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Topic: unemployment statistics
Replies: 7   Last Post: Nov 5, 2011 4:16 PM

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 PT Posts: 17 Registered: 10/19/08
Re: unemployment statistics
Posted: Nov 4, 2011 6:56 PM
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On Oct 28, Rich Ulrich <rich.ulr...@comcast.net> wrote:
> >Thsi post is motivated by a remark in Steven
> >Landburg's "The Armchair Economist", regarding
> >unemployment statistics.

>
> >he discusses the problem of estimating the average
> >length of unemployment, among the (known)
> >unemployed, at a particular moment of time.  He
> >states that it is biased in the upward direction,
> >because one with a longer period out of work
> >has a greater chance, i.e. more time, to be
> >selected/sampled than someone of relatively
> >shorter duration.  Assume a simple samplng
> >method, i.e. telephoning random
> >individuals listed as collecting unemployment.

>
> >Now, there seems to me an obvious logical
> >fallacy here.  In addition, there is a
> >fundamental question: given an unbiased uniform
> >sample of a  population,

>
> Here is your problem.  Just exactly *what*  is the
> "population"?  What defines it?

All members of the set characterized by
'unemployed'.

> And what, then, constitutes an "unbiased
> uniform sample" of that population?

Samples chosen according to a uniform
distribution. Presumably one has access
to a random number generator.

> We regularly talk about something like the
> "sampling frame".

?
Don't know that one.

> For the usual question of "how long does today's
> new episode of unemployment last?", your typical
> phone sample of a cross-section (Are you
> unemployed today?)

... and "how many days?"

> will miss almost everyone whose unemployment
> was only a few days. Sampling bias, for that
> question.

hmmmm...
But if the distribution is stationary (or
nearly), the short-term unemployed person
will be replaced by another, newly unemployed.
So that effect cancels.

This observation is also an answer to the
claim "the long term unemployed has a greater
chance to be selected". We note that the
short-timers move in and out of the population
more often, and hence have a greater chance
of selection, as there are more of them.

But at a simpler level, I find both of these
'bias explanations' specious.

Look, we have a random variable. We sample
from a population of that variable. We get
a bunch of numbers, and infer statistics;
"Hello, are you out of work? If yes, how
many days?"

What could be simpler?

Seen this way, the 'long term unemployed
represent an upward bias' objection looks
specious. Of course, the larger numbers
shift the average upwards, they're SUPPOSED
to do that! But it's not a bias.

(another point: a particular individual
out of work 100 days could have been sampled
on any day of that period, uniformly. So he
might contribute a small number, as well as
a large. But this argument isn't necessary. )

> On the other hand, you *can*  frame the question
> in such a way that the answer matches the
> sampling frame; in that case, the answer is
> unbiased.

Elaborate please.

> For the piece that you paraphrased, it is not
> clear that he must be talking about what *I*
> consider the usual question in economics.  On
> the other hand, now that you know the correct
> perspective, you can check and see
> whether he is actually that sloppy, or if you
> missed some important distinction.

It isn't so precisely spelled out.

> Epidemiologists work with similar "biases" when
> evaluating the two technical quantities of
> Incidence and Prevalence of a disease.  So it is
> a regular cause for being careful.

Examples? And definitions -

> >a sample statistic must converge to the true
> >statistic, must it not?  Regardless of the
> >underlying distribution of that population.
> >Are there anyexceptions to this rule?

Are there any pathlogical distributions,
which resist estimation by uniform sampling?

---
Paul T.

Date Subject Author
10/28/11 PT
10/28/11 R Kym Horsell
10/28/11 R Kym Horsell
10/31/11 Geode
10/29/11 Richard Ulrich
10/31/11 jgharston
11/4/11 PT
11/5/11 Richard Ulrich

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