Tuesday, December 11, 2012

So? None of your conclusions follow from your arguments

Krugman has a post on the effects of technological change on employment. Here is a very illustrative case of the limitations of mainstream marginalist (neoclassical) economics, which leads a reasonable and intelligent economist to all sorts of mistakes. He says:
"start with the notion of an aggregate production function, which relates economy-wide output to economy-wide inputs of capital and labor. Yes, that sort of aggregation does violence to the complexity of reality. So?"
Implicit here is the incorrect notion that the problem with the aggregate production function is over-simplification. Nope, that is a feature of all theories of course. The problem is far worse; it is that it leads to logical mistakes.* So, as we will see, none of Krugman's conclusions follow from his analysis, and that is kind of a problem. Lack of logical coherence and empirical evidence are after all the two main criteria of demarcation between scientific knowledge and the half-baked notions of ideologues.

His first point, which is based on the marginalist theory of distribution**, is that:
"in competitive economy ..., we would expect the labor force to achieve full employment by accepting whatever real wage is consistent with said full employment."
In other words, wage flexibility guarantees the full utilization of labor. A reduction in the real wage in the case of unemployment would lead to full employment (yes, he actually does not defend this in policy discussions, because he thinks that nominal wage rigidities preclude adjustment; mind you his real preocupation is that the rate of interest of equilibrium is negative, precluding adjustment in capital markets).

Of course this is nonsense. A reduction in real wages, and I'm not even talking about the effects of deflation on demand which were discussed by Keynes in the chapter 19 of the General Theory, may not lead to an increase in the demand for labor. First, it must be noted that if wages go down, since wages are part of the cost of production of produced means of production (i.e. capital), the price of the latter also goes down. There is a priori no reason to say that firms will substitute labor for capital (on capital debates go here; really Krugman should read this stuff).

Second, once the idea that the intensity of the use of a 'factor of production' is inversely related with its remuneration is abandoned (by the way there is no evidence for the notion that real wages are inversely related to employment utilization, in fact, if anything, the evidence points in the other direction, with real wages being slightly pro-cyclical), there is no reason to believe that real wages are connected to productivity (and again there is no evidence for that relation either, which means that when Krugman asks "what is that real wage?" and replies that it is "the marginal product of labor at that point," he is also incorrect). Yes real wages have stagnated, since the bargaining power of the working class has deteriorated, with productivity still growing since the 1970s.

So, what is the problem Mr. Krugman? That your conclusion, that the effects of technical change on employment are ambiguous, does not follow logically from your arguments. Ricardo's discussion of the effects of technical change on employment, in his famous chapter on machinery, is far more interesting and coherent than Krugman's (see the paper here). Not just the idea of a natural rate has to be abandoned, but the essential principle of substitution, which allows for the natural rate, must be dropped too. Logical coherence and evidence require it.

* For a serious discussion of the limitations of the aggregate production function go this paper by Jesus Felipe and Franklin Fisher here.

** The quote of Hicks classic presentation of the marginalist theory of wages leaves little doubt of where Krugman stands, if you had any.


  1. I wrote my last post before reading this. I find this somewhat freaky.

  2. "The problem is far worse; it is that it leads to logical mistakes."

    Does it? It's easy to construct a logically-consistent model where Krugman's arguments would hold (basic one-sector Solow growth model with CES production function should do). Capital controversies showed that it's also possible to construct models where they wouldn't hold. So what? Krugman didn't claim that his arguments follow automatically from pure logic alone, just that they might be a reasonable approximation to reality. He could be wrong, but that's question that cannot be decided by logic alone.

    1. Hi Ivan. The problem is that the models you cite are not logically consistent. Solow depends on the inverse relation between capital intensity and remuneration. That is not a general case, and its conclusions are not general. I suggest you read the link I posted on the capital debates.

    2. I've read it. Unless people have been overlooking mathematical mistakes for half a century, Solow model is consistent, given its assumptions. I agree that conclusions from one-sector models are not general in the sense of being robust to relaxing some of those assumptions, but that's not the same thing as logical inconsistency per se.

      For example, say that I claimed that raising minimum wage will lead to increase in unemployment. This is not general conclusion, since there are models like monopsony which would predict opposite outcome. But that by itself doesn't mean I'm making a logical mistake - after all, it's still possible that minimum wage will increase unemployment. I would be making a logical mistake only if I claimed that my prediction is true in the same sense that mathematical theorems are true (in which case even a hypothetical counterexample would indeed prove me wrong), but that's not how most economists think.

    3. Nope, people did not overlook it and it is inconsistent. See Samuelson (1966). The model presupposes that higher capital intensity is associated with lower rates of interest, and you have marginal decreasing returns to capital. Substitution works and you get with cheaper capital more demand for the factor of production. All features that the capital debates show that are not general, as admitted by Samuelson.

    4. By the way, that is the problem. No model that tries to prove that prices (normal long term prices are determined by supply and demand) is consistent, meaning that its conclusions do not follow from the assumptions. That is a result of the capital debates.

    5. I have to disagree. Bit more formally, let's consider assumptions: one-sector model (A), neoclassical production function (B), competitive equilibrium (C), and claim: "higher capital intensity is associated with lower interest rate" (D). Then implication A + B + C ==> D is true (so conclusions of Solow model _do_ follow from its assumptions). What capital debates showed is that if we drop A, the result may no longer follow, i.e. implication B + C ==> D is false. However, none of this tells us by itself whether D is true or false.

      In the end, this is of second-order importance. The point of Krugman's post was that technological progress may lead to changes in distribution of income between capital and labor (which of course doesn't rule out other explanations), and direction of the effect will depend on characteristics of the particular change in technology. Generally speaking, this seems pretty uncontroversial even if you reject neoclassical models.

    6. That's not true. Either the economy has only one sector [which is unreal], or you get one 'jelly' K. You say that competitive equilibrium implies determining prices and distribution [prices of factors] following their marginal productivity, ie, the return to the owners of K should be the marginal productivity of K. But you don't know what K means. You are solving the math, but you're not solving the economic part. Economically, there is a logical contradiction in aggregating capital goods into K by using relative prices [and distribution] to determine... relative prices and distribution¡.
      And when that can be said to be true and useful? Only when capital intensity between branches of production are equal. And this, of course, never happens.
      Now, you're saying that technological progress [A?, the Solow residual?]may lead to changes in distribution. Well, if you can't use K to determine prices, you cannot use either A. There is no Y as f[A,K,L]; there is only Y as wL+rK once you've determined prices, and that only happens when you have determined distribution as an exogenous variable.

    7. Again Ivan his point is that technological progress leads to in income distribution given the changes in relative prices associated with relative scarcity of factor of production (the marginal productivities). That is simple not logically correct. Admited by Paul Samuelson. No point of revisiting the capital debates. That's algebra. Mind you, you are right that the point that technical change may affect income disttribution is important, but the channels must deal, as Paul has noted in a more recent post, with social relations (who owns capital and who doesn't, his words by the way).

    8. Also, I should note, as Genaro is suggesting, that the point made by Felipe and Fisher is that you cannot prove from an empirical point of view the existence of a production function, since you always measure the identity of income. The Solow Residual (TFP) is not productivity, but the weighted average of the rate of growth of wages and profit. Again a simple algebraic fact. Not open to controversy really.

  3. ALL labor can be liquidated. And it can be done humanely. And it can drive WalMart wages higher:


    more later...