Accounting for Growth: Human capital and ‘raw’ labor

Last week, I wrote about how the growth rate of per capita Gross Domestic Product (GDP) can be broken down into the share that comes 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 “raw” labor component of human capital.

Human capital from “raw” labor: Employment

As it is the growth rate of GDP per capita we are interested in, we’ll start with the growth rate of employment (E) in each state.

As Figure 1 shows, over the period from 2008 to 2023, employment growth in Minnesota came in at an average annual rate of 0.6%, which ranked a middling 23rd among the fifty states.

Figure 1: Average annual growth rate of total employment (E), 2008 to 2023

But remember what we saw last week: 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 Minnesota’s average rate of employment growth actually remained steady between the two subperiods, at 0.6% annually. But while this compared to an average rate across the fifty states of 0.1% in 2008-2014 as the economy slowly recovered from the financial crisis and ranked fifth, it was exactly on the average in 2014-2023, as growth picked up, and ranked 29th. So, while the growth rate of employment contributed nothing to any change in the growth rate of per capita GDP, it did contribute something to the declining ranking of that rate and to Minnesota’s relative growth slowdown. To some extent, it is a result of superior performance in the period 2008-2014.

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

Can Minnesota generate a faster growth rate of per capita GDP with a faster growth rate of employment?

The key thing to note here is that it is increasing the share of a given population employed — the employment ratio (E/N) — which matters for increasing per capita GDP growth, not necessarily increasing the population itself. Per capita GDP is calculated simply by dividing total GDP by the population so new workers entering an economy add to the denominator of the equation — population — as well as the numerator, GDP. It follow from this, also, that there is an upper limit to how much more per capita GDP growth can be wrung from increasing the employment ratio: Once you hit 100%, you’re maxed out.

Minnesota is closer than most states to this situation. As Figure 3 shows, our state’s employment ratio stood at 52.5% in 2023, and was the fourth highest out of the fifty states. You might note, as we have before, that Minnesota’s neighbors with their very different economic policies are also up there. Either way, given the relatively high share of our population already in employment, the scope for driving a faster rate of per capita GDP growth with a faster rate of employment growth is probably somewhat limited. The same would not be true of, for example, Mississippi, which would seem to have abundant scope for that.

Figure 3: Employment ratio, 2023

Human capital from “raw” labor: Hours

The other component of “raw” labor is the number of hours each worker works in a year (hours).

It is true that increasing the number of hours each worker works would, ceteris paribus, increase per capita GDP, but we ought to remember that the point of all this is to maximize utility — “a measure of happiness or satisfaction” — not GDP or even GDP per capita, which is a means to that end. The economist George Borjas notes that “the typical person employed in production worked 55 hours per week in 1900, 40 hours in 1940, and just under 34 hours in 2020” and argues that this is because, as wages have risen, the “income effect reduces hours of work” as workers can maintain their level of income while working for fewer hours, allowing them to purchase more leisure time.

Nevertheless, these numbers do enter into our calculations, so they are worth a look. Figure 4 shows that the average annual growth rate of the average number of hours worked in Minnesota held steady over our two subperiods, coming in at 0.0%. Like employment growth, changes in this rate contributed nothing to changes in the growth rate of Minnesota’s per capita GDP because there was no change. Indeed, Minnesota’s ranking actually “improved” here, rising from 27th to 20th, but you might not view this as a good thing from the point of view of utility.

Figure 4: Average annual growth rate of average annual hours worked

Nobody likes longer hours, but if Minnesotans are working exceptionally few, then it might be worth considering. Figure 5 shows that this is not the case. In 2023, the average Minnesotan worker worked 1,522 days, which ranked 16th highest out of the fifty states. Maybe folks in Maryland might want to pick up a few extra shifts, or maybe they’re happier doing whatever it is people do in Maryland when they’re not working.

Figure 5: Average annual hours worked, 2023

Here again, there are limits to increasing the rate of GDP per capita growth by increasing the growth rate of hours worked annually. There are, after all, only 8,760 hours in a year, after that you’re maxed out.

These limits do not apply to the measures of the quality of the labor provided, the skills arising from education or experience. We will look at those next week.

Conclusion: The Minnesota work ethic

For now, we can conclude that Minnesotans are a hardworking bunch, with high ranks on their employment ratio — fourth out of fifty states — and hours worked, 16th. This “raw” labor is a crucial ingredient of our state’s relatively income. The fact that our income is slipping, relatively, while our raw labor remains relatively high, suggests that the explanation for Minnesota’s relative growth slowdown must lie elsewhere.

All the figures in this post were constructed using the American Experiment United States Tables, available for download here.