Saturday, December 31, 2016
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.
Wednesday, May 20, 2015
"In the conventional specification, total capital K is implicitly defined as being proportional to the sum of all different types of capital. This definition implies that all capital goods are perfect substitutes. One additional dollar of capital in the form of a truck has the same effect on the marginal productivity of mainframe computers as an additional dollar's worth of computers. Equation (1) expresses output as an additively separable function of all the different types of capital goods so that one additional dollar of trucks has no effect on the marginal productivity of computers." -- Paul Romer (1990).
Does Romer think that the so-called factor price curve for all techniques must be an affine function? That price Wicksell effects are always zero? Or maybe he just is trying to buffalo his reader with an ill-thought out use of mathematical symbols.
On his twitter feed, he expresses a disinterest in knowing what he is talking about:
"Sorry, but the capital controversies were a waste of time. No relevance then or now." -- Paul Romer, 16 May 2015, 1:09 PM.
I suppose one might possibly be able to defend this view:
"Economists usually stick to science. Robert Solow (1956) was engaged in science when he developed his mathematical theory of growth. But they can get drawn into academic politics. Joan Robinson (1956) was engaged in academic politics when she waged her campaign against capital and the aggregate production function." -- Paul M. Romer (2015).
One might say Solow was looking to empiricalism when he developed his non-rigorous, loose theory of growth. And, I suppose one could say that some political views were involved in Joan Robinson's insistence that Keynes' theory applies to all runs, both the short run and the long run. And in her attempt to combat the development of pre-Keynesian theories after Keynes, even if such developments were the product of those who called themselves Keynesians in some other context.
But to make such an argument, one would have to have read at least some of Joan Robinson's work from the era. It is clear that Romer has not:
"When I learned mathematical economics, a different equilibrium prevailed. ...when economic theorists used math to explore abstractions, it was a point of pride to do so with clarity, precision, and rigor. Then too, a faction like Robinson’s that risked losing a battle might resort to mathiness as a last-ditch defense, but doing so carried a risk. Reputations suffered.
If we have already reached the lemons market equilibrium where only mathiness is on offer, future generations of economists will suffer... Where would we be now if Robert Solow’s math had been swamped by Joan Robinson’s mathiness?" -- Paul M. Romer (2015).
When, during the Cambridge Capital Controversy, did Robinson try to buffalo readers with pretend rigorous manipulations of imprecisely defined mathematical symbols. How about never? Is never good for you?
- Romer, Paul M. (1990) Endogenous Technological Change, Journal of Political Economy V. 98, N. 5 (Oct): S71-S102.
- Romer, Paul M. (2015). Mathiness in the Theory of Economic Growth, American Economic Review, V. 105, N. 5: pp. 89-93.
Saturday, May 16, 2015
I think it important to oppose errors, both when they are formulated by supposedly rigorous economic thinkers and when they are popularly repeated. The relationships between ideas on different levels can be complicated.
I like writing about minimum wages because it is a clear case where:
- Textbook teaching is wrong, both on empirical and on theoretical grounds.
- Until recently at least, surveys of economists showed that they, by and large, accepted the mistaken teaching.
As I understand it, "free trade" is a policy area where economists have even more agreement, based on mistaken theory. (I suppose I should include a link to survey of economists somewhere in this post. Any suggestions?) The book from which the following quote is taken contains a structured literature survey, and is written for the general reader:
"Even if I were wrong about this, and the most sophisticated of mainstream economists did think that there was something flawed about the connection between free trade policies and comparative advantage on its own terms (and not merely where its assumptions have been debased), a further point should be raised... We are here engaged in a project of critiquing the ideological effect generated by comparative advantage - of the rationalization that it provides for certain kinds of policies and socioeconomic arrangements. The views of the most sophisticated of academic economists are one - although not the only - part of this, particularly when a less sophisticated version of their ideas predominate outside the halls of economics departments. The manner in which the ideas of intellectuals permeate education, the media and public debate are often more important to the practices of actual agents, policy-makers, and so on, than the most sophisticated renderings of those ideas that emerge from the academy. It matters little if the most sophisticated of economists doubt the connection between free trade and comparative advantage if politicians, commentators, policy-makers or indeed, the public at large, buy the connection between the two and therefore support free trade policies. Indeed, my point - and this enquiry as a whole - is lent its sharpness by its relevance to the world of action, to policy, to normative concerns, to what people do - and think is right to do - because of the ideas that are peddled by intellectuals." -- Vishaal Kishore (2014). Ricardo's Gauntlet: Economic Fiction and the Flawed Case for Free Trade (Anthem Press).
Thursday, May 07, 2015
As far as I can see, mainstream economists generally believe:
- Policy changes that raise the level of growth of the economy are more important than one over changes to the level of output1.
- Free trade is a desirable policy.
- This policy preference falls out of the theory of comparative advantage.
- Abolishing protectionist tariffs will result in a one-time increase of the level of output of the economy, but not the rate of growth.
As I understand it, Post Keynesians generally think theories of growth cannot be neatly be separated from theories of business cycles - that is, theories of short run fluctuations in the level of output. This intertwining complicates policy recommendations. Nevertheless, one can look back to Keynes2 to see a concern with economic growth.
It is hard to see how the two beliefs in the list above are consistent. Why should mainstream economists these days care much about whether countries put in place so-called free trade agreements? Maybe the question is one of who should govern. Anyways, economists in the public sphere should strive to be clear on what they advocate, and why they do.Footnotes
- Robert Lucas famously said (that is, I do not know where), "Once you start thinking about growth, it's hard to think about anything else". I do know that in Lucas (1987), he estimated that consumers "would surrender 42 per cent across the board [in consumption] to obtain an increase in the growth rate from [3 per cent] to [6 per cent." On the other hand, to eliminate aggregate consumption variability of the magnitude seen in the USA from the end of the Second World War to the 1980s would be worth "something less than a tenth of a percentage point" in average consumption.
- Keynes wrote this paean to economic growth in the midst of the Great Depression:
"The modern age opened; I think, with the accumulation of capital which began in the sixteenth century... From that time until to-day the power of accumulation by compound interest, which seems to have been sleeping for many generations, was re-born and renewed its strength. And the power of compound interest over two hundred years is such as to stagger the imagination.
For I trace the beginnings of British foreign investment to the treasure which Drake stole from Spain in 1580. In that year he returned to England bringing with him the prodigious spoils of the Golden Hind. Queen Elizabeth was a considerable shareholder in the syndicate which had financed the expedition. Out of her share she paid off the whole of England’s foreign debt, balanced her Budget, and found herself with about 40,000 [pounds] in hand... Thus, every 1 [pound] which Drake brought home in 1580 has now become 100,000 [pounds]. Such is the power of compound interest!
If capital increases, say, 2 per cent per annum, the capital equipment of the world will have increased by a half in twenty years, and seven and a half times in a hundred years. Think of this in terms of material things--houses, transport, and the like.
At the same time technical improvements in manufacture and transport have been proceeding at a greater rate in the last ten years than ever before in history. In the United States factory output per head was 40 per cent greater in 1925 than in 1919. In Europe we are held back by temporary obstacles, but even so it is safe to say that technical efficiency is increasing by more than 1 per cent per annum compound. There is evidence that the revolutionary technical changes, which have so far chiefly affected industry, may soon be attacking agriculture... In quite a few years-in our own lifetimes I mean-we may be able to perform all the operations of agriculture, mining, and manufacture with a quarter of the human effort to which we have been accustomed.
...All this means in the long run that mankind is solving its economic problem. I would predict that the standard of life in progressive countries one hundred years hence will be between four and eight times as high as it is to-day. There would be nothing surprising in this even in the light of our present knowledge."
- John Maynard Keynes (1931). "Economic Possibilities for our Grandchildren", in Essays in Persuasion, W. W. Norton.
- Robert E. Lucas, Jr. (1987). Models of Business Cycles, Basil Blackwell.
- Dani Rodrik (4 May 2015). The War of Trade Models
Saturday, May 02, 2015
I have been reading the Younger Edda. I am not sure if I will finish it. Anyways, when I came to an account of the dwarves, I found I recognized many of the names.
"Then the gods set themselves in their high-seats and held counsel. They remembered how the dwarfs had quickened in the mould of the earth like maggots in flesh. The dwarfs had first been created and had quickened in Ymer’s flesh, and were then maggots; but now, by the decision of the gods, they got the understanding and likeness of men, but still had to dwell in the earth and in rocks. Modsogner was one dwarf and Durin another. So it is said in the Vala's Prophecy:Then went all the gods,
The all-holy gods,
On their judgment seats,
And thereon took counsel
Who should the race
Of dwarfs create
From the bloody sea
And from Blain’s bones.
In the likeness of men
Made they many
Dwarfs in the earth,
As Durin said.
And these, says the Vala, are the names of the dwarfs:Nye, Nide,
Thek, Lit, Vit,
But the following are also dwarfs and dwell in the rocks, while the above-named dwell in the mould:Draupner, Dolgthvare,
But the following come from Svarin’s How to Aurvang on Joruvold, and from them is sprung Lovar. Their names are:Skirfer, Virfir,
The above list includes all but one of the thirteen dwarves who travel with Bilbo Baggins in Tolkien's The Hobbit. These are Thorin, Fili (File), Kile (Kile), Oin, Gloin, Dwalin (Dvalin), Ori (Ore), Dori (Dore), Nori (Nore), Bifur, Bofur (Bafur), and Bombur (Bombor). (Presumably, Tolkien had a different opinion on the translation of the alphabet for the Eddas.) Balin, the remaining one of Tolkien's thirteen, is the name of a knight in Thomas Malory's Le Morte d'Arthur. Dain and Durin are two other dwarf names apparently taken from the Eddas. According to the Younger Edda, Gimle (Gimli?) is the name of a palace in the south of the world. Gandalf, Tolkien's greatest wizard, is also a name on the above list.
Tuesday, April 21, 2015
|Figure 1: "Labor Demand" in the Consumer Goods Industry|
In this post, I work through an example created by Arrigo Opocher and Ian Steedman. In this example, circulating capital is represented by machines of one of a continuum of types, and I compare stationary states. Unskilled and skilled workers use the machines to produce corn, along with more machines. The output of machines are needed to sustain production in future periods. In the stationary states, the same rate of profits is earned in all industries with a positive output. In fact, only the special case when the rate of profits is zero is considered here.
The (slice of) the so-called factor price frontier in this example resembles Paul Samuelson's surrogate production function. Aggregate relationships in this example are "non-perverse". In other words, they do not violate the outdated and exploded intuition of neoclassical microeconomics. The aggregate production function shows positive, but diminishing, marginal returns, in the relevant range, to inputs of factors of production. Lower wages for unskilled labor are associated with capitalists desiring to employ more unskilled labor in the economy overall.
But a perverse relationship arises in the market for corn. Corn is the only consumer good in the example. If capitalists are to want to employ more unskilled labor directly in the production of corn, the wage for unskilled labor must be higher, not lower (Figure 1). If more unskilled labor is available for production, and markets clear, more corn is produced. But when capitalists choose the cost-minimizing technology, at prices and wages they take as given, the quantity of unskilled labor used as input, in the corn industry, per bushel corn produced, decreases. This decrease overwhelms the increased output of corn, and the employment of unskilled labor in the corn industry declines.2.0 The Technology
Consider a simple capitalist economy, composed of (unskilled and skilled) workers and capitalists. After replacing (circulating) capital goods, output consists of a single consumption good, corn. Unskilled workers are paid the wage w, and skilled workers are paid the wage W out of the harvest. Both wages are in units of bushels corn per person year. Capitalists obtain the rate of profits r. The technology consists of an infinite number of Constant-Returns-to-Scale (CRS) techniques, indexed by s. Table 1 presents the coefficients of production for a single technique.
|Unskilled Labor||a(s) l(s) Person-Years||l(s) Person-Years|
|Skilled Labor||a(s) t(s) Person-Year||t(s) Person-Years|
|Machines||a(s) Machines||1 Machine|
|Outputs||1 Machine||1 Bushel Corn|
Notice that the first column of inputs in Table 1 is proportional to - that is, a constant multiple of the - second column. This is akin to Karl Marx's assumption of a constant Organic Composition of Capital, an unrealistic assumption that simplifies price theory.
The index s for the technology is chosen from a set of real numbers, with √ 6 ≤ s ≤ 3. The parameters of a technique are defined in terms of the index as follows:
a(s) = 2 - (6/s) + (6/s2)
l(s) = 1/s
t(s) = 1/s2
Each different value of the index s is associated with the use of a different type of machine. And different quantites of unskilled and skilled labor must be used with each different type of machine to produce the output.
I compare stationary states under these assumptions:
- L person-years of unskilled labor are available for employment in the economy, with √ 6 ≤ L ≤ 3.
- T = 1 person-years of skilled labor are available for employment in the economy.
- r = 0% is the rate of profits in the stationary states considered here.
- The markets for skilled and unskilled labor both clear.
- The production of machines and corn are adapted to a stationary state. So the endowments of machines (by type) are found by solving the model, not givens.
Given the type of machine, suppose the quantity of corn, c(s), produced is:
c(s) = [1 - a(s)]/t(s) = s2 [1 - a(s)]
Let the number of machines, m(s), produced be:
m(s) = 1/t(s) = s2
Table 2 shows the output of the machine and corn industries, scaled to produce these gross outputs.
|Unskilled Labor||s a(s) Person-Years||s [1 - a(s)] Person-Years|
|Skilled Labor||a(s) Person-Year||[1 - a(s)] Person-Years|
|Machines||s2 a(s) Machines||s2 [1 - a(s)] Machines|
|Outputs||m(s) Machines||c(s) Bushels Corn|
For these quantity flows, the total employment of unskilled labor is s. The total employment of skilled labor is one person-year. The total inputs of machines, which are used up each year, are replaced by the output of the machine industry.4.0 Stationary State Prices in the Special Case
Section 3 specifies quantity flows in a stationary state, given the type of machine. The capitalists choose the technique, including the machine, based on price. Let corn be numeraire, and suppose workers are paid at the end of the production period. If the same rate of profits is earned in the production of machines and corn, the following pair of equations must be satisfied for the technique in use:
p a(s)(1 + r) + a(s) l(s) w + a(s) t(s) W = p
p(1 + r) + l(s) w + t(s) W = 1
These equations have two degrees of freedom. One is eliminated by only considering the special case in which the rate of profits is zero. The other can be seen by expressing the solution as a function of, say, the wage for unskilled labor. In this sense, the solution of the system of equations for prices in a stationary state, given the special case assumption and the technique, is:
p = a(s)
W = [1 - a(s) - l(s) w]/t(s)
p = 2 - (6/s) + (6/s2)
W = - s2 + s(6 - w) - 6
The wage of skilled labor, given the technique, is an affine function of the wage of unskilled labor. Figure 2 illustrates this function for three different techniques. This figure is akin to Figure 2b on page 197 of Samuelson (1962), which shows how to construct the so-called factor price frontier for Samuelson's surrogate production function.
|Figure 2: Wage-Wage Curves|
In a stationary state, capitalists will have adopted the cost-minimizing technique. The cost-minimizing technique, given the wage of unskilled labor, corresponds to the technique on the outer envelope (that is, the frontier) formed from all (uncountably infinite) functions that one might plot in Figure 2. One can find the technique on the frontier by setting the derivative, with respect to the index s, of the wage-wage curve equal to zero:
dW/ds = 0
Thus, the machine type used by the cost-minimizing technique, in this special case, is the following function of the wage of unskilled labor:
s = (6 - w)/2
The frontier has the equation:
W = (1/4)w2 - 3 w + 3
The wage, w, of skilled labor ranges from 0 to (6 - 2 √ 6 ). The wage of skilled labor, W, ranges from 0 to 3. If the rate of profits were positive, the wage-wage frontier would lie inside the frontier found here.5.0 Some Aggregate Markets
The results found so far can be combined.5.1 The Market for Unskilled Labor
I have postulated that L person-years of unskilled labor and one person-year of skilled labor are available for employment in a stationary state. For quantity flows in a stationary state to fully employ both types of labor, the index for the machine type must be:
s = L
For this machine type to correspond to the cost-minimizing technique, given a rate of profits of zero and market clearing for both labor markets, the wage of unskilled labor must be the following function of unskilled labor:
w = 6 - 2 L
Figure 3 plots the wage for unskilled labor, under these assumptions, with the amount of unskilled labor firms want to hire in a stationary state. In this example, for more unskilled labor to be hired in a stationary state, its real wage must be lower. This property is particular to this example; it does not generalize.
|Figure 3: Employment of Unskilled Labor|
The analysis so far has shown how to determine the cost minimizing technique and the wage for unskilled labor as a function of the amount of unskilled labor employed in a stationary state. And the wage for skilled labor is a function of the wage for unskilled labor, as shown by the wage-wage frontier. The wage for skilled labor can accordingly be expressed as a function of the amount of unskilled labor employed in a stationary state.
W = L2 - 6
Figure 4 shows the wage of skilled labor plotted against the quantity of skilled labor firms desire to hire in this example. In some sense, this function neither slopes up nor down.
|Figure 4: Employment of Skilled Labor|
Under the above assumptions, one can find the type and number of machines, m(s), produced in a stationary state. For stationary states in which different quantities of unskilled labor are employed, different types of machines will be produced. Quantities of different types of machines are incommensurable; physical measures of different types of capital cannot be plotted together on the same axis. A numeraire measure of the quantity of capital, k, can be found by taking the product of the price of machines and their physical quantity:
K = p m(s) = a(s) m(s)
Under the assumption that markets for unskilled and skilled labor clear, one can express numeraire units of capital as a function of the person-years of unskilled labor employed in a stationary state.
K = 2(L2 - 3 L + 3)
Figure 5 shows the rate of profits plotted against the above quantity of capital. In this special case, the rate of profits of capital is a non-increasing function of the quantity of capital.
|Figure 5: Value of Capital|
The previous section shows that no phenomena that violates outdated neoclassical price theory arises in aggregate markets for unskilled labor, skilled labor, or capital, in this particular example. But consider how much unskilled labor firms, under these assumptions, want to employ in the production of corn. Figure 1 shows the graph of the wage, w, for unskilled labor against the unskilled labor, l2, hired in the production of corn. That function can be found as:
l2 = (-L2 + 6 L - 6)/L
And this function slopes up, contrary to what neoclassical economists would have expected about half a century ago.7.0 Conclusion
If you work through enough examples in production theory, you ought to conclude that it is hard to find any justification for mainstream theories in microeconomics. Why so many economists continue to teach archaic balderdash, and (mis)train their intuition accordingly, is a question.References
- Arrigo Opocher and Ian Steedman (2013). Unconventional results with surrogate production functions Global and Local Economic Review, V. 17, No. 1: pp. 45-53.
- Paul A. Samuelson (1962). Parable and realism in capital theory: The surrogate production function, Review of Economic Studies, V. 29, No. 3: pp. 193-206.
Thursday, April 16, 2015
In a Bloomberg News piece, Noah Smith makes some false claims. I think his mistakes - what Eatwell and Milgate call an imperfectionist view - are widely shared among many macroeconomists. My belief that these mistakes are widely shared is not overthrown, I think, by the confusions put forth in these later posts by Stephen Williamson and Noah Smith, respectively.
First, we have the mistaken belief that in a perfect world, capitalist economies would move quickly towards equilibrium. Smith starts his column with an anecdote:
"One time, at a dinner, I asked a famous macroeconomist: 'So, what really causes recessions?'
His reply came immediately: 'Unexplained shocks to investment.'"
I take this to be an expression of the freshwater view, as embodied in models of Real Business Cycles. Cycles are to be understood as equilibrium paths responding to exogeneous stochastic shocks. Risk exists, but uncertainty does not. Recessions and depressions occur when workers voluntarily decide to take long vacations.
Second, we have mistaken understandings of price theory and how equilibrium is established:
"The market adjusts by the price mechanism. If the cost of something goes up, the price goes up to match. If demand falls, the price drops until the market clears."
I take this to be a claim that equilibrium prices are indices of relative scarcity, a belief shown to be without logical foundation about half a century ago. Ever since Robert Lucas put forth his critique in the 1970s, mainstream macroeconomists have claimed to be developing models with rigorous microfoundations. And those foundations are supposed to be provided by General Equilibrium Theory, in which agents optimize under constraints.
But many macroeconomists seem to be just ignorant of price theory, as experts in GET, such as Frank Hahn explained long ago. In the most rigorous neoclassical theory, with many commodities and many agents, the assumptions do not lead to the conclusion that prices behave that way. Nor do the theorists have a good story about how equilibrium is established. The mathematics used in mainstream macroeconomists does not allow one to find clear statements of assumptions. At least, I am unable to understand what assumptions mainstream economists think they are making on tastes, technology, and endowments in multicommodity models to justify their macroeconomic modeling. I would rather that economists turn to non-equilibrium modeling, a position that I think Robert Lucas still finds incoherent.
Third, suppose you hold that observed fluctuations in employment and output in capitalist economies can hardly be an equilibrium response. If you held the mistaken ideas about price theory that Noah Smith does, you would think that the empirical behavior of economies could only be explained by introducing some imperfection, some failure of competition, some information asymmetry, or some stickiness or slow adjustment into your theory. And given your empirical beliefs, you would think the development of theory in such a direction is a triumph of science:
"But despite these scattered denunciations and grumbles, sticky prices are enjoying a hard-fought place in the sun. The moral of the story is that if you just keep pounding away with theory and evidence, even the toughest orthodoxy in a mean, confrontational field like macroeconomics will eventually have to give you some respect."
But it is not the case that markets, including the labor market, would rapidly clear if only imperfections did not exist in a market economy. For economists to have reached this as a consensus position is a failure of their profession, not an achievement. Business cycles neither need to be explained as an equilibrium phenomenon, nor need sticky prices be invoked to explain the failure of markets to clear.
Is the topic of the above post orthogonal to a debate Paul Krugman overviews? I am of two minds on Krugman's post. I cannot be too hostile to a blog post illustrated with a homoclinic bifurcation. Maybe a solid appreciation of nonlinearity in macroeconomics is associated these days with heterodox, but not necessarily non-mainstream economics.References
- John Eatwell and Murray Milgate (2011). The Fall and Rise of Keynesian Economics, Oxford University Press.
- Richard M. Goodwin (1990). Chaotic Economic Dynamics, Oxford University Press.
- Murray Milgate (1982). Capital and Employment: A Study of Keynes's Economics, Academic Press.