📈 economics

Self-Employment as a Signal: Career Concerns with Hidden Firm Performance

This paper models a stationary labor market where risk-averse workers with private talent choose between self-employment, which generates public performance records, and firm employment, which hides performance, demonstrating that a unique equilibrium exists where occupational choices follow a talent cutoff and firm wages are discounted to reflect the adverse selection of lower-talent applicants relative to the self-employed.

Original authors: Georgy Lukyanov, Konstantin Popov, Shubh Lashkery

Published 2026-07-17

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CC BY 4.0

Original authors: Georgy Lukyanov, Konstantin Popov, Shubh Lashkery

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where your resume isn't just a list of jobs, but a living, breathing scoreboard that updates every time you take a risk. This is the playground of labour economics, a field that studies how people find work and how companies decide who to hire. At the heart of this paper's story are two big ideas: signalling and career concerns. Think of signalling like a musician playing a song in a busy park; the music is a public signal that says, "I'm good!" to anyone listening. Career concerns are the worry that if you don't keep playing, people will forget you, or if you play badly, they'll remember that forever. Everyone wants to look good to get a better job later, but sometimes, showing off your skills is scary because if you fail, the whole world sees it. This paper asks a fascinating question: What happens when you have to choose between playing a risky solo show where the crowd sees every note, or taking a steady, safe gig in a quiet room where nobody knows how well you actually played?

The authors, Georgy Lukyanov, Konstantin Popov, and Shubh Lashkery, dive into this dilemma using a mathematical model that acts like a giant, invisible simulation of a job market. They imagine a world where workers have a hidden "talent level" that only they know. Every worker faces a choice: become a self-employed adventurer or take a firm job. The adventurer gets to produce a public result—a win or a loss—that everyone can see. This result gets added to their permanent record, like a badge of honor or a scar. The firm worker, however, gets a steady paycheck, but their performance stays hidden inside the company walls. Their public record doesn't change; it just sits there, frozen in time.

Here is the tricky part the paper solves: The public record is a bit of a mystery box. If you see a worker with a record of "5 wins and 2 losses," you don't know if they are a genius who just got unlucky, or a mediocre worker who got lucky. But the paper reveals that the record is even more complex because it includes people who chose to stop playing the game. Some workers with great records might have stopped taking risks and went to work in a firm, hiding their true skills. So, the group of people applying for a firm job at any given record isn't a random mix; it's a carefully selected crowd.

The paper finds that when the future isn't too far away (a condition the authors call a "short horizon"), a very neat pattern emerges. It's like a talent cutoff line. At any specific record, there is a specific talent level that acts as a divider. Workers with talent above that line decide to keep playing the risky game of self-employment because they are confident they will win more often than they lose. Workers with talent below that line decide to quit the public stage and take the safe firm job.

This leads to a surprising discovery about wages. When a company hires from this specific group of applicants (those who chose the safe job), they are paying a wage that is lower than the average talent of everyone who holds that same record. Why? Because the "stars" (the high-talent workers) stayed behind to keep making public wins, leaving the "average" and "below-average" workers to apply for the firm job. The paper proves that this wage discount is exactly equal to the number of people who stayed self-employed multiplied by the gap in talent between the stayers and the leavers.

Furthermore, the paper shows that once a worker decides to take the safe, opaque firm job, they tend to stay there. Because their record doesn't change while they are in the firm, and the wage stays the same, they have no reason to suddenly decide to go back out and take risks. It's like stepping into a quiet room and deciding to stay there until you leave the building entirely.

The authors are very careful to say that this is a theoretical model, a "proof of concept" that shows how these choices could work in a steady state. They don't claim to have measured real-world wages or simulated a specific country's economy. Instead, they have built a logical machine that demonstrates: if workers choose between public risk and private safety, the market will naturally sort them by talent, creating a predictable gap between what applicants earn and what the "hidden" average talent of that group actually is. The paper suggests that if we look at real-world data—like online freelancers with public ratings versus office workers with hidden performance reviews—we should see this exact pattern: the people applying for the safe jobs will, on average, perform worse later on than the ones who kept playing the public game, and their wages will reflect that hidden selection.

Technical Summary: Self-Employment as a Signal

Problem and Motivation
This paper investigates a stationary labor market where risk-averse workers possess private information regarding their permanent talent ( $\theta$ ) and must choose between two distinct occupational paths: risky self-employment and firm employment. Self-employment generates portable, public outcomes (successes or failures) that update the worker's public record but expose the worker to output risk. Conversely, firm employment offers a stable, competitive wage but keeps individual performance opaque, leaving the worker's public record unchanged.

The central theoretical challenge addressed is the endogeneity of the public record. A worker's public record (a history of successes and failures) is not merely an exogenous sequence of outcomes; it is the result of a complex selection process involving:

Entry and Survival: New entrants and survivors from previous periods.
Occupational Choice: The decision to generate a new public outcome (self-employment) or retain the current record (firm employment).
Application Selection: Firms hire only from the subset of workers who apply, creating a second layer of selection on top of the population holding a specific record.

Standard models often treat observed outcomes as exogenous or price all record holders uniformly. This paper argues that such approaches miss critical selection effects: the population at a specific record depends on every occupational path leading to it, and the applicant pool is further conditioned on the decision to seek opaque employment.

Methodology and Model Structure
The authors construct a stationary sequential competitive equilibrium model with the following key components:

Environment: Time is discrete. Workers have a fixed, privately known talent $\theta \in [0,1]$ . New entrants draw talent from a distribution $F_0$ . Workers survive with probability $\rho$ and discount future utility by $\delta$ . The effective continuation factor is $\gamma = \delta\rho$ .
Public Record: The state $s = (g, b)$ represents the count of public successes ( $g$ ) and failures ( $b$ ) generated via self-employment. Firm employment produces no public signal, so the record remains static during such spells.
Belief Formation: The model explicitly tracks the stationary type–record distribution $m_s(\theta)$ $m_{s} (θ)$ . This density is derived recursively from inflow equations (entrants and transitions from predecessor records) and retention decisions (workers staying at $s$ $s$ via firm employment).
- Public Belief ( $G_s$ ): The market's belief about a worker's talent given they hold record $s$ , derived from $m_s(\theta)$ .
- Applicant Belief ( $\nu_s$ ): The market's belief about a worker's talent given they hold record $s$ and apply for firm employment. This conditions $m_s(\theta)$ on the decision rule $\sigma_s(\theta) = 0$ (choosing firm employment).
Wage Setting: Firms are risk-neutral and competitive. The wage $w_s$ for applicants at record $s$ is set to the expected talent of the applicant pool: $w_s = \int \theta \nu_s(d\theta)$ .
Worker Optimization: Workers maximize expected discounted utility, choosing between the utility of the firm wage $u(w_s)$ and the expected value of self-employment, which depends on current output and future continuation values.

Key Assumptions

Assumption 1 (Short Horizon): The effective continuation factor satisfies $\gamma < 1/2$ . This condition is sufficient to ensure that the value of self-employment is strictly increasing in talent, preventing complex non-monotonicities in the value function.
Stationarity: Strategies, wages, and distributions are stationary.
Fixed Talent: Workers know their talent; there is no private learning about $\theta$ in the baseline model.

Main Results

Existence and Cutoff Structure:
Under Assumption 1, a stationary sequential competitive equilibrium exists. Crucially, occupational choice follows a talent cutoff at every record $s$ . There exists a threshold $c_s \in [0,1]$ such that:
- Workers with $\theta < c_s$ strictly prefer firm employment.
- Workers with $\theta > c_s$ strictly prefer self-employment.
- Mixing occurs only at the indifference point (which has zero mass).
  This result holds without assuming that a success always yields a higher continuation value than a failure; the cutoff structure emerges from the endogenous selection mechanism.
Persistence of Firm Employment:
If a worker of type $\theta$ strictly prefers firm employment at record $s$ (i.e., $\theta < c_s$ ), they will continue to choose firm employment in all subsequent periods, conditional on survival. Because firm employment does not alter the public record or the stationary wage, the worker faces the same decision problem repeatedly. Thus, opaque employment spells are absorbing for strictly preferred types and follow a geometric duration distribution.
Within-Record Selection and Wage Discounts:
At any record where both occupations are chosen ( $D_s > 0$ and $R_s > 0$ ):
- Positive Selection into Self-Employment: Higher-talent workers ( $\theta > c_s$ ) select into self-employment, while lower-talent workers ( $\theta < c_s$ ) apply to firms.
- Applicant Wage Discount: The competitive wage $w_s$ is strictly below the mean talent of the entire population holding record $s$ ( $\bar{\theta}_s$ ).
- Decomposition: The wage discount ( $\bar{\theta}_s - w_s$ ) decomposes exactly into the share of workers remaining self-employed ( $R_s/M_s$ ) multiplied by the talent gap between self-employed workers and applicants ( $p^S_s - w_s$ ).
Limitations on Global Comparisons:
The model yields robust within-record predictions but does not impose a global ordering of wages or cutoffs across different records. A longer record (more $g+b$ ) does not necessarily imply higher wages or higher talent, as the composition of the record depends on the specific history of occupational choices leading to it.

Significance and Contributions
The paper's primary contribution is the construction of public and applicant beliefs from the endogenous stationary flow of workers through records. By explicitly modeling how the population at a record is formed by both new entrants and workers who retained the record via opaque employment, the authors demonstrate that:

Selection is Dual-Layered: Beliefs must first aggregate all paths leading to a record (including retention) and then condition on the current application decision.
Cutoff Behavior without Ordering: It is possible to establish a simple talent-cutoff equilibrium without assuming that successes strictly dominate failures in terms of future value, a common requirement in other reputation models.
Empirical Implications: The model generates testable, within-record restrictions:
1. Conditional on the same public record, applicants for opaque employment will exhibit lower subsequent performance than those who remain in self-employment.
2. Applicant wages will display a specific discount relative to the mean talent of the record-holding population.
3. Opaque employment spells will persist for workers who strictly prefer them, rather than being transient.

The authors maintain a modest scope, noting that these results rely on fixed talent, hidden firm performance, and stationarity. Extensions involving private learning, observable age, in-firm signals, or hidden effort would require reconstructing the state space and equilibrium conditions, potentially altering the persistence and selection results. The paper does not claim to determine whether the market produces too much or too little information, but rather characterizes the equilibrium outcomes given the choice structure.

Technical Summary: Self-Employment as a Signal

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