class: center, middle, inverse, title-slide # Human Capital ## EC 350: Labor Economics ### <a href="https://kyleraze.com">Kyle Raze</a> ### Winter 2022 --- # Human Capital ### **What is it?** Human capital is set of **acquired skills and experiences** that a worker brings into the labor market. - **Increases productivity** beyond a worker's innate abilities - Includes basic literacy and numeracy as well as more-advanced skills - Non-transferable - Varies in specificity (*e.g.,* knowing how to code *vs.* knowing how to code in an obscure language) -- ### **Why does it matter?** Human capital is an important source of **economic growth** and **inequality**. - Increasing human capital can improve living standards! - Differences in human capital accumulation generate differences in earnings across workers. --- # "Typical" age-earnings profiles .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-1-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ Earnings increase with experience and eventually decrease with age. ] --- count: false # "Typical" age-earnings profiles .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-2-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ Earnings increase with experience and eventually decrease with age. - **Q:** How does going to college alter this relationship? ] --- count: false # "Typical" age-earnings profiles .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-3-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ Earnings increase with experience and eventually decrease with age. - **Q:** How does going to college alter this relationship? **Q:** What do areas A, B, and C represent? ] --- count: false # "Typical" age-earnings profiles .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-4-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ Earnings increase with experience and eventually decrease with age. - **Q:** How does going to college alter this relationship? **Q:** What do areas A, B, and C represent? - Area A represents the **explicit cost** of college (tuition, books, *etc.*). - Area B represents the **opportunity cost** of college (forgone earnings). - Area C represents the monetary **returns to education**. ] --- # The benefits of education College is costly! - Tuition, books, room and board, forgone earnings, stress, *etc.* -- **Q:** Why did *you* **choose to incur the costs** of going to college? -- - To live the life of the mind? - To increase your earnings potential? - To expand your social network? - To accrue social prestige? - To set yourself apart? - To party? - To find love? -- While education may have consumption value, we will consider schooling decisions **as investments.** --- # Education as investment **Q:** When is it "worth it" to go to college? - **Benefits?** Going to college causes us to **earn more later in life**. - **Costs?** Going to college forces us to **forgo earnings now** (and pay tuition, *etc.*). -- Evaluating this tradeoff requires us to compare dollar amounts spent and received in different time periods. - To do this, we will use the idea of **present value**, which tells us how much an amount of money received in the future is **worth today**. --- # Education as investment ## **Present value** `$$\text{PV} = \dfrac{y}{(1 + r)^t}$$` - `\(y\)` is the dollar amount received `\(t\)` periods in the future. - `\(r\)` is the discount/interest rate. **The idea?** Getting 100 dollars today is worth more today than getting 100 dollars next year. - If you got 100 dollars today, you could invest it and end up with `\(100 \times (1 + r)\)` one year from now! --- # Education as investment ## **Present value** `$$\text{PV} = \dfrac{y}{(1 + r)^t}$$` - `\(y\)` is the dollar amount received `\(t\)` periods in the future. - `\(r\)` is the discount/interest rate. **Q:** If the interest rate is 10 percent, what is the present value of receiving 1,000 dollars two years from now? -- **A:** 826 dollars and 45 cents. `$$\begin{align} \text{PV} &= \dfrac{y}{(1 + r)^t} = \dfrac{1000}{(1 + 0.1)^2} = \dfrac{1000}{1.1^2} = \dfrac{1000}{1.21} = 826.45 \end{align}$$` --- # Education as investment .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-5-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** When is it "worth it" to go to college? **A:** Assuming that your objective is to maximize the present value of your **lifetime earnings**, college is worthwhile when `\(\text{PV}_\text{College} > \text{PV}_\text{HS}\)`. ] --- count: false # Education as investment .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-6-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** When is it "worth it" to go to college? **A:** Assuming that your objective is to maximize the present value of your **lifetime earnings**, college is worthwhile when `\(\text{PV}_\text{College} > \text{PV}_\text{HS}\)`. `$$\begin{align} \small \text{PV}_\text{HS} &= \small w_\text{HS} + \dfrac{w_\text{HS}}{(1 + r)}+ \dfrac{w_\text{HS}}{(1 + r)^2} + \cdots + \dfrac{w_\text{HS}}{(1 + r)^{46}} \end{align}$$` `$$\begin{align} \small \text{PV}_\text{College} = & \small - H - \dfrac{H}{(1 + r)} - \dfrac{H}{(1 + r)^2} - \dfrac{H}{(1 + r)^3} \\ & \small + \small \dfrac{w_\text{College}}{(1 + r)^4} + \dfrac{w_\text{College}}{(1 + r)^5} + \cdots + \dfrac{w_\text{College}}{(1 + r)^{46}} \end{align}$$` ] --- class: clear-slide **Example:** You are deciding whether to go back to school. - You just turned 60, and it would take you 2 years to finish a master's program, which would cost you 10,000 dollars per year. - You currently earn 80,000 dollars per year. With a master's degree, you could earn 83,000. - Regardless of your decision, you are going to retire at 65. **Q:** If your discount rate is 5 percent, will you choose to go back to school? --- class: clear-slide **Example:** You are deciding whether to go back to school. - You just turned 60, and it would take you 2 years to finish a master's program, which would cost you 10,000 dollars per year. - You currently earn 80,000 dollars per year. With a master's degree, you could earn 83,000. - Regardless of your decision, you are going to retire at 65. **Q:** How would the following change your odds of going back to school? - Your discount rate increases? - Your post-master's earnings increase? - Tuition increases? - You plan to postpone your retirement? --- # Returns to education .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-7-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ## .hi-pink[Wage-schooling locus] > The amount of money that employers are willing to pay *a particular worker* at every level of schooling. ] --- count: false # Returns to education .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-8-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ## .hi-pink[Wage-schooling locus] > The amount of money that employers are willing to pay *a particular worker* at every level of schooling. 1. Upward sloping .mono[-->] more school, more money. 2. Slope at a given point .mono[-->] marginal return of an additional year of schooling. 3. Concave .mono[-->] diminishing returns to schooling. ] --- # Returns to education .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-9-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ## .hi-pink[Marginal rate of return] > The percentage increase in earnings from an additional year of schooling: `$$\text{MRR} = \dfrac{\%\Delta w}{\Delta e}$$` ] --- # Schooling decisions ## **The stopping rule** **Q:** How does a worker choose the optimal.super[.hi-pink[<span>†</span>]] amount of schooling? .footnote[.super[.hi-pink[<span>†</span>]] "Optimal" in the sense of maximizing the present value of lifetime earnings.] -- **A:** A worker chooses the optimal amount of schooling `\(e^*\)` where the marginal rate of return equals the discount rate: `$$\text{MRR} = r$$` -- - If `\(\text{MRR} > r\)`, then schooling education would increase the present value of lifetime earnings. - If `\(\text{MRR} < r\)`, then the worker has "gone too far"—she could had a higher present value of lifetime earnings if she had completed less schooling. --- # Schooling decisions .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-10-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ## **The stopping rule** A worker chooses the optimal amount of schooling where the marginal rate of return intersects the discount rate. ] --- # Comparing schooling decisions .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-11-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ## **Differences in discount rates** Higher discount rate .mono[-->] less access to credit or stronger preferences toward immediate payoffs. - Given two individuals with the same ability, the person with a **higher discount rate** will complete **fewer years** of schooling. - In either case, the person with the higher discount rate will earn less money. ] --- count: false # Comparing schooling decisions .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-12-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ## **Differences in discount rates** Higher discount rate .mono[-->] less access to credit or stronger preferences toward immediate payoffs. - Given two individuals with the same ability, the person with a **higher discount rate** will complete **fewer years** of schooling. - In either case, the person with the higher discount rate will earn less money. **Implications for policy?** Expanding educational opportunities to person with the higher discount rate will close the earnings gap! ] --- # Comparing schooling decisions .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-13-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ## **Differences in ability** A .purple[higher-ability individual] "gets more" out of the same amount of schooling than a .pink[lower-ability individual] .mono[-->] higher marginal rate of return. - Given the same discount rate, then the .hi-purple[higher-ability individual] will complete **more schooling** and earn **more money**. ] --- count: false # Comparing schooling decisions .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-14-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ## **Differences in ability** A .purple[higher-ability individual] "gets more" out of the same amount of schooling than a .pink[lower-ability individual] .mono[-->] higher marginal rate of return. - Given the same discount rate, then the .hi-purple[higher-ability individual] will complete **more schooling** and earn **more money**. **Implications for policy?** Closing the schooling gap won't close the earnings gap! ] --- count: false # Comparing schooling decisions .pull-left[ <img src="14-Human_Capital_files/figure-html/unnamed-chunk-15-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ## **Differences in ability** A .purple[higher-ability individual] "gets more" out of the same amount of schooling than a .pink[lower-ability individual] .mono[-->] higher marginal rate of return. - Given the same discount rate, then the .hi-purple[higher-ability individual] will complete **more schooling** and earn **more money**. **Implications for policy?** Closing the schooling gap won't close the earnings gap! **Implications for data analysis?** ] --- # Arteaga (2018) ## **Discussion** **Q.sub[1]:** What is the research question? Why does it matter? **Q.sub[2]:** What is the research design? What are the comparison groups? **Q.sub[3]:** What are the main results? What story do they convey? --- # Housekeeping Problem Set 3 is due by **~~Friday, February 25th~~** **Monday, February 28th at 11:59pm**.