Humankapital Flashcards
What is human capital?
Any individual characteristic that affects productivity and thus wages (and
probably things like working conditions as well)
* We might think in terms of a worker’s production function
* A (very!) simple model would be to say that a worker produces according
to 𝑌 =𝑓 𝑇,𝑒,𝐻 …
* …where 𝑇 is working time (e.g., full or part-time), 𝑒 is the worker’s effort, and 𝐻 is the worker’s human capital
* In this model, we would have 𝑑𝑓/𝑑𝐻 >0: more human capital increases
productivity
Probably Y=𝑓 𝑇,𝑒,𝐻 is too simple though
* Human capital 𝐻 was unidimensional: as if there were only one type of
skill and you either have more or less of it
* More likely, 𝐻 is multidimensional, leading to a model like 𝑌 =
𝑓 𝑇,𝑒,𝐻1,…𝐻𝑛
* 𝑛 different types of human capital
* Example: having a lot of knowledge vs. being good at structuring one’s
work process
Hard and soft skills
Hard skills:
– Knowing how to operate a machine
– Knowing the derivative of 𝑦=𝑥2
– Knowing how to remove a patient’s appendix
Soft skills:
– Communication skills
– Leadership skills
– Problem-solving
– Planning
– Emotional and social skills
What’s the point of Human Capital
Generally, research on human capital relates to how the education system affects the level and distribution of skills:
– To what extent are income differences across countries due to different levels of human capital?
– To what extent are income differences within countries due to different levels of human capital?
– How is human capital affected by education: what are the returns to schooling?
– (How) should the education system be reformed to increase human capital –
particularly in disadvantaged groups?
Non-economic benefits
Examples of non-monetary benefits to the individual:
– The learning process may be enjoyable! (?)
– Satisfaction from having acquired knowledge or skills (example: being ”well read”)
Benefits to society as well? Better democratic processes (governance,
discourse)? Education as a public good?
Human capital formation
The main example of human capital accumulation is formal education in
schools and universities. Also: on-the-job training, learning-by-doing,
autodidacticism…
Research has also shown that human capital is strongly affected by
experiences in childhood and even in utero (before birth) – factors beyond
the individual’s control
Investing in one’s human capital brings about streams of benefits and
(opportunity) costs over time
Studying may…
– Be costly (tuition fees, etc.)
– Lead to foregone earnings during the study period
– Involve effort and other types of psychic costs
On the other hand, studying is likely to lead to higher monetary earnings
in the future! (And also probably to non-monetary benefits.)
Exponential discounting
Assume the individual discounts future costs and
benefits at some fixed discount rate, 𝑟( ”exponential discounting”)
In Ehrenberg & Smith, the discount rate is the market interest rate
More likely, the discount rate reflects the individual’s
degree of impatience as well
* Note: any sequence of 𝐵1,𝐵2,…𝐵𝑇 is possible, including ones where 𝐵𝑡 =0 for some 𝑡
Simplicity exponential discounting
Assume for simplicity that the investment only has a single cost 𝐶 that is
paid now and is thus not discounted
* With exponential discounting, this would be compared with the present
value (i.e., discounted sum) of future benefits
* Thus, the individual makes the investment if
(We could also have a stream of current and future costs, in which case the benefit present value would be compared with the cost present value)
Predictions exponential discounting
Let’s think about what this would imply about people’s behavior!
* Suppose this is the decision to go to university after high school: short-
term costs but long-term benefits
* More likely to do so if benefits are high →students will:
– Be relatively young (longer stream of benefits)
– Be relatively patient (less discounting of future benefits)
– Concentrate in fields with high monetary returns to education: law, medicine, etc, rather than ancient Greek (larger monetary benefits)
– Enjoy studying more than average (larger non-monetary benefits)
Also, more likely to do so if costs 𝐶 are low:
– Lower tuition fees →more students
– Recession →more students (lower monetary opportunity cost)
– Students are disproportionally good at studying (lower psychic costs but also
probably higher benefits from education)
* Much of this seems reasonable, but note that it:
– Assumes people know their own benefits/costs in advance
– May still be consistent with e.g., discrimination (higher costs, lower benefits)
Early life human capital formation
It seems likely that much of a person’s human capital formation happens
during childhood
* This means that investments are primarily determined by the choices of
the parent rather than the child…
When should society spend the most resources trying to help
disadvantaged children? Kindergarten, elementary school, high
school?
* Cunha and Heckman (2007) argue that the ”technology of skill
formation” is such that the earlier, the better. For two reasons:
– Self-productivity: skills acquired early on tend to persist (learning the alphabet,
doing sums)
– Dynamic complementarity: successful early investment increases the payoff of
later investment (reading books, learning algebra)
What is the effect/benefit of more formal education regarding a person’s earnings?
Important because it tells us something (though not everything) about the
effect of interventions in the education system on people’s welfare – like
building more schools in disadvantaged areas
* Note: the question concerns causality: whether more education causes
higher wages, and not just whether the two are correlated
* The question is also empirical: to answer it, we need some sort of
quantitative real-world information ( = data)
Returns to schooling: linear regression
This equation created the data:
Index 𝑖 is for each person (observation)
ln𝑤𝑎𝑔𝑒𝑖 =𝛼+𝛽×𝑠𝑐ℎ𝑜𝑜𝑙𝑖 is a straight line showing the relationship between the log of wages and years of schooling
𝜀𝑖 is a random variable that we assume accounts for the fact that most points in the data will be off the line: we have a ”swarm” of points
When we say that we regress ln𝑤𝑎𝑔𝑒𝑖 on 𝑠𝑐ℎ𝑜𝑜𝑙𝑖, what we mean is just that we (or more likely, a statistics program) does a particular calculation on the data that produces the regression estimates of coefficients 𝛼 and 𝛽 that ”best fit” the data (i.e., it finds the line)
Linear regression “best fitting straight line”
It can be shown that what the regression calculation actually does is to
minimize the sum (across all 526 observations in the data/points in the
figure) of squared vertical distances from the line
The squared distance for observation 𝑖 would be equal to
So why take the square of the distance? Because points below the line would otherwise have negative distances
- Squaring translates the negative distances into positive numbers. We want to minimize all the distances, not just those of points above the line!
The line with the smallest sum of squared distances will ”pass through the middle” of the swarm of data points
Because linear regression minimizes the ”sum of squares”, it is also called ordinary least squares.
But we are not done here
Omitted variable bias
We have found a relationship between years of education and income,
but this relationship is highly unlikely to be causal: it is probably just a
correlation
But the questions we look at assume there is causality: we need to know
what would happen if we change something?
* Why is the relationship we have found not causal?
Omitted variable bias - example
An example: suppose young workers have more education, because
fewer people went to university in previous decades
* But older people have more work experience
* Assume both experience and education lead to higher wages
* Let’s specify a matrix of wage levels to help us think about this!
Now suppose – to illustrate the problem – that ALL workers are either low experience/high education (𝐶) or high experience/low education (𝐵)
* Also, suppose that it happens to be the case that 𝐶 >𝐵, so the high-
education types do have higher wages than the low-education types
* Our relationship would then mostly reflect that difference: 𝐶−𝐵!
Now consider a high school graduate. We want to know what would
happen to that person’s entry wage if they get a university degree: the causal effect of the degree
* Since the person would start out with little experience, in any case, this is a comparison between 𝐴and 𝐶 – but this is not the comparison that our the estimated relationship reflects!!
The problem is that we did not control for work experience: estimate the effect of an education conditional on the level of work experience
* An example of omitted variable bias: failing to control for experience
means that the regression finds the wrong relationship: one that does not reflect causality
* In our case, we confounded the effect of education with the effect of experience, failing to separate one from the other
In general, omitted variable bias arises whenever we have a variable that we do not control for, i.e. include in the regression equation (like work experience)…
* …that is correlated with both the outcome (wages) and our explanatory variable (education)
* If you only learn one idea from econometrics ( = statistics for
economists), make sure it is this one!
Work experience
Luckily, we can control for work experience, because there is a variable for
it in the data. Consider the following regression equation:
Adds two more explanatory variables: work experience and work experience squared, since the effect of experience is probably nonlinear: wages peak at some point
Quite feasible to run this multivariate regression – but since we have four
variables in total, we cannot show the line in a two-dimensional figure
The logic is exactly the same as before: the regression calculation will
estimate coefficients 𝛼,𝛽,𝛾, and 𝛿
The coefficient 𝛽 is again the ”slope” of the line with respect to the schooling variable: percentage effect on wages of one more year of education
Also: under some conditions, 𝛽 can now be interpreted as the effect
conditional on work experience!
This particular regression is so standard that it has a name: the Mincer equation
Can we interpret this estimate as the causal returns to schooling?? No
