Unions: A Slow Fade

I bring you today a graphic I think of as old and familiar. We published it at ECDI back a ways when the most current data were for the year 2000. This chart is brought up to speed now showing union membership from 1964 to 2011. Data for the period 2000-2011 are available from the Bureau of Labor Statistics (link); the earlier data are preserved in Social Trends & Indicators USA, Volume 1—or if you need them, send me an e-mail. Those data are also originally from the BLS.

In this period unionized labor has shifted from the private to the public sector. In 1983, for instance 67.6 percent of union members worked in the private and 32.4 percent in the public sector.  The situation in 2011 was 48.8 percent of union members were in the private and 51.2 percent in the public.

Perhaps because employment dropped steeply in 2008—but public employment was, then anyway, less affected, the percent of union members and of those covered by union increases slightly in 2008 and then continues its downward drift the following year. The decline of unionization in the United States represents the weakening of the working population—of which union members are an elite. Do I hear a great sucking sound up there in the stratosphere where the 1 percent live?

Windy Today

As this image shows, I have the solar wind in mind. According to NASA, a big solar wind is emanating from roughly the S-shaped area around 3:30 on the sun-clock. All this turbulence dates back to last Friday when an X2 magnitude solar flare made a spectacle of itself. Herewith a graphic showing it:

The chart is quite informative. If you examine the scale on the right, you will see NASA’s categorization of solar flares: A, B, C, M, and X. An X2 flare, such as that shown for last Friday, is considered a major event. It is accompanied on earth by the fading of short wave signals and strong radio bursts that interfere with satellite-to-earth communications. Note particularly that the distances between the subdivisions of each class are logarithmic rather than linear; on that scale the distance between 1 and 2 is huge!

The image of the sun is from NASA’s Solar Observatory/Atmospheric Imaging Assembly, the graph is from the National Oceanic and Atmospheric Administration’s Space Weather Prediction Center. That NOAA name always amuses me: it suggests that we are able to “administer” the oceans and the atmosphere…

Autos: The Domestic Industry

Here some interesting “Quick Facts” from a feature of that name provided by the International Trade Administration of the U.S. Department of Commerce (link). These data give us a somewhat novel view of the U.S. Auto Industry. That phrase all too frequently evokes thoughts of GM, Ford, and Chrysler…

… but in actuality nearly half (45.6%) of the domestic auto industry is run by foreign companies operating on U.S. soil. They employ American labor and purchase American supplies. The percentages are based on cars, SUVs, and light trucks produced in 2010.  No. This second half of the domestic industry is not centered on Detroit. This listing (hope I have them all) shows that most plants are in the South.

BMW, Spartanburg, SC

Honda, Anna, OH

Honda, East Liberty, OH

Honda, Greensburg, IN

Honda, Lincoln, AL

Honda, Marysville, OH

Hyundai, Montgomery, AK

Kia, West Point, GA

Mercedes-Benz, Vance, AL

Nissan, Canton, MS

Nissan, Decherd, TN

Nissan, Smyrna, TN

Subaru, Lafayette, IN

Toyota, Blue Springs, MS

Toyota, Buffalo, WV

Toyota, Georgetown, KY

Toyota, Huntsville, AL

Toyota, Princeton, IN

Toyota, San Antonio, TX

Volkswagen, New Stanton, PA

Volkswagen, Chattanooga, TN

Something to keep in mind when the press talks about the U.S. auto industry.

Work v. Blog

A brief post to take note of a simple fact. When I’m involved with actual work on matters economic or statistical, as just happens to be the case, blogging on the subject tends to suffer. For the first time ever in the history of LaMarotte, a week has passed without a post.  Blame the economy. It has reached down into retirement and has pulled me in, briefly, to produce things that actually fetch m-o-n-e-y! My, my. Is a recovery really in the offing?

Greek Debt

The Greek sovereign debt is in the news today. I got to wondering just how big it is. Meaningful numbers are difficult to find, but I succeeded after a while by consulting the German Spiegel (link). It carries a listing of the debt subdivided into categories—thus the institutions that actually hold it. I show this in a tabulation. Only money actually dispersed, thus actually paid out, to Greece is included. Much more has been promised. My conversion of Euros to dollars uses a rate of $1.2671 per €1, a quite low rate reached this morning.

Greek Debt
	€ bill.	$ bill.	%
European States	41	52	18.0
European Central Bank	50	63	21.9
IMF	18	23	7.9
Greek banks	50	63	21.9
Foreign banks	39	49	17.1
Foreign funds	30	38	13.2
Total	228	289	100.0

Much of the fretting in the media circles around the smallest number here, the holdings by foreign funds (13.2% of the total); some of these are hedge funds. The reason for the barely suppressed hysteria is that hedge funds insure their holdings using credit default swaps; such instruments still exist and may still be sold as derivatives, hence the liabilities are spread God-only-knows where. The invisible consequences may materialize, who knows, even in this humble basement where I write, and I may succumb to dark evil things that will suddenly attack from thin air.

To get some feel for these numbers, I looked up the GDP of the European Union; granted, that is greater than the Euro Zone. That number was $16,282 billion in 2010. The Greek debt, therefore, represents 1.8 percent of the gross domestic product of all Europe. In 2010 Greek GDP stood at $305 billion. Germany’s was $3,315 billion—and the Greek debt, expressed as a percent of German GDP, was 8.7 percent.

The debts are high but are they monstrously high? Not at all. The dangers lie in our virtually non-existent powers of collective self-control—and our much vaunted markets that can spread panic in the flash of an eye.

Negative Numbers

Reading a superb book on the history of mathematics (Mathematics: The Loss of Certainty by Morris Kline) reminded me of the extent to which we take things for granted, especially when we learned them very early in life. One subject that used to plague the ancients was negative numbers. So I got to thinking. If we view mathematics as a language, then the meaning of that language rests on an agreement by all the parties using it what different notations mean. So let us look at one possible explanation for negative numbers:

-9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9

One way to see this series is that negatives belong to one domain, positives to another, and the big divide between them is the zero. When it comes to addition or subtraction, we simply begin at the point indicated by the sign of the first number and then march left or right as indicated by the sign between them and the sign of the second number. Here is 3 + 5:

-9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9

                                     |______________|

Here is 3 + -5. The negativity of the 5 indicates that we need to march to the left.

-9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9

                      |______________|

Now let us take -3 + -5:

-9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9

    |______________|

And its inverse, -3 + 5:

-9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9

                   |______________|

Now I discover what is really a seeming inconsistency in our language—provided, of course, that it is based on equivalent domains separated by a zero. Consider the following. 2 * 2 = 4; this means that we move two positions to the right from 2. And -2 * 2 = -4. That’s also consistent—because, finding ourselves in the negative domain, we move two positions to the left of -2 as shown for both cases here:

-9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9

                |_____|           |_____|

Here the general rule would be that when we multiply, we move in the increasing direction of the domain if the multiplier is positive and in the decreasing direction, still of that domain, if the multiplier is negative. But consider next what happens when we take -2 * -2 = 4 or 2 * -2 = -4. In the negative domain, we should move right if the multiplier is negative; in the positive domain, with a negative multiplier, we should move to the left. As above.  If we applied that rule, both cases would yield zero as shown below.

-9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9

                      |_____|_____|

But they do not. What we do is multiply the two number first and then we assign the sign based on a rule of signs. This is an arbitrary element in our math or, minimally, is no long capable of being tracked in a visual model. The inconsistency continues when we use exponents, which indicate multiplication. For example, both 2² and -2² yield four (one must believe Excel). And -2^-2 yields 0.25. Here we still cling to the explanation that multiplication of values of the same sign yields a positive number.

What these results tell me is that our mathematics uses a different conceptualization for the negative numbers than that of a domain. It uses the notion of gain and loss. Thus -2² is positive because it reduces the losses by 4, as does the equivalent -2 * -2. The last answer, 0.25 as the result of -2^-2, results because the negative exponent signals successive divisions rather than multiplications. Thus that number means:

-2^-2 = (1 / -2) / (-2) = 0.25

But if we chart that result, thus moving to the right, because division means decrease,  we should end up with -0.25, not with a positive value. But the number becomes positive because of our rules. The first result is -0.5 which, divided by -2, turns positive—albeit it is still on the negative side of the zero. We get exactly the same result if we solve for 2^-2. Thus the notion of a domain, as depicted above, corresponding to some physically imaginable plain, has been “suspended” here. 2^-2 should result in 0.25, -2^-2 should yield -0.25.

This field might have been so very different if, instead of the concept of negation, we would have viewed negative numbers as differently colored. Call them red. 

Retail Wrap-Up: 2011

The U.S. Bureau of the Census released data December 2011 retail sales yesterday. Thus we have a complete picture. In a nutshell, 2011 was a pretty good year. To get a good overview of the recent downturn of the economy and our slow recovery from it, I present first a graphic showing retail sales by month, but excluding automobiles, for the years 2007 through 2011.

This is an interesting picture. What it shows is that 2009 and 2010 were “lost years,” as it were. 2009 produced results lower than 2007; 2010 underperformed 2008 until September—when, in 2008, people finally began to reflect in their purchases the facts on the ground, namely that the economy was tanking.

In 2007 December sales were lower than November sales, that decline matched, and in spades, the year after. In the entire period 1992-2010, December sales exceeded November sales by about a hair in every year except three: 2005, 2007, and 2009. The fact that 2011 also lagged its own November sales tells me that public confidence has still not fully recovered. The media reported a 0.1 percent gain, but here I am excluding autos. And 2011 December sales ($328.7 billion) were lower than November’s ($329.4 billion), a 0.21 percent drop.

Next a look at a subcategory, General Merchandise Stores. Here is a graphic on just November and December sales for the same years:

The general pattern is very similar, but the drop-off from November to December was larger. It fell by 0.82 percent. Could that difference be accounted for, in part, by shifts from brick-and-mortar to Internet purchasing? Based on our own family’s experience, the answer seems to be yes.

I obtained the data shown using a Bureau of the Census Internet data server (link).

Steel: Numbers are Sometimes Deceptive

In the context of another project, I charted economic census data for the Iron and Steel industry (NAICS 331111). Hello! I said, looking at the numbers. I had charted a series on Value of Shipments for the 1997-2010 period. What these numbers showed was a gradual decline of the industry early in the period followed by a dramatic upturn beginning in 2003. But everything else I read about the industry seemed to indicate quite the opposite. No one in the industry was trumpeting the glories of a renascent steel industry. I don’t like growth trends unless I can explain them, so I went to work. What I understood before I started were a few big facts about this industry:

• It is maturing, shrinking, and consolidating in the West, thus in the developed world.
• It is booming in Asia, especially in China and India. China can’t get enough steel.
• Prices have been trending up, in part because of fierce Chinese demand, in part because of the rising costs of coke, the stuff you need to render iron ore into pig iron.

My efforts to explain that rise in U.S. steel performance eventually yielded this interesting graphic:

What I am showing here, using U.S. Geological Survey data (link), is that steel production in the United States, measured in metric tons, has been trending down, that the price of steel has been trending sharply up, and that domestic shipments have been echoing the price increase much more than reflecting the gradual erosion of physical output.

I’m showing production and price data as an index to keep the graphic readable. Domestic shipments are rendered in billions of dollars. The first two items come from the USGS and the series ends in 2009;  the shipment data come from the U.S. Bureau of the Census.

While I was engaged in this, I also discovered that U.S. exports of steel, while smaller than imports, have been rising much more rapidly than production for domestic use (both measured in dollars). Rising world prices affect domestic prices even when 83 percent of an industry’s shipments (as was the case here in 2010) are consumed locally—and the price increases are driven by Chinese demand. It’s a global market, isn’t it?

In most industries value of shipments data can be taken at face value. When a basic industry moves overseas for all practical purposes, and when other markets have the hammer hand, one has to be careful in assessing rising curves.

Counting Public Libraries

My own beleaguered public library is clamoring for a 0.7 mill temporary millage rate increase—lest it be forced to close one of three branches and cut hours and staff by 30 percent. This made me curious about public libraries generally. I got data going back to 1989 from IMLS. Never heard of IMLS? Not surprised. Neither had I. The letters stand for the Institute of Museum of Library Services. That sounds like an association but is actually a federal agency created by the Museum and Library Services Act of 1996 (renewed in 2003 and again, with not even a hint of publicity, in 2010). The agency gives grants and publishes data. The U.S. Bureau of the Census collects data for the agency, and I got my numbers laboriously, looking at 21 files in sequence, from them (link). Herewith the data.

Because these data are not—so far as I could discover—tabulated in one place, I have reproduced the actual counts at the base of the bars; to see these, click on the image; to return, press Esc. Not shown, but each entity has additional stationary facilities (thus not counting bookmobiles) averaging to 1.8 per library counted. In FY 2009, for example, the 9,225 libraries had 16,698 stationary facilities. I could not discover any explanation for the unusual drop in libraries between FY1991 and FY1992—beyond hazarding the guess that the 1990-1991 recession had an unusually severe impact. But other recessionary periods have left no similar trace. IMLS reports do not discuss year-to-year trends.

The IMLS data deserve to be published in more accessible formats; they are very detailed and rich in information, but using them is a little like eating a slice of bread richly smeared with jelly after it has managed to fall face-down on the beach-sand.

German Unemployment Rate

Worth noting here that the unemployment rate in Germany dropped to 6.6 percent in December 2011. That made news in at least some German-language publications even in the United States. Looking backward in time, this rate turns out to be better than the rate had been in 1992 when, in January of that year, unemployment had stood at 7.3 percent. Available data don’t go back earlier than that. The Great Recession and its radiations? The Euro crisis? Well, Germany is coping, as one might say. And the name of the lady responsible for this starts with an M.

Employment Change by Sector, November-December 2011

The 200,000 jobs gained in December were distributed by sector as shown in the following graphic:

Notable this month is the gain in every private sector of the economy—a first since I began publishing such details on LaMarotte. Government still showed a loss of 12,000 jobs. The massive gainer in employment was the Transportation and Warehousing sector. Here is the detail of the industries that it contains:

Transportation and warehousing	50.2
Air transportation	0.8
Rail transportation	0.5
Water transportation	0.7
Truck transportation	5.1
Transit	-0.4
Pipeline transportation	0.8
Scenic and sightseeing	-0.4
Support activities	-0.7
Couriers and messengers	42.2
Warehousing and storage	1.6

The real growth here came from courier and messenger services—the categories where UPS and FedEx belong. That number probably highlights a major change in Christmas season purchasing behaviors—and indirectly points to the increasing importance of Internet retail.

Employment Update: December 2011

The Bureau of Labor Statistics reported today an increase in total employment of 200,000 in December over November 2011 (link). The actual increase is slightly overstated, however. BLS revised October numbers by increasing them by 12,000 and reduced November numbers by 20,000, with a net effect of lowering results up to November by 8,000 jobs. Thus, overall, we gained 192,000, better than the average monthly increase for the year, which was 137,000. The graphic is here:

As a year ago, so today I am presenting an annual chart, showing gains and losses by year for the period 2007-2011.

The recovery is underway. The rate of recovery is slow. In 2008-2009 we lost 8.66 million jobs, in 2010-2011 we regained 2.58 million, thus 29.8 percent of all losses. That result is shown in the pie chart that follows:

The deeper the recession, the steeper the hill we must climb to get out of it again. Pacman here is still predominantly blue. I’ll feel better when it looks like the red will gobble up the blue. Notable in this month’s report is the 20,000 down-ward revision of employment in November; it suggests that the peak month of the retail season once more failed to live up to its promise; but to confirm that we still lack data. They will appear fairly soon. The next question for me is: Will December results also be adjusted downward when I look at January results on February 4? We shall see. The very slow discovery—unless it accelerates—today suggests that we will need five more years before we reach employment levels last enjoyed in 2007. Detail’s of this month’s change will be up here tomorrow.

How Do You Define “Parallel”

It amused me yesterday to discover that to ambitious mathematicians the word parallel need not mean what the dictionary says. Webster’s says, “extending in the same direction, everywhere equidistant, and not meeting.”

The crux of the definitional problem arises from Euclid’s Fifth Postulate. It says:

If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.

Not what you might call an elegant postulate. To make it plain we encounter it usually with an illustration, such as you see to the left. The sum of the two angles is greater than 180°, therefore the lines converge. Now what underlies this postulate are some assumptions. One is the nature of the plane on which the lines live: flat and two dimensional. Another  is that straight on such a plane is not curved in any way. A third is embedded in Euclid’s Second Postulate, namely that any line segment can be extended continuously—no limits.

The Scottish mathematician John Playfair (1748-1819) formulated a simpler version. Here it is:

Given a line and a point not on it, at most one parallel to the given line can be drawn through the point.

That postulate is also usually illustrated, as shown. The point Playfair mentions is the P, the dotted line the only parallel line. Playfair obviously understood that a parallel line means a line always at the same distance from another line to which it is parallel.

Non-Euclidean geometries all rely on two assumptions. One is that line segments may be limited in length or that the plane on which they persist may be curved. Here for instance is an illustration of how the word “parallel” is abused (in my opinion). I show a diagram and quote the explanation for it—it concerns the Beltrami-Klein model of non-Euclidean geometry. The link to the site is here:

The Beltrami-Klein model considers the region strictly inside a circle as a model of a plane. Note that the region does not include points on the circle itself. Lines are chords connecting points on the circle with the endpoints excluded. (For lines should belong to the plane.) Line AC and BD pass through point P and both are parallel to AB. Furthermore, all the lines between AC and BD (inside the angles APD and BPC) are also parallel to AB. It's very easy to verify that the first four Euclid’s postulates hold but there is [sic] infinitely many lines through a given point and parallel to a given line.

Note that here “parallel” obviously means “lines that do not intersect.” And that possibility exists only because the nature of the plane has come to be defined in a limited way. Using that definition, of course, the very illustration used above to make Euclid’s Fifth Postulate plain shows “parallel” lines if we restrict the plane to the illustration’s white area.

Too much of modern science relies on such trickeries to be inventive of brand new concepts, among them my favorite bête noire, spacetime.

In the Economy It’s Still 2011

We never see how the sun looks right now. Even when staring through a telescope with the appropriate filters, what we see right now is how the sun looked 8 minutes and 20 seconds ago—because it takes that long for light to travel 93 million miles. New Years day would be the ideal time to put up some numbers to show how our economy performed in 2011, but economies are extremely vast structures, thus by analogy similar to the sun and—given the time it takes to take measurements and to translate them into useful statistics—at least as far away. Right now we have some preliminary numbers for the way the economy performed in November of 2011. So far as our eyesight of that year’s concerned, December hasn’t happened yet. The first early indicators for employment in that month will issue on January 7, a week away. And those will be preliminary too, with November data probably changed. In effect it turns out that the sun is closer to us than the economy. Eight minutes is pretty good compared to a week for the first ever glimpse of 2011.