Table of Contents
1. Introduction……….2
2. The Opportunistic Political Business Cycle………3
3. The Partisan Political Business Cycle……….7
4. Empirics………....13
5. A New Model………16
5.1 The Alesina Model………....16
5.2 Endogenising the Alesina Model………..19
5.3
Static
Expectations………23
5.4 The Political Business Cycle……….27
1. Introduction
Do politicians manipulate the economy in order to win elections? Of course they do! At least, that is the sentiment among the average citizen and a great number of political scientists and
economists. Ever since Nordhaus (1975) formalized a model of the political business cycle, it has been a constant source of inspiration to political economists. There are so many variations on the original model, that one may ask himself what the definition of a political business cycle is. The one thing all the different models have in common is that they each describe a recurring pattern -a cycle- in some economic variable, where the pattern is dependent upon the time between two elections. To say that this definition leaves a lot to be filled in would be an understatement. Fortunately, the literature can roughly be divided in two parts, the opportunistic political business cycle and the partisan political business cycle. Nordhaus (1975) wrote the seminal article in the opportunistic political business cycle field. He felt that a politician is best described as an opportunist that only cares about being in office. Hibbs (1977) wrote the seminal article in the partisan literature. He was the first to introduce a politician that has partisan goals.
These early models both feature non-rational expectations. Later on, rational expectations have been introduced by Rogoff and Sibert (1988) and Alesina (1987) for the opportunistic and partisan political business cycles, respectively:
These four models will be the backbone of the next two sections of my thesis. In section two I will go over the opportunistic political business cycle and the innovations in that field as well as the debate concerning the theory. Section three contains an overview of the literature on the partisan political business cycle. In that section, I will also discuss theoretical criticisms of this part of the literature and show some of the weak points in the existing models, some of which are unresolved. Section four discusses the empirical evidence that has been found in support of the different models. In section five I present a new model of the partisan political business cycle, that has some advantages over the existing models in this field. The final section will be the conclusion, in which I will summarize my findings and add some discussion points.
Opportunistic Partisan
2. The Opportunistic Political Business Cycle
In the opportunistic model, the policymaker only cares about staying in office. Note however, that this is not necessarily bad. If, for instance, the public would always choose the policymaker that gives them the highest utility, the best thing a policymaker can do is to make policy in such a way that the public’s utility is maximized. This would always be the case in an ideal world, with a rational, forward-looking public and no uncertainty. When non-rationality is introduced, or when there is uncertainty, opportunities for a political business cycle arise. The first to model a political business cycle was Nordhaus (1975). His model features non-rational expectations and a
backward looking public.
The Nordhaus (1975) model of the opportunistic political business cycle rests upon the following assumptions:
1) The economy can be described by an expectations adjusted Phillips curve, that is to say, an increase in unexpected inflation reduces unemployment1.
2) Expectations are adaptive.
3) Policymakers control the money supply, which they can increase to create inflation. 4) Policymakers are opportunistic; they only care about holding office.
5) Voters are retrospective; they only care about the past performance of the incumbent policymaker and see a policymaker that has created low unemployment as competent. The outcome of this model is that a cycle in unemployment will arise. The policymaker will want to create low inflation in the first part of his term. He can do this by setting a low rate of money growth; the Nordhaus model assumes that a one percent increase in the money supply will create one percent of inflation. Because expectations are adaptive (expected inflation is a weighted average of current inflation and the expected inflation from the previous year), low expectations of inflation will then be created. In the year(s) before an election the policymaker will create an inflationary surprise, which lowers unemployment. Because unemployment is low in the election year, the public views the incumbent as competent and will assign a higher probability of re-election to him. This creates a cycle which will repeat itself every x years, where x is the time between two elections. In the first years, inflation will be low and unemployment high, while in later years, inflation will be high and unemployment low.
The model has been criticized by many authors on many points. It has been pointed out that in most countries, especially those in the OECD, the money supply is not in the hands of the
government, but is under control of the central bank, so that the policymaker would not be able to exploit the Phillips curve, because it simply can not alter the money supply, he can only use fiscal policy.
The model also suffers from the Lucas critique: expectations are not rational. Rational expectations would alter the model in that the policymaker would not be able to create
unexpected inflation, since the public would anticipate the money growth that the policymaker would set. As such, the policymaker is unable to influence the unemployment rate, which changes only because of unexpected inflation.
Yet another critique is based on the way the public votes. In the Nordhaus model, the public only looks at the past performance of the government, while their votes influence what will happen in the future. This dilemma goes back to a disagreement between Downs (1957) and Key (1966). Key stated that the public would reward or punish an incumbent government based on its past performance; while Downs argues that the public is necessary forward-looking when electing a new government, because their decision would only affect the government they would be stuck with for the next couple of years. The Nordhaus (1975) model is of the Key (1966) school of thought, in that the votes for the incumbent politician are based on his past behavior, not on what they can expect from him in the future.
Finally, there is little agreement on the assumption of opportunism. The partisan school of thought, with Hibbs (1977) and Alesina (1987) as its primary advocates, propose a model of the political business cycle in which the policymaker is partisan (left- or right-wing) instead of opportunistic.
All in all, the Nordhaus (1975) model provides some early insight in the workings of the political business cycle, but is far from perfect. The second generation of opportunistic political business cycle models, based on models by Rogoff and Sibert (1988) and Rogoff (1990) deal with most criticisms of the Nordhaus model.
Like the Nordhaus model, the Rogoff and Sibert (1988) model features an opportunistic policymaker and the public rewards competent incumbents. The similarities end there, though. In the Rogoff and Sibert (1988) and Rogoff (1990) models, the government in power provides a public good to the public2. Because the government in power uses fiscal policy instead of
monetary policy (as Nordhaus’ model assumed), there is a possibility of influencing the economy
2 In the Rogoff and Sibert (1988) model, the government only supplies a consumption good, while the
that does not depend on mistaken expectations, for instance by expanding government expenditures or lowering taxes.
In this model policymakers differ in the amount of taxes that need to be levied to supply a given amount of government services. Less competent policymakers need to levy more taxes to supply the same amount of public goods that a competent policymaker supplies.
Rogoff and Sibert (1988) assume that there are only two types of taxation: distortionary and non-distortionary taxation. Distortionary taxation affects the next period, by increasing the inflation rate in that period. An example of real world distortionary taxation could be seignorage or government debt. As such, the government is worse off in the next period if it uses distortionary taxation.
It should be obvious that the public prefers a competent policymaker to an incompetent one, because the public gets public goods at a lower cost from a competent policymaker than from an incompetent one. Under full information, this would not be a problem. The public would observe the competence of the incumbent directly as being either high or low. As such, the public
compares this competence to the expected competence of the opposition and chooses to either re-elect the incumbent, or not. Since the public has no way of knowing anything about the
competence of the opposition, it forms an expectation on that competence as a weighted average of the high and low competence-type. This expected competence always lies in between the high competence type and the low competence type (since it’s a weighted average) so that it is always higher than the low competence type and lower than the high competence type. This ensures that if the public observes that the incumbent has high competence, the public will re-elect the incumbent, while the public will vote for the opposition if the incumbent is of the low competence type.
If there is asymmetric information, so that the policymaker knows more about his competence type than the public, the incumbent has to signal his competence type indirectly. Rogoff and Sibert assume this is done by the incumbent by setting the tax-mix. As is usual in signaling models, the timing of information is crucial. It is assumed that the public can observe the lump-sum taxation and government spending before an election, while the competence and the amount of distortionary taxation are unobserved. The public makes inferences of the latter based on the observation of the former.
the economy if an incompetent policymaker would take office in the period afterwards. In contrast, in a separating equilibrium the incompetent policymaker never distorts the economy. Because his type will always get known, there is no incentive for the incompetent policymaker to distort the economy.
The effects that the policymaker has on the economy in the Rogoff and Sibert model are similar to Nordhaus’ results, in that the government stimulates the economy in the period before an election (by lowering taxes), while creating inflation just after the election. However, the main difference is that the public is rational in re-electing a policymaker that engages in this kind of behavior, since only the competent policymaker would create a political business cycle.
Furthermore, the fact that a political business cycle arises might not even be undesirable, since it only keeps the competent policymaker in office, while eliminating the incompetent policymaker. It should be noted that Persson and Tabellini (1990) sketched a model that has the same
implications as the Rogoff and Sibert (1988) and Rogoff (1990) models. The difference between them is that the Persson and Tabellini (1990) model uses the monetary channel in order to signal competence, with the more competent type facing a flatter Phillips curve (so that less inflation is needed to reduce unemployment by one percent). Their result is the same as the Rogoff and Sibert (1988) result.
While the Rogoff and Sibert (1988) model improves upon the Nordhaus (1975) model, it still has some noticeable flaws. One of the more serious flaws is that only a competent policymaker would create a political business cycle. This makes little sense intuitively. If a competent policymaker weakens the economy, while an incompetent policymaker would not, which policymaker is the more capable one?
The setup of the model is similar to the Rogoff and Sibert (1988) model, in that a more competent policymaker is able to provide public goods at a lower cost. As such, the public prefers a more competent policymaker to an incompetent one. As in the Rogoff and Sibert (1988) model, this model also depends on the government having an unobservable way to generate spending, such as unobserved government debt. This government debt could be hidden administratively, as Shi and Svensson (2003) propose, or could be borrowed between budgetary checks. Given that the public thinks that a more competent politician would be able to supply public goods at a lower price, the government has an incentive to supply more public goods and appear more competent. Since both competence types have the incentive of supplying a lot of public goods, the political business cycle arises for both. The incompetent type needs to borrow more unobserved government debt than the competent type does, but behaves in the same way. As such, no unobservable
assumptions about the incumbents competence type are created in this model.
Shi and Svensson (2002) use a similar model, but include a measure of aware and unaware voters and a measure of the gains from being in office. As Persson and Tabellini (2000) they find that the incumbent always provides more public goods before an election. They also find that the political business cycle gets bigger as the degree of uniformed voters is bigger and as the rewards for being in office are bigger.
3. The Partisan Business Cycle
In the opportunistic models of the political business cycle, the policymaker only cares about staying in office. Opposed to this are the models of the partisan policymaker. In these kinds of models, the policymaker has a personal (partisan) preference for the unemployment and inflation rates. These models usually feature two different sorts of policymakers, a left-wing policymaker and a right-wing policymaker. It is assumed that the left-wing policymaker represents the low incomes in a society, which rely mostly on labor income. As such, they benefit most from a reduction in unemployment. On the other hand, the right-wing policymaker is assumed to represent the higher incomes in a society. The higher incomes rely more on capital incomes and as such are hurt most when unexpected inflation drives the real interest rate down. By this assumption, the left-wing policymaker cares more about reducing unemployment and the right-wing policymaker cares more about reducing inflation.
business cycle, this issue changes the outcome of the model with respect to the effects it has on the economy.
The non-rational model was first presented by Hibbs (1977). In his model, he introduces a left-wing and a right-left-wing policymaker that differ in their social loss functions. In particular, when compared to the right-wing party, the left-wing party likes employment to be higher, inflation to be lower and it assigns a lower cost to inflation with respect to the costs of unemployment3. The economy is described by a Phillips curve that relies on static expectations, so that there is a trade-off between unemployment and inflation. The result of the model is, unsurprisingly, that if a left-wing policymaker is in office, inflation is higher and unemployment is lower than under the rule of a right-wing policymaker.
Because of static expectations, any increase of the inflation rate caused by the government reduces unemployment, so that the unemployment is permanently lower (higher) under a left-wing (right-left-wing) government. The model has been criticized on the non-rationality of mistaken expectations, but it has been noted by, amongst others, Drazen (2000b) that a political business cycle that moves along the Phillips curve doesn’t need to rely on mistaken expectations, but could also be true if the party in office uses fiscal policy instead of monetary policy in order to
manipulate the economy. Fiscal policy that is perfectly anticipated can have real effects on the economy, for instance by raising government spending or lowering taxes, so that the Hibbs (1977) model can be an accurate description of the process behind the political business cycle in which the government only controls fiscal policy.
As with the opportunistic political business cycle, there are two variants of the partisan political business cycle, a model based on mistaken expectations and a rational-expectations model. Alesina (1987) introduces rational expectations to the partisan political business cycle literature. Again, the economy is described by a Phillips curve, but now expectations are rational. This implies that the policymaker can not fool the public into forming incorrect expectations. In this model, the public knows the preferences of both types of policymakers. So, for both the left-wing and the right-wing policymaker, the public knows exactly what his preferred inflation rate, his preferred unemployment rate and the weights the policymaker puts on the losses of inflation relative to the losses from unemployment are. As such, the public perfectly expects the inflation rate when it is known which policymaker holds office and the policymaker will not be able to create unexpected inflation. Since unexpected inflation is what reduces unemployment in the Phillips curve, the policymaker can not reduce unemployment in non-election years; the
3 Not all of these three statements have to be true. The model produces the same outcomes as long as one of
outcomes found for inflation and unemployment are the same as found by Kydland and Prescott (1977) and Barro and Gordon (1983) in their models on dynamic inefficiency, where
unemployment is equal to the natural rate and inflation is greater than zero. Uncertainty arises in the Alesina model in election years. Then, there is uncertainty about the actual inflation rate after the elections. If the left-wing party wins, the inflation rate will be higher than if the right-wing party wins. Since no party wins for sure, the public will have to form an expectation on the inflation after the election by assigning a probability that each party will win. Because of this, the inflation expected by the public necessarily lies between the actual inflation that will be set by the left-wing party and the actual inflation that is set by the right-wing party. This implies that when the left-wing party wins, there is positive unexpected inflation (actual inflation is higher than expected inflation) so that unemployment will go down, while the opposite happens when the right-wing party wins. Thus, after an election, the Alesina model predicts a boom after a victory of the left, while a victory of the right would cause a recession. Then, in the following year, when there is no uncertainty about the type of the policymaker anymore, the unemployment rate adjusts to its natural level once more. As such, the main difference between the Alesina (1987) and the Hibbs (1977) model is that the effects of a change in office are permanent in the Hibbs model, while they are temporal in the Alesina model.
There are some criticisms of the rational expectations model. Alesina (1987) himself notes that the outcome of his model is suboptimal. In fact, if the two parties would agree to follow the same policy, there would be less fluctuation in the results and both parties would be better off.
However, it may be difficult to force a binding commitment upon the policymaker. It is quite likely that the policymaker will break his promise once he is in office and just carry out his own preferred program.
Rogoff (1988) disagrees with the way the expectations of the public enter the model. If electoral uncertainty is such a big determinant of fluctuations in wage contracts, then why don’t workers wait until they know the election outcome before they sign their contracts. Drazen (2000a; 2000b, Chapter 7) supports this claim and cites a paper by Garfinkel and Glazer (1994) as proof.
Garfinkel and Glazer (1994) find that in the year before an election, there is a tendency for the signing of contracts to be postponed until after the election, thus cancelling out the effect of electoral uncertainty. It appeared that 39 percent of all contracts were signed in or after November in off-election years, while 50 percent of all contracts were signed in or after November4 in election years. Alesina (1995) first calls this the ‘Achilles’ heel’ of the rational partisan political business cycle theory, but later he [Alesina (2000)] refutes this and claims the Garfinkel and
Glazer (1994) result is perfectly in concordance with the rational partisan theory. The fact that the signing of some contracts is postponed proves the significant effect that electoral uncertainty has on wage contracts, while the fact that not all contracts get postponed means that the election still has an influence on the economy.
Yet another criticism of the rational partisan model is the way in which electoral surprises influence the economy. As the unemployment rate changes most when the actual inflation rate is very different from the expected inflation rate, one would expect big changes in the
unemployment rate after an election outcome that is predicted badly. So elections that are close should produce the biggest fluctuations in the unemployment rate after an election. Hibbs (1992), among others, notes that this is not the case when looking at some of the evidence. For example, the 1968 election was a very close one, with Nixon winning with 43.4% of the votes5. Yet, even though the election was very close, the resulting recession was the smallest observed after a Republican victory. On the other hand, the 1964 election was as close to a sure bet as far as elections go, with Johnson taking 61.1% of the votes6. As such, one would expect only a small change in the unemployment rate, but economic growth was highest among any Democratic policymaker in the two years after Johnson took office. When looking at election results ex-post the theory does not match very well with the empirics. However, true election surprises can not be found in the results of an election. One need only think of the historical picture in which the newly elected president Truman holds up a Chicago Daily Tribune which heads ‘Dewey defeats Truman’. Clearly, the ex-ante expectation was different than the ex-post result. To try and find ex-ante election probabilities, Alesina, Roubini and Cohen (1997; Chapter 5) construct a variable for electoral surprise based on pre-election Gallup polls7. They perform tests on two variables, namely the forward interest rate after an election that is given a couple of months in advance and the amount of change in economic growth following an election. In general, their tests favor the rational partisan model.
It should also be noted that the probability that a party is elected is exogenous in the rational partisan model. Because of this, the policymaker’s behavior is not relevant for the election outcome. Therefore, he has no incentive to change the election outcome. This is quite unlike the opportunistic political business cycle, where the ability to change the election outcome is the main incentive for the policymaker to influence the economy. In the fifth section of this paper, I will show that there is reason to believe that the probability of being elected in the partisan model
5 His opponent, Humphrey, got 42.7%of the votes. 6 His opponent, Goldwater got 38.5% of the votes.
7 A Gallup poll is an opinion poll used by the mass media representing public sentiment, such as their
is not exogenous if some persistence in unemployment is introduced and that this in turn gives incentives to the policymaker to influence the economy.
Hibbs (1994) formulates a model which has the same outcome as the Alesina model, but is based on his static-expectation framework. As such it produces a rationale for a policymaker that uses fiscal policy to produce the same outcomes as the Alesina model. In this model, the effects of an election on the economy are also greatest shortly after an election and diminish over time, but instead of depending on rational expectations, he assumes that the policymaker has incomplete information about the economy. Hibbs (1994) states that if the policymaker is too optimistic about the natural unemployment rate, he will choose a rate of inflation that is too high to be consistent with the real natural unemployment rate. As a result, inflation will be too high for the policymakers optimum. Because he observes the outcome of his policies on the economy, he now has a better understanding of the economy and he will adjust inflation in the second term
accordingly. As such, the Hibbs (1994) model has the exact same outcome as the Alesina (1987) model, but it is based on a different set of assumptions. The model does have its weak points, since it depends on policymakers that can not look back very far. Consider, for instance, a policymaker that has been in office in the term before an election. In this period he has a good feel for what the natural unemployment rate is. However, when he is re-elected, he suddenly loses this knowledge. This need not only apply in the case of re-election. For instance, a party that is not in power could observe the policy made by the incumbent and the reaction of the economy on this policy. As such, he would also be able to get a good feel for what the natural unemployment rate is. Although the setup of the model does provide a rationale for the Alesina (1987) outcome in a fiscal policy world, it doesn’t seem very realistic.
Some authors, like Alesina and Rosenthal (1995) and Sieg (2006), have tried to combine the opportunistic and partisan models into one model. Their models describe policymakers that have partisan interests, but those policymakers also care about staying in office. This creates a model that has aspects of opportunistic and partisan models. On the one hand, the policymaker cares about the economy from a partisan point of view, while on the other hand he just wants to be re-elected. Note that a politician that has only partisan goals and no opportunistic features would still prefer to be re-elected, so that he can change the unemployment and inflation rates to be closer to his preferences.
modeling is that it is more difficult to test for empirically. For instance, when a left-wing party increases its spending before an election, does it do so because it wants unemployment to be low to ensure that unemployment is closer to the left-wingers desired policy, or does the party do it to appear competent? Similarly, if economic growth goes up in the second half of a right-wingers term, is that because he is a Nordhaus (1975) type of opportunistic policymaker, or is the economy adjusting to the recession in his first term, that the Alesina (1987) model predicts? Which of the effects is relevant to the politician’s behavior? And if both effects are of influence, which one dominates? All questions that add more complexity to the model and take away degrees of freedom in testing.
4. Empirics
In this section, I will go over the empirical results for the political business cycle. First of all, let it be said that the empirics on the subject of the political business cycle are ambiguous to say the least. This has several reasons. First of all, there is the distinct lack of observations. Since most tests of the political business cycle focus on the United States after the second World War, these tests only consider twelve to fifteen observations. This leaves very few degrees of freedom. Even if another arbitrary starting date is chosen, such as 1900, this only adds twelve observations, if wartime elections are included. Exclude those, and the number diminishes even further. As such, any result found by these kinds of studies should not be considered as set in stone.
A second reason results are ambiguous, is that the models overlap in some areas. Consider the effect on the economy predicted by the rational partisan model and the opportunistic models. Although these models differ when a left-wing party is in office, they predict the same outcome when a right-wing party is in office, namely a recession in the first half of the term and a boom in economic activity in the second half. With roughly half of the administrations being right-wing, there are few observations left to distinguish these models from one another.
However, since testing with a limited amount of data points is better than no testing at all, I will provide some empirical results in this section. Drazen (2000a) gives an excellent overview of the literature.
The results split out into the answers to three questions: 1. Does the state of the economy affect the elections? 2. Do the elections affect the economy?
3. Is there is a partisan effect?
Also, there have been tests as well that try to answer the three questions above, but using policy instruments instead of policy outcomes.
The answer to the question of whether or not the economy is affected by the elections, is not as clear however. There is little evidence that there is an opportunistic political business cycle in economic growth. Early work by McCallum (1978) as well as later work done by Alesina, Roubini and Cohen (1997) and Faust and Irons (1999) contradict the notion of an opportunistic political business cycle in the United States. They find that the rate of economic growth is not significantly higher in election years than it is in other years. Also, Lewis-Beck (1988) and Alesina, Roubini and Cohen (1997) do not find an opportunistic business cycle in other
developed countries. However, Alesina (1988) does find support for a rational partisan business cycle in GDP and rejects the Hibbs (1977) partisan cycle. The same result was later found by Alesina, Roubini and Cohen (1997) and Faust and Irons (1999), who also found a rational partisan business cycle in the United States.
Although there is not much support for a political business cycle in developed economies, there is evidence to be found in favor of a political budget cycle, instead of a political business cycle. In a political budget cycle, the politician doesn’t influence the economy, but does change the amount of government consumption or taxation, generally to target specific groups with tax cuts or provide public goods to those groups in order to secure the votes of those groups. Tufte (1978) found that veterans’ benefits typically get increased in October or November in an election year. Keech and Pak (1989) confirm this result for elections between 1961 and 1978, but find that the effect disappears after 1978. This result has been confirmed by Alesina (1988) and Alesina, Roubini and Cohen (1997) who test for all government transfers. They find a result similar to Tufte for the 1961-1985 sample, but find that the result disappears if earlier data (from 1947) or later data (up to 1994) is included.
A lot of evidence for opportunistic business cycles has been found for developing economies. The reasoning behind this is twofold. First of all, developing economies often have democracies that are still in their infant stages. As such, there is little transparency and accountability, so that a political business cycle is less easily observed and it is harder to hold the responsible government accountable. Furthermore, the party structure in most developing countries does not follow the typical left-right structure often observed in developed economies. Schuknecht (1996) finds considerable evidence for a political budget cycle in developing countries, with transfers
expenditures react more to elections than tax cuts do, and argues that this may be because government expenditure is more directly visible to the public.
Persson and Tabellini (2002) as well as Shi and Svensson (2002) find support for a political budget cycle using data for sixty countries, including both developed and developing economies. However, Brender and Drazen (2004) claim that this result is only found because developing countries are included. If the data is disaggregated into a group of developing countries and a group of developed countries and tested seperately, the political business cycle disappears in developed countries, but remains in developing countries. However, Mink and de Haan (2006) do find a political budget cycle in the European Union for the period 1999-2004, so the last word has not been said. Gonzalez (1999) relates the degree of democracy to the size of the political budget cycle and finds that countries with a medium amount of democracy have the biggest cycles, which is exactly the result one would expect, since in countries with a degree of democracy that is very low, such as dictatorships, there is no need to create a political budget cycle, since the incumbent will be re-elected anyway, while countries with a very high degree of democracy have voters that are typically highly informed about the system, thus making it hard for the incumbent to cheat the people. Shi and Svensson (2002) find these results as well, backing up their model. All in all, the empirics seem to provide the following results:
1. There is little evidence for an opportunistic business cycle in economic outcomes. 2. There is evidence for an opportunistic budget cycle.
3. There is a lot of disagreement about in which countries and in what time period these budget cycles took place.
4. However, there is evidence that political budget cycles are bigger in developing countries.
5. There is evidence of a partisan effect in economic outcomes in the United States, as well as in some other developed economies. The effects are largest in the first half of a policymakers term.
The empirics do not provide an answer as to whether the opportunistic or the partisan model describes reality better. But the opportunistic model of the political business cycle is
5. A New Model
In this section, I will propose a new model of the partisan political business cycle, that explains the pattern in economic outcomes found by Alesina (1987), but is not dependent upon a government that controls the money supply and also does not need the policymaker to have a mistaken view of the natural unemployment rate, as the Hibbs (1994) model requires. This model is based upon the Milesi-Ferretti (1995) line of reasoning reviewed above, which states that parties use counterintuitive policy just before an election.
But before getting into the model, I will show why I will use a static expectations model instead of rational expectations model in the next subsection by showing that the Alesina (1987) model does not lend itself very well for endogenisation. Here, I will provide the entire model. This serves two purposes. First of all, I will use a highly simplified version of this model in order to show that the model does not endogenise well. Second, the Hibbs (1977) type of model, which uses static expectations and which I will use in order to model the political business cycle, is a specific -simplified- form of the Alesina (1987) model. As such, it will be useful to write out the entire model.
5.1 The Alesina Model
In the Alesina model, two parties compete for office, a left-wing party and a right-wing party. The two parties both suffer a loss when unemployment and inflation differ from their desired amounts. These losses are assumed to be quadratic and as such can be formulated as:
2 2 2 2 ~ ~ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = Λ j t j j j t j t j U U
π
π
θ
For party j. Where: t jΛ = Loss suffered by party j (either L for left-wing or R for right-wing) at time t
t j
U = Unemployment set by party j at time t
j
U
~
t j
π
= Inflation that is set by party j at time tj
~
π
= Inflation desired by party j at time tj
θ
= The weight a party puts on the losses from inflation, relative to the losses from unemployment.For this model, it is assumed that a left-wing party desires a lower unemployment rate, a higher rate of inflation and attaches less weight to the losses from inflation than a right wing party, or:
R L R L R L U U
θ
θ
π
π
< > < ~ ~ ~ ~Both parties are bound by a Phillips curve:
⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − = − − t e t j t t j U U 1
π
π
As is usual, unemployment depends negatively on unexpected price changes. The −1
t
U term was added to create persistence in unemployment. The reasoning behind this could be that labor contracts adjust slowly to price changes. If that is the case, unemployment will not change to its natural level immediately. In this Phillips curve, contracts do not respond to price changes at all. This has been done to simplify the model. A more realistic way of modeling the Phillips curve would be to let unemployment adjust slowly to its natural level.
_ 1 (1 )U U U t t e t j t j
π
π
⎟+α
+ −α
⎠ ⎞ ⎜ ⎝ ⎛ − − = −This Phillips curve adjusts slowly towards its natural level (U_ ) over time. For this analysis I will use the simpler version, since the intuition behind the results will not change because of it, so that it would unnecessarily complicate the results.
Agents possess rational expectations in this model, so that ⎟⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = t t t e E
π
π
1 .However, during election years, there is uncertainty about which party is going to win the election. Therefore, the public must assign a probability for each party to win the elections and create expectations accordingly. This means that the expected inflation will be equal to the inflation set by the left-wing party times the chance that the left-wing party will win, plus the inflation set by the right-wing party times the chance that the right-wing party will win:
(
)
t R t L t e P Pπ
π
π
= + 1− Where:P = the chance that the left-wing party will win (so that (1-P) is the chance that the right-wing party will win)
Using these equations, the model can be solved by minimizing the loss function for both parties with respect to their decision variables (
t L
π
for the left-wing party andt R
π
for the right-wing party) and then substituting in the Phillips curve. This has the following as a result (See Appendix 1 for the details):* ) 1 ( * t R L t L L t L k k
π
π
π
= + − * * ) 1 ( t R R t L R t R k kπ
π
π
= − + Where: L R L R L R L L P P P kθ
θ
θ
θ
θ
θ
θ
+ + − + = ) 1 ( L R L R R L R R P P P kθ
θ
θ
θ
θ
θ
θ
+ + − + − = ) 1 ( ) 1 ( And: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − = ~ 1 ~ −1 * t L L L t L U Uθ
π
π
⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − = ~ 1 ~ −1 * t R R R t R U Uθ
π
π
The public’s inflation expectation will necessary be between t L
π
and t Rπ
, because it is formulated as a weighted average of the two. This means that the public expects a lower inflation than the actual inflation that the left-wing party will set if it wins and it expects a higher inflation than the right-wing party will set if that party wins. This in turn implies that if the left-wing party is elected, unemployment will go down, because of positive unexpected inflation. Vice-versa this implies that unemployment will go up if the right-wing party is elected, because of negative unexpected inflation ( t R t eπ
π
> ).5.2 Endogenising the Alesina model
In this subsection I will endogenise the probability of election in the Alesina (1987) model, by letting the public choose the probability that the left-wing party will win, and show that the result is, although intuitive, not useable.
From the model it is learned that the inflation rate a party will choose is a function of some exogenous variables that are set by preferences (such as j
U
~
,
π
~ j andθ
j) and the chance that aparty is elected, P. In order to complete the model, the public must now choose P in order to minimize its expected losses from the election.
In order to do this, the public needs a loss function, which I will formulate as:
2 2 2 2 ~ ~ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = Λ P t j P P t j t P U U
π
π
θ
The symbols are the same as before, with the superscript ‘P’ standing for the public’s preference on unemployment ( P
U
~
), inflation (
π
~P) and the tradeoff between the two (θ
P). So the loss ofthe public increases as the gap between the public’s desired unemployment and actual
unemployment increases and as the gap between the public’s desired inflation and actual inflation increases.
The loss function can be divided in two parts, the loss that the public faces when a left-wing party wins, (Left)
t P
Λ and the loss that the public faces when a right-wing party wins, (Right)
t P
Λ .
) ( ) 1 ( ) ( ) ( P Left P Right E ΛPt = ΛPt + − ΛPt
The public chooses this P in the election, so that P is their decision variable. The public will try to minimize this function by choosing their optimal P, taking into account that (Left)
t P Λ and ) (Right t P
Λ also depend on P, through the inflation rates set by both parties.
If the left-wing party wins, it will set inflation equal to πL and if the right-wing party wins, it will set inflation equal to
t R
π
. Expected inflation is, as before:(
)
Rt t L t e P Pπ
π
π
= + 1−Using the Phillips curve − − =−⎜⎝⎛ − ⎟⎠⎞
t e t j t t j U
U 1
π
π
, the unemployment rates set by the parties become: 1 ) )( 1 ( − − + − − = t t R t L t L U P Uπ
π
if the left-wing party wins, and:
1 ) ( − + − − = t t L t R t R U P U
π
π
if the right-wing party wins
The loss to the public if a left-wing party wins then becomes:
2 2 2 2 ) )( 1 ( ) ( ~ ~ 1 ⎟⎠ ⎞ ⎜ ⎝ ⎛ − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛− − − + − = Λ − P t L P P t t R t L t P U U P Left
π
π
θ
π
π
and the loss to the public when a right wing party wins:
2 2 2 2 ) ( ) ( ~ ~ 1 ⎟⎠ ⎞ ⎜ ⎝ ⎛ − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛− − + − = Λ − P t R P P t t L t R t P U U P Right
π
π
θ
π
π
Since πL and πR are functions of just P and exogenous variables (that are formed by preferences), the model can be solved by letting the public choose a P that minimizes their losses.
But before that, it is useful to rewrite the expected loss function in a form that is friendlier to work with.
2 2 ) 1 ( 2 2 ) ( 2 1 ) ( 2 ) 1 ( ) ( ~ 2 ~ ~ 1 2 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + − + − − = Λ − P t R P P t L P P t t R t L t P P P U U P P E
π
π
θ
π
π
θ
π
π
Since P is the decision variable for the public, the public may differentiate its loss function to P in order to minimize its losses.
⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + − − − + − − = Λ P t R t R P P t R P P t L t L P P t L P t R t L t R t L t R t L t P dP d P dP d P dP d d P P P dP d ~ ~ ~ ~ 2 ) 1 ( 2 2 1 2 2 ) ( ) ( ) 1 ( ) ( 2 2 1
π
π
π
θ
π
π
θ
π
π
π
θ
π
π
θ
π
π
π
π
π
π
If this is set to zero, the minimal loss of the public is obtained.
One thing to note from this equation is that the public’s desired unemployment (~ P)
U totally drops out of the public’s decision. The reason for this will later be elaborated upon.
Unfortunately, the formulas for
t L
π
andt R
π
are not easily differentiated to P. Therefore, I shall simplify these values, leaving intact the general result from the Alesina model, namely that after an election, a left-wing party will cause a boom in employment, while a right-wing party will cause a recession.In order to get the simplest possible expressions for
t L
π
andt R
π
, it will be assumed that the left-wing party cares only about unemployment and the right-left-wing party cares only about inflation. In terms of the previous model, this means thatθ
L=0andθ
R→∞.This can be filled into the formulas for
t L
π
and t Rπ
to obtain: ) 1 ( 1 ~ ~ P U U t L R t L − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − =π
−π
R t Rπ
~π
=So, as long as the target rate of unemployment for the left-wing party is lower than current unemployment, this will ensure that the left-wing party will choose a higher degree of inflation than the right-wing party.
⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = − − P R t L U U P ~ ~ 1 ~ ) 1 (
π
π
This result seems quite intuitive when looking at the denominator. A greater difference between the public’s desired inflation and the right-wing party’s desired inflation (
π
~R−π
~Pis more negative8) will decrease the chance that the right-wing party is elected (1-P). This is entirely intuitive.
Unfortunately, a less intuitive result is found for the relation between current unemployment and (1-P); a higher degree of unemployment will increase the likelihood that the right-wing party is elected and hence decrease the chance that the left-wing party is elected. This is a strange result at first sight. Since the left-wing party chooses a higher inflation and as such reduces unemployment more than the right-wing party would, one would expect the public to rather have a left-wing government when unemployment is high and as such expect a positive relationship between
1 −
t
U and P. Instead, the opposite is true. This has to do with the setup of the model, specifically with respect to the way employment is created. Since employment is created by unexpected inflation, the public needs to vote in such a way that it creates unexpected inflation. This is impossible however, since by choosing a higher P, the public will automatically choose a higher expected inflation, thus canceling out the unemployment effect. This is also the reason why the variable
P
U
~
drops out of the equation in the first place.
If this is taken into account, the result seems intuitive again. The higher unemployment in the previous period was, the higher is the inflation that the left-wing party will choose. Given that the public can only influence the inflation it will face, this means that a high previous unemployment would give them a high rate of inflation when the left-wing party is elected. As such they are less inclined to vote for that party. On the other hand, if unemployment is very low, the public is more inclined to vote for the left-wing party, because a lower unemployment in the previous period implies a lower rate of inflation if the left-wing party is elected.
5.3 Static Expectations
In a Rational Expectations world the public can not influence the expected unemployment in the next period. Therefore a different kind of expectation formation has to be considered. In this section, I will take a static expectation model, like the Hibbs (1977) model and endogenise it. The static expectation framework can be thought of as a setup for a model where the policymaker controls fiscal policy, as stated above. Also, as Alesina (2000) notes, it is not important if the political business cycle is caused by monetary or fiscal policy, the important thing is that the cycle exists.
Static expectations can be modeled by adjusting the Phillips curve used above (so that there is still persistence in unemployment) by assuming
t e
π
to be constant. I will use the easiest case andassume
t e
π
equal to zero. This makes the Phillips curve look like:t j t t j U U − −1=−
π
From the Phillips curve, it can be derived that:
1 − + − = t t L t L U U
π
1 − + − = t t R t R U Uπ
For both parties, the model can be solved in the same way as before. The loss function of party j is still described as:
2 2 2 2 ~ ~ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = Λ j t j j j t j t j U U
π
π
θ
The Phillips curve can be plugged into this equation to obtain:
2 2 2 2 ~ ~ 1 ⎟⎠ ⎞ ⎜ ⎝ ⎛ − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛− + − = Λ − L t L L L t t L t L U U
π
π
θ
π
For the left-wing party, and:
2 2 2 2 ~ ~ 1 ⎟⎠ ⎞ ⎜ ⎝ ⎛ − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛− + − = Λ − R t R R R t t R t R U U
π
π
θ
π
As before, both parties minimize their losses by differentiating their loss function with respect to the decision variable.
The left-wing party sets an inflation rate of:
⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + − = − L L L L t t L U U
θ
π
θ
π
1 ~ ~ 1The right-wing party sets an inflation rate equal to:
⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = − R R R R t t R U U
θ
π
θ
π
1 ~ ~ 1(See Appendix 5 for the derivation)
The thing to note about the final expressions for
t L
π
andt R
π
, is that they are not dependent on P.Therefore, dP d t j
π
will be equal to zero for both parties (this will only change when the setting is made dynamic – see below). For now, the focus is just on the one-shot game.
The loss function of the public is defined as before:
2 2 2 2 ~ ~ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = Λ P t P P t t P U U
π
π
θ
The public will minimize this function, using their decision variable, P. Since it is ex-ante uncertain which of the parties will win, the public has to make ex-ante predictions of the unemployment and inflation rates:
t R t L t PU PU U = +(1− ) t R t L t P
π
Pπ
π
= +(1− )By plugging this into the Loss Function and differentiating to P (the decision variable for the public) an intuitively plausible result is found for P (See Appendix 6 for the derivation):
The farther the preferences of the right-wing party deviate from the publics preferences, the higher is P, the chance that the right-wing party will not get elected. Intuitively, this makes a lot of sense.
This expression for P can now be used to find a relationship between P and −1
t U . Intuitively, 1 − t dU dP
would be positive, since if unemployment is high, the public would likely
want high inflation in order to lower unemployment and bring it closer to its desired level. This would imply that the public prefers a left-wing party to win the elections. Alternatively, when unemployment is low, the public would prefer the right-wing party to win, because it would set a lower inflation.
In order to obtain an easy and unambiguous solution for 1 −
t
dU dP
, an additional set of assumptions
needs to be made.
The first change to the model that I made is turning the right-wing party in a kind of ‘control party’, which is to say that I will assume that the right-wing party does not care about
unemployment, only about inflation. This can be done by assuming that
θ
R approaches infinity,so that: R R R R R t t R U U ~ ~ ~ 1 1
π
θ
π
θ
π
= ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + − = −This means the right-wing party will always choose its own desired level of inflation. This simplification has been made in order to derive the behavior of the left-wing party more easily. In a more complicated model, the behavior of the right-wing party would probably mirror that of the left-wing party, but for now I will assign the right-wing party a non-strategic role, so that only the behavior of the left-wing party matters.
The second assumption is that both parties and the public agree that the optimal rate of inflation is zero (so that
π
~L=π
~ R=π
~P=0). This cleans the model up tremendously. The rates of inflation⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − = − L L t t L U U
θ
π
1 ~ 1 0 = t Rπ
So that the inflation set by the left-wing party is positive and as such lowers unemployment, while the right-wing party always has an inflation rate equal to zero, thus keeping unemployment at the same level as it was in the period before.
Using this, P can be rewritten to:
t L P P t R U U P
π
θ
) 1 ( ) ( ~ + − =This can be rewritten by filling in the Phillips curve:
t L P P t t R U U P
π
θ
π
) 1 ( ) ( 1 ~ + − + − = −This is equal to:
⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = − − L t P P t L U U U U P ~ 1 ~ 1 1 1
θ
θ
Differentiating this to −1 tU and equaling the result to zero gives the following expression for the relationship between P and −1
t U : 2 1 1 ~ 1 ~ ~ 1 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = − − L t L P P L t U U U U dU dP
θ
θ
Since the publics preferred higher level of unemployment is higher than that of the left wing party, P L U U ~ ~ > so that P L U U ~ ~
− is positive. This implies that 1 − t dU dP is positive, which is
This result has some implications for the political business cycle. If the government in power can influence the unemployment rate at time t, that government can influence the possibility that they are re-elected at time t+1 and as such create a political business cycle. In the next subsection, I will explore this possibility.
5.4 The Political Business Cycle
In order to check whether or not a political business cycle will occur, I will use the static expectations model from the previous subsection and expand it to turn it into a 2-period game. In this game, there are two periods in which a decision has to be made. In period 1, the left-wing party is in power and sets the inflation (and corresponding unemployment) rate for that period. Then, at the beginning of period two, there is an election, after which either the left-wing or the right-wing party gets the office. That party then gets to set the inflation rate. After two periods, the game ends.
At the beginning of the game, the left wing party faces the following loss function:
⎥⎦ ⎤ ⎢⎣ ⎡ Λ + − Λ + ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − + − = Λ ( ) + ( ) (1 ) +( ) 2 ) ( 2 1 1 1 2 ~ 2 ~ right P left P U U Lt L tL tL L L t L t L
θ
π
π
β
This is similar to the loss function used above, only now the loss function covers two periods. The loss in the second period is discounted with a factor of β (0<β<1) and is the weighted average of the loss the party incurs if it wins itself ( 1(left)
t L
+
Λ ) and the loss the party incurs if the
right-wing party wins (ΛtL+1(right)).
Writing out the loss function gives:
⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − + − − + − + − + ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − + − = Λ + + + + 2 ~ 1 2 ~ 1 2 ~ 1 2 ~ 1 2 ~ 2 ~ ) ( 2 ) 1 ( ) ( 2 ) 1 ( ) ( 2 ) ( 2 ) ( 2 ) ( 2 1 L t R L L t R L t L L L t L L t L L L t L t L P U U P P U U P U U
π
π
θ
π
π
θ
β
π
π
θ
public agree that the optimal inflation rate is zero, so that R t R
π
~π
= and that 0 ~ ~ ~ = = = R P Lπ
π
π
, so that the above function becomes:⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − + + − + ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ + − = Λ + + + 2 ~ 1 2 1 2 ~ 1 2 2 ~ ) ( 2 ) 1 ( ) ( 2 ) ( 2 ) ( 2 ) ( 2 1 L t R t L L L t L t L L L t L t L U U P P U U P U U π θ β π θ
The Phillips Curve can be augmented into this formula to obtain:
⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − + − − + + − + − − + ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ + − + − = Λ − + − + − 2 ~ 1 2 1 2 ~ 1 1 2 2 ~ 1 ) ( 2 ) 1 ( ) ( 2 ) ( 2 ) ( 2 ) ( 2 1 L t t L t L L L t t L t L t L L L t t L t L U U P P U U P U U π π θ π π β π θ π
Now the party optimizes its loss function with respect to its decision variables, namely 1 +
t L
π
forthe second period and
t L
π
for the first period:When differentiating to +1
t L
π
, the result that was found in the one-shot game is found here as well.0 ) ( ) ( ~ 1 1 = ⎥⎦ ⎤ ⎢⎣ ⎡− − + − + = Λ + + t L L L t t L t L t L U U d
π
θ
π
β
π
L L t t L U Uθ
π
+ − = + 1 ~ 1This is the same result as found above, since the game ends after the second period, so that the party can simply set its optimal inflation, as it would in the single-period game.
Differentiating to
t L
π
gives a slightly different result fort L
0 ) )( 1 ( ) ( ) ( ) ( ) ( 2 ) 1 ( ~ 1 ~ 1 1 2 ~ 1 2 1 2 ~ 1 1 ~ 1 = ⎥⎦ ⎤ ⎢⎣ ⎡− − − + − − − − + − + ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − + − − + − + − − + ⎥⎦ ⎤ ⎢⎣ ⎡ + − + = Λ − − + − + − + − L t t L L t t L t L L t t L t L t t t L t L t t L L t t L t L t L t t L t t L L t L t L U U P U U P U U dU dU dP dU dU dP U U dU dU dP U U d d π π π β π π π π θ π π π β π θ π
This consists of three parts. The first part is the change in the loss that the party receives in the first period as a result of the change of the inflation it sets in that period. The second part is the change in the loss the party receives in the second period as a result of the change in the chance the party is elected. The third part is the change in the loss the party receives as a result of the change in the unemployment, since the party has to take effort to change the unemployment situation back to its desired level.
These parts return in the solution for
t L
π
(See Appendix 7 for a complete derivation):t L L L L t L L t L L L L L t L L L L t L dU dP P U U U U P P U U P ) 1 ( ) 1 )( 1 ( 2 2 ) ( ) 1 ( ) 1 )( 1 ( ) 1 ( ) ( ) 1 ( ) 1 )( 1 ( 1 ~ ~ 1 ~ 1 θ β θ θ β θ β θ θ θ β θ β θ θ θ π + − + + + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − − + − + + + + − + − + − + + + + = − −
This expression consists of three parts. These three parts are very similar to the result Milesi-Ferretti (1995) found.
The first part is dependent on the unemployment situation in the first period. The higher unemployment is compared to the left-wing party’s preferred level, the higher inflation will be. This is similar to the result that was found for the single-period model9.
The second part is dependent on the loss the party will experience during the second period. This part has a positive effect on
t L
π
. It can be seen as a way for the policymaker to smoothe the economy or to tie the hands of his successor. In order to see this, consider this model, but assume P to be independent of Ut-1. In that case, the party will want to set the inflation rate a little higher than he normally would, in order to lower the unemployment for the next period a little right now. Also, even if the left-wing party loses, he can still set unemployment at such a relatively low level that unemployment would stay close to that level in the second period, even if the right-wing party wins and sets a low inflation. This is more or less equivalent to the ‘tying the hands’ effect that plays a big role in government debt management theory.In order to visualize this effect, assume
t
dU dP
to be zero and P=1. In this case, the policymaker is
sure of his re-election and will set inflation equal to:
) ( ) 1 )( 1 ( 1 ~ 1 L t L L L L L t L U −U + + + + + = − βθ θ θ βθ θ π Since L L L L L L
θ
βθ
θ
θ
βθ
θ
+ > + + + + + 1 1 ) 1 )( 1 ( 1this is higher than the inflation he would set if he did
not take the next period into account. This way, he can smooth the costs of inflation over the two periods. Similarly, consider the effect if
t
dU dP
is zero and P=0. In this case, the policymaker is
sure he will lose the next election and he will set inflation equal to:
9This can be seen if β=0. If that is the case, we are back in the single period model, since the politician
does not care about the next period at all. In this case, the solution would be:
) ( ) 1 ( 1 ~ 1 L t L t L U −U + + + = − β θ β π Since L L
β
θ
θ
β
+ > + + + 1 1 ) 1 ( 1this is higher than the inflation he would set if he did not take the
next period into account. This way, the policymaker can set inflation higher than he would in the absence of a next period, in order to keep unemployment at a lower level in the next period under a right-wing policymaker.
The third part is perhaps the most interesting part, since it reflects the political business cycle. It is the only part that is dependent on
t
dU dP
. This implies that this is the reward for the politician
for manipulating the economy in such a way that he is re-elected. This effect is clearly negative, as a higher inflation implies a lower unemployment, which would imply a lower chance of getting re-elected. This is quite unlike the opportunistic political business cycle, where any incumbent chooses a high inflation rate before an election.
Of course, if a right-wing party would be in power, it would want unemployment to be low and inflation to be high just before an election, so that the probability that the left-wing party gets elected goes down.
All in all, this means that the results that this model predicts are the same as the results predicted by Alesina (1987), namely that a left-wing party will first ensure an economic boom, after which the economy cools down, while a right-wing party has precisely the opposite effect on the economy, because they want to be re-elected. The public is unable to punish the incumbent for this behavior. Consider the left-wing party as the incumbent. Before an election, the left-wing party raises unemployment and lowers inflation. The public sees this, but its options are limited. If they vote for the left-wing party, they haven’t punished him for creating a political business cycle. On the other hand, if they vote for the right-wing party, unemployment will go up even more! As such, the public is perfectly rational in voting for a candidate that creates a political business cycle. The public is more or less trapped.
This model has the same outcome as the Alesina (1987) and Hibbs (1994) models, but operates on assumptions that are more in line with reality. The Alesina (1987) model is based on the policymaker being able to control the money supply. In the United States however, the
