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.

Tuesday, September 02, 2014

Failing to Empirically Render Visible What Was Hidden

Figure 1: Wage Share versus Ratio of Rate of Profits
1.0 Introduction

Consider the theory that Sraffa's standard system can be used to empirically predict distribution and prices in existing economies. Although individual commodities might be produced with extremely labor-intensive or capital-intensive (at a given rate of profits?) processes, large bundles of commodities chosen for technical characteristics, such as net output or wage goods, would be expected to be of average labor intensity. And the standard commodity formalizes the idea of a commodity of average capital intensity.

The data I looked at rejected this theory as a universal description of economies around the world.

2.0 Theory

The standard system is here defined for a model of an economy in which all commodities are produced from labor and previously produced commodities. The technique in use is characterized by the Leontief input-output matrix A and the vector a0 of direct labor coefficients. The gross output, q, of the standard system is a (right hand) eigenvector of the Leontief input-output matrix, corresponding to the maximum eigenvalue of the matrix:

(1 + R) A q = q,

where R is the maximum rate of growth (also known as the maximum rate of profits). The maximum rate of profits is related to the maximum eigenvalue, λm, by the following equation:

R = (1λm) - 1

From previous empirical work, I know that the maximum rate of profits is positive for all countries or regions in my data. The standard system is defined to operate on a scale such that the labor employed in the standard system is a unit quantity of labor:

a0 q = 1

The standard commodity, y, is the net output of the standard system:

y = q - A q

In the standard system, such aggregates as gross output, the flow of capital goods consumed in producing the gross output, the net output, the commodities paid in wages, and the commodities consumed out of profits all consist of different amounts of a single commodity basket, fixed in relative proportions. Those proportions spring out of the technical conditions of production in the actual economy.

Prices of production represent a self-reproducing system in which tendencies for capitalists to disinvest in some industries and disproportionally invest in other industries do not exist. In some sense, they arise in an economy in which all industries are expanding so as to maintain the same proportions. Such prices can be represented by a row vector, p, satisfying the following equation:

p A(1 + r) + a0 w = p,
where r is the rate of profits and w is the wage paid out of the net product. The adoption of the standard commodity as numeraire yields the following equation:
p y = 1

One can derive an affine function for the wage-rate of profits. (Hint: multiply both sides of the first equation above for prices of production above on the right by the standard commodity.) This relationship is:

w = 1 - (r/R)

Prices of production in the standard system can easily be found for a known rate of profits.

p = a0 [I - (1 + r) A]-1 [1 - (r/R)]

If wages were zero, the rate of profits would be equal to its maximum in the standard system. If the rate of profits were zero, the wage would be equal to unity. The wage represents a proportion of the net output of the standard system. It declines linearly with an increased rate of profits.

The gross and net outputs of any actually existing capitalist economy cannot be expected to be in standard proportions, particularly since some (non-basic) commodities are produced that do not enter into the standard commodity. But do conclusions that follow from the standard system hold empirically? in particular, the average rate of profits, the proportion of the net output paid out in wages, and market prices are observable. Given the average rate of profits for the economy as a whole, the proportion of the standard commodity paid out in wages can be calculated. Is this proportion approximately equal to the observed proportion of wages? Do the corresponding relative prices of production calculated with the standard commodity closely resemble actual relative market prices? This post answers the question about wages. The empirical adequacy of prices of production is left to a later post.

3.0 Results and Discussion

I looked at data on 87 countries or regions, 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. The data covers up to 57 industries. (Not all industries exist in each country.)

For each country or region, I calculated:

  • The observed proportion of the net output paid out on wages.
  • The observed rate of profits, as the proportion of the difference between net output and wages to the total prices of intermediate inputs.
  • The maximum rate of profits for the standard system.
  • The ratio of the observed rate of profits to the maximum rate.

Figure 2 shows the distributions of the observed and maximum rate of profits.

Figure 2: Distribution of Actual Rate of Profits and Maximum in Standard System

Four countries or regions in the data had an actual rate of profits exceeding the theoretical maximum rate of profits: The rest of North America, Uruguay, Belgium, and Cyprus. The rest of North America is a region consisting of Bermuda, Greenland, and Saint Pierre and Miquelon. The four countries and regions are excluded from the linear regression and statistics given below.

Figure 1 shows the results of a linear regression of the wage on the ratio of the rate of profits. If, for each country or region, the standard system were empirically applicable to that country or region the intercept of the regression line would be near one, and the slope would be approximately negative one. But the 99% confidence intervals of the intercept and slope do not include these values. In this sense, the theory is rejected by the data.

Figure 1 points out the twelve countries with the wage furthest away from the prediction from the standard system. Why might the theory be off for these countries and the four excluded from the regression? Perhaps the net output is not near standard proportions. This possible variation of between the proportions of the standard commodity and the actual net output is abstracted from when plugs the observed rate of profits into the wage-rate of profits function for the standard system. I have looked at wage-rate of profits curves, drawn with the observed technique in use and the observed net output as numeraire. And countries far from the theory generally stick out as having wage-rate of profits curves with extreme curvatures.

Another possibility is that the industries in an economy are not earning nearly the same rate of profits, not merely because of barriers to entry but because of the economy not being in equilibrium. Prices of production, for any numeraire do not prevail.

Another possibility is that the Leontief matrix and the vector of direct labor coefficients do not capture the economic potential of the country or region. For example, the calculation of the rate of profits abstracts from the existence of land and fixed capital. Most interestingly, suppose the country or region does not characterize an isolated economic system. A region in the data combines several countries for which data is difficult to get. And the above analysis highlights several of these regions: the rest of North America, Central America, and the rest of Middle East (which consist of all of the Middle East besides Turkey). Or the country under consideration might be small and heavily dependent on imports and exports. You might notice Hong Kong and Singapore, which are important international ports. Think also of small countries that provide off-shore banking facilities. Recent events have alerted me to Cyprus serving this purpose for the countries that were formerly in the Soviet Union. I do not know much about Ireland, but recent discussion of how Apple shields its profits makes me wonder about the reported profits for its economy.

I do not know what to fully make of this analysis. The empirical use of the standard commodity seems to be more of a heuristic than the application of a claimed universal law. And the failure of its application seems to point out aspects of the deviating countries that seem of economic interest.

Appendix: Data Tables
Table 1: Descriptive Statistics for Rate of Profits (Four Countries Removed)
Rate of
Rate of
Ratio of
Observed Rate
To Maximum
Sample Size838383
Std. Dev.26.08814.8980.138
Coeff. of Var.0.3070.3060.234
1st Quartile66.19539.9470.476
3rd Quartile104.13958.1240.662
Interquartile Range/Median0.4400.3840.323
Table 2: Descriptive Statistics for Wages (Four Countries Removed)
StatisticWage in
Sample Size8383
Std. Dev.0.1380.085
Coeff. of Var.0.3380.198
1st Quartile0.3380.360
3rd Quartile0.5240.491
Interquartile Range/Median0.4380.289
Update (16 September 2014): The analysis reported above is based on Leontief input-output matrices which include investment as a sector. Apparently, it is common in Computational General Equilibrium (CGE) models to treat investment as endogenous, in some sense. I plan on redoing the analysis with this sector removed and with disaggregated investment included in final demands.