Felipe & McCombie: The Aggregate Production Function And The Measurement Of Technical Change

 

In a recent post, see here, it was explicated that TFP only leads to confusion in mainstream analysis of economic growth. Jesus Felipe & John S.L. McCombie's new book provides an invaluable extensive analysis of the issue at hand. 

Felipe and McCombie have gathered all of the compelling arguments denying the existence of aggregate production functions and showing that econometric estimates based on these fail to measure what they purport to quantify: they are artefacts. Their critique, which ought to be read by any economist doing empirical work, is destructive of nearly all that is important to mainstream economics: NAIRU and potential output measures, measures of wage elasticities, of output elasticities and of total factor productivity growth. – Marc Lavoie, University of Ottawa, Canada

See here

Total Factor Productivity does NOT measure what you think it does

The conventional discussion of Total Factor Productivity (TFP) starts from a production function. For that reason most people when they hear about the problems with TFP, think that it refers to aggregation problems (which on top many confuse with the capital debates, which did involve a critique of the production function, but was about more than that). 

The problem is that TFP is NOT productivity at all. So start from a Cobb-Douglas production function (it doesn’t really matter what production function for our argument):

Log-linearizing and deriving with respect to time you obtain:

Where alpha is the share of wages in national income. Solow suggested that the residual (dA/A) must be the combined effect of the increase in productivity of all factors of production (TFP).

Now consider the income identity that by definition tells us that net income (net of taxes) is composed by the remuneration of capital and labor. We have:

There is no need here to be concerned with aggregation questions. This is an identity and the data reflects NOT a theoretical construct, like the production function, but a national accounting identity. 

The total derivative of the identity would be:

Diving by Y, and with some manipulation, knowing that r=R/K, we get:

Note that the first two terms can be re-written using the above notation for the shares of profits (R) and wages (wN) in total income. We have:

Note any similarity with the growth accounting equation? The Solow residual is basically a weighted average of the rate of growth of profits and wages. This is what is being measured, since the data actually comes from the identity, not an imaginary production function. Even if you had a production function, you still would be measuring the identity.

Jesus Felipe and John McCombie have done extensive work, building on the work of Franklin Fisher, Herbert Simon, Anwar Shaikh and others. The use of TFP, when the evident measure of productivity should be labor productivity, only leads to additional confusion in mainstream analysis of economic growth (the other big problem being the supply constraint and the notion of a natural rate).

PS: There are several papers that one should read on (subscrirequired), but I suggest the following one (subscription required) by Felipe and McCombie that shows the kind of confusion that using TFP leads to when applied to the interpretation of the East Asian growth experience.

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.