Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

> 0) raises the wage (dw > is illustrated in Figure 9.1. An

'n in both the wage and ft :ted in Figure 9.2. Finally, a d the vacancy-unemployment

e corresponding graph and

rate raises both the unemplovrounding Figure 9.2. By usin7

in V and

(A9.4)

vacancy rate is ambiguous in square brackets on the right- ' *ion is satisfied. First we note

t-hand side of (A9.5) can be

I

q

dw 77

(A9.8)

a sufficient condition for the

(A9.9)

e relative bargaining power of sfied and the term in square he sufficient condition is quite

Chapter 9: Search in the Labour Market

weak. Even for the relatively high unemployment rate of 25% (U = 0.25) the condition is satisfied if /3 > 1/9. See, also Pissarides (1990, p. 16) who derives a more stringent sufficient condition.

In section 2.1 we modify the model to take into account the effects of taxation on the labour market. An increase in the labour income tax rate operates just like an increase in the unemployment benefit so the results follow immediately. Keeping all exogenous variables other than the payroll tax constant we find by differentiating (9.33) and (9.38):

(

where it follows from (9.38) that the numerator of (A9.11) is positive.

In section 2.2 we study the effects of an increase in the deposit on labour, b. Keeping all exogenous variables other than the deposit constant we find by differentiating (9.42) and (9.45):

235

Macroeconomic Policy,

Credibility, and Politics

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

1.What do we mean by dynamic inconsistency. When is economic policy dynamically inconsistent and hence not credible?

2.How can reputation effects come to the rescue if the optimal policy is inconsistent?

3.Why does it sometimes pay to appoint a conservative to head the central bank?

4.How can the taxation of capital give rise to dynamic inconsistency?

10.1 Dynamic Inconsistency

10.1.1 A classic tale

As anyone with more than a fleeting interest in literature knows, Ulysses had a hard time getting back to his island of Ithaca after helping the Greeks win the war against the Trojans. Apparently the Greeks had forgotten to suitably thank the gods upon winning the war, and this had irritated them to such an extent that they decided to make the Greeks suffer. To cut a long story short, it took Ulysses ten years plus a lot of trouble to get home. During this journey he and his men have to pass the island of the Sirens. These Sirens were twin sisters and excellent singers but had a dangerous streak to them. As the witch Circe warns Ulysses:

Your next encounter will be with the Sirens, who bewitch everybody that approaches them. There is no home-coming for the man who draws near them unawares and hears the Sirens' voices; no welcome from his wife, no little children brightening at their father's return. For with the music of their song the Sirens cast their spell upon him, as they sit there in a meadow piled high with the mouldering skeletons of men, whose withered skin still hangs upon their bones. (Homer, 1946, p. 190)

Ulysses is fac would not?) but t also suggests a sol his men, their L— Sirens, and:

I alone ... might I. stir from the spot 114 lashed round the m bonds. (Homer, 194k

The plan is execu to release him. He his pleas and add t problems.

Ulysses' decisi( Circe's suggestion for Ulysses and his After all, they are k leads to death and ( Ulysses commit hin ears of his crew, ar brief spell, he and consistent but si.,:o]

10.1.2 A neoclas

Dynamic inconsistt the simplest exai etary policy with ar 1977). Our version supply of goods y rprise Jr — n- e , anC

y= + a [7r —

►nere y and j■ are t seeds the expect

LAJour supply is to(

We assume that L. itkixicted inflation

ne wonders why --iss with beeswax. That save been ensured. Hot

1 0

S:

economic policy dynamically

ptimal policy is inconsistent? head the central bank?

iconsistency?

knows, Ulysses had a hard Greeks win the war against lbly thank the gods upon extent that they decided Kok Ulysses ten years plus his men have to pass the xcellent singers but had a

:PS

p

body that approaches them. [a wares and hears the Sirens' it their father's return. For m, as they sit there in a xe withered skin still hangs

Chapter 10: Macroeconomic Policy, Credibility, and Politics

Ulysses is facing a difficult choice. He would like to listen to the Sirens (who would not?) but he does not want to end up as a skeleton just yet. Fortunately Circe a! \o suggests a solution to the decision problem Ulysses faces. As Ulysses later tells his men, their ears should be plugged with beeswax so that they cannot hear the Sirens, and:

I alone ... might listen to their voices; but you must bind me hard and fast, so that I cannot stir from the spot where you will stand me, by the step of the mast, with the rope's end lashed round the mast itself. And if I beg you to release me, you must tighten and add to my bonds. (Homer, 1946, p. 193; emphasis added)

The plan is executed, they sail past the Sirens' island, and Ulysses instructs his men to release him. He wants to go to the island. His men, suitably instructed, ignore his pleas and add to his bonds. They escape the perilous Sirens with no additional problems.

Ulysses' decision problem is a classic example of dynamic inconsistency, and Circe's suggestion constitutes a smart solution to the problem. The optimal policy for Ulysses and his men is to listen to the Sirens and continue the journey to Ithaca. After all, they are good singers. Unfortunately, this policy is inconsistent, since it leads to death and decay, and Ithaca will not be reached. Circe's solution is to make Ulysses commit himself to his long-term goal of reaching Ithaca by plugging the ears of his crew, and tying himself to the mast. By giving up his authority for a brief spell, he and his men are better off as a result. The commitment solution is consistent but suboptimal, as his men don't get to hear the music. 1

10.1.2 A neoclassical tale

Dynamic inconsistency also features prominently in the economics literature. One of the simplest examples of dynamic inconsistency concerns the conduct of monetary policy with an expectations-augmented Phillips curve (Kydland and Prescott, 1977). Our version of their example makes use of the Lucas supply curve. Aggregate supply of goods y depends on the full employment level of output y, the inflation surprise 7 — 7 e , and a stochastic error term c (with properties EE = 0 and EE2 = a 2 ):

y = p + a [7r — ± E , a > 0, (10.1)

where y and y are both measured in logarithms. If the actual inflation rate, .71- , exceeds the expected inflation rate, 7e , workers have overestimated the real wage, labour supply is too high, and output is higher than its full-employment level.

We assume that agents hold rational expectations (REH, see Chapter 3), so that the expected inflation rate coincides with the mathematical expectations of the actual

One wonders why Ulysses did not tie all his men but one to the mast, and plug that one man's ears with beeswax. That way a higher level of welfare would have been attained and consistency would have been ensured. Homer does not explain. Perhaps the mast only held one person.

237

where 8 measures the degree of inflation aversion of the policy maker. The higher 0, the higher the welfare costs associated with inflation, and the stronger is the inflation aversion. The policy maker cannot directly influence the expectations held by the private agents and consequently takes n- e as given in its optimization problem. There is information asymmetry in the sense that the policy maker can observe the realization of the supply shock, E, but the public cannot. As a result, the policy-ineffectiveness proposition (PIP) fails and economic policy has real effects (see Chapter 3). The policy maker chooses the inflation rate and output level such that social costs (10.2) are minimized subject to the Lucas supply curve (10.1). The Lagrangean for this problem is:

so that the first-order conditions are:

By combining (10.4)-(10.5) we obtain the "social expansion path", giving all combinations of inflation and output for which social costs are minimized:

Y y* = - (0/01)7r •<# n = - (a/P) [Y yl • (10.6)

This downward-sloping line has been drawn in Figure 10.1. Graphically the line represents all points of tangency between an iso-cost curve of the policy maker and a Lucas supply curve. In view of the definition of the social welfare function (10.2), the iso-cost curves are concentric ovals around the bliss point E, where it = 0 and

2 Obviously, the first-best policy would be to remove these pre-existing distortions directly. It is assumed that this is impossible, however, so that monetary policy is used as a second-best instrument to boost output. See Persson and Tabellini (1989, p. 9).

Figure 10.1. Consiste

I

y = y*. The slope of the isci

It follows that the iso-cost dyoo) for it = 0. 1

By combining (10.1) any discretion, denoted

= ire + (i/a) [y — —

(1 + fl/a2)7 = 7re + 'c

a 27T e ± a fy* _

7TD p

We use the term "discretic rate in each period as it pleai (10.8) says that inflation un ambition of the policy ma, supply shock (e < 0, which

he policy maker is assumed

Dcial welfare function) which er than the full employment the policy maker deems the societal point of view. This 3r unemployment benefits. 2

(10.2)

policy maker. The higher 3n, and the stronger is the influence the expectations is given in its optimization that the policy maker can

cannot. As a result, the )mic policy has real effects rate and output level such supply curve (10.1). The

(10.3)

(10.4)

(10.5)

Mansion path", giving all osts are minimized:

=

(10.6)

1.1. Graphically the line we of the policy maker and ial welfare function (10.2), point E, where 7r = 0 and

- cting distortions directly. It is

used as a second-best instrument

I

Chapter 10: Macroeconomic Policy, Credibility, and Politics

Figure 10.1. Consistent and optimal monetary policy

y y*. The slope of the iso-cost curves is obtained in the usual fashion:

It follows that the iso-cost curve is horizontal (d7 r I dy = 0) for y = y* and is vertical

oo) for 7r = 0.

By combining (10.1) and (10.6), we obtain the expression for inflation under discretion, denoted by 7TD:

We use the term "discretion" because the policy maker chooses the optimal inflation rate in each period as it pleases, i.e. after it has observed the supply shock E. Equation

(10.8) says that inflation under discretion is high if expected inflation is high, if the ambition of the policy maker (i.e. is large, and if there is a negative aggregate supply shock (E. < 0, which is the case, for example, with an OPEC shock).

239

The Foundation of Modern Macroeconomics

This is not the end of the story, of course, since under rational expectations agents in the private sector know that the policy maker will choose the inflation rate 7rD under discretion, so that they will form expectations accordingly:

where we have used EE = 0 (agents do not observe the supply shock but expect it to be zero). Equation (10.9) is the rational expectations solution for the expected inflation rate. By substituting (10.9) into (10.8) and (10.6), respectively, we obtain the expressions for actual inflation and output under discretionary monetary policy:

YD = + a2 ± ) E.

These results are intuitive. Equation (10.10) says that under the REH the actual inflation rate is high if the output ambition of the policy maker is high or if there are negative supply shocks. Equation (10.11) shows that, for example, a negative supply shock is partially accommodated by expansionary monetary policy (only partially as fl/(a2 +13) < 1). This is especially the case if the policy maker has "leftist" preferences, i.e. has a low aversion towards inflation, represented by a low value of 13. A left-wing policy maker attaches a greater importance to the stabilization of output (and hence, employment) fluctuations. A similar conclusion is obtained if the Lucas supply curve is very flat. In that case, a is very large and a large degree of accommodation takes place.

The problem with the discrete solution is that it is suboptimal! This can be demonstrated graphically with the aid of Figure 10.1. The discrete solution is represented by point ED , where we have drawn the Lucas supply curve, LSCD, for a realization of the supply shock equal to E = 0. Suppose, however, that the policy maker could announce to the public that it would choose a zero inflation rate, i.e. 7 = 0. If the public believes this announcement, the REH implies that expected inflation will also be zero, i.e. ire 0, so that the relevant Lucas supply curve would be the one through the origin (i.e. LSCR which passes through point E R ). Through this point, there21is an iso-cost curve Q R that is closer to the bliss point E, and consequently involves strictly lower social costs, i.e. OR < CID . Hence, for this case the solution is:

where we have used the subscript "R" to designate that this is policy under a rule. Instead of choosing the optimal inflation and output combination each period, the

policy maker follow! rate is zero, as prop shocks is possible inflation, which viol, under the rule, as (10

The problem with illustrated with the al is given at point ER , (LSCR). But the policy LSCR, namely the "C the iso-cost curve Qc

surprise it > nR = 711?' = Formally, the cheat

substituting 7 e = 71.R =

1

so that output is:

2

yc = + /3 y

The upshot of this is, not credible. Only if the "mast" of zero inflati( Before turning to oni ment up to this point in the current setup. It follow a zero-inflation (10.15)). By substituti: welfare cost function (1

expressions:

C C =1 2 a2 +

? = Ysi2 ►

from which we infer the bliss point, is crec and satisfies REH, i solution under discreti

rational expectations agents choose the inflation rate 7rD ccordingly:

(10.9)

supply shock but expect it

,s solution for the expected 6), respectively, we obtain

cretionary monetary policy:

(10.10)

under the REH the actual -v maker is high or if there at, for example, a negative ary monetary policy (only policy maker has "leftist" presented by a low value of [rice to the stabilization of it conclusion is obtained if large and a large degree of

ptimal! This can be demon-

. fe solution is represented rve, LSCD, for a realization at the policy maker could >n rate, i.e. Tr = 0. If the iat expected inflation will ly curve would be the one t ER ). Through this point, oint E, and consequently )r this case the solution is:

(10.12)

(10.13)

is policy under a rule. bination each period, the

Chapter 10: Macroeconomic Policy, Credibility, and Politics

policy maker follows a simple money growth rule that ensures that the inflation rate is zero, as promised. Equation (10.13) shows that no accommodation of supply ocks is possible under this rule (obviously, since accommodation would lead to lation, which violates the promise). The advantage is that there is no inflation

der the rule, as (10.12) shows.

The problem with this optimal policy is that it is inconsistent! This can also be illustrated with the aid of Figure 10.1. The solution under the inflation rule 7rR = 0

is given at point ER , and the relevant Lucas supply curve goes through that point (LSCR). But the policy maker has an even more attractive option than ER if it faces

LSCR, namely the "cheating" point Ec , where there is a tangency between LSC R and the iso-cost curve C2c. In the cheating solution, the policy maker creates an inflation surprise r > 7Q? = 7rf? = 0 in order to boost output y >

Formally, the cheating solution for inflation, denoted by 7C, substituting Ire = 7ER = 0 into (10.8):

The upshot of this is, of course, that the solution under the zero-inflation rule is

not credible. Only if the policy maker is able to commit himself by being tied to the "mast" of zero inflation (just like Ulysses), does the rules solution have credibility.

Before turning to one possible commitment mechanism, we summarize the argument up to this point. There are three possible options that the policy maker has in the current setup. It can pursue discretionary policy (equations (10.10)-(10.11)), follow a zero-inflation rule (equations (10.12)-(10.13)), or cheat (equations (10.14)- (10.15)). By substituting the different solutions for output and inflation into the welfare cost function (10.2) (assuming e = 0 for simplicity), we obtain the following expressions:

from which we infer that OD > C2R > S2c > 0. The cheating solution is closest to the bliss point, is credible but it violates the REH. The rules solution is optimal and satisfies REH, but is open to temptation and is hence not credible. Finally, the solution under discretion is suboptimal, satisfies REH, and is credible.

241

The Foundation of Modern Macroeconomics

10.1.3 Reputation as an enforcement mechanism

In the previous subsection we have shown that the only policy which is both credible and consistent with rational expectations is the suboptimal discretionary policy. Given the structure of the problem, it appears that the economy is likely to end up in the worst possible equilibrium. In an influential article, however, Barro and Gordon (1983b) have demonstrated that reputation effects can come to the rescue, and prevent this worst-case scenario from materializing. Their argument can be made with the aid of the model developed in section 1.2. In order to develop the simplest possible model, we assume that there are no stochastic shocks (E 0). There is repeated interaction between the policy maker and the public (represented, for example, by the unions who set the nominal wage rate).

The cost function of the policy maker consists of the present value of the costs incurred each period, and is defined as:

where r is the real discount factor (e.g. the real rate of interest), and Sgt is the cost incurred in period t:

12 0 2 [Yt Y* 1 + " .7rt ►

and the Lucas supply curve is given by:

yt = y + a — 7rn, a > 0.

It is assumed for simplicity that both y* and k are constant over time and thus do not feature a time subscript.

As in section 1.2, there are again a number of choices that the policy maker can make. A discretionary policy involves setting inflation according to (10.10) in each period (with c = 0 imposed). This yields a cost level of C2D in each period (see (10.18)), so that the present value of social costs equals VD:

Now consider what happens if the policy maker chooses tosfollow a constant-inflation rule, 7rt = n-R, where we generalize the previous discussion by allowing the constant inflation rate 7rR to be non-zero. If this inflation rate is believed by the public, it will come to expect it, so that the expected inflation rate will also be equal to Ttp in each period, so that output will equal y in each period. By substituting these solutions into (10.20) the periodic cost level under the rule is obtained:

where S2R is the welfare cost under the zero-inflation rule as defined in (10.17), and we have indicated that under the more general inflation rule, the cost level depeiltis

positively on the . present value of Cu),

Finally, as before, the for the policy make inflation rate CR. B the expression for ti,

which implies that a

YC = 2 1

I

By substituting (10._ cheating is obtained:

where Qc depends on and (10.16) coincide value of TrR.

We are now in a po) ysis. Suppose that the promise in the previa do). If that is the case. that inflation will be s its promise in period expects the discrete sc mechanism adopted i

7TR if :re . 7rD,t if n't

Equation (10.28) impli prisoner's dilemma gL, "misbehaves" it gets pt the case, consider the

m

policy which is both crediptimal discretionary policy.

)nomy is likely to end up e, however, Barro and Gorin come to the rescue, and eir argument can be made order to develop the sim-

,tic shocks (E 0). There he public (represented, for

present value of the costs

(10.19)

nterest), and Qt is the cost

Chapter 10: Macroeconomic Policy, Credibility, and Politics

positively on the chosen inflation level. By substituting (10.23) into (10.19), the present value of costs incurred under the rule V R (7TR ) is obtained:

Finally, as before, the cheating solution is derived by determining the optimal choice for the policy maker given that the public expects it to stick to the announced inflation rate 7rR. By substituting 7re = 7rR into equation (10.8), and setting E = 0, the expression for the cheating inflation rate 7rc is obtained:

which implies that output under cheating is given by:

By substituting (10.25)-(10.26) into (10.20), the periodic cost level associated with cheating is obtained:

The Foundation of Modern Macroeconomics

and assume that the policy maker has credibility in that period (i.e. in period —1 it has kept its promise) and so expected inflation in period 0 equals the level specified

by the rule, i.e. no =

The first scenario that the policy maker can follow in period 0 is to keep its promise, and to produce inflation equal to The public observes this inflation rate, concludes that the policy maker is trustworthy, and continues to expect that inflation will be set according to the rule. By sticking to its promise, the policy maker has maintained its reputation, and no punishment takes place.

The second scenario that the policy maker can follow is to cheat in period 0. It has an incentive to do so since the periodic cost level attained in period 0 is then given by (10.27) which is lower than periodic cost under the rule as given in (10.23). In fact, the temptation that the policy maker is subjected to in period 0 can be calculated:

where we have used (10.27) and (10.23), and T(7R) is the temptation to cheat if the policy rule stipulates an inflation rate 71-R. In Figure 10.2 we have plotted this quadratic temptation function. Several points of this function are easy to find. If the

Enforceable region

Figure 10.2. Temptation and enforcement

Chat

rule inflation rate gR = 0,

T(0) — QC = (

and T(7rR) = 0 if the rule (10.10) (with E = 0 impose

T(1rD)= 0.

The inflation rate under For higher inflation rates,

But under the second sa it did not keep its promi • maker, and expects the

to be higher than they wa costs must be taken into a

the rule in period 0. From 1 receives consists of the di

QD OR(7rR)

P(gR) = 1 + r

a2

o2 fi-t- P )

= r C

where we have used (10. ishment curve can be foul, to:

comparing (10.33) and for the discrete inflation ra

P(JrD) = 0.

Finally, for rule inflation ra: function P(gR ) has been dra In period 1 the public t

inflation rate 7tD, and gi% L to do so. Hence, in period 1 in the policy maker is res:

inflation rate to be produc