Abstract
Expectations are used in almost every branch of economics. And alternative theories of expectations have been developed, including the theory of rational expectations (RE) introduced by Robert Lucas (Jr.). The use of RE in macroeconomic models has changed radically many well-developed earlier results and policy prescriptions. The purpose of the present paper is twofold—first, to discuss the various theories of expectations, and secondly, to show how the Phillips curve in macroeconomics dealing with the celebrated trade-off between inflation and unemployment—yield different results, if alternative expectations mechanisms are used. We thus discuss different versions of the Phillips curve—first, its initial version due to Phillips, showing the existence of a permanent trade-off between inflation and unemployment, next the Friedman–Phelps version using static expectations and showing the existence of only temporary, but no permanent trade-off, and finally, the new classical version with rational expectations showing the absence of any trade-off even temporarily. We add that no new result has been proved here; rather, our objective is mainly to help the students to understand these topics clearly—students who might have felt that the discussion of these topics in the standard textbooks is not always up to expectation.
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Notes
- 1.
I guess, this objective suits the basic objective of this volume—the volume which is being brought out in honour of Professor Sarmila Banerjee who was a very popular and respected teacher in the Department.
- 2.
A good discussion on the cobweb model is given in Chakraborty (2002, Appendix).
- 3.
The derivation of the equilibrium price \( \bar{p} \) and the solution of Eq. (7) are shown below. Given \( p_{0} \), we have \( p_{1} = bp_{0} + a \) and hence, \( p_{2} = bp_{1} + a = b\left\{ {bp_{0} + a} \right\} + a = b^{2} p_{0} + a\left( {1 + b} \right) \). By making repeated substitutions in this way, one gets \( p_{3} = bp_{2} + a = b\{ b^{2} p_{0} + a\left( {1 + b} \right)\} + a \) = \( b^{3} p_{0} + a\{ 1 + b + b^{2} \} = b^{3} p_{0} + a\left( {1 - b^{3} } \right)/\left( {1 - b} \right) \). Hence, \( p_{t} = b^{t} p_{0} + a\left( {1 - b^{t} } \right)/\left( {1 - b} \right) = b^{t} [p_{0} - a/\left( {1 - b} \right)] + a/\left( {1 - b} \right) \), which may be rewritten, by inserting the expressions for b and \( \bar{p} \) as: \( p_{t} = \left( { - \delta /\beta } \right)^{t} (p_{0} - \bar{p}) + \bar{p} \)
- 4.
Metzler (1941) introduced another expectations mechanism, namely extrapolative expectations, where the expected value depends on the past value of the variable as well as on its direction of change in the past: \( p_{t}^{e} = p_{t - 1} + \in (p_{t - 1} - p_{t - 2} ) \), where \( \in \) is called the coefficient of expectations. However, this model has not been a very popular one. For further discussion on it, see Carter and Maddock (1984, pp. 17–18).
- 5.
Note that static expectation is a special case of this mechanism with \( \theta = 1 \).
- 6.
The concept of the natural level of output is explained later in Sect. 3.1 when we start discussing the different versions of the Phillips curve.
- 7.
The first-order linear difference Eq. (17), if solved, will have a stable equilibrium at a positive value, \( \bar{e} = \sigma g/\theta \).
- 8.
Recall that in our Example I, discussed earlier, the “forecasting error”, under adaptive expectations, was found to be increasing over time, ultimately settling at a positive value.
- 9.
Note that when \( u_{t} \)’s are serially correlated, the past realisations, \( u_{t - 2} \), \( u_{t - 1} \), etc., contain information which will be available at the end of the period in question and hence will be used—according to the rational expectations hypothesis—in forming expectations like \( E_{t} \left( {u_{t} } \right) \), \( E_{t} \left( {p_{t} } \right) \), etc., and in this case, \( E_{t} \left( {u_{t} } \right) \) need not be zero, even if \( E\left( {u_{t} } \right) = 0 \) for each t.
- 10.
As we have seen, the cobweb model with rational expectations and the cobweb model with other expectations mechanisms (e.g. the static expectations, \( p_{t}^{e} = p_{t - 1} \)) yield completely different results.
- 11.
“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” (Phillips 1958, p. 283).
- 12.
“At any moment of time, there is some level of unemployment which has the property that it is consistent with equilibrium in the structure of real wage rates” (Friedman 1968, p. 8). Friedman termed this level of unemployment (as a proportion of the total labour force) the natural rate of unemployment and argued that an unemployment higher (lower) than the natural rate would indicate that there was an excess demand for (supply of) labour that would produce upward (downward) pressure on real wage rate.
- 13.
- 14.
As Friedman (1968, p. 11) writes, “there is always a temporary trade-off between inflation and unemployment; there is no permanent trade-off. The temporary trade-off comes not from inflation per se, but from unanticipated inflation, which generally means, from a rising rate of inflation. The widespread belief that there is a permanent trade-off is a sophisticated version of the confusion between ‘high’ and ‘rising’ that we all recognise in simpler forms. A rising rate of inflation may reduce unemployment, a high rate will not”.
- 15.
By adding \( p_{t - 1} \) to both sides of Eq. (29), it may be rewritten as \( y_{t} - y^{*} = \left( {1/\beta } \right)\left[ {p_{t} - E_{t} \left( {p_{t} } \right)} \right] \). This version is known as the famous Lucas supply function [see Blanchard and Fisher (1989, p. 358); but \( y^{*} \) is not mentioned there].
- 16.
One may also incorporate in each of our previous two models (viz. original Phillips curve and the Friedman–Phelps model), the (AD)t curve given by Eq. (30) and draw the two curves in a diagram like Fig. 2 and then derive those results in the way done here. We leave it as an exercise for the students.
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Maiti, P. (2019). Theories of Expectations Including Rational Expectations and Their Uses in Different Versions of the Philips Curve. In: Bandyopadhyay, S., Dutta, M. (eds) Opportunities and Challenges in Development. Springer, Singapore. https://doi.org/10.1007/978-981-13-9981-7_1
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