The Encyclopedia of Economic Principals

Chapter 77

Political Competition, Coalitions, and Redistribution

Elections, coalitions and survival shape what governments deliver.

Four of the chapter's worked examples, made interactive: inflation surprises from an uncertain election, a pre-election stimulus and its hangover, coalition size and public goods, and a ruler who blocks a productive reform. Change one value at a time and watch the figure, the numbers and the hand calculation respond.

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

Election uncertainty and partisan inflation surprises

Why does the winner of an election move output even when everyone knows each party's inflation plan?

Wage contracts average the two platforms by their probabilities, so whichever party wins delivers a surprise. The less expected the winner, the larger the surprise and the output movement, while the average gap across outcomes is zero.

Equation, written in LaTeX: \pi^e=0.65(5.5)+0.35(1.5)=4.1

Equation, written in LaTeX: y_L-y^n=0.4(5.5-4.1)=0.56

Equation, written in LaTeX: y_R-y^n=0.4(1.5-4.1)=-1.04

Equation, written in LaTeX: (0.4)^2(0.65)(0.35)(5.5-1.5)^2=0.5824.

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Party L would run inflation pi_L and party R 1.5 percent; q is L's chance of winning when wages are set. Contracts build in expected inflation pi^e, and the output gap is alpha = 0.4 times the inflation surprise.

Predict first. Which winner produces the larger output movement, the favorite or the underdog?

Your prediction

Choose an example

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Figure: Election uncertainty and partisan inflation surprises. Two bars: an output gap of 0.56 if L wins and -1.04 if R wins, around a mean of zero, with expected inflation 4.10.
Probability party L wins: 0.65, Platform gap pi_L minus pi_R (points): 4
Constructed example: the chapter's hypothetical economy (5.5 and 1.5 percent platforms, L's chance 0.65, slope 0.4); win chances 0.35, 0.50 and 0.80 and platform gaps of 2 and 6 points are added for comparison.

Calculated values

Expected inflation
4.10
Gap if L wins
0.56
Gap if R wins
-1.04
Mean gap
0.00
Expected squared gap
0.5824

Contracts build in pi^e = 0.65 x 5.5 + 0.35 x 1.5 = 4.10. If L wins the gap is 0.4 x (5.5 - 4.10) = 0.56; if R wins it is -1.04. Party L is the favorite, so its victory is mostly anticipated; the underdog R produces the larger movement, 1.04 points against 0.56. The mean gap is zero, but the expected squared gap is 0.5824.

Worked steps

  1. pi^e = 0.65 x 5.5 + 0.35 x 1.5 = 3.575 + 0.525 = 4.10
  2. Gap if L = 0.4 x (5.5 - 4.10) = 0.4 x 1.40 = 0.56
  3. Gap if R = 0.4 x (1.5 - 4.10) = 0.4 x (-2.60) = -1.04
  4. Expected squared gap = 0.16 x 0.65 x 0.35 x 4^2 = 0.5824

Use the idea

Expect the largest real effects after elections whose result was least anticipated when contracts were set, and none when indexation or an independent bank removes the surprise.

Where the conclusion applies

One-year contracts set before the vote, a known platform for each party and a fixed 0.4 slope. Win chances 0.35, 0.50 and 0.80 and platform gaps of 2 and 6 points (R held at 1.5) are added for comparison.

Check your understanding: If L's chance were 0.50, what is expected inflation and the gap if R wins?
pi^e = 0.5 x 5.5 + 0.5 x 1.5 = 3.5; the gap if R wins is 0.4 x (1.5 - 3.5) = -0.8 (the 0.50 probability is constructed).

Chapter 77 source: section "Partisan business cycle".

Demonstration 2 of 4

Pre-election stimulus and the post-election hangover

How can an incumbent buy lower unemployment before a vote, and who pays for it afterward?

The stimulus works only as a surprise. Once expectations adjust, returning inflation to normal is itself a negative surprise, so the pre-election gain is repaid after the vote.

Equation, written in LaTeX: u_2=6.5-0.35(6-2.5)=5.275

Equation, written in LaTeX: \pi_3^e=2.5+0.4(6-2.5)=3.9

Equation, written in LaTeX: u_3=6.5-0.35(2.5-3.9)=6.99

Equation, written in LaTeX: u_4=6.5-0.35(2.5-3.34)=6.794.

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u_t is unemployment and pi_t^e expected inflation in period t. Natural unemployment is 6.5, the Phillips slope is 0.35, normal inflation is 2.5, and expectations close a share rho of the last error each period. The election falls at the end of period 2.

Predict first. If the incumbent does not stimulate (period 2 inflation stays at 2.5), what happens to the cycle?

Your prediction

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Figure: Pre-election stimulus and the post-election hangover. Left: unemployment over four periods, 6.5, 5.275, 6.99 and 6.794, with the election after period 2. Right: actual inflation and expected inflation over the same periods.
Election period inflation: 6, Expectation adjustment speed: 0.4
Constructed example: the chapter's hypothetical economy (normal inflation 2.5, natural rate 6.5, slope 0.35, adjustment 0.4, election inflation 6 or 2.5); election inflation of 4 and 8 and adjustment speeds 0.2 and 0.7 are added for comparison.

Calculated values

u_2
5.275
pi_3^e
3.9
u_3
6.99
pi_4^e
3.34
u_4
6.794

Raising election-period inflation to 6 surprises contracts by 3.5 points, so u_2 = 6.5 - 0.35 x 3.5 = 5.275, a fall of 1.225 points before the vote. Expectations then catch up to 3.9, and with inflation back at 2.5 unemployment rises to 6.99, 0.49 points above natural, then 6.794 in period 4 as expectations close 0.4 of each error.

Worked steps

  1. u_2 = 6.5 - 0.35 x (6 - 2.5) = 6.5 - 1.225 = 5.275
  2. pi_3^e = 2.5 + 0.4 x (6 - 2.5) = 3.9
  3. u_3 = 6.5 - 0.35 x (2.5 - 3.9) = 6.5 + 0.49 = 6.99
  4. pi_4^e = 3.9 + 0.4 x (2.5 - 3.9) = 3.34
  5. u_4 = 6.5 - 0.35 x (2.5 - 3.34) = 6.5 + 0.294 = 6.794

Use the idea

When unemployment falls sharply just before an election on an inflation surprise, expect a rise afterward as contracts catch up.

Where the conclusion applies

Adaptive expectations, a linear Phillips curve and voters who look only at the election period. Election inflation of 4 and 8 and adjustment speeds 0.2 and 0.7 are added for comparison.

Check your understanding: With the book's values, how far above natural is unemployment in period 3?
u_3 = 6.5 - 0.35 x (2.5 - 3.9) = 6.5 + 0.49 = 6.99, so 0.49 points above 6.5.

Chapter 77 source: section "Political business cycle".

Demonstration 3 of 4

Coalition size and the price of public goods

Why does a leader backed by a small coalition underprovide services that a broad coalition would accept?

Private rewards are divided among few people in a small coalition, so each member's share is large and a universal service is a poor substitute. In a large coalition each share is small, and the same service is worth more than what members give up.

Equation, written in LaTeX: b_A=\frac{1{,}200-240-160}{20}=40.

Equation, written in LaTeX: \lambda_A=\frac{20}{1{,}000}=0.02.

Equation, written in LaTeX: \frac{300}{600}=0.5

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Revenue R = 1,200; the leader keeps k = 240 and spends g = 160 on broad services, leaving 800 for private rewards shared among the W members of the winning coalition. S = 1,000 is the selectorate. A shift moves units from private rewards to a service worth 0.7 to every resident.

Predict first. Above what coalition size does the 300-unit shift become acceptable to insiders?

Your prediction

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Figure: Coalition size and the price of public goods. Left: a private reward of 40.00 per insider with a coalition of 20. Right: no shift proposed.
Winning coalition size: 20, Units moved to universal service: 0
Constructed example: the chapter's hypothetical leader (R 1,200, k 240, g 160, S 1,000, W 20 or 600, a 300-unit shift worth 0.7 per resident); coalition sizes 100 and 430 are added for comparison.

Calculated values

Private reward per insider
40.00
Loyalty ratio W / S
0.020
Loss per member from shift
0.0000
Gain per member
0.0000
Net per member
0.0000
Verdict
no shift proposed

With 20 essential supporters, each insider receives (1,200 - 240 - 160) / 20 = 800 / 20 = 40.00, and the loyalty ratio is 20 / 1,000 = 0.020. No shift is proposed, so insiders keep the full private reward.

Worked steps

  1. b = (1,200 - 240 - 160) / 20 = 800 / 20 = 40.00
  2. Loyalty ratio = 20 / 1,000 = 0.020

Use the idea

To predict whether a regime will fund a broad public good, compare the private reward each essential supporter would lose with what they gain from the good.

Where the conclusion applies

A fixed budget, equal private shares and a service valued equally by all residents. Coalition sizes 100 and 430 are added for comparison.

Check your understanding: For W = 600, what is each member's net from the shift?
Loss 300 / 600 = 0.5, gain 0.7, net +0.2; acceptance needs 300 / W < 0.7, i.e. W > 428.6.

Chapter 77 source: section "Selectorate winning-coalition principle".

Demonstration 4 of 4

Reform that raises output but threatens the ruler

Why would a ruler block a reform that raises national output and his own revenue?

The ruler weighs reform by its effect on his own survival, not on output. A power-sharing charter that holds down replacement risk can flip the decision where cheaper finance cannot.

Equation, written in LaTeX: 270+(1-0.08)700=914.

Equation, written in LaTeX: 340-30+(1-0.28)700=814.

Equation, written in LaTeX: (0.28-0.08)700=140.

Equation, written in LaTeX: 340-30+(1-0.12)700=926,

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The ruler's payoff is current revenue minus implementation cost plus (1 - q) V, where q is the probability of being replaced and V = 700 the value of another term. Reform lifts revenue from 270 to 340 but raises q from 0.08.

Predict first. Will a loan that cuts implementation cost to 20 make the ruler reform?

Your prediction

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Figure: Reform that raises output but threatens the ruler. Stacked bars: status quo 914 (270 revenue plus 644 expected tenure value) against reform 814 (310 net revenue plus 504).
Replacement probability after reform: 0.28, Implementation cost: 30
Constructed example: the chapter's hypothetical ruler (revenue 270 and 340, cost 30 or 20, V 700, replacement 0.08, 0.28 or 0.12); a replacement probability of 0.20 is added for comparison.

Calculated values

Status quo payoff
914
Reform payoff
814
Net fiscal gain
40
Replacement cost
140
Decision
block

Reform pays 340 - 30 + (1 - 0.28) x 700 = 814 against 914 under the status quo. It adds 40 of revenue net of implementation but the higher replacement risk costs 140 of expected tenure, so the ruler blocks it, whatever happens to national output.

Worked steps

  1. Status quo: 270 + (1 - 0.08) x 700 = 270 + 644 = 914
  2. Reform: 340 - 30 + (1 - 0.28) x 700 = 310 + 504 = 814
  3. Net fiscal gain = 340 - 270 - 30 = 40
  4. Replacement cost = (0.28 - 0.08) x 700 = 140
  5. 40 - 140 = -100: block

Use the idea

When a profitable reform stalls, ask how it changes the incumbent's chance of losing power, not only its cost.

Where the conclusion applies

A fixed value of another term and replacement probabilities taken as given. A replacement probability of 0.20 is added for comparison.

Check your understanding: Under a power-sharing charter (replacement probability 0.12), what is the reform payoff?
340 - 30 + 0.88 x 700 = 310 + 616 = 926 > 914, so reform proceeds; the loan alone gives 824 < 914.

Chapter 77 source: section "Political replacement effect".