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Testing theory: marginal product and wages

Economic theory tells us that, in a perfectly competitive labor market, labor should be paid according to its “marginal product.” Now, without the jargon: The last workers to be hired by a business should receive pay that is equal to their contribution to the output of that business. So, let’s compare the data with the theory…

Unfortunately, we have no data on the marginal product. But fortunately, we have data on average product. Although it’s not a certainty, these two products should be correlated. So, the graph above shows real growth rates for average product and the average wage. But again, there’s a limitation to the data: We must use the wage of production workers only if we want a series that’s long enough to compare with average product.

Ultimately, it doesn’t look like these series are closely related. The two data limitations we have here could be undermining the relationship. Or the labor market could be less than perfectly competitive. Or the theory could be wrong. It’s difficult to say. But such is the life of an economist… For some more-rigorous research on this topic, take a look at this recent Economic Synopses essay.

How this graph was created: Search for “real output per hour” and select the series shown here. In the “Edit Graph” panel, add the next series by searching for “average hourly earnings” and taking the series with the longer duration. Then modify this series by adding the CPI data series and applying the formula a/b. Select “Percent Change from Year Ago” as the units.

Suggested by Christian Zimmermann.

View on FRED, series used in this post: AHETPI, CPIAUCSL, PRS84006091

No space in the overhead bin: The rise of the airline “load factor”

Does it feel more crowded on airplanes these days? FRED has some data on that. Specifically, we look at “load factor,” an industry term for passenger-miles as a percentage of available seat-miles, which measures how full a flight is.

The graph offers data for domestic and international flights that have clearly not been seasonally adjusted. Just look at all the turbulence: Summer months are highly popular; international flights are much less full in February; and domestic flights seem to do a double dip, first in September and again in January.

But back to our question: Yes, flights seem to be slightly fuller than before. The load during popular months hasn’t risen much. But low-load months, especially domestically, have seen large increases. So your seatback may be in the upright position more often than not. Still, it may be more likely that you’re simply on a popular, crowded flight and not more likely that every flight will be more crowded.

The most extreme signal in this graph, of course, is the steep decline in airline travel after September 11, 2001.

How this graph was created: Search for “load factor,” select the two series you want, and click “Add to Graph.”

Suggested by Christian Zimmermann.

View on FRED, series used in this post: LOADFACTORD, LOADFACTORI

Juggling jobs

Some jobs pay less because they’re part-time. Some jobs just pay less. And these jobs may not provide enough income for workers to make ends meet, bring down debt, or pay for family health expenses. Whatever the reason, some workers have multiple jobs. Let’s consult FRED to see how common this is.

The Current Population Survey from the Bureau of Labor Statistics offers data on the fraction of workers (among all workers) who hold multiple jobs. It’s not a large number, but it’s not negligible either: Today, it’s about 5%. Its slow decline over time suggests that the need for multiple jobs, often some sort of financial distress, is becoming less frequent. By looking at the graph, we see that recessions (shown by the gray bars) seem to have no significant impact on this measure.

How this graph was created: Search for “multiple jobholders,” select the series, and expand the sample period to the maximum range.

Suggested by Christian Zimmermann.

View on FRED, series used in this post: LNS12026620

Measure for measure: Judging the economy

How do you know if the economy is improving? FRED has plenty of commonly used data to help you. Typically, you’d measure real gross domestic product (GDP)—in particular, its growth rate. This rate is almost always positive. Because population growth is also almost always positive, this isn’t too surprising. So FRED lets you measure real GDP per capita—that is, GDP divided by the population.

But let’s complicate matters, because economies can go through demographic transitions. In fact, because many industrialized countries now face a substantially older population, dividing GDP by the overall population may not be precise either. So, FRED lets you divide GDP by the working age population, age 15 to 64. FRED even lets you refine the measurement by considering only the working age population in the labor force—that is, by excluding those who choose not to work or who cannot work. Finally, FRED lets you measure only those who are actually working by excluding the unemployed still looking for work. (By the way, dividing real GDP by the working population corresponds to labor productivity.)

The graph above shows these five different measures of U.S. economic growth since 1948. Each has its merits, but their growth rates look remarkably similar—so much so that it may not seem worthwhile to distinguish between them. One possible exception is the last series, since the working population fluctuates much more than any of the other population measures.

How this graph was created: All five lines use real GDP, so add real GDP to the graph five times. For line 1, change units to “Percent Change from Year Ago.” For line 2, add the monthly population series, apply formula a/b, and change the units again for this new, transformed line. Repeat this for the remaining lines by searching for and selecting the other population data to divide with. Finally, use the “Format” panel to remove the many axis titles.

Suggested by Christian Zimmermann.

View on FRED, series used in this post: CLF16OV, GDPC1, LFWA64TTUSQ647S, PAYEMS, POP

A counterclaim on countercyclical policy

Keynesian theory tells us that, when economic activity falls, government expenditures should rise. That is, government expenditures should be countercyclical and lean against the business cycle. Has this happened in the U.S.? In the graph, the red line shows growth of government expenditures and the blue line shows growth of private (nongovernmental) economic activity. And it looks like when one line is high the other is low. Does this mean government expenditures are countercyclical?

Actually, this is partly an optical illusion: On average, government expenses have grown more slowly than the rest of the economy, and thus the red line is more often low and the blue line is more often high.

A better way to examine this question is with a scatter plot, shown below. Each axis represents one indicator, and each dot corresponds to a quarterly data point. If government expenses were countercyclical, the cloud of dots would have a somewhat negative slope, with more dots in the top left and bottom right quadrants than the top right and bottom left. The scatter plot actually has a congregation in the middle, which shows there’s little correlation between the public and private sectors of the economy, at least in terms of expenditures.

How these graphs were created: For the top graph: From the Domestic Income and Product release, select “Real Gross Domestic Product, Chained Dollars” and then “Quarterly”; select the GDP and government expenses series; click “Add to Graph.” In the “Edit Graph” panel, add to line 1 (GDP) the government expenditure series again and apply the formula a-b. Use “Percentage Change from Year Ago” as units for the lines and use the slider to start the data in 1953:Q2 (which is after the explosion of government expenses for the Korean War) to avoid distorting the view. For the bottom graph: Use the top graph, but use the format tab to select graph type “Scatter.”

Suggested by Christian Zimmermann.

View on FRED, series used in this post: GCEC1, GDPC1


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