Friday, February 21, 2014

Not Always on the PPF – Problems with the Hayekian Triangle

There are three shortcomings of the Hayekian triangle I wish to bring to light.
1) Empirically, prices in all stages of production tend to move together.
2) Related to critique 1, the Hayekian triangle assumes an economy at full employment equilibrium.
3) The Hayekian triangle is an incoherent representation of the macroeconomy.
In his book, Risk and Business Cycles, Tyler Cowen considers points 1) and 2)

Positive comovement [in prices of goods at both the early and latter stages of production] poses a dilemma for theories of the business cycle which start with the assumption of full employment. Comovement requires that all, or nearly all sectors of the economy expand at once, as we usually find in the data. (30)
This poses a problem for Hayek’s analysis where resources are moving from the latter stages to the earlier stages of production. This process is depicted below (Prices and Production, 44, 52).

Notice that the triangle gained two rows. This gain comes at the loss of the length of the already existent rows. That is, investment increases at the expense of consumption in the early stages of the boom. Hayek’s model is a static one where the economy starts at a full-employment equilibrium. In the case of credit expansion it is pushed from this equlibrium. Consumption does not reduce to compensate for the lengthening of production and there is even an increase in consumption as wages rise. Consumers compete with producers for resources in an unsustainable boom that is inevitably followed by a bust. Hayek’s model describes an aspect of reality, but how significant is that aspect? Is artificial expansion of credit necessary for this scenario? 

The model assumes that the economy is at the edge of the PPF, that it is at a full-employment equilibrium. A more likely scenario is that the economy is constantly oscillating between the edge of the PPF and the origin. Of course, an economy with well-functioning markets likely operates in greater proximity to the PPF than the origin. Central bank intervention will distort this natural fluctuation, though it is unclear in what ways and to what extent. The state of the economy is always in flux, so the same intervention will not always lead to the same results. The assumption of full employment equilibrium obscures the interaction between natural fluctuations and central bank intervention, and thus the model overemphasizes a unique case. This might be corrected by expanding the model to include different levels of employment.

As a model of the macroeconomy the triangle is represents a snapshot at a given point in time. In this interpretation, the triangle is an aggregation which describes the macro economy in a misleading manner. We might represent an individual good in Hayekian form, and trace out changes in different stages with only minor distortion, but when used to represent the entire economy the triangle must implicitly assume price levels similar to those for which he critiques his peers. In his critique of Hawtrey’s discussion of the price level Hayek writes,

But the main concern of this type of theory is avowed, with certain suppositions ‘tendencies, which affect all prices equally, or at any rate, impartially, at the same time in the same direction.’ And it is only after the alleged causal relation between changes in the quantity of money and average prices has thus been established that effects on relative prices are considered. (5)

But Hayek refers to the price ratios between the stages of production. In referring to the macro economy, he must be referring to the ratio of price levels between the stages (assuming that stages can be neatly represented at this level of analysis). Hayek did not to apply this critique to his own theory. 

As a representation of the macro economy, the triangle also errs in predicting the nature of new investments. Consider Hawtrey’s critique of Hayek’s stages.

It is quite likely that the additional investment will be predominantly in the earlier stages, but it is not necessarily so. It might happen that the next most remunerative openings for investment are mainly or exclusively among the later stages. There is no necessary connection between the margin of investment and the stages, and the introduction of the stages into the exposition of the extension of investment serves no useful purpose. (243) 

There may be a tendency for increased investment in the later earlier stages, but that tendency ought not preclude a broadening of the triangle’s base. Hawtrey also argues that there is a continual deepening of the capital structure during booms and depressions. Expansion may augment this deepening but it can also broaden the capital structure during the boom period if there are unrealized gains in the later stages that result from the lowering of the interest rate.

Unlike the problem first discussed, I am not sure that these last two can be easily corrected. In terms of macroeconomic analysis, we are left with a triangle whose usefulness is exceeded by its obscurantism.


  1. I haven't been able to read the whole post, so maybe I'm jumping the gun, but that consumers' goods prices and producers' good prices (on aggregate, wrt the latter) go up together is not the same thing as comovement of prices between stages of production. And, I'm not sure it qualifies as a shortcoming of the theory, either, since both Mises and Hayek were aware of the empirical fact and actually argued that it helped their case rather than undermine it (since, productive expansion "backed" by real savings implies falling consumers' good prices).

    1. Also, re: Hawtrey, I'd have to read his whole critique, but that excerpt doesn't satisfy me. If we're faithful to the ideal type, initial investment will occur in later stages, not earlier stages. This increases profit margins for earlier stages, because a price rise in the 2nd stage will attract investment into the 3rd stage (to produce the inputs the 2nd stage demand). So, in reality, we should see an increase in investment throughout the entire structure of production, not just earlier stages -- and, in terms of volume, most of the new investment will be in the middle and later stages, not in the earliest stages.

    2. Yes, the theory says that we should see a short-run expansion of the entire triangle if growth is due to artificial credit expansion. Garrison conveys this well by moving the economy of the PPF in his model.

      If expansion is due to savings, the model says we should see resources shift to the earlier stages and over time, the latter stages will expand sustainably.

      I'm puzzled by the second sentence of your second comment:

      "If we're faithful to the ideal type, initial investment will occur in later stages, not earlier stages."

      But you go on to say that the expansion in the latter stages occur as a result of an increase in the profit margins of earlier stages. I don't believe we are in disagreement.

    3. I just noticed that I used the word later when I should have said earlier after the Hawtrey quote. That should clear up some confusion. The expansion in the latter stages can occur alongside, rather than as a result, of expansion of earlier stages.

  2. "the introduction of the stages into the exposition of the extension of investment serves no useful purpose."

    "In terms of macroeconomic analysis, we are left with a triangle whose usefulness is exceeded by its obscurantism."

    A baseball bat is not a particularly good tool for opening a can of beans. To this extent, the triangle as a descriptive and analytical tool also has its limitations. However, baseball bats are particularly good for clubbing people over the head; the triangle is similarly percussively effective at demonstrating the heterogeneity of capital investment. It matters where investment is going. Combined with the knowledge problem confronted more effectively by decentralized rather than centralized planning, you have established a presumption against government-directed investment.

    Bloody useful, I'd say.

  3. Good, clear post. I has inspired me to post as well, taking the contrarian view that the problem with the Hayekian triangle as microeconomic explanation is that it does not take the heterogeneity of capital sufficiently seriously.

    1. sure, but the hayekian triangle doesn't pretend that it is not aggregating, it is just a pedagogical tool for understanding size and temporal distribution of resources in a given line of production, basically.