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The Cost of Non-Decreasing Pay: Tenured Academics and Civil Servants Stanimir Morfov State University - Higher School of Economics 7th Biannual Conference of the Society for Economic Design, Montreal, June 15-17, 2011 Morfov, S. (Higher School

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The Cost of Non-Decreasing Pay: Tenured Academics and Civil Servants

Stanimir Morfov

State University - Higher School of Economics

7th Biannual Conference of the Society for Economic Design, Montreal, June 15-17, 2011

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 1 / 25

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Introduction

Long-term contracts with non-decreasing wages

Examples

Civil servants Tenured academics

Legislation and usual practice

Hidden information vs. hidden action Disincentives Cost

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 2 / 25

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Relation to literature

Non-decreasing wages

Harris and Holmstrom (1982): incompl. sym. info, risk-neutral …rms Holmstrom (1982): career concerns Stevens (2004): random matching and on-the-job search

Academic tenure

Carmichael (1988): truthful revelation in OLG McPherson and Schapiro (1999), Siow (1998): obsol., underspecial. Freeman (1977): sym. info about productivity Glaeser (2002): faculty vs. administration Khovanskaya, Sonin and Yudkevich (2007): university budgets Li and Ou-Yang (2003): incentive e¤ects Oyer (2007): insider advantage

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 3 / 25

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Relation to literature

In…nite-horizon characterization

Green (1987): temporary incentive compatibility Spear and Srivastava (1987): recursivity Abreu, Pearce and Stacchetti (1990): SGP equilibria in dyn games Phelan (1995): self-enforcement

Repeated moral hazard with hidden action

Phelan and Townsend (1991): convexif. and APS on probabilities Wang (1997): APS on continuation utility Fernandes and Phelan (2000): history-dependence through action Doepke and Townsend (2006): history-dependence through income Sleet and Yeltekin (2001): income shocks and separations

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 4 / 25

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Two periods

Assumptions

Principal-agent Unobservable e¤ort One-sided commitment Realized wage today becomes minimum wage tomorrow Outcomes: y < y E¤ort: a < a

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 5 / 25

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Two periods

Assumptions

Probability of y conditional on a: π(y, a)

π := π(y, a) π := π(y, a) 0 < π < π < 1

Given outcome y, e¤ort a, and wage w

principal’s period utility: y w agent’s period utility: v (w) a common discount factor: β

Agent’s outside wage: v 1 (V )

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 6 / 25

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Two periods with unrestricted pay

Single-period problem

max

a,w (.) ∑ y2Y

(y w)π (y, a) s.t.: a 2 A (fa)

∑

y2Y

(v (w) a)π (y, a) V (ir) a 2 arg max

a02A ∑ y2Y

(v (w) a0)π

y, a0

(ic)

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 7 / 25

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Two periods with unrestricted pay

Optimal contract

C < 0 ) low e¤ort is optimal and implemented by v C 0 ) high e¤ort is optimal and implemented by: v (1 π) k if outcome is bad v + πk if outcome is good v := V + a k := aa

ππ

C := E (yja) πv 1 (v (1 π) k) (1 π) v 1 (v + πk) E (yja) + v 1 (v)

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 8 / 25

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Myopia

MYOPIA = SHORT-TERMISM Ignoring future utility It could be driven by beliefs about:

changes in legislation leaving the relationship

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 9 / 25

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Two periods with non-decreasing pay

Full myopia

G0 G1 G2

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 10 / 25

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Two periods with non-decreasing pay

Full myopia

C < 0 implies G0 C 0 and D < 0 imply G1 C 0 and D 0 imply G2

D := E (yja) E (yja) + (1 π) (v 1 (v + πk) v 1 (v + (1 + π) k))

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 11 / 25

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Two periods with non-decreasing pay

Myopic agent

Given an e¤ective minimum wage w1, the principal can implement: (a) low e¤ort by maxfv (w1) , vg; (b) high e¤ort by v2 after a bad outcome and v2 + k after a good

utcome, where v2 := maxfv (w1) , v (1 π) kg

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 12 / 25

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Two periods with non-decreasing pay

Myopic agent

If the principal chooses among G0, G1 and G2: (a) K < 0 and (1 + β ¯ π) C + (1 β) ¯ π maxfK, Lg < 0 imply G0; (b) (1 + β ¯ π) C + (1 β) ¯ πL 0 and K < L imply G1; (c) (1 + β ¯ π) C + (1 β) ¯ πK 0 and L K < 0; or K 0 imply G2.

K := E (yja) ¯ πv 1 (v + πk) (1 ¯ π) v 1 (v + (1 + π) k) E (yja) + v 1 (v)

L := v 1 (v) v 1 (v + πk)

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 13 / 25

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Two periods with non-decreasing pay

Myopic agent

G3 G4 G5

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 14 / 25

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Two periods with non-decreasing pay

No myopia

Binding minimum wages imply that second-period individual rationality is slack Downward adjustment of …rst-period wages is not constrained by single-period individual rationality as long as two-period individual rationality holds ) Principal is better o¤ when agent is fully rational

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 15 / 25

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In…nite horizon

Framework

Repeated moral hazard Hidden action One-sided commitment Realized wage today is a minimum wage tomorrow

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 16 / 25

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In…nite horizon

Assumptions

Discrete time, t Initial period of contracting 0 Stationary set of N distinct outcomes, Y Stationary, compact set of actions, A Stationary, compact set of transfers, W Current outcome depends on current action only For any action, the support of the distribution is Y

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 17 / 25

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In…nite horizon

Assumptions

Principal

u : W Y ! R, cont., decr. in transfer, incr. in outcome; discounts the future by a factor βP 2 (0, 1); commits to long-term contracts

Agent

ν : W A ! R, cont., incr. in transfer, decr. in action; discounts the future by a factor βA 2 (0, 1); reservation utility V

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 18 / 25

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In…nite horizon

Notation

c := (a, w) a supercontract signed at the beginning of period 0 Ut

c, yt1

principal’s expected discounted utility at node yt1 Vt

c, yt1

agent’s expected discounted utility at node yt1

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 19 / 25

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In…nite horizon

Dynamic contract

sup

c U0 (c) s.t.:

at (.) 2 A (fa) wt

yt1, .

2 W \ [wt1(yt1), ∞) (fw) Vt (a, .) Vt

a0, .
, 8 feasible a0

(iic) Vt (.) V (ir)

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 20 / 25

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In…nite horizon

Recursivity: State space

Optimal contract with unrestricted pay

Agent’s continuation utilities (Spear and Srivastava (1987)) Start with large initial guess, iterate on an APS operator and converge to largest …xed point (e.g., Wang (1997))

A natural initial guess is V0 = h v(min W ,max A)

1βA

, v(max W ,min A)

1βA

i

Optimal contract with non-decreasing pay

Enlarge the state space by including lower bounds on wages: f(V , w) : V 2 V C (w), w 2 W g Start with large initial guess, iterate on an APS operator and converge to largest …xed point

A natural initial guess is f(V , w) : V 2 V0, w 2 W g

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 21 / 25

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In…nite horizon

Recursivity: Stationary contracts

cs := f(as, ws(y), Vs(y)) : y 2 Y g maps state space into actions, contingent minimum wages and continuation utilities Bellman equation which holds for any point (V , w) of the state space: U (V , w) = maxcS Eas fu (ws, .) + βPU (Vs)g s.t.: as 2 A (fa) ws (.) 2 W \ [w, +∞) (fw) V = Eas fv (ws, as) + βAVsg Ea0 v

ws, a0 + βAVs
, 8a0 2 A

(tic,pk) Vs (.) 2 V C (ws(.)) (cp)

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 22 / 25

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In…nite horizon

Extension: Base salary and bonus

cs := f(as, ws, ws(y), Vs(y)) : y 2 Y g maps state space into actions, minimum wages, contingent wages and continuation utilities Bellman equation which holds for any point (V , w) of the state space: U (V , w) = maxcs Eas fu (ws, .) + βPU (Vs)g s.t.: as 2 A (fa) ws (.) 2 W \ [w, +∞) (fw) ws = min

y2Y ws(y)

(mw) V = Eas fv (ws, as) + βAVsg Ea0 v

ws, a0 + βAVs
, 8a0 2 A

(tic,pk) Vs (.) 2 V C 0(ws) (cp)

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 23 / 25

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In…nite horizon

Generalization

cs := f(as, ws(y), ws(y), Vs(y)) : y 2 Y g maps state space into actions, contingent minimum wages, wages and continuation utilities Let f : W N ! W N continuous Bellman equation which holds for any point (V , w) of the state space: U (V , w) = maxcs Eas fu (ws, .) + βPU (Vs)g s.t.: as 2 A (fa) ws (.) 2 W \ [w, +∞) (fw) ws(yn) = fn(fwsg), 8yn 2 Y (mw) V = Eas fv (ws, as) + βAVsg Ea0 v

ws, a0 + βAVs
, 8a0 2 A

(tic,pk) Vs (.) 2 V C 00(ws(.)) (cp)

Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 24 / 25

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