Compensating Wage Differentials

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# Compensating Wage Differentials
## EC 350: Labor Economics
### <a href="https://kyleraze.com">Kyle Raze</a>
### Winter 2022

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# Jardim et al. (2017)

## **Discussion about the** [**Seattle minimum wage study**](https://evans.uw.edu/faculty-research/research-projects-and-initiatives/the-minimum-wage-study/)

**Q.sub[1]:** What data did the authors bring to bear? How do these data differ from other studies?

**Q.sub[2]:** How did the authors estimate the impact of Seattle's minimum wage increase?

**Q.sub[3]:** What did the authors find?

**Q.sub[4]:** How do the findings compare to other studies?

**Q.sub[5]:** What are the weaknesses of the study? How might those weaknesses affect the results?

**Q.sub[6]:** What are the policy implications of the study?

**Q.sub[7]:** Did the study make you update your beliefs about the minimum wage? Why or why not?

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# Compensating wage differentials

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# Compensating wage differentials

**Q:** Why are some workers paid more than others?

- Differences in preferences?
- Differences in human capital?
- Discrimination?
- Differences in .pink[working conditions?]

.center[**Even within the same industry, some jobs are riskier than others!**]
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<img src="risky_job.jpg" width="359" style="display: block; margin: auto;" />
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<img src="safe_job.jpg" width="350" style="display: block; margin: auto;" />
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# Compensating wage differentials

**The idea?** Wages can compensate for non-monetary aspects of a job.

> The whole of the advantages and disadvantages of different employment of labour and stock must, in the same neighbourhood, be either perfectly equal or continually tending to equality. .right[&mdash; [Adam Smith](https://en.wikipedia.org/wiki/Adam_Smith)]

**Examples?**

- Hazard pay for grocery store workers during the pandemic
- Wage premium for risky jobs (*e.g.,* [*Deadliest Catch*](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1807236))
- Wage penalty for fun/fulfilling occupations (*e.g.,* art, music, ["lifestyle PhDs"](http://noahpinionblog.blogspot.com/2013/05/if-you-get-phd-get-economics-phd.html#:~:text=1.,sitting%20and%20thinking%20about%20stuff.), *etc.*)

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# Market for risky jobs

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## .hi-pink[Supply]

.pink[Workers] care about wages `$w$` and the risk of injury `$\rho$`: `$$U = f(w, \rho)$$`

- Workers are risk averse.
    - Wages are a "good:" `$U$` increases with `$w$`.
    - Injury risk is a "bad:" `$U$` decreases with `$\rho$`.
- An employer would need to pay a **wage premium** to convince a worker to take a **riskier job**.

]
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# Market for risky jobs

.pull-left[
## .hi-pink[Supply]

.pink[Workers] care about wages `$w$` and the risk of injury `$\rho$`: `$$U = f(w, \rho)$$`

]
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## .hi-purple[Demand]

.purple[Employers] care about profit, which depends on compensation bundles of wages `$w$` and injury risk `$\rho$`.

- Both wages and safe working conditions are costly.
    - To **increase wages** and keep the same profit, an employer would need to **cut back on safety** initiatives.
    - To **reduce injury risk** and keep the same profit, an employer would need to **cut wages**.

]

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# Risk preferences

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]
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An **indifference curve** shows all of the wage-risk bundles that yield the same utility.

1. **Upward sloping:** Additional risk requires additional pay to keep the same utility.
2. **Convex** 
3. Wage-risk bundles on **higher indifference curves** yield **higher utility**.

]

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# Risk preferences

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**Different workers** can have **different risk preferences**.

- Some workers dislike injury risk more than others.
    - Workers with steeper indifference curves are more risk-averse.
    - Workers with flatter indifference curves are less risk-averse.

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# Profit

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]
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An **iso-profit curve** shows all of the wage-risk bundles that yield the same profit.

1. **Upward sloping:** Safety and wages are costly.
    - To keep the same profit, increasing one requires reducing the other.
2. **Concave:** Diminishing returns to safety lead to increasing marginal cost of risk abatement.
3. Wage-risk bundles on **higher iso-profit curves** yield **lower profit**.

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# Equilibrium

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In equilibrium, workers **match** with employers.

- Most risk-averse worker .mono[<->] safest employer
- Least risk-averse worker .mono[<->] riskiest employer

The **Hedonic wage function** describes the relationship between wages and job characteristics (*e.g.,* injury risk).

- Upward sloping for "disamenities."
- Downward sloping for amenities (*e.g.,* generosity of health insurance plan).

]

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# Safety regulation

**Case 1:** Workers fully aware of workplace hazards.

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# Safety regulation

**Case 2:** Workers misinformed about workplace hazards.

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# Value of a statistical life

**Q:** How much money are workers willing to give up in exchange for a marginal reduction in fatality risk?

- **Q:** Or, how much money would workers willingly accept in exchange for a marginal increase in fatality risk?

Other things being equal, **riskier occupations tend to pay more** than safer occupations.

- **Example:** Employer Y has a riskier work environment than Employer X, but workers at Y willingly accept this added risk because they are paid a compensating differential of $7,600 per year.

| Employer | Probability of fatal injury | Annual wage earnings |
|:--------:|:---------------------------:|:-------------------------------------------:|
| X | *&rho;*.sub[X] | *w*X |
| Y | *&rho;*.sub[X] .mono[+] 0.001 | *w*.sub[X] .mono[+] $7,600 |

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# Value of a statistical life

The **value of a statistical life**.super[.hi-pink[&#8224;]] (VSL) describes the strength of the relationship between fatality risk and wages.

.footnote[.super[.hi-pink[&#8224;]] A prime example of how *not* to brand a useful concept.]

- The **hypothetical amount of money** a person would accept to increase their probability of death from 0 to 1.
- Despite its dismal name, VSL is estimated from observed **responses to small changes** in fatality risk.

**How is this useful?** Helps governments weigh the tradeoffs of safety regulations and environmental policies.

- Safety regulations can save lives (benefit) in exchange for reduced economic activity (cost).
- Easy to ignore benefits when they aren't directly comparable to the costs!

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# Value of a statistical life

## **Estimation**

Using data on wages and fatality risk for different occupations, a researcher can estimate a **Hedonic regression:** `$$\text{Wage}_i = \alpha + \beta~\text{Risk}_i + \text{other variables} + \varepsilon_i$$`

- `$\text{Wage}_i$` represents the annual wage for occupation `$i$`.
- `$\text{Risk}_i$` represents the annual probability of death in occupation `$i$`.
- `$\beta$` represents the value of a statistical life..super[.hi-pink[&#8224;]]

.footnote[.super[.hi-pink[&#8224;]] Previously published VSL estimates range from 1 to 12 million dollars. The Environmental Protection Agency uses a VSL of $10 million for cost-benefit analysis.]

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# Value of a statistical life

## **Discussion**

`$$\text{Wage}_i = \alpha + \beta~\text{Risk}_i + \text{other variables} + \varepsilon_i$$`

**Q.sub[1]:** Estimates of `$\beta$` are often *negative* when researchers fail to include "other variables." Why?

**Q.sub[2]:** What "other variables" should a researcher include to isolate the causal effect of risk on wages?

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# Housekeeping

**Assigned reading for Wednesday:** [The effect of human capital on earnings: Evidence from a reform at Colombia's top university](https://www.sciencedirect.com/science/article/abs/pii/S0047272717301809) by Carolina Arteaga (2018).

- Reading Quiz 8 is due by **Wednesday, February 23rd at 12:00pm (noon)**.
- The quiz instructions will include a reading guide.

**Problem Set 3** is due by **Friday, February 25th at 11:59pm**.