Piketty and the need for validating assumptions

26 Jul, 2020 at 13:32 | Posted in Economics | 3 Comments

validateAssumptions_cropped-401x321Say we have a diehard neoclassical model (assuming the production function is homogeneous of degree one and unlimited substitutability) such as the standard Cobb-Douglas production function (with A a given productivity parameter, and k  the ratio of capital stock to labor, K/L) y = Akα , with a constant investment λ out of output y and a constant depreciation rate δ of the “capital per worker” k, where the rate of accumulation of k, Δk = λyδk, equals Δk = λAkαδk. In steady-state (*) we have λAk*α = δk*, giving λ/δ = k*/y* and k* = (λA/δ)1/(1-α)Putting this value of k* into the production function, gives us the steady-state output per worker level y* = Ak*α= A1/(1-α)(λ/δ))α/(1-α)Assuming we have an exogenous Harrod-neutral technological progress that increases y with a growth rate g (assuming a zero labor growth rate and with y and k a fortiori now being refined as y/A and k/A respectively, giving the production function as y = kα) we get dk/dt = λy – (g + δ)k, which in the Cobb-Douglas case gives dk/dt = λkα– (g + δ)k, with steady-state value k* = (λ/(g + δ))1/(1-αand capital-output ratio k*/y* = k*/k*α = λ/(g + δ). If using Piketty’s preferred model with output and capital given net of depreciation, we have to change the final expression into k*/y* = k*/k*α = λ/(g + λδ). Now what Piketty does in Capital in the twenty-first century is to predict that g will fall and that this will increase the capital-output ratio. Let’s say we have δ = 0.03, λ = 0.1 and g = 0.03 initially. This gives a capital-output ratio of around 3. If g falls to 0.01 it rises to around 7.7. We reach analogous results if we use a basic CES production function with an elasticity of substitution σ > 1. With σ = 1.5, the capital share rises from 0.2 to 0.36 if the wealth-income ratio goes from 2.5 to 5, which according to Piketty is what actually has happened in rich countries during the last forty years.

Being able to show that you can get these results using one or another of the available standard neoclassical growth models and Piketty’s two crucial assumptions — β = K/Y and σ > 1 — is of course, from a realist point of view, of rather limited value. As usual — the really interesting thing is how in accord with reality are the assumptions you make and the numerical values you put into the model specification.

Professor Piketty chose a theoretical framework that simultaneously allowed him to produce catchy numerical predictions, in tune with his empirical findings, while soaring like an eagle above the ‘messy’ debates of political economists shunned by their own profession’s mainstream and condemned diligently to inquire, in pristine isolation, into capitalism’s radical indeterminacy. The fact that, to do this, he had to adopt axioms that are both grossly unrealistic and logically incoherent must have seemed to him a small price to pay.

Yanis Varoufakis

3 Comments

  1. SOUR GRAPES
    ——————
    1. Aesop’s fable : “The Fox and the Grapes”
    A hungry Fox saw some fine bunches of grapes hanging from a vine that was trained along a high trellis.
    He did his best to reach them by jumping as high as he could into the air.
    But it was all in vain, for they were just out of reach.
    So he gave up trying, and walked away with an air of dignity and unconcern, remarking, “I thought those grapes were ripe, but I see now they are quite sour.”
    —-
    2. A football team consistently played skillful football and won the championship.
    But die-hard supporters of a traditionally rival team refused to recognise this achievement.
    They resorted to drunkeness and hooliganism, claiming that the rival team’s success was due to luck and dirty play.

    3. A diligent French economist carefully explored and assembled voluminous date on incomes over several centuries in many countries. He exposed clear patterns consistent with mainstream neoclassical economics.
    Prof. Syll and other heterodox economists with Marxist tendencies realised that this undermined their blinkered class-warfare view of how economies work.
    Unable to produce any data or empirical results of their own, they slandered the French explorer alleging that he failed to consider whether his assumptions “accord with reality” and for adopting “axioms that are both grossly unrealistic and logically incoherent”.
    —-
    4. A populist businessman and TV personality unexpectedly won a democratic presidential election.
    He revived prosperity throughout the economy, reduced uneployment and racial inequalities, withdrew from foolish overseas wars, abolished unnecessary bureaucratic regulations, drained the elitist establishment swamp, and protected the people from illegal immigration and unfair foreign competition.
    This provoked a frenzy of paranoid hatred among rival politicians and media.
    They regarded the President’s supporters as “deplorables” and sought to undermine the President by foul means. They spied on, lied about and imprisoned the President’s friends, spread fake news, instigated hostile inquiries and baseless impeachment procedings, suppressed freedom and rights through lockdowns on the pretext of a pandemic, allied themselves with neo-Marxist revolutionaries, promoted racist woke identity politics and “political correct” language, fostered vicious protests to destroy the nation’s culture, and damaged law and order by slandering and defunding the police.

    • The problem is that in the real world supply chains are payment chains in reverse, i.e. payments come before production. Money production precedes real production; and money production is arbitrary, administered. Option volumes are greater than their underlyings. Derivatives are more liquid than the stocks they are derived from. The financial economy is the dog, the real economy is the tail.
      .
      The above story is inherent in Piketty’s observation that r > g, but I guess economists are unwilling to confront the implications of that statement.

  2. I suppose I simply do not understand what you are talking about. What test would “validate” his assumptions and to what purpose? Shouldn’t you be able to say?
    .
    Piketty’s analysis forms a heuristic in one way, and in another, a seduction. I respect the need his research imposed, for the heuristic. The heuristic is not especially prejudicial, and it lets us see the accounting relationships in what is at base, accounting data.
    .
    The seduction is more troubling to me. Using work horses of the mainstream hackocracy like Cobb-Douglas production functions is not a concession I would think to make, but it sets up an irresistible puzzle, for mainstream economists who cannot think in any other frame. Production functions make no sense as a theory of production, which is well-known to economists who are not idiots, but production functions are a theory of income distribution and Piketty is clever to return them to their original use. Confronting production functions, applied to income distribution, with data is interesting or should be interesting and is certainly instructive concerning how ill-conceived “capital” really is by mainstream economics.
    .
    Too many economists are content to validate their assumptions by solipsistic means, and too few confront any data with ugly, unstylized facts.


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