Brouhaha Over Krugman On Endogenous Money

I recently posted about the theory that the money supply is endogenous and under the control of a country's central bank, such as the Federal Reserve. Paul Krugman dismisses the theory.

Proponents of Modern Monetary Theory, in the comments and elsewhere, have taken issue with Krugman. I have in mind, for example, Dean Baker, Peter Cooper, Scott Fullwiler, Greg Hannsgen (of the Levy Institute), Bill Mitchell, Warren Mosler, Cullen Roche, and Pavlina Tcherneva (cross-posted). James Galbraith appears in various comments, for example, in this one, in which he says, "I was a student of Godley (and even more so, of Kaldor) many years ago and a close observer of monetary policy during my years on Capitol Hill, so this material came easily to me."

Elsewhere

• Steve Keen, in the Australian newspaper The Business Spectator simultaneously praises Paul Krugman for building on Hyman Minsky's work, while criticizing him for "embod[ying] everything that is bad in neoclassical economics."
• Bill Mitchell argues, in last week's Nation, that government responses to the global economic crisis have been based on a series of economic myths. (Will the winning cruciverbalist for the Nation be paid in the "high two figures"?)
• John T. Harvey also warns, but in Forbes, against cutting the deficit.
• Branko Milanovic, in a guest post for D. M. Nuti, explains the connection between rising income equality and the global economic crisis.

H/T: Peter Cooper for the links to the second and third links.

Some British Nineteenth Century Controversies In Monetary Theory

Britain suspended convertibility during the Napoleonic wars. During that period, until 1821, money in England was paper, unbacked by gold. The restoration of convertibility was followed by a stagnant period in British development, with a crisis in 1825 and a reform in 1844 called the Bank Charter Act.

This post recalls some debates in monetary theory among British political economists while these events were occurring. (I don't consider myself expert on monetary theory during the Classical period.) Table 1 shows some schools of thought in monetary theory. The term schools is traditional with respect to the currency and banking schools, but should not be interpreted too strongly for any groups in the table. These schools, unlike, say, the Physiocrats, do not have a recognized leader, followers, popularizers, etc. Rather, they are more like the Mercantilists, a diverse set of pamphleteers and politicians grouped together by later writers.

Table 1: Some "Schools" and Example Members

Years	Contending Schools
1797-1821	Bullionists Henry Thornton David Ricardo	Anti-Bullionists Robert Torrens Robert Malthus
1825-1844	Currency School Robert Torrens Samuel Jones Lloyd Mountifort Longfield	Banking School Thomas Tooke John Stuart Mill
2nd Half of the 20th Century	Quantity Theory Milton Friedman	Endogenous Money Nicholas Kaldor

In each period shown in the table, I have listed two schools. Economists in the first school in each row argued that the money supply was exogenous and that the price level varied with amount of money issued by central bank. Economists in the second school in each row argued that the money supply was endogenous, that is was not capable of being controlled by the central bank, and that it varied with demand for it. The details of these arguments varied among these and other economists.

The last row suggests that these arguments are still current. In fact, advocates of Modern Monetary Theory currently argue that the money supply is endogenous.

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.

Three Routes To The Choice Of Technique

1.0 Introduction
I think the analysis of the choice of technique in a steady state is a settled question. (The meaning of Sraffa's equations in wider contexts can be debated.) One strength of the analysis of the choice of technique is the existence of several methods of analysis, all reaching the same conclusion. If one wanted to overthrow this analysis, one would need to show that one is not attacking just one such method, but all of them - or at least as many as possible. This post illustrates this strength of the analysis by presenting three such methods.

2.0 Example Technology
I need an example technology (Table 1) to use in stepping through different methods for analyzing the choice of technique. Each process requires the inputs shown to be purchased at the start of the production period (a year) for each unit of output produced and available at the end of the year. Two processes are known for producing steel, and two other processes are likewise known for producing corn. The coefficients are fairly arbitrary. In this example, to produce any net output in a steady state, all commodities - that is, both steel and corn - must be produced.

Table 1: Constant-Returns-to-Scale (CRS) Production Processes

Inputs	Industry Sector
	Steel Industry		Corn Industry
	First Steel-Producing Process	Second Steel-Producing Process	First Corn-Producing Process	Second Corn-Producing Process
Labor (Person-Yrs)	3220/3321	13930/63099	3115/3321	1
Steel (Tons)	0	0	1/2	9/20
Corn (Bushels)	1/18	2752/7011	0	0
Output	1 Ton	1 Ton	1 Bushel	1 Bushel

The analysis of the choice of technique calculates which production process would be adopted for each combination of prices and interest rates. For this technology to be compatible with a steady state, at least one process for producing steel and one process for producing corn must be adopted. A "technique" consists of one process from each of the industries in this example. Table 2 defines the four techniques, each named with a greek letter. (I think this convention of using greek letters in this context may have been introduced by Joan Robinson.)

Table 2: Techniques and Production Processes

Technique	Steel-Producing Process	Corn-Producing Process
Alpha	First	First
Beta	First	Second
Gamma	Second	First
Delta	Second	Second

A technique, in this case, is expressed by a 2-element row vector of direct labor coefficients and a square Leontief Input-Output matrix. For example, the labor coefficients, a₀^α, for the first technique are:

a₀^α = [(3220/3321) (3115/3321)]

The Leontief Input-Output matrix, A^α, for the first technique can be expressed as two columns a_.1^α and a_.2^α:

A^α = [ a_.1^α a_.2^α]

The first labor coefficient and the first column in the Leontief Input-Output matrix come from the specified production process from the steel industry for that technique:

a_.1^α = a_.1^β = [0, (1/18)]^T

The second labor coefficient and the second column in the Leontief Input-Output matrix come from the specified production process from the corn industry for that technique:

a_.2^α = a_.2^γ = [(1/2), 0]^T

I leave to the reader how to completely specify a₀^β, A^β, a₀^γ, A^γ, a₀^δ, and A^δ.

3.0 Direct Method
Heinz D. Kurz and Neri Salvadori refer to this method for analyzing the choice of technique I describe here as the "Direct Method". Before proceeding, I need to introduce some notation. Let p be a two-element row vector of prices:

p = [p₁, p₂]

where p₁ is the price of a ton steel and p₂ is price of a bushel corn. Let w be the wage, assumed to be paid at the end of the year for each person-year of labor expended during the year. Let r be the rate of interest, also called the rate of profits.

I need to introduce a column vector to represent the numeraire. Let e₂ be the second column of the 2x2 identity matrix:

e₂ = [0, 1]^T

The assumption that e₂ is the numeraire implies the following equation:

p e₂ = 1

This specification of the numeraite implies that, p₂, the price of a bushel corn is unity.

The problem is to find a pair (p, w), given the interest rate r, such that

• No process can be operated with costs less than revenues.
• For any process that is operated, the costs do not exceed the revenues.

The first condition implies the following four inequalities must hold:

p a_.1^α(1 + r) + a₀₁^α w ≥ p₁

p a_.1^γ(1 + r) + a₀₁^γ w ≥ p₁

p a_.2^α(1 + r) + a₀₂^α w ≥ p₂

p a_.2^β(1 + r) + a₀₂^β w ≥ p₂

The conjunction of the requirement that steel be produced with the second condition implies that one of the first two inequalities must be met with a strict equality. The analogous requirement for corn production implies that at least one of the last two inequalities must be met with equality.

These specifications are easily graphed (Figure 1). Given the interest rate, the first two inequalities yield upward-sloping lines in the the figure. The last two inequalities yield the downward-sloping lines. The first condition implies the solution must lie on or above all of the lines in the figure. The second condition implies that the solution must lie on

• At least one of the upward-sloping lines
• At least one of the downward-sloping lines.

The only point that satisfies these conditions is graphed. It lies on the upward-sloping line corresponding to the first steel-producing process and the downward-sloping line corresponding to the second corn-producing process. Thus, this analysis shows that the beta technique is cost-minimizing at an interest rate of 100%. The solution wage and price of steel can be read off the figure.

Figure 1: Direct Method Illustrated At r = 100%

The direct method is easily generalized to any finite number of techniques. Each additional production process results in an additional line in the figure, upward-sloping for the steel industry and downward-sloping for the corn industry. The method also generalizes for any finite number of commodities. Each additional commodity results in the introduction of another dimension to the figure. Although the figure quickly becomes unvisualizable, the mathematics generalizes.

4.0 Indirect Method
The indirect method generalizes to cases in which an uncountably infinite number of techniques are available. It is based on constructing the wage-rate of profits frontier as the outer envelope of the wage-rate of profits curve for each technique (Figure 2). I illustrate how to construct the wage-rate of profits curve for the Alpha technique.

Figure 2: Indirect Method Illustrated

The condition that the same rate of profits be earned for each process comprising a technique yields a system of two equations:

p A^α(1 + r) + a₀^α w = p

One also has the equation setting the price of the numeraire to unity:

p e₂ = 1

For a given interest rate r, the above is a linear system of three equations for three variables (p₁, p₂, and w). One can solve the system to express each of these three variables as a function of the interest rate. The wage, for example, can be found as:

w = 1/(a₀^α [ I - (1 + r)A^α]^-1e₂)

One knows, from a theorem due to Perron and Frobenius, that the inverse exists between an interest rate of zero and some maximum interest rate.

Figure 2 shows the wage-rate of profits curves for each of the four techniques. The cost-minimizing technique at each rate of interest is the one with the highest wage. Points at which the rate-rate of profits curves for two or more techniques interesect on the outer frontier are known as switch points. The two switch points are shown in the example. The Gamma technique is cost-minimizing for a very low interest rate. For a somewhat larger interest rate, the Delta technique is cost-minimizing. Finally, the Beta technique is cost minimizing for larger interest rates. My exposition illustrates that the direct and indirect methods give the same conclusion. For example, the wage-rate of profits frontier shows that the Beta technique is cost-minimizing for an interest rate of 100%.

5.0 Cost Minimization Algorithm
This method I take from J. E. Woods. He provides an algorithm for finding the cost-minimizing technique(s), given the interest rate.

1. Pick an initial technique. (For illustration, I start with the Beta technique in the example.)
2. Solve the equations specifying the wage-rate of profits curve for the selected technique. So you now have a price vector p and the wage w.
3. Using p and w, calculate the cost of producing a ton steel with each of the known production processes (Figure 3).
4. If the steel-producing process in the selected technique is cheapest, go to Step 6. Otherwise go to Step 5. (In the example, one would go to Step 5 for low interest rates and to Step 5 for higher interest rates.
5. Replace the steel-producing process in the technique analysed in Step 2 with the cheapest steel-producing process identified in Step 4. Solve the equations specifying the wage-rate of profits curve for the newly selected technique. Use the resulting p and w in Step 6. (In the example, one would calculate the wage-rate of profits curve for the Delta technique for a sufficiently low interest rate.)
6. Using the specified p and w, calculate the cost of producing a bushel corn with each of the known production processes (Figure 4).
7. If cost of producing corn could be found in Step 6 for the technique selected in Step 2 and the corn-producing process in that technique is cheapest, then stop. You have identified the cost-minimizing technique. Otherwise, replace the corn-producing process in the technique analyzed in Step 6 with the cheapest corn-producing process identified in Step 6. (In the example, the algorithm would terminate in one-pass for a sufficiently high interest rate, with the Beta technique identified as the cost-minimizing technique.)
8. Go to Step 2.

Figure 3: Costs of Producing Steel with Prices for the Beta Technique

Figure 4: Costs of Producing Corn with Prices for the Beta Technique

Figures 3 and 4 suggest that for a sufficiently low interest rate, the technique consisting of the second steel-producing process and the first corn-producing process, that is, the Gamma technique, is cost-minimizing. For a somewhat higher interest rate, the technique consisting of the second steel-producing process and the second corn-producing process, that is, the Delta technique, seems to be cost-minimizing. And, as noted above, the algorithm terminates with the Beta technique identified as the cost-minimizing technique at an even higher interest rate. In other words, the graphs suggest that the above algorithm converges to the same solution as the indirect method.

6.0 Conclusions
I have not exhausted the methods available for analyzing the choice of technique. For example, I have not formulated any Linear Programs above. Nor have I presented the diagram in my 2005 Manchester School paper. Furthermore, I have glossed over many interesting mathematical questions, such as proving the existence of solutions and proving that all methods give the same result. But this post is already too long.

References

• Heinz D. Kurz and Neri Salvadori (1995) Theory of Production: A Long-Period Analysis. Cambridge University Press.
• J. E. Woods (1990) The Production of Commodities: An Introduction to Sraffa, Humanities Press.

Great Female Economists

This is a selection. I always exempt those alive in making such judgements.

• Jane Marcet
• Harriet Martineau
• Rosa Luxemburg
• Mary Paley Marshall
• Beatrice Webb
• Charlotte Perkins Gilman
• Elizabeth Boody Schumpeter
• Joan Robinson
• Krishna Bharadwaj

Lost Knowledge In Economics

Economists' concerns can be expected to change as the world changes. In a serious scholarly discipline, however, such changes in emphasis should be theorized and argued. They should not be just a matter of fads and the following of changes in the political environment. I am not sure economics meets this standard. Anyways, here are examples I came up with today for exploring this question:

• Managerial theories of the firm (as developed by, e.g., Robin Marris)
• Markup pricing
• Sidney Chapman's theory of the length of the working day (as opposed to the textbook analysis of tradeoffs between leisure and commodities) (Derobert (2001), (Spencer 2003), and (Walker 2007)).
• Co-operatives (Kalmi 2007).
• Sidney and Beatrice Webb's analysis of labor markets (Kaufman 2008).

References

• L. Derobert. "On the Genesis of the Canonical Labor Supply Model". Journal of the History of Economic Thought, V. 23, N. 2 (2001): 197-215.
• Panu Kalmi. "The Disappearance of Cooperatives from Economics Textbooks". Cambridge Journal of Economics, V. 31 (2007): 625-647.
• Bruce Kaufman. "How a Minimum Wage Can Improve Efficiency Even in Competitive Labor Markets: The Webbs and the Social Cost of Labor". Andrew Young School of Policy Studies Research Paper Series, Working Paper 08-16 (July 2008).
• D. A. Spencer. "The Labor-Less Labor Supply Model in the Era Before Philip Wicksteed". Journal of the History of Economic Thought, V. 25, N. 4 (2003): 505-513.
• Tom Walker. "Why Economists Dislike a Lump of Labor". Review of Social Economy, V. 65, N. 3 (2007).

Coase Theorem Not About Markets

Mainstream economists tend to think of the "laws of demand and supply", for example, as applying to all of human history and independent of institutional structure¹. Geoffrey Hodgson has noted the difficulty of finding a definition of "markets" in mainstream economics.

To me, a market must allow for repetitive purchases and sales of a commodity where participants have information on, for example, prices from previous purchases and sales. A contract drawn up between two organizations to last for several years is a bilateral negotiation, not a market transaction, when neither organization is simultaneous to draw up parallel contracts with competing organizations².

One application of this idea is to labor unions. Maybe the difficulties mainstream economists have with defining "markets" is connected with their backward notions on labor unions, backward notions that others have recently pointed out³.

I was inspired to write this post by Hahnel and Sheeran's article. An train engine with tracks through a farmer's field is an example of application of the Coase Theorem. If vegetation isn't kept a certain distance from the rails, supposedly sparks from the train wheels are likely to start a fire and burn the crops. Do the farmers have a well-defined property right not to have sparks ejected on their fields? Or do trains have a well-defined right to emit sparks? Depending on the answers to these questions, the legal liability for maintaining the track and paying for any resulting fires is different. But, according to the Coase "theorem", if property rights are well-defined and no transaction costs exist, the farmer and the railroad will negotiate an efficient price for allowing the trains to emit sparks. Some conclude that it is government's job to ensure property rights are well-defined and perhaps lower transaction costs. Then the market will come to an efficient solution to the problem of externalities, however property rights are allocated.

Among other criticisms, Hahnel and Sheenan point out that the conclusion is a non-sequitur. This is not an example of a market. I think their treatment of information asymmetries is a formalization of a point I first read from Michael Albert. The Coase set-up will encourage those with property rights to act as bullies, to threaten obnoxious behavior they wouldn't otherwise do, so as to extort payments from their victims.

¹ An interesting experiment would be to count the number of occurrences of the word "capitalism" in, say, the American Economic Review or the Journal of Political Economy in the last decade and contrast those counts with the same counts in, say, the Cambridge Journal of Economics, the Review of Political Economy, or the Review of Radical Political Economics.

² Even if you object to this usage of "market", you should see that the game theoretic models appropriate for a bilateral negotiation under various assumptions about available information is not the typical model of demand and supply schedules.

³ Haven't the criticized economists heard of the theory of the second best? I thought that the case of a large employer and a labor union was a canonical example.

References

• Michael Albert. "Nobel Nerve", Z Magazine (Nov. 1991).
• Robin Hahnel and Kristen A. Sheeran. "Misinterpreting the Coase Theorem" Journal of Economic Issues. V 43, N. 1 (March 2009): 215-238.
• Geoffrey M. Hodgson Economics and Institutions: A Manifesto for a Modern Institutionalist Economists, Basil Blackwell (1989).
• R. G. Lipsey and Kevin Lancaster. "The General Theory of the Second Best", Review of Economic Studies, V. 24, N. 1 (1956-1957): 11-32.