Choosing Institutional Microfeatures:Endogenous Seniority

Kenneth A. Shepsle Harvard University

Keynote Address

Second Annual International ConferenceFrontiers of Political Economics

Higher School of Economics and New Economics School Moscow

May 29-31, 2008

Introduction

INSTITUTIONS:

• Imposition -- institutional designers

• Choice -- institutional players

• Emergence -- historical process

Ubiquity of Seniority

• Legislatures

• Age grading

• LIFO union contracts

• PAYG pensions

• Academic & bureaucratic grade-and-step systems

Previous Modeling Approaches

• Binmore’s Mother-Daughter game

• Hammond’s Charity game

• Cremer and Shepsle-Nalebuff on ongoing cooperation

Can an equilibrium privileging a senior cohort or generation be sustained?

Modeling the Choice of Institutions

• Legislators choose a seniority system • Tribes select and sustain ceremonies and rights-of-

passage between age-grades

• Unions and management negotiate last-in-first-out hiring/firing rules

• Social security and pension policies are political choices

• Grade-and-step civil service and academic schemes are arranged or imposed

McKelvey-Riezman

• Three subgames – institutional, legislative, electoral

• Definition: A legislator is senior in period t if he or she was

–a legislator during period t-1

–reelected at end of period t-1

McKelvey-Riezman Institutional Subgame

Majority Choice: In period t shall seniority be in effect? (yea or nay)

Yea

Seniors have higher initial recognition probabilities

Nay

The recognition probability is 1/N for all legislators

McKelvey-Riezman Legislative Subgame

– Baron-Ferejohn Divide-the-Dollar

– Random recognition with probabilities determined by seniority choice

– Take-it-or-leave-it proposal

– Recognition probabilities revert to 1/N if proposal fails

McKelvey-Riezman Election Subgame

– Voter utility monotonic in portion of the dollar delivered to district

– Legislators care about perks of office (salary) and a %age of portion of dollar delivered to district

– Voters reelect incumbent or elect challenger

– Incumbent and challenger identical except former has legislative experience

McKelvey-Riezman Time Line

–Decision on seniority system

–Divide-the-dollar game

–Election

McKelvey-Riezman Main Result

– In institutional subgame, incumbents will always select a seniority system

– In equilibrium it will have no impact on legislative subgame

– Because in the election subgame it will induce voters to re-elect incumbents

McKelvey-Riezman Main Result: Remarks

• Implication: In equilibrium all legislators are senior

• Implication: Divide-the-dollar game observationally equivalent to world of no seniority. But seniority has electoral bite

McKelvey-Riezman Main Result: Remarks

• Seniority defined as categorical (juniors and seniors) and restrictively

• Recognition probability advantage to seniors only initially

• In a subsequent paper they show that rational legislators would chose the “only initial” senior advantage, not “continuing” advantage

Muthoo-Shepsle Generalization

• Seniority still categorical

• But the cut-off criterion is an endogenous choice

Muthoo-Shepsle Generalization: Institutional Subgame

• Each legislator identified by number of terms of service, si

• s = (si) state variable

• Each legislator announces a cut-off, ai

• The median announcement is the cut-off

s* = Median {ai}

Muthoo-Shepsle Generalization

• si > s* → i is senior

• s* = 0 → no seniority system

• s* > maxi si → no seniority system

Muthoo-Shepsle Generalization: Basic Set Up

• For cut off s*, let S be the number of seniors

• 1/S > pS > 1/N – senior recognition probability

(pS ranges from 1/S if only seniors are recognized to 1/N if seniors have no recognition advantage)

• pS = (1 - S pS)/(N – S) – junior recognition probability

• pS < pS

Muthoo-Shepsle Generalization: Results

• Lemma (Bargaining Outcome). For any MSPE, state s, and cut off s* selected in the Institutional Subgame and discount parameter δ:

– If S=0 or S=N, then all legislators expect 1/N of the dollar

– 0 < S < N, then the expectation of a senior (zs) and a junior (zj):

zs = δ/2N + (1 – δ/2)pS

zj = δ/2N + (1 – δ/2)pS

• Expected payoff monotonic in recognition probabilities for each type

• Lemma (Incumbency Advantage). In any MSPE voters re-elect incumbents.

Muthoo-Shepsle Generalization: Results

Theorem (Equilibrium Cut Off). If pS is non-increasing in S and pS is non-decreasing in S, then there exists a unique MSPE outcome for any vector of tenure lengths s in which the unique equilibrium cut off, selected in the Institutional Subgame is

s* = sM

where sM is the median of the N tenure lengths in s.

• A seniority system is chosen and the most junior senior legislator is the one with median length of service.

Muthoo-Shepsle Generalization: Results

•Alternative seniority system?

•Definition. For s any element of s, P(s) is a probability-of-initial-recognition function.

•Theorem (Alternative seniority system). If a legislator is restricted to announce P(s) non-decreasing in s, then he will announce

0 if s < si

Pi(s) = 1/N(si) if s > si

where N(si) is the number of legislators whose length of tenure is at least as high as si

Muthoo-Shepsle: A Summing Up

• Under specified conditions the legislator with the median number of previous terms served will be pivotal

• She will set the cut-off criterion at her seniority level, even if she can offer a more fully ordinal schedule

• Selected categorical seniority system: most junior senior legislator has median number of previous terms of service

THANK YOU!