class: center, middle, inverse, title-slide # Signaling ## EC 350: Labor Economics ### <a href="https://kyleraze.com">Kyle Raze</a> ### Winter 2022 --- # Signaling **Q:** Why do college graduates earn more than high-school graduates? -- - They learn new skills that increase their productivity? - They separate themselves from people who couldn't make it through college? - Getting through may correlate with productive attributes. -- ### **Asymmetric information** One side of a market often has less information than the other. - In the labor market, employers often have to "take a chance" on new employees—they don't know exactly who is a good fit for a job. - To separate those who would be a good fit for the job from those who wouldn't, employers can 1) rely on **signaling** by potential employees or 2) employ a **screening** test. --- # Education as a signal of ability The **Spence model**.super[.hi-pink[<span>†</span>]] posits that education can help higher-ability workers separate themselves from lower-ability workers when employers cannot directly observe ability. - In contrast to models of human capital, the Spence model assumes that **education has no impact on productivity**. .footnote[.super[.hi-pink[<span>†</span>]] Named after the economist Michael Spence, who developed the model in [Job Market Signaling](https://www.jstor.org/stable/1882010), *The Quarterly Journal of Economics* (1973).] -- **The players?** 1. High-ability workers 2. Low-ability workers 3. Employer - Willing to pay a premium for high-ability workers over low-ability workers. - But...unable to observe worker types. --- # Education as a signal of ability The **Spence model**.super[.hi-pink[<span>†</span>]] posits that education can help higher-ability workers separate themselves from lower-ability workers when employers cannot directly observe ability. - In contrast to models of human capital, the Spence model assumes that **education has no impact on productivity**. .footnote[.super[.hi-pink[<span>†</span>]] Named after the economist Michael Spence, who developed the model in [Job Market Signaling](https://www.jstor.org/stable/1882010), *The Quarterly Journal of Economics* (1973).] **And their objectives?** 1. High-ability workers **want to separate** themselves from low-ability workers. 2. Low-ability workers **want to pool** with high-ability workers. 3. Employer **wants to identify** worker **types**. --- # Spence model ## **Setup** If the employer could observe types, then they would pay a salary that corresponds to each individual's present value of lifetime productivity. | Worker type | Proportion of population | Present value of lifetime productivity | |:-----------:|:------------------------:|:--------------------------------------:| | Low-ability | *q* | $250,000 | | High-ability| 1 .mono[-] *q* | $350,000 | -- Workers know their ability, but the employer doesn't! .mono[-->] **asymmetric information!** --- # Spence model ## **Pooling equilibrium** With asymmetric information, **the employer treats all workers the same**, paying an identical salary that averages the lifetime productivity of both groups: `$$\begin{align} \text{Salary} &= \text{250,000} \times q + \text{350,000} \times (1 - q) \\ &= \text{350,000} - \text{100,000} \times q \end{align}$$` -- - **Low-ability workers are overpaid** and **high-ability workers are underpaid**. - **The employer also suffers** because workers are not necessarily assigned to the appropriate job. -- **Q:** Why can't a high-ability worker just tell the employer that they are highly-able? -- **A:** Because **talk is cheap!** - A low-ability worker can just as easily claim that they are highly-able! --- # Spence model ## **Ability signaling** High-ability workers have an incentive to provide **a credible signal** of their ability to employers. - If employers learn their type, then they get a higher wage. -- Likewise, employers have an incentive to **extract signals** that separate workers by ability. - Knowing worker types allows employers to **avoid mismatches** between workers and jobs. -- **Q:** When is a signal *credible*? -- **A:** When it is sufficiently **costly!** - Costly enough to discourage low-ability workers from pursuing. - Cheap enough for high-ability workers to willingly pursue. --- # Spence model ## **Separating equilibrium** Employers can choose a level of education `\(\bar{e}\)` that separates low-ability types from high-ability types. * Anyone with less education than `\(\bar{e}\)` .mono[-->] low-ability. * Anyone with `\(\bar{e}\)` or more education .mono[-->] high-ability. -- The existence of a separating equilibrium **requires that education is more costly for a low-ability worker** than for a high-ability worker. - Both types face the same tuition rates, book prices, *etc.* - But low-ability types pay more in extra tutoring, re-taking failed classes, additional stress, *etc.* -- Assume that low-ability workers pay $30,000 per year and high-ability workers pay $20,000 per year. --- # Spence model ## **Separating equilibrium** Employers can choose a level of education `\(\bar{e}\)` that separates low-ability types from high-ability types. * Anyone with less education than `\(\bar{e}\)` .mono[-->] low-ability. * Anyone with `\(\bar{e}\)` or more education .mono[-->] high-ability. The low-ability worker **will not obtain** `\(\bar{e}\)` if the low-ability wage exceeds the higher wage minus the cost of education: `$$\begin{align} \text{250,000} &> \text{350,000} - \text{30,000} \times \bar{e} \\ \bar{e} &> 3.33 \end{align}$$` --- # Spence model ## **Separating equilibrium** Employers can choose a level of education `\(\bar{e}\)` that separates low-ability types from high-ability types. * Anyone with less education than `\(\bar{e}\)` .mono[-->] low-ability. * Anyone with `\(\bar{e}\)` or more education .mono[-->] high-ability. The high-ability worker **will obtain** `\(\bar{e}\)` if the high-ability wage minus the cost of education exceeds the low-ability wage: `$$\begin{align} \text{350,000} - \text{20,000} \times \bar{e} &> \text{250,000} \\ \bar{e} &< 5 \end{align}$$` --- # Spence model ## **Separating equilibrium** Employers can choose a level of education `\(\bar{e}\)` that separates low-ability types from high-ability types. * Anyone with less education than `\(\bar{e}\)` .mono[-->] low-ability. * Anyone with `\(\bar{e}\)` or more education .mono[-->] high-ability. In our running example, the employer chooses 3.33 .mono[<] `\(\bar{e}\)` .mono[<] 5, which separates high-ability from low-ability workers. - High-ability workers get `\(\bar{e}\)` years of education and earn a lifetime salary of $350,000. - Low-ability workers get zero years of education and earn a lifetime salary of $250,000. --- # Spence model ## **Implications?** For the **role of education?** -- - Under a pure signaling model, education is nothing more than a **sorting mechanism**. - You professor's job? Make sure A's only go to high-ability students. -- For **economic efficiency?** - On the one hand, **education is "wasteful"** in the sense that it doesn't increase productivity. - On the other hand, **education reduces worker mismatch** caused by asymmetric information. --- # Spence model ## **Implications?** For **you?** -- - Taking difficult classes can set you apart, *even if you don't learn anything*. -- - Not all A's are created equal. -- - Cheap talk on your résumé might not increase your odds of landing a job, at the margin. - You're a *detail-oriented, self-motivated, team player*? Sure. --- # Sheepskin effects The empirical relationship between earnings and years of education **isn't smooth**. - There are significant **"jumps"** in average earnings **where you'd expect them**—12 years, 16 years, *etc.*.super[.hi-pink[<span>1</span>]] - *Holding years of education constant*, workers with a degree earn more than those without a degree, on average..super[.hi-pink[<span>2</span>]] .footnote[.super[.hi-pink[<span>1</span>]] Thomas Hungerford and Gary Solon (1987), [Sheepskin Effects in the Returns to Education](https://www.jstor.org/stable/1937919), *The Review of Economics and Statistics.* <br> .super[.hi-pink[<span>2</span>]] David A. Jaeger and Marianne E. Page (1996), [Degrees Matter: New Evidence on Sheepskin Effects in the Returns to Education](https://www.jstor.org/stable/2109960), *The Review of Economics and Statistics.*] -- That is, the simple act of having obtained that piece of paper—your degree—seems to matter a lot. **Q:** Does this provide evidence for signaling? -- **A:** It's debatable, though the [more-convincing arguments](http://noahpinionblog.blogspot.com/2017/12/sheepskin-effects-signals-without.html) suggest that sheepskin effects are not evidence of pure signaling. --- # Signaling *vs.* human capital ## **Discussion** **Q.sub[1]:** Why do I make you take exams? **Q.sub[2]:** Why do we give gifts? **Q.sub[3]:** What is the purpose of initiation rituals (*e.g.,* to join a gang)? --- # Housekeeping **Problem Set 3** is due by **Monday, February 28th at 11:59pm**. **Assigned reading for Wednesday:** [Are Emily and Greg More Employable Than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination](https://www.aeaweb.org/articles?id=10.1257/0002828042002561) by Marianne Bertrand and Sendhil Mullainathan (2004). - **Reading Quiz 9** is due by **Wednesday, March 2nd at 12pm (noon)**. - The quiz instructions will include a reading guide.