sector, and a neoclassical capital-for-capital-goods-production sector. Comparative static analysis reveals that both monetary and fiscal policy variables have ambiguous short run effects on real variables in this heterogeneous three-sector model, which may be the minimum level of detail consistent with the observed behavior of US manufacturing industries.     

Endogenous technological progress in a multi-sector growth model

This paper presents an endogenous growth model driven by human capital, where human capital can be allocated across three sectors: the production of the final consumption good, the educational sector and the production of technological capital (in the form of knowledge or ideas). In our model, which also includes public expenditure and population growth, labor augmenting technical progress is endogenous and this enriches the transitional dynamics of the economy. With respect to ideas-based growth models, we assume knowledge is produced according to a neoclassical technology, combining ideas and human capital. Such an assumption is motivated by empirical works showing the existence of significant decreasing returns in the creation of ideas at the aggregate level (as Kortum, 1993; and Pessoa, 2005) and of the weak relationship between some inputs of the knowledge production process (as the number of researchers) and the total factor productivity growth rate (as Jones, 2002). Under some general conditions, this economy exhibits the existence of a steady state equilibrium and an unstable multidimensional manifold. Numerical examples are provided to show the existence of stable arms.     

LONG-RUN GROWTH PROJECTIONS AND THE AGGREGATE PRODUCTION FUNCTION: A SURVEY OF MODELS USED BY THE U.S. GOVERNMENT

This paper examines the theory and method behind the long-run growth projections of four prominent models used within the U.S. government. The growth models of the Congressional Budget Ofice, the Social Security Administration, the Office of Management and Budget, and the General Accounting Office are all firmly based on the neoclassical framework of an aggregate production function, but several practical dfferences exist. Most notably, the CBO and GAO models endogenize capital accumulation, while the SSA and OMB simply assume that labor productivity growth will continue at historical rates. Although recent endogenous growth theory and the expanding empirical literature on cross-sectional variation emphasize alternative factors, the US. government agencies remain appropriately committed to the traditional, neoclassical framework as a tool for projecting long-run growth.     

Three levels of education and the economic growth

The aim of this article is to solve the question how the three main stages of education contribute to the labour productivity growth in selected 125 countries in the period 1999–2014. The model is based on the neoclassical production function enhanced with human capital. The authors draw on the Penn World Tables 9.0 and UNESCO databases. The key benefit of this article is that human capital is characterized according to the returns to education from average number of years of formal schooling at the primary, secondary and tertiary level. Based on the panel data analysis, the contributions of capital and of the three levels of education to the growth of labour productivity are estimated. At the same time, the model allows to estimate the contribution of total factor productivity. The results of the analysis show that tertiary education has the strongest impact on labour productivity across the considered economies. At the same time, the breakdown of aggregate human capital by level of education leads to better clarification of the effects of human capital and physical capital on labour productivity. The conclusions also indicate a tendency towards rising returns to scale induced by the secondary and tertiary education.     

Recursive equilibrium in endogenous growth models with incomplete markets

This paper analyzes the existence of recursive equilibria in a class of convex growth models with incomplete markets. Households have identical CRRA-preferences, production displays constant returns to scale with respect to physical and human capital, and all markets are competitive. There are aggregate productivity shocks that affect aggregate returns to physical and human capital investment (stock returns and wages), and there are idiosyncratic shocks to human capital (idiosyncratic depreciation shocks) that only affect individual human capital returns. Aggregate and idiosyncratic shocks follow a joint Markov process. Conditional on the aggregate state, idiosyncratic shocks are independently distributed over time and identically distributed across households. Finally, households have the opportunity to trade assets in zero net supply with payoffs that depend on the aggregate shock, but markets are incomplete in the sense that there are no assets with payoffs depending on idiosyncratic shocks. It is shown that there exists a recursive equilibrium for which equilibrium prices (returns) only depend on the exogenous aggregate shock variable (the wealth distribution is not a relevant state variable). Moreover, the allocation associated with this recursive equilibrium is identical to the equilibrium allocation of an economy in which households live in autarky and face both aggregate and idiosyncratic risk.I would like to thank for helpful comments Peter Howitt, Bob Lucas, Michael Magill, Tomo Nakajima, Herakles Polemarchakis, Martine Quinzii, Kevin Reffett, an anonymous referee, and seminar participants at various universities and conferences.     

Trevor Swan on Equilibrium Growth with Technical Progress

There is an important difference between Swan's 1956 exposition of neoclassical growth and that of Solow. In particular, Swan's focus is on the output–capital ratio and its behaviour over time while Solow's focus is on the capital–labour ratio and its behaviour over time. Related to this, is the clear (and correct) statement to be found in Swan's article of the behaviour of the output–capital ratio in equilibrium and the determination of the equilibrium rate of growth of output in the presence of technological progress.     

Growth,economic structure,and residential distribution of a small city

This article presents a growth model of a small open city with economic structure and geography. The city which is located along a line segment has three, industrial, services and housing, sectors. The spatial growth model of a small city synthesizes the main ideas in some important models in the neoclassical growth theory, urban economics, and the literature of economic growth of small open economies. We show that the dynamic system has a unique equilibrium. We also simulate the motion of the urban economy over time and space. The unique feature of our approach is to treat production activities, economic structure, residential distribution, capital accumulation, and consumption on the basis of microeconomic mechanism as an integrated whole. Our simulation provides some important insights into the processes of the urban economic growth. For instance, under certain conditions, when the industrial sector’s productivity is increased, the wage rate, price of services, capital intensities of the services and industrial sectors, and per-worker output levels of the two sectors are increased. The total labor supply, the capital stocks employed by the three sectors and the labor forces by the service and industrial sectors are all increased. The shares of the three sectors are not affected by the technological change in the long term, even though the shares are initially affected. The per capita consumption level of the industrial goods rises and the consumption level of services falls. The land and housing rents are increased and the consumption of housing per household falls. Moreover, the current account balance tends to be more in surplus and the growth rate is increased.     

Australian Business Investment: A New Look at the Neoclassical Approach*

This paper attempts to reconcile neoclassical theory with Australian investment data. We argue that, by focusing almost exclusively on the demand for capital services, neoclassical investment theory neglects two related decisions: the decision to own the existing capital stock, and the decision to produce new capital goods. We propose a simple model of investment behaviour that integrates production decisions with portfolio decisions. Careful consideration is given to the determination of the price of capital, the rental price of capital, and the return on capital. The model is estimated by FIML, and a number of simulation results are reported.     

A Post-Keynesian Model of Accumulation with a Minskyan Financial Structure

Abstract

Minsky's theory of financial instability is a strong alternative to neoclassical theory. Many Post-Keynesian authors use this analysis in order to elaborate models that give rise to crises or business cycles. Nevertheless, none of them has directly linked growth and financial structure. This article proposes a simple macroeconomic model linking the accumulation of capital and the state of the financial structure as defined by Minsky. The analysis shows how a capitalist economy may become financially fragile, and it suggests that instability is apt to be the rule.