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Lucas developed the relationship between wage-price inflation and the level of economic activity known as the Phillips curve, it was in the theory of the labour market that the Phillips curve was most vulnerable. The New Zealand economist A. W. Phillips (1958) had shown that a logarithmic relationship between the unemployment rate and wage inflation in Great Britain from 1861 to 1913 was able to be fitted satisfactorily to data for 1948-57. The relationship was such that high
unemployment was associated with low wage growth, while low unemployment was combined with a rapid growth of wages. That was generally interpreted as one between excess demand and those variables. A stimulus to demand (say from
government spending) would increase output and reduce unemployment, but the cost of that achievement was higher inflation. Conversely a reduction in demand would reduce inflation, but at the cost of increased unemployment. Those trade-
offs were an accepted part of policy formulation in the 1960, as Philips curve had been found to exist in major countries.
During the late 1960 and early l970 the relationship had received renewed attention from economists because the apparently stable negative relationship between inflation and unemployment identified by Phillips and others had come into question as new data appeared to indicate both rising inflation and lower economic
activity. Friedman suggested that the reason for the success of the Phillips curve in its original ‘misspecified’ form over the late 1950s and 1960s was the low level of inflation in that period which meant that nominal changes and real changes to wages did not diverge much over the period. His prediction was soon afterwards shown tobe true as the inflation rate accelerated in the early 1970s, widening the gap between nominal and real changes to wages, and the empirical regularity, which provided the main justification for the Phillips curve break down.Friedman (1968) and Phelps (1970) put forward the hypothesis that this was because the process by which wages were negotiated, which determined the fate of inflation, involved expectations of future conditions. There contention was that the Phillips curve was failing to account for the impact of expectations on the wage inflation process and as a result of the misspecification was failing to explain the true nature of the relationship between inflation and unemployment. The misspecification of thePhillips curve was revealed by two inconsistencies with neoclassical economics which Friedman corrected by specifying the relationship in real rather than nominal terms and as a relationship between the level, not the change, of the wage and the rate of unemployment. To deal with the first of these
issues Friedman expressed the Phillips curve in real terms, and ‘augmented’ it with price expectations, enabling the model to predict accurately the change to prices over the period for which wages were being negotiated. Without this
adjustment money illusion would never be corrected, workers would continue to mistake nominal for real changes to their wages and would never learn from their mistakes. To deal with the second issue, he noted that should the relationship be written in terms of the change to wages and the rate of unemployment then there
should be a ‘natural rate of unemployment’ to which the economy would converge in the absence of disturbances. The natural rate repreents the long-run level of unemployment consistent with any level of nominal wage inflation, given that there is no money illusion and that price expectations correct for nominal changes in wages.
Objectives of theory
In this theory, we will study expectations augmented short-term and long- term Philips curve, Philips curve and Lucas Island model.
Explanation of model
To understand the model certain assumptions are as follows:
Assumptions of the model
1. There are no involuntarily unemployed in the economy.
2. Inhabitants were able to accurately and continuously determine the prices on their own island, but could only infer from these likely
contemporaneous prices on other islands.
3. The people are often better informed about their own enterprise and local economy than they are about the economy at large.
4. The restriction on information about prices implied that the inhabitants would need to form expectations about the contemporaneous general
price level using the information on the behavior of prices on their own island.
5. The labour supply is assumed to be elastic and the market is assumed to clear continuously without the hindrance of nominal wage rigidities,
firms with which inhabitants negotiated are profit-maximizing.
Friedman suggested that statistical evidence for a negative relationship was due to temporary money illusion and the possibility that in the short-run there could be an exploitable trade-off between inflation and unemployment. In the long-term the
true change to the real wage would become apparent as nominal prices and wages were observed; this would mean that expectations would change and the short-run deviation from the natural rate of unemployment would be corrected. In the,expectations augmented version of the Phillips curve, there can be no money illusion
in the long-run and the Phillips curve must be vertical at the natural rate of unemployment.
In diagrammatic terms the rational expectations augmented Phillips curve can be illustrated in
Figure 1. Drawing the graph with the change in money wages on the vertical axis and unemployment on the horizontal axis, the original Phillips curve is labelled AA and shows a negative relationship between wage inflation and unemployment. Friedman’s model concurs with this curve in the short-run when there is money illusion to overturn the neutrality result, so AA is a short-run expectations augmented Phillips curve, but BB represents the long-run Phillips curve which is vertical above the natural rate of unemployment U*. To consider the dynamics of price
expectations in this context, suppose that the labour market clears at a real wage consistent with expectations that prices will be equal to some
value Po.
broke down in the early 1970s.
We turn now to Lucas, who was quick to appreciate the wider significance of the informational errors. His contribution was to pick up on the notion that expectations entered the process of inflation generation and, by accurately specifying theoretical micro-foundations, to explain how expectations formation could affect the inflation process. This was a first indication that Friedman’s concern for predictive accuracy was not enough for Lucas who wanted to develop a coherent and consistent underlying theory. Friedman had used neoclassical principles to come to his conclusions but had no formal model behind them; it was the development of a formal model which Lucas provided in the form of the ‘islands model’.
Lucas’s approach was to imagine a theoretical model in which inhabitants lived on a number of islands. Inhabitants were able to accurately and continuously determine the prices on their own island, but could only infer from these likely
contemporaneous prices on other islands and hence the general price level pt, which they could observe only with a lag. These assumptions replicated the idea that people are often better informed about their own enterprise and local economy than they are about the economy at large. The restriction on information about prices implied that the inhabitants would need to form expectations about the contemporaneous
general price level using the information on the behavior of prices on their own
island.
Ez(Pt) =E(Pt /Pt(z), Ωt−1) ....(1)
where Ez (Pt ) is the expectation of sellers in market z of the general price level Pt, given information on prices in market z at time t(pt(z)) and last period’s information on the general price level and other factors Ωt−1.Suppose the information from the past period expectation of prices in time t is weighted with the information
from market z to allow expectations to be formed as
Ez(Pt)=θ(Pt(z)+(1-θ)Ez-1*pt. .......(2)
Then the seller in market z faces a signal extraction problem: re is a signal
in the data, but it is contaminated by market-specific noise. The solution to such a
problem results in:
It was assumed that the inhabitants would need to know the general price level in order to be able to conduct negotiations over wages in the labour market.The inhabitants were assumed to be fully rational using all available information to calculate their expectation of the general price level. The labour supply is assumed to be elastic and the market is assumed to clear continuously without the hindrance of nominal wage rigidities, firms with which inhabitants negotiated are profit-
maximizing. In such a model Lucas considered the inter-temporal substitution problem faced by the inhabitants who have a choice of taking leisure today or leisure Tomorrow a rise in wages entails both an income effect and a substitution effect as
greater wages create incentives to reduce working hours, in response to the level of income earned, and to increase hours, in response to the marginal return to the extra hours worked. Lucas suggested that the dominance of the substitution effect
over the income effect was responsible for the observed negative correlation between prices and output levels. Through the use of the model it was possible to show that expectations about changes in real wages could alter the labour supply by encouraging or discouraging inter-temporal substitution between leisure today and leisure
tomorrow. The correspondence between decisions to work (or not work and hence be unemployed) and the behavior or real wages period to period, which depend heavily on expectations of the general price level, create a Phillips curve trade- off. From this foundation the Phillip’s curve could be regarded as a solution to the labour market problem when the price level is imperfectly observed. Labour supply simply responds to the expected real wage from one period to the next on the basis of expectations of the general price level.
The Lucas-Rapping model asserts that it is only the random and unpredictable contemporaneous events for which expectations cannot account that lead to departures from the natural rate of unemployment. Their notion of expectations is
a fully rational one in which all information is used to update expectations such that there are no systematic errors. Consequently, departures from the vertical long-run Phillips curve BB figure 1 occur only for one period after which the error is
incorporated into the information set and future expectations take account of it.
In other words, movements along the short-run Phillips curve occur only as one-period
departures from equilibrium, whilst in Friedman’s case they can persist so long as money illusion exists, which may be for several periods. The implications of this last point become apparent once the Phillips curve is rearranged into a form
resembling an aggregate supply curve. Consider the expectations augmented Phillips curve which can be written as
Pt=(Yt-Y*)+Et-1.pt+εt. ....(4)
In this form the equation is a relationship between the price level and the departures from the natural rate of output (which can be thought of as a scale
variable which proxies for unemployment) and the expectations of prices based on the information available in the previous period. Here there is an error term, indicating that random events can affect prices. By rearrangement, it is possible to write equation (4) in such a way that output deviates from the natural rate when unexpected events cause changes to prices which expectations cannot account for in the current period:
Yt=Y*+(Pt-(Et-1)Pt−εt. ......(5)
This has become known as the Lucas supply function or ‘surprise’ function since only unexpected surprises cause output to deviate from the natural rate, Note that the surprise effect is only influential for one period, after which it becomes part of the information set and is incorporated into the process of expectations
formation.
The Lucas Critique:-
A key macroeconomic question in the late 1970s was whether the aggregate supply curve was best thought of as new classical formulation or an alternative type. Sargent and Wallace (1973) used tests of the direction of causality between economic variables to try to validate Lucas’s new classical model on econometric grounds, thereby concluding that the new classical approach was not inconsistent with the data. Barro (1977, 1978) attempted to confirm these results by modelling
directly the aggregate supply relationship. In order to do this he specified the money supply process and from it derived estimates of the unexpected changes to monetary policy. He then introduced both variables into a model to explain output
and found that whilst anticipated monetary policy did not have a statistically significant effect on output as unexpected component did seeming to confirm the new classical approach. Shortly after the publication of these results, however, Sargent (1979) established from theoretical first principles that these econometric approaches could be mis-leading. His reasoning was to become known as the observational equivalence argument by which it is possible to show that a model which seems to show that systematic monetary policy can affect output can be rearranged with some reasonable additional assumptions to show the contrary,
i.e., only unanticipated policy can affect output. The problem for the econometric work is that while these models have different assumptions which set them apart in theory, they are observationally equivalent in practice because it is not possible to specify them in such a way that they can be separated on econometric grounds
when estimated in reduced form.
Lucas introduced a rider to this debate which became a turning point in relation to the econometric estimation of economic models involving expectations, known as the Lucas critique. His observation was that many reduced-form models treat the expectational terms in the same way as they treat the structural parameters
of the model. The obvious objection to this
practice is that, unlike structural parameters, expectations are liable to change with the policy process. The models which do not treat them in such a way that this change can be accommodated will generally give misleading results.
Conclusion:-
In this lesson we have studied expectations augmented short-term and long term Philips curve, Philips curve and Lucas Island model. A. W.Phillips had shownthat a logarithmic relationship between the unemployment rate and wage inflation was able to be fitted satisfactorily to data for 1948-57. The relationship was such that highunemployment was associated with low wages growth, while low unemployment was combined with a rapid growth of wages. Lucas was quick to appreciate the wider significance of the informational errors. His contribution was to pick up on the notion that expectations entered the process of inflation generation and,by accurately specifying theoretical micro foundations, to explain how expectations formation could affect the inflation process.
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