In equation (10.1) votes are a decreasing function of P and U. Figure 10.3

shows the contours (iso-vote lines) of the aggregate voting function (V1, V2

and so on), which indicate the percentage of votes acquired by the incum-

bents for a given policy outcome. Since in¬‚ation and unemployment are

˜bads™, V1 > V2 > V3 > V4. Voters prefer any point on V1 to any point on V2 but

are indifferent between points on the same contour. Governments seeking to

528 Modern macroeconomics

win elections will endeavour to manipulate the economy towards the highest

feasible vote contour so as to coincide with the election period.

The macroeconomic framework adopted by Nordhaus involves an expecta-

tions-augmented Phillips curve framework summarized by equations (10.2)“

(10.5).

Expectations-augmented Phillips curve:

Pt = f (Ut ) + »Pt e

™ ™ (10.2)

Adaptive expectations hypothesis:

Pt e ’ Pt e 1 = ±[ Pt ’1 ’ Pt e 1 ], and ± > 0

™ ™’ ™ ™’ (10.3)

Equilibrium condition:

Pt = Pt e

™™ (10.4)

Long-run Phillips curve trade-off:

f (U )

Pt =

™ (10.5)

(1 ’ » )

Nordhaus assumes that 1 > » > 0 which yields a long-run Phillips curve

which is less favourable (steeper) than the short-run relationship. In Figure

10.3 the short-run curves are indicated by SG, SW and SM and the position of

each curve depends on the expected rate of in¬‚ation. The long-run Phillips

curve is labelled LRPC. If the » coef¬cient is unity, the Phillips curve be-

comes a vertical line at the natural rate of unemployment (see Friedman,

1968a). However, as Nordhaus (1975, p. 176) notes, ˜a vertical long-run

Phillips curve makes no difference in principle™ to the substantial conclusions

of the model.

10.6.1 Optimal in¬‚ation and unemployment

Given assumption N4, the social welfare function (W) of the policy makers

will be the discounted value of the aggregate voting function. In the absence

of political constraints a social planner will seek to maximize the welfare

function given by equation (10.6) subject to the macroeconomic constraints

given by equations (10.2)“(10.5):

∞

W = « g(Ut , Pt )e rt dt

™’ (10.6)

0

The new political macroeconomics 529

Figure 10.3 The Nordhaus political business cycle model

There are several possible outcomes depending on the policy makers™ choice

of discount rate (r). Where future generations are given the same weight as

the current generation (r = 0), the outcome is indicated by G in Figure 10.3.

Here the LRPC is at a tangent to the aggregate voting function (V2) and this

represents the best sustainable combination of in¬‚ation and unemployment.

Nordhaus calls this outcome the ˜golden rule™ policy solution, which involves

™

in¬‚ation = PG and unemployment = UG. Where the policy makers care only

about the current generation (in¬nite discount rates are applied) a ˜purely

myopic™ policy results in an outcome indicated in Figure 10.3 by point M,

where SM is at a tangent to V4. In other words, ˜myopic™ policies which ignore

™

the welfare of future generations lead to higher in¬‚ation ( PM ) and lower

unemployment (UM) than golden rule policies (Nordhaus, 1975). Where the

policy maker cares about both generations (∞ > r > 0), an outcome Nordhaus

refers to as the ˜general welfare optimum™ (W) results. In this case U = UW

and P = PW .

™™

10.6.2 Long-run implications of the Nordhaus model

Where incumbent politicians are concerned about their re-election prospects,

the Nordhaus model predicts that ˜democratic systems will choose a policy

on the long-run trade-off that has lower unemployment and higher in¬‚ation

530 Modern macroeconomics

than is optimal™. This outcome is the result of the following behaviour.

Suppose before an election the economy is located at point G in Figure 10.3.

The incumbent government can increase its chances of re-election by engi-

neering an expansion of the economy and move up the short-run trade-off SG

to point E1. This represents the best position that the government can achieve

since SG is tangential to V1 at E1. Since E1 lies to the left of the LRPC,

equation (10.3) indicates that SG will shift up to the right as expectations

adjust to the higher rate of in¬‚ation. In contrast, if the short-run electoral

outcome position lay to the right of LRPC, the incumbent party could im-

prove its popularity by policy choices which move the economy back to a

position on the LRPC. The long-run dynamics of the Nordhaus model over

the course of many elections are shown in Figure 10.4, where E0E0 is the

election outcome locus. The long-run equilibrium is determined where E0E0

intersects the LRPC at E* = M. Since M is on both the LRPC and SM, ˜the

incumbent party cannot improve its performance by moving along the short-

run trade-off curve™ because SM is also at a tangent to the iso-vote contour V4

(Nordhaus, 1975). The ¬‚atter the short-run Phillips curves, the higher will be

the steady state equilibrium rate of in¬‚ation.

The interesting outcome of opportunistic behaviour over many electoral

regimes is that the long-run solution to the model corresponds to the myopic

position M. Thus democratic systems are predicted to produce a steady state

equilibrium with higher in¬‚ation and lower unemployment than is optimal,

Figure 10.4 The long-run solution in the Nordhaus model

The new political macroeconomics 531

that is, an in¬‚ation bias (with » = 1 and a vertical Phillips curve, the outcome

involves an in¬‚ation bias only).

10.6.3 Short-run outcomes: the ˜political business cycle™

In his analysis of short-run behaviour, Nordhaus introduces the possibility

that voters have a ˜decaying memory™ (assumption N5). Voters place more

weight on recent events than distant events from the past. In this case equa-

tion (10.1) is replaced by (10.7), where T is the length of the electoral period

and z is the decay rate of voters™ memories:

T

VT = « g(Ut , Pt )e dt

™ zt (10.7)

0

The modi¬ed vote function (10.7) indicates that although voters hold the gov-

ernment responsible for in¬‚ation and unemployment in the current period, their

decaying memory provides the incumbents with the opportunity to systemati-

cally fool the electorate. A typical short-run political business cycle would

progress as follows. As before, suppose the economy is initially located at point

G in Figure 10.3 in the period immediately preceding an election. By expand-

ing aggregate demand the government can lower unemployment and achieve a

position such as E1, which will generate more votes than is possible at G (that

is, V1 > V2). The cost of this manoeuvre is a (delayed) acceleration of in¬‚ation

(SG eventually shifts up to the right as expectations adjust). However, this cost

tends to arise after the election has already been won. Even if in¬‚ation acceler-

ates just before the election, with adaptive expectations it will take time for

economic agents and voters to realize that in¬‚ation has increased. Having

caused higher in¬‚ation, the government now needs to reduce it. Therefore,

immediately following an election victory the government will de¬‚ate aggre-

gate demand which, by increasing unemployment, will eventually reduce

in¬‚ationary expectations, thereby shifting the short-run Phillips curve back

towards SG. Because voters have a decaying memory, this strategy can be