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
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
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
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
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
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
Two periods with unrestricted pay Single-period problem a , w ( . ) ∑ ( y � w ) π ( y , a ) s.t.: max y 2 Y a 2 A (fa) ∑ ( v ( w ) � a ) π ( y , a ) � V (ir) y 2 Y � y , a 0 � ( v ( w ) � a 0 ) π a 0 2 A ∑ a 2 arg max (ic) y 2 Y Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 7 / 25
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 + π k if outcome is good v : = V + a k : = a � a π � π C : = E ( y j a ) � π v � 1 ( v � ( 1 � π ) k ) � ( 1 � π ) v � 1 ( v + π k ) � E ( y j a ) + v � 1 ( v ) Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 8 / 25
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
Two periods with non-decreasing pay Full myopia G 0 G 1 G 2 Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 10 / 25
Two periods with non-decreasing pay Full myopia C < 0 implies G 0 C � 0 and D < 0 imply G 1 C � 0 and D � 0 imply G 2 D : = E ( y j a ) � E ( y j a ) + ( 1 � π ) ( v � 1 ( v + π k ) � v � 1 ( v + ( 1 + π ) k )) Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 11 / 25
Two periods with non-decreasing pay Myopic agent Given an e¤ective minimum wage w 1 , the principal can implement: (a) low e¤ort by max f v ( w 1 ) , v g ; (b) high e¤ort by v 2 after a bad outcome and v 2 + k after a good outcome, where v 2 : = max f v ( w 1 ) , v � ( 1 � π ) k g Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 12 / 25
Two periods with non-decreasing pay Myopic agent If the principal chooses among G 0 , G 1 and G 2 : (a) K < 0 and ( 1 + β ¯ π ) C + ( 1 � β ) ¯ π max f K , L g < 0 imply G 0 ; (b) ( 1 + β ¯ π ) C + ( 1 � β ) ¯ π L � 0 and K < L imply G 1 ; (c) ( 1 + β ¯ π ) C + ( 1 � β ) ¯ π K � 0 and L � K < 0; or K � 0 imply G 2 . π v � 1 ( v + π k ) � ( 1 � ¯ π ) v � 1 ( v + ( 1 + π ) k ) � E ( y j a ) + v � 1 ( v ) K : = E ( y j a ) � ¯ L : = v � 1 ( v ) � v � 1 ( v + π k ) Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 13 / 25
Two periods with non-decreasing pay Myopic agent G 3 G 4 G 5 Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 14 / 25
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
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
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
In…nite horizon Assumptions Principal u : W � Y ! R , cont., decr. in transfer, incr. in outcome; discounts the future by a factor β P 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 β A 2 ( 0 , 1 ) ; reservation utility V Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 18 / 25
In…nite horizon Notation c : = ( a , w ) a supercontract signed at the beginning of period 0 � c , y t � 1 � principal’s expected discounted utility at node y t � 1 U t � c , y t � 1 � agent’s expected discounted utility at node y t � 1 V t Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 19 / 25
In…nite horizon Dynamic contract sup c U 0 ( c ) s.t.: a t ( . ) 2 A (fa) � � 2 W \ [ w t � 1 ( y t � 1 ) , ∞ ) y t � 1 , . w t (fw) � � a 0 , . , 8 feasible a 0 V t ( a , . ) � V t (iic) V t ( . ) � V (ir) Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 20 / 25
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)) h v ( min W , max A ) i , v ( max W , min A ) A natural initial guess is V 0 = 1 � β A 1 � β A 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 V 0 , w 2 W g Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 21 / 25
In…nite horizon Recursivity: Stationary contracts c s : = f ( a s , w s ( y ) , V s ( 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 ) = max c S E a s f u ( w s , . ) + β P U ( V s ) g s.t.: a s 2 A (fa) w s ( . ) 2 W \ [ w , + ∞ ) (fw) V = E a s f v ( w s , a s ) + β A V s g � E a 0 � � w s , a 0 � + β A V s � , 8 a 0 2 A v (tic,pk) V s ( . ) 2 V C ( w s ( . )) (cp) Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 22 / 25
In…nite horizon Extension: Base salary and bonus c s : = f ( a s , w s , w s ( y ) , V s ( 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 ) = max c s E a s f u ( w s , . ) + β P U ( V s ) g s.t.: a s 2 A (fa) w s ( . ) 2 W \ [ w , + ∞ ) (fw) w s = min y 2 Y w s ( y ) (mw) V = E a s f v ( w s , a s ) + β A V s g � E a 0 � � w s , a 0 � + β A V s � , 8 a 0 2 A v (tic,pk) V s ( . ) 2 V C 0 ( w s ) (cp) Morfov, S. (Higher School of Economics) The Cost of Non-Decreasing Pay 23 / 25
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