Behavorial Personnel Economics

Gneezy and Rusticini 2000 Psychologist claim that financial incentives can crowd out intrinsic motivation. The did a randomized study in a child care center where picking up your child late was punished with a fine for one group. Results: The control group remained in the same pattern while the treatment group was late more often. Explanation: A fine is something that can be bought. Before it was norms and good manner that led to parents arriving on time. Know it's acceptable to pay a price for late arrival. After removing the fine: The fine was removed but people were still way more late on average compared to the control group! Sticky business

A fine is a price - study

1) we know that efficient solution: E=d 2) E* = alpha * d * S ==> S = E*/(alpha*d) ==> S* = R*(E*/d) 3) Workers expected income: ==> a + 0.5*S

Achieving the optimal tournament - optimal S*

CE = Exp(Y) - 0.5 * r * Var(Y) r = arrow Pratt RP = 0.5 *r*Var(Y)

Approximation of certainty equivalent and risk premium

b* = 1 holds even if we change the following: 1) Linear Production Q =d*E, Any increasing function works 2) Quadratic V(E) => Any convex cost of effort function works 3) Linear reward Y (a+b*Q), non linear works as well 4) If the agent is risk-neutral uncertainty doesn't matter 5) If all Outputs are equally good measurable there can be more than one type 6) If agents work independently there can be multiple agents

Assumptions in the P-A Problem that do NOT matter

V(E) = E^2/2 d=1

Baseline Model assumptions

The benchmark/ first best Solution assumes that the agents effort level is known and the contract conditioned on that We get an E(FB) = 1 same as in the non risk case But unlike before we now want the piece rate to be b=0 Therefore the optimal contract would be: a(FB) = V(E(FB)) if E = E(FB) a(FB) = 0 if E =/= E(FB) ==> Contract is incentive compatible because the agent will choose the optimal effort level E(FB) ==> Participation constraint is satisfied because the agent gets compensated for the cost of effort

Benchmark - contingent contract

The study in 12' showed that relative wages compared to your reference group do influence your satisfaction. But on average it might be that secrecy makes workers happier than knowing wages of agents outside your reference group.

Can wage secrecy have a positive effect?

1) Procrastination 2) self control problems 3) time inconsistency ==> Present if your future choices are different from the ones your current self would like your future self to make

Consequences of present bias

1) income effects lead to people working 40 instead of 72 hours 2) permanent tax cuts for high earners might reduce their workeffort 3) Increasing piece rate (b) for a long time or lifetime can backfire and result in lower work effort due to income effects

Effect of permanent wage increases

Study by Fryer, Levitt, List and Sadoff 2012 They tried framing and loss aversion to make financial incentives more effective. They divided teachers in 3 groups (control, gain, loss) gain: could gain 8k if students performed well loss: were given 4k and might loss/win another 4k Findings: 1) Standard gain plan had no effect 2) Framing the exact same plan as a loss by giving money upfront ==> students showed significantly better results Do firms use this framing in real life? Not really cause it might seem to unethical

Enhancing the efficacy of teach... 2012

By appropriate choice of pay parameters (a,b) for piece rates and (a,S) for tournaments, any overall outcome can be achieved by both schemes.

Equivalence of tournaments and piece rates

Every situation where two or more workers are rewarded on the basis of their relative performance 1) Competing for a promotion 2) Bonuses for top performers Functions of tournaments: 1) employee selection 2) work incentives for not yet promoted agents

Examples for tournaments + Functions

1) Buy or Make decision ==> If you outsource you always sell the job to some worker 2) Franchising: the agent has to pay for a franchise contract or license which gives him the right to operate something 3) Other examples include: taxis in ny, hairdressers, fedex, amazon

Examples of selling your job to the worker

If the error term isn't uniformly distributed but normally we need to find the nash equilibrium E* = f(0)*d*S f(eps.) is the function of the difference between error term 2 and error term 1

Excursus: normally distributed error terms

1) Principal proposes contract 2) Agent must have incentive to accept (Participation constraint) 3)Agent max. his utility (Incentive compatibility constraint) 4) Payments are made

Four Stages of optimal contracting

Gary asked himself if raising fines for illegal parking or hiring more officers was economically more efficient Severe Punishment with lax enforcement seemed optimal

Gary Beckers - Monitoring puzzle

Often used to think about principal-agent interactions 1) Principal as first mover who hires the agent for a certain time and pay 2) Then the agent has to decide how much effort to put in 3) Multiplying the effort by two: gains for both through effort ==> in our early model this would be like the case where a>0 and b=0

Gift exchange game - basics

A Study from 1924-32' showed that workers positively changed there behaviour and performance no matter which treatment they received. It was concluded that the effect was due to the workers being studied and observed and not due to the effect of the treatment. Was safelites PPP also hawthorned? no because he measured productivity shortly after and also month later with the same result.

Hawthorne Effect + Effect on safelite study

Higgs analyzed land contracts with different crop risk and 3 different contracts types 1) rental 2) share 3) wage labor He showed that counties with higher crop risk had more wage labor contracts (b=0) and fewer rental or shared contracts. These findings support the predictions that incentives are lower in environments with higher risk

Higgs 1973 - insurance incentives trade off

1) At the reference point the agents marginal benefit of effort will jump down from mbd to nbd. E(R) = (R-a) /b*d mbd = marginal utility from working harder Bunching effect: Most people will pick the same effort level E(R) even tough they have different costs of effort. They won't pick the same effort level as before because after their reference point the marginal benefit of working is just way too small.

How does E* change with loss aversion + reference point?

Instead of a linear contract that might requires a negative base-pay or rather an up-front payment/investment from the agent there's a non linear solution, which allow the agent to not make an entry up-front payment With an implicit (non-linear) reward schedule the agent does need to achieve an output Q0 to get paid. On all output in excess of Q0 the agent receives 100% commission.

Implicit Payments - How do they work?

1) Difference between humans and pigeons: humans can save and borrow so consumption and income mustn't be the same in one period 2) therefore temporary wage increases are unlikely to give rise to a backward bending curve. Among humans only temporary effects would have such an effect. ==> Battalios experiment is good to provide a model for studying effects of permanent or long term wage changes on humans such as caused by technological change or changes in tax policy

Importance of income effects

b* = 1/[1+r+Var(eps)*V''(E)] d==> The larger the marginal productivity the larger b* V''(E) ==> The more the agent reacts to incentives, the smaller V'' is the larger b* is r==> The larger the risk aversion the smaller b* Var(eps) ==> Larger uncertainty, smaller b* In a world full of uncertainty und risk aversion we'll get an E<1

Incentive Intensity

Battalio et al 1981' implemented exactly our linear incentive scheme into the study with pigeons b.c it would be really expensive with humans Output Q is generated by pecking on a key Y is 3 secs. of access to grain a & b were manipulated to find things out Wage was measured like this: 50 ==> (1000/50)*10 = 200 pecks needed for food 800 ==> (1000/800)*10 = 12.5 Findings: 1) changing piece rate ==> first increase in effort then back to normal level ==> contradicts prediction of higher b more effort 2) When given free income they drastically reduced their work rate 3) Starting at the max. wage the wage could be cut down by factor 16 without a significant negative effect on performance 4) the results are consistent with the model of the backward bending supply curve more a and higher b ==> less work ==> the effort reducing income effect outweighs the effort raising substitution effect

Income Leisure study

If an experiment is conducted but the two groups aren't randomly assigned causality isn't given. It is likely that the groups differ in other ways that could also affect their performance. This difference is also known as omitted variable bias. If we look precisely it is possible that the two groups are quite different from each other. However the within-group-effect could still be zero!

Inferring Causality - Non Experimental Setting

Abeler et al 11' Do wee see bunching at reference points? Participants had to count numbers in a real effort experiment After a coin flip the participant was either paid for their performance or given a fixed rate depending on the coin flip result. The fixed payment was once 3 once 7 Dollars: Expectation: For a rational agent it wouldn't make sense to let the outcome in case performance didn't count (fixed payment) effect the effort. Findings: 1) An unusually large number of participants decided to earn exactly the same amount in the variable and in the fixed outcome ==> there was bunching at the reference point 2) Reference points can indeed be manipulated as shown here.

Manipulating reference points - study

Ariely et al 2008 Two groups of students had to assemble lego. One group had every lego bionicle lined up as a motivation in front of them. The other "sysyphus" group saw how every single bionicle was disassembled in front of them while they were working. For every next bionicle they received less money. Findings: 1) Subjects built more lego in the meaningful group than in the sysy group. 2) The difference can be seen as disutility of meaningless work which was 39 cent in this case ==> other way around to get the same output as in the meaningful group you'd have to pay 40 cents more per unit Bottom line: 1) Meaningful work can lead to workers being more productive and work more for less money 2) Employees truly care about what they do not only cash 3) Meaningfulness can foster intrinsic motivation

Meaningfulness study 2008

1) experimental methods 2) Regression analysis Experiment Example: randomized controlled trial (RCT) In an RCT a new HRM policy wouldn't be introduced in all locations but only in some at the same time. ==> Divide the pool of workers or locations randomly into 2 groups 1 gets the treatment while 1 is a control group without treatment Randomization ensures that others effects which mich affect performance like weather, business conditions, changing technologies are roughly on average the same RCT's also allow to compare more than just 2 different methodes

Methods to isolate causal effects - RCT

2 workers compete and the one with the better performance gets promoted. They both produce output Q which is dependant on effort and luck. If both outputs are observable and verifiable they could be paid via an individual piece rate Alternatively they could be could run a tournament where both get a base pay (a) and the winner a prize (S) The player wins if his relative effort outweighs the other players luck

Model of a tournament

1) Stiffer fines: Imposing a fine on shirking. Denote the highest possible fine F* (which would be getting fired). F is seen as a transfer for worker to firm. 2) Monitoring workers more closely to make sure the really work. This comes at the cost c(p) ==> If the workers are risk neutral they will refrain from shirking under the following no shirking condition: Benefit (B) <= p*F Assumption: preventing shirking is socially beneficial G - B > C(p*) The gain from prevention is bigger than the cost

Monitoring - deter shirking

Factory in China that produced simple goods (GPS, alarm clock) ==> Effect of introducing cash incentives for extra output Findings: 50% increase in the numbers of units produced 97% increase of defect rate ==> dysfunctional incentives ==> shift from quality to quantity

Multi Tasking - Hong(2013)

If the principle wants the agent to engage in both tasks he need to balance the incentives b1 = b2 (perfectly balanced if they're perfect substitutes. If they're not perfect substitutes they still need to be balanced, just not perfectly anymore If one task can only be measured with a lot of noise ==> low incentive intensity to keep the risk low, b.c the agent would want to be compensated for the risk he has to take Extreme case: No incentives at all if the risk is to high (b*=0) if b=0 for all tasks they all have the same incentives

Multi Tasking - Piece rates in different cases

1) Non reward tasks will be neglected 2) Incomplete incentives ==> Incentives that apply to some but not all tasks performed by an agent that the principle cares about 3) Complements: One task is strongly preferred over the other Substitutes: Indifferent between both tasks 4) If tasks are substitutes the agent will perform mainly tasks with high financial incentives 5) The biggest effect on efficiency: If two tasks are complements(both important) for the principle and substitutes for the agent the effect of different incentives on efficiency is biggest.

Multi Tasking - Summary

2011-15 Gr8 Eight initiative - selling 8 financial products to each costumer ==> pressure findings: Workers opened 1.5 mil deposit accounts without asking costumers 0.5 mil credit card applications without asking Used ATM cards without asking ==> Illegal activity resulted in share price loss, penalties, fired workers Again: Wrong incentives shifted the workers focus from dimensions like honesty and quality to quantity

Multi Tasking - Wells Fargo

If the agent has multiple tasks of which some are easier to measure performance than others, there's a problem. Example: 2 Dimensions; quality and quantity. quantity is easier to measure while quality is harder ==> If the agent focuses only on quantity because he gets paid for the measurable part the quality falls. In general ==> The agent will focus on the task with the higher marginal utility Assumption V(E1) = V(E2) ==> Then the marginal utility is only dependant on the relative size of b1 and b2

Multi tasking problem

If the nor random experiment is analyzed with linear regression there's the omitted variable bias because the store type wasn't taken into account. In a multiple regression the store type(take out vs restaurant) can be taken into account. If the store type is held constant there is no bias. Multiple Regression would look like this: S = a + b*t+c*E+eps a = Result of non treated store b= Within group effect of a treated store c= Effect of the store type

Multiple Regression - Pizza Hat Example

1) a loss of flexibility ==> adjustment for unforeseen productivity shocks or effort cost shock like illness isn't as efficient 2) More risk to the workers through the contract ==> can be solved though higher basepay and rewarding other observable inputs 3) Self-control problems might be best adressed though the employer rather than by workers themself.

Negative effects of nonlinear contracts (present bias related)

The wage payment can't be conditioned on effort, only on output The agent once again max. his utility ==> b - V'(E) = 0 assuming V(E) = E^2/2 ==> E* = b Same solution as in no risk case: Because the risk cannot be affected by choosing E. Risk only depends on b & Var(epsilon)

Non contingent solution - second best

If the luck(epsilon) component isn't observable it isn't possible to make a contract which depends on the state of nature If epsilon = +-k/2 we get an income gap of b*k ==> The gap gets bigger the higher the piece rate ==> more volatility in the agents income

Non-contingent contracts

1) a = U(alt) - b^2/2 2) b* = 1 regardless of how well of we want the agent to be it's always profit maximizing to give all gain from effort to the agent. Compared to a=0, the profit stays the same, but the utility of the agent is higher than before

Optimal Contract if =/= 0

In a socially efficient arrangement workers will never get B, never pay F, always receive Y and always expend effort E* Total Welfare: Q(E*) - V(E*) - C(p) Optimal contract: Pick the highest possible F* and therefore the smallest cost of monitoring In this contract shirkers will rarely get caught but if they do it's costly. Even though there are two ways to prevent shirking the firm should not use monitoring but only really high fines.

Optimal Monitoring - What should firms focus on?

Assuming V(E) = E^2/2 ==> E* = alpha*d*S 1) the bigger alpha, the smaller the luck component and the more precise the measurement the bigger E* is 2) the bigger productivity the bigger E* 3) the bigger the prize-spread "S" the bigger E* ==> a low alpha can always be compensated by a higher S ==> For uniform distributions one agents E* is independent from the effort of the other agent ==> for other distributions E* depends on the others effort too, meaning we need to find the nash equilibrium

Optimal effort in a tournament - uniform distribution

Principle is by assumption risk neutral ==> r=0 Utility = d*E - (a+b*E) Utility = Expected profit - wage payment

Optimal non contigent contract - principals utility

a + b*E = Expected Income 0.5*r*b^2* Var(epsilon) = Cost of risk V(E) = cost of effort Utility = a + b*E - 0.5*r*b^2* Var(epsilon) - V(E)

Optimal non contingent contract - Agent's utility

d*E - 0.5*r*b^2*Var(epsilon) - V(E) Once again the expected wage payment which is just a transfer inside the company that doesn't effect the welfare cancels out.

Optimal non contingent contract - Maximizing the sum of principles profit and agents utility

Offerman 2002 - hurting hurts more than helping helps Hot response game : 2 groups of first (principal) and second (agent) movers 1) Principal chooses to be either: 1.1) hurtful subtract 4$ agent, add 11$ to his own purse 1.2) helpful adds 4$ agent, 8$ to his own purse 2) agent chooses to either: 2.1) Reward 9$ to himself, 4$ to the principle 2.2) Punish 9$ to himself, 4$ to the principle 2.3) cool 10$ to himself ==> principle can raise the agents wage by 4 for 3 ==> agent can raise the principles wage by 4 for 1 Rational equilibrium ==> (hurtful ;cool) Reality: often (hurtful; punish) why? 2 different ways to this experiment: - flesh and blood as described above - nature 50/50 dice picked helpful (1,2,3) and hurtful (4,5,6) Findings: 1) agent is in both ways more likely to reward if helped and more likely to punish if hurt 2) Much stronger responses by agents when hurt by flesh and blood than by nature (83% vs 16%) ==> principles intentions mattered for the agents behaviour

Outcome based fairness - study

1) output rises when giving an incentive ==> when a prize was introduced but no peer evaluation was done the average quality and quantity rose 2) when peer evaluation was introduced: ==> general output fell because rational workers anticipated that their work will be undervalued anyway ==> not worth the effort ==> Quality measured by peers also drastically declined

Output interpretation of the sabotage study

Study conducted by Lazear (2000) Convinced CEO to switch fixed wage to piece rate compensation Performance pay plan was introduced in a staggered basis 2 Ways to calculate wage: Old system: hourly rate - 160/day New system: piece rate per windshield 32/shield Break even point: 5 Predictions: 1) Before PPP we expect every worker to do the minimum 2) After PPP we expect high ability to do Q1 3) low ability workers will still do just de minimum Findings: 1) 44% higher productivity under PPP 2) Seasonality made the effect even more significant 3) Half of the effect was due to workers working harder and half was due to high ability workers self selecting into the firm ==> HRM innovations can generate substantial improvements ==> Effects come from both higher motivation of already established workers and self selection of new workers

Performance pay at Safelite

Another study by Gneezy and Rusticini In an experiment participants had to solve tasks and were randomly assigned to different groups. The different groups received different piece rates per correct answer ranging from 0-3. Findings: 1) The group receiving 0 performed better than the group receiving 0.1. This might be due to the fact that the intrinsic motivation of the 0.1 group was killed by the minimalistic incentive. 2) The group performed way better when they received 1 instead of 0 as piece rate. Consistent with the expectations of extrinsic motivation 3) Additional experiment: a principle is assigned to every agent and chooses the piece rate from 0 to 0.1. The majority chose 0.1 and earned less than the ones choosing 0.

Piece Rate study - 2000

1) Tournaments can save monitoring cost ==> Principle might needs to spend monitoring cost to observe quality and quantity of agents output, but it might be quite easy to observe RELATIVE output => ranking. Workers need to be risk neutral for the tournament to work equally good. 2) Noisy performance measures are no problem ==> compensating measure error with higher spread S* 3) Tournaments can explain large salary jumps ==> If a promoted agent gets 50% more salary it's hard to imagine he's 50% more productive. A tournament which has to be won first might explain these salary jumps better. 4) If both workers are exactly the same only luck matters. That's no problem though, cause the tournament does what it was meant to do; inducing efficient levels of work among both agents

Piece rates vs tournaments

Do agents act more strongly on positive or negative reciprocity? ==> Same study by Offerman showed that intentioned based negative reciprocity is much stronger than intention based positive reciprocity. 1) Punished when hurt ==> unintentional 16% vs 83% intentional 2) Rewarded when helped ==> un. 50% vs 75% intentional ==> way bigger delta when hurt

Positive vs negative reciprocity

kaur, kremer and mullainathan 2015 - self control at work Field experiment with a piece rate for solving tasks 4 different contracts ==> 1) linear piece rate (dominates all others!) 2) nonlinear target contract 3) set-your-own target night before 4) set-your-own target morning. ==> The different contracts are there to study if commitment devices such as these contracts would be used voluntarily by workers. Piece rates dominates them all, you needed a certain output to earn the same ==> no other reason than self control to do it Paydays were randomly assigned to tuesday, thursday, saturday to study payday effects. Findings: 1) payday effects 8% increase as random payday approached 2) 36% chose a dominated contract, and even more of the payday effect workers ==> 6% (9%) increase in production, 2% total 3) same result would need an 18% piece rate increase - letting workers chose was for free 4) workers seemed to learn about their self control problems, payday effected workers chose this contract more often

Present bias - study

present bias: disproportionate emphasis on current utility compared to utility in any other future period. It applies only to the present utility discounting: same but it applies to all periods

Present bias vs utility discounting

1) E = b (Agents incentive constraint), Q=E 2) Max. = b - (a + b^2) ==> b - b^2, cause a = 0 3) b* = 0.5 ==> Profit is maximized if b = 0.5, therefore 50% of the profit goes to the agent 4) Principals profit = 0.25 5) Agents utility = 0.125

Principle optimal baseline contract if a=0

We assume d=1 an eps. is uniformly distributed [-5:5] Worker 1 wins if: E1-E2>eps 1) same effort E1=E2 0>eps ==> 50% probability 2) E2 = 0 2.1) E1 = 1 ==> prob 1 > eps = 0.6 2.2) E1 = 5 ==> prob 1>eps = 1 Generally: p(E1,E2) = 0.5 + alpha*d*(E1-E2) a= density function

Probability of winning the 2 player tournament

b* = 1 isn't valid if: 1) Uncertainty with risk-avers agents 2) Multiple tasks which aren't equally good measurable 3) The principle supplies effort too 4) Multiple interacting agents (tournament) 5) Repeated P-A Interactions which lead to punishing/rewarding, reputations, timing gaming 6) Behavorial agents

Problems in the P-A Model b* =/= 1

According to Kahneman and Twersky's prospect theory people evaluate their wellbeing compared to a reference point. Further, a 1$ loss hurts more than a 1$ gain sparks joy. ==> People roughly suffer twice as much from a loss below the reference point than the enjoy a gain above it.

Prospect Theory 79'

Bloom et al. 2014 - Does working from home work CTrip - Chinese company which considered letting some people work from home due to expensive offices, long commuting and tasks were easy to monitor Of 250 workers who qualified for work at home roughly 50% were randomly chosen. The company was mainly interested in calls/week Findings: 1) A lot of week-to-week noise in performance 2) Pre-assignment both groups performed quite similarly 3) Treatment group performed better than control group 13% more productive - same quality Why did WFH increase productivity? 1) Fewer breaks 9.2% more work per shift 2) Fewer sick days - wouldn't have come to office 3) More calls/minute b.c of the quieter workplace 4) More satisfied and less likely to quit 5) 1900$ more profit per employee Negatives: 1) WFH people are less likely to get promoted After the study: 1) More WFH opportunities for workers 2) Self selection into the best fitting environment (In an RCT self-selection effects are precluded)

RCT - Example

New Utility function: U = H(Y) -c*V(E) H(Y) = U - m(R-Y) if R<=Y H(Y) = U + n(Y-R) if R>= Y m>n

Reference Point

1) conflict of interest ==> principle wants more effort, agent more money 2) Equilibrium ==> principle holds 12 sends 0, agent puts in 0 effort 2.1) agent puts in 0 effort because his utility declines with effort 2.2) principle anticipates that an sends nothing 3) if the principle can expect the agent to reciprocate a generous offer with high effort there are better solutions to the game ==> most people choose positive wages when playing the game ==> reciprocity, fairness and trust

Results from the give 0-12 gift exchange game

Risk aversion ==> a person is risk-avers if she prefers a safe payment over a lottery with an equal expectation value. In other words if the utility of the exp. value is higher than the exp. value of the utility Certainty equivalent ==> Is the exact amount that makes a risk-avers person indifferent between choosing the lottery or the fixed amount Risk premium ==> Exp. value - certainty equivalent ==> the amount a decision maker is willing to pay to receive the expectation value of the lottery instead of receiveing the lottery

Risk Aversion, certainty equivalent, risk premium

Agents will lose when helping coworkers or sharing information Agents will gain by sabotaging their coworkers Study by carpenter et al 2010 real effort experiment stuffing envelopes for 30 minutes ==> after the study all the candidates examined each other output, counting letters and rating quality 2 different treatments: 1) piece rates 1$ per envelope 2) fair tournament 1$ per envelope + 25$ bonus 3) tournament with sabotage Findings: 1) Piece rate more generous rating from workers than from the independent post officer 2) fair tournament, where the peer evaluation had no influence on the ranking and the prize, but only the postal workers ==> less generous than the expert 3) sabotage: in the rigged tournament where giving worse ratings to your peers and miscounting gave yourself an advantage the average generosity was much lower compared to the postal worker

Sabotage - study

If the loser doesn't have to leave the firm but rather stay there and continue working in his position the rewards for all groups who stayed there for these 3 stages looks like this: G0= 4*Wo G1= W0+3*W1 G2= W0+W1+2*W2 G3=W0+W1+W2+W3 Reward on every stage: S1= W1-W0= 3(W1-W0) S2=W2-W1 = 2(W2-W1) S3= W3-W2 = W3-W2 The reward schedule that equalized all the inter-rank spreads in total rewards must have an accelerating pattern of raises: W1-W0=S1= 1/3*S3 W2-W1=S2=1/2 * S3 W3-W2=S3 ==> again there must be an even higher jump at the end because of the missing option value

Salary structure in firms after Rosen's structure

1) sequential contests Players choose their effort level sequentially. Players who choose later can observe others. Problem: Intermediate feedback can lower effort if the winner is already decided 2) multi stage contests Overall winner depends on number of contests won. Important example: elimination contest ==> promotion ladders ==> winning a stage offers 2 rewards: 1) the prize for that stage, if any 2) the right to move to the next level (option value)

Sequential contests and multi stage contests

No, just looking at motivation without looking at selection can be misleading. Some people might self-select into such environments. These people will then perform way better than a randomized group would in such an environment.

Should high stakes incentives be avoided?

Welfare = profits - costs of effort W = d*(E1+E2) - E1^2/2-E2^2/2 Socially efficient solution: E=d marginal cost (E) equals marginal revenue (d)

Socially efficient effort levels - two agent tournament

1) U = Y -V(E) 2) U = a +b*Q - V(E), Q=E 3) our assumption to make it easy: U = a + b*E - E^2/2 4) E* = b E* ==> V'(E) = Y' mc = mr

Solution to the agent's maximization problem

If the contracts depends on the state of nature i.E good/bad times, we call it a state-contigent contract For this to work the luck-parameter must be observable ==> Two different pairs of a&b for good and bad times If the agent is risk-avers while the principle is risk-neutral b=1 still counts but we have different base payments (a) ==> a(bad) is higher than a(good) a therefore acts as an insurance for the agent in bad times, it could even be positive in some states

State-Contigent Contracts

Strategy method: The agent has to choose how he'll react to the principles action before knowing what the principle does ==> binding choice Direct response: The principle makes a choice which is then communicated to the agent. The agent then decides what to do.

Strategy Method vs Direct response Method

Linear Regression: Statistical technique for removing confounding effects of a single observable factor in situations where a treatment of interest has been assigned by a non random process. They can give misleading estimates of causal effects because of other omitting variables. Multiple Regression: Here we try to remove multiple observable factors. MR can control multiple confounding factors but only if they can be measured! Relevant factors that are left out can cause biases.

Summary - Regression

Worker is paid for output Y=R(Q). Example: Selling cars 1) smoothed out over months or 2) high volatility over months Concave R(Q) ==> The worker will earn more by smoothing his output over time Convex R(Q) ==> The worker will prefer an uneven or highly variable pattern of output ==> If the incentive scheme is nonlinear (convex or concave) there is an incentive to change the timing of reported or actual performance, known as timing gaming

Timing Gaming

1) Oyer 98' Strong fiscal-year ends effect ==> linked to bonus contracts for managers. 2) Larkin 14' Convex commission scale led to salespeople of software (SAP,Oracle) trying to make as many sales as possible in a certain quarter. Giving discounts to costumers resulted in 6-8% lower revenue for the employer. 3) Owan, Tsuru, Uehara 13' Car dealerships in Canada with nonlinear incentives ==> high jumps in salary at certain points ==> 23% of sales on the last day of the month ==> Discount pricing to game the system, cars with the most profit for the dealer were given with the highest discount ==> mainly sales bunching at the end of the month, no postponing into the next month because of uncertainty

Timing Gaming - Examples

Same prize S*, more players - more/less effort? ==> 2 opposing effects: 1) competition effect: Agent needs to beat more competitors ==> more effort will be needed 2) 1/N effect: it gets less likely to win the more agents compete If luck is uniformly independent distributed these two opposing effects will cancel each other out ==> S* does not necessarily need to be higher in this situation.

Tournaments with multiple players - influence on prize and effort

1) if uniformly distributed luck and risk neutrality there mustn't be more than one prize ==> agents only care about the expected value 2) if agent's are risk averse or have different abilities the prize structure matters 3) there's a possibility to have no discrete prize at all but wage payments depending on relative effort, where every agent is compared to the groups average output.

Tournaments with multiple players - prize structure

Piece rates vs tournaments Piece rate: Any amount of pay is possible ==> higher risk tournament: Either a or a+S as salary ==> less risky because of less volatility Raised risk because everything inbetween can't be achieved Common shocks: If the agent's performance is highly affected by shocks tournaments can be less risky for both agent and principal State-contingent contracts: Would be optimal in the case of high uncertainty ==> this is exactly what tournaments do by rewarding on relative performance because they filter out all common shocks

Tournaments with risk-avers agents

Falk and Kosfeld 2006 - the hidden cost of control 1) Agents get 120$ and can choose effort x from 0-120 that costs them but reward the principle with 2x 2) principle moves first and decides whether or not to impose a minimum effort level on the agent (5,10,20) Predictions: 1) rational agents, zero effort, highest min 2) Outcome based fairness: Agents would solely choose outcome based an wouldn't care about the principles requirement xmin 3) Reciprocity/ Control aversion ==> backfire Findings: 1) Agents gave more money back when there was no minimum 2) There was bunching at 40$ which meant that a lot of agents were inequity averse and tried to smooth payouts 3) When controlled a lot of agents sent only the minimum ==> control aversion confirmed Take away: 1) small minimum is like a small incentive ==> kills intrinsic motivation 2) Trusting often results in better effort 3) if control is hard and the benefit small don't control at all

Trust can pay - study

Ariely et al. 2009 People were split in 3 groups (low/medium/high) which earned different amounts of money for solving tasks with good performance. The experiment was conducted in India and even the low amounts were a lot money for them. They expected to see some choking under pressure in the high amount group. Findings: 1) The group with high incentives did indeed choke under pressure 2) This can be due to the fact that high extrinsic motivation leads to high arousal. Arousal has a an inverted u-shaped effect on performance.

Very large incentives study

Charness and Kuhn 2007 Tested if wage difference in a firm where workers were paid differently would have an influence on workers effort. Findings: No direct influence on effort because of relative wage but the principle were expecting a negativ effect from large wage gaps

Wage different among workers - study 07

Card, Mas, Moretti and Saez 2012 Inequity at work 2 groups of university employees 1) Only Treatment group gets an email about website that shows all salaries of public worker in California 2) Few days later both groups were asked to take part in a survey According to the relative income model learning about your peers wage should increase high-earners utility and decrease low-earners According to the loss aversion model: low earners loss should be bigger than high earners gain from this knowledge According to rational updating model your peers wage shouldn't influence you at all or should make you happy ==> wage could be higher someday Findings: 1) Overall no effect on job-happiness on average 2) Below-median earners in treatment group showed lower satisfaction levels and higher chances of looking for a new job ==> relative income model Critiques: 1) High-earners could be better informed initially 2) Rational explanation possible 3) No results on actual behaviour just what was reported

Wage fairness -study 12'

The principle can't see the agent's effort, therefore he cannot base the contract on effort (Y(E) isn't possible). Y(Q) ==> Agent is paid according to his Output Q

What are incomplete contracts?

1) increases with own effort and decreases with others effort 2) Depends only on relative effort 3) increases the bigger alpha = 1/R is ==> higher precision 4) increases with the workers productivity d

What increases the probability of winning the tournament?

a => base-pay has no influence on effort b => the higher the piece rate, the bigger the optimal effort d => the higher the productivity, the bigger the optimal effort

What influence do the parameters (a,b,d) have on E* of the agent?

Same solution with b = 1 We maximize the Welfare/Social Surplus which consists of the principals profit and the agents utility. W = Q -V(E), because Y doesn't affect welfare it's just a transfer It makes sense to just maximize the total welfare regardless of how we ultimately decide to divide it Baseline solution dividing the welfare: W = 0.5 The agent is willing to work as long as a >= -0.5 The principle if a <= 0

What is the best solution for both the agent and the principle? (Welfare max)

1) Reduction of intrinsic motivation 2) Incomplete contracts: Without a piece rate the contract is seen as a fixed fine for the whole task for example showing up to the lab and doing a test. With a very small piece rate the contract could be seen as a fixed fee for showing up and a piece rate for my work while I'm there. if the rate is really small I don't feel like working hard. ==> financial incentives can destroy intrinsic motivation, but data shows that a big enough incentive can overcompensate the effect ==> incomplete contracts ==> Perception of the task matters a lot, what is expected and owed? ==> Perceptions might be sticky as seen in daycare example

Why do small incentives destroy the performance?

1) The incentives should be put where the decisions are made ==> Agent decides how much effort to put in 2) If b<1 only part of the surplus goes to the agent while he carries 100% of the cost of effort ==> A selfish agent wouldn't participate here

Why is b* = 1 optimal?

1) The base pay cannot be negative==> limited liability 2) The agents effort can only be measured with noise ==> luck plays a role and therefore there are no contingent contracts and the agent is also risk avers

Why is b<1 in the real world?

1) Fines are not net cost to society but rather a transfer. Monitoring cost on the other hand are a net cost to society. 2) Even if penalties are a cost to society if they're severe enough they will never be inflicted. However: A real workplace wouldn't really like this kind of optimal monitoring. People want fairness and punishments that fit the crime.

Why is the optimal monitoring so one-sided? Other aspects

a* = 0.5*ra*b^2*Var(eps)+V(E*(b*))+Ualt-b*E(b) Base pay compensates the agent for 1) risk exposure 2) the cost of effort 3) the forgone outside option, minus the compensation that results from the variable incentive pay The optimal a* can be positive for sufficient high levels of uncertainty

a* in non contingent contracts

In economics, a backward-bending supply curve of labour, or backward-bending labour supply curve, is a graphical device showing a situation in which as real (inflation-corrected) wages increase beyond a certain level, people will substitute leisure (non-paid time) for paid worktime and so higher wages lead to a decrease in the labour supply and so less labour-time being offered for sale.[1] Higher wage should see more work because labor gets relatively more expensive but leisure time is a normal good which gets consumed more when given higher wages.. Which effect is stronger? Studies show that leisure time first gets less than at some wage more again

backward bending labor supply curve

1) equivalence independent of linear production function or quadratic cost of effort function. It also doesn't need a uniform distribution of relative luck. 2) the equivalence does depend on risk-neutrality 3) For every other distribution of luck other than the uniform one the workers will depend der optimal effort E* on what the other worker does

generality of equivalence theorem

fehr, klein and schmidt 07' - fairness and contract design Comparison of 3 different contracts: 1) incentive contract ==> fixed w, e* and fine(F), audited with prob(p), has to pay the fine if his effort falls short of e* - probabilistic 2) trust contract ==> fixed w, e* is expected by the principle but the agent can choose any effort e - GEG contract 3) bonus contract ==> fixed wage, desired e* and a bonus if e>e* - quid pro quo GEG contract Expected effort rational agents: zero effort, principal no bonus or zero wage contract ==> tested through two different treatments: 1) principal chooses incentive or trust 2) principal chooses incentive or bonus Findings: 1) Incentive contracts performed better than trust contracts 2) The majority of principals chose bonus contracts and they outperformed incentive contracts on average. ==> unenforceable bonus worked better than enforceable incentive contracts with auditing and fines did Explanation: 1) reciprocity through agents 2) part of pay before and part as bonus helped as incentive 3) why did incentive contracts underperform ==> maybe because they signal distrust

gift exchange game - study

implicit: Not specified in writing but understood by both parties contractible: if a contract can be written and enforced depending on performance it's contractible incomplete: if the agents salary is not linked to every aspect of his performance that the principle cares about it's an incomplete contract ==> GEG is an extreme example of an incomplete contract

implicit, contractible, incomplete contracts

Integrator (large company) hires a group of growers for a certain service (raising chicks) The integrator/principal wants to keep the costs as low as possible. The growers/agents price depends only on relative cost compared to the other agents in the area why is a tournament used here? ==> not for promotion or lower monitoring cost ==> Knoeber 89' argues that it's due to common shock coming from things like different breed, weather and disease outbreaks. Tournaments protect growers from common shocks. ==> using tournaments eliminates about half the variance while keeping incentives intact other advantages of tournaments in this market: ==> positive shocks like technology affects all growers the same ==> Integrator can experiment without posing much risk on agents ==> no temptation for the principle to misrepresent the agents true level of performance

market for broilers example + study

Rosen 86' pairwise elimination tournament 2^n competitors in an n-stage tournament n+1 groups Example with 2^3 competitors an 3 stages Group 0: 4 losers in round 1 with 0 wins ==> W0 Group 1: 2 Losers in round 2 with 1 win ==> W1 Group 2: 1 Loser in round 3 with 2 wins ==> W2 Group 3: 1 Winner in round 3 with 3 wins ==> W3 How should the inter rank prize structure be to guarantee high effort levels i.e S1 (W1-W0)? ==> if all workers are equally able, optimal structure is the same on every level except the last one which is larger because it yields no option value

multi stage contests - study

1) increasing a and b in our model might reduce the supply of effort 2) difference to our simple model: we always assumed that utility is a linear function of income which meant that the agent had a constant marginal utility of income resulting in NO income effects.

neoclassical model of labor

No present bias is modelled as a particular form of non-exponential utility discounting - laibson 97' O'donoghue and rabin 99' Now there's a present bias parameter (beta) ranging from 0-1 and the same discount factor as before - Beta = 1 means no present bias Result t=0: for delta 0.9 and 3 days day 1: beta*0.81, day 2: 0.9 day 3: 1 Result t=1 day 1: beta*0.9, day 2: 1 ==> there is time inconsistency, every new day the worker wants to work less because of the present bias. ==> time inconsistency leads to effects like procrastination and payday effects. Seen in Oyer 98' for salespeople.

preferences WITH present bias - 3 days example

1) preferences with exponential utility discounting - no present bias The further a day lies in the future the bigger the discount factor ==> if he discounts the future his effort will increase daily as he approaches the payday. Example: his discount factor is 0.9 ==> Effort day 1: 0.81; day 2:0.9; day 3: 1 ==> his optimal strategy remains the same, even when coming closer to his payday. he has NO time inconsistency

preferences with NO present bias - 3 days example

What explaines the non zero-effort level from the agent? Mustn't be a kind act by the agent for the high wage. Agent might choose different just out of fairness because they don't like inequity==> outcome-based inequity aversion

reciprocity vs outcome-based preferences

Safelite was baught by Belron. They decided to not just focus on quantity but rather on other dimensions like quality, worker satisfaction, worker safety reputation and so on. ==> The study showed that financial incentives can work ==> The current situation also shows the importance of the multi-tasking-model. Apparently the focus shifted away from quality which led to dem abandoning PPP again.

safelite in 2014

1) The goal is to design performance measures that leave nothing out and measure everything. Examples: Balanced scorecard system or 360 degree feedback. ==> Problem: some tasks like honesty are really hard to measure 2) Reducing strength of incentives: picking b well below 1. This way the agent may lay more focus on non incentivized tasks. This makes sense under the following conditions: -some tasks are really hard to measure -severe effects of effort misallocation -agents have high levels of intrinsic motivation -input-based employment contracts ==> pay four hours at workplace 3) Job Design - Grouping tasks in different jobs easy-to-observe jobs ==> strong financial incentives, screening not as important and high discretion hard-to-observe jobs ==> weak financial incentives, careful screening for high intrinsic motivation and giving less discretion about work hours for employees

Designing efficient contracts