On Disequilibrium Sraffian Economics

Sraffa’s work was among the most important creations in the history of heterodox economics. His approach to relative prices and distribution, following from an alternative view of Ricardo’s economics, led to a unified system that allowed for explanation of relative prices movements and the determinants of the wage and profit rate without regards to marginalistic preferences; a feat in itself. However, a frequent critique that I have seen online, unfortunately by many Post-Keynesians too, is the claim that Sraffians rest upon a crude construction of temporary equilibrium in real, rather than historical time, and hence devoid of uncertainty of economic life. Marxists and Neo-Classical economists have also frequently leveled these criticisms, generally positing that Sraffa on reproduction was simply an example of either a special case of general equilibrium, or a special case constructed under ex nihilo reproduction(1). All of these criticisms generally from a line of thought that Sraffian cases of reproduction can only exist under equilibrium conditions, and some take these criticisms to the extreme, that of which Sraffian cases of reproduction may only be permitted to exist within special cases of equilibrium. These criticisms, however, have not been left alone by many Sraffians and broad tent Post-Keynesians. It’s important to note that Sraffian results are perfectly consistent under many generalized schemes of reproduction; and this blogpost is simply to briefly go over the responses to the equilibrium critiques by many heterodox and orthodox economists. 

To not begin with Rosser Jr. on reswitching would be a crime, as his introduction of econophysics, particularly catastrophe theory, to Sraffian economics through bifurcations caused by reswitching was brilliant. Before I am to go onto the general approach used by Rosser Jr., it’s better to first explain what catastrophe theory is and its role in economics. Catastrophe theory, essentially, is a branch of bifurcation theory dealing with structural instabilities stemming from degenerate critical points of a function. The importance of this system, outside of pure mathematics, is quite vast, especially having to do with qualitative changes in the structural stability of an economic system stemming from a bifurcation or degradation of a critical point. We can follow the examples given in Mattuck’s seminal notes on ODEs, for the sake of expository clarity. To begin with, the question of the definition of “what” structural (in)stabilities are, is important. Structural instabilities have to do with the stability of a system’s critical points, i.e., if any variation in the parameters of the function do not cause a major geometrical change in the mathematical system, we can say that the system is structurally stable. A structural instability occurs when a change in the parameters of a function induces a major qualitative change in the geometrical structure of the mathematical system and its critical points. We can follow Mattuck’s notes for a rudimentary system where we may be able to describe structural stabilities with regards to changes in the parameters of a function (Or system of functions), from the 2 x 2 linear system: 

x =ax+by

y = cx+dy

Which is said to be structurally stable if it happens to be a saddle, spiral, or a node. A saddle is essentially where, when using the quadratic formula, starts from a system where A and C have different signs in:

sqrt[B2-4AC]

This leads to the occurrence of a moving point originally tending towards (0,0) before tending towards infinity, essentially having to do with decaying or growing exponentials (If stable, there are no sines and cosines). Carrying on, we can continue with the above 2 x 2 linear system: 

λ2-(a+d) λ+(ad-bc) =0

The eigenvalues of which being: 

λ1, λ2=(a+d) +/- sqrt[(a+d)^2-4(ad-bc)]/2

Assuming that λ1 and λ2 are real (and distinct), Mattuck gives the possibilities with regards to the stability of the system: 

λ1 > 0, λ2 > 0, an unstable node occurs

λ1 < 0, λ2 < 0, an asymptotically stable node occurs

λ1 > 0, λ2 < 0, an unstable saddle node occurs

    What Mattuck shows, in essence, is that the roots (λ1, λ2) depend on a, b, c, and d. What this means is that a change in any of the parameters, even very slightly, e.g., a minor perturbation to the system’s parameters, a change would follow with the roots. This by itself is not interesting, but when considering special eigenvalues, a variation to the system’s parameters creates a major geometrical change. An example of this is provided below in the notes, e.g., imaginary eigenvalues, one zero eigenvalue, and a repeated real eigenvalue all have major implications for geometrical changes when varying parameters. In catastrophe theory, mathematicians deal with these major qualitative geometrical changes with regards to pure mathematical systems (ODEs) but also with physical systems (Uses in physics, particularly with states of water) and in economics, e.g., Puu’s work on the stability of an economic system(2). Rosser Jr,’s work was more or less a continuation of Puu’s work on disequilibrium in an economic system caused by a change in the parameters of an economic system, e.g., with the basic copied example above of a purely mathematical system.

    Rosser Jr. (1983)(3) demonstrates that reswitching acts as a cause of discontinuous jumps along an optimal dynamic path. Reswitching then, acts as a cause of structural stability within an economic system traveling along a dynamic path, causing discontinuities that the system cannot merely “jump” over contra Bruno. These paradoxical zones can be seen as a demonstration of structural instabilities within Neo-Classical models which severely compromise the theoretical soundness of these models. Rosser Jr. provides a visual example of the reswitching model on page 185, demonstrating factor price movements with regards to the wage and profit rate cannot be treated as a smooth linear path, rather, a path that can generate complex movements and discontinuous jumps within the choice of technique. Roser Jr. observes that there are no discontinuities if k < minimum optimal steady state path k’; but a closer examination of the k-π relationship shows divergent pairs of π with regards to k’ and k’ increases beyond k’ min. The increasing divergence between π’s and the steady state k implies a larger discontinuous jump further away from the cusp point, the diagrammatical version being given on page 190. A variation of the rate of profit along the wage-profit frontier, for the sake of argument we can just assume that the variation will be smooth, the K/L ratio can vary in complex and disconnected ways. What’s important within these models is that Rosser Jr casts his results under a disequilibrium framework, in between steady states.

    This means that one of the largest contributions to economic theory by Sraffians, particularly on choice of technique analysis (Which is in fact a constructive addition to economic theory, rather than being destructive as many economists seem to suggest, laying the foundation for technique analysis within joint product industries too), can be cast under disequilibrium conditions. This is in direct contrast to what many people, such as Burmeister, seem to suggest with regards to the validity of reswitching (Burmeister, however, does seem to have recanted his position on reswitching). Rosser Jr’s discontinuous capital-profit intensities simply demonstrates, in a more generalized manner, that the traditional marginal productivity theory of profit and wages, along with the interest rate dependent investment story, are simply too simplistic and cannot be thought of as valid in a real economy, especially when Rosser Jr’s model can cast upon capital theoretic paradoxes such as Bruno’s dynamic adjustment model. The wage, profit, and capital-per-worker value, can all have a leaping phenomena over intermediate values (Hence, non-linearity of the profit-capital relationship), or maintain a complex relationship with major discontinuous jumps, while the growth rate and consumption per worker reaches a final steady state. The importance of this cannot be understated, the economy in between steady states (The Hicksian traverse) can have multiple sources of instability through discontinuous jumps in the K/L and K/W ratio. Having been in-between steady states, the criticism of the Sraffian choice of technique analysis cannot hold, as it is in disequilibrium despite being on the traverse to a final steady state. It’s worth noting that this solution to reswitching’s usefulness in disequilibrium also resolves multiple issues debated within Post-Keynesian economics, e.g., the usefulness of the Sraffian analysis of technique under “radical uncertainty”. 

Readers who have read parts of my older blog-posts should be aware of my position on uncertainty strongly echoicing that of George Shackle and Paul Davidson. While I have not fully recanted that position, I believe my previous analysis held many errors, I still maintain that uncertainty and analysis of decision making theory under uncertainty is integral to a proper functioning theory of choice of technique. Now, Joan Robinson’s critique(4) was primarily centred around the erroneous nature of a completely certain environment that Sraffa (1960) operated under for his single and joint product industries. Without an assumption of exogenously given “blueprints” and certainty about the viability of a production technique, the Sraffian analysis of choice of technique “missed its mark”, so to speak. Many Sraffians hold immense respect for Joan Robinson as a leading scholar in the Post-Keynesian tradition, albeit her questionable time as an ideologue for Maoist China, which has lead to this question being a hotly debated issue amongst Fundamentalist Post-Keynesians and Sraffians. A lot of recent work has been done by economists such as Fratini and Parrinello, but for the start of this section I’ll briefly talk about Rosser Jr’s solution to the Robinsonian critique. Rosser Jr, in his book From Catastrophe to Chaos: A General Theory of Economic Discontinuities, in chapter 8, extensively discusses the Sraffian approach to choice of technique analysis. Later in the chapter, a major point of discussion is the Robinsonian critique that Sraffian choice of technique analysis cannot hold under uncertain disequilibrium conditions. Aside from the given example above by Rosser Jr, that one cannot hold that reswitching can only occur in crude steady states rather than disequilibrium, he also provides a defense of the Sraffian analysis on a different ground. Rather than treating the blueprints and technical details of the technique itself, Rosser Jr. applies a technique cluster approach to reswitching of techniques. The Robinsonian critique is primarily centred around further heterogeneity of the choices of technique, i.e., techniques often have different composition dependent on its base, such as the differences between an iron based technique and a copper based technique.While the discontinuities may occur and the profitability of a certain technique relative to the profit rate being a complex function might hold theoretically, with transaction costs it makes little sense to suppose the major change in techniques with different basis’ would ever occur. Rather than adopting a more orthodox notion with a few finite techniques (This is not to say that reswitching isn’t possible under infinite technique conditions), what should be adopted is a conception of “technique clusters”. Technique clusters are techniques with similar technical similarities but are still heterogeneous enough to constitute a switch in the choice of technique and have the same implications for the marginalist theory of wages and profits. Rather than switching between completely different techniques, which is a possibility albeit not very likely, switching within technique clusters allows for a relatively “smooth” change while maintaining the complex non-linearities within the profit-capital relationship. Considering reswitching under more localized subgroups allows for a more microeconomic based analysis of reswitching while keeping the main analysis of Sraffa intact, which resolves the 2nd part of the Robinsonian critique. The final critique to be considered is that of radical uncertainty in an economic environment, to which reference to the aforementioned authors Fratini and Parrinello is in order. 

Fratini(5) and Parrinello(6) both take the approach of treating prices and quantities as a stochastic variable, rather than treating them as something definitive and known with complete certainty. This analysis can incorporate the concept of gravitation into Post-Keynesian economics, rather than treating it as a deterministic process, prices and the concept of gravitation can hold as a stochastic concept which can still hold under random perturbations to the gravitation process (Parrinello also holds that the Sraffian choice of technique analysis can also hold under random perturbations, more on that later). Following Fratini, we can set up the probabilistic system as: 

π_n,t=1/t (t^\sum_t=1 π_n,t)

The vector, again following Fratini, of average market prices (after t observations) is πt=[π1,t , π2,t , … , πN,t]. We can then put forth conceptual ideas with the random vector πt and its relationship to gravitation. Before continuing, it’s worth noting that this entire analysis is predicated on the non-exact-ness of the solutions to Sraffa’s equations, i.e., if we take these concepts as a stochastic rather than deterministic process, we lose the rigorous certain solution generated by a deterministic system; but retain the main components of Sraffa’s analysis on choice of technique and gravitation, after the initial deterministic price system has been solved for. The absolute value of the random vector πt subtracted by π is the (Euclidian, or non-curvature based gravitation path) distance between πt and π, in-line with the Euclidean addition postulates. 

pr(|π1-π|) < ε

Is the probability that this distance is smaller than, a real number given to the equation. The conditions of natural prices, or prices of production, or the initial deterministic prices generated by Sraffa’s simultaneous equation method, to be the centre of gravitation for market prices would then be: 

lim_t ->∞ pr(|π1-π|< ε =1

Which implies that market prices converge to the system’s “Sraffa prices” probabilistically, rather than being a certain deterministic process. Parrinello (1990) also suggests, additionally, near the end of the paper, that one can incorporate random perturbations into the Sraffian choice of technique analysis. Rather than treating the Sraffian choice of technique analysis as a cost minimizing technique under a steady state growth path, one can incorporate the effect of “seasonality” into the Sraffian choice of technique analysis as a statistical characteristic perturbing the Sraffian system. One can maintain that all of the usual components of the criterion for the choice of technique in the Sraffian system is correct, and hence the results from which (capital paradoxes) are valid, while incorporating some statistical characteristics of randomness into his analysis. Incorporating the effect of the weather, a random variable, particularly chaotic more than random, into the Sraffian choice of technique analysis would render it a more generalized system while maintaining the core components of Sraffa’s analysis. The distribution of random events in the Sraffian system can impact the choice of technique analysis, e.g., the weather, but it does not serve to invalidate the Sraffian analysis in a sufficient manner. 

This short blog-post was to simply elucidate some of the Sraffian results that can hold in disequilibrium by copying and bringing together a few examples from various authors. I apologize for having to crudely format equations onto here, the equation function on blogger seemingly is terrible. I will attempt to resolve this, but for now, please bear with me.

With reference to my long break from this blog, I have had a lot of work recently to take care of, such as academics and research papers. I will resume a regular update schedule again, starting this week. 

References: 

1. )  Jefferies, W. (2019). Piero Sraffa’s physical price system and reproduction without production. Capital & Class, 44(1), 63–83. https://doi.org/10.1177/0309816819852771

2.)  Puu, T. “Regional Modelling and Structural Stability.” Environment and Planning A: Economy and Space, vol. 11, no. 12, 1979, pp. 1431–1438., https://doi.org/10.1068/a111431.

3.)  Barkley Rosser, J. (1983). Reswitching as a cusp catastrophe. Journal of Economic Theory, 31(1), 182–193. https://doi.org/10.1016/0022-0531(83)90029-7

4.)  Robinson, Joan. “The Unimportance of Reswitching.” Quarterly Journal of Economics 89 (1975): 32-39.

5.)  Fratini, Saverio M. and Naccarato, Alessia, The Gravitation of Market Prices as a Stochastic Process (November 2016). Metroeconomica, Vol. 67, Issue 4, pp. 698-716, 2016, Available at SSRN: https://ssrn.com/abstract=2847407 or http://dx.doi.org/10.1111/meca.12116

6.)  Parrinello , Sergio. Some Reflections on Classical Equilibrium, Expectations, and Random Disturbances. Centro Sraffa, www.centrosraffa.org/pe/6,1-2/6,1-2.12.%20Parrinello.pdf

Chaos in Non-Linear Business Cycle Models

 Chaotic Dynamics Within Kaldor's Non-Linear Business Cycle Model

This week’s post is shorter than average unfortunately, but I found it worth demonstrating one of the wide array of conditions in which economic models can generate unstable chaotic motions, e.g., Kaldor’s/Goodwin’s non-linear business cycle model. This brief argument laid out for the existence of unstable chaotic motions within the economy’s business cycles can further research on the relationships of chaos with business cycles, primarily attractor merging crises and the transition from weak to strong chaos, consequently. The Kaldorian system may demonstrate chaotic motions when the perturbation contains a strange attractor, leading to the perturbed system (Kaldor’s business cycle model in this case) displaying irregular, aperiodic, and highly sensitive behavior. Multiple arguments with Kaldor’s non-linear investment and savings functions have outlined the existence of complex phenomena that occasionally generate chaotic phenomena, too. 

A general defining characteristic of strange attractors is sensitive dependence on initial conditions, we can demonstrate this with the following system: 

Z = f (a, γ), a ∈ R, γ ∈ R

The system generates “sensitive dependence on initial conditions” if any variations in a(n) lead to major differences in the time series of the system in a short period of time. These systems, generated by a dynamic function, are deterministic in a crude sense. The evolution of the system is hypothetically predictable granted complete knowledge of initial conditions, i.e., the variances of a(n) generating new time series that are considered “chaotic”; along with future random perturbations that may influence the evolution of the deterministic non-linear system in a stochastic manner. A lesser known phenomena with chaotic systems is aperiodicity, i.e., the chaotic time series remain bounded within certain values but remain aperiodic, to be distinguished from functions such as f(x) = 2x, in which as x → ∞ the values never repeat themselves. Remaining confined in a certain space yet never repeating itself, aperiodic, is the reason for certain shapes created that resemble a “butterfly” when graphed in phase space. The phase space trajectory is incredibly complex for the original systems Lorenz studied which exhibited chaotic motion, and due to being bounded generated the “butterfly” sort shape for which the colloquial name of the “butterfly effect” follows. Now consider the model for an economy, Kaldor’s model: 

Y ′ = α[I(Y, K) − S(Y, K)]

K′ = I(Y, K) − δK

Which follows Y being income, I being gross investment, K is the capital stock, and S is savings.  δ being the depreciation rate and α being the adjustment coefficient.  The second equation is a general capital accumulation equation with not many distinct properties for the example being studied currently. Now following Akhmet et al.[1] we can specify the above system even more, given S(Y, K) = sY & I(Y, K) = Y −aY3+bK as they did: 

Y ′ = α[(1 − s)Y − aY3 + bK]

K′ = Y − aY3 + bK − δK

The specifications for the constant parameters remain the same as in the example provided by Akhmet et al., we can recognize a steady state solution if only δs < δ + bs. For the sake of the gross formatting mistakes that occur on Blogger occasionally, I will refrain from applying the transformations derived to the system above. Now we may also explore Kaldor’s model given foriegn capital investment and the consequent Hopf bifurcations that follow said system: 

S `= αY + pS(k − Y2 )

Y` = v(S + F)

F` = mS − rY

S being the savings of households, Y  being GDP, K being potential GDP, F being foreign capital, and t is time. If we set k to 1, potential output, the above identities are given as multiples of potential output, k. We also have α being marginal propensity to save, 1/V the K/Y ratio, and m capital inflow/savings ratio. Now that we have specified: 

S` = αY + 0.1S(1 − Y2) 

Y` = 0.5(S + F)

F` = 0.19S − 0.25Y

According to Pribylova (2009)[2] the system given above generates a Hopf bifurcation at α = α(0) ≡ 0.25. A Hopf bifurcation is generally described as a point in which the stability of a system switches through a change in the stability properties of the dynamical equation.[3] This is quite important for Kaldor’s business cycle, as the general business cycle model with the non-linear investment and savings function as the original model proposed by Kaldor was attempting to demonstrate the shifts from unstable equilibria. Demonstration of chaotic dynamics within the Kaldorian non-linear investment and savings functions results in a realization of the possibilities of changes in the local stability conditions, leading to Hopf bifurcations and other chaotic motions. Endogenous chaotic business cycles can either be generated by an attractor merging crises, which I will explain in the following paragraph, or by a change in the stability conditions followed by a Hopf bifurcations at certain values.  

A familiar condition of chaotic dynamics is the inability to forecast them outside of the very immediate future, e.g., within economic systems, 1-2 days. If a system is demonstrated to have a chaotic attractor, the behavior of the economic system is near impossible to forecast outside of the immediate short term. Another property of chaotic systems worth discussing quite briefly for such a short post is the existence of attractor merging crises highlighted by Pribylova (2009) and Chian (2007)[4]. Following Chian (2007), we can reduce relaxation oscillations that exist within Goodwin’s non-linear accelerator/multiplier model and Kaldor’s non-linear business cycle model:

x+μ(x2 −1)x`+ x=0

Which is the forced Van der Pol model used originally to describe oscillations within an electrical circuit model of a heartbeat. We may also attempt to understand the use of the forced Van der Pol using Goodwin’s non-linear accelerator-multiplier model, in contrast to the Samuelsonian vulgar linear accelerator-multiplier model: 

x`+ A(x)X̂  + B(x) = I(t) 

A(x) being an even function with A(0) > 0, and B(x) an odd function with B(0) = 0, following Chian (2007). Continuing:

I(t) = a sin(ωt) 

a being the amplitude of exogenous force, and ω, its frequency: 

A(x) = μ(x2 − 1), B(x) = x

We again obtain a forced Van der Pol model of non-linear business cycles: 

x`+ μ(x2 − 1)X̂  + x = a sin(ωt)

Using the forced Van der Pol model we are enabled with the tools that allow for us to comprehend the phenomena of an attractor merging crises, where an attractor finds an unstable fixed point that is inside a basin of attraction. In this example, when this occurs, two (or more) chaotic attractors merge together to form a stronger chaotic attractor, this can be used to explain the transition from booms to recessions within Kaldorian unstable equilibria transitions and Goodwin’s non-linear accelerator-multiplier model of the business cycle. The ability to forecast, and consequently uncertainty, tends to increase along with volatility during an attractor merging crises which may be the upper turning point within these models of the business cycle, leading to a consequent recession or a flight of capital from an economy. 

In this (very) brief blog post I have demonstrated the possibility of endogenous business cycles following from Goodwin’s and Kaldor’s non-linear models of the business cycle and introducing chaotic dynamics following from the work of other more knowledgeable mathematicians. Growth models and chaotic dynamics will most likely remain the focus of this blog for the next few weeks as there is a lot left unanswered with such a short blogpost. Chaotic dynamics offers a more physical argument of fundamental uncertainty in the market economy, contrasted to the a priori “ontological uncertainty” of present day fundamentalist Post-Keynesians, considering the great deal of theoretical conditions of which chaotic dynamics can occur and its implications for market stability that I have very briefly considered above. I hope that in the future I can clarify some of the open ended questions that were briefly addressed such as the implications for financial instability or the use of the forced Van der Pol model. 

References:

1.  Akhmet, M., Akhmetova, Z., & Fen, M. O. (n.d.). Exogenous versus endogenous for chaotic business cycles. https://arxiv.org/pdf/1509.01034. 

2.  Pribylova, L. (2009), Bifurcation routes to chaos in an extended Van der Pol’s equation applied to economic models, Electronic Journal of Differential Equations

3.  Mohd, Mohd Hafiz, et al. Dynamical Systems, Bifurcation Analysis and Applications. Springer Nature, 2019

4.  A. Chian, 2007. "Complex Systems Approach to Economic Dynamics," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-39753-3, June.

Meng Hu on Reswitching: Grossly Mistaken

A Brief Critique 

Just when I was about to finish my reswitching streak (2 posts, barely) before a commenter on my last post sent Meng Hu’s terrible piece on reswitching. Austrians have a general tendency to either assert a metaphysical aspect to reswitching and other capital paradoxes or simply claim they are empirically non-existent or negligible, such as Garrison (2006). Meng Hu, somehow, manages to group them all and make an incredibly ignorant piece on reswitching and its implications for the Austrian business cycle theory, along with simply just spewing quote vomit absolutely everywhere. 

“And it doesn’t appear to be a very common phenomenon and casts doubt on its relevance in the real world. Young (2012) found evidence that the more roundabout industries have seen their industrial prices increased by more than the less roundabout, on the onset of the subprime episode. Besides, Roger Garrison expresses his doubts about the plausibility of the reswitching hypothetical example, as follows:”

Meng Hu, being the “go to” empiricist for the internet Austrians, of course first attacks reswitching on an empirical rather than theoretical ground as most vulgar Neoclassical and Austrian economists have attempted to do in the past, e.g., Ferguson (1969) and Garrison (2006). This entire argument, as I’ve pointed out in my last post, is incredibly ignorant of the main point demonstrated by the existence of reswitching and reverse capital deepening is that there is no possible argument to be made that there lies an inverse linear relationship between capital intensity and interest rates, if such an argument is demonstrated to have paradoxical results. On a methodological point, it is not necessary to invalidate the Austrian business cycle theory by positing an empirical relationship/likelihood of reswitching occurring with production processes, meaning the percentage of reverse capital deepening and reswitching occurring within production processes in the economy (economies?) drawn from NIPAs is irrelevant to the general validity/invalidity of the Austrian business cycle theory. What the Sraffians in the CCC demonstrated was that there was no inverse relationship between the quantity of capital and rates of profit, and extended to reverse capital deepening, there is no inverse relationship between capital intensity and the rate of interest. With reverse capital deepening, the Sraffians demonstrated, the entire relationship between capital and the interest rate simply does not follow a monotonic decreasing relationship, with reswitching it is indeterminate and with reverse capital deepening the relationships is not an inverse deepening relationship, it’s an relationship with the quantity of capital moving “up” as the rate of interest moves “up”. The demonstration of an existence of a paradox does not need empirical data to refute the existence of theories which depend upon the paradox generating theory, the demonstration of a paradox means the entire relationship cannot exist as posited by the Austrian theory. The same follows for the excerpt from Garrison’s paper on reswitching, it doesn’t matter about the cost differences inasmuch as a paradox has been demonstrated in which unless the paradox itself does not exist, the theory is bankrupt. Garrison did not demonstrate that the middle technique on the w-r frontier could be readopted, he demonstrated that the cost difference is smaller than expected which is not sufficient to refute the demonstration of the existence of reswitching or reverse capital deepening. This all stems from a general methodological error by the Austrians and Neoclassicals, that it needs to be empirically demonstrated that the existence of reswitching is frequent to refute the marginal productivity theory of distribution and the aggregate production function or the Austrian theory of the business cycle. Another point, on Young (2012), is that Young’s regression did not incorporate the capital paradoxes into his regression, meaning there could be many misspecifications for Young’s model and other Austrian macro models caused by reswitching and reverse capital deepening’s effects, causal indeterminacy, among others.

“Meng Hu” then proceeds to cite Rothbard on the theoretical dependence of capital intensity by the Austrian business cycle theory: 

“Credit expansion always generates the business cycle process, even when other tendencies cloak its workings. Thus, many people believe that all is well if prices do not rise or if the actually recorded interest rate does not fall. But prices may well not rise because of some counteracting force – such as an increase in the supply of goods or a rise in the demand for money. But this does not mean that the boom-depression cycle fails to occur. The essential processes of the boom – distorted interest rates, malinvestments, bankruptcies, etc. – continue unchecked. This is one of the reasons why those who approach business cycles from a statistical point of view and try in that way to arrive at a theory are in hopeless error. Any historical-statistical fact is a complex resultant of many causal influences and cannot be used as a simple element with which to construct a causal theory. The point is that credit expansion raises prices beyond what they would have been in the free market and thereby creates the business cycle. Similarly, credit expansion does not necessarily lower the interest rate below the rate previously recorded; it lowers the rate below what it would have been in the free market and thus creates distortion and malinvestment. Recorded interest rates in the boom will generally rise, in fact, because of the purchasing-power component in the market interest rate. An increase in prices, as we have seen, generates a positive purchasing-power component in the natural interest rate, i.e., the rate of return earned by businessmen on the market.”

Rothbard’s claim in this excerpt is extremely illogical because it takes the unhampered market rate of interest as a given, and furthermore, that the market rate of interest itself is determined by non-monetary subjective temporal preferential factors, i.e., “time preference”. Unless the theorist himself is aware of the state of prices, including the interest rate, in an unhampered market without an interventionist central bank or “State”, the theorist himself is in a state of causal indeterminacy. Aside from the major empirical issues of the inability to properly theorize about the ABCT when the statistical empirical analysis necessarily requires, in Rothbard’s own words, an unhampered standard to theorize off of. Until such a state is satiated, it’s impossible for anyone to take the Austrian theory seriously as it posits some sort of metaphysical relationship, taking for granted the necessity to prove the theory using an existent standard of measurement. Another ignorant argument by Rothbard is that the problem with historical-statistical data is that it is impossible to isolate a single causal factor. This is true in a very crude sense, i.e., while it’s impossible to find a general singular causal factor it is definitely possible to find a general trend which through a line of causal events leads to a final conclusion of the phenomena analyzed statistically. The same argument follows for Huerta De Soto’s argument of the non-necessity for the interest rate to actually decline, it assumes an unhampered standard to theorize from, which cannot exist due to the immense of causal factors the theorist must analyze before attempting to even start predicting the various prices in the market economy. 

“And Ludwig Von Mises (1940, p. 50; 1949 [1996] pp. 558-559, 795) himself focuses on the credit (over)expansion, not the interest rate as such. When the amount of credit supply diverges from individuals’ time preference, with more credit than people’s willingness to wait, the entrepreneurs are left to believe there is more savings than what is actually available. Even an increase in the interest rate will not necessarily stop speculation and malinvestments to be accumulated if the borrowers are determined to complete the new capital goods stages begun and which they begin to see threatened. Mises uses this example to say that the origins and end of the boom were not to be found in the interest rates but credit expansion.”

A very common occurrence, I’ve found with reading on the Austrians, is that their claims generally follow an institutionally backward non-credit based economy.  The Misesian theory posits a general divergence from the rate of savings and the amount of loans in the economy, i.e., that savings rates in an unhampered market economy itself would drive loans and the monetary overexpansion driven by the central bank or government through fiscal policy causes more loans to be expanded than there is real savings. If real savings are in a disconnect with the amount of loans, then there is not enough “real resources” in the economy to complete projects which necessarily results in liquidation of the malinvested projects. This may hold true for a commodity based economy or a fiat economy, but this is not true for a credit based economy in which the amount of loans and the amount of savings don’t ever matter. Real resources are not purchased by savings expanded through loans, they’re purchased using credit administered from banks in a circuit like manner, i.e., a financial provision is first expanded to the firms which transfers itself into means of production purchases and finally discharged into profits and wages, which make their ways back to the banks. The incredibly important thing to note is that banks are not ever savings constrained and that real resources are barely ever purchased by savings and by a transitive property, a lack of savings caused by monetary overexpansion would cause a shortage of real resources; banks are always lending out of line with savings and will continue to do so in an advanced credit economy, real resources are purchased through credit and a shortage of savings does not imply, in most general cases, a shortage of real resources as credit in the economy is not reserve constrained at all. The “monetary overexpansion” and a lack of real savings causing a shortage of real resources itself ignores the logical possibility of idle resources & that savings purchase very little consequential things in the business world compared to credit. 

Citing De Soto: 

“An increase in saving (and thus a decrease in the interest rate, other things being equal) may result in the replacement of a certain technique (the Roman plow, for instance) by a more capital-intensive one (the tractor). Even so, a subsequent drop in the interest rate may permit the reintroduction of the Roman plow in new production processes formerly prevented by a lack of saving (in other words, the established processes are not affected and still involve the use of tractors). Indeed a new lengthening of production processes may give rise to new stages in agriculture or gardening that incorporate techniques which, even assuming that production processes are effectively lengthened, may appear less capital-intensive when considered separately in a comparative static equilibrium analysis.

What De Soto (And in effect Meng Hu) is attempting to claim is that regardless of the adoption of techniques by economic actors, the structure of production will increase a priori. This approach itself has multiple flaws, starting from the argument that an increase in the rate of saving has anything to do with the rate of interest. Austrians who make this claim (And Neoclassicals) assume the loanable funds theory of interest, i.e., an increase in the amount of loanable funds caused by increased savings triggered by “time preference” will cause a general decrease in the rate of interest. This approach, however, is sorely mistaken by assuming a general property of savings immediately being turned into loanable funds without regards for liquidity preference. Liquidity preference ensures that there is no direct relationship with the quantity of savings and the amount of loans in the economy, as a hedge against uncertainty individual economic actors will invest in liquid assets. This means that any increase in saving does not lead to an equivalent increase in the supply of loanable funds, which by the principle of supply and demand, lowers the rate of interest. Another important thing to consider is what was pointed out in the paragraph above, that the level of savings in the economy has nothing to do with the amount of real resources or amount of loanable funds in a credit based economy. De Soto also takes for granted that any increase in the stages of production (Better termed, complexity) will cause the business cycle. An adoption of less capital intensive processes implies that the entire structure of production does not need to move towards “Earlier” or “Higher” stages of production, they can remain in a stage of production that is near the “middle”; which means that the phenomena of stretching of the stages of production in the ABCT does not exist at all. De Soto, like other Austrian others, takes the theory as true a priori and then simply claims that any increase in savings lengthens the structure of production despiste an adoption of techniques which lie along a “middle” stage of production”. In effect, De Soto completely isolates the structure of production from its own composition, the techniques of production and economic actors. Something must be wrong here! 

The same argument applies for Rizzo and O’Driscoll point on the increased roundaboutness even though there’s a decline in consumption per head and the amount of capital employed, i.e., they posit some sort of independence between the structure of production itself and the techniques which consist of the structure of production, a foolish notion to anyone who understands how very basic complex composition works. Another thing is that, as pointed out, time preference is not a satisfactory cause for the rate of interest’s determination at it supposes, very importantly, loanable funds for the theory to cause a fall in the rate of interest. If loanable funds were to be non-existent in the Austrian interest rate determination model, then the entire argument falls apart as there is no proper causal factor which can cause a decline in the rate of interest caused by supply and demand mechanisms: 

“… In the Cambridge formulation the rate of interest is treated as an exogenous variable. The changes in the interest rate that supposedly induce technique reswitching are themselves unaccounted for. This simply makes for bad theory – theory in which changes in the level of savings are neither a cause nor a consequence of changes in the rate of interest. In the reswitching models, the only change in production activities allowed for is a change in the technique employed. A change in the rate of interest either has no effect whatever or provokes a change in the production technique. The relevance of such a model – even to Böhm-Bawerk’s formulation of Austrian capital theory – is questionable. And the particular way in which the analysis is carried out raises still further questions. Despite claims to the contrary, the fundamental distinction between the comparison of alternative equilibrium states and the description of the process by which the economy is moved from one state to another is hopelessly blurred. This is a virtually inevitable consequence of the failure to specify what particular preference or policy change caused the initial change in the rate of interest. While these aspects of Cambridge capital theory are grounds for dissatisfaction with the theory itself, they have been largely overlooked in the present treatment in order that the thematic distinction between subjectivist and objectivist views of a capital-using economy could be emphasized.” 

Accounting for the determination of the rate of interest, aside from being an exogenous entity as pointed out by Basil J. Moore[1], is relatively inconsequential for the demonstration of the phenomena of reswitching. As has been pointed out, the argument that the rate of interest is determined by time preference is logically invalid, which means another causal factor must be attributed. Adopting an either horizontalist or structuralist conception of endogenous money, i.e., exogenous short-long run interest rates or exogenous short term and endogenous long term rates, still doesn’t change the conclusion of reswitching for the ABCT. It isn’t a bad theory, considering exogenous rates or liquidity preference determination of the interest rate means very little for the theory itself, the Austrians are grasping at straws from a fallacious theory of interest rates. Rizzo and O’Driscoll’s arguments of “subjectivism” or “objectivism” are inconsequential for the theory as they again suppose independence of the structure of production from the techniques of production. Adoption of reswitching does not cause increased stages of production, it rather leads to a decline or indeterminate relationship about the level of complexity and the rate of interest. For these projects to be unsustainable, what is necessary is that savings must be equated to loans, which is not true for a credit based economy. 

“At this point, however, one particular misunderstanding of the theorem that roundabout processes of production are more productive may be mentioned, as it is due to a confusion between these two concepts. It has sometimes been argued that an increase of capital is more likely to shorten than to lengthen the time during which we have to wait for the product. And this is quite true when we speak of the time interval which will elapse before a given quantity of output will emerge. But this is quite compatible with a simultaneous increase in the periods for which we have to wait for the product of particular units of input.”

For most of the rest of the post, Meng Hu presupposes there is a fundamental non equivalence between the structure of production and composition of the production techniques. What must result is causal indeterminacy, one is completely unable to draw any reasonable conclusions about the Austrian theory if one posits indeterminacy of the relationships between composition of the production structure and the structure itself. To prove the Austrian theory, it is near impossible to draw a relationship between over-roundaboutness, the interest rate, and money supply as the independence means that there cannot be any relationship between the composition of the structure of production and its “roundaboutness”! Mateusz Machaj, an Austrian I do like a great deal on capital and interest theory, expresses the ridiculous nature of De Soto et al. on reswitching:

“The one argument that supports those conclusions is that with every shift and change of circumstances, the system resets. All factors have a new life with every switch, so Huerta de Soto would not allow us to compare various ways of producing goods. Such a statement may be doubtful, but let us assume it is true. Taking a future-oriented perspective, we can still show a potential reswitching between two ways of producing a particular good, depending on the interest rate. We do not have to rely on bygones and include past costs in any way. The reswitching challenge can be presented in a forward-looking manner. Moreover, the more we look into Huerta de Soto’s statements, the more questionable they become. In a sense, he tries to completely separate the notions of “technique” and “length of production.” But why? What if by “technique” we also mean length of production, as in the reswitching debate? A contradiction appears since, in Huerta de Soto’s terms, we would have to state that the productive structure lengthens regardless of whether we choose a shorter production technique—even if all sequences of techniques are in sum taking shorter time! Put differently, we would have to state “savings always causes, in prospective terms, a ‘lengthening’ of the productive structure, irrespective of whether techniques are shorter.”Obviously there is something missing here.”[2]

On the presentation of reswitching in a forward looking manner, blogger Robert Vienneau and Saverio M. Fratini[3] have both reframed the argument in a forward looking manner, Vienneau taking the argument even further by demonstrating around switchpoints entrepreneurs are indifferent to production processes and need not even adopt a project with more capital intensity and a higher NPV, which again refutes the Neo-Austrian notion based off of the “Rehabilitated” “Average Period” measure of the structure of production. 

“One result of the recent discussion on “reswitching” is to the advantage of the Austrian school. As long as all capital is regarded as homogeneous, managers may respond to a marginal fall in the rate of interest by a marginal act of substitution of capital for labor. But heterogeneity of capital entails a regrouping of the existing capital combination; some capital goods may have to be discarded, others acquired. It is no longer a marginal adjustment that is called for but entrepreneurial choice and decision. As Pasinetti pointed out, “Two techniques may well be as near as one likes on the scale of variation of the rate of profit and yet the physical capital goods they require may be completely different.” In a world of disequilibrium, entrepreneurs continually have to regroup their capital combinations in response to changes of all kinds, present and expected, on the cost side as well as on the market side. A change in the mode of income distribution is merely one special case of a very large class of cases to which the entrepreneur has to give constant attention. No matter whether switching or reswitching is to be undertaken, or any other response to market change, expectations play a part, and the individuality of each firm finds its expression in its own way. Yet only “reswitching” has of late attracted the interest of theoreticians. There is more in the world of capital and markets than is dreamt of in their philosophy.” 

I am quite unaware of the manner of which this is to attempt to refute the Sraffians on reswitching, it’d help if Meng Hu could explain this quote more clearly as it does in no possible way refute the Sraffian notions of reswitching! Yes, entrepreneurs are forced to consider other phenomena occurring in the economy and plan ex ante to adjust to these expected changes, which include income distribution. Even presuming that for some reason a firm will not choose the cost minimizing less capital intensive process due to expected ex ante plans, it still does no good for the Austrian theory as Lachmann ends up accepting that there is no monotonic relationship between the structure of production, interest rates, and capital intensity and adds on to the Sraffians. I do enjoy Lachmann’s work a great deal, being incredibly interested in his heterogenous theory of capital and analysis of the kaleidic world and consequent ex ante planning in a kaleidic world, and this insight offered by him does not refute the Sraffian theory at all, merely adds on a more “subjectivist” angle to entrepreneurial decisions in a kaleidic market economy. 

“This premise is that each technique of production involves a simple, unidimensional ‘quantity’ of time, such that different techniques can be unambiguously ‘objectively’ ranked as involving greater or lesser quantities of time (or waiting). In fact, there is no reason at all to accept this premise. The cases that yield the capital-reversing paradoxes all arise from production processes involving more or less complex dating patterns for inputs and outputs. (In a stylized example made by Samuelson (1966), a given quantity of output can be obtained in year 4 from one technique that calls for the input of two units of labour in year 1, and six units of labour in year 3; or alternatively by a second technique of production calling only for the input of seven units of labour in year 2.) It appears obviously mistaken (or at least to involve an arbitrary and possibly misleading oversimplification) to wish to collapse the possibly incommensurable quantities of time associated with individually dated input components of a given complex production technique into a single simple unidimensional quantity of time.”

It’s worth briefly mentioning the erroneous argument made by Kirzner that reswitching models are hyper-aggregated and consequently cannot explain choice of technique or other phenomena satisfactorily. Aside from the ability for reswitching to analyze disequilibrium situations[4] such as being existent in types of structural instabilities like cusp catastrophes, which necessarily entail non-equilibrium disaggregated structural instabilities by virtue of its own nature, reswitching can also be formalized in a forward looking disaggregated manner as pointed out above. Kirzner’s comment is out of line and has little knowledge of Sraffian literature outside of the very barely Sraffian argument made by the Neoclassical Synthesis Keynesian Paul Samuelson, as most Austrians discussing reswitching. The rest of Meng Hu’s blogpost is just a vomit of quotes, all of which repeats itself and would be inconsequential to repeat here as it has already been covered. 

“The reswitching paradox appears crystal clear now. The error was to consider the interest rate as being the fundamental cause behind the technique reswitching while, in reality, the relative prices were really what mattered most. The distortion of those relative prices through money expansion can indeed predict the technique reswitching. This reveals those attacks on the ABCT to be misleading and completely outside the point.” 

Aside from the heterogeneity in the “ABCT” itself, i.e., differences between the Misesian/Rothbardian and Hayekian theory of the business cycle, it has been demonstrated throughout this blogpost that the alternative views cannot be sustained on account of taking given unhampered market price benchmarks, assuming independence of the structure of production and its composition leading to causal indeterminacy, or primarily as a cornerstone assuming loanable funds. All of the arguments raised by Meng Hu simply do not stand in light of the vast Sraffian literature on differential types of reswitching or are simply erroneous.

References:

1.  Moore, B. J. (1988). Horizontalists and verticalists: The macroeconomics of credit money. Cambridge [England: Cambridge University Press]

2.  Machaj, M. (2017). Money, Interest, and the Structure of Production: Resolving Some Puzzles in the Theory of Capital (Capitalist Thought: Studies in Philosophy, Politics, and Economics). Lexington Books.

3.  Saverio M. Fratini, 2019. "A note on re-switching, the average period of production and the Austrian business-cycle theory," The Review of Austrian Economics, Springer;Society for the Development of Austrian Economics, vol. 324, pages 363-374, December.

4.  Rosser, J. Barkley, Jr. 1983. “Reswitching as a Cusp Catastrophe,” Journal of Economic Theory 31:1, 182-193.