### Discussion Paper

## Abstract

Using the statistical technique of fuzzy clustering, regimes of inflation and unemployment are explored for the United States, the United Kingdom and Germany between 1871 and 2009. We identify for each country three distinct regimes in inflation/unemployment space. There is considerable similarity across the countries in both the regimes themselves and in the timings of the transitions between regimes. However, the typical rates of inflation and unemployment experienced in the regimes are substantially different. Further, even within a given regime, the results of the clustering show persistent fluctuations in the degree of attachment to that regime of inflation/unemployment observations over time. The economic implications of the results are that, first, the inflation/unemployment relationship experiences from time to time major shifts. Second, that it is also inherently unstable even in the short run. It is likely that the factors which govern the inflation/unemployment trade off are so multi-dimensional that it is hard to see that there is a way of identifying periods of short run Phillips curves which can be assigned to particular historical periods with any degree of accuracy or predictability. The short run may be so short as to be meaningless. The analysis shows that reliance on any kind of trade off between inflation and unemployment for policy purposes is entirely misplaced.

## Comments and Questions

This paper provides a valuable additional statistical assessment of the relationship between unemployment and inflation which has become known in economics as "the Phillips curve", using fuzzy clustering. However I believe that the paper should give a more nuanced treatment of the Phillips curve concept itself than has been the ...[more]

... norm for economic debate of this concept.

Firstly, though the inflation-unemployment relation is colloquially called "the Phillips Curve", Phillips's original relation was between the unemployment and the rate of change of money wages. That was after all the title of his original paper (A.W. Phillips, 1958, "The Relationship between Unemployment and the Rate of Change of Money Wages in the UK 1861‐1957”, Economica, 25, pp. 283‐299). Though inflation and the rate of change of money wages are closely related, they are not the same thing. This should be acknowledged by the authors.

Secondly, though Phillips did attempt to fit a relationship between money wages and unemployment to the data, he actually specified 3 factors in his analysis:

1. Level of unemployment (highly nonlinear relationship)

2. Rate of change of unemployment

3. Rate of change of retail prices “operating through cost of living adjustments in wage rates… when retail prices are forced up by a very rapid rise in import prices … or … agricultural products.” [Economica 1958 p. 283-4]

Only the first was in fact fitted, due to technological issues at the time and the paucity of data. This should also be acknowledged by this paper.

Using the three causal factors that Phillips specified, one might find a far more stable relationship over time, but one which is also highly time dependent in a fashion in which a single argument function is not.

Though the regressions in Figure 1 are only for illustration purposes, these somewhat distort Phillips's intentions since he was emphatic that his curve was nonlinear. Nonlinear regressions should also be applied.

This raises an important point about Phillip's proposition that may remain valid even if the inflation-unemployment tradeoff interpretation is justifiably rejected. Nonlinearity allows for money wages to be sticky downwards, even if they are not flexible upwards due to changes in the capacity of workers to bargain for higher wages. A linear regression obscures this point, since a linear regression can't capture this discontinuity.

This floor to wage falls is somewhat evident in Figure 1--and I am sure that the divergence for the UK is for the years 1921 and 1922, when as Phillips observed, the UK wage fell due to a cost of living adjustment agreement negotiated by the TUC just before the UK went back on the gold standard (see Figure 9 in Phillips 1958).

It is thus therefore possible to reject the Phillips Curve analysis of inflation and the rate of change of money wages in the stable or weak regimes identified by the fuzzy clustering technique, while also finding that the "sticky money wages" proposition in Phillips's nonlinear curve is still valid.

I would appreciate seeing how the fitting of a 2 factor nonlinear model for the Phillips curve to the empirical data set (possibly 3 factor, using the fuzzy clustering concept to identify the cost of licving changes caused by Wars that Phillips also included in his argument) would affect the author's conclusions.

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