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Phillips Curve

Phillips Curve

INFLATION AND THE OUTPUT GAP

EVIDENCE

BIBLIOGRAPHY

The term Phillips curve originated in the work of New Zealand-born economist A. W. Phillips (19141975). In a 1958 article, Phillips plotted annual observations on wage change against unemployment in the United Kingdom for the 18611957 period, and he fitted a nonlinear curve by trial and error to the six grouped observations on wage change and unemployment (using an unusual technique, as noted by Desai [1975]). The resulting equation of w = 0.900 + 9.638 U -1.394, where w is the (annual) rate of change of money wages and U is the unemployment rate, displays the negative relationship between wage change and unemployment. The equation also places a floor under money-wage annual change of 0.9 percent.

The term Phillips curve has subsequently been used in a variety of ways and to invoke a number of mechanisms. Paul Samuelson and Robert M. Solow (1960) converted the curve into a relationship between price inflation and unemployment by deducting the presumed rate of growth of productivity from growth of wages to provide a presumed growth of prices. Later, there was an appeal to the links between output and unemployment to derive an equation linking price inflation and output (or capacity utilization or output gap).

Precursors can be found: For example, Irving Fishers 1926 article A Statistical Relation between Unemployment and Price Changes was reprinted in 1973 under the heading I Discovered the Phillips Curve. Fisher argued that surprises in inflation (i.e., unanticipated inflation) lead to supply responses, with the postulated positive effect of unanticipated inflation on economic activity. Anthony Thirlwall (1972) argues that Arthur Brown (1955) has a strong claim to the discovery of an empirical relationship between wage changes and unemployment. His diagram (Brown 1955, p. 199) maps out the wage change-unemployment observations for the United Kingdom from 1880 to 1914. Even earlier, Karl Marx (18181883) argued that the industrial reserve army of the unemployed regulated the movement of wages.

Richard Lipsey (1960) provided a theoretical justification for the Phillips curve on the basis of a labor-market adjustment process whereby wages change in response to the level of excess demand for labor, and unemployment is viewed as a (negative) proxy for excess demand for labor. Milton Friedman argued that Phillips analysis of the relation between unemployment and wage change contained a basic defectthe failure to distinguish between nominal and real wages (1968, p. 8). This observation led to the expectations-augmented Phillips curve, such as w = pe + f (U Un ) (abstracting from the general trend upward of real wages), where pe is the expected rate of inflation and Un is the natural rate of unemployment, with the significant property that money wages would rise in line with expected inflation when U = Un. When unemployment was below this natural rate, then wages would rise faster than prices, and inflation overall tends to rise. The natural rate was viewed as the level that would be ground out by the Walrasian system of general equilibrium equations, provided there is embedded in them the actual structural characteristics of the labor and commodity markers, including market imperfections, stochastic variability in demands and supplies, the cost of gathering information about job vacancies and labor availabilities, the costs of mobility, and so on (Friedman 1968, p. 8).

Edmund Phelps introduced a sort of Phillips Curve in terms of the rate of price change, rather than wage change, that shifts one-for-one with variations in the expected rate of inflation (1967, p. 254) with the rate of inflation depend[ing] upon the utilization ratio and upon the expected rate of inflation (p. 261). Using the idea that expectations were adaptive, Phelps developed the idea of a vertical long-run relationship between inflation and output, with output at the level determined by the equilibrium utilization ratio.

Expressing the argument in terms of wage changes and unemployment, in the short-run, with a given state of expectations, there is a trade-off between wage change and unemployment. But expectations will adjust to (or even anticipate) the experience of wage inflation (and the subsequent price inflation). When expected price inflation fully incorporates wage inflation, then pe = p = w, and hence f (U Un ) = 0: This became known as the vertical long-run Phillips curve. This has enormous policy implications: The economy has to operate at the natural rate if continuously rising or falling inflation is to be avoided. Specifically, unemployment below the natural rate would see escalating inflation, leading to hyperinflation.

Many of the arguments developed by Friedman were anticipated by David Champernowne. Champernowne concluded that no period of monetary employment or of monetary unemployment is likely to last for very long. We expect there to be alternate periods of monetary employment and of monetary unemployment, so that the actual level of unemployment would oscillate above and below the level of basic unemployment (1936, p. 206), where basic unemployment is the amount of unemployment that there would be in that situation if each man demanded neither more nor less than his basic real wage (p. 203). But a significant difference was that Champernowne postulated responses from the monetary authorities through interest rates as the mechanism by which actual unemployment moved to the level of basic unemployment.

INFLATION AND THE OUTPUT GAP

The term Phillips curve is now widely used to signify the relationship between price inflation, expected price inflation, and the output gap, which feature heavily in the new consensus macroeconomics (e.g., Meyer 2001; Woodford 2003). The new Keynesian approach to the Phillips curve is based on price decisions being forward looking, and at the level of the individual firm price decisions depend on the expectations of prices to be charged by other firms in the future. But price decisions are staggered (following Calvo 1983), and only a proportion of firms change their price in any given period. Each firm is postulated to produce a differentiated product, and faces a constant price elasticity of demand curve for its product. In each period, a proportion of firms change price (but others do not). In each period, the probability that a firm changes price is α, which is independent of any change of price in the preceding period. The aggregate price level is then a weighted average of the lagged price level and the optimal price (derived from forward-looking profit maximization) set by those changing price. These considerations yield an equation involving prices and marginal costs: A typical form would be (from Galí and Gertler [1999], equation 3): pt = λmct + βEt {pt+ 1 }, where mc is real marginal costs, β is the subjective discount factor, and λ depends on the frequency of price adjustments and β. Some approximations and the assumption that marginal cost is positively related with output yield an equation of the form: pt = λKxt + βEt {pt+1}, where k is the output elasticity of marginal cost, and x is the output gap.

EVIDENCE

The origins of the Phillips curve were empirical rather than theoretical. Throughout its history, there have been claims and counterclaims on the extent of the empirical support for the Phillips curve, and on its disappearance and its reappearance. The initial proposition from the Phillips curve literature was a negative relationship between wage changes and unemployment. This was augmented by a proposition that the coefficient on expected price inflation was unity and there was a natural rate of unemployment consistent with constant inflation. Although the natural rate has often been treated as a constant, it can rather be seen, reflecting the quote from Friedman above, as influenced by a range of supply-side factors, but viewed as independent from the course of the level of aggregate demand or economic activity.

Although the Phillips curve as a single equation features in much theoretical literature, the empirical approach generally draws on a two (or more) equation approach involving both wage and price determination. This entry limits its discussion to the single-equation approach of a Phillips curve. The differences in the empirical results are reflected by the following. Robert Gordon (1997) considered a basic model (for the United States) in which inflation is regressed on lagged inflation, current and lagged demand (unemployment gap, output gap), change in productivity, in relative import price, and in relative price of food and energy (and Nixon incomes policy on/off). Gordon tried three alternative price indices. He reports that estimated sums of coefficients on the inflation inertia variable are very close to unity, while those on the unemployment gap are always highly significant and of the correct sign. The significance of the various supply variables differs, but with two exceptions of insignificant coefficients, they all have the correct sign (Gordon 1997, p. 24). Taken as a group, the inclusion of the supply side variables makes a substantial difference, especially during the 19731981 period, which is influenced by adverse supply shocks (p. 25). The sum of coefficients on lagged inflation is 1.01 (but 24 lags on quarterly basis) and on the unemployment gap the sum is 0.61 (current plus four lags).

In contrast, Robert Eisner separated out the effects of high and low unemployment and found great disparities in the relations involving high and low unemployment (1996, p. 118). For example, he found that unemployment had a negative impact on inflation when unemployment was high, but a positive effect when unemployment was low. Furthermore, the coefficients on lagged inflation were below unity when unemployment was low. Overall, Eisner concluded that there may indeed be no stable universal relation among unemployment and all the various factors that may contribute to inflation, let alone accelerating inflation (1996, p. 128).

For the new Keynesian Phillips curve, N. Gregory Mankiw argued that it has many virtues, [but] it also has one striking vice: It is completely at odds with the facts (2001, p. C52). In a similar vein, attractive though the need to establish a direct inflation-output link may be, as an empirical framework for explaining inflation over the business cycle, the New Keynesian Phillips Curve in inflation-output space has not been particularly successful (Chadha and Nolan 2004, p. 271). Jordi Galí and Mark Gertler noted that it is often difficult to detect a statistically significant effect of real activity on inflation using the structural formulation implied by the theory, when the measure of real activity is an output gap (i.e., real output relative to some measure of potential output). Failure to find a significant short-run link between real activity and inflation is unsettling for the basic story (1999, p. 196; see also Galí et al. 2005).

The experience since the beginning of the 1990s, at least in the United States and the United Kingdom, could be characterized by a rather stable rate of inflation as unemployment declined substantially (at least until 2001), which some have described as akin to a horizontal (rather than a vertical) Phillips curve.

The shifts in estimates of the natural rate of unemployment were illustrated by Stephen Nickell (1990), who estimated the equilibrium rate of unemployment in the United Kingdom as having risen as follows (with actual rates of unemployment given in parenthesis):

19561959: 2.2 percent (2.24 percent)

19601968: 2.5 percent (2.62 percent)

19691973: 3.6 percent (3.39 percent)

19741980: 7.3 percent (5.23 percent)

19811987: 8.7 percent (11.11 percent)

19881990: 8.7 percent (7.27 percent)

Richard Layard, Nickell, and Richard Jackman (1991, p. 436) report actual and equilibrium unemployment for nineteen countries for each of three decades, and an essentially similar pattern is providednamely, the two types of unemployment move together. Oliver Blanchard remarks that the natural rate is at best a weak attractor and that the natural rate is often as much an attractee as it is an attractor (1995, p. xiii). The natural rate of unemployment is seen to vary over time, but that leaves open the question of why it does so.

SEE ALSO Friedman, Milton; Inflation; Phillips, A. W. H.; Policy, Fiscal; Policy, Monetary; Samuelson, Paul A.; Solow, Robert M.; Unemployment

BIBLIOGRAPHY

Ball, Laurence, and N. Gregory Mankiw. 2002. The NAIRU in Theory and Practice. Journal of Economic Perspectives 16 (4): 115136.

Blanchard, Oliver. 1995. In The Natural Rate of Unemployment: Reflections on 25 Years of the Hypothesis, ed. Rod Cross, XIII-XIV. Cambridge, U.K.: Cambridge University Press.

Brown, Arthur J. 1955. The Great Inflation, 19391951. Oxford: Oxford University Press.

Calvo, Guillermo A. 1983. Staggered Prices in a Utility Maximizing Framework. Journal of Monetary Economics 12: 383398.

Chadha, Jagjit, and Charles Nolan. 2004. Output, Inflation, and the New Keynesian Phillips Curve. International Review of Applied Economics 18 (3): 271288.

Champernowne, David G. 1936. Unemployment, Basic and Monetary: The Classical Analysis and the Keynesian. Review of Economic Studies 3 (3): 201216.

Desai, Meghnad. 1975. The Phillips Curve: A Revisionist Approach. Economica 42 (1): 119.

Eisner, Robert. 1996. The Retreat from Full Employment. In Employment, Economic Growth, and the Tyranny of the Market: Essays in Honour of Paul Davidson, vol. 2, ed. Philip Arestis, 106130. Aldershot, U.K.: Edward Elgar.

Eisner, Robert. 1998. The Decline and Fall of the NAIRU. In The Keynesian Revolution, Then and Now, 454487. Cheltenham, U.K.: Edward Elgar.

Fisher, Irving. 1926. A Statistical Relation between Unemployment and Price Changes. International Labor Review 13 (6): 785792. Reprinted as Lost and Found: I Discovered the Phillips Curve. 1973. Journal of Political Economy 81 (2): 496502.

Friedman, Milton. 1968. The Role of Monetary Policy. American Economic Review 58 (1): 117.

Galí, Jordi, and Mark Gertler. 1999. Inflation Dynamics: A Structural Econometric Analysis. Journal of Monetary Economics 44 (2): 195222.

Galí, Jordi, Mark Gertler, and David López-Salido. 2005. Robustness of the Estimates of the Hybrid New Keynesian Phillips Curve. Journal of Monetary Economics 52: 11071118.

Gordon, Robert. 1997. The Time-Varying NAIRU and its Implications for Economic Policy. Journal of Economic Perspectives 11 (1): 1132.

Layard, Richard, Stephen Nickell, and Richard Jackman. 1991. Unemployment: Macroeconomic Performance and the Labour Market. Oxford: Oxford University Press.

Lipsey, Richard G. 1960. The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 18611957: A Further Analysis. Economica 27 (105): 131.

Mankiw, N. Gregory. 2001. The Inexorable and Mysterious Tradeoff between Inflation and Unemployment. Economic Journal 111: C45-C61.

Meyer, L. H. 2001. Does Money Matter? Federal Reserve Bank of St. Louis Review 83 (5): 115.

Nickell, Stephen. 1990. Inflation and the UK Labour Market. Oxford Review of Economic Policy 6 (4): 2635.

Phelps, Edmund S. 1967. Phillips Curves, Expectations of Inflation, and Optimal Employment over Time. Economica 34 (3): 254281.

Phillips, A. W. 1958. The Relation between Unemployment and the Rate of Change of Money Wages in the United Kingdom. Economica 25 (4): 283289.

Samuelson, Paul, and Robert Solow. 1960. Analytical Aspects of Anti-inflation Policy. American Economic Review 50 (2): 177194.

Thirlwall, Antony. 1972. The Phillips Curve: An Historical Note. Economica 39 (155): 325.

Woodford, Michael. 2003. Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton, NJ: Princeton University Press.

Malcolm Sawyer

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Phillips curve

Phillips curve In a famous article on ‘The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861–1957’, published in the journal Economica (1958), the economist A. W. Phillips argued that an inverse relationship existed between unemployment and wage inflation in the UK throughout the period in question. The rate of change in money wages tended to be high in conditions of low unemployment and low (or even negative) when unemployment was high. Thus, the so-called Phillips curve suggested that maintenance of full employment would necessarily involve some inflation, whereas inflation was only likely to be reduced by an increase in unemployment. This belief informed much economic discussion, and formed part of the accepted wisdom that provided the backdrop to policy-making throughout the two decades that followed, since it suggested that it was possible to calculate the terms of the trade-off between the policy objectives of full employment and zero inflation. However, the statistical association at the core of the argument clearly broke down (in Britain and elsewhere) during the 1970s, and its interpretation was challenged by the rise of monetarist explanations of inflation and unemployment.

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