X unemployment and Inflation

Phillips Own Version of The Phillips Curve

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Phillips Own Version of The Phillips Curve

The Phillips curve has been used by macroeconomists to link the level of economic activity to the movement in the price level. In the Phillips curve framework, the level of economic activity is represented by the unemployment rate. The presumption is that when the unemployment rate rises above some irreducible minimum then economic activity is declining, and as the unemployment rate moves towards that irreducible minimum, the economy moves closer to full capacity and full employment.

We will see in a later section that the Phillips curve and Okun’s Law, which links changes in the unemployment rate to output gaps (the difference between potential output and actual output) coexist comfortably in macroeconomic theory. The latter provides the extra link between unemployment and output.

In some textbooks you will find inflation models that conflate the two concepts (Phillips curve and Okuns’ Law) and directly relate the inflation rate to the output gap. We prefer for reasons that will be obvious not to take that approach in this text book.

In 1958, New Zealand economist Bill Phillips published a statistical study, which showed the relationship between the unemployment rate and the proportionate rate of change in money-wage rates for the United Kingdom. He studied that relationship for the period 1861 to 1957.

Phillips believed that given that money wage costs represent a high proportion of total costs that movements in money wage rates will drive movements in the general price level.

He had earlier written a paper in 1954 which can be considered a precursor to his 1958 empirical study, which serious students should read in conjunction with his 1958 study.

One of the graphs he produced in his 1958 article is reproduced as Figure X.5. It shows two separate periods of data. First, the curve fitted with statistical methods to fit the data for the period 1861-1913. Second, the scatter plot of the data for the period 1913-1948. Phillips produced a number of graphs like this to show how he built up his overall curve for the entire period 1861 to 1957. The detail of his method is not relevant here but for those interested in the early efforts using regression techniques a thorough reading of his article is recommended.

Figure X.5 Phillips 1958 Figure 9 – Unemployment and Money Wage Inflation, 1913-1948

How did Phillips explain this relationship? In his 1958 article (Page 283) he provided a basic theory to add behavioural meaning to the empirical relationship he found that linked the unemployment rate to the growth of money wage rates.

He wrote:

When the demand for a commodity or service is high relatively to the supply of it we expect the price to rise, the rate of rise being greater the greater the excess demand. Conversely when the demand is low relatively to the supply we expect the price to fall, the rate of fall being greater the greater the deficiency of demand. It seems plausible that this principle should operate as one of the factors determining the rate of change of money wage rates, which are the price of labour services. When the demand for labour is high and there are very few unemployed we should expect employers to bid wage rates up quite rapidly, each firm and each industry being continually tempted to offer a little above the prevailing rates to attract the most suitable labour from other firms and industries. On the other hand it appears that workers are reluctant to offer their services at less than the prevailing rates when the demand for labour is low and unemployment is high so that wage rates fall only very slowly. The relation between unemployment and the rate of change of wage rates is therefore likely to be highly non-linear.

Phillips also buttressed this excess demand for labour explanation with two other factors which could influence the rate of change of money wage rates. First, he noted (Page 283) that the “rate of change of the demand for labour, and so of unemployment” (emphasis added) was important to consider.

When business activity was rising:

… employers would be bidding more vigorously for the services of labour than they would in a year during with the average percentage unemployment was the same but the demand for labour was not increasing.

Similarly, when business activity was falling:

… employers will be less inclined to grant wage increases, and workers will be in a weaker position to press for them, than they would be in a year during which the average percentage unemployment was the same but the demand for labour was not decreasing.

He thus recognised that in the context of wage bargaining between employers and workers, the direction of change in the economy was a factor that had to be considered quite apart from the level the economy was currently at.

The other factor Phillips thought was essential to consider was the “rate of change of retail prices”, which could drive the growth in money wage rates “through cost of living adjustments” (Page 283). He thought this impact would be of less importance unless there was a “very rapid rise in import prices” (Page 284).

But in recognising that the movement in retail prices is intrinsic to understanding the movement in real wages and that this link worked through adjustments in the money wage rates, Phillips was reinforcing the arguments made by Keynes that the real wage was not determined in the labour market and that workers could not directly manipulate the real wage prevailing at any time.

Soon after Phillips had published his work on the UK, the American economists Paul Samuelson and Robert Solow published an article in 1960, which produced a Phillips curve-type relationship using US data over the period 1934 to 1958.

Building on the recognition that money wage costs represent a high proportion of total costs that movements in money wage rates will drive movements in the general price level, Samuelson and Solow’s “Phillips curve” was a relationship between the rate of growth in the general price level (that is, price inflation) and the unemployment rate.

Samuelson and Solow also defined the Phillips Curve as a policy tool, which the government could use to lessen the burden of unemployment.

The timing of the Samuelson-Solow contribution is important. Between 1960-61, the US economy was mired in a deep recession and the unemployment rate was rising. The work of Samuelson and Solow was designed to be a major intervention into the policy debate and provide policy makers with a new framework for understanding the consequences of policies designed to reduce the unemployment rate.

Figure X.6 replicates Figure 2 from Samuelson and Solow (1960) which they call their “price-level modification of the Phillips curve” (Page 192). Note the sub-text – a “menu of choice”, implying that policy makers could choose points along their estimated Phillips curve to reach preferred combinations of inflation and unemployment.

This introduced the idea of a policy trade-off between unemployment and inflation. If the government wanted to sustain lower unemployment rates then the cost of that policy decision would be higher inflation.

Figure X.6 The Samuelson-Solow “Modified” Phillips Curve for The US Economy

Source: Samuelson and Solow (1960) Figure 2, “Modified Phillips Curve for U.S.”
This shows the menu of choice between different degrees of unemployment and price stability as roughly estimated from last twenty-five years of American data. [text from original source].

They interpreted their Phillips curve in the following way (Page 192):

1. In order to have wages increase at no more than 21/2 percent per annum characteristics of our productivity growth, the American economy would seem on the basis of twentieth-century and postwar experience to have to undergo something like 5 to 6 per cent of the civilian labor force’s being unemployed. That much unemployment would appear to be the cost of price stability in the years immediately ahead.

2. In order to achieve the nonperfectionist’s goal of high enough output to give us no more than 3 per cent unemployment, the price index might have to rise by as much as 4 to 5 per cent per year. That much price rise would seem to be the necessary cost of high employment and production in the years ahead.

Relating these assessments to the graph (Figure X.6), price stability (no inflation) is defined at Point A (where the unemployment rate was estimated to be 5.5 per cent) and Point B is where a 3 per cent unemployment rate corresponds to an inflation rate of 4.5 per cent per annum.

Samuelson and Solow qualified their work in this way (Page 193):

Aside from the usual warning that these are simply our best guesses we must give another caution. All of our discussion has been phrased in short-run terms, dealing with what might happen in the next few years. It would be wrong, though, to think that our Figure 2 menu that relates obtainable price and unemployment behavior will maintain its same shape in the longer run. What we do in a policy way during the next few years might cause it to shift in a definite way.

In other words, the “trade-off” they proposed between inflation and unemployment might shift in the longer run in response to policy makers exploiting it in the short-run. As we will see this warning was very prescient.

However, despite this warning, the Phillips curve “trade-off” became conventional wisdom among mainstream economists profession and policy makers and the latter proceeded to design policy as if the choice was stable over time.

It is also significant, that the work of Phillips and Samuelson and Solow and some other economists at the time, shifted the debate about what constitutes full employment. Whereas the Keynesian orthodoxy in the 1940s and 1950s defined full employment in terms of a number of jobs – that is, there had to be at least as many of vacant jobs available as there were persons seeking employment – the introduction of the Phillips curve and its emphasis on unemployment changed that focus.

Initially, this change in focus involved a debate about what constituted the irreducible minimum rate of unemployment. The work of Bancroft (1950), Dunlop (1950) and Slichter (1950) were important contributions to this shift in emphasis.

But soon the debate became tangled up in models of unemployment and inflation after the work of Phillips and, then, Samuelson and Solow were published. The debate shifted from considering how many jobs were required to be generated to achieve full employment to consideration of the existence and nature of a trade-off between nominal (inflation) and real (unemployment) outcomes.

The Keynesian orthodoxy considered real output (income) and employment as being demand-determined in the short-run, with price inflation being explained by a negatively sloped Phillip’s curve (in both the short-run and the long-run). Policy-makers believed they could manipulate demand and exploit this trade-off to achieve a socially optimal level of unemployment and inflation. Significantly, the concept of full employment gave way to the rate of unemployment that was politically acceptable in the light of some accompanying inflation rate. Full employment was no longer debated in terms of a number of jobs.

Friday, February 22, 2013 by bill

I am now continuing Section 12.6 on the Phillips Curve …

To see how the Samuelson and Solow (1960) price inflation Phillips curve can be rationalised, we go back to Chapter 9, where we introduced a model of mark-up pricing where firms price by adding a percentage margin to unit costs, which reflects their desired revenue. This, in turn, is consistent with their desired rate of return on capital.

The simplified price mark-up model we introduced in Chapter 9 was:

(X.2) P = (1 + m)WN/Y

where P is the price of output, m is the per unit mark-up on unit labour costs, W is the money wage, N is total employment and Y is total output. WN is the total wage bill.

We also learned that N/Y is the inverse of labour productivity (Y/N), which means that we could express the mark-up model as:

(X.3) P = (1 + m)W/LP

If we expressed this in rates of change we would be able to say that the inflation rate will be stable if the mark-up is constant and the growth in money wages is exactly offset by the growth in labour productivity.

In other words, growth in labour productivity provides the economy with non-inflationary room to expand money wages (and real wages). As long as money wages grow in proportion with labour productivity growth, unit labour costs (W/LP) will be constant and our simplified mark-up model would predict that prices would be stable.

Consider Figure X.7, which plots two Phillips curves. Note on the vertical axis we are measuring both the rate of change of money wages and the rate of price inflation. In that sense, we are combining the Phillips (1958) curve, which related money wage inflation to the unemployment rate and the modified Phillips curve outlined in Samuelson and Solow (1960), who related price inflation to the unemployment rate.

The curve denoted Phillips (1958) shows that money wage inflation per annum is zero when the unemployment rate is 8 per cent. When the unemployment rate is at 2 per cent, the state of the labour market is such that money wage inflation rises to 3 per cent (per annum).

The Samuelson and Solow (1960) curve is the price inflation modified Phillips curve. It cuts the horizontal axis at an unemployment rate of 2 per cent, which means that the rate of price inflation is zero, whereas the rate of money wage inflation is 3 per cent.

The vertical difference between the two curves – measured by the distance AB – is the current rate of productivity growth (which in this case would be 3 per cent per annum).

In other words, in this example, the unemployment rate that is consistent with zero (stable) inflation is 2 per cent.

Figure X.7 Wage and Price Phillips Curves

A more complex and realistic price mark-up model would take into account non-labour costs such as raw material and energy costs (denoted rm). We might define total unit costs to be the sum of labour and non-labour costs per unit of output produced and the resulting mark-up equation would be:

(X.4) P = (1 + m)[W/LP + rm/Y]

This means that with a constant mark-up (m), firms will increase their prices if there is a raw material price shock even if unit labour costs are constant.

We will return to the role of so-called supply shocks (for example, raw material price rises) later when we discuss theories of inflation and the way in which an external price shock can complicate the conflict that workers and capital have over the distribution of national income, which plays out in efforts to defend real wages and mark-ups.

The price inflation Phillips curve was accepted by policy makers in the 1960s and into the 1970s as an integral part of their macroeconomic tool box. By assuming it was stable over the policy setting horizon and would not shift in response to policy changes (that is, they assumed it was not an endogenous relationship), the Phillips curve immediately defined attainable and unattainable combinations of unemployment and inflation.

Consider Figure X.8 which shows a price inflation Phillips curve (price inflation on the vertical axis). Policy makers considered any point along an estimated Phillips curve to be feasible given the dynamics of the labour market. So it could choose to target a lower unemployment rate, for example, Point A, knowing that in relation to say, Point B the policy choice would lead to higher inflation than before.

From any particular point on the curve, the slope of the curve (denoted here at Point A by the red line) would tell the government how much inflation they would have to bear for a given reduction in the unemployment rate. The slope of the Phillips curve is thus the magnitude of the trade-off between inflation and unemployment.

Another way of thinking about this is that the slope told the government the percentage point rise in the unemployment rate for every percentage point reduction in the inflation rate. So they could use the Phillips curve to calculate the real impacts of a contractionary fiscal and/or monetary policy strategy designed to reduce inflation.

Furthermore, it is obvious that any combination of inflation and unemployment “inside” the Phillips curve (the shaded area in Figure X.8) are unattainable. The trade-off forced on the government by the dynamics of the pricing process and the way that firms responded to rises or falls in excess demand for labour dictated the possible outcomes.

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