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« August Employment Preview | Main | Weighing the Week Ahead: Here Comes the Government! »

September 02, 2011



StillStudying -- I think the results from our readers were quite good.

I was trying to illustrate probability, but the application in screening is important, as you note. The emphasis is on finding real positives. The false positives can then get further testing.

In investing, a false positive about a recession may lead to a poor decision, just as much as failing to miss the signs.

You are correct to note that the standard varies.




rs-- I had a nice chat with Mish at the Kauffman Foundation meeting this year. He is passionate and committed, and he has a successful business model for his blog.

And yes, he is one of those who are certain about recession chances.



bfuruta -- I am delighted at your skepticism about the odds.

Concerning the liquidity trap debate, I am a regular reader of Krugman and DeLong, so I am familiar with their argument. Both are serious scholars of top rank. I happen not to find them as useful for investors.

My objection mostly comes from the fact that people who do not really understand economics (and I am not putting you in that group) and do not want to consider data, simply grab a term like this and use it to bring the analysis to a close.

Thanks again for commenting so carefully, and I hope this clarifies my obscure point.



HG -- Point taken! I agree about implying false precision. Mostly I was trying to show people how to do this sort of calculation.

I actually treated every answer of 8% or so as "correct" in my scoring.

Thanks for reminding us about one of the most important elements in quantitative analysis.



I have a bone to pick with your answer. The answer, in my opinion is 7.8%. We don't have enough significant digits to make the answer more precise than that. My students nowadays seem to have never been even introduced to the concept of significant digits, so it's a pet peeve of mine. Sorry for the rant, but I think understanding precision is an important part of quantitative analysis.


Thanks for the Q. The question has even have appeared on a 6th grade exam here believe it or not. Though it's a different type of puzzle, it was still fun; you can tell the probabilistic muscles have been stretched by the newfound hesitation in the face of seemingly innocent numbers.

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The correct answer is 7.764%. Readers of "A Dash" did pretty well with 36% emailing me with correct answers (allowing for some rounding). 20% believed the probability was 90.4%. 25% thought the chances were 1 percent or less. 14% of readers thought the odds were about 10%.


I saw this problem only now. It reminded me of the other time I recently exercised my Bayesian skills recently - to solve the problem described on page 21 here . The other gem in this survey was of course,
A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?
which only 12% answered correctly.


Jeff: From your survey, 66% of us (your readers) pegged the solution at 10% or less. Good enough for government work, especially if some just eyeballed the situation rather than going to find a calculator and working it out. Pretty darn good. I'd say for investing purposes a metric with a 10% chance of predicting a possible outcome vs one with a 7.8% chance gets the same (failing) grade.

Which goes a long way towards explaining why routine mammograms might not be the holy grail....


A valued friend (who also submitted a correct answer to the problem) has the following suggestion for future questions and entries:

"I see the problem. If you write to each person for permission, it may take a long time until you can write the next post. Even if you don't really need permission, you don't want to annoy the customer base or start a flame war or anything like that.

How about this: Make the default be opting out. When making the initial invitation to submit answers, say nothing will be posted unless the writer includes something like:

OK to use my answers but no name in blog post.
OK to use my answers and real name in blog post.
OK to use my answers with name BigFly in blog post.

You could include examples in your text, formatted for easy copy and paste as a template. After a few times, a short note and a link to a page with explanation and example template should do the trick.

When you write up the next post, say there were other really nice examples, but the writer did not opt in."

My friend has explained this well. It would be fun to do some problems and recognize the most astute readers.

Maybe I can get my friend to write a comment himself!



Here's one who "knows" we are already in a recession (note the tone and certainty in the article coupled with source for each point for convenience):

These indications are the priors like the 1% of women with cancer, but what about the conditional probabilities that change the likelihood?

It's been really interesting to see how the excessive optimism in May has eased off till the point of recession calls now.


Jeff, in reply to your questions:

1) Yes, my BS meter went off with the wording used in the piece: specifically "slam dunk" and "long history." I also wondered when reading Eddy's piece, without taking the time to look it up, how many times the spread between the 30-year and the 10-year Treasuries was 138 basis points or more. The reliability of any indicator is low when the number of cases is small.

2) No, of course I don’t think there is a 100% chance of a recession; just as Eddy said there is a chance of falling back into recession, even as he cited the Bloomberg piece. Eddy is indeed citing facts. My point is that he is picking the facts that support his opinion and ignoring those that do not.

I am not trained in economics, so I try to learn from blogs like yours and others. Paul Krugman has been writing about the liquidity trap, with data and a model. The predictions from the model have been accurate so far. From your comment, I have to ask you a question. Do you think "liquidity trap" is an empty catch phrase with no data behind it?

Jeff, I want to thank you for your work. As I have said before, I appreciate your approach and the information you share in this blog. I will certainly look for your weekend article.


bfuruta --

Eddy is citing a fact from the article, and he did it accurately. He did not try to portray the source as having a certain opinion.

I have a couple of questions for you:

1) How many recessions have there been since 1948? Doesn't your BS meter go off when someone cites the "long history" of the indicator? If not, I have failed in this series of articles!

2) Do you think that we now have a 100% chance of a recession in the next year? That this will always happen when GDP goes below 1.5%?

I'll put aside the policy questions for the moment (although look for this weekend's article) because this is about data analysis. I think that people use arguments like "liquidity trap" because they do not want to use data. Most people are more comfortable following the parrots than doing actual analysis. People are easily fooled.

BTW -- Your source cited "Bloomberg" not a person. I am sure you know that Bloomberg quotes a wide variety of sources of varying reliability. They leave it up to you to figure it out. I am curious about the person behind the quote.

Thanks for joining in, and for participating in the problem. As you say, time will tell.



Jeff, you wrote, "Eddy, as usual, is careful and accurate in formulating the question."

I could make a case that Eddy has confirmation bias. The Bloomberg paragraph he quoted appeared under the heading "Growth Slowed" and had two parts. Here is the entire paragraph:

While Commerce Department figures showed gross domestic product climbed at a less-than-previously estimated 1 percent annual rate from April through June, the economy has never contracted with the difference between 10-year and 30-year Treasury yields as wide as the current 1.38 percentage points, or 138 basis points.

It is a balanced paragraph. Eddy left out the part about low GDP. He also didn't bother looking for any implications of GDP slowing that much. Here is what he could have found:

Source: Bloomberg

The YoY change in real GDP, presently at 1.5%, is a slam dunk indicator of recession: "Since 1948, every time the four-quarter change has fallen below 2 percent, the economy has entered a recession. It's hard to argue against an indicator with such a long history of accuracy" Bloomberg reports. Adding that "every time real YoY GDP has dropped below 1.5%, this has led to a negative nonfarm payroll number."

I personally think that you and Eddy are not giving enough weight to the larger economic environment. We are in a liquidity trap. As Eddy does state, it is fear that is driving down the yield on the 10-year Treasury. Too much debt and lack of aggregate demand are the problems, not high interest rates due to the Fed fighting inflation. The FOMC can do very little to help the situation. The politicians here and in Europe, unfortunately, are not up to the task. Unlike Eddy, I think there is good reason for the fear.

Time will tell.

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