Accounting for Growth: Human capital and education

A couple of weeks ago, I wrote about how the growth rate of per capita Gross Domestic Product (GDP) can be broken down into the shares that come from growth in human capital, physical capital, or Total Factor Productivity using a technique called “growth accounting.” That is what I do for the fifty states for the period 2008 to 2023 in our new report, “Accounting for Growth: Measuring the sources of per capita economic growth at the state level.” This matters because:

Determining how a country or state is performing with regard to these sources is vital for identifying policies that will boost real per capita GDP growth. Policies that increase employment or skills raise human capital; policies that stimulate increased capital investment elevate the amount of physical capital; and policies that spur increased innovation and entrepreneurship catalyze TFP growth.

Calculating human capital

The first step in this exercise is to construct estimates of human capital in each state. For this, I used — and slightly adapted — the method economist Dietrich Vollrath uses in his book Fully Grown: Why a Stagnant Economy is a Sign of Success. Simply put, I use the following equation:

H = E x hours x hEduc x hExp

which takes the number of people employed in a state (E, which comes from the Bureau of Labor Statistics going back to 1976) and multiplies it by the average hours each worker in a state works annually (hours, which also comes from the BLS going back to 2007) and multiplies that by the average level of skill each worker possesses arising from education (hEduc, which is constructed using Census Bureau data going back to 2008) and then multiplies that by the average level of skill each worker possesses arising from experience (hExp, which is constructed using BLS data going back to 1999). That gives you the total stock of human capital in a state in a given year (H) which you then divide by the total population (N) to get a per capita human capital number (h), since it is changes in per capita GDP which we are investigating.

Broadly speaking, E and hours together give you a measure of the “raw” labor provided in a state and hEduc and hExp give you a measure of the quality of that labor. Today I’ll look at the human capital arising from education.

Human capital from skills: Education

The first step in analyzing the contribution of the human capital — or skills — arising from education to the growth of human capital overall or GDP is to quantify them. This isn’t as easy as it is with the “raw” labor components, where you just download the data.

Following Vollrath’s method, we construct a measure of the skills arising arising from education by dividing the workforce into groups based on educational attainment. We award each group points. The we multiply the points by the number of people in each group to get the total per group. Then we sum the totals for these groups to get the total stock of human capital arising from education in a state. Finally, we divided this total stock by the population to get a per capita number.

As it is the growth rate of GDP per capita we are interested in, we’ll start with the growth rate of skills per capita arising from education (hEduc) in each state. As Figure 1 shows, over the period from 2008 to 2023, the growth in skills per capita arising from education in Minnesota came in at an average annual rate of 0.2%, which ranked a middling 26th among the fifty states.

Figure 1: Average annual growth rate of human capital arising from education (hEduc), 2008 to 2023

We can dig a little further. The rate of growth of human capital arising from skills per capita is the sum of the growth rate of employment (E) plus the growth of human capital arising from skills per worker (hPW) minus the rate of growth of the population (N).

Table 1 shows this break down of the rates seen in Figure 1. We see, for example, that the growth rates of employment and population in Minnesota from 2008 to 2023 netted each other off so that the entire growth of human capital arising from skills per capita came from an increase in the skills per worker. Illinois, for comparison, saw flat employment growth but the skills arising from education of each worker growing by 0.2% annually, on average. With population falling by an average of -0.1% a year, this, paradoxically perhaps, boosted the average level of skills arising from education per capita by an average of 0.3% annually.

Table 1: Growth accounting of human capital arising from education, 2008-2023

But remember what we saw a couple of weeks ago: That, relative to the United States’ average, Minnesota saw a slowdown of per capita GDP growth from 2014 onwards. What do we see if we break the period 2008-2023 into two subperiods, 2008-2014 and 2014-2023?

Figure 2 shows that the average growth rate of skills per capita arising from education in Minnesota was much steadier between the two subperiods than most other states. But while Minnesota’s growth rate of 0.1% compared to an average annual decline across the fifty states of -0.5% in 2008-2014 and ranked third, its 0.2% growth rate compared less favorably to an average of 0.6% in 2014-2023 and ranked 42nd. To some extent, Minnesota’s relative decline on this ranking is a result of superior performance in the period 2008-2014.

Figure 2: Average annual growth rate of total employment (hEduc)

How can we explain these changes? As noted, our measure of the skills arising from education is based on assigning scores to members of the labor force based on their educational attainment. It follows that if the composition of the labor force changes with regard to educational attainment, so will the average level of skills, on either a per capita or per worker basis.

Figure 3 illustrates this. We see that Minnesota did not do particularly well in increasing the share of its labor force with at least some college between 2008 and 2023. But this is, in large part, because such a high percentage of Minnesota’s workers were already educated to that level at the start of our period in 2008, 73.7%, the fourth highest ranking out of the fifty states. Even with Kentucky’s impressive growth on this measure — 8.1 percentage points from 2008 to 2023, the second best out of fifty states — it has still only seen its ranking rise from 47th to 44th. Minnesota, meanwhile, with its lower rate of growth, has bumped up to a ranking of third, as Figure 4 shows, with 78.0% of its workforce having at least some college education.

Figure 3: Change in share of labor force with at least some college, percentage points

Figure 4: Share of labor force with at least some college, 2023

There are two things to note here.

First, as we look at the components of human capital to see how we might stimulate faster per capita GDP growth, this is a source that is close to tapped out. With our workforce so highly educated, there is not the scope for driving faster per capita GDP growth by educating our workforce further than there is in, say, West Virginia. As with employment last week, we must look elsewhere, and for the same reason.

Second, a caveat. Given our method for measuring the human capital arising from skills, it follows that there is a limit to the growth we can record here. Once every worker has a PhD, say, no more growth would be possible in either per capita or per worker terms. While this might not matter much over a fifteen year span, over a longer span it would. A worker with a degree in physics gained in 1923 would probably have less knowledge than a worker with a degree in physics gained in 2023, such have been the advances in knowledge over that time. Our method, however, does not capture that. As we work to push our estimates back in time, we will have to find a way to account for this.