January 28, 2015

Naive arithmetic

Comment on Lars Syll on 'NAIRU — more religion than science'


You summarize: “It [NAIRU] has fallen out of favor partly because its conceptual foundation is weak and partly because its empirical track record does not inspire confidence.”

The conceptual foundation is not weak but false.

The original Phillips curve was about the relation between the rate of unemployment and the rate of change of the wage rate (Phillips, 1958). Phillips studied more than a century's worth of data and established the stable inverse relation for the United Kingdom. Phillips's original curve was a remarkable empirical finding. It has to be emphasized that Phillips ‘had not made an explicit link between inflation and unemployment’ (Ormerod, 1994, p. 120).

The original curve was transformed by Samuelson with the simple formula: rate of inflation = rate of wage growth − rate of productivity growth (Samuelson and Nordhaus, 1998, p. 590). This formula, according to Samuelson an ‘important piece of inflation arithmetic’, says that price inflation runs in tandem with wage inflation and that both have basically the same effect on employment respectively the rate of unemployment. The difference between the original and the bastard Phillips Curve consists of a 1 percent productivity growth. This naive arithmetical exercise led to the far-reaching policy conclusion that there exists an exploitable trade-off between inflation and unemployment.

Needless to say that this basic version experienced refinement, reinterpretation, and qualification in the sequel. It was completely overlooked in the ensuing filibuster, though, that, to begin with, the underlying arithmetic was fallacious. The lack of a sound theoretical foundation did not prevent the application of the Samuelson-Solow Phillips curve. Quite the contrary. Phillips is said to have remarked ‘if I had known what they would do with the graph I would never have drawn it.’ (Quiggin, 2010, p. 91).

You summarize: “Despite the extensive press coverage the NAIRU concept has received recently, the theory of the inflation unemployment relationship that it is part of is quite controversial.”

The correct inflation-unemployment relationship is given for the most elementary case by this equation on Wikimedia AXEC34
Roughly speaking, this structural Phillips curve says: if price inflation is ‘stronger’ than wage inflation unemployment increases; if price inflation is ‘weaker’ than wage inflation unemployment decreases; if both are of ‘equal strength’ then the structural Phillips Curve is vertical at the actual unemployment rate. For the details see (2012).

Egmont Kakarot-Handtke

Kakarot-Handtke, E. (2012). Keynes’ Employment Function and the Gratuitous Phillips Curve Disaster. SSRN Working Paper Series, 2130421: 1–19. URL
Ormerod, P. (1994). The Death of Economics. London: Faber and Faber.
Phillips, A. W. (1958). The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957. Economica, 25: 283–299. URL
Quiggin, J. (2010). Zombie Economics. How Dead Ideas Still Walk Among Us. Princeton, Oxford: Princeton University Press.
Samuelson, P. A., and Nordhaus, W. D. (1998). Economics. Boston, Burr Ridge, etc.: Irwin, McGraw-Hill, 16th edition.