Wages, Employment Not Determined By Supply And Demand

1.0 Introduction
One theme of this blog is that the introductory textbook model of the labor market is incorrect. Two recent papers make this point from the perspective of institutional economics.

2.0 The Impossibility of a Perfectly Competitive Labour Market
The abstract of the first paper under consideration states:

Using the institutional theory of transaction costs, I demonstrate that the assumptions of the competitive labour market model are internally contradictory and lead to the conclusion that on purely theoretical grounds a perfectly competitive labour market is a logical impossibility. By extension, the familiar diagram of wage determination by supply and demand is also a logical impossibility and the neoclassical labour demand curve is not a well-defined construct. The reason is that the perfectly competitive market model presumes zero transaction costs and with zero transaction costs all labour is hired as independent contractors, implying that multi-person firms, the employment relationship and labour market disappear. With positive transaction costs, on the other hand, employment contracts are incomplete and the labour supply curve to the firm is upward sloping, again causing the labour demand curve to be ill-defined. As a result, theory suggests that wage rates are always and everywhere an amalgam of an administered and bargained price. -- Bruce E. Kaufman (2007). "The Impossibility of a Perfectly Competitive Labour Market", Cambridge Journal of Economics, V. 31: 775-787

Kaufman states that, "Institutional, post-Keynesian, radical and other heterodox economists have for many years expressed scepticism about the theoretical and empirical validity of the competitive model of labour markets." He cites the following literature:

• C. Kerr (1950). "Labour Markets: Their Character and Consequences", American Economic Review, V. 40 (May): 278-291
• G. Hodgson (1988). Economics and Institutions: A Manifesto for a Modern Institutional Economics, Philadelphia: University of Pennsylvania Press.
• D. Vickers (1996). "The Market: The Tyranny of a Theoretical Construct", in Employment, Economic Growth, and the Tyranny of the Market, (ed. by P. Aretis), Brookfield: Edward Elgar
• W. Streeck (2005). "The Sociology of Labour Markets and Trade Unions", in The Handbook of Economic Sociology (ed. by N. Smelser and R. Swedberg), 2nd edition, New York: Russel Sage
• S. Fleetwood (2006). "Rethinking Labour Markets: A Critical-Realist-Socioeconomic Perspective, Capital & Class, V. 107 (Summer): 59-89

As far as I can tell, none of these papers are about the Cambridge Capital Controversy, which is the basis of my favorite critique of the introductory textbook model of labor markets.

3.0 Professor Lester and the Neoclassicals
The abstract of the second paper follows:

"This article revisits what is remembered as the 'Marginalist Controversy' in light of its immediate context and object: the substantial late 1940s increase in the federal minimum wage. Richard Lester's critique of 'marginalist theory,' and its implication that the minimum wage would be detrimental to labor was founded upon empirical studies and surveys that supported an Institutionalist conception of the business firm, the labor market, and economic policy. His disputants, Fritz Machlup and George Stigler, countered his points on the basis of what they took to be 'economic theory'. By any measure, including those of their own intellectual allies, Machlup and Stigler faired poorly. Interestingly, they are collectively remembered as having been triumphant in this debate. The essay suggests that what triumphed was not their arguments but rather the Neoclassical school of economics that Stigler represented." -- Robert E. Prasch (2007). "Professor Lester and the Neoclassicals: The 'Marginalist Controversy' and the Postwar Academic Debate Over Minimum Wage Legislation: 1945-1950", Journal of Economic Issues, V. 41, N. 3 (September): 809-826."

I had not known that the context of the debate about full cost pricing included minimum wage policies. Prasch makes the point that neoclassicals often misrepresent their position as a defense of economic theory, instead of as of a specific theory. In addition to drawing on a specific school of thought, Institutionalist economics, Lester had survey data supporting his position that the typical firm does not operate in a region of increasing marginal cost. It is this sort of data, which has been repeatedly replicated, that Milton Friedman argued, in his famous paper on positive economics, should be ignored.

Negative Price Wicksell Effect, Positive Real Wicksell Effect

1.0 Introduction
I have previously suggested a taxonomy of Wicksell effects. This post presents an example with:

• The cost-minimizing technique varying continuously along the so-called factor-price frontier
• Negative price Wicksell effects
• Positive real Wicksell effects
• Price Wicksell effects greater in magnitude than real Wicksell effects.

This example is due to Saverio M. Fratini ("Reswitching and Decreasing Demand for Capital").

2.0 Technology
Suppose technology consists of a continuum of techniques indexed by the parameter θ, where θ is a real number restricted to the interval [0, 1]:

0 ≤ θ ≤ 1

Each technique consists of the three Constant-Returns-to-Scale processes in Table 1. No commodity is basic, in Sraffa's sense, in any technique in this technology. In the first process in a technique, θ-grade iron is produced directly from unassisted labor. In the second process, labor transforms the θ-grade iron into θ-grade steel. Finally, in the third process, labor transforms θ-grade steel into corn, the consumption good in the model. All processes take a year to complete, and all processes totally use up their input.

Table 1: The Technique Indexed by θ

Inputs	Industry Sector
	θ-Grade Iron	θ-Grade Steel	Corn
Labor (Person-Yrs)	1/(1 + θ)	θ	3/(1 + θ)
Iron (Tons)	0	1	0
Steel (Tons)	0	0	1
Corn (Bushels)	0	0	0
Output	1 Ton	1 Ton	1 Bushel

Capital goods are specific in their uses in this example. θ₁-grade steel cannot be made out of θ₂-grade iron when θ₁ ≠ θ₂.

3.0 Stationary-State Quantity Flows
Suppose in Table 1 that:

• The first process is used to produce (1 + θ)/(4 + θ + θ²) tons of θ-grade iron
• The second process is used to produce (1 + θ)/(4 + θ + θ²) tons of θ-grade steel
• The third process is used to produce (1 + θ)/(4 + θ + θ²) bushels corn

Then one person-year would be employed over these three processes. Capital goods would consist of (1 + θ)/(4 + θ + θ²) tons of θ-grade iron and (1 + θ)/(4 + θ + θ²) tons of θ-grade steel. The capital goods would be used up throughout the latter two sectors, but reproduced at the end of the year. Net output would consist of (1 + θ)/(4 + θ + θ²) bushels corn per person-year.

4.0 Prices
Given the technique, stationary state prices must satisfy the following three equations:

[1/(1 + θ)] w = p₁

p₁(1 + r) + θ w = p₂

p₂(1 + r) + [3/(1 + θ)] w = 1

where:

• p₁ is the price of a ton θ-grade iron;
• p₂ is the price of a ton θ-grade steel;
• w is the wage;
• r is the rate of profits.

A bushel corn is the numeraire. The above equations embody the assumption that labor is paid at the end of the year.

The above is a system of three equations in four unknowns, given the technique. It is a linear system, given the rate of profits. The solution in terms of the rate of profits is easily found. The so-called factor-price curve for a technique is:

w(r, θ) = (1 + θ)/[3 + θ(1 + θ)(1 + r) + (1 + r)²]

The price of a ton θ-grade iron is:

p₁(r, θ) = 1/[3 + θ(1 + θ)(1 + r) + (1 + r)²]

The price of a ton θ-grade steel is:

p₂(r, θ) = [(1 + r) + θ(1 + θ)]/[3 + θ(1 + θ)(1 + r) + (1 + r)²]

Given the technique and the rate of profits, these prices can be used to evaluate the value of the capital goods used in a stationary state.

5.0 The Cost-Minimizing Technique
The optimal technique to use at any given rate of profits maximizes the wage. The first-order condition for such maximization is found by equating the derivative of the factor-price curve to zero:

dw/dθ = 0

Or:

3 + θ(1 + θ)(1 + r) + (1 + r)² - (1 + θ)(1 + 2θ)(1 + r) = 0

For 0 ≤ r ≤ 2, the cost-minimizing technique is then:

θ(r) = {[3 + (1 + r)²]/(1 + r)}^1/2 - 1

For r > 2, a corner solution is found:

θ(r) = 1

Figure 1 illustrates the cost-minimizing technique.

Figure 1: The Choice of Technique

The graph in Figure 1 reaches a minimum at a rate of profits of (3^1/2 - 1). For (12^1/4 - 1) < θ < 1, two rate of profits have the corresponding cost-minimizing technique indexed by the given value of θ. In other words, this is an example of reswitching.

The index for the cost-minimizing technique can be plugged into the factor price curve for the technique to which it corresponds at a given rate of profits. Figure 2 displays the resulting so-called factor price frontier. The index θ varies continuously for 0 ≤ r ≤ 200% in Figure 2. As the rate of profits increases without bound, the frontier approaches a wage of zero.

Figure 2: The Factor-Price Frontier

6.0 Capital and Labor "Markets"
Fratini’s notes that this is a reswitching example in which the capital market initially appears to be in accord with out-dated neoclassical intuition. The above analysis has shown how to find physical quantities of capital goods per worker, how to evaluate them at equilibrium prices, and how to find net output per worker. Figure 3 shows the resulting plot of the value of capital per unit output. Fratini looks at the value of capital per worker instead. Either curve is continuous and downward-sloping. The regions above and below the rate of profits of (3^1/2 - 1) appear qualitatively similar and visually indistinguishable. This curve might be said to be a downward-sloping demand function for capital.

Figure 3: The Capital Market

The analogous curve looks very different for the labor market (Figure 4). The region with a positive Wicksell effect is a region with a high rate of profits and thus a low real wage. The demand function for labor might be said to be upward-sloping in the region with a positive real Wicksell effect.

Figure 4: The Labor Market

7.0 Conclusion
The example makes Fratini’s point. The shape of the relationship between the value of capital, either per worker or per unit output, and the rate of profits is not necessarily a good indicator of the presence of reswitching or reverse capital-deepening.

A "Nobel" Prize For Epicycles In Labor Economics?

Peter Diamond, Dale Mortensen, and Christopher Pissarides won the "Nobel" prize in economics this year. I do not have Bill Mitchell’s expertise on search theory and labor economics. Nevertheless, I thought I’d record my reactions.

As I understand it, Diamond, Mortensen, and Pissarides think labor would be described by by the interactions of well-behaved supply and demand functions for labor if it were not for the heterogeneity of workers and jobs and the time to form matches between them. The orthodox theory would be wrong even if workers and jobs were homogeneous. So I find puzzling why I should approve of this year’s award. I think my opinion is consistent with some of Alessandro Roncaglia’s observations of trends in mainstream economics.

David Ruccio and Richard McIntyre & Michael Hillard (Hat tip to Nick Kraft) have been critical of this year’s award. Paul Krugman has praised it. Doubtless, one could find more praise in the blogosphere.

Impact of Capital Controversies On Labor Economics

I think some with some exposure to economics might not be impressed by the Cambridge Capital Controversy because of the abstractness of capital. "Capital" can refer to finance, and it can refer to the means of production. And even if one thought that interest rates were determined by supply and demand, what quantity would be supplied or demanded? Loanable funds? Savings? One might expect capital theory to be complicated, even in the view of the defenders of mainstream theory. So why, some might rationalize, should one be surprised by aggregation problems?

I like to emphasize the labor market. This market might seem more concrete to many. (This is one of the illusions created by competition.) Consider cases in which firms have adapted their capital equipment and production techniques to the prices prevailing on both product and factor markets. A logical implication of capital reversing is that, given the level of output, such firms employ more workers at a higher wage. (I have deliberately worded the above to avoid saying, "Increasing wages lead to greater employment" - which is a claim about dynamics.) The sort of example I have in mind doesn't seem to depend on aggregating labor. I often motivate discussion of these matters with the introductory neoclassical textbook story on minimum wages, which is theoretically unfounded and only taught by bad economists. (Nose counting as a refutation of the above statement is a fallacy.)

I realize lots of literature backs up my position; I am not being original. I like to cite Graham White (2001) and Tony Aspromourgos (2001). I recently stumbled upon another economist who forcefully states a similar position.

John Weeks has been updating his 1989 book, A Critique of Neoclassical Macroeconomics. Two parts of the update-in-progress are currently available online: part I, part II. I extract some random quotes from the relevant chapter in part II:

"Reswitching implies an unexpected conclusion: theory tells us that in general capitalists will not necessarily select more labour-intensive techniques when wages fall.

This result is a potential disaster for the neoclassical macro model and its parable about real wages and employment."

"In the introduction to this book a quotation from The Times was cited, which ventured the assertion that '...few economists would argue with the general proposition that lower real wages will mean higher employment...' If it refers to theoretically competent neo-classical economists, this statement is false."

"One can conclude that when referring to actual economic outcomes, there is no theoretical basis for the generalization that lower real wages will stimulate more employment. The opposite conclusion has equal theoretical merit. The neoclassical parable, upon which so many policy prescriptions are based, is a false guide to real economies."

References

• Tony Aspromourgos (2001) "Is Labour Cheapening a Means to Reducing Involuntary (Labour) Unemployment?", History of Economics Review, V. 34: (Summer) pp. 7-18
• John Weeks (1989) A Critique of Neoclassical Macroeconomics
• Graham White (2001) "The Poverty of Conventional Economic Wisdom and the Search for Alternative Economic and Social Policies", The Drawing Board: An Australian Review of Public Affairs, V. 2, N. 2 (November): pp. 67-68.

Historians and Philosophers on Empirical Failures of Neoclassical Economics

Empirical evidence went against neoclassical economics in the following three cases:

• Empirical studies and surveys of businessmen found that they followed a full cost policy, not marginalism
• Behavioral economists have accumulated a body of experimental evidence, including preference-reversals and violations of transitivity, that people are not utility maximizers.
• David Card and Alan Krueger found that increased minimum wages did not decrease employment.

These incidents present data for philosophers, historians, and sociologists of economics. They can explore how mainstream economists reacted to these empirical findings. And three have done just this. Daniel Hausman and Philippe Mongin compare and contrast the reactions to full cost pricing and preference reversals. Tim Leonard compares and contrasts the reaction of mainstream economists to their findings on full cost pricing and on the minimum wage. In keeping with current trends, these articles are descriptive, not prescriptive. That is, they try to understand the positions of participants without passing judgement.

References

• Daniel M. Hausman and Philippe Mongin (1998) "Economists' Responses to Anomalies: Full-Cost Pricing versus Preference Reveresals" [Should this link work?]
• Thomas C. Leonard (2000) "The Very Idea of Applying Economics: The Modern Minimum-Wage Controversyand Its Antecedents, History of Political Economy, V. 32, Annual Supplement: 117-144

Card And Krueger's Research On Minimum Wages Superceded

I think of David Card and Alan Krueger's empirical demonstration that increased minimum wages do not reduce employment as having two main components:

• Natural experiments, especially one comparing and contrasting New Jersey and Pennsylvania.
• A meta-analysis of previous published research on minimum wages.

Recent researchers have replicated Card and Krueger's results for both components. And this recent research is more comprehensive and rigorous. (Since Card and Krueger's work, many economists have adopted the methods of natural experiments and meta-analysis, aside from the specific application to labor "markets".)

For natural experiments, I look to a paper by Dube and others. Here's their abstract:

"We use policy discontinuities at state borders to identify the effects of minimum wages on earnings and employment in restaurants and other low-wage sectors. Our approach generalizes the case study method by considering all local differences in minimum wage policies between 1990 and 2006. We compare all contiguous county pairs in the U.S. that straddle a state border and find no adverse employment effects. We show that traditional approaches that do not account for local economic conditions tend to produce spurious negative effects due to spatial heterogeneities in employment trends that are unrelated to minimum wage policies. Our findings are robust to allowing for long term effects of minimum wage changes." -- Andrajit Dube, T. William Lester, and Michael Reich. "Minimum Wage Effects Across State Borders: Estimates Using Contiguous Counties". Review of Economics and Statistics, V. 92, N. 4 (Nov. 2010): 945-964.

For meta-analysis, I look to some studies by Doucouliagos and others. Here's the abstract of an accessible working paper:

"Card and Krueger’s (1995a) meta-analysis of the employment effects of minimum wages challenged existing theory. Unfortunately, their meta-analysis confused publication selection with the absence of a genuine empirical effect. We apply recently developed meta-analysis methods to 64 US minimum wage studies and corroborate that Card and Krueger’s findings were nevertheless correct. The minimum wage effects literature is contaminated by publication selection bias, which we estimate to be slightly larger than the average reported minimum-wage effect. Once this publication selection is corrected, little or no evidence of a negative association between minimum wages and employment remains. --Hristos Doucouliagos and T. D. Stanley (2008). "Publication Selection Bias in Minimum-Wage Research? A Meta-Regression Analysis". Deakin University, Australia.

I don't expect orthodox economists to absorb any time soon my unoriginal point that economic theory gives no foundation for the belief that minimum wages must lead to disemployment, even when one abstracts from less than perfect competition, principal agent problems, information asymmetries, etc. After all, mainstream economists are trained in mumpsimus.

Minimum Wages In The U.K.

The Australian Fair Pay Commission's Minimum Wage Research Forum met in Melbourne on 30 and 31 October 2008. Stephen Machin summarized recent experience in the United Kingdom (in the 2008 Minimum Wage Research Forum Proceedings, Volume 1).

Minimum wages were set by industry in the United Kingdom up until 1993. The wage councils were abolished in 1993, except for the Agriculture Wages Board which continues to this day. Outside of agriculture, the UK did not have a minimum wage between 1993 and 1999. From 1999 on, the National Minimum Wage was in effect in the UK, as recommended by the UK Low Pay Commission, established in 1997 by the newly elected Labour government. Notice that the trend in employment visually appears unaffected by the introduction of the national minimum wage and subsequent increases in it. The trend appears the same before as afterwards. This seems like disconfirmatory evidence to me of the simple neoclassical model of wages and employment as determined by supply and demand functions. Some of us know that model is without theoretical foundation anyways.

Hat tip to Bill Mitchell