Estimated Relative Standard Errors in Housing Data

Regarding yesterday’s New Home Starts, an emailer writes: 

You used to discuss the Commerce Dept.’s standard statistical error regularly. In light of that surprising Housing Start number, could you please update that?

Sure thing. I love this sort of data sifting exercise. (I used to do this all the time, but I could actually hear readers falling asleep through my screen).

Let’s go to the Census Department release.

Privately-owned housing starts in April were at a seasonally adjusted annual rate of 1,032,000. This is 8.2 percent (±14.5%)* above the revised March estimate of 954,000, but is 30.6 percent (±6.7%) below the revised April 2007 rate of 1,487,000.

As is so often the case, the devil is in the details:

As far as the April Hosuing Starts go, a monthly change (seasonally adjusted annual rate) was 8.2%, versus an
estimated relative standard error of ±14.5%.  Hence, the monthly change is not statistically significant; that is, it is uncertain whether there was an increase or decrease in Housing Starts from March to April.

As to the 30.6% year over year drop — that is ±6.7% — and therefore is statistically significant.

[UPDATE: Flenerman in comments asks the same question]


And I thought I was the only one who cared about such mathematical trivialities . . .


Manufacturing and Construction Division
U.S. Census Bureau, MAY 16, 2008 AT 8:30 A.M. EDT

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What's been said:

Discussions found on the web:
  1. Blutskralle commented on May 17

    Your geek street cred is fully intact, do not worry.

    Do you know how they compute their error bounds, by any chance? As in, is that a credible number in the first place?

  2. dave commented on May 17

    BR, sorry for the off topic query, I was looking for an old post of yours re subprime trading losses, MS specific. Turned up a bunch via the search function, not the one I was looking for.
    Re housing, is FHA the next subprime? Anecdotally, the remaining mortgage brokers in business seem to think so.

  3. Curt commented on May 17

    Great stuff Barry! Having been a statistician for most of the past 20+ years (now a currency trader and fundamentals analyst/coach), I totally appreciate seeing anyone bringing the concept of error to the masses.

    So many otherwise intelligent people focus only on estimates such as averages or differences between averages, which only tell part of the story.

  4. Winston Munn commented on May 17

    Geekdom is not really the issue. “Statistically insignificant” is a phrase everyone can grasp.

  5. Mel commented on May 17

    “estimated relative standard error of ±14.5%”

    That seems very high–making seasonal adjusted rate semi fictional.

  6. STS commented on May 17

    Noting standard errors in discussion of data like this is hardly a “triviality”. Failing to include it is effectively “lying”.

    I’d like to see people who understand the math stop the reflexive apology. It’s an annoying tic which reinforces our “ignorance is strength” culture.

  7. jimcos42 commented on May 17

    Why the quibbling over statistical nuances, as if one or another conclusion is going to amount to a hill of beans?

    Just go pull up a long-term chart on housing starts and you’ll see that, generally, we’ve had housing starts in this zone in 1966, 1974-75, 1980-82, 1991 and now now.

    In those past cases, such lackluster readings have been part of a bottom. I suspect this time is NOT different. In my mind the only question is how long this takes to mend itself. My sense is, longer rather than shorter.


    BR: Why Quibble? Because the details that make up reality matters.

  8. bart commented on May 17

    Econometricians uber alles…

  9. dblwyo commented on May 17

    My econometrics is a few years ago but the distribution of the sample will generate the standard error depending on widely it’s dispersed around the mean; i.e. the S.E. is calculable from the data in the best of my recollection. All that aside there are really two important things – first off the Starts data is Single + Multi-family starts and the latter is very volatile while the former is still dropping like a rock and is the majority of the total starts. More importantly the S.E. noise issue goes away when you look at the time-series and trend, by eyeball if necessary, but YoY changes are a great proxy. You can look at the data or dload it yourself at the STL Fed FREDII site which has also a very nice little graphing facility. If you’ll trust my spreadsheet skills YOY% change for starts -30.6%, less than Mar. 36.1% but 1-family’s went from 41.1% to 42.2%; i.e. the cliff-diving is accelerating. In any case -20, -30, -40 it’s all painful.

  10. Darkness commented on May 17

    If the estimate is more survey than estimate, the margin could just be reporting a high variance in the data, not so much “error” in the data. Sorry, too much to do today to actually read the report methodology… just throwing that out as a general comment.

  11. AGG commented on May 17

    In theory, housing starts should be “negative”. What? That’s right, they should be tearing them down. Why aren’t they tearing them down?

    “The tooth fairy is out of town. She sold her San Francisco condo and now resides in Baja California. She left no forwarding address.

    When the cat’s away, the mice will play. From 1996–2006, the cat was away. The mice played. What did they play? Fast and loose.

    I received this note from John Schaub, whose site,, is one of the best sources of information on single-family home investing.

    There was a lot of mortgage fraud in the intercity areas of many big cities like Atlanta. They would take a house worth $5000 and sell it for $50,000 to a friend who would get a loan based on the $50,000. That did not make the house worth $50,000 but the tax assessor would pick up the new “value” off the recorded deed. Other properties were sold with owner financing at terrifically inflated prices, then the loans (first mortgages on single family houses – how could you go wrong) were sold to investors. I’ve long advised never to buy a loan unless you are willing to go see the property. Many of these houses have negative value. It would cost more to tear the house down than the lot is worth.”
    Gary North

  12. Michael Donnelly commented on May 17

    I was a tad upset. The multi starts were up 40%, and we know the inventory picture is worst at the condo/multi level. So the big pickup didn’t make sense.

    Then I realized it wasn’t statistcally signifcant m/m and was amazed it wasn’t y/y either.

  13. dblwyo commented on May 17

    Emanuelle – have you reviewed CalculatedRisk’s work on Res. Investment and Non-Res, etc. ? You might find it very worthwhile. His latest on Non-Res, it’s relation to RI and the impact on the Economy can be found here:

    As CR points out RI is a major leading indicator for business cycles – IMHO largely because Investment in general is the swing factor, or the accelerator as they used to call it, in the macro-econ stuff. Besides that the Housing ATM was generating ~ $800B/year in consumption expenditures thru MEW.

    Barry is therefore, again of course IMHO, definitely right to be worried about Housing.


    BR: Don’t bother its my ex-girlfriend, the troll

  14. Toby commented on May 17

    Believe it or not there is demand for multi-family (apartments). Even in areas with high single family vacancy rates. My guess is the foreclosurees need a place to live.

    As to the housing starts, they are really only useful looking back 3 months or using a six month moving average.

    The emphasis on all of these economic metrics is a phenomenon of the cable news channels. They were once buried deep on page 6 of the WSJ. Anything is news these days.

  15. D. commented on May 17


    I’m curious, are Heinz, Cottonelle, Exxon, Pizza Pizza and Disney in the 5% of the economy or 95%?

    Because I know a whole whack of people who refied their house and used the money to go on trips (Disney).

    A whole whack who ordered a lot of pizza when they renovated.

    A whole whack who bought a few bottles of ketchup and rolls of toilet paper for their mutiple homes and toilets.

    A whole whack who spent more gas going on trips or driving from their home to their second home.

    Actually I have trouble finding one single sector which did not benefit from refi money!

  16. Winston Munn commented on May 17

    I cannot match a growth in disposable income with the following reporting:

    Palm Beach Post Staff Writer

    Thursday, May 15, 2008

    “A recent national survey found about 83 percent of consumers use credit cards to buy gas, up from 55 percent to 60 percent five years ago, said Jim Smith, chief executive officer and president of the Florida Petroleum Marketers and Convenience Store Association in Tallahassee. Credit card fees are soaring along with gas prices.

    ‘Visa and MasterCard are making more per gallon than the retailer,’ Smith said.”

    When consumers are forced to use credit for essential purchases, it is not consistent with increased disposable income.

  17. wunsacon commented on May 17

    Winston, could it be that much of the increase just comes from the convenience of using a card?

    I spend maybe $50 in cash per month. I put everything thru the card.

    What are the relative contributions of these two factors (desperation vs convenience) to the trend you see? (I am not trying to give you or anyone here a “homework assignment”. Personally, I don’t know and don’t have the time to look either.)

  18. Greg0658 commented on May 17

    I use a credit card to get a receipt and to save a walk inside. And its easier than hitting the ATM for $60 to fill the tank.

    Not nice to the station I suppose, ie: surcharge.
    I wonder if armored car deliverys balance out the surcharge?

  19. wunsacon commented on May 17


    Would a reading of:

    (a) -2.2 percent (±14.5%)

    differ from

    (b) 8.2 percent (±14.5%)


    Even though “-2.2” is within the “14.5%” deviation from “8.2”, does the difference mean anything at all to you? If so, is the difference between those values “meaningful” to a statistician? Is the difference “significant”?

    Yes, I’m asking what may or may not be repetitive questions. Why? Because depending on how some terms are supposed to be defined (on which I’m not an authority), I can imagine different answers.


    BR: Neither is statistically significant — yet another reason to emphasize year over year data

  20. Consumer driven commented on May 17

    Why did the gas stations make it so convenient to use the charge card when:

    a. It lets the consumer come and go without ever going into the store to be tempted on the high margin items.

    b. The store has to pay a fee to the credit card company reducing their profit?

    Must have been people were looking for convenience. Now it may be they don’t have the money.

  21. BLV commented on May 17

    With ATM fees sharply increasing ($2-3) to get cash, I am trying to put everything on the credit card (American Express with cash back is my favorite). I definitely use more of plastic this year, pay the entire balance in full and get nice cash back each month. I have no debt, but I use plastic more often because of convenience, hate ATM fees, get cash back, etc.

    Personally, my disposable income and savings rate are growing nicely. I feel no recession, none what so ever. I guess other people are in trouble (at least this is what the media has been singing lately), but I do not see any slowdown (knock on wood).

  22. Winston Munn commented on May 17

    Wunsacon wrote, “Winston, could it be that much of the increase just comes from the convenience of using a card?”

    I would think there is a difference between credit card use and cash card use. Myself, I pay for almost everything with a cash card – but there is a substantial difference between having the money in your checking account and using a convenience card and having no money in your checking account and being forced to used your credit card.

    I can’t say what the reason for the sharp increase that was reported by the article, but it suggests to me less ability to pay than more. 5 years ago was not the dark ages, and to believe that a 25% or so increase in usage was due to a “sudden” realization of the convenience of credit card use doesn’t strike me as a likely explanation.

    However, I have been wrong before and will be so again. Of that I am sure.

  23. DRich commented on May 17

    Don’t you believe that it is not interesting. I love factual detail, just don’t have the time to keep up with all the people lying to me. I spend a lot of time sorting out the lies in my own line of work. Love hearing about it from other quarters.

  24. dblwyo commented on May 17

    Winson, the way I read the surge in consumer debt, including cards, is that people were already living beyond their incomes via the housing ATM and now, either keeping up the spending or because of lost jobs, etc. are charging normal consumption purchases. Which makes sense if you think it’s a temporary thing but is personally dangerous and macro-economically scary when the bills start coming due. Not to mention that the consumption components of the GDP haven’t in total tanked yet but only services held up.

  25. Darkness commented on May 17

    Why did the gas stations make it so convenient to use the charge card when:

    a. It lets the consumer come and go without ever going into the store to be tempted on the high margin items.

    It doesn’t have to play out that way. If the customer needs something from the minimart at the gas station then the switching costs of making yet another stop on the way home are still much higher than simply going inside for another transaction…. and wonder of wonders, because all the gas-only customers are not clogging up line for the till, the line is short enough to reinforce to the mini-grocery customer that the gas station quick buy is worth the extra price you pay.

  26. eh commented on May 18

    I don’t see how the fact that data is not statistically significant can be said to be ‘trivial’.

  27. wunsacon commented on May 18

    Winston, I was mainly playing devil’s advocate (not really believing my own alternative explanation).

    But, how ’bout this: Many times, people just take the “quick $100” from the ATM. In the past, a fillup used to be maybe $20 or 1/5 of what they took out. Now, it’s nearly half. Better to “put it on the tab” than to have to go right back to the ATM again or carry around so much cash just for gas.

    Nevertheless, I don’t believe people have more disposable income either, certainly not in real terms.

  28. kio commented on May 18

    Great post, Barry!

    It demonstrates clearly how biased you are in estimation of data. I have looked through several on your previous posts and found that you did not mention any S.E. in them despite changes in relevant variables were also inside 1-sigma. Effectively, the only thing what you could claim in these previous posts is that data are not reliable to draw any conclusion.

    I would propose to treat this current post as a big trap which you have digged with own hands. This post should provide a Golden Standard for any of your future (and past , we can judge now how reliable were your statements – are they “statistically significant”) posts. As a consistent researcher and analyst you must follow up this high standard of statistical significance and robustness.

    I think you need an experienced opponent to check you posts before publishing for side effects.

  29. Barry Ritholtz commented on May 18


    I’m not sure I understand your comments. A simple Google site-search, using the words “Census statistically significant,” reveals numerous prior posts on S.E. :

    This leaves me scratching my head as to whether you are serious about statistical error, or merely an asshat.

    Everyone is entitled to their own opinions, but not their own facts. And in case you missed our terms of use, anyone that pollutes the comment stream with false and easily verifiable information, will lose their welcome here.

  30. kio commented on May 18


    For the sake of accuracy I have to admit that I was wrong in the definition of the bias.
    Before I leave this blog, I just ask for the fairness. If you could please to allow this last post. (Actually, it is addressed to you, mainly)

    1. from 7 links you gave in your previous coment only 2 are associated with S.E. for decreasing housing sales. In one case, S.E. is below the observed change. So, you have mentioned S.E. only one time (September 27, 2007) commenting not significant negative change in these 7 posts.

    2. 5 links lead to posts which use S.E. to deny any significance of positive changes.

    3. I rechecked some previous months in 2008 and late 2007. No S.E. is reported for statistically not sinificant negative changes (except the one given in your link.

    4. I do not call this observation “bias” anymore. My statistics on your posts is just my opinion.

  31. Matthew Morse commented on May 18

    It’s worth considering what “statistically significant” means. A phrase like “8.2 percent (±14.5%)” implies a percentage confidence. This is often 95%, but is not necessarily. Assuming 95% confidence, this means that, based on the data currently avaiable, it is 95% likely that the change in housing starts from March to April was between -6.3% and +22.7%.

    This implies several things. 5% of the time, the actual change will be either less that -6.3% or greater that +22.7%. If you are making an investment based on the change being in that range, there is still a 5% risk that you are starting from a faulty assumption.

    One way of restating this is that if the number were to be 8.2 percent (±8.2%), this result may be “statistically significant”, but there’s still a 2.5 percent chance of negative growth (assuming symmetric distribution, the result will be on the low side of the distribution range half of 5% of the time).

    If you know what the probability distribution looks like, you can determine the probability that the outcome is in any particular range. If you are more interesting in the question of whether the change is positive or negative than in what the actual value is, you can estimate a probability based on the stated value and the size of the error.

    In the case of 8.2 percent (±14.5%), it is not certain that the actual value is positive, but the probability that the value is positive is well over 50%. (I can’t do the calculation off the top of my head, and any calculation would require making assumptions about the shape of the distribution curve, but I’m guessing this range gives around an 80% chance of an overall positive monthly change.

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