How Should Labor Productivity Be Measured?

[NWRatCon]

Discussions on other threads got me thinking about how we measure "productivity". How Should Labor Productivity Be Measured? (St. Louis Fed blog) "Gross domestic product (GDP) per capita is often used as the barometer when comparing labor productivity and the standard of living across countries." In other words, divide the GDP by the number of people - but does that really make sense? It gives some information, but it doesn't really measure the "effectiveness" of an economy, does it? And it is skewed by a number of irrelevant factors, like birth rate, that give a premium to first world economies where the birthrate is low; and does not factor in (consistently) non-native labor.

Citing an article by Ana Maria Santacreu, Measuring Labor Productivity: Technology and the Labor Supply, an economist with the St. Louis Fed, the article compares the productivity of a number of nations using the metric of GDP per hour (rather than GDP per capita), with interesting results.

Interestingly, the two GDP measures can differ widely within a given country and relative to the United States. For instance, in 2013, Spain's GDP per capita was about 57 percent of that of the United States, while its GDP per hour was much closer—about 74 percent of the U.S. level. Singapore's GDP per capita, on the other hand, was 16 percent higher than that of the United States, while its GDP per hour was 62 percent of the U.S. level.

Noting that in most economic growth models "differences in productivity are mainly driven by technological differences", she asserts that, "GDP per hour worked, therefore, rather than GDP per capita, may be a better measure of labor productivity because it captures technology."

I found this development fascinating, as it helps explain the disparity between labor-intensive economies (like in Asia and Latin America) and technologically-advanced economies, like North America's and Europe's.

 

[KevinKohler]

Or GDP per payroll dollar. Accentuate the differences in pay as it relates to over all productivity.

 

[TheEconomist]

Measuring Labor Productivity: Technology and the Labor Supply[/URL], an economist with the St. Louis Fed, the article compares the productivity of a number of nations using the metric of GDP per hour (rather than GDP per capita), with interesting results. Noting that in most economic growth models "differences in productivity are mainly driven by technological differences", she asserts that, "GDP per hour worked, therefore, rather than GDP per capita, maybe a better measure of labor productivity because it captures technology."

I can try to clarify matters. The math is very light to show what they're talking about.

Dividing output by whatever measure of labor you choose to use gives you the avarege productivity of labor, but it's not exactly what our models are about though it is sometimes related to it. The simplest model of economic activity would represent the supply side of the economy using what we call a Cobb-Douglas production function. In other words, with output , labor input (L) and capital input (K), we have (I add t to emphasize that it depends on time):

y(t) = A(t)*(K(t)^a)*(L(t)^(1-a))

where A(t) is some factor capturing total productivity. The term 'a' is a parameter between 0 and 1. It can be shown to capture the stylized fact that the labor's share of output (w(t)*L(t))/Y(t) is roughly constant over many decades in countries like the US. A(t) presumably changes over time, shows a long term growth trend and is usually modeled as a random process which may or may not depend on other things. In this kind of model, you assume the entire economy behaves like one giant firm that maximizes profits. This assumption implies that inputs are paid at their marginal productivity, meaning wages depend on capital and labor quantities in equilibrium. For those who cannot take partial derivatives, the marginal productivity of labor MPL(t) is defined as:

MPL(t) := A(t) * (1-a) * K(t)^a * L(t)^(-a)

If you are mathematically astute, you probably noticed the production function has a nice property:

MPL(t) = (1-a)*y(t)/L(t) = (1-a)*APL(t),

where APL(t) := y(t)/L(t) is the average productivity of labor at time t.

I can make this complicated by introducing the idea of using intermediate goods, monopolistic competition, price frictions or requiring firms to finance some of their activity through banks, to name just a few. As I move away from that benchmark, things start creeping into that nice formula. One way to see what this means is to call the production sector with one giant firm an approximation of reality. All the things I listed above might be important for how the economy evolves over time, in which case this approximation will induce some mistakes. If you forget about financial intermediation and other frictions like adjustment costs for capital, what really happens is that some of those movements get implicitly attributed to other parts of the formula when you take it to the data. Here, this means A(t) will capture a bunch of things that have nothing to do with total productivity per se. That's why if I put this into a full-blown dynamic model of the economy (DSGE), I will get absurdities like a 35 to 40% percent odds of falling in a recession at any point in time in the US -- I need A(t) to move way too much for things like hours and capital to account for the high variability we see in output.

Another aspect here is that I use just one firm. I won't go into the details, but it is equivalent to considering that, although we really do have an entire distribution of firms (some more productive than others) in the real world, just looking at their average is enough. We do not always have the data to do this, but it's good to be aware that aggregating all types of labor and all production to compare things across countries is valid when looking at averages is a good approximation. An example of a case where this wouldn't work well is if you have a very asymmetrical distribution of firms, with a plethora of very small businesses that all borrow money and a sudden tightening of loans can throw many of them out of the market. These things don't matter in "average-is-enough" kind of world (because this thing relies on the skewness of the distribution to happen).

 

[OrphanSlug]

The question for economics is what does a shift in the measurements for comparing productivity really tell us? Then the follow up is from the graph listed in the article (linked below) why would we see some nations not change much between GDP per capita vs. GDP per hour with others showing wild difference? Hours per worker seems to be an influencer but to unknown ends.

Link:
https://files.stlouisfed.org/files/htdocs/publications/es/15/ES_5_2015-02-27_chart.pdf

 

[NWRatCon]

The question for economics is what does a shift in the measurements for comparing productivity really tell us? Then the follow up is from the graph listed in the article (linked below) why would we see some nations not change much between GDP per capita vs. GDP per hour with others showing wild difference? Hours per worker seems to be an influencer but to unknown ends.

Link:
https://files.stlouisfed.org/files/htdocs/publications/es/15/ES_5_2015-02-27_chart.pdf

The point was to take technology into consideration. The differential should reflect the influence that advancing technology has on productivity.

 

[NWRatCon]

Or GDP per payroll dollar. Accentuate the differences in pay as it relates to over all productivity.

I have no objection to slicing the data in multiple ways, so long as it provides a useful metric for a particular application. My goal would simply be providing useful data rather than just manipulating it to support a particular viewpoint.

 

[Lord Tammerlain]

A prime example of this was from a few years ago

France was more productive than the US per hour not because it was a high tech paradise but because it produces luxury goods.

An example, France might produce 100 bottles of wine that sell for $100 each in 8 hrs, while say the US produces 200 bottles of wine for $40 per bottle in 8 hrs. By economic output (productivity ) France is higher but in actual units being produced, it lagged behind drastically.

In Asia (outside of Japan and to a lesser degree South Korea) They do not produce a significant amount of high value products, or at least the part of the product that has the high value. Lets look at cell phones the majority of the components come from various factories in Asia, the final assembly in Asia. The software is generally controlled/owned by US companies (Android and Ios Apple) and the modem chip by Qualcomm and Broadcom. The IP value from that provides the US companies with a high productivity rate and as such for the US. Now the cell phone gets exported from Asia to say the US, the value for that cell phone doubles when it is sold. So the 30 000 Apple store employees generate $50 in value added revenue per phone, while the 150 000 Foxcon employees doing the assembly of the cell phone generate $4 in value added per phone

 

[James972]

I found this development fascinating, as it helps explain the disparity between labor-intensive economies (like in Asia and Latin America) and technologically-advanced economies, like North America's and Europe's.

Dear, we are richer and more productive today than in Stone Age because of the Republican supply of new technological inventions. Now you understand supply side economics and why demand side libcommieism does not work. Did you know that USSR never produced one consumer product innovation?? NOw you know why. With all you've learned are you now a conservative/libertarian??