Good Math, Bad Math

It’s just been a week for metric errors. Via Media Matters comes an impressive
list of stories in the media about the automobile companies financial problems, where they cite labor costs as a major issue. So far, so good. But in virtually every
story about this, you’ll find a statement along the lines of: “union workers make $71 an hour in wages plus benefits”.

In many cases, they even go so far as to specifically compare that figure as wages to other companies. For example, this quote, from a conservative
talking head:

“When you’re paying $73.73 an hour to those people with salary and benefits and your competition is paying $48 to its workers, you’re going to get your butt kicked in the marketplace unfortunately.”

Here’s the problem with that. The roughly $70/hour figure is a statement of labor costs, not wages. What’s the difference?

Let me pull an example from my own experience. The numbers are fudged somewhat – both because I have no interest in telling you what my salary at IBM was;
and because I’m afraid IBM would still come after me if I gave up real information
about how they charge for employees. The very rough proportions are based on
my (imperfect) memory of the real breakdown, but I’m really making this up based on the rough structure of how the figure was computed.

IBM had an internal figure that it used as my labor cost. For simplicity, let’s
say that that figure was $100,000. That cost was broken down as:

  1. $40,000 salary and related taxes.
  2. $25,000 benefits. This includes insurance, 401K, etc.
  3. $20,000 office expense. This was their cost for providing me with office
    space. The rent/operations cost of the building was dividing among the employees,
    and treated as a labor cost.
  4. $15,000 equipment and technical support. This covered the cost of my computer, network bandwidth, backups, technical support, etc.

A full third of my “labor cost” had absolutely nothing to do with actually paying me. And that’s typical: when you want to make something look expensive, you can find all sorts of ways of transferring costs to it. Never trust
the figure that a company cites for what it’s workers cost unless you get to see the real, entire balance sheet, and see what costs they’re including, and what income they’re excluding.

Let’s get back to the auto-workers. How do they get that labor cost figure?

The company takes every expense that they can plausible associate with past or
present workers: salaries, benefits, insurance, pensions, etc. Then it divides that by
the number of hours worked by current active employees. The result is the “per hour
labor cost”. This is a very artifical number. It’s specifically set up to
include pension payments to retired workers, while excluding the money that they paid into pension funds. So the entire expense of pensions and benefits for retired workers is added to the “labor cost” of current workers.

So, they’ve created a very artifical metric, and then used it to try to make it sound as if auto workers are making an outrageous amount of money.

What’s the real per-employee hourly wage, including benefits? The average wage is around $28 per hour. Being generous, and assuming that benefits fully
double the salary, (and that’s a pretty damned dubious assumption; $28/hour comes to
$58,240 in yearly wages if you assume no unpaid vacation time, while insurance averages around $12K/family/year. What benefits are there that come close to the cost
of medical coverage?) and you get a cost of $56/hour.

Now, it’s absolutely true that the automobile companies have to pay pensions and benefits for retired employees. But you’ve also got to remember that the employees were contributing to a pension fund – they exchanged part of their wages for retirement benefits. The automobile companies have squandered those funds; when times were good, they found ways to skim “excess” profits from the pension trust funds, and you can be damned sure that they didn’t subtract those from their “labor costs”.

So now, when the economy is in the dumps, and the trust funds that the companies were maintaining don’t have enough money to pay the benefits they committed to pay,
they want to dump the full cost of all retirement benefits onto the heads of current workers, to try to make it look like they’re demanding unreasonable
wages.

It’s bullshit. They’re using one metric – total labor costs including
benefits to retirees (which are supposed to come from a separate pool of money), and pretending that it’s a totally different metric – wages + benefits for current workers.

In comparisons with foreign automakers, like the ones with Toyota, they’re
explicitly comparing (wages + benefits) for current employees at American plants of foreign companies) with (wages + benefits) for current employees + (retirement payments for all retired employees) for employees at American companies.

You can’t get a fair result from comparing different metrics. In fact, if you really look at the math, after the concessions made by UAW workers over the last few years, current workers for American car companies are paid slighly less in wages plus benefits than their counterparts at foriegn companies.

None of this should be taken as my supporting bailing out the automobile companies. I honestly can’t make up my mind whether I support that. On one side,
the companies really, basically deserve to fail. They made huge quantities of
money selling giant SUVs for a few years, and used it to go on a spending spree,
paying ridiculous amounts of money to their executives, and investing next to nothing in actually planning for the future. Now they’re producing cars no one wants to buy,
and due to their own stupidity, they’ve got no capacity to produce things that people want. That sounds like a formula for failure – and it is. It would be downright
criminal for the assholes running those companies to be allowed to pocket the money they made destroying them, have the government rescue them, and then pocket the
resulting profits when they get back on their feet. But on the other side, there are tons of people who don’t deserve to be out of work, and who are going to be hurt
by the companies failure much, much more than the people who are actually responsible. So I’m at a loss; I don’t know what the right thing to do is.

But what I do know is that you can’t have an honest discussion if you’re
starting it with a big ol’ lie. And the $70/hour labor cost is a lie.

Comments

  1. #1 Jason Orendorff
    December 5, 2008

    You should probably close comments on this post. The math content of the discussion will be nil. :-\

    on the other side, there are tons of people who don’t deserve to be out of work

    Regardless of whether people deserve unsustainable jobs, they ultimately sort of can’t have them, right? If we can bail out the workers (rather than their employers) by paying to educate and retrain them, that seems like the way to go.

    Now–the workers themselves would probably prefer the easier, less disruptive (to them) route of bailing out their employers, so it’s important to decide precisely what you think they deserve: the jobs they’re in, or mere economic opportunity.

  2. #2 Kurt
    December 5, 2008

    It’s just been a week for … errors.

    Indeed!

  3. #3 Tophe
    December 5, 2008

    I think they should let the “Big 3″ fail and instead give some money to new companies to get their electric vehicles into production (like Tesla Motors and others). Also, some money should be used to establish an X prize type incentive to foster more innovation.

  4. #4 NoAstronomer
    December 5, 2008

    So are they actually double counting the retirement benefits?

    Once for paying the benefits out to retirees and again for contributing to the retirement plan.

  5. #5 jay
    December 5, 2008

    The company takes every expense that they can plausible associate with past or present workers: salaries, benefits, insurance, pensions, etc. Then it divides that by the number of hours worked by current active employees

    You know this? How?

    comparing cost per workers is common, and while PR spinners may sometimes misquote, accountants understand this. The key point in the auto industry is there is a lot of legacy load on the cost structure (including things like 95% pay for layoff periods, and a really really rich medical package). These don’t exist in other industries or even the US plants of foreign based manufacturers.

  6. #6 Joshua Zelinsky
    December 5, 2008

    Is this really how they count labor costs? This seems like it would make it very hard to prevent repeated counting. For example, the the labor cost of the tech support for you is also counted as part of the salary for the tech support guy who is also an employee of IBM. If I’m reading this correctly labor cost should only be even remotely reasonable if you are talking about a narrow set of employees all doing almost the exact same thing. Otherwise double counting will result. However, in all the articles I’ve read no such breakdown is attempted.

    Am I missing something here?

  7. #7 Anonymous
    December 6, 2008

    I think the auto companies should be given loans because it is the credit crunch that made sales drop 41%, not the cars they decided to build. If it weren’t for the credit market collapse, they would have probably been able to muddle through (and borrowed some money through normal channels) until the Chevy Volt hits the road.

  8. #8 Brian Utterback
    December 6, 2008

    The actual cost of a worker should include all the costs that actually go down as you decrease the number of workers and none that go up. If all the costs were continuous functions, then there is a particular amount saved by having one less worker, and a particular amount that is paid additionally for having one more. Anything that is included in the total calculation that does not follow this precept is not in the “cost per employee” realm.

  9. #9 Jonathan Vos Post
    December 6, 2008

    Corporations are not evil for paying people less than those people’s time is worth.

    The profits of the corporation — and, under American law the for-profit corporation can ONLY have profit as a motive — come from the difference between what a person’s time is worth (to the bottom line) and what the person is paid for that time.

    Marx did not understand this, nor that automation can boost productivity (odd, for someone funded by an owner, Engel, of factories). Demogaogues on Left, Right, and Libertarian positions (as well as anti-globalism anarchists) seem likewise clueless.

    “At a time of great crisis with mortgage foreclosures and autos, he [Obama] says we only have one president at a time,” [House Financial Services Committee Chairman Barney] Frank said. “I’m afraid that overstates the number of presidents we have. He’s got to remedy that situation.”

    The math is indeed trivial. The interpretation of the Math is everything here. [JVP now takes off his Mathematical Economist hat, earned through many peer-reviewed papers]

  10. #10 Jimmy
    December 6, 2008

    The labor costs of their competitors are $60/hr – the figure that is usually presented anyway.

    And for some interesting information, most of the foreign auto makers pay them $25/hour salary

  11. #11 Jonathan Vos Post
    December 7, 2008

    Need I point out that $1.00 (or its equivalent in local currency) does not buy the same basket of goods in one country as in another, that the cost of an average apartment or home differs from one country to another, that the number of workers per family differs from one country to another, that the Class system is different one country to another… and that there is heterogenity within each country, and down to house-by-house scale?

    Need I point out that the official ranking of the size of national economies by the UN, which ranks China at #2 in the world, is based on many assumptions that not everyone finds reasonable?

    Hence comparing a nominal $25/hour salary for a non-USA automobile worker to a nominal $60/hr for a USA automobile worker does not tell us enough about the relative life styles of the two workers, nor that of their families, nor how they will fare if they become ill or retire.

    For what I earned in the Aerospace Industry, or the Internet industry, or as a professor in greater Los Angeles I could have lived in a high-tech neighborhood of Bangalore or Mumbai, with a bigger house, a cook, a chauffer, a bodyguard, and a maid, in a life style which is Upper Class in the USA?

    Apples and oranges. People can spin the numbers anyway that they want. But I do resent GM, Ford, or Chrysler executives (and some egregious GOP congressmen such as Shelby of Alabama) blaming the United Auto Workers. UAW is not the source of the stupid decisions which essentially bankrupted the Big 3 automakers.

  12. #12 Kaleberg
    December 7, 2008

    When I was in the consulting business, the general rule was that overhead was about 130%. That is, if we had a project and paid someone $50,000 a year to work on it, their annual labor cost would be 2.3 x 50,000 = $115,000. We used roughly this number for both public sector and private sector contracts. I don’t know if the number has changed much, but that 130% included benefits, taxes, real estate, equipment, furniture, support services, management and so on. We referred to such costs, when pricing contracts, as “labor, fully loaded”. Our profit and specific contract line items, such as expensive pieces of software and deliverable hardware, were added on top of this.

    My guess is that $70 is Detroit’s fully loaded labor cost.

    Accounting uses relatively simple mathematics, but the metaphysics are quite interesting since there are concepts like depreciation and sinking funds which can be quite exotic. When GM, Ford, and Chrysler entered labor contracts back in the 1950s and 1960s, they built a future cost structure towards paying pensions, just as when they built a factory, they built a future cost structure towards its replacement. In each case, there was an annual charge taken from current expenses to be applied towards future payments. Such costs are considered a current expenses, so they are tax deductible in the year it is incurred.

    Accounting is a lot like quantum mechanics. Anything is possible, but some things may be improbable. This means that physicists can talk about negative energy, but negative energy can only hang around long enough to balance certain interactions. Similarly, an accountant can show any number anywhere on a report, but only for a certain length of time.

    Failure to put aside enough money can be catastrophic, as Detroit is seeing now. On the other hand, failure to put aside enough money can allow you to show higher profits in the present, and since executive bonuses are computed based on annual earnings without regard towards future expenses, they could do very well by putting aside less than would be needed. The good investment climate in the 90s made things worse. It gave executives an opportunity to change their actuarial assumptions about how much money needed to be set aside. Why let all that money build up against replacing future plant and paying future pensions when it can be paid to upper management?

    In accounting there are different kinds of expenses. If you take out a loan and fail to make the payments, someone can come to you with a piece of paper and threaten to foreclose. If you build a factory and don’t set aside sufficient depreciation, no one comes to you with a brick and threatens you. However, if you negotiate future payments in the form of pensions, someone will come to you with a contract and demand that you keep your word.

  13. #13 pokny
    December 7, 2008

    This all is due to the fact that in reality, income deferred to the employee is not deferred to the employer. Each year, the employer should put into a fund the current value of the promises made to the employee – pension, COLA, health care and inflation on the health care….. Unfortunately, the Big 3 haven’t done this, especially for health care, and are using current income to pay for this error. IMHO, the only way to get out of this situation will be a bankruptcy, and the unfunded liabilities will get in line will all the other creditors. After that is accomplished, with a clean slate, then one can compare “labor costs” between equals

  14. #14 Kyle Lahnakoski
    December 8, 2008

    I say help the people directly, not the companies. By letting one (or more) fail, it will increase the market for the other companies without changing the production chain too much.

    The people that are out of a job need support and retraining. Hopefully, in three years, we wil have them integrated back into the economy.

    There are about 240,000 employed in the Motor Vehicle Manufacturing (NAICS code 336100). If we assume 1/2 will be laid off (based on the drop in sales recently), and we assume the parts manufactures employ are 5x that many people (wild guess), we can say 600K people will be out of work.

    Seeing that $34B + $25B will be spent on the manufactures, that works out to $98,000 per job lost.

  15. #15 Chris
    December 8, 2008

    I’m reminded of my parents filling out the FAFSA years ago. My dad worked for the government, so they had a lot of expenses that went into calculating FAFSA eligibility. We were a bit surprised when it showed him as making some 80k+/year more than we saw.

  16. #16 Jonathan Vos Post
    December 8, 2008

    Re #15, for the non-United States of America readers.

    To receive student financial aid, you need to fill out a Free Application for Federal Student Aid (FAFSA) every school year.

    The Federal Government insures the banks and other institutions that lend students money.

    Those students under 18 have their parents responsible for repaying the loans. Those students over 18 are themselves responsible for repaying the loans. Hence the younger students depend upon their parents precision in reporting income and wealth, consistent with the data filed with tax authorities.

    My son, for example, has to borrow $60,000 per year for 3 years to pay for law school. The law school can charge an arm and a leg, knowing that lawyers will mostly earn enough money to repay their loans.

    When I had Federal loans to pay for college and grad school, there was (Carter administration) inflation of roughly 20% per annum. Since my loans were at 3% interest, it was (I oversimplify) as if they were paying me 17% per annum NOT to quickly repay the loans.

    This reminds me that the questions of salary and labor cost also depend upon macroeconomic variables. What is the present value of the future benefits? It depends…

  17. #17 mike
    December 8, 2008

    “You can’t get a fair result from comparing different metrics. In fact, if you really look at the math, after the concessions made by UAW workers over the last few years, current workers for American car companies are paid slightly less in wages plus benefits than their counterparts at foriegn companies.”
    Absolutely false. Mark is simply talking out of his ass.
    UAW members make a lot more than employees working in states with the right to work (not to mention the national average of wages [and for unskilled labor!]). I’m from Detroit. UAW cleaning maids make more than 70$ an hour. The UAW always demands that all previously fired workers be rehired before wage negotiations begin, many of whom were fired for stealing etc. It’s blackmail, plain and simple. Being a UAW employee in Michigan means you get paid comfortable wages regardless of the work you do so long as the company survives.
    Michigan citizens simply do not have the right to work outside of a union. “Workers for foreign auto companies” are also American; they work in places like the South. People have the wrong idea and think that we are comparing apples to foreign oranges, but to be clear the problem with American car companies is absolutely the United Auto Workers Union.

  18. #18 Jonathan Vos Post
    December 10, 2008

    $73 an Hour: Adding It Up
    By
    By DAVID LEONHARDT
    Published: December 9, 2008

    Seventy-three dollars an hour.

    Multimedia
    Figuring Autoworkers’ PayGraphic

    That figure — repeated on television and in newspapers as the average pay of a Big Three autoworker — has become a big symbol in the fight over what should happen to Detroit. To critics, it is a neat encapsulation of everything that’s wrong with bloated car companies and their entitled workers.

    To the Big Three’s defenders, meanwhile, the number has become proof positive that autoworkers are being unfairly blamed for Detroit’s decline. “We’ve heard this garbage about 73 bucks an hour,” Senator Bob Casey, a Pennsylvania Democrat, said last week. “It’s a total lie. I think some people have perpetrated that deliberately, in a calculated way, to mislead the American people about what we’re doing here.”

    So what is the reality behind the number? Detroit’s defenders are right that the number is basically wrong. Big Three workers aren’t making anything close to $73 an hour (which would translate to about $150,000 a year).
    [truncated]

  19. #19 lboyd
    December 11, 2008

    Everything that Mike said in his post is not true (except maybe for his name?) Just saying.

  20. #20 Steve-O
    December 11, 2008

    “Marx did not understand this, nor that automation can boost productivity (odd, for someone funded by an owner, Engel, of factories).”

    Huh?

    While Adam Smith extolled the virtues of the division of labor and rising labor productivity, Marx argued that this bias towards labor saving technological innovation, in the long run, would lead to a host of problems for capitalism.

    In fact, there’s a rather ironic passage in Wealth of Nations where a worker makes an innovation that eliminates his job. Smith just gushes on about how wonderful the whole thing is.

    Changes in labor productivity are one of the chief observations of the classical economists such as Smith, Ricardo and Marx.

  21. #21 Kroger
    December 11, 2008

    This is an idiotic opinion not based on fact. Please excuse me but US automaker wages ARE MUCH HIGHER than the Japanese and/or Korean companies pay at home or at their transplant factories in the US south. This is not in dispute. Also, US companies have been forced, via poor labor contracts, to pay 95% of those outrageous wages in job banks where thousands of lazy “workers” sit an play cards all day in perpetuity. Furthermore, the US gov’t, by imposing wacko CAFE – Corporate Average Fuel Efficiency – standards, prevents the big 3 from solely making SUV’s and pickups which are PROFITABLE for the companies (save for when gasoline is $4.50/gallon). High gas prices are also the fault of the leftist politicians who refuse to allow onshore or offshore drilling for gas (including ANWR). IT IS RIDICULOUS TO SAY THAT THE COMPANIES ARE IN TROUBLE BECAUSE OF SOMETHING THEY DID. The US could and should have immensely profitable and globally dominant auto companies and gas prices less than $2.00/gallon. It’s a shame that the real geniuses who run congress have screwed it up so bad. Americans DO NOT WANT SMALL CARS – just ask any politician what they drive. Right Charlie Rangel (D-NY) – big fat Caddie?

  22. #22 Brian Nee
    December 18, 2008

    Regarding the authors thoughts on the bailout. I agree let the Big Three fail, and not only let them fail but make it a crime to overcompensate the fat of these companies which have dragged them to the ground. So do away with the criminals who created this mess and indeed initiate a bailout, only not to the Big Three, but to consumers via automobile grants which would spur growth. I mean if we’re giving money away at least give it to the consumer base so that there’s actually capital to purchase new cars, which in turn would obviously trickle up. See, it’s not that the politicians in Washington don’t realize this, they just make a lot more ignoring this to the favor of their coffers.

  23. #23 Jonathan Vos Post
    December 20, 2008

    When I was a little boy, I heard about the worst salary ever, from my downstairs Catholic neighbors (on the first floor) the Mara family:

    “For the wages of sin is death…”
    [Romans 6:23]

    I figured, if that’s what the Union arrived at through collective bargaining, how awful was the original salary offer from Management?

    Joe and Mary Mara hoped that they could convert me by their linear combination of having an Encyclopedia Britannica (one of the most important sources of my education), a TV set for watching “The Mickey Mouse Club”, and taking me to certain movies such as the 1956 Cecil B. DeMille production of The Ten Commandments, released by Paramount Pictures in VistaVision on 5 October 1956 (so I would have seen it later in October, or sometime before Thanksgiving 1956). It was directed by Cecil B. DeMille and starred Charlton Heston in the lead role. Co-stars included Yul Brynner as his adoptive brother, Pharaoh Ramesses II, Anne Baxter as Nefretiri, John Derek as Joshua, Edward G. Robinson as Dathan, Yvonne De Carlo as Sephora, Cedric Hardwicke as Pharaoh Seti I, Vincent Price as Baka, and John Carradine as Aaron.

    To this day my notion of Catholic theology combines Charlton Heston, Yul Brynner, and Italian-American Annette J. Funicello, clearly the sexiest Mouseketeer. Wikipedia reminds me that she was discovered by Disney when performing in the dance recital, Swan Lake. After Funicello left Disney, she starred in several “Beach Party” movies. Walt Disney did not want her to appear promiscuously in any of the movies though. Funicello did not fully comply with the request as she decided to wear some sexy swimsuit outfits in a couple of the “Beach Party” movies.

    In my dreams, I open the Encyclopedia Britannica to, say, the great section on Nuclear Physics, and there’s Yul Brynner leading an army of horsemen and chariots through the parted Red Sea towards the Israelites on the far side who are lying on beach towels while Annette Funicello dances to a transistor radio, one of the top-10 hits of October 1956, such as Hound Dog/Don’t Be Cruel – Elvis Presley (RCA), or Whatever Will Be, Will Be (Que Sera) – sung by Doris Day (Columbia).

    “Whatever Will Be, Will Be” was one of my two favorite tautologies of the time, along with the TV ad: “Only G.I. Joe is G.I. Joe!”

    So much for Quantitative Finance and Theology.

  24. #24 Anonymous
    December 24, 2008

    Clearly the bailout money will vaporize in order to enter the pockets of the rich and powerful executives and to fight law suits against raising AQMD standards and the Big-3 will go under anyway. For 25 years they have resisted raising fuel efficiency; its too late now.

    The last concern, of the Big-3 is that of the workers; it’s never been about the workers. “Too many people will be put out of work if we fail.” That’s simply a smoke screen to tug at the hearts of Congressmen and Congresswomen in order to get the $$.

    The bailout money, as Tophe rightly suggested, should be directed to retraining workers for an entirely new automobile. New green manufacturing plants should be built to the specs of X project winners for electric cars.

    To Anonymous on 12/6; No, in fact it was the Big-3s’ failure to innovate that precipitated their decline.

  25. #25 Adrian Brook Collins
    December 24, 2008

    I only write this to take credit for the comments above on 12/24 at 1:55 AM (it’s actually 10:55PM on 12/23 but why split hairs.)

  26. #26 Jonathan Vos Post
    December 26, 2008

    Putting a Value on the Work We Do,
    The New York Times,
    Published: December 25, 2008

    Re “A Race to the Bottom” (column, Dec. 23):

    Bob Herbert’s reminder of the importance of teachers and the average worker hits at a fundamental problem with our society — when given the choice to value people who are providing worthwhile services or people who exist purely to satiate their own wealth and fame, we choose the latter.

    How else to describe a society that believes that the average teacher or autoworker should take a pay cut while the average millionaire shouldn’t be overly taxed?

    We can point fingers at Bernard L. Madoff as a bad apple in a basically well-intentioned system, but really he is a reflection of the economy we have chosen for ourselves.

    Until we face this fact, no amount of bailout money will save us from a profoundly dysfunctional society in which actors, pop stars and hedge fund managers impress us more than the people teaching our children how to read.

    Lynne Goldhammer
    Brooklyn, Dec. 23, 2008

    [truncated before several other fine letters to the editor]

  27. #27 Jonathan Vos Post
    December 27, 2008

    “Let the working man and the employer make free agreements, and in particular let them agree freely as to the wages; nevertheless, there underlies a dictate of natural justice more imperious and ancient than any bargain between man and man, namely, that wages ought not to be insufficient to support a frugal and well-behaved wage-earner. If through necessity or fear of a worse evil the workman accept harder conditions because an employer or contractor will afford him no better, he is made the victim of force and injustice.”

    [Rerum Novarum, ยง 45, an encyclical issued by Pope Leo XIII on May 16, 1891]

    Wikipedia as of today includes the comment:

    Rerum Novarum was an open letter, passed to all Catholic bishops, that addressed the condition of the working classes. The encyclical is entitled: “Rights and Duties of Capital and Labour”. Wilhelm Emmanuel von Ketteler and Henry Edward Cardinal Manning were influential in its composition.