# An equilibrium politico-economic model.

AN EQUILIBRIUM POLITICO-ECONOMIC MODEL

I. INTRODUCTION

Recent empirical studies by Alesina and Sachs [1986] and Haynes and Stone [1987] have found that political elections have significant implications for the time paths of employment and inflation. Explnations of this phenomenon fall into two general categories: political business cycle theories and partisan theories. In political business cycle models it is assumed that the government has both the ability and desire to manipulate the economy for electoral purposes. Partisan theories suggest that if competing parties follow different policies, it is the surprise of an election result that causes a response from the economy. However, partisan theories can only explain why different parties experience different levels of employment and output early in an electoral term. Here a partisan model is developed in which economic and political shocks before an election have asymmetric effects on inflation, employment and voting behavior, depending on which party is in power and which economic variables effect voting.

II. POLITICAL STRUCTURE AND VOTING

Two political parties compete periodically for control of the government. The parties are distinguished by their expected monetary growth rates denoted [mu].sup.H (high) and [mu].sup.L (low).

The electorate consists of a continuum of voters distributed uniformly on the interval (-p, p). Individuals located closer to -p are more favorably pre-disposed to party H. Let X.sub.t be an index of the relative popularity of the parties at time t. If X.sub.t > 0, party H has a plurality of support; if X.sub.t < 0, party L has a plurality. The government's popularity is determined by past events and the performance of the economy during its period in office; specifically, X.sub.t+1 = A.sub.t + [beta].sub.0.[pi].sub.t + [beta].sub.1.U.sub.t + Z.sub.t.. (1) [pi].sub.t and U.sub.t denote the inflation and employment rates in period t. [beta].sub.0 and [beta].sub.1 are nonpositive coefficients if H holds power, and nonnegative otherwise. The incumbent administration is blamed for the state of the economy. Z.sub.t is a political shock distributed Z.sub.t.[is approx.]N(0, [sigma].sup.2/.sub.Z.) uncorrelated over time. A.sub.t captures the effects of prior political and economic events (here it makes no qualitative difference what assumptions are made about voter memory. On election day the relative popularity of the parties is X.sub.t+1., where [alpha].sub.t+1., where [alpha].sub.t+1 is a random variable distributed uniformly on the interval (-a, a), representing election day uncertainty. The probability of party H winning an election at the beginning of period t+1 is [rho].sub.t+1 = P + [lamda].sub.0.[pi].sub.t + [lamda].sub.1.U.sub.t + [lamda].sub.2.Z.sub.t' where P = (a-A.sub.t.)/2a,[lamda.sub.0 = -[beta].sub.0/2.sub.a., [lamda.sub.1 = -[beta.sub.1./2a and [lamda].sub.2 = 1/2a. The probability of party L winning is 1 - [rhp].sub.t+1..

In nonelection years the expected monetary growth rate will be the incumbents' trend rate, while in election years it will be the probabilistically weighted average of the two parties' expected monetary growth rates.

III. ECONOMIC STRUCTURE

The economy is described by a rational expectations macro model. Unemployment is determined by the surprise Phillips curve U.sub.t = [eta].sub.0 + [eta].sub.1 (.sub.t+1.[pi].sup.e.sub.t - [pi].sub.t.) + [epsilon].sub.t' where sub.t-1.[pi].sup.e.sub.t denotes expected inflation and [epsilon].sub.t a real shock distributed [epsilon].sub.t.[is approx.]N(0, [sigma].sup.2.sub.[epsilon].), independent over time [eta].sub.0 [is greater than] 0 and [eta].sub.1 [is greater than] 0 are constants. [eta].sub.0 is the natural rate. The rate of inflation is given by [pi].sub.t = [mu].sup.s.sub.t - [mu].sup.d.sub.t., where [mu].sup.s.sub.t and [mu].sup.d.sub.t are respectively the growth rates of the nominal money supply and demand for real beginning-of-period cash balances. (Hereafter a bar will indicate a real variable.)

The expected growth in demand for real cash balances is sub.t-1.[mu].sup.de.sub.t = (.sub.t-1.M.sup.de.sub.t+1 - sub.t-1.M.sup.de.sub.t.) / sub.t-1.M.sup.de.sub.t., where sub.t-1.M.sup.e.sub.t is the expected demand for beginning-of-period real cash balances. Using unemployment as a proxy for real output, the demand for real cash balances depends on the expected unemployment and nominal interest rates: sub.t.M.sup.de.sub.t+1 = [gamma].sub.0 + [gamma].sub.1t.R.sup.e.sub.t+1 + [gamma].sub.2t.U.sup.e.sub.t+1., where [gamma.sub.0 [is greater than] 0, [gamma]sub.1 [is less than] 0 and [gamma].sub.2 [is less than] 0 are constants. The expected nominal interest rate is the sum of the real interest and inflation rates, so sub.t-1.R.sup.e.sub.t+1 = r + sub.t-1.[pi].sup.e.sub.t+1..

The real interest rate r is assumed constant (endogenising it using an IS curve only adds algebraic complexity).

The model is closed by assuming that expectations are formed rationally, but that only a small minority of individuals know the model, and all others adopt the inflation forecasts of the well informed. The vast majority of individuals are unaware that economic policy is neutral and hold the incumbent administration responsible for the economy's performance.

The rational expectations equilibrium may be described by the triple ([pi].sup.*., [rho].sup.*., [eta].sub.0.), which must satisfy [rho].sup.*.sub.t+1 = P + [lamda].sub.0.[pi].sup.*.sub.t + [lamda].sub.1.[eta].sub.0..

Note that the equilibrium is contigent on P, which captures the influence of past political and economic events.

IV. REAL ECONOMIC AND POLITICAL SHOCKS

It is well recognized in the rational expectations literature that an anticipated change in government will change both the expected post-election and pre-election inflation rates. Here it is argued that contemporaneous political and real economic shocks affects election probabilities and hence change expected monetary growth and inflation rates. A surprise change in the expected inflation rate changes the expected nominal interest rate leading to an adjustment in the rate of accumulation of real balances. The pre-election inflation and unemployment rates change due to the adjustment in the real balance accumulation rate, and this leads to a further change in election probabilities. Pre-election shocks trigger politico-economic feed back effects which may either amplify or dampen the initial shock. If shocks occur in period one, the model may be solved to give [pi].sub.t = [pi].sup.*.sub.t + [gamma].sub.1.([mu].sup.L - [mu'.sup.H.) ([lamda].sub.1.[epsilon].sub.t. + [lamda.sub.2.Z.sub.t.)/[[gamma'.sub.0 + [gamma.sub.1(r + [pi].sub.t.) + [gamma].sub.2[eta'0 - [gamma'.sub.1.([mu].sup.L - [mu'.sup.H.) [lamda].sub.0 - [lamda].sub.1[eta]0.)].

The second term on the right-hand side of (9) captures the politico-economic feedback effects of real economic or political shocks on the pre-election inflation rate. The effects of shocks on the unemployment rate and election probabilities are given by U.sub.t - [eta.sub.0 = -[eta].sub.1.([pi].sub.t - [pi].sup.*.sub.t.) + [epsilon].t and [rho].sub.t+1 - [rho].sup.*.sub.t+1 = ([lambda].sub.0 - [eta].sub.1.[lambda].sub.1.) + [lambda].sub.1.[epsilon].sub.t + [lambda].sub.2.Z.sub.t.

For any given political or economic shock, the effects on the equilibrium will depend on which party holds power and whether unemployment or inflation is the electorate's primary concern.

Case 1: Unemployment Determines Election Probabilities.

Suppose that unemployment is the electorate's main concern, so [lambda].sub.0 = 0, and [lambda].sub.1 is negative if party H holds office and positive otherwise. Equation (9) shows that a real economic shock, [epsilon].sub.t > 0 and Z.sub.t = 0, will lower or raise inflation as office is held by parties H and L respectively. Expression (10) gives the effects of the shock on unemployment; with H in office, the impact effect and the deviation of inflation from its expected rate work in the same direction, and unemployment unambiguously increases. With party L in office, [pi].sub.t > [pi].sup.*.sub.t and the two effects work in opposite directions; unemployment will rise less. The effects of a real shock on election probabilities follow from (11); an L incumbent is less severely affected.

The effects on inflation, unemployment, and election probabilities of an adverse political shock are also given by equations (9) to (11). An adverse shock is characterized by Z.sub.t < 0 for party H, and Z.sub.t > 0 for party L. Further, let [epsilon].sub.t = 0. If party H holds office the shock lowers its prospects of reelection. This lowers both the expected future and current inflation rates, causing unemployment to rise and thus lowering party H's reelection prospects further. If party L is in office, the impact effect of a shock is to lower its probability of reelection, but this raises expected future and current inflation rates, reducing current unemployment and causing L's reelection prospects to recover. The politico-economic feedback effects work in opposite directions for the two parties.

Case 2: Inflation Determines Election Probabilities.

Consider the effects of shocks when inflation is the electorate's main concern. The results follow from equations (9) to (11), with [lambda].sub.1 = 0 and [lambda].sub.0 negative if H holds office; [lambda].sub.0 is positive otherwise. Equation (11) reveals that a real economic shock has no politico-economic feedback effects if inflation is the electorate's only concern.

Political shocks have interesting effects. When party L holds office the impact and politico-economic feedback effects of an adverse shock work in the same direction. A shock lowers party L's probability of reelection, thereby raising both the expected future and current inflation rates, which causes its prospects of reelection to deteriorate further. When party H holds office the impact and feedback effects of an adverse shock work in opposite directions. This is because an initial decline in popularity lowers current and expected future inflation rates, at least partially reversing the popularity loss. The results of this section are summarized in Table I.

Comparison of the effects of adverse political shocks when inflation and unemployment are the electorate's main concern reveals further asymmetries. When unemployment is the crucial variable, adverse shocks cause a greater reduction in the popularity of an H government. When inflation is the crucial variable, an adverse shock does more damage to an L government's popularity. These conclusions follow directly from the trade-off between inflation and unemployment along the surprise Phillips curve. A shock that produces a particular movement along the Phillips curve will produce different politico-economic feedback effects depending on whether inflation or unemployment currently concerns the electorate.

V. CONCLUSION AND POSSIBLE EXTENSIONS

This paper has provided one explanation why, for given shocks, the behavior of the economy may differ under different governments even when expectations are formed rationally and systematic government policy is neutral. The model can be extended to address many interesting questions. Nominal shocks can be incorporated into the current structure. The hypothesis that the government is punished for a bad performance, but not rewarded for a good one, might be investigated. One important extension would be to allow economic heterogeneity across voters; this could lead to the number of parties and their policies being endogenously determined.

The aim of this paper has been to develop a simple politico-economic model in which expectations are formed rationally. Unlike standard partisan models, the structure developed here can explain why different parties experience different political and economic reactions to identical shocks late in an electoral term.

I. INTRODUCTION

Recent empirical studies by Alesina and Sachs [1986] and Haynes and Stone [1987] have found that political elections have significant implications for the time paths of employment and inflation. Explnations of this phenomenon fall into two general categories: political business cycle theories and partisan theories. In political business cycle models it is assumed that the government has both the ability and desire to manipulate the economy for electoral purposes. Partisan theories suggest that if competing parties follow different policies, it is the surprise of an election result that causes a response from the economy. However, partisan theories can only explain why different parties experience different levels of employment and output early in an electoral term. Here a partisan model is developed in which economic and political shocks before an election have asymmetric effects on inflation, employment and voting behavior, depending on which party is in power and which economic variables effect voting.

II. POLITICAL STRUCTURE AND VOTING

Two political parties compete periodically for control of the government. The parties are distinguished by their expected monetary growth rates denoted [mu].sup.H (high) and [mu].sup.L (low).

The electorate consists of a continuum of voters distributed uniformly on the interval (-p, p). Individuals located closer to -p are more favorably pre-disposed to party H. Let X.sub.t be an index of the relative popularity of the parties at time t. If X.sub.t > 0, party H has a plurality of support; if X.sub.t < 0, party L has a plurality. The government's popularity is determined by past events and the performance of the economy during its period in office; specifically, X.sub.t+1 = A.sub.t + [beta].sub.0.[pi].sub.t + [beta].sub.1.U.sub.t + Z.sub.t.. (1) [pi].sub.t and U.sub.t denote the inflation and employment rates in period t. [beta].sub.0 and [beta].sub.1 are nonpositive coefficients if H holds power, and nonnegative otherwise. The incumbent administration is blamed for the state of the economy. Z.sub.t is a political shock distributed Z.sub.t.[is approx.]N(0, [sigma].sup.2/.sub.Z.) uncorrelated over time. A.sub.t captures the effects of prior political and economic events (here it makes no qualitative difference what assumptions are made about voter memory. On election day the relative popularity of the parties is X.sub.t+1., where [alpha].sub.t+1., where [alpha].sub.t+1 is a random variable distributed uniformly on the interval (-a, a), representing election day uncertainty. The probability of party H winning an election at the beginning of period t+1 is [rho].sub.t+1 = P + [lamda].sub.0.[pi].sub.t + [lamda].sub.1.U.sub.t + [lamda].sub.2.Z.sub.t' where P = (a-A.sub.t.)/2a,[lamda.sub.0 = -[beta].sub.0/2.sub.a., [lamda.sub.1 = -[beta.sub.1./2a and [lamda].sub.2 = 1/2a. The probability of party L winning is 1 - [rhp].sub.t+1..

In nonelection years the expected monetary growth rate will be the incumbents' trend rate, while in election years it will be the probabilistically weighted average of the two parties' expected monetary growth rates.

III. ECONOMIC STRUCTURE

The economy is described by a rational expectations macro model. Unemployment is determined by the surprise Phillips curve U.sub.t = [eta].sub.0 + [eta].sub.1 (.sub.t+1.[pi].sup.e.sub.t - [pi].sub.t.) + [epsilon].sub.t' where sub.t-1.[pi].sup.e.sub.t denotes expected inflation and [epsilon].sub.t a real shock distributed [epsilon].sub.t.[is approx.]N(0, [sigma].sup.2.sub.[epsilon].), independent over time [eta].sub.0 [is greater than] 0 and [eta].sub.1 [is greater than] 0 are constants. [eta].sub.0 is the natural rate. The rate of inflation is given by [pi].sub.t = [mu].sup.s.sub.t - [mu].sup.d.sub.t., where [mu].sup.s.sub.t and [mu].sup.d.sub.t are respectively the growth rates of the nominal money supply and demand for real beginning-of-period cash balances. (Hereafter a bar will indicate a real variable.)

The expected growth in demand for real cash balances is sub.t-1.[mu].sup.de.sub.t = (.sub.t-1.M.sup.de.sub.t+1 - sub.t-1.M.sup.de.sub.t.) / sub.t-1.M.sup.de.sub.t., where sub.t-1.M.sup.e.sub.t is the expected demand for beginning-of-period real cash balances. Using unemployment as a proxy for real output, the demand for real cash balances depends on the expected unemployment and nominal interest rates: sub.t.M.sup.de.sub.t+1 = [gamma].sub.0 + [gamma].sub.1t.R.sup.e.sub.t+1 + [gamma].sub.2t.U.sup.e.sub.t+1., where [gamma.sub.0 [is greater than] 0, [gamma]sub.1 [is less than] 0 and [gamma].sub.2 [is less than] 0 are constants. The expected nominal interest rate is the sum of the real interest and inflation rates, so sub.t-1.R.sup.e.sub.t+1 = r + sub.t-1.[pi].sup.e.sub.t+1..

The real interest rate r is assumed constant (endogenising it using an IS curve only adds algebraic complexity).

The model is closed by assuming that expectations are formed rationally, but that only a small minority of individuals know the model, and all others adopt the inflation forecasts of the well informed. The vast majority of individuals are unaware that economic policy is neutral and hold the incumbent administration responsible for the economy's performance.

The rational expectations equilibrium may be described by the triple ([pi].sup.*., [rho].sup.*., [eta].sub.0.), which must satisfy [rho].sup.*.sub.t+1 = P + [lamda].sub.0.[pi].sup.*.sub.t + [lamda].sub.1.[eta].sub.0..

Note that the equilibrium is contigent on P, which captures the influence of past political and economic events.

IV. REAL ECONOMIC AND POLITICAL SHOCKS

It is well recognized in the rational expectations literature that an anticipated change in government will change both the expected post-election and pre-election inflation rates. Here it is argued that contemporaneous political and real economic shocks affects election probabilities and hence change expected monetary growth and inflation rates. A surprise change in the expected inflation rate changes the expected nominal interest rate leading to an adjustment in the rate of accumulation of real balances. The pre-election inflation and unemployment rates change due to the adjustment in the real balance accumulation rate, and this leads to a further change in election probabilities. Pre-election shocks trigger politico-economic feed back effects which may either amplify or dampen the initial shock. If shocks occur in period one, the model may be solved to give [pi].sub.t = [pi].sup.*.sub.t + [gamma].sub.1.([mu].sup.L - [mu'.sup.H.) ([lamda].sub.1.[epsilon].sub.t. + [lamda.sub.2.Z.sub.t.)/[[gamma'.sub.0 + [gamma.sub.1(r + [pi].sub.t.) + [gamma].sub.2[eta'0 - [gamma'.sub.1.([mu].sup.L - [mu'.sup.H.) [lamda].sub.0 - [lamda].sub.1[eta]0.)].

The second term on the right-hand side of (9) captures the politico-economic feedback effects of real economic or political shocks on the pre-election inflation rate. The effects of shocks on the unemployment rate and election probabilities are given by U.sub.t - [eta.sub.0 = -[eta].sub.1.([pi].sub.t - [pi].sup.*.sub.t.) + [epsilon].t and [rho].sub.t+1 - [rho].sup.*.sub.t+1 = ([lambda].sub.0 - [eta].sub.1.[lambda].sub.1.) + [lambda].sub.1.[epsilon].sub.t + [lambda].sub.2.Z.sub.t.

For any given political or economic shock, the effects on the equilibrium will depend on which party holds power and whether unemployment or inflation is the electorate's primary concern.

Case 1: Unemployment Determines Election Probabilities.

Suppose that unemployment is the electorate's main concern, so [lambda].sub.0 = 0, and [lambda].sub.1 is negative if party H holds office and positive otherwise. Equation (9) shows that a real economic shock, [epsilon].sub.t > 0 and Z.sub.t = 0, will lower or raise inflation as office is held by parties H and L respectively. Expression (10) gives the effects of the shock on unemployment; with H in office, the impact effect and the deviation of inflation from its expected rate work in the same direction, and unemployment unambiguously increases. With party L in office, [pi].sub.t > [pi].sup.*.sub.t and the two effects work in opposite directions; unemployment will rise less. The effects of a real shock on election probabilities follow from (11); an L incumbent is less severely affected.

The effects on inflation, unemployment, and election probabilities of an adverse political shock are also given by equations (9) to (11). An adverse shock is characterized by Z.sub.t < 0 for party H, and Z.sub.t > 0 for party L. Further, let [epsilon].sub.t = 0. If party H holds office the shock lowers its prospects of reelection. This lowers both the expected future and current inflation rates, causing unemployment to rise and thus lowering party H's reelection prospects further. If party L is in office, the impact effect of a shock is to lower its probability of reelection, but this raises expected future and current inflation rates, reducing current unemployment and causing L's reelection prospects to recover. The politico-economic feedback effects work in opposite directions for the two parties.

Case 2: Inflation Determines Election Probabilities.

Consider the effects of shocks when inflation is the electorate's main concern. The results follow from equations (9) to (11), with [lambda].sub.1 = 0 and [lambda].sub.0 negative if H holds office; [lambda].sub.0 is positive otherwise. Equation (11) reveals that a real economic shock has no politico-economic feedback effects if inflation is the electorate's only concern.

Political shocks have interesting effects. When party L holds office the impact and politico-economic feedback effects of an adverse shock work in the same direction. A shock lowers party L's probability of reelection, thereby raising both the expected future and current inflation rates, which causes its prospects of reelection to deteriorate further. When party H holds office the impact and feedback effects of an adverse shock work in opposite directions. This is because an initial decline in popularity lowers current and expected future inflation rates, at least partially reversing the popularity loss. The results of this section are summarized in Table I.

Comparison of the effects of adverse political shocks when inflation and unemployment are the electorate's main concern reveals further asymmetries. When unemployment is the crucial variable, adverse shocks cause a greater reduction in the popularity of an H government. When inflation is the crucial variable, an adverse shock does more damage to an L government's popularity. These conclusions follow directly from the trade-off between inflation and unemployment along the surprise Phillips curve. A shock that produces a particular movement along the Phillips curve will produce different politico-economic feedback effects depending on whether inflation or unemployment currently concerns the electorate.

V. CONCLUSION AND POSSIBLE EXTENSIONS

This paper has provided one explanation why, for given shocks, the behavior of the economy may differ under different governments even when expectations are formed rationally and systematic government policy is neutral. The model can be extended to address many interesting questions. Nominal shocks can be incorporated into the current structure. The hypothesis that the government is punished for a bad performance, but not rewarded for a good one, might be investigated. One important extension would be to allow economic heterogeneity across voters; this could lead to the number of parties and their policies being endogenously determined.

The aim of this paper has been to develop a simple politico-economic model in which expectations are formed rationally. Unlike standard partisan models, the structure developed here can explain why different parties experience different political and economic reactions to identical shocks late in an electoral term.

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Author: | Ellis, Christopher J. |
---|---|

Publication: | Economic Inquiry |

Date: | Jul 1, 1989 |

Words: | 2002 |

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