The Nordhaus Opportunistic Model
The modern literature on political business cycles was stimulated by the
seminal paper of Nordhaus (1975). In the electoral model popularized by
Nordhaus the party in power ‘chooses economic policies during its incumbency
which maximize its plurality at the next election’. Since voters are
influenced by a government’s macroeconomic performance before an election,
politicians will be tempted to manipulate policy instruments so that
policy outcomes are most favourable around the election period. The important
consequence of such behaviour is that policies are implemented in
democracies which are biased against future generations (see also Lindbeck,
1976; MacRae, 1977). Thus while elections and electoral competition are
necessary to increase the accountability of government, they are also likely to
introduce potentially damaging distortions into the policy-making process. In
producing this result Nordhaus makes a number of important assumptions,
namely:
N1 The political system contains two parties between which there has been
complete policy convergence as predicted by the median voter theorem
of Downs (1957).
N2 Both parties are interested in maximizing political profit rather than
engaging in ideological programmes. Only election outcomes matter to
these opportunistic non-partisan politicians.
N3 The timing of elections is exogenously fixed.
N4 Individual voters are identical and have aggregate unemployment (Ut)
and inflation (P˙t ) in their preference functions and low inflation and
unemployment rates are preferred. Policy makers are fully informed of
voters’ preferences but have no specific preferences with respect to
inflation and unemployment.
N5 Voters make political choices based on the past performance of incumbent
politicians in managing the economy during their term of office.
Not only are voters retrospective in their voting behaviour (they have
no foresight); they also have a decaying memory (a high discount rate
on past economic performance), that is, they are myopic.
N6 The macroeconomic system can be described by an expectations-augmented
Phillips curve where the short-run trade-off is less favourable
than the long-run trade-off. Voters are ignorant of the macroeconomic
framework.
N7 Expectations of inflation (P˙t )
e are formed adaptively, that is, agents are
backward-looking.
N8 Policy makers can control the level of unemployment by manipulating
aggregate demand via fiscal and monetary policies.
Nordhaus assumes (N4) that policy decisions will be based on the observed
aggregate voting function (Vt) which reflects individual preferences; this is
described by equation (10.1):
Vt = g(Ut ,P˙t ), where g′(Ut ) < 0, and g′(P˙t ) < 0 (10.1)
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 incumbents
for a given policy outcome. Since inflation 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
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 expectations-
augmented Phillips curve framework summarized by equations (10.2)–
(10.5).
Expectations-augmented Phillips curve:
P˙ f (U ) P˙ t t t
= + λ e (10.2)
Adaptive expectations hypothesis:
P˙ P˙ [P˙ P˙ ], t
e
t
e
t t
− = − e > −1 α −1 −1 and α 0 (10.3)
Equilibrium condition:
P˙ P˙ t t
= e (10.4)
Long-run Phillips curve trade-off:
˙ ( )
( )
P
f U
t =
1− λ
(10.5)
Nordhaus assumes that 1 > λ > 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 inflation. The long-run Phillips
curve is labelled LRPC. If the λ coefficient is unity, the Phillips curve becomes
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 inflation 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 dt
= rt ∫∞ − 0
( , ˙ ) (10.6)
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 inflation and unemployment.
Nordhaus calls this outcome the ‘golden rule’ policy solution, which involves
inflation = ˙PG and unemployment = UG. Where the policy makers care only
about the current generation (infinite 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 inflation (P˙M ) 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˙ = P˙W .
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 inflation
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 engineering
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 inflation. In contrast, if the short-run electoral
outcome position lay to the right of LRPC, the incumbent party could improve
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 shortrun
trade-off curve’ because SM is also at a tangent to the iso-vote contour V4
(Nordhaus, 1975). The flatter the short-run Phillips curves, the higher will be
the steady state equilibrium rate of inflation.
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 inflation and lower unemployment than is optimal,
Figure 10.4 The long-run solution in the Nordhaus model
that is, an inflation bias (with λ = 1 and a vertical Phillips curve, the outcome
involves an inflation 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 equation
(10.1) is replaced by (10.7), where T is the length of the electoral
The modified vote function (10.7) indicates that although voters hold the government
responsible for inflation and unemployment in the current period, their
decaying memory provides the incumbents with the opportunity to systematically
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 expanding
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 inflation
(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 inflation accelerates
just before the election, with adaptive expectations it will take time for
economic agents and voters to realize that inflation has increased. Having
caused higher inflation, the government now needs to reduce it. Therefore,
immediately following an election victory the government will deflate aggregate
demand which, by increasing unemployment, will eventually reduce
inflationary expectations, thereby shifting the short-run Phillips curve back
towards SG. Because voters have a decaying memory, this strategy can be
repeated at the next election: recent events are ‘more poignant’ than ‘ancient
ills’. Hence the government can benefit from opportunistic behaviour which
deliberately destabilizes the economy to produce a politically induced business
cycle. This outcome is clearly at odds with the basic Keynesian notion that a
major objective of government is to stabilize the economy.
The Nordhaus model gives clear predictions about the pattern of unemployment
and inflation during the electoral cycle. In the first half of an
electoral period unemployment should be rising, GDP falling and inflation
(eventually) falling. In the run-up to an election, the second half of the
electoral period should be characterized by falling unemployment and rising
GDP. In the immediate post-electoral period inflation rises and a recession
sets in. Nordhaus tested this hypothesis for nine countries over the period
1947–72 and concluded that ‘given both casual and formal evidence of economic
behaviour, and the historical record in the countries examined, it is
clear that a political business cycle is a significant factor in the operation of
some capitalist economies’ (Nordhaus, 1975, emphasis added). Later, Nordhaus
(1989) argued that there can be no monocausal explanation of the political
influences on economic cycles, but in his view the impact of ideological
considerations remained secondary to opportunistic behaviour.
Perhaps the best example of opportunistic behaviour was observed towards
the end of the first term of Richard Nixon’s Presidency in the USA. The
deliberately induced 1970–71 recession was quickly reversed by expansionary
policies in the run-up to the 1972 election. According to Tufte (1978),
Nixon ensured that all social security recipients received a letter in the period
just before the 1972 presidential election. With each letter was a cheque
containing a social security benefits increase of 20 per cent. Apparently
Nixon was concerned that his defeat by Kennedy in 1960 was due to the
failure of President Eisenhower to reflate the economy. It is therefore hardly
surprising that Richard Nixon has been described by Rogoff (1988) as the ‘all
time hero of political business cycles’.
Given the potentially serious nature of this phenomenon, Nordhaus suggested
a number of possible remedies which included increasing the
information available to voters and entrusting monetary policy to an independent
central bank (see section 10.13).
The modern literature on political business cycles was stimulated by the
seminal paper of Nordhaus (1975). In the electoral model popularized by
Nordhaus the party in power ‘chooses economic policies during its incumbency
which maximize its plurality at the next election’. Since voters are
influenced by a government’s macroeconomic performance before an election,
politicians will be tempted to manipulate policy instruments so that
policy outcomes are most favourable around the election period. The important
consequence of such behaviour is that policies are implemented in
democracies which are biased against future generations (see also Lindbeck,
1976; MacRae, 1977). Thus while elections and electoral competition are
necessary to increase the accountability of government, they are also likely to
introduce potentially damaging distortions into the policy-making process. In
producing this result Nordhaus makes a number of important assumptions,
namely:
N1 The political system contains two parties between which there has been
complete policy convergence as predicted by the median voter theorem
of Downs (1957).
N2 Both parties are interested in maximizing political profit rather than
engaging in ideological programmes. Only election outcomes matter to
these opportunistic non-partisan politicians.
N3 The timing of elections is exogenously fixed.
N4 Individual voters are identical and have aggregate unemployment (Ut)
and inflation (P˙t ) in their preference functions and low inflation and
unemployment rates are preferred. Policy makers are fully informed of
voters’ preferences but have no specific preferences with respect to
inflation and unemployment.
N5 Voters make political choices based on the past performance of incumbent
politicians in managing the economy during their term of office.
Not only are voters retrospective in their voting behaviour (they have
no foresight); they also have a decaying memory (a high discount rate
on past economic performance), that is, they are myopic.
N6 The macroeconomic system can be described by an expectations-augmented
Phillips curve where the short-run trade-off is less favourable
than the long-run trade-off. Voters are ignorant of the macroeconomic
framework.
N7 Expectations of inflation (P˙t )
e are formed adaptively, that is, agents are
backward-looking.
N8 Policy makers can control the level of unemployment by manipulating
aggregate demand via fiscal and monetary policies.
Nordhaus assumes (N4) that policy decisions will be based on the observed
aggregate voting function (Vt) which reflects individual preferences; this is
described by equation (10.1):
Vt = g(Ut ,P˙t ), where g′(Ut ) < 0, and g′(P˙t ) < 0 (10.1)
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 incumbents
for a given policy outcome. Since inflation 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
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 expectations-
augmented Phillips curve framework summarized by equations (10.2)–
(10.5).
Expectations-augmented Phillips curve:
P˙ f (U ) P˙ t t t
= + λ e (10.2)
Adaptive expectations hypothesis:
P˙ P˙ [P˙ P˙ ], t
e
t
e
t t
− = − e > −1 α −1 −1 and α 0 (10.3)
Equilibrium condition:
P˙ P˙ t t
= e (10.4)
Long-run Phillips curve trade-off:
˙ ( )
( )
P
f U
t =
1− λ
(10.5)
Nordhaus assumes that 1 > λ > 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 inflation. The long-run Phillips
curve is labelled LRPC. If the λ coefficient is unity, the Phillips curve becomes
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 inflation 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 dt
= rt ∫∞ − 0
( , ˙ ) (10.6)
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 inflation and unemployment.
Nordhaus calls this outcome the ‘golden rule’ policy solution, which involves
inflation = ˙PG and unemployment = UG. Where the policy makers care only
about the current generation (infinite 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 inflation (P˙M ) 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˙ = P˙W .
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 inflation
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 engineering
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 inflation. In contrast, if the short-run electoral
outcome position lay to the right of LRPC, the incumbent party could improve
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 shortrun
trade-off curve’ because SM is also at a tangent to the iso-vote contour V4
(Nordhaus, 1975). The flatter the short-run Phillips curves, the higher will be
the steady state equilibrium rate of inflation.
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 inflation and lower unemployment than is optimal,
Figure 10.4 The long-run solution in the Nordhaus model
that is, an inflation bias (with λ = 1 and a vertical Phillips curve, the outcome
involves an inflation 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 equation
(10.1) is replaced by (10.7), where T is the length of the electoral
The modified vote function (10.7) indicates that although voters hold the government
responsible for inflation and unemployment in the current period, their
decaying memory provides the incumbents with the opportunity to systematically
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 expanding
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 inflation
(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 inflation accelerates
just before the election, with adaptive expectations it will take time for
economic agents and voters to realize that inflation has increased. Having
caused higher inflation, the government now needs to reduce it. Therefore,
immediately following an election victory the government will deflate aggregate
demand which, by increasing unemployment, will eventually reduce
inflationary expectations, thereby shifting the short-run Phillips curve back
towards SG. Because voters have a decaying memory, this strategy can be
repeated at the next election: recent events are ‘more poignant’ than ‘ancient
ills’. Hence the government can benefit from opportunistic behaviour which
deliberately destabilizes the economy to produce a politically induced business
cycle. This outcome is clearly at odds with the basic Keynesian notion that a
major objective of government is to stabilize the economy.
The Nordhaus model gives clear predictions about the pattern of unemployment
and inflation during the electoral cycle. In the first half of an
electoral period unemployment should be rising, GDP falling and inflation
(eventually) falling. In the run-up to an election, the second half of the
electoral period should be characterized by falling unemployment and rising
GDP. In the immediate post-electoral period inflation rises and a recession
sets in. Nordhaus tested this hypothesis for nine countries over the period
1947–72 and concluded that ‘given both casual and formal evidence of economic
behaviour, and the historical record in the countries examined, it is
clear that a political business cycle is a significant factor in the operation of
some capitalist economies’ (Nordhaus, 1975, emphasis added). Later, Nordhaus
(1989) argued that there can be no monocausal explanation of the political
influences on economic cycles, but in his view the impact of ideological
considerations remained secondary to opportunistic behaviour.
Perhaps the best example of opportunistic behaviour was observed towards
the end of the first term of Richard Nixon’s Presidency in the USA. The
deliberately induced 1970–71 recession was quickly reversed by expansionary
policies in the run-up to the 1972 election. According to Tufte (1978),
Nixon ensured that all social security recipients received a letter in the period
just before the 1972 presidential election. With each letter was a cheque
containing a social security benefits increase of 20 per cent. Apparently
Nixon was concerned that his defeat by Kennedy in 1960 was due to the
failure of President Eisenhower to reflate the economy. It is therefore hardly
surprising that Richard Nixon has been described by Rogoff (1988) as the ‘all
time hero of political business cycles’.
Given the potentially serious nature of this phenomenon, Nordhaus suggested
a number of possible remedies which included increasing the
information available to voters and entrusting monetary policy to an independent
central bank (see section 10.13).
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