Wednesday, December 31, 2014


I study economics as a hobby. My interests lie in Post Keynesianism, (Old) Institutionalism, and related paradigms. These seem to me to be approaches for understanding actually existing economies.

The emphasis on this blog, however, is mainly critical of neoclassical and mainstream economics. I have been alternating numerical counter-examples with less mathematical posts. In any case, I have been documenting demonstrations of errors in mainstream economics. My chief inspiration here is the Cambridge-Italian economist Piero Sraffa.

In general, this blog is abstract, and I think I steer clear of commenting on practical politics of the day.

I've also started posting recipes for my own purposes. When I just follow a recipe in a cookbook, I'll only post a reminder that I like the recipe.

Comments Policy: I'm quite lax on enforcing any comments policy. I prefer those who post as anonymous (that is, without logging in) to sign their posts at least with a pseudonym. This will make conversations easier to conduct.

Friday, October 17, 2014

r > g In A Steady State

1.0 Introduction

This post presents a model of distribution that Luigi Pasinetti developed. It is one of a family of models. Other important models in this family were developed by Richard Kahn, Nicholas Kaldor, and Joan Robinson. These models have been extended in various ways and presented in textbooks. One can see this family as having extended work by Roy Harrod, and as being related to the work of Michal Kalecki and even of Karl Marx.

2.0 The Model

2.1 Definitions

Consider a simple closed economy with no government. All income is paid out in the form of either wages or profits:

Y = W + P,

where W is total wages, P is total profits, and Y is national income. Total savings is composed of savings by workers and by capitalists, where capitalists are a class whose members receive income only from profits:

S = Sw + Sc

S is total savings. Sw is workers' savings, and Sc is capitalist savings. Profits are also split into two parts:

P = Pw + Pc,

where Pw is returns on the capital owned by the workers, and Pc is the return on the capital owned by the capitalists. The behavior assumption is made that both workers and capitalists save a (different) constant proportion of their income:

Sc = sc Pc
Sw = sw (W + Pw)

sc is the capitalists' (marginal and average) propensity to save. sw is the workers' (marginal and average) propensity to save. The propensities to save are assumed to lie between zero and one and to be in the following order:

0 ≤ sw < sc ≤ 1

Workers' savings are assumed to be insufficient to fund all the investment occurring along a steady-state growth path.

The value of the capital stock is divided up into that owned by the workers and by the capitalists:

K = Kw + Kc,

where K is the value of the capital stock, Kw is the value of the capital stock owned by the workers, and Kc is the value of the capital stock owned by the capitalists

2.2 Steady State Equilibrium Conditions

Along a steady-state growth path, in this model, all capital earns the same rate of profits, r:

r = P/K = Pc/Kc = Pw/Kw

It follows from the above set of equations that the ratio of the profits received from the workers to the profits received by the capitalists is equal to the ratio of the value of capital that each class owns:

Pw/Pc = Kw/Kc

Likewise, one can find the ratio of total profits to the profits obtained by the capitalists:

P/Pc = K/Kc

The analysis is restricted to steady-state growth paths where the value of the capitalists' capital and the value of the workers' capital is growing at the same rate:

S/K = Sc/Kc = Sw/Kw

The ratio of profits to savings is the same for the economy as a whole and for workers:

P/S = (P/K)/(S/K) = (Pc/Kc)/(Sc/Kc) = Pc/Sc

Or, after a similar logical deduction for workers:

P/S = Pc/Sc = Pw/Sw

Along a steady-state growth path, planned investment, I equals savings:

I = S
2.3 Deduction of the Cambridge Equation

The following is a series of algebraic substitutions based on the above:

P/I = P/S = Pc/Sc = Pc/(sc Pc) = 1/sc


P = (1/sc) I

The share of profits in national income is determined by the savings propensity of the capitalists and the ratio of investment to national income:

(P/Y) = (1/sc) (I/Y)

Recall that the rate of profits is the ratio of profits to the value of capital:

r = P/K = (1/sc) (I/K)

Recognizing that I/K is the rate of growth, g, one obtains the famous Cambridge equation:

r = g/sc

As long as the capitalists consume at least some of their income, the rate of profits is greater than the rate of growth along a steady-state growth path. And along such a path the share of income going to profits will be constant.

3.0 Discussion

If one assumes given investment decisions, the Cambridge Equation tells us what rate of profit is compatible with a steady state growth path in which the expectations underlying those investment decisions are satisfied.

Consider two steady states in which the same rate of growth is being obtained. Suppose that along one path workers have a higher propensity to save. Within broad limits, this greater willingness to save among workers has no effect on determining either the share of profits in income or the rate of profits. Only the capitalists' saving propensity matters for the steady state rate of profits, given the rate of growth. Would a capitalist economy have a tendency to approach such a growth path, given a sufficient length of time? I think such stability would entail the evolution of institutions, conventions, the labor force, and what is seen as common sense, including among dominant political parties.

The above model might have some relevance to current political economy discussions elsewhere.

Tuesday, October 14, 2014

Jean Tirole, A Practitioner Of New Industrial Organization

I have occasionally summarized certain aspects of microeconomics, concentrating on markets that are not perfectly competitive. Further developments along these lines can be found in the theory of Industrial Organization.

One can distinguish in the literature two approaches to IO know as old IO and new IO. Old IO extends back to the late 1950s. Joe Bain and Paolo Sylos Labini laid the foundations to this approach, and they were heralded by Franco Modigliani. I have not read any of Bain and only a bit of Sylos Labini. Sylos was a Sraffian and quite critical of neoclassical economics. He also had interesting things to say about economic development.

As I understand it, new IO consists of applying game theory to imperfectly competitive and oligopolistic markets. I gather new IO took off in the 1980s. Jean Tirole, the winner of this year's "Nobel" prize in economics, is a prominent exponent of new IO.

One can tell interesting stories about corporations with both old IO and new IO. For example, Tirole has had something to say about vertical integration which, based on what I've read in the popular press, might be of interest to me. (Typically, when I explore the theory of vertical integration, following Luigi Pasinetti, the integration is only notional, not at the more concrete level of concern in IO.)

I wonder, though, whether economists can point to empirical demonstrations of the superiority of new IO over old IO. Or have economists studying IO come to embrace new IO more because of the supposed theoretical rigor of game theory? Are specialists in IO willing to embrace the indeterminism that arises in game theory, what with the variety of solution concepts and the existence of multiple equilibria in many games? Or do they insist on closed models with unique equilibria?

  • Franco Modigliani (1958). New developments on the Oligopoly Front, Journal of Political Economy, V. 66, No. 3: pp. 215-232.

Update (same day): Corrected a glitch in the title. Does this Paul Krugman post read as a direct response to my post?

Tuesday, September 30, 2014

Noncommunicating Literatures?

During the 20th century, a number of economists more or less independently developed ideas associated with input-output analysis, activity analysis, modeling the economy as a self-sustaining circular flow, and the revival of classical political economy. I think of:

  • Leonid Kantorovich: The Soviet economist who shared the 1975 Nobel Memorial Prize in Economic Sciences with Tjalling Koopmans.
  • Wassily Leontief: Always emphasized developing an empirically operational version of these ideas.
  • Father Maurice Potron: I stumbled across two references to him. I know nothing otherwise about his work.
  • Walter Isard: Extended input-output analysis to regional economics.
  • Richard Stone: Developed the idea of a Social Accounting Matrix and conventions for national income accounting.
  • Jacob Schwartz: Criticized the mainstream economics of his time on the basis of linear economic models.
  • Piero Sraffa: Criticized the mainstream economics of his time on the basis of linear economic models.
  • John Von Neumann: A mathematician, not an economist.

I wonder how many make connections between the scholarly literature building on the work of each of these researchers. I am not at all sure anybody explicitly and consciously built on Potron or Schwartz.

  • Wassily W. Leontief (1936). Quantitative Input and Output Relations in the Economic Systems of the United States, Review of Economic Statistics, V. 18, N. 3 (Aug). pp. 105-125.
  • Walter Isard (1951) Interregional and Regional Input-Output Analysis: A Model of a Space-Economy, Review of Economics and Statistics, V. 33, No. 4 (Nov.): pp. 318-328.
  • Jacob T. Schwartz (1961). Lectures on the Mathematical Method in Analytical Economics, Gordon and Breach.
  • Piero Sraffa (1960). Production of Commodities by Means of Commodities: A Prelude to a Critique of Economic Theory, Cambridge University Press.
  • J. Ricard N. Stone (1966). The Social Accounts from a Consumer Point of View, Review of Income and Wealth, V. 12, Iss. 1 (Mar.): pp. 1-33. [I HAVEV'T READ THIS OR ANYTHING ELSE BY STONE]
  • John von Neumann (1945-1946) A Model of General Economic Equilibrium, Review of Economic Studies, V. 13, No. 1: pp. 1-9.

Friday, September 19, 2014

Hayek Not Opposed To Keynes On Political Principle

With characteristic cheerful carelessness, Noah Smith misinforms hapless Bloomberg readers:

"Friedrich Hayek tried to argue against Keynes' theories, but for whatever reason, he lost the debate among economists in the 1930s. But Hayek would have the last laugh, because in his book, 'The Road to Serfdom,' he attacked Keynes from a very different angle. Instead of saying Keynes' theories were wrong, Hayek prophesied that Keynesian stabilization policies would lead down the slippery slope to totalitarianism."

As a matter of fact, Hayek said nearly the opposite:

"There is, finally, the supremely important problem of combating general fluctuations of economic activity and the recurrent waves of large-scale unemployment which accompany them. This is, of course, one of the gravest and most pressing problems of our time. But, though its solution will require much planning in the good sense, it does not - or at least need not - require that special kind of planning which according to its advocates is to replace the market. Many economists hope, indeed, that the ultimate remedy may be found in the field of monetary policy, which would involve nothing incompatible even with nineteenth-century liberalism. Others, it is true, believe that real success can be expected only from the skilful timing of public works undertaken on a very large scale. This might lead to much more serious restrictions of the competitive sphere, and, in experimenting in this direction, we shall have to carefully watch our step if we are to avoid making all economic activity progressively more dependent on the direction and volume of government expenditure. But this is neither the only nor, in my opinion, the most promising way of meeting the gravest threat to economic security. In any case, the very necessary efforts to secure protection against these fluctuations do not lead to the kind of planning which constitutes such a threat to our freedom." -- Frierich A. Hayek, The Road to Serfdom (1944), Chapter IX.

Both Hayek and Keynes drew on nineteenth-century Liberalism. They agreed that the inherited lines limiting government action needed to be redrawn. Keynes said as much in the 1920s, in his essays republished in Essays in Persuasion. Hayek's reference above, to the "timing of public works" is to Keynes' ideas. Keynes doubtless would have redrawn the lines more broadly then Hayek. But Hayek explicitly says above that Keynes' approach is neither necessarily a threat to freedom, nor a station on the way to totalitarianism. Hayek says his differences with Keynes are pragmatic, a dispute over what is likely to be effective.

Wednesday, September 17, 2014

On And Off The Wage-Rate Of Profits Frontier

Figure 1: Wage-Rate of Profits Frontier for Seven Countries

This post reports on the analysis of wage-rate of profits frontiers drawn for each of 87 countries or regions. The input-output tables used for this analysis are derived from the GTAP 6 Data Base, compiled by the Global Trade Analysis Project at Purdue. (I had help extracting the database and putting it in a format that I can use.) GTAP 6 data is meant to cover the year 2001. Figure 1, above, presents seven examples of such frontiers. Figure 1 also shows two points:

  • The observed wage share and rate of profits as a point, typically off the frontier.
  • The nearest point on the frontier, in some sense, to the observed point.

The wage-rate of profits frontiers is a decreasing function relating the wage to the rate of profits. The wage, in this case, is expressed as a proportion of the output of the unit output of the industry producing the numeraire commodity basket. I take the numeraire to be in the same proportions as observed net outputs (also known as final demands) in the data. The numeraire-producing industry is conceptually scaled to a level such that the system that produces it employs one unit labor. Since different countries produce commodities in different proportions, the wage is measured for a different numeraire for each wage-rate of profits frontier on my graphs.

The wage-rate of profits frontier is drawn based on several assumptions. First, one assumes the existence of steady state prices. That is, relative prices are the same for inputs and outputs. Under this assumption, the same rate of profits is earned in all industries in a country or region. I also assume wages are paid out of the output at the end of the year, not advanced at the beginning of the year. Prices, with the distribution of income under these assumptions, are known as prices of production.

One might expect the curvature of empirically-developed wage-rate of profits frontiers to deviate from a straight line, with the convexity even being different for different parts of a frontier. Such curvature arises from variations in capital-intensities, so to speak, between net output and the intermediate goods used in producing net output.

The observed wage and rate of profits might be off the frontier for a number of reasons. Wages are paid throughout the year, so even if prices of production prevailed, the assumptions with which I am drawing the frontiers are not exact. But points will also lie off the frontier because prices of production cannot be expected to prevail. Entrepreneurs will have different expectations. Some of these expectations will be disappointed, and some will not be optimistic enough. I also wonder about the importance of foreign trade. If a country is thoroughly integrated in the global economy, might its rate of profits be somewhat independent of the system formed by domestic production?

Anyways, this data allows one to explore the empirical adequacy of the theory of prices of production. How far away do the countries or regions, as described by this dataset, lie from the wage-rate of profits frontier? In the data, nine countries or regions had an actual rate of profits exceeding the theoretical maximum: the Philippines, Sri Lanka, the Rest of North America, Uruguay, Austria, Belgium, Croatia, Cyprus, and the Rest of Middle East. These countries are excluded from the histogram and the statistics given below.

Using the observed rate of profits, one can predict the wage from the wage-rate of profits frontier. Figure 1 shows the distribution of the absolute error in such predictions, while Table 1 provides descriptive statistics for this distribution. Uganda, Singapore, Vietnam, Hong Kong, Luxembourg, and Central America are the countries or regions with the wage on the frontier, at the observed rate of profits, furthest from the observed wage. I find encouraging how the countries or regions that stick out as most anomalous are, mostly, either regions that, for purposes of data collection, consist of disparate countries aggregated together; small countries that presumably have economies that cannot be regarded as systems separate from the economies of their neighbors; or countries and ports that are notable for heavy involvement in international trade.

It seems that most countries lie close to the wage-rate of profits frontier constructed from their observed input-output relations and produced commodities.

Figure 2: Distribution of Distance to Wage-Rate of Profits Frontier

Table 1: Descriptive Statistics for Wages (Four Countries Removed)
to Frontier
Sample Size78
Std. Dev.0.08998
Coeff. of Var.1.30187
1st Quartile0.01915
3rd Quartile0.08330
Interquartile Range/Median1.63703

Thursday, September 11, 2014

Survey Of Empirical Evidence Showing Nonexistence Of Supply And Demand Curves

A theme of this blog is that wages and employment are not determined by, and cannot be determined by, the interaction of well-behaved supply and demand curves in the so-called labor market. I here bring to your attention two new papers supporting this claim:

  • Steve Fleetwood, Do labour supply and demand curves exist?, Cambridge Journal of Economics, V. 38, Iss. 5 (Sep. 2104): pp. 1087-1113.
  • The objective of this paper is to show that circumstantial and empirical evidence for the existence of labour supply and demand curves is at best inconclusive and at worst casts doubt on their existence. Because virtually all orthodox models of labour markets, simple and complex, are built upon the foundation stones of labour supply and demand curves, these models lack empirically supported foundations. Orthodox labour economists must, therefore, either provide stronger evidence or stop using labour supply and demand curves as the foundation stones of their models. The conclusion discusses implications for future orthodox and heterodox labour economics.
  • Daniel Kuehn, The importance of study design in the minimum wage debate, Economic Policy Institute (4 Sep. 2014).
  • This paper reviews the empirical literature on the employment effects of increases in the minimum wage. It organizes the most prominent studies in this literature by their use of two different empirical approaches: studies that match labor markets experiencing a minimum-wage increase with an appropriate comparison labor market, and studies that do not. A review of this literature suggests that:
    • The studies that compare labor markets experiencing a minimum-wage increase with a carefully chosen comparison labor market tend to find that minimum-wage increases have little or no effect on employment.
    • The studies that do not match labor markets experiencing a minimum-wage increase with a comparison labor market tend to find that minimum-wage increases reduce employment.
    A better understanding of which approach is more rigorous is required to make reliable inferences about the effects of the minimum wage. This paper argues that:
    • Labor market policy analysts strongly prefer studies that match "treatment" with "comparison" cases in a defensible way over studies that simply include controls and fixed effects in a regression model.
    • The studies using the most rigorous research designs generally find that minimum-wage increases have little or no effect on employment.
    • Application of these findings to any particular minimum-wage proposal requires careful consideration of whether the proposal is similar to other minimum-wage policies that have been studied. If a proposal occurs under dramatically different circumstances, the empirical literature on the minimum wage should be invoked with caution.