First impression is something everyone cares about . In certain cases, first impression is critical, so much so that it is the deciding factor in things such as getting a new job, or getting a promotion or even attracting our crush, But first impression may not always be everything. Over a longer period, our well-kept flaws may no longer be a secret — in this case, our perfect first impression could even work against us, as high expectations heaped on us burst into disillusionment.
In reality, things are even more complicated: our bosses, or crushes would also anticipate our attempt to impress them. Like a feedback loop, this in turn will also distort our behavior, which then affect their behavior, which then affect our behavior and so on.
This short blog, inspired by the comic above (which could be applied to areas other than the academic route) and banter with a colleague, attempts to give a brief, systematic explanation of this dynamics — the dynamics of impressing people. We show for example, how in an initial attempt to impress others, we might be led to “over-work” or become a “try-hard”. Bengt Holmtrom, winner of the 2016 Nobel Prize, Paul Milgrom, and Jean Tirole, the 2014 winner, among others, have made a series of momentous contribution to this field. This field is also known as the contract theory. Contract theory has been applied in various other fields, including labor, industrial organization (eg. banks regulation) and finance.
A. Career concern model: When reputation matters to impress your bosses
A good starting point is the career concern model due to Holmstrom (1999). Let us start with a 2-period model and later extend this model to a multiperiod horizon. We also utilize an office setting, where rewards come in the form of wages, to better illustrate the model. This class of models is also referred to as “signal jamming” models (Tirole at al, 1984), for reasons that will be clear by the end of this section. Below are the 6 basic specifications of the model (for more details, refer to Holmstrom, 1999):
1. Output(t) = Ability + Effort(t) + Noise(t), where t=1,2.
The above means that output produced at time t, depends on our ability, effort at time t, and some noise. For example, when producing a good slide, it depends on our ability, effort and perhaps some luck.
2. Noise(t) is normally distributed with mean 0 and variance 1/Precision(Noise).
3. Everyone shares prior belief about the agent’s Ability. Ability has prior normal distribution with mean Mean(Ability) and variance 1/Precision(Ability).
4. Ability and Noise(1) and Noise(2) are independent.
5. Agent’s instantaneous utility function is: u( Wage(t), Effort(t) ) = Wage(t) – C(Effort(t)),
where u(.) is the agent’s utility, and C(.) is the cost to the agent for exerting effort. But this is a dynamic world, so the agent instead maximizes:
U( Wage, Effort ) = sum_{t=1}^{T} (Discount factor) [Wage(t) – C(Effort(t))],
where (Discount factor) refers to the agent’s discount factor and T is the length of horizon, which is just 2 here. Assume (Discount factor) is less or equal to 1.
The name “signal jamming” makes sense: it arises from the fact that agent might have an interest in working harder in order to improve the perception of the market about his ability. The name “career concerns” originates from the fact that the agent cares about perception: Loosely speaking, in an equilibrium, a higher perception of the market about the Ability of the agent will translate into higher wages for the Agent.
6. Standard assumptions on cost function: c’>0, c”>0, c'(0) = 0 to guarantee a unique interior solution.
B. Sequence of events in career concern model
Below is the information structure:
1. Effort(t) is privately chosen by agent at time t. Meaning that the agent’s boss did not observe the agent’s effort. This is the classic moral hazard problem.
2. Ability, Noise(1) and Noise(2) are initially unknown to everyone, including the agent.
3. Outcome(t) is publicly observed at the end of period t.
Thus, the world can be summarized as
Period 1
1) Boss offers to the agent Wage(1) ;
2) Effort(1) is privately chosen by the agent;
3) Output(1) = Ability + Effort(1) + Noise(1) is realized.
Period 2
1) Boss offered wage Wage_(2)_(Output(1)). Meaning that agent’s wage in period 2 is determined by his output in period 1;
2) Effort(2) is privately chosen by the agent;
3) Output(2) = Ability + Effort(2) + Noise(2) is realized.
C. Interpreting the maximization problem of career concerns model in 2-period
We skipped the derivations in the interest of space and time**. Carrying out the maximization problem, we obtain the first-order condition:
C'(Effort(t)*) = sum_{t=1}^{T} [Discount factor][Precision(Noise)] / [Precision(Ability)+Precision(Noise)]
The interpretations of this equation is straightforward. Comparative statics show that:
1. Effort level is increasing in Precision(Noise). Intuitively, a greater Precision(Noise) implies that there is less variability in the random component of performance. In other words, luck plays less of a role in deciding the outcome This implies that any given increase in performance is more likely to be attributed to ability, so the agent is more tempted to jam the signal by exerting more effort.
2. Effort level is decreasing in Precision(Ability). Intuitively, the lesser Precision(Ability) means that there is more variability in Ability. This again incentivises the agent to give an impression of having high ability by exerting more effort.
3. Effort level is increasing in Discount factor. Intuitively, greater Discount factor means that the agent has a higher level of patience for future rewards. Thus, the agent discounts the future less, and so he exerts more effort because future rewards depend on his historical efforts.
D. Career concerns in multiple periods leads to “over-working” effect
Holmstrom shows that extending T to be sufficiently large, there exist a period X such that Effort(t < X) is greater or equal to Effort (Optimal), which is greater or equal to Effort (t > X).
In other words, workers work too hard when young and not hard enough when old — Acemoglu gives an example of the working hours of assistant professors versus tenured faculty. Importantly and interestingly, these effort levels depend on the horizon (time periods), but not on past realizations.
E. Conclusion
Applying this finding to an office setting, a new hire may have a lot of incentives to “over-work” in the beginning, and scale down his/her effort later over the years. In a romance setting, the pursuer may “over-impress” or become a “try-hard” in the beginning, and later scale down his/her effort. This blog only touches the surface of contract theory — for more insight, below is a list of some important readings in this field.
Footnote
**In sum, the appropriate equilibrium concept is Perfect Bayesian Equilibrium. Also, as the wage contract is dependent on the effort level, and vice versa, the optimal strategies are determined simultaneously. One famous implication of the posterior normal distribution from DeGroot (1970) simplifies the problem.
Links for further reading:
1) Holmstrom 1999 paper
2) Homstrom and Milgrom 1991 paper
3) Gibbons and Murphy 1992 paper
4) Fudenberg and Tirole 1986 on Signal-Jamming
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About the author
Zul-Fadzli is an associate economist at the Monetary Policy Department, Bank Negara Malaysia.
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