Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

Who is ' Macroe

Rational Expectations and

Economic Policy

The purpose of this chapter is to discuss the following issues:

1.What do we mean by rational expectations (also called model-consistent expectations)?

2.What are the implications of the rational expectations hypothesis (REH) for the con - duct of economic policy? What is the meaning of the so-called policy-ineffectiveness proposition (PIP)?

3.What are the implications of the REH for the way in which we specify and use macroeconometric models, and what is the Lucas critique?

4.What is the lasting contribution of the rational expectations revolution?

3.1 What is Rational Expectations?

3.1.1 The basic idea

More than three decades ago, John Muth published an article in which he argued forcefully that economists should be more careful about their informational assumptions, in particular about the way in which they model expectations. Muth's (1961) point can be illustrated with the aid of the neoclassical synthesis model under the AEH that was discussed in Chapter 2. Consider Figure 3.1, which illustrates the effects of monetary policy over time. The initial equilibrium is at point E0, with output equal to Y* and the price level equal to Po. There is an expectational equilibrium, because P = Pe at point Eo. If the monetary authority increases the money supply (in a bid to stimulate the economy), aggregate demand is boosted (the AD curve shifts to ADO, the economy moves to point A, output increases to Y*, and the price level rises to P'. In A there is a discrepancy between the expected price level and the

P -I

actual price It expected pricy A, In the diagram towards point f The adjustm, (e.g. household time paths for t the expectation is slowly elim A, negative, and a This is very opposed to the economics. Thi occupies cent'. result, Muth pi future events, a theory" (1961. With respect hear at time to relevant econo level for the n supply (PC = P1 jumps from E0 adjustment st, sition. Since ti

onsistent expecta-

'Pa° for the con- ey-ineffectiveness

specify and use

ution?

ich he argued ational assump- L Muth's (1961) iodel under the i illustrates the nt E0, with outla' equilibrium, money supply ( the AD curve ', and the price

level and the

AD0

Y*

Figure 3.1. Monetary policy under adaptive expectations

level. This discrepancy is slowly removed by an upward revision of the expected price level, via the adaptive expectations mechanism (e.g. equation (1.14)). In the diagram this is represented by a gradual movement along the new AD curve towards point El , which is the new full equilibrium.

The adjustment path of expectations is very odd, however, because agents (e.g. households supplying labour) make systematic mistakes along this path. The time paths for the actual and expected price levels are illustrated in Figure 3.2, as is the expectational error (Pe — P). The initial shock causes an expectational error that is slowly eliminated. All along the adjustment path, the error is negative and stays negative, and agents keep guessing wrongly.

This is very unsatisfactory, Muth (1961) argued, because it is diametrically opposed to the way economists model human behaviour in other branches of economics. There, the notion of rational decision making (subject to constraints) occupies centre stage, and this does not appear to be the case under the AEH. As a result, Muth proposed that: "expectations, since they are informed predictions of future events, are essentially the same as the predictions of the relevant economic

theory" (1961, p. 316).

With respect to the model illustrated in Figure 3.1, this would mean that agents hear at time to that the money supply has been increased from M0 to M1, use the relevant economic theory (equations (2.1)—(2.2)), calculate that the correct price level for the new money supply is P 1 , adjust their expectations to that new money

supply (11 = P1), and supply the correct amount of labour. As a result, the economy jumps from E0 to E1, output is equal to Y* and the price level is P i . Of course, this

adjustment story amounts to the PFH version of the policy-ineffectiveness proposition. Since there is no uncertainty in the model, forecasting is not difficult for

The Foundation of Modern Macroeconomics

Pe

P

A

to

— P

0

to

Figure 3.2. Expectational errors under adaptive expectations

the agents. They realize that a higher money supply induces a higher price level and thus adjust their wages upwards. As a result, the real wage, employment, and output are unaffected.

In reality all kinds of chance occurrences play an important role. In a macroeconomic context one could think of stochastic events such as fluctuation in the climate, natural disasters, shocks to world trade (German reunification, OPEC shocks, the Gulf War), etc. In such a setting, forecasting is a lot more difficult. Muth (1961) formulated the hypothesis of rational expectations (REH) to deal with situations in which stochastic elements play a role. The basic postulates of the REH are:

(i) information is scarce and the economic system does not waste it, and (ii) the way in which expectations are formed depends in a well-specified way on the structure of the system describing the economy.

In order to clarify these postulates, consider the following example of an isolated market for a non-storable good (so that inventory speculation is not possible). This

market is describe

Q4D = ao _ I

Qs = bo -r. k

QtD (215 I

where Pt is the p the quantity su, to hold in period impinge on the Ut could summa::. the weather, cr(

Equation (3.1) In other words, tt events occurrin income fluctuatio pliers must dedd be the price at basis of all inform information tht.

set, Ot-1:

Qt-1 ==- (Pt-

What does this rr including period the information s the structure of ti used by agents). I agents as is the stn realization of al, distribution of to■ is distributed as a autocorrelation where E(.) is the tion is written in that the normal u Figure 3.3. Fourt know past obser . out what the corn

The REH can na

Pte. = E [Pt I 0

daptive

luces a higher price level wage, employment, and

-cant role. In a macroe- Lich as fluctuation in the

,n reunification, OPEC

ilot more difficult. Muth

( REH) to deal with situaoostulates of the REH are: waste it, and (ii) the way c. --d way on the structure

I

example of an isolated )n is not possible). This

Chapter 3: Rational Expectations and Economic Policy

where Pt is the price of the good in period t, Qtli is the quantity demanded, Qis is the quantity supplied, and P; is the price level that suppliers expect in period t - 1 to hold in period t. The random variable Ut represents all stochastic elements that impinge on the supply curve. If the good in question is an agricultural commodity, Ut could summarize all the random elements introduced in the supply decision by the weather, crop failures, insect plagues, etc.

Equation (3.1) shows that demand only depends on the actual price of the good. In other words, the agents know the price of the good, and there are no stochastic events occurring on the demand side of the market, such as random taste changes, income fluctuations, etc. Equation (3.2) implies that there is a production lag: suppliers must decide on the production capacity before knowing exactly what will be the price at which they can sell their goods. They make this decision on the basis of all information that is available to them. In the context of this model, the information they possess in period t - 1 is summarized by the so-called information

set, Qt-i.

2t -1 {Pt -1,Pt -2, Qt Qt_2, ...;ao, ai, bo, bi; Ut N(0, 0-2)} (3.4)

What does this mean? First, the agents know all prices and quantities up to and including period t - 1 (they do not forget relevant past information). Obviously, the information set Qt-i does not include Pt, Qt, and Ut . Second, the agents know the structure of the market they are in (recall: "the relevant economic theory" is used by agents). Hence, the model parameters c/o, al , bo, and b1 are known to the agents as is the structure of the model given in (3.1)-(3.3). Third, although the actual realization of the stochastic error term Ut is not known for period t, the probability distribution of this stochastic variable is known. For simplicity, we assume that Ut is distributed as a normal variable with an expected value of zero (EUt = 0), no

autocorrelation (EUt Us = 0 for t s), and a constant variance of a 2 E(Ut - EUt)2], where E(.) is the unconditional expectations operator. This distributional assump-

tion is written in short-hand notation as N(0, a 2 ). Recall from first-year statistics that the normal distribution looks like the symmetric bell-shaped curve drawn in Figure 3.3. Fourth, past realizations of the error terms are, of course, known. Agents know past observations on Qt_i and Pt_i, and can use the model (3.1)-(3.3) to find

The Foundation of Modern Macroeconomics

Figure 3.3. The normal distribution

where Et_1 is short-hand notation for E(. I Qt---1.), which is the conditional expectation operator. In words, equation (3.5) says that the subjective expectation of the price level in period t formed by agents in period t -1 (Pt) coincides with the conditional objective expectation of Pt, given the information set Qt-t.

How does the REH work in our simple model? First, equilibrium outcomes are calculated. Hence, (3.3) is substituted into (3.1) and (3.2), which can then be solved

Equation (3.6) is crucial. It says that the actual price in period t depends on the price expected to hold in that period, and the realization of the stochastic shock Ut . More precisely, a higher expected price level or a positive supply shock (bigger Pt or Ur) boosts the supply of goods and thus the equilibrium price level must fall in order to clear the market. The REH postulates that individual agents can also calculate (3.6) and can take the conditional expectation of Pt:

Consider the three terms on the right-hand side of (3.8) in turn. The first term is obvious: the conditional expectation of a known constant is that constant itself. The second term can similarly be simplified: Pt is a known constant, so that E t_i/I = The third term can be simplified by making use of our knowledge concerning the distribution of Ut . Since Ut is not autocorrelated, the conditional expectation of it is equal to its unconditional expected value, i.e. Et-1 Ut = 0. As a result of all these simplifications, Et_iPt can be written as:

- bo) (b1

Et-iPt = (ao --) /Pt. (3.9) aial

but the REH states in expectation, coinc

L.c solution for

Pt = a() -

al a

The final expression

The actual price levc,

;ply shock Ut ). By si

(ao - bo Pt = al +

where P I,. (ao - bo), no stochastic elem,: Pt fluctuates randornt

-(1/ai)Ut , and exhi' so that agents do

supply shock, for ex - What would have be tational errors do dis1

says that the expect, actual price level and

I

Pre = XPt_i + (1 -I

By using (3.6) and (3.

Pt - (1 - ))Pt-1

C.* — a l

x(ao al

rao -

Pt =

a l

Equation (3.13) shov4: recognizable pattern. term displays autot.

The issue can be ill paths of the price k

tively, the REH and

computer was instruc tribution with mean,.